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T a g d e r w i s s e n s c h a f t l i c h e n A u s s p r a c h e : 1 7 . D e z e m b e r 2018
B e r l i n 2 0 1 9
Abst r act
In last deca des, the s tudy of the in tera ction betwee n inorganic nanopa rticles and phospholipid mem-
bra nes gaine d m ore attention as it may ena ble new attra ctive applica tion possibili ties i n nanomedicine .
In this context vesicles composed of phospholipid m e mbrane s ser ve as a model for bi olo gic al mem-
bra nes. Fur t hermor e, the interac tion with m ore or less soft nanoparticles ha s a great re levanc e, as the
para m eter sof tness will modulate the a dsorptio n af finity towa rds me mbranes. Ther efor e, we studied the
intera ction of soft and har d nanopa rticles with lip id me m bra nes. The for mer was synthes ized by means
of surfac e-initiated atom transfe r ra dical pol ymeriz ation (ATRP) . The soft proper ties ar ise from havin g
a surfac e graf t ed polymer brush. P o l yelec t rolytes such as ca tioni c poly- dimethylaminoe thyl -metha cry-
late (PDMAEMA) and poly-methac ryli ca cid (PMAA) we r e used as they enhanc e the collo idal stabili ty
in solu ti on due to elec trostatic repulsion . As the y a re p olyelectrolyte s the charge density ca n be tuned
by the so luti on pH. Fur thermore , we ca n contro l t he am ount of graf ted polymer via the synthetic proc e-
dure. A deta iled analysi s of such cor e-shell structures w as done, where structura l deta ils (siz e, shape,
shell thickness, m olec ular we ight) wer e obtained by a combination of small angle scatter ing exper iments
(light, X-ra ys and neutrons) .
In the second part of t he work previous ly synthe sized cationic nanopar ticles were m ixed with anionic
or zwitterionic lip id membranes on cur ved (vesicle s) a nd planar (su pported lipid b ilayers) surfac es. As
a re sult of attra ctive Van der Waa ls and electrosta tic int er actions nanopar ticles adsorb onto the li pi d
membra ne but unti l u p to a cer tain amount of graf ted polymer. Then the in terac t ion becomes m ainly
re pulsi ve, e ven if a n elec trostatic at trac tion is pre sent. Static mea surements w ere done v ia qua rtz cr ystal
microba lance with d i ssipat ion (Q CM -D), whe re the re sona nce freque ncy change recor ds the spontane-
ous supported lipid bilaye r format ion with s ubsequent nanopar ticle adsorption . Essential para meter s
such as char ge density of the pol ymer brush and the p lanar surfa ce, amount of graf ted po lymer, par ticle
size a nd m ate rial of the planar surface we r e studied. The se exper iments showed, that until a given
amount of gra fted polymer or charge density the nanopar ticles do not adsorb at t he surfac e. B eside st atic
expe riments the kinetics of the nanopa rticle adsorption on vesicles of the same bilayer s w as investigated.
Samples were used with nanoparticle s containing a mode rate amount of gra fted pol y m er . The kinetic
measur ements were done by t he stopped -flow technique , which allows rapid mixing of two sm all vol-
umes compo sed of a ves i cle and a nanopar ticle solutio n in to a measure ment ce ll. The vesicle- nanopa r-
ticle aggr egate for mation was fol lowed by tim e resolved turbidity and sm all angle X-ra y scattering
(SAXS) me asure ments. Wi t h inc rea sing nanopa rticle t o vesicle ratio an incr ea se of the kinetic t im e was
observe d . The ne t cha rge of the vesicle s was inverte d by adsorbing N Ps and the ne t c harge of dec orated
surfa ce s re pels further appr oaching NPs away from the sur fac e.
Zusamm e nfassun g
In den l etz ten Jahre n hat die Bedeutung der Untersuc hung der Wec hselwirkung zw ischen anor ganische n
Nanopa rtikeln und Phospho l ipidme mbrane n z ugenommen, denn diese e rmöglichen neue attraktive An-
wendungsmöglichke iten von Nanopar t ikeln in der Medizin. In diese m Kon text fung iere n Vesikel aus
Phospholipidmem bra nen als Model lsyst eme für biologische Zellmembrane n. Nebe n harten anor gani-
sche n Nanopar tikel kann di e Inte raktion auc h mit wei chen Nanopar tikel von große r Bedeutung sein ,
denn der Parame ter Weic hheit wird d as Adsorptions- u nd De sorptions ver halten verände rn. Die vorlie-
gende Arbeit beschä ftigt sic h mit der Inte raktion von weiche n Silikana nopartikel mit Pho spholipid-
membra nen. Erster e w urden über eine oberfläc h eninitialisi er te Atomt ransf er R adikalpoly m er isation
(ATRP) synt hetis iert, wobei die Weichhe i t der Nanopar tikel durch aufge pfropfte Polym er bürsten auf
den Ober fläc hen entsteht. Da bei wurden Po lyelektrolyt e verw ende t, di e di e Obe rfläc henladung der Na-
nopar tikel er höht, um eine kolloida le stabile wässrige Lösun g zu erha lten. E s hande l te s ich dabei um
die Polyelektroly t e Poly-Di methylaminoe t hyl-Methac rylat (PDMAEMA, kationisc h) und Poly-Metha c-
rylsäur e (PMAA, anioni sch), dere n Ladungsdichte mit t els des pH-W erte s gesteue rt werde n kann, da es
sich um schwa che Polyelektroly te handelt. Des We iter en wurde die aufge pfropf te P olymerme nge vari-
iert. Eine detaillierte Analyse der Kern-Schale Nanopa rtikel wurde mitt els mehre rer Analyse methoden
durc hgeführ t, wobei exakte st rukture lle Details (Gr öße, S chale ndicke, Mole kularge wi cht) über ver-
schiede ne Kleinwinkelstre umethoden (Licht , Röntgenst rahlung, Neutr onen) untersuc ht wur den.
Im zweiten Teil der Arbeit wurden die zuvor herge stell ten Nanopar tikel mit anionischen sow ie zwitte-
rionischen Phosphol ipi dmembra nen auf gekrümm ten ( Vesi kel) sowie planare n Oberf läche n (unter stüt-
ze nde Lipidschichten) vermi scht. Aufgr und anz i ehe nder Van-der-W a als und ele ktrostatischer We chsel-
wirkung adsor biere n die Nanopa rtikel auf die Lipidmem bran, jedoch nur bis zu einer besti mmt en Menge
an aufge pfropftem Polymer. Dana ch ist d ie W echse lwirkung ha uptsächlich repuls iv , obw ohl eine e lekt-
rostatische Anziehung vorliegt. S tatische Untersuchun gen wurde n mitt els Qua rz -Kristall-Mikrow aage
mit Ener giever lust auf p l ana ren Obe rflä chen untersuc ht, wobei über d i e R esonanzfre quenzverä nde rung
die Ausbildung der „supported l ipid b il aye r“ und die an schließende Nanopa rtikeladsorption beobac htet
wurde n. Wesentliche P ar ameter , wie die Ladungsd i chte der Partikel und Lip i de, aufge pfropf te Polymer -
menge, Partikelgröße und Materia l de r plana ren Oberf lä che, wurde n untersucht . Erge bnisse zeigen, dass
eine zu große P oly mermenge sowie eine zu hohe Ladun gsdichte der Nanopa rti kel di e Repulsion förde rn .
Nebe n den statischen Ex perimente n wurde auc h die Dy namik der Na nopartikela dsorption auf Vesikeln
untersuc ht. Es wurde n ausschließlich Nanopar tikel verw endet, welche eine modera te Menge an aufge-
pfropf ten P olymer erha lten. Dabe i wurde n m itt els der St opped-Flow-Te chnik Vesikel- und Nanopa rti-
kellösung schnell gemischt u nd dann übe r zeitaufge l ös te Trübungs- und Kleinwi nkelröntgenstreumes-
sungen die St rukturbi ldung der Vesikel-Nanopa rtikel-Aggr egate be obachte t. Es stel lte s ich he raus, da ss
sich mi t zunehme ndem Nanopa rtikel z u Vesikel Verhäl tnis das G leichge wicht langsamer e instellte. Zu-
er st adsorbiere n kationi sche Nanopa rti kel auf die anion i sche n Ve sikel. Nach einer bestimmten Anza hl
an adsorbier ten P artikeln wird die Oberf läche nladung umgepolt, sodass das Annäher n weiter e r Nano-
par tikel er schwer t bzw. verhinde rt.
1. T ab l e of Content s
1 Introduction ............................................................................................................... 1
1.1 Motivation ................................................................ .............................................. 1
1.2 T heoretical background ......................................................................................... 3
1.2.1 Nanoparti cle sy nthesis ......................................................................................................................... 3
1.2.2 Surface modifi cation of si lica by polym e rs ................................ ........................................................... 4
1.2.3 Atom tr ansfer r adica l p olymer ization (AT RP) ................................ ...................................................... 5
1.2.4 Properties of pol y mers ................................................................ ......................................................... 7
1.2.5 Polyele ctrolytes ................................................................ ................................................................... 8
1.2.6 Polymer brushes ................................................................................................ .................................. 9
1.2.7 Polyele ctrolyte brushes ....................................................................................................................... 10
2 Me thods ................................................................ ................................................... 15
2.1 D iffer ent scatter ing tec hn iques a nd their co n trast relation ................................ ....... 15
2.2 D efinition of the scatt ering ve ctor q ......................................................................... 16
2.3 Small angl e scat ter ing ............................................................................................. 16
2.3.1 Descriptio n o f the sm a ll angle s catterin g expe rimen t ........................................................................... 17
2.3.2 Formfacto r of n a nop articles for ne u t ron and x-scatteri ng ..................................................................... 19
2.3.3 Distributio n p roperti es ........................................................................................................................ 19
2.3.4 Model fr e e an al ys is ............................................................................................................................. 20
2.3.5 Formfacto r of core -sh e l l nanopar t i cles for n e utron a nd x -ray s cattering used i n this w ork ..................... 22
2.3.6 Fractal stru c t ure facto r ................................ ........................................................................................ 24
2.3.7 Dynamic light sc a tter ing ..................................................................................................................... 25
2.3.8 Static l ight sc attering ........................................................................................................................... 26
2.3.9 Quartz crystal microba l ance with dissip a tion (QCM- D) ....................................................................... 28
2.3.10 Fraction t r a pp ed liquid cal culation for NPs in this wo rk ....................................................................... 31
2.3.11 Surface covera ge cal culat ion ............................................................................................................... 35
2.3.12 ζ -potenti a l ........................................................................................................................................... 35
3 Experime ntal part ................................................................................................ ...... 37
3.1 N anop artic le synthesis ............................................................................................ 37
3.1.1 Materials ............................................................................................................................................ 37
3.1.2 Methods ............................................................................................................................................. 37
3.1.3 SiO 2 - NP -synth e sis ................................ .............................................................................................. 41
3.1.4 SiO 2 @NH 2 - NP -syn t hes i s ................................................................................................................... 42
3.1.5 SiO 2 @B r-NP syn the s i s – in troduct ion of su rface init iator ................................................................ .... 42
3.1.6 Polymeri zation – pr e parat ion of SiO 2 @PDM AEMA- NP ..................................................................... 43
3.1.7 Polymeri zation – pr e parat ion of SiO 2 @PMA A- NP .............................................................................. 43
3.1.8 Sample prepar ation SANS-measure m e nt ................................ ............................................................. 44
3.1.9 Synthesis of SiO 2 @PDMA EMA/FOM A- NPs ...................................................................................... 45
3.1.10 Polymeri zation of SiO 2 @PA M- NPs .................................................................................................... 45
4 Res ult s and discus sion ............................................................................................. 46
4.1 N anop artic les synthesis and ana lysi s ....................................................................... 46
4.1.1 Preparat ion of polyme r mod ified s ilica n anopart icles ........................................................................... 46
4.1.2 Polymeri zation .................................................................................................................................... 48
4.1.3 Polymer- m odifie d SiO 2 - NPs – variati on o f po lymer type ................................................................ ..... 49
4.1.4 pH respo nsible prop erties .................................................................................................................... 53
4.1.5 Complex a tion Behav ior of S iO 2 @PD MAEMA- NPs ............................................................................ 56
4.1.6 Tra ns mi ssio n electron micros copy an alysis ................................ ......................................................... 59
4.1.7 Analysis of pol ymer grafted NPs v ia SAN S ......................................................................................... 60
4.1.8 Degraftin g diffi culties ................................................................ ......................................................... 73
4.1.9 Dye lab eling of S i O 2 @PDM AEMA- NPs ................................................................ ............................. 75
4.1.10 Polymer modifi cation on sm aller NP s wi th diam e ter of 17 nm ............................................................. 76
4.2 M embrane – NP inter action .................................................................................... 78
4.2.1 Spontaneous suppor te d lipi d bil aye r form a tion ................................ .................................................... 79
4.2.2 Variation o f po lymer densit y and charg e densi t y of S LB ...................................................................... 80
4.2.3 Variation o f the charg e densi t y of th e NPs via t he pH ................................ .......................................... 86
4.2.4 Effect of NP concen tration on the ad sorp ti o n p rocess .......................................................................... 88
4.2.5 Variation o f the type of t h e f lat subs t rate ................................................................ ............................. 92
4.2.6 Variation o f the NP si z e ...................................................................................................................... 93
4.3 Pr op ert ies of S iO 2 @PDMA EMA-NPs b rus hes ......................................................... 94
4.4 Elec trost atic conditions ........................................................................................... 95
4.4.1 Other poss ible i n teractio ns i nfluen c ing th e surfa ce cover a g e ................................ ................................ 99
4.4.2 VdW-d epe n de n ce of adso rption for differe nt surfa ces ................................ ........................................ 100
4.4.3 DLVO in tera ct i on ................................ ............................................................................................. 101
4.4.4 Concentr ation depend e nce of adsorp ti o n ........................................................................................... 104
4.5 A dsorption kinetics ................................................................ ............................... 105
4.5.1 Time reso l ved sc a tter i ng measur emen ts ................................................................ ............................. 108
4.5.2 Adsorptio n rat e f or ca ti on ic NPs with anion i c ves i cles ................................................................ ....... 111
4.5.3 Visual insp e c ti o n of Ves icles NP mixt ures ........................................................................................ 113
4.5.4 Discussion of ki n e tic measu remen ts ................................ .................................................................. 115
5 Conclusion ............................................................................................................. 118
5.1 Pr eparation of nan o particle s (NPs) modified w i th di ffe rent p oly m er shells ............. 118
5.2 Phospholi pid me m brane i nter action ................................ ...................................... 118
6 Outlook .................................................................................................................. 119
7 Reference s ................................................................................................ .............. 121
8 Lis t of abbrevia ti ons .............................................................................................. 128
9 Appendix ................................................................................................................ 129
9.1 C alculation of the molecular weight of polyme r g ra fted NPs ................................ 129
9.2 Surface potential calculation ................................................................ ................ 130
9.3 Simulation details of the scattering intensity for N Ps adsorbed on ves icles ........... 131
9.4 L ogar ithmic plotti ng style of F igur e 94 ................................................................ 132
9.5 Transmis sion plot in logarithmic scale according to Figure 97 ............................. 132
9.6 Theoretical time calculation f or diffus ion limi tation ............................................. 133
1
1 Introduct i on
1.1 Motivati on
Figure 1 : Left: Sc hematic stru ct ur e of 1 , 2-dio le oy l- sn -g lycer o-3-phospho cho li n e mol e cu le w it h in differ e nt co lor
coded functiona l groups . 1 Rig ht: S c h ematic for mation of a bilayer membr ane for mation a s an exam ple for one
vesicle .
Phospholipids ar e amphiphilic molecules compo sed of a head group wi th a hydrophil ic phospha te uni t
and mostly two lipid unsatura ted or saturated ca rbon chains. 1 In water phospho l ipids self-assemble into
bilayer membrane s usually at ver y low critical micellar conce nt ra tion (cmc ) , wher e the hydrophilic hea d
group is di re cted t owa rds the water and the hydrophob i c lipid chains inwar ds the m embra ne. The for-
mation of the bi laye r is re lated to a cylindrical m olecule st ruc ture desc ribed by a packing par amete r
value p betwee n 0 .5 – 1. 2 -4 The low cmc makes them att rac tive for building up ce lls membrane s, which
ar e invol ved in ce llul ar ac tivities like transport of none- and specif ic compound s, food entra pment , en-
er gy transfe r or shielding inner cellular compou nds fro m the env ironment. 5 There are sever al types of
phospholipids, which diffe r by their head group and the fatty acid molec ul e and may be i on i c or
nonionic, which g ives the mol ec ules a nd c orre sponding membrane cha racte ristics prope rties. F or exam-
ple, t he chain mel ting t emper atur e T C of saturate d chains is above phys i ological temper ature s , while that
of unsatura ted li pids is below T C = 0 ° C. As a conseque nce, m embra nes build up from saturated cha i ns
a rathe r rigid at physiologica l tempera tures beca use molec ules are locked in p l ac e , so ca lled solid s tate
phase ( T C > 37 °C, gel phase L α ). 6 In contrast , membrane s bui ld up from unsaturated chains ar e more
flexible and t he membrane i s fluid ( T C < 37 °C, liquid phase L ß -phase ). Acc ordingly, the flexibility of
membra ne ca n be t uned by the melti ng temper ature T C , wher e more doubl e bonds w i thin t he ca rbon
cha in cor rela tes wit h a decr ease of T C . Howeve r, the flu idi ty (ratio of unsaturated versus saturated l ipid
cha ins) and the cha rge density (ratio of charge d versus non -cha rged headgr oups) can be tune d by the
lipid ra tios as d iffer ent l ipids can pac k together. Furthe rmore, the addition of inverted-c one lipids (pac k-
ing para meter p > 1) such as phospha tidylethanolam ine a nd cholesterol straightens the hydroc ar bon
cha ins and reduce s t heir flui dity , causing the “condensa tion” of the lipids and “stiffening” of m em-
bra nes. 5 Most euka ryotic cells contain pho spholipids wi th a choline head group . 6 ,7 – a l ipid wi t h a zwit-
terionic head group, but al so some phospholipid s with a phosphate group and theref ore cells have an
anionic surf ace cha rge. While cell membrane s are ra ther complex and diff icult t o study as they are
mainly bu i ld up from phospho lipids bila yers but are e mbedded with proteins such as cha nnel pro teins,
ca rrier molec ul es, glycol prote ins, e tc…, one often switc h to mode l membrane s (bilaye r membrane s) a s
these intera ction are ea sier t o understand in a funda me ntal study. P ure bilaye r membrane s t end to form
as t her modynamically most stable phase a lamellar p h ase, whil e vesicles are in most case s only meta-
stable. 8 Those ves icles (ofte n ca lled liposo mes) ar e fre quently used in pharmac eutical and cosmetic ap-
plications, 9, 10 or serve in drug deliver y. 11 , 12
In the l ast deca des the resea rch in the field of nanotech nology incre ased dra stically due t o many pote n-
tially attractive applica t io n possi b i lities. 13 – 19 In particular, nanopar ticles ar e attra ctive as they exhibit
2
strongly size-de pendent proper ties and so they also ha ve gre at po t ential for severa l biologic al app lica-
tions. 16 This opens a new important field in the context of using nanopa rticles in nanome dicine . Bu t one
also ha s to t h i nk a bout the fie ld of nanotoxicology. 17, 18 I n ge nera l, one find s a ma rked depe ndence of the
ef fective c ell tox icity on the size of the na noparticle s 20 , 21 and their shape. 22 F urther more, thi s i ntera ction
and the associa ted potentially toxic effe ct wil l depe nd on the t ype and the m ate rial of nanoparticles. 2 3
For e xample, silver nanopar ticles a re highly toxic for b acte ria cell, whic h ar e used as anti-fouling m ate -
rial or sweat odor repe llent i n the textile industry. Even if the materia l in bulk is no n-toxic (for exa mple
SiO 2 ) nanoparticles compose d of t he same mate rial m ay be t oxic to cells due to the size depende nt
prope rties. One may t hink about S iO 2 -NPs – they m ay adsorb on to t he cell membrane s due to strong
adhe sion forc es. 24 – 26 Howe ver, t he mater ial Si O 2 is iner t to biologica l chemistry and no che m ical rea c-
tion between t he adsorbed NP s and t he cell m embra ne shou l d be expecte d. But, d ue t o the attra ctive
adhe sion forc es and the almo s t none re active proper tie s, such NPs m ay rema in on t he outer ce ll mem-
bra ne and shi elds the ce llul ar membrane from the environme nt. In that respe ct, t he cell membrane cannot
communicate with the environment and the cell will somehow die due to sta rvation. C el l m embra nes
ar e complex, bu t they are mos tly built up fr om phosph o lipid membra nes. Thus , to unde rstand t he inter-
ac tion betwee n NPs and m embra nes in the fundame nta l point of view one may sw itch to a simplified
model system of pho sphol ipid vesicles or supported lipid bi layer s and t heir m ixtures with nanopar ticles .
M IC HÉL and G RAD ZIEL SKI sh owed that N P membrane int er action depends largely on cha rge, NP size,
but also on solution pH , ion ic st rength of the di spersin g medium, and s trong l y on the properties of t he
phospholipid bilaye rs. 8 For the mixture of vesicle s and s ilica nanopa rticles, such nanopa rticles are highl y
attra cted to the vesicle surface. They adsorb on the ve sicle surfa ces and form nanopar ticle decor ated
vesicle s. If the surfac e char ge of the nanopar ticles i s hi gh, decor ated vesicles are st abilized by ele ctro-
static repulsion mediated by the surf ace cha rge of t he NPs but onl y above critical NP to vesicle ratio.
Below t he critica l ratio such decor ated NPs acc eler ates the vesicle aggrega t ion due to local l inkage of
fe w NPs betwe en multiple vesic les. Dec orated vesicles can transf er into NP loaded vesicles as well .
Her e it might be noted, that the t ra nsport of nanopa rticl es acr oss a membra ne involves t he wra pping of
the nanopar ticle by thi s membra ne and t hus re quires a l ow membrane rigidity (fluid membrane s) . 24 The
loaded vesicle s are controlled by the ratio of nanopa rti cles size, adhe sion ene rgy betwee n nanopa rticle
and membra ne (vdW forc e), the elec trostatic inte rac t ion energy, and the bending elasticity of the mem-
bra ne. 24 – 26 Further one may observe d adsorp tion on the vesicle outside for froze n bila yers, which may
enha nce colloi dal stabilit y of the vesicle s lar gely 27 , 28 , 24 or i ncor poration of the nanopartic les int o the
vesicle s for flu i d bilayers. 29 , 25 Wh ile most in vestigation s have focused on phosphatidylcholines as model
phospholipids some studies also emp loyed more com pl ex system s such pulmonar y surfac tant . Those
intera ction with alumi na nanopartic les led to t he formati on of m icron -size d aggre gates at a given mixing
ra tio . 30
Howe ver, at l ea st as i mportant as t he static beha vior i s t he kinetics of t he nanopa rticle/membra ne i nter-
ac tion, a s in c olloidal sys tems one may have largely ret arde d struc tural formation . It may de pend on the
colloidal stability of the compone nts in volved. In tha t conte xt , the uptake kinetics of nanoparticle s i nt o
ce lls has bee n studied to some extent , 31 typica l ly depends on size and shape of the nanopar ticles 32 and
is, of cour se, di re ctly relate d to t he adhesion tendenc y of the nanopar ticles to the cell membrane. 33 How-
eve r, the fundamenta l ki netics of t he i ntera ction of nano particle s with a phosph olipid bi layer , as a model
system for cell me mbrane s, has hardly bee n studied and so fa r little syste matic information is know n in
that respec t .
Acc ordingly, in this work a key parame ter i s the inter ac tion betwe en t he nanoparticle s and the mem-
bra ne. So far, one has m ainl y concentr ated on rather “hard” nanopar ticles, 24 but certa inly it is equally
intere sting to i nvest igate “ soft” nanopar t icles, not only with respe ct to t heir inte rac t ion with membra nes
but also for introduc ing the particle softness as an additional tuning par amete r. Th is ca n be achieve d by
3
having a polyme r shell ar ound t he nanopa rticles , where si lica nanopa rticles here are par ticularly attrac -
tive due to t he we ll -develope d surfac e chemistry of si l ica, which allows diff er ent ways of attaching a
polymer shell t o a silica sur fac e. By doing so one can intr oduce a soft, ster ic inter ac tion potent ial due to
the pre sence of the polym er on the nanopar ticle surfa ce and se condly also has t he possi b i lity t o have
modified ele ctrostatic i ntera ctions if a charge d polymer chain is employed. For t hat p urpose we modi fied
silica nanopa rticles ( Si O 2 - NP s) from “hard” anionic (S i O 2 ) to cationic “hard” (NH 2 -moiety che misor bed
at the su rf ace ) or “soft” anion ic or c ationic N Ps co ntaining a polye lectrolyte br ush c ompose d of
poly(methac rylic acid) ( P MAA) or po ly N , N -dimeth yl aminoethyl-methac rylate (PDMAEMA) . 34 Poly-
mer graf ted S iO 2 @ P DMAEMA-N Ps are intere sti ng be cause t he para meter softness im p l emente d fr om
the polymer shell ca n be contro ll ed with a systema tic varia tion of t he graf ting density re sulting in an
ef fective softness control. The NP cha rge densities bec ome tunable by t he graf ting dens i ty or pH as the
amino group i s posi t ively charged under ac i dic condi tions and bec omes more neutral at higher pH . 34
Prior into discussing all re sults, we briefly i ntroduce the theory of sil ica nanopar ticle prepa ration, surfa ce
polymeriza t ion poss ibilities wi t h a deta iled foc us on t h e atom transf er radi ca l polymeriza tion (ATRP) .
Fur thermore , the theory of polymer brushes compos ed of neutral polyme rs and polyele ctrolytes is
shortly explai ned, whic h is importa nt for the compre hension for t he soft N P membrane interac tion. Re-
lated to the t wo main l y u sed a nal yzing technique s we br iefly discuss the t heor etical bac kground of scat-
tering ana lysi s and quartz cr ystal microba lance with d issipa tion.
1.2 Theoreti cal back gro und
1.2.1 Nano par tic le syn th esis
In year 1968 W ER NER S TÖ BER et al. publis hed first t ime an attrac tive c hemica l proc ess to prepa re silica
nanopa rticles (SiO 2 -N P s ) of control l able and uni for m size from t he prec ursor tetrae thylortho si licate
(TEO S) 3 5 and remains today on e of t he most wi dely used chemistry for NP pre p ara tion. The Stöbe r
proc ess is a sol-ge l proc ess, where TEOS reac ts with w ater by hydrolysis into orth osilicic acid usuall y
in an alcoholic sol ut ion (Figure 2) . Subse quentially, the orthosi licic acid conde nsates into a networ k of
SiO 2 -polyme rs. Hydrolysis and conde nsation are ca tal yzed either by acidic or basic condit ions . How-
eve r, the shape of the network is inf luence d by t he pH of the solution, due to the condensa tion aff init y
of orthosil ic acid m olec ules on molecula r sca le at ce rt ain soluti on pH. In detail , the condensa tion is a
nucleophile substitutio n rea ction. In acidic conditi ons t he elec tron density on poorly substi tuted silicon
atoms is low and the nucle ophile substitution of S iO H occ urs prefera bl e on a terminal sili con atom.
Thus, in acidic condit i ons the sol gel proce ss yi elds elo ngated cha ins of si l ica and cre ates a network on
a m ac roscopic scale. In basic conditions the silicon ato m has the h ighest elec tron densi ty and the anionic
Si O – attacks nucleoph ile on the alkox ide. This attack is more probable on silicon ato m with a h igh degree
of substitution due t o strong r educe d elec tron de nsity. T hus , in basic cond iti on s the network forms c l us-
ters, which l ea ds to particles of diff ere nt shapes and sizes depending on rea ctions cond itions . 36 In a
typical Stöber process amm oni a (NH 3 ) is used as the ca talyst and yields in spheric al N Ps . Beside of the
cluster forma tion tendenc y of orthosili c acid, t he deprotonation of hydroxyl moieties at the surfac e in-
cr ease s the char ge density of the surfac e and t hen NP coa gulation i s interrupted m edia ted by electrosta tic
re pulsi on.
4
Figure 2 : Sch e m e of 1) hydrolysis, 2 ) c on dens ation and 3) bru t to rea ct ion eq uation of sil ica for m ation f rom TEOS .
Size, shape and particle dist rib uti on are deter mined by the choice of conditions such as rea ctant, con-
ce ntration, ca t alyst s and tempera ture. Nowa days, th ere exist many instructi ons for si lica nanoparticle
pre para tion allowing to control t he NP si ze fr om 50 to 500 nm . 37 One attractive method was propose d
by D AVI S et al , which leads to mor e monodispe rse parti cles of spheric al shape. It is a S TÖBE R m o di fied
re action e mploying am i no a cids inst ea d of ammonia as ca talyst ( L -lysin or arginine) and thus c om par ed
to am moni a a wea kene d base resul ting in beni gn re ac tion condi tions and to a m ore con trollable particle
growth, re spectively. 38,3 9
1.2.2 Surface mod i fication of silica by polymer s
Figure 3 : Pol ymeri zation possi bi lit i es on su rfaces: a) g ra f ti ng to an d b) gr afting from appr oach .
The well-deve loped chemistry of silica allows diffe rent ways of attaching a polymer onto the surfa ce,
which can be divided into two gene ral methods (Figur e 3) . The first one i s the “graf ting to” approa ch
wher e a pre -pre pa red polymer chain bec omes covalently bond onto the surfac e. While m olecula r weight
of a cha in M W ,chain can be adjust ed in advanc e, the proc ess yields in l ow polymer grafting density ( σ P )
due t o ste ric repulsion of the po lymer cha ins. If highe r gr afting densi ties are desire d, it can be established
from the so calle d “gra fting from” method , wher e the polymer grows di re ctly from the surfa ce . 40 This
re quires a surfa ce- initi ated m odifica tion, depending on finally use d of available polyme rization t ec h-
niques . In principa l, the re a re plenty pol ymeriza t ions te chniques to graft poly mers v ia a surfa ce initia ted
polymeriza t ion such as nitrox i de-me diated poly merization (NM P), 41,4 2 rever sible addition – fra gm enta-
tion chain transfe r poly meriza t ion (RAFT) , 43 and one ma y also em ploy the technique of surfac e-ini tiated
5
atom t ra nsfer radic al polymer ization (ATRP) for at taching pH -responsive poly mer brushes as done for
poly(2-(die thylamino)ethyl methac rylate) (P DEA) and mul ti responsive po ly(2 -( dimethylamino) ethyl
methac rylate) (PDMAEMA). 44,45 In a similar fa shion by this method po ly(2 - (2 -methoxyethoxy) ethyl
methac rylate) (PMDM) has been attac h ed there by yi el ding nanopartic les possessing a lower critical
solution tempera ture (LCST) in aqueous solution 46 and this had similar ly been repor ted bef ore for the
ca se of poly(N-isopropylac rylamide (PNIPAM) . 47 S o f ar, ATRP is widely used due to relative benign
re action conditions, tole rant to plenty mono mers, func tional groups , moisture and leads t o nar row mo-
lecula r weight dist r ibut ion s . 48, 49
1.2.3 Atom t ransfer rad ical polymer izat ion (AT R P)
ATRP is describe d as a controlled living polymer izatio n , due to mainly avoiding t he cha in -cha i n termi-
nation a nd othe r si de r eac tion by a n equilibri um of an i n ner spher e elec tron tra nsfe r involving a reve rsi-
ble (pseudo)ha logen transfe r from a dorm a nt spe cies of R – X (a lkyl halide) with transitio n m etal com-
plex (M n /Ligand) to an active spec ies of ra dicals R * wi th oxidized transi ti on me tal complex (M n +1 /Lig-
and) (a )). C o nsequently, the equi li briu m is shifted towa rds the dormant spec ies, wher e the rate constant
of the equilibr ium is desc ribed as K A TRP (Figure 4a). 50 ,51
𝐾 ARTP = 𝑘 act
𝑘 deac wi th
k
deac >>
k
act
eq. 1
Figure 4: a) S cheme of a n A T RP, b) Con tri b ut ion r e act ion fo r the rate cons t an t K AT RP .
The ra te of pol ymeriz ation depends on K AT RP , t he ra te of monomer propaga t ion k P , the conc entra tion of
the initiator [ I ] and m onomer [ M ] respec tively: 50
𝑅 P = 𝑘 p ∙ [ 𝑀 ] ∙ [ 𝑃 + ] = 𝑘 𝑝 ∙ [ 𝑀 ] ∙ 𝐾 ATRP ∙ [ 𝑃𝑋 ] ∙[𝑀 𝑍 ∙ 𝐿 ]
[𝑋 ∙𝑀 𝑍+1 ∙𝐿 ] .
eq. 2
In detail, t he AT R P equilibrium is a c ontribution of seve ral r ever sible r eac tions such as elec t ron transf er
betwe en metal comp lex ( K ET ) , elec tron affinity of the ha l ogen ( K EA ), bond dissociation ener gy of alkyl
halide ( K B ) and the heter olytic di s sociation of the met al M n +1 – X bond ( K X ) named as hal idophilicity
(F igure 4b) . For main para meter s influenc es the activit y of K ARTP : tempera ture, solvent, the alkyl hal ide
and the cata lyst. 5 2 – 5 4
𝐾 ATRP = 𝑘 act
𝑘 deact = 𝐾 ET 𝐾 EA 𝐾 BD 𝐾 X .
eq. 3
Tempe rature : The solubi lity of the ca talyst and both rate constant k P and K AT RP incre ases with i ncr easing
temper ature, so higher degre e of p ol ymeriz ation shou ld be expe cted on higher temper ature s. Howe ver,
side reac t ions are more probable at highe r t empe rature s as well . The opt imum tempera ture depe nds on
the monome r (solubi l ity, rate of propaga tion, etc… ), ca talyst and t he targe ted mole cular we ight. 55
6
Initiator/ Alkyl halide : If the initia tion i s fast and termi nation neglectable, then the amount of growing
cha ins is cons tant . In principa l , the i nitiator rea ctivi ty ca n be influence d by living time of the initiator
ra dicals . Living ti me is influence d by radica l stabiliz ation group s (the m ore meso mere s st ructur es the
more stable are the ra dicals) degree of substitut ion (primary < seconda ry < tertiar y) and the leaving
group (Cl < Br < I) , wh ich sho uld match wi t h the halide of the meta l for the h i ghest activa tion eff i-
cienc y . 56 – 58
Solvent : K ARTP incr ea ses with po larity of t he solvent . H oweve r, the control over the degr ee of poly mer-
ization is easier in non-polar compare d to high polar solve nt as smaller values of K ATRP allow a more
ac curate control over the degree of polymeriz ation via the re action time . The o pt imum sol vent depends
on the monomer and catalyst solubil ity, K ATRP and the ta rgeted molecular weight.
Catalyst : The ca talyst is t he mos t i mportant component of ATRP . In case of m etal hal i des a w i de ra nge
of m etals can be employed including Ti , Mo , R e, Fe, R u, Os , Rh, Co, Ni, Pd and Cu. Nether theless ,
coppe r has proven to be the metal of choice, due to a broad range of copper complexe s, monomers and
solvent applic ations . Further more, t he choice of the suitable l igand is important because i t dr amatica ll y
af fects the value s of both rate constant s k act and k deac a nd there fore K AT RP . If the monome r propagation
constant k p is low o ne should use high ac tive ca t alyst wi th a high K ATRP othe rwise for hi gh k p low ac tive
ca talyst might be better . The mai n role of t he li gand is to solub ilize the t ra nsition metal sal t in the solve nt
but the structur e of the l igand str ongly i nfluenc es the ac tivi ty of t he co mplex . 50 De pending on the polar-
ity of t he solvents the st ruc ture of t he complex varies, where ionic complexes are better st abilize d in
polar solvents, wh i ch might raise the activit y of co mple x. 50 However , t he exac t str ucture of the ac tive
ca talyst is not yet under stood comple tely. There a ple nty of li gands a vailable. For copper m editate d
AT RP n itrogen base d ligands wo rks par ticular we ll and in contra st sulfur, oxy gen or phosphor us ligands
ar e less eff ective. The ratio betwe en t he metal and the li gand is i mportant and severa l monomer s can
complex with the meta l too. 50 I n som e ca ses t he mono mer c an poison the c om p lex if it contains car boxy
ac id groups for example. 50
In case of syn thesizing pol y m er s with narrow M W cha in distributio ns, liga nds wh ich have high dea cti-
vation ra te constants, are the optimum . Equation (eq. 4) ill ustrate s how the poly dispersity index i s in-
fluenc ed by a prep ar ed polymer from ATRP i n the abse nce of chain – ch ain ter mination and disproportion
but re lates to the conc entra tion of initiator (RX) and de activator (D) , the rate constant of propagation k P
and k D and the monomer concentr ation [ M ]: 50
𝑀 W
𝑀 n = 1 + ( ( [ 𝑅𝑋 ] 0 − [ 𝑅𝑋 ] 𝑡 ) ∙𝑘 P
𝑘 D ∙ [ 𝐷 ] ) ∙ ( 2
[ 𝑀 ] − 1)
eq. 4
The rate constants of k act and k d eac for sever al [Cu(I) /L] complexe s in ace t onitrile wer e inve stigated by
M ATY J ASZ EW S KI group in Figure 5 . The structure of th e complex was var ied by the st ruc ture of nitro-
gen-ba sed ligands . Remarka bly, PMDETA show the highe st deac tivation rate cons tants and so fa r, the
lowest molecular weight d istribution shou ld be e xpec ted f or PMDETA . Alterna t ively , PDI dec rea ses by
adding small amoun ts (5 – 10 mo l% of M n ) o xidized met al M n +1 .
7
Figure 5 : a) chem ical s tructur e of init iator and lig a nd N,N , N ´, N´´-p enta met hyldie thylen e tria mi n e ( PMDE TA );
PMD E TA is used i n this work a s t h e li g a nd in the ATRP b) Diff ere n t s tudied k act a n d k deac va lues for diff e ren t
ligands b y M ATYJASZEWSKI a nd c owork ers for initi ator (EtB riB r) in ace tonitrile . 56 F igure repr i nted w ith p ermis-
sion.
Surfac e i nitiated ATRP
The optimum condi tions for a surfac e init iated ATR P c ompared to a l iquid polyme riza tion may differ ,
due to the di ffusion limi t ation of m onomer t o t he surfa ce and thus , an exac t choose of solvent , catalyst
and initiator i s ne cessa ry. Fur thermore , N P aggr egation must be avoided, so po lymeriza tion i s only pos-
sible i n polar solvents as then surfac e potentials of surfa ce modified SiO 2 @Br-NPs ar e high enough to
protec t particles from agglomera tion. To compensate th e diffusion of the mo nomer towar ds the surfa ce
the living time of the surface ini t iator must be extend.
1.2.4 Pr op erties of polym ers
Polym er s cova lently bond at a surfa ce re prese nt a wide r ange of appl i ca tions by crea t ing funct ionalized
surfa ce s with re spect to d iffer ent desired abili ties like the re spond to exte rnal stimuli , 44 – 47,5 9 pat t er ning,
colloidal stability , 59 exhibition of ant ifouling 60 and high ly adhe sive m ate rials. 59 The to pic is in a funda-
mental point of v iew very intere sti ng, be cause the combina tion of the the rmodynam i cs of polyme rs a nd
conf inement eff ect l ea ds to unique int er esting physical prope rties, which wer e i ntens i vely s tudied for
neutra l a nd cha rged polymer br ushes in theor etical and expe rimental works in l ast deca des. 5 9 Before we
discuss the details about pol y m er brushes. We briefly i n t roduc e i m portant par amete rs for descr ibing
polymers in solu tion .
Mac romolecule s composed of sever al i dentica l repe ati ng unit s (m onom er s) ar e pol ymers. Typical pa-
ra meters to descr ibe polym er s are the degr ee of polyme rization N P (number of repe ating unit s) , the
length of one mono mer a and t he end t o end distance of t he polymer cha in L = N P a 2 . 6 1,62 Howeve r, to
desc ribe a more realistic beha vior of a pol ymer, it is importa nt to i n t roduc e a segment length , which
includes the flexibi l ity of the chain know n as the Kuh n le ngth b . 6 3 I t i s large for st i ff polymer s a nd small
for flexible polymer s and one assu m es that N P subunits of t he length a re replac ed by N Kuhn sub chains
8
of the length b , which is than L = Nb 2 . 63 Another impor tant size sca le to introduce i s t he ra dius of gyra-
tion R G (ra dial distanc e from the whole mass of the body is assu med to be concentr ated) . I t ca n be
ca lculated fr om the position vector of ce nter mass R J an d is given b y:
𝑅 cm
= 1
𝑁 ∑ 𝑅 J
𝑁
𝑖 =1 .
eq. 5
The squar e ra dius of gyration can be expr essed by the sum of all mass points R i subtra cted from the
mass center R J via: 61 ,6 2
𝑅 cm
= 1
𝑁 ∑ 〈 ( 𝑅 𝑖
− 𝑅 cm
) 2 〉
𝑁
𝑖 =1 = 1
𝑁 ∑ 〈 ( 𝑅 𝑖
− 𝑅 𝐽
) 2 〉
𝑁
𝑖=1 ,
eq. 6
wher e 〈 ( 𝑅 𝑖
− 𝑅 cm
) 2 〉 is the ense mble ave rage over the conf ormation of a polymer chain. After simple
math it can be writ ten i n t o :
〈 𝑅 G
2 〉 = 𝑏 2 𝑁
6 ,
eq. 7
and descr i bes the size of the conforma tion of an ideal p ol ymer cha in. It has no informa tion abou t mon-
omer- mo nomer or monomer solvent inte rac tion , which of cour se is important to cons ider. F or e xample,
the mono mers of a p olym er dissolved in a ba d solve nt (f or example hydrophobic chains i n pola r solvent)
pre fer to int er act with monomers i nstead wi th solve nt m olec ules. As a consequenc e of i t , t he polymer
cha in is contra cted but until a given size and beyond it is physi cally unrea listic as the m onomer -mono-
mer intera ctions lea d to steric repulsion at very smal l se para tion distance s . In contra st, for good so l vent
conditions i t is a balanc e betwee n an e nergy gain due to maximizing t heir entropy of t he m onomers a nd
the ela sti c energy of the cha in and t he pol ymer chain swe lls. S o fa r, it i s impor tant to introduc e a swelling
par ameter , which leads to di ffe rent scaling behavior betwee n t he end-to end dist ance L as func tion of
the solvent quality . It is give n by:
𝐿 = 𝑏 𝑁 𝜐 ,
eq. 8
wher e υ i s t he Flory exponent and has the value υ = 1/3 , 1/2, and 3/ 5 for bad , ϴ ( moderate intera ctions)
and good solvent cond it ion s. 61,62
1.2.5 Polyelectrolytes
Pol yele ctrolytes are used for soft brush graf ted NPs , as they i ncr ea se the colloi dal stabilit y due to elec -
trostatic in tera ction, we further i ntroduce brief ly t he end -e nd t o dist an ce L of pol yele ctrolytes . Eac h
monomer unit can contain a charge able unit. P roper ties of such pol ymers depe nd on t he fol lowing pa-
ra meters: the counter l ength Nb , wher e N is the number of Kuh n seg ments of leng t h b ( b ~ 0 . 5 nm flex-
ible polyme r), the degr ee o f ionization β (fra ctions of ch arge d Kuhn segments), B jerr um length λ B which
is t he dist anc e of two elementa ry cha rges i ntera ct with the thermal ene rgy kT = e 2 / ε λ B in the solvent
with dielectric constant ε (in water λ B = 0.7 nm ). Each polyelectrolyte has the number of elementar y
cha rges Nβ distrib uted along the cha in and is balanc ed by the same number Nβ coun terions. The coun-
terion conce ntration along the bac kbone leads to an osmotic pressur e, where the Coul om b elec trostatic
ene rgy of a chain: 6 4
𝑊 = 𝑘𝑇 ∙ 𝜆 B ∙ ( 𝛽𝑁 ) 2
𝐿 ,
eq. 9
is bala nced by the elastic energy of t he cha in
𝐹 elas tic = 𝑘𝑇 ( 𝐿
𝑏𝑁 𝑣 ) 1
1−𝑣 ,
eq. 10
which leads to the ave rage end-end to d istance for a polye l ec trolyte i n in the bulk solu tion :
9
𝐿 ~ 𝑏𝑁 ∙ ( 𝜆 B
𝑏 ∙ 𝛽 2 ) 1− 𝑣
2−𝑣 .
eq. 11
υ is the exponent , which desc ribes the swell i ng of a p olyelec trolyte in the solvent and has a value of
υ = 1 /2 for a ϴ solve nt and υ = 2/7 for a good solve nt , re spectively. 64
1.2.6 Polym e r brushes
Figure 6: a) Mushr oom regi me, b) brush reg ime.
Typica lly, pol y m er brushes are describe d by scaling p roperties, where the brush height H scale s with
gra fting densit y σ , degr ee of polyme riza tion N and the solvent conditio ns . Howeve r, t he key para m eter
is the gra fting density and desc ribes the number of a nchor ed chains per unit are a. 65,66 On surf ac es a
neutra l polym er layer can be describe d t o be within the mushroom or brush regime. Which regime i s
existent, is main ly a function of the gra fting densit y . At l ow gra fting distance s t he polymer chains want
to m axi mi ze t heir entropy and have a si mil ar s tructure as a fre e poly mer chain in solvent . The height of
the polym er l aye r on a pla nar surfa ce scale s with H ~ 2 R G and i s constant with ra isi ng graf ting density
until a critical σ crit . Then the chain-cha i n inte rac tion i n cr ease s and polymers are forc ed to s t re tch per-
pendicula r from the sur fac e to avoid over lapping of adj ace nt cha ins . At σ crit a transi tion from the mush-
room into brush regime is observa ble. 59,6 7
The height of t he polymer brushes is deter mined by a fre e energy balanc e between the polymer with
solvent molecules . The stretching is a conse quenc e of maximizing the entropy by s imultane ously re duc-
ing the unfavor able energy of steric i ntera ctions or i n oth er words to avoid the overla p of adjac ent cha ins .
So , w ith i ncre asing gr afting density the he ight of t he po lymer brush inc rea ses linear ly. The e ntropy loss
is proportional to the degr ee of polymeriza tion N with respe ct to σN / H and H 2 / b 2 per chain, wher e b is
the Kuhn le ngth of the po l ymer. Mathematically the fre e ener gy cost of a p olymer chain is: 59
𝛥𝐹 = 𝑘𝑇 ∙ ( 3 𝐻 2
2𝑁𝑏 2 + 𝜐𝑁 𝜎𝑁
𝐻 ) ,
eq. 12
υ is the excluded volu me para meter and describe s the r epulsion of chain units. The minimization of the
fre e ene rgy leads to: 59
𝐻 ~ 𝑁 ( 𝜐𝜎 𝑏 2 ) 1
3 ,
eq. 13
which shows that the ave ra ge height scale s with the degr ee of polymeriza tion at constant grafting density
or vice versa. Howeve r, theoretic al predic tions could be confirmed with experimenta l data, where the
height scales in good solvent condit i ons in the mushroom re gime with H ~ N 3/ 5 (compa rable t o a swell-
ing dependenc y of single po l ymer cha ins i n bulk soluti on ) and in t he brush regime wi th H ~ σN 1/3 . 59
10
1.2.7 Polyelectrolyte brushes
Figure 7 : Schem atic depe ndency of p olyel ectroly te brus hes i n i onic str engt h fre e solutions . Plot s cale is l ogar ith-
mic. Re d dots il lustrat e the count e rio n distr i bution . 64
Henc e yet descr ibed are polymer brushes of non-e lectric polymers. For b rushe s composed of polyelec -
trolytes t he Poisson Boltzmann m odel explains, that t h e volume frac t ion of po lyelec trolytes is strong ly
coupled t o the i on conce nt ra tion within t he poly ele ctrol yt e brush, which again is a func t ion of the gra ft-
ing de nsit y , end to end di stance of the pol yelec t rolyte L and the i on i c s trength in bul k solution. 64 ,6 8 Fir st
diffe rent brush conf ormations wi ll be discussed for th e assumption of an ioni c st re ngth fr ee sol ut ion
(F igure 7). The n , in t he following section the influenc e of t he ionic st re ngt h is di scussed in detail . At
ver y sm all grafting de nsit ies ( L << σ ) the p olyelectr olyte i s in t he cha rged mushroom regi me (CM).
Diffe rent t o non -ele ctric polymers, polyelectrolytes in t he CM regime int er act with each other. At thi s
re gime c ounterions c an escape from the polye lectrolyte, which crea t es a surfa c e cha rg e density of e βN σ
and corre sponding perpendic ular elec t ric field. As a c onsequence of that electr ic field an energy gain
occ urs by orienta ting ea ch chain perpe ndi cular to the surf ace at the graft ing density σ orien t : 6 4,68
𝜎 orien t ~ 1
𝜆 B ( 𝛽𝑁 ) 2 𝐿 .
eq. 14
Below σ orien t cha ins are fr ee to rotate and above σ o rient t he force i s strong enough to orie ntate the cha ins
primarily perpe ndi cular but not strong enoug h t o elong ate them signi fica ntly. With ris i ng grafting den-
sity counte rions are st il l able to esc ape from the surfa ce. At a critica l value of σ * the force mediated
from the electr ic field of esca ped counter ions begins t o elongate the chain beyond the end to end cha in
length L and we enter the so called Pincus brush re gime (PB ) . It exists only at very low ionic st re ngth,
small grafting densit ies and for we akly char ged poly elec trolytes with t he gra fting density range of
σ * < σ < σ osm . If ionic st re ngth s are high and polyele c trolytes are strongly cha rged , the n there is no
Pincus re gime. 64,6 9 It i s note wort hily, t hat in re alistic c onditions t he Pinc us brush r egime is not existing.
With further rising gra fting density a cross over from t he P incus brush re gime into the osmotic regime
(OB) begin at σ o sm . Now counterions become localize d within the polyele ctrolyte brush , wh ich want t o
maximize their entropy (osmo t ic pressure ). The balanc e of the osm otic pressure wit h the ela sti c par t of
11
the fre e ener gy pe r c hain ~ β N kT pre dicts t hat the brush l aye r H is independe nt from the grafting dens ity
σ : 64
𝐻 ~ 𝑏𝑁 𝛽 1 −𝑣 ,
eq. 15
and the polyelectrolyte i s st rongly stretche d compare d to its fre e polymer chain L in bulk solution.
At ver y high graf ting densities beyond σ N the quasi ne ut ra l brush (q-NB) is entere d. Now the di s tance
betwe en cha ins is small and the ene rgy of the short ra nge exc luded volumes betwe en monomers is hi gher
than the counte rion osmotic con tribution of the brush free ener gy . Po lyelectr olyte brushes have the same
prope rties t han neutra l brus hes . Thus , the thickness of suc h brushe s ca n be describe d by t he Alexa nder
de Gennes sca ling model for neutral brushes, which simpl if ies into the heigh t H of the pol y m er l aye r
to: 6 4 , 70 ,71
𝐻 ~ 𝑏𝑁 ( 𝜎 𝑏 2 ) 1−𝑣
2𝑣 ,
eq. 16
and is a function of the gra fting density and the degre e of pol ymeriz ation . The gra fting density scales
with the exponent (1- υ )/ 2υ and i s half of the exponen t for the P incus brush regi me. For a ϴ sol vent
( υ = 1/2) the expone nt sim p lifies into 1/2 and for a good solvent υ = 3/5 t he exponent is 1/ 3 64 and similar
to eq. 13.
1.2.7.1 Count eri on escape ment of brushe s
The elec trostatic potential inside a polyelec trolyte brus h is para bolic and is produc ed by the combined
elec t ric cha rge of polyelectr olytes and counterions . Th e para bolic electric pote ntial i s equivalent to a
linear electr ic field (de rivative of the elec t ri c potentia l) away fr om the surfa ce. Howeve r, the l inear
incre ase of the elec tric field implies by the Gauss law, tha t t he net charge density in t he brush is uniform .
The net cha rge density is betwee n the char ges of the monomers and counter ions, which leads t hat the
polymer density profile follows t hat of the counterions. Howe ver, t he net charge of the pol ymer brush
is not exac t ly z ero and some c ounterions Δ n pe r c hains ca n e scape from the brush. The se e scape d c oun-
terions cre ates a capacitor w ith the thickness of t he poly mer brush H plus of a Gouy-Chapmann l aye r λ ,
wher e λ is proport ional to esca ped char ge e Δ n out side the brush λ ~ ( λ B σ Δ n ) – 1 . 6 4
The ele ctrostatic ene rgy per unit ar ea:
𝐹 elect ~ 𝑘𝑇 𝜆 B 𝜎 2 Δ𝑛 2 (𝐻 + 𝜆 )
eq. 17
is bala nced by the entropic gain for the fre e ener gy of escape d counterions normalized to the unit are a:
𝐹 Δ S = 𝑘𝑇𝜎Δ𝑛 ln ( 𝑐 out
𝑐 in )
eq. 18
with c out = Δ nσ / λ as the counterion conc entra tion outs ide the brush and c in = fNσ / H as t he counte rion
conc entra tion insi de the brush. The Gouy-C hapman lay er is compar able to the brush thickness and th e
net number of esca ped counter ions depe nds re ciproc ally on the brush t hi ckness and graf ting density σ :
Δ𝑛 ~ 1
𝜎 𝜆 B 𝐻 .
eq. 19
1.2.7.2 Influence of the ionic str ength
Not di scussed yet but no t to be neglecte d is the influen ce of the ion ic strength in bulk solution . Previ-
ously discusse d regime s consider ionic strength fr ee soluti ons (no added salt). Howe ver, the height of
the pol yele ctrolyte brushes is sens iti ve to the ionic s trength and decr ea ses wit h i ncr easing salt conc en-
tration. The reason i s an incre ase of the screening of t he C oulomb repulsion betwee n char ged monomers
with incre asing salt conc entration. The swellin g i s bal anc e of the ela stic force of the chain versus the
osmotic pre ss ure per chain due to i on differ enc e between a brush interior αc and bulk c s sol u tion as : 68
12
∆П
𝑘𝑇 = 2𝑐 𝑠 [ √ ( 𝛼𝑐
2 𝑐 s ) 2 + 1 − 1 ] ~ { 𝛼𝑐 𝑐 𝑠 ≪ 𝛼𝑐
(𝛼 𝑐 ) 2 𝑐 s
⁄ 𝛼𝑐 ≪ 𝑐 𝑠 .
eq. 20
If c s << αc the osmotic pressure is dominate d by the co unterions within the brush and the brush swells
(osmotic regime) . If αc << c s the osmotic pressure is do m inated by the ions in the bulk sol ution and the
brush collapses . This is the salt d ominated regime (sal ted brush) and such brushes of pol yelec t rolytes
have si milar properties to neutral ones. In betwe en tho se extre mes the brush height scales i n first ap-
proximation from compu t er si m ulation with H ~ c S – 0.33 or in rece nt publica tion with H ~ c S – 0.43 . How-
eve r, available expe rimental data does not allow t o d i ff er betwee n the expone nts of -0.33 or -0.43 . 68,7 2 –
74 In detai l the sal t depe ndence scaling e xponent f or the brush he ight is a function of t he solvent qual ity,
the degre e of ioniza t ion potential (we akly or strong c ha rged polyelectr olytes) a nd the salt c oncentra tion
and ca n be rea d in detail from refe rence 68 .
Note, t hat the De bye scre ening length κ – 1 in the brush is diff ere nt to that of the bulk sol u tion and is
ca lculated from t he counterion conc entration pl u s that of the salt conce ntration wi thin the brush . It is
given as: κ – 1 ~ ( c S + αc ) 0.5 ~ ( c s + ( Nβσ / H 0 )) 0.5 and usually very hi gh . Howe ver, in the osmo tic r egime κ –
1 ~ ( αc ) 0.5 and is do minated by the counte rions from the brush.
Fur thermore , the degre e of ioniz ation of polyelec trolytes is diff ere nt compar ed to a polyelec trolyte in
bulk solution. Let us assume, that polyelec trolytes i n s olution have the same degree of polymeriz ation
than i n brushes . Then , at very low ioni c strength the degree of ionization of t he brush β is smaller than
the degre e of i onization β B of the polyelec trolyte in solution due to hi gh er i on conc entra tion within the
brush α B < α and ca n be describe d by fol lowing eq uatio n: 7 5
𝛽 = 𝛽 B
1−𝛽 B ∙ √ ( 𝐶 H +𝐶 s )
𝑐 P ,
eq. 21
C H proton conc entration, C S salt ion conc entra tion and c P as brush chara cteristics.
As a brief summa ry , the brus h regime can be influenc ed by the graf ting dens i ty, degre e of polyme riza-
tion and io nization and the ionic str ength of t he solvent . Note, that most releva nt brush regime s to con-
sider ar e the osm o t ic and sa lted brush re gime dependin g on the ionic st rength of the bul k solution .
1.2.7.3 Brush density on planar and curved s urfa ces
Late r im portant for the detailed structural ana lysis via SAN S on po l ymer gra fted sili ca nanopartic les is
the di scuss ion about the p ol ymer volume density profil e of such poly mer brushes. For pla nar surfa ces
the volum e fra ction of brushe s with non -ele ctric polym ers can be described by a si gmoidal dec ay from
the surfac e to the bul k sol ution. 76 The degre e of the curvatur e is i mportant, whe re the segment dens ity
profile of t he brush for particles with small curva ture ca n be describe d in a si m ilar fashion of pl ana r
sca ling models. However, wit h increa sing curva ture th e deca y of the segment densi ty profile i ncr eases
and cha nges fr om a sigmoidal to an exponent ial deca y . 77 – 80 If t he surf ace curva ture i s large such particle s
ca n be appr oximated w ith a si m ilar model as for star pol ymers. It assumes that all cha ins are bond in t he
ce nter and eac h cha in is stretche d wit h an i dentica l dista nce towar ds the bulk solution. The model was
first introduc ed by D AOUD and C OTT ON 80 a nd defines that the br ush is se gmented into blobs ( Figure 8) .
Eac h blob has a spher ical symmetr y and con tains par ts of the polymer chain. The si ze of ea ch blob ξ ( r )
is assumed to be identic al at the radial dist anc e r from t he cente r surface but eac h s izes incr ea ses with
incre asing dist anc e t o approximate swelling of the brus h. The swelling i s denoted by δ ( r ):
𝛿 ( 𝑟 ) = 𝜉 (𝑟 )
𝜉 0 ( 𝑟 ) ,
eq. 22
wher e ξ 0 ( r ) is the unperturbe d size of the bl ob at a dista nce r . The volume fr action profile as a function
of distance is segmented into three parts and is describe d:
13
Φ ( 𝑟 ) =
{
1 (𝑟 < 𝑅 𝐶 ~𝑓 1
2 𝑏)
( 𝑟
𝑏 ) −1 𝑓 1
2 (𝑅 𝐶 < 𝑟 < 𝑅 1 ~𝑓 1
2 𝑣 −1 )
( 𝑟
𝑏 ) − 4
3 𝑣 − ( 1
3 ) 𝑓 2
3 ( 𝑟 > 𝑅 1 ) ,
eq. 23
with b the segment length , f the number of a rms of a s tar polymer a nd v the e xcluded vol ume pa rame ter.
R C is the core radius and R 1 is a ra dial di stance for the fi rst blobs from the center of a s tar polymer. The
height of the brush layer is rela ted to eac h region is:
𝐻 ~ 𝑁 1
2 𝑓 1
4 𝑏 for t he unswoll en reg ion,
eq. 24
and
𝐻 ~ 𝑁 3
5 𝑣 1
5 𝑓 1
5 𝑏
eq. 25
for the swollen region.
The vol ume frac tion dec ays expone ntially i n the form of r – α at constant chain l ength and the brush height
sca les as func tion of α wi th:
𝐻 ~ 𝑓 ( 2−𝛼 ) :(6−𝛼 )
eq. 26
Figure 8: a) S chem at i c illus tration of t h e cal culation appro ach i n troduce d from D AOUD and C OTTON and b) the
corresp onding s e gm ent d ensity profi l e . 80
The scaling law and the segment de nsity of po lymer bru shes first introduced by D AOUD and C OTT ON is
valid for good s olvent condit i ons and non-e lectric pol y mers and motivate d other rese arc her s to expa nd
their appr oac h to curved surfac es . For exa mple, W I JMA NN and Z HU LIN A st udied the effe ct of the density
profile as a function of t he cur vature and solvent quali ty. 81 Under good solvent cond i tions and highly
cur ved surfa c e the segment densit y has s imilar results from theoretica l calcula tion from D AOUD and
C OTT ON . In contra ry, the volume frac tion prof ile becomes constant in bad solvent conditions , due to
collapse d conforma tion of polymer chains. The ef fec t of the cur vature l ea ds to a para bolic profile for
the volume fr ac tion at sma ll curva t ure a nd is compar abl e to the pr ofile of a plana r surfa ce. Espe cially at
low curva ture chains are more stre tched awa y from the surfac e, due t o avoid overlapping of adjace nt
cha ins (stronge r size exc luding e ffe cts) . Howeve r, the size exc luding effe ct reduc es with increa sing
cur vature (F igure 8 ) so stronger collapsed chains can b e expec ted for higher cur vature.
1.2.7.4 Segment den s ity prof ile prediction for S i O 2 @Polyele ctrolytes
We prepar ed brush gra fted NPs co mposed of polyelec trolytes. Theor etica l pre dictions show , that the
polyelec trolyte densit y prof ile follow s t hat of the count erion density profile. 64 We est imated in chapte r
4.3 the os moti c re gime (low salt conce nt ra tion and proba bl y high graf ting densi t ies ) fo r the synt hesize d
brush graf ted NPs. Thus, brushes ar e strongly swo ll en a nd pol y mer cha ins ar e orientate d primar ily per-
pendicula r towar ds t he bul k so luti on . The segme nt dens ity profile is expec ted to dec ay expone ntial from
14
the spherica l particle surfac e even if a sm al l curva tur e i s present for particle di ame ters d = 50 , 70,
140 nm . This could be proofed wi t h small angle neutr on sca ttering ( SANS) while appr oxi mating t he
sca ttering intensi ty I ( q ) of such spheric al cor e-she ll str ucture s with a cor e-she ll mo del with a spherica l
symmetry. Fit ting results exh i bit, that the scatter ing len gt h density of shell decays expone ntial towards
the bulk solu tion . Deta ils about that model are depicted i n chapter 4.1.7.
15
2 Methods
2.1 Differen t sca tterin g techniq ues a nd their contrast r ela tion
An attrac tive and eff ec tive method to char acter ize nano si ze d structure s is sma ll angle scatter ing. S cat-
tering expe riments have plent y of advantage s compa red t o electr on microsc opy m aking them attrac tive
as an analyzing tool in t he field of soft matter technology. 82 One hu ge advanta ge of sca ttering m ethods
is , that they provide information about the structura l av era ge of the system. The major require ment for
a sca ttering exper iment i s the contrast of ele ctromagn etic irra diation (light, X-r ays) and neutr ons be-
twee n dispersed mater ial and the bulk solution . In case of l ight scatter ing the contra st re lies on di ffe r-
enc es i n the refr active index betwe en sol vent and dissolve d/dispersed material mediated by the pol ar -
izability c hange from one me dium t o another mediu m. Howe ver, ligh t int er acts on ly with wea kly bound
elec t rons, wh ile in c ont ra st X-r ays, due t o the ir h igher ener gy c ompare d to light, ar e interac t ing with a l l
elec t rons. If the elec tron density diff ers betwe en di s perse d mater ial and the solvent a contrast i s pre-
sent. 83 The hea vier an atom , the more proba ble is that X -ra ys i ntera cting w ith elec trons, thu s X-ra ys are
strongly intera cting with heavy elements . Differ ent t o X-ra ys, neutrons scatter ing is n ot of elec t romag-
netic nature . Neutrons are neutra l partic les with a spin s = ½ . A neutron has a m agne tic m oment and a
li ve time about 15 minu tes. Due to t he spi n of s = ½ neutrons are int er acting wi th o ther sub -atomic
par ticles with half spi ns and inte gral multiple s ( s = ½ + n with n = 0, 1 , 2… ) and t her efor e they ar e main l y
intera cting wit h the nucleus of an atom or unpaired el ectr ons. Differ ent isotope s have d i ffe rent spins
and t hus differ ent i ntera ction po t ential. Related in soft matter the m ain diffe rence s in the con trast are
betwe en deuterium (nuc leus spi n s = 1) and hydrogen ( nucleus spin s = 1/2) . Fre quently i n small angle
neutron sca ttering (SANS) experiments the di sperse d material is hydrated while the bul k mater ial is
deuter ated. The h uge advantage of neutr on scattering to X-ra y scattering is that orga nic mater ials can
have a contrast just by repla cing H by D, there by hardl y aff ecting the chemical environment . Further -
more, t he contra st ca n be modified by either the so lvent or disperse d materia ls ratio (H/D), where l oca l
domains may bec ome m atc hed ou t to get more ac cura t e details wh ile analyzing the data . 84
Figure 9: Cartoo n of co re -sh ell nanop a rtic les a nd t h e prin cipal contrast of differe nt s cattering me thods (D LS,
SAX S; SAN S).
All these d iffe rent contra st require ments give the possi bi lity to ana lyze s pher ical S iO 2 -NPs w i th a pol-
ymer coating with diffe rent scattering techniques to ob tain m ore acc ura te information abou t struc tural
details of particle shape, size polyd ispersity , shell thic kness and poly mer segment density profile . As
depicte d in F i gure 9 the total s ize of SiO 2 @ Polymer -NPs ca n be obtained from dynam ic ligh t scatte ring
wher e t he hydrodynamic ra dius re sults from t he silica core plus surrounding polymer m atrix. Details
about the silic a cor e and dispersity (size and molecula r weight) can be measure d using X-r ay and neutron
sca ttering. Howeve r, for X-r ays the contrast betwee n t h e pol ymer matrix and solvent is ver y sm all thus
the major scatter ing intensity result from t he silica core . In contrast , for neutron sca ttering detai ls abou t
the core- shell structure can be seen in in fu l l contra st o r that of the polymer shell only if the scattering
intensity of the silica core i s matched by the bulk sol ve nt .
16
2.2 Definitio n of the sca tter ing vec to r q
Figure 10 : a) Prin c ipal setup for a scat t ering exper i ment . A t angle θ t h e s c att e ring intensit y c an b e record e d w it h
a d e tec tor. b) d e fin ition of the sc attering cros s se ct ion ( E wa ld sphe re ) 85 ,8 6
Valid and nec essar y for all scatter ing exper iments (L S, S ANS , S AXS) is the defini ti on of the amou nt
of the scattering vec tor q , which i s the diffe renc e of the wave vector of scattered bea m 𝑘 s
and the primary
bea m 𝑘 i
. Its re lation is give n:
𝑞 = |𝑞 |
= 4∙π∙𝑛
𝜆 ∙ sin ( 𝜃
2 )
eq. 27
with ϴ the angle of scatter ed beam re fer red to primary beam, λ the wavelength, n the re fra ctive index
(X- rays, neutrons ~ 1).
2.3 Small a ngle sc atterin g
Figure 11 : S cheme of scatter e d cir cular wave from p lana r in ciden t p l ane wav e.
In all small angle sca ttering experiment a cohe rent foc used beam (neutr on, X-r ays, light) penetra t es the
sample, will be sca ttere d and t he magnitude of t he sca ttering inte nsity is detected by a detector at a
ce rtain sample to dete ctor dista nce (SDD) . In det ail, wh en an incide nt plane wave 𝜓 0 e i𝑘
𝑧 int er acts wi th
the scatter ing ce nter at pos iti on r J , tha t ce nter scatter the wave − 𝑏
𝑟 J
𝜓 s e i𝑘 S
∙𝑟 J
spherica l in all room direc-
tions. No t e, that Ψ 0 and − 𝑏
𝑟 J
Ψ s are t he scatter ing amp litude s , b is the scattering length and 𝑟 J
the scat-
tering ce nter.
The constructive and destructive interfe rence of all sphe rica l scattere d waves leads to a complex scat-
tering amplitude A ( 𝑞 ) at a cer tain angle or corre spons ive scat tering vector q . Differ ent nanosc opic ob-
jects will l ea d to diffe rent in terf ere n ces, where the ov er lap of all waves final ly g i ves a cha rac t er isti c
sca ttering pattern at the detector, which is a func tion of concentr ation, contra st , size, shape and their
interpar ticle int er action. If the sca ttering only cha nges in the direc tion but not the energy, the proce ss is
named as elastic sca ttering. For fur ther discussio n only the elastic scatte ring is a ssumed , and we suppose
17
that incident pl ane wave is strictly monoch romatic. In practice the result ing amplitude of elast ic sca t-
tere d wave Ψ s in a three -dimensional room for n nuclei will be give n as :
𝜓 𝑆 = − ∑ ( 𝑏 𝑛
𝑟 J
) e 𝑖 𝑘
∙𝑟 J
∙
𝑛 e 𝑖 𝑘 S
∙𝑟 J
.
eq. 28
Her e is b t he scattering length of eac h individual nucle i, Ψ s the ampli tude of the scatter ed wave , 𝑟 J
center
position, 𝑞 the scattering vector. The total scatter ing am plitude A ( 𝑞 ) can be ca lculated via the Fourier
transf ormation, w hich g ives infor matio n over the di st ri bution of all sc attering ce nters w ithin the sa mple
volume V S :
𝐴 ( 𝑞 ) ≈ 𝜓 0 = ∫ 𝜂 (𝑟
𝑉 𝑆 ) ∙ e 𝑖 𝑞
𝑟 ∙ 𝑑 3 𝑟 .
eq. 29
Fr om eq. 29 the scatter ing amp l itude corr elates with scattering length dens ity η . Latter is the su m of all
sca ttering lengths withi n a certa in vo lume and η describes the probabil ity of an ela sti c sca tteri ng event
at position 𝑟 . It is note worthily, tha t scatter ing patterns only occur i f differ ence s of η betwee n the na-
nosized obj ec t and t he surrounding mater ial is prese nt . I n other wor ds , a sca ttering c ont ra st is nec essar y
otherw ise all sca ttering ce nters scatter with the same p robability and nanos ized objects are “invis ible”
compar ed to the bulk mate rial. The scattering l ength b i s an atomic pr operty but in a typical sma ll angle
sca ttering expe riment the l ength scales are much larger than the si ze of a si ngl e nucleus. 87 Thus, on a
macr oscopic sca l e it i s much easier to use collective m ate rial proper ties compare d to c onside r ea ch
individual nucleus with its indi v i dual scattering length b . T he scatter i ng length density η of a mater ial
ca n be calcula ted by the sum of all sca ttering lengths b i corre sponding the rele vant m olecula r vol ume
V n composed of these ato ms:
𝜂 = ∑ 𝑏 𝑖
𝑛
𝑖 𝑉 𝑛 = 𝜌 ∙𝑁 A ∑ 𝑏 𝑖
𝑛
𝑖
∑ 𝑢 𝑖
𝑛
𝑖 = 𝜌∙𝑁 A ∑ 𝑏 𝑖
𝑛
𝑖
𝑀 W .
eq. 30
V n can be estimated with t he knowledge of the density of the material ρ , Avogadr o num ber N A and the
molecular weight M W , which is the sum of all elements with t he atomi c m ass u i .
Howe ver in al l SA S expe rim ents t he detector measure s the scattering int ensi t y I ( 𝑞 ) and not the sca ttering
amplitude A ( 𝑞 ). Latte r is connec t ed with I ( 𝑞 ) over:
𝐼 ( 𝑞 ) ~ | 𝐴 ( 𝑞 ) | 2 ,
eq. 31
but the square of A ( 𝑞 ) l ea ds t o a loss of t he phase infor mation. Thus , it is d ifficult to get informa tion
about η from t he sca t tering intensity. F urther η is cons ide red t o be f ixed, if approximat ing the scattering
intensity fr om modeling .
2.3.1 Descript i on of the s mall a ngle scatte ri ng e xpe rim en t
In a typical sma ll angle scattering e xperiment t he sca ttering intens ity is rec orded via a 2D dete ctor ,
wher e the detec tor ca n be positioned at a cer tain sampl e t o detector d istance. Howeve r , for covering a
whole q -ra nge usually one must position the detec tor at sever al posi tions. The in tensity I ( q ) is propor-
tional to the number of neutr ons/photon s sca ttered by the sample at a solid angle eleme nt Δ Ω t o the
detec t or during the time Δ t (F igure 10b):
𝐼 ( 𝑞 ) = 𝜙 ∙ Δ𝛺 ∙ 𝑇 S ∙ d𝑆 ∙ d𝑡 ∙ 𝜀 ( 𝜆 ) ∙ d𝜎
d𝛺 (𝑞 ) ,
eq. 32
ϕ is the flux ( n wav es /time [cm – 2 ∙ s – 1 ]), T S transmission of t h e sample (rela tive change of t he beam intensity) ,
d S and d t as t he sample are a (cm 2 ) and t h ickness (cm) , ε ( λ ) the detector effic iency for a gi ven wavele ngth
λ a nd d σ /d Ω is the dif fer ential sc atter ing cr oss sec tion (c m – 1 ). Latter is the number of scattere d ne utrons
or photons passing through the sample ar ea d S per time :
18
𝑣 ∙ d𝑆 ∙ | 𝜓 S | 2 = 𝑣 ∙ d𝑆 ∙ ( 𝑏 i
𝑟 J
) 2 = 𝑣 ∙ 〈 𝑏 2 〉 d𝛺 ,
eq. 33
wher e v i s velocity of neutrons/p hot ons , Ψ S the elastic scattere d wa ve, b i the scattering length for the
sca ttering center 𝑟 J
. The cr oss section ca n be re written int o :
d𝜎
d𝛺 = 𝑣 ∙𝑏 2 ∙d𝛺
𝜙 ∙d𝛺 = 〈 𝑏 2 〉 .
eq. 34
The sc at t ering cross s e ction d σ /d Ω can be des c ribed if c ombi ni ng eq. 28 – eq. 31 an d eq. 34 into:
𝐼 ( 𝑞 ) ~ d𝛴
d𝛺 ( 𝑞 ) = 𝑁 P
𝑉 ∙ d𝜎
d𝛺 ( 𝑞 ) = 1
𝑉 ∙ | ∫ 𝜂 ( 𝑟 𝐽
)
𝑉 ∙ e 𝑖𝑞 𝑟 J
∙ d 𝑟 J
| 2 .
eq. 35
With N P the partic le number within scatter ing v olume V , η ( 𝑟 J
) the sca ttering l ength density at t he scat-
tering pos i tion 𝑟 J
and d Σ /d Ω the diffe rential mac roscopic cross sec tion – a n ormaliza tion t o the scatter ing
volume of the diffe rential cr oss section Σ = σ / V ca n be done to get scattering intensity in absolute scale.
It consists of a cohere nt (coh), incohere nt (inc) and abs orptive (abs) part:
d𝛴
d𝛺 ( 𝑞 ) = d𝛴 coh
d𝛺 ( 𝑞 ) + d𝛴 inc
d𝛺 + d𝛴 abs
d𝛺 ,
eq. 36
wher e onl y the coher ent part i s a functi on of the scatte ring vector and thus only conta ins information
about the sca ttering structur e. The incoher ent part has no valuable information but influence s the scat-
tering intensity as backgr ound noise. The absorpt i ve pa rt is the i maginar y part of the scattering length
b , is usual ly very small and re duces the measure d scatter ing intens ity by the absorbed amount .
For nano si ze d objects (nanopar ticles, poly m er s, vesic les, proteins , mi ce lles etc …) dispe rsed in bulk
medium the scatter ing arises from coun table particle s N P withi n the macr oscopic scattering cr oss section
d Σ /d Ω . Lat ter i s a functio n of the particle shape, where mathematica lly it ca n be descr ibed as the sum
of all scatter ing center s at mass center posi tion 𝐺 i
of N P pa rticles in t he scattering vol ume with scatter ing
length b i . The formfac tor of the particle P i ( 𝑞 ) i nclude s all sca ttering cente rs N within each par ticle at
position 𝑋 J
relative to 𝐺 i
with scatter ing length b J :
𝑃 𝑖 ( 𝑞 ) = ∑ 𝑏 iJ ∙ e 𝑖 ∙𝑞
∙𝑋 J
𝑁 P
i
eq. 37
The intensity is then:
𝐼 ( 𝑞 ) = d𝛴
d𝛺 ( 𝑞 ) = | 𝐴 ( 𝑞 ) | 2 = 1
𝑉 ∙ | ∑ 𝑏 i ∙ 𝑒 𝑖 𝑞
∙𝐺 𝐼 ∑ 𝑏 J
𝑁
J
𝑁 P
i ∙ 𝑒 𝑖 𝑞
∙𝑋
𝐽 | 2 = 1
𝑉 ∙ | ∑ 𝑏 iJ ∙ 𝑒 𝑖 𝑞
∙𝐺 𝐼 ∙ 𝑃 i ( 𝑞 )
𝑁 P
i | 2
.
eq. 38
The scatter ing i ntensi ty not only results from the form fa ctor P ( 𝑞 ) but also from the dista nce betwe en
N P particles at position 𝐺 𝑖
and gives informati on about the avera ge localiza t ion of the object , known as
the structure factor S ( q ):
𝐼 ( 𝑞 ) = d𝛴
d𝛺 ( 𝑞 ) = | 𝐴 ( 𝑞 ) | 2 = 𝑁 P
𝑉 ∙ | 𝑃 i ( 𝑞 ) | 2 ∙ 1
𝑁 P ∙ | ∑ 𝑏 i ∙ 𝑒 𝑖 𝑞
∙ 𝐺 𝐼
𝑁 P
i | 2 .
eq. 39
Equation eq. 38 and eq. 39 l ea ds to the fundamenta l eq uation of descr ibing the scatter ing inte nsity as a
func tion of the scattering vector q : 83
𝐼 ( 𝑞 ) = d𝛴
d𝛺 ( 𝑞 ) = 𝑁
1 ∙ 𝑃 ( 𝑞 ) ∙ 𝑆 ( 𝑞 ) + BG ,
eq. 40
w ith q as the amount of the scatter ing vector 𝑞 , 1 N being the par ticle density ( 1 N = N P / V ), P (q) t he form
fa ctor, S ( q ) the structure fac ture and the backgr ound in tensity BG . If NPs are strongly d ilut ed there is
no i nterpa rtic le i n tera ction and the structur e fac tor can be neglec ted so S ( q ) = 1 . O t her wise with raising
par ticle conc entra tion S ( q ) ≠ 1. The infor m ation ab out the shape of the par ticles is given in
19
P ( q ) = | 𝐴 ( 𝑞 )| 2 resulting from the isot ropic form factor i ntensi ty. The formfac t or also includes infor-
mation about the V P the particle vo lume and the scattering contrast η . It can be rew ritten as
P (q) = V P 2 η 2 ∙ P ’(q) , bu t on ly if the scattering contra st i s hom ogenous. For re asonable data interpre t ation
P (q) must be modelle d ac cordingly . Further m ore, t he sc attering l ength densities and of all compoun ds
and partic le number de ns ity 1 N have to be ca lculated and set a s a fix par amete r . 1 N ca n be obta ined from
gra vimetric mass conc entration me asure ments with the knowledge of the m ea n molec ular weight of the
NPs vi a:
𝑁
1 = 𝑐 g ∙ 𝑁 A
𝑀 W, NP ,
eq. 41
with c g as we ight conc entra tion, N A Avoga dro constant , M W,NP molecula r weight of the nanopa rticles.
2.3.2 Fo rm factor o f nanoparticles for neutron and x -scatter ing
The scattering i ntensi ty of spherica l nanopar ticle withou t any polymer shell can be describe d by a sphe r-
ical form factor of a homogenous sca ttering lengt h den s i ty. The gene ral expre ssion of the form fac tor
is: 88
𝐴 ( 𝑞 ) = ∫ ( 𝑏 i − 𝑏 s ) ∙ exp ( 𝑖 𝑞 𝑟 ) d 𝑟 ,
eq. 42
which ca n be written for a spher ical particle in :
𝐴 ( 𝑞 ) = ( 𝑏 i − 𝑏 s ) ∙ ∭ e xp ( 𝑖 𝑞 𝑟 ∙ c os𝜃 ) ∙ si n𝜃 d𝜑 d𝜃 𝑟 2 d𝑟
∞ 𝜋 2𝜋
0 0 0 ,
eq. 43
and afte r the int egr ation i n al l t hree -room direc tions with Δ η = b i - b s :
𝐴 ( 𝑞 ) = Δ𝜂4𝜋 ∙ sin ( 𝑞𝑅 C ) − 𝑞 𝑅 C c os (𝑞 𝑅 C )
𝑞 3 = Δ𝜂4𝜋 𝑅 C
3 ∙ sin ( 𝑞 𝑅 C ) −𝑞𝑅 C c os (𝑞𝑅 C )
( 𝑞𝑅 C ) 3
eq. 44
and can be transf err ed into the form fac tor P ( q ) = | 𝐴 ( 𝑞 )| 2 :
𝑃 ( 𝑞 , 𝑅 C ) = | 𝐴 ( 𝑞 , 𝑅 C , ∆𝜂 ) | 2 = ( 4
3 𝜋 𝑅 C
3 Δ𝜂 ∙ 3 sin ( 𝑞 𝑅 C ) −𝑞𝑅 C ∙c os ( 𝑞 𝑅 C )
( 𝑞 𝑅 C ) 3 ) 2 .
eq. 45
q is t he scatter ing ve ctor, R C the core radius of the spher e and Δ η the sca ttering length density diff ere nce
betwe en particle a nd matrix ( Δ η = η sph ere – η b ulk ). Ac cor ding to eq . 45 the scattering intensity of a sphere
is simulated for a core radius of 25 nm and dep icted in Figure 12a) . The in tensity as a function of the
sca ttering vec tor i s constant (de pending on the si ze ) at small q -values un til a ce rtain q -value known as
the intensi ty pla teau. Wit h raising q the intensit y decays with q – 4 for spherica l NPs and have int ensi t y
minim a ´s at tan( qR C ) = qR C .
2.3.3 Distribu tio n p ro p erties
Neither the wave length nor NPs are perfectly monodispe rsed, and distributi o n must be consider ed while
appr oximating the sc atter ing in tensity. The polydispe rsi ty leads t o a smea ring in t he sca t tering intensity
and intensity mi nima´s vanis hes as can be seen in Fig ure 12a. There are plenty dis tribution func tion
ava ilable. In th is work the core r adius R C i s a ssumed to be log-normally distrib uted, with t he m ea n a t R C
and a rela tive st anda rd-devia tion p :
𝑝𝑑 𝑖 ( 𝑥 , 𝑅 C , 𝑝 ) = 1
𝑥𝑠 √ 2𝜋 exp [ − ln 𝑥 − ln 𝑚
2𝑠 2 ] ,
eq. 46
with 𝑚 = 𝑅 C
√ ln 𝑝 2 +1 and 𝑠 = √ ln ( 𝑝 2 + 1 ) .
20
2.3.4 Model f ree a nalysis
Figure 12 : a) Si mulat ed scatt ering i ntensi t y pattern (1D image) , I ( q ) plotted ov e r q and show a sph erical f orm
factor with a ho mogenous Δ η = 9.8 nm – 2 and a radius R NP = 25 nm and parti cle numb e r dens it y 1 N = 0 .5 cm – 1 nm –
2 of eith er perfec tl y monodispers e or po l ydisp erse parti cles with a PDI = 0.15 . b ) Sche mes of c orr e spond i ng s ize
scale (picture a r e not in sc ale) , c ) S ame for m fac t or wi th same p a ram e ter but the intens it y pl ate aus in the l ow q -
regime w as si mulat ed wi th a fr actal s tructur e factor (s ee chapter 2 .3.6) . The divis i on of I 0,fract a l against I 0, single cor-
respond to an a ggr egation nu m b e r N agg = 5 792 and V a gg = 3.7 9 ∙ 10 8 nm 3 .
In previous chapter the shape is k nown and t he int ensi t y as a function of the scatte ring vector can be
appr oximated acc ordingly . Howe ver, shape, siz e or i nte rpartic le interac tion ar e often compli ca ted or not
known in abso l ute prec ision so the model independe nt char a cte rization can be a useful t ool to describe
the scatter ing data . The sca ttering int ensity is plotted v ersus reciprocal space ( q have the units in 1/dis-
tance ) and i ncr easing q leads to a dec rea se of the corr e sponding ob serve d si ze ra nge, respe ctively (see
Figur e 12b). In other words which structure can be seen , depe nds on the scatte ring vector q and for a
better comparison the total q -r ange is seg mented into thre e m ain re gi mes (low- q , mid q and high q ,
Figur e 12).
21
Low q -re gime
In the low q -regime the scatte ring intensity ar ises from the total s ize of the nano s i ze d object and is
independe nt of t he form fa ctor P ’ ( q ) = 1. Thus, below a certa in q -vector the scattering intensity is con-
stant (intensi t y pl atea u), named as the forwar d scattering I 0 . T he magnitude of I 0 depends on the bac k-
ground BG, si ze /volum e V P and the contrast Δ η of the nano si ze d ob j ec t with (abbr eviated from eq . 40
under assumption that P ’ ( q) and S (q) = 1(ve ry dilute sy stems)):
𝐼 0 = 𝑁 ∙ 𝑉 P 2 ∙ 𝛥𝜂 2
1
eq. 47
Equation eq. 47 ca n be rewr itten i nto eq. 48 to ca lculate t he mo lecula r weight M W from t he for war d
sca ttering intensity I 0 :
𝑀 W
𝑎𝑝𝑝 = 𝑁 A 𝐼 0 𝜌 2
Δ𝜂 2 ∙𝑐 g ,
eq. 48
with N A the Avogadr o c onstant , c g the weight conc entra tion, ρ the mater ial de nsity of the objects , Δ η the
sca ttering contra st and I 0 the forwa rd scattering. From eq. 47 the magnitude of the scatter ing intensity
sca les with the square of the volume and contrast of the nanosize d objects. Bu t t he m agn itude of the
forw ard scattering is proportional to the total mass . Thu s, ass umi ng a polymer par ticle swe l l ing i n wate r
the magnitude of I 0 i s irrespe ctive of the swelling ma gnitude , due t o the tota l mass of th e NP is not
cha nging, respec tively. In othe r word s, from eq . 47 a V P incre ase is balance d by an Δ η dec rea se, due t o
the contra st is adjus t ing t o the value of t he so lvent with incre asing swel li ng .
In contra st , if obje cts interac t , for example aggre gation, the i ntensity incre ases towards lower q -values
until the a ggrega tion vo l ume V ag g = N agg ∙ V P i s r eac hed, where N ag g is t he aggre gation number. La t ter can
ea sily be calcula ted from both forw ard sca ttering value s of aggre gates and single par ticles w ith:
𝑁 agg = 𝐼 0 ,agg
𝐼 0,sing le ,
eq. 49
under assumption that the t otal scattering contra st is co nst ant. Furthe r, in the low q -re gime t he Gui nier
appr oximation i s valid and al lows the determina tion of the objec t size (gyra t ion ra dius R G ) irre spective
of the shape:
𝐼 ( 𝑞 ) = 𝛥𝜂 2 ∙ 𝑉 P 2 ex p ( − 1
3 𝑞 2 ∙ 𝑅 G
2 ) ,
eq. 50
and is valid if the sy stem i s dilute (no s tructure factor is prese nt) , the 2D scatte ring patter n is isotropic
and qR G < 1. It is also a practic e t ool to approxi mate t h e magnitude of the forw ard scatter ing intensity
towar ds lower q -va lues, if experimenta l data points do not rea ch the i n t ensity plateau. 88
Mid q -ra nge
The formf actor P´ ( q ) ≠ 1 in the mid q -ra nge and the sha pe of the nano si ze d objec t i s ob tained by mod-
eling P ( q ). Extending from t he intensity plateau it decays as a functi on of q wi th:
𝐼 ( 𝑞 ) ~𝑞 𝛺 ,
eq. 51
wher e the e xponent Ω is equa l t o 4 for sphe res, 2 for th in disks and 1 f or th in rods due to the di mensio n-
ality of the objects . Thu s, one can pre dict the ave rage shape from the sl ope .
High q -range
If ther e is a sharp boarder betwe en two pha ses t he inte n sity alwa ys dec ays with q – 4 at the h i gh q -regime
known as the P orod sca ttering. The physical rea son und er t his assu mpti on is , th at the observe d structura l
22
size i s ve ry s mall, which c an be see n a s a two- phase mo del of well se para t ed phases of diffe rent sc atter-
ing length dens it ies (mater ial and m atrix) . With q → ∞ the Porods law is val i d and gives informa tion
about the sur fac e area A of the particle s:
𝐼 ( 𝑞 ) ~ 𝑁 2π 𝐴
𝑞 4
1 ∙ Δ𝜂 2 .
eq. 52
Note, th a t t he Porod sc atter ing i s in the sa me r ange with background scatte ring and an a ccur ate subt rac-
tion of the backgr ound intensity is nec essar y. 87
2.3.5 Fo rm factor of core- shell nanop arti c les fo r ne utron a nd x -ray sca ttering
use d in this w ork
Figure 13: S c hema tic sc attering l ength densi t y profil e of η c ore-s h e l l . The absolut e scatt ering leng th d e nsity of the
core η C is fix ed , const ant at a ny di s t an ce d and r epresent t h e de nsit y p rofile that of th e s i lica core. T h e s cattering
le ng th dens it y o f t he bulk solut ion η solv is cons tant . In case for neut rons t h e abso l ute value of η solv is bi gg er than
that of the c or e i n full con tra s t c o nditions (FC ) but η solv can be adjust e d to η C wi th a D 2 O/H 2 O m ixture , noted a s
contrast mat ch condi ti on ( CM, m atching t h e s cattering intens ity of t h e c or e ). Th e s cattering len gth d e nsity p rofile
of t he shell i s a fun c tion of th e swellin g para meter X C a n d t h ei r dec ay α . Not e, that the amount of the integral in
the shell for the d ifferen t profi les m ust b e constant as the forward scatterin g I 0 ca n not depend on de tails of the
mass distr i bution in t he she ll.
Howe ver, polym er grafte d nanoparticle is in first approximation core-she ll structure with a spher ical
symmetry, whe re the density profile of the cor e is hom ogenous but that of t he shel l deca ys expone ntial
towar ds the bulk solution. The latter has the reason in a st rongly swollen polye lectrolyte brush due to
the os moti c regime assumptio n eve n if a curvature is pre sent. In this sec tion we intr oduce the mathe-
matical descr ipti o n of a core-she ll model, wher e the scatte ring length density of the shell is a funct i on
of the swelling and their deca y towards the con tinuum is desc ribed by the parame ter α , i . e . describing
an expone ntial, reve rse expone ntial, linea r or constant dec ay. 8 9
The scatte ring l ength density profile of the core- shell η c or eExpSh ell can be descr i bed as follows :
23
𝜂 CoreExpShell ( 𝑡 s hell , 𝑅 C , 𝛼, 𝜂 C , 𝑋 C , 𝑋 shell ) = { 𝜂 C 𝑑 < 𝑅 C
𝜂 Shell 𝑅 𝐶 < 𝑑 < 𝑅 𝐶 + 𝑡 shell
𝜂 sol v 𝑑 > 𝑅 𝐶 + 𝑡 shel l ,
eq. 53
and that of η shell :
𝜂 shell ( 𝑑 ) = { 𝜂 shel l ,𝑅 C + ( 𝜂 shell,𝑅 C +𝑡 s hell − 𝜂 shell ,𝑅 C ) 𝑑 ∙ exp ( 1 − 𝑑 ) ∙ 𝛼 𝛼 < 0
𝜂 shell,𝑅 C − 𝜂 shell,𝑅 C +𝑡 shell ( 1 − 𝑑 ) ∙ exp ( − 𝑑𝛼 ) + 𝜂 shell,𝑅 c +𝑡 shell 𝛼 > 0 ,
eq. 54
wher e d i s the radial distanc e of t he shell from the cor e, η shell, RC is t he shell SLD at the core radius R C ,
η Shell,RC+ t shell i s the outer shell SLD at the solvent and α de scribes the parame ter for the expone ntia l change
of the scatter ing length dens ity of the shell. The effe ctive scatte ring l ength density of the po lymer shell
at the core and shel l thic kness η shell,RC and η shell,tshell ar e:
𝜂 shell,𝑅 C = [ 𝑋 C ∙ 𝜂 solv + ( 1 − 𝑋 C ) 𝜂 po lymer ] ,
eq. 55
and
𝜂 shell ,𝑡 shell = [ 𝑥 shell ∙ 𝜂 solv + ( 1 − 𝑋 shell ) 𝜂 p olymer ] ,
eq. 56
with X C is volume fra ction of wa ter at the core ra dius and X she ll is volume fra ction of wate r at the shell
thickness and is set to X shell = 1 due to smo oth decay η shell of t he pol ym er shell to the so lvent ( Figur e 13) .
Then R C + t shell in eq. 56 simpl ifies in:
𝜂 shell,𝑡 shell = [ 𝜂 solv ] .
eq. 57
Respec ting the sc atter ing length densiti es of so lvent η D2O/H2 O , po lymer shell η shell and core η core the SLD
diffuse of the shel l i s def ined:
- α > 0 expone nt ial deca y of the SLD shell profi le dec ay
- α = 0 linea r deca y of the SLD shell profile
- α < 0 re ver sed exponential deca y of the S LD shell prof ile decay
- α < – ∞ constant SLD till t shell than 0
The sca ttering int ens it y for a ra dial ly symmetric dens ity profile η Shell can be ca lculated by the integr al:
𝐼 ExpSh ell ( 𝑞 ) = ∫ 4𝜋 𝑑 2 ∙ sin ( 𝑞𝑑 )
𝑞𝑑 𝜂 Shell d 𝑑
∞
0 .
eq. 58
The scattering int ensi t y of a core-shell- against a sphere -for m fa ctor is depicte d in Figure 14. Idea lly,
the core -shell-for m factor desc ribes the swelling of the polyelectrolyte brush with solvent . Thus, the
magnitude of t he forw ard scattering in the low q - regime should be identica l. As α and t shell corre l ate with
ea ch other, the shell thickness decre ases if α reduc es from 5 (expone ntial dec ay) to 0 (l inear deca y). If
α = 0 and the shell thic kness is set t o 10 nm the m agnit ude of the for war d scatte ring is much bigger as
ca n be seen i n Figure 14. Compared to t he scattering intensity of a spherica l form factor the primary
minim u m is shifted towards l ower q -value s for the core -shell form fac tor a nd the m agnitude of the shift
is a function of t he amou nt of mass in t he shell. Thu s , with increa sing polymer density the primar y
minim u m is sh i fted towa rds smaller q -values. De t ails a b out the dec ay of the SLD prof ile in t he shel l can
be seen in the hi gh q -re gime.
24
Figure 14 : Simul ated SANS scat te r i ng i ntensit y a s a fun ctio n of scat tering v e ctor. The parti cle nu m ber d ensity is
set to N = 0.4 cm – 1 nm – 2 , η C = 3 . 475 ∙ 10 – 4 nm – 2 , η s hell = 1.0 00 ∙ 10 – 4 nm – 2 , η solv ent = 5 .003 ∙ 10 – 4 nm – 2 , X C = 0 , X s o l-
ven t = 1 , R C = 25 nm .
2.3.6 Fracta l structur e f actor
As the p olymer gr afte d N Ps wer e conce nt ra ted to reduc e the measur ing time of a single sa mple a s much
as possible som e of those NP s aggre gated. Not al l aggre gates could be removed by s onication and fil-
tration vi a the samp le pre para tion. Espec ially , for the smallest NPs the scattering patterns show at low
q a q – (1 – 3) -de pendenc y indicating f rac tals a s aggr ega ted NPs. F or bigge r N Ps fra ctals should be consider
too but scatter ing intensity of t he fra ctal structure factor i s not in the q -r ange anymore .
The st ructur e fac tor c an be ca lculated vi a a pair c orrelation functio n g (r), which desc ribes the tota l nu m-
ber of spherica l particles N ( r ) ce ntere d in a frac tal obj e ct of a spherica l sy mmetry with the radius r : 90
𝑁 ( 𝑟 ) = 𝛷 ∙ ∫ 𝑔 ( 𝑟 ) ∙ 4𝜋 𝑟 2 d 𝑟
𝑟
0
,
eq. 59
wher e ϕ is t he volume frac t ion. The fra ctal object can b e cha racterized by a spati al distribution of indi-
vidual scattering o bjects:
𝑁 ( 𝑟 ) = ( 𝑟
𝑟 0 ) 𝐷
,
eq. 60
wher e D is t he frac t al dim ens ion coeff icient and r 0 is the radius of an individua l scattering object (as-
suming spheric al sym metry) within the frac tal objec t of the size r . Differ entiation of eq. 60 and subs ti-
tution of d N from the abbre viation of eq. 59 lea ds after si mple ma th into :
𝜙 ∙ 𝑔 ( 𝑟 ) = 𝐷
4∙𝜋 ∙𝑟 0 𝐷 ∙ 𝑟 𝐷 −3 .
eq. 61
Usually D is sm aller than 3, the pair corr elation funct ion goes to zer o w it h incre asing radius , which is
clea rly unphysical bec ause a sample ha s a macr oscopic density. T hus , a c ut -off f unction h ( r , ζ ) has to be
introduce d, where ζ is the cut-off distance of the frac tal to describe the behavior of the pair cor rela tion
at large distance . The a nalytical from the structure fa ctor S ( q ) can be ca l culate d a ssumi ng subtrac tion of
uniform densit y for gene ral theory of liqu ids.
4 ∙ 𝜋 ∙ 𝜙 ∙ [ 𝑔 ( 𝑟 ) − 1 ] = 𝐷
𝑟 0 𝐷 ∙ 𝑟 𝐷 − 3 ∙ ℎ (𝑟, 𝜁 ) .
eq. 62
It repr esents the char ac teristic distance above, which the m ass distribut ion i n the sample is no longer
desc ribed the fr acta l law . In prac t ice, it ca n repr ese nt the si ze of an aggre gate or a corre lat ion length in
a disorder ed materia l , wh i ch is for i so tropic syste ms:
25
𝑆 ( 𝑞 ) = 1 + 4 ∙ 𝜋 ∙ 𝜙 ∫ [ 𝑔 ( 𝑟 ) − 1 ] sin ( 𝑞𝑟 )
𝑞𝑟 𝑟 2 d𝑟
∞
0
eq. 63
and combined with:
𝑆 ( 𝑞 ) = 1 + 𝐷
𝑟 0 𝐷 ∫ 𝑟 𝐷 −3 ∙ ℎ ( 𝑟 , 𝜁 ) ∙ sin ( 𝑞𝑟 )
𝑞𝑟 𝑟 2 d𝑟
∞
0
eq. 64
Sever al cut-of f function for h( r , ζ ) have been desc ribed and compare d by S ore nsen et al. Her e we use a
simple exponent ial cut off : 8 2,91,92
ℎ exp ( 𝑟, 𝜁 ) = ex p [ − 𝑟
𝜁 ] .
eq. 65
The cut-off function can be solved ana lyti ca lly. The s tructure fa cture with an exponentia l cut off is than
desc ribed as:
𝑆 exp ( 𝑞 , 𝜁 , 𝐷 , 𝑟 0 ) = 1 + 𝐷 ∙𝛤 (𝑥 )∙ ( 𝐷 −1 ) ∙sin( [ 𝐷 −1 ] arctan ( 𝑞𝜁 ) )
( 𝑞 𝑟 0 ) 𝐷 [ 1+ 1
𝑞 2 ∙𝜁 2 ] 𝐷 −1
2 ,
eq. 66
wher e D is the fra ctal dimension , ζ i s a cu t-off l ength for the fra ctal cor rela tion, r 0 the radius of the single
par ticle (assumption of spherica l symme try) and Γ ( x ) is a gamma functi on. Note, t hat t he radius of singl e
par ticle m ust be alwa ys smaller t han the cut-off length f or the frac tal corr elation.
Deta ils about t he sphere , core-she ll and frac tal structur e fac tor are summarize d in the manual from t he
progra m packa ge of S asF it. 89
2.3.7 Dy namic lig ht scattering
Nanosiz ed objects are consta ntly moving i n solu tion known as B rown ian mot ion . The origin of the
Brownian motion resul ts from local density fluctuat i on s of the solvent acc eler ating disperse d particle s
due to perma nent im pac ts of all individual solve nt m o lec ules at the particle surfa ce. If monochromat ic
light pene trates the sa mp le those density f luctuation s pe rmane nt ly in- and de cre asing the d ist anc e of the
sca ttering center s and the measur ed int ens ity of the scat t ere d light fluctuates from the ave rage intensit y
<I(t) > 2 . 83,9 3,94
Figure 15 : Left) typic al i ntensi ty fl uctua ti on ove r t h e time ; Ri ght ) c o rrespon di ng auto correla ti o n funct i on as a
function of th e time .
The intensity will be measur ed in short t imescale s Δ t n ormally much s maller tha n the time of in tensity
cha nge. S umming all intensit ies from the in itial intens ity leads to the aut o corre lation function :
1
𝑡 M ∙ ∑ 𝐼 (t) ∙ 𝐼 (𝑡 + τ) ∙ ∆𝑡
𝑡 M
t=0 = 〈 𝐼(t ) ∙ 𝐼 (𝑡 + τ) 〉 .
eq. 67
26
All intens i ties I ( t ) at the ti me t will be sum med up w ith the delay t ime I ( t + τ ). F or s mall dela y ti mes τ t he
auto corre l ation function re prese nts the ave ra g e square of t he intensity ( 〈 I 2 ( t ) 〉 bec ause the particles do
not m o ve fr om the initial state. With incr easing τ the value from the auto corr elation funct ion deca ys to
the avera ge int ensity of the squar e 〈 I ( t ) 〉 2 (F igure 15b) . If t he intens ity is divided b y 〈 I ( t ) 〉 2 one obtains
the normalize d i n tensity ti me -auto corr elation functio n g 2 ( τ ):
𝑔 2 ( τ ) = 〈 𝐼 (𝑡 )∙𝐼 (𝑡+ 𝜏) 〉
〈 𝐼 ( 𝑡 )〉 2 .
eq. 68
The detector measure only the intensity of the scatter ed light . But the scattere d ligh t can be polarize d
and t hus the elec tric field for ea ch scatte re d elec t romagnetic wave may diffe r. The strength of t he electric
field is descr ibed in the field ti me auto correla tion funct ion:
𝑔 1 ( τ ) = 〈 𝐸 ( t ) ∙𝐸 ∗ (t+τ) 〉
〈 𝐸 (t )∙𝐸 ∗ ( t )〉 2 ,
eq. 69
wher e E is t he electric field of sca ttered wav e. The time auto corr elation func tion g 2 ( τ ) i s associate d with
field time-auto corr elation g 1 ( τ ) over the S IE GER T -re l ation: 9 5
𝑔 2 ( τ ) = 𝐵 + 𝛽 ∙ 𝑔 1 ( τ ) 2 .
eq. 70
B i s a constant and β a corr ection factor that depends o n the geometry of alig nment of the li ght source .
For the monodisper se case t he field autoc orre lation fu nction deca ys exponent ially with decay rate Γ ,
which is the produc t of the diffusion coef ficient multipl ied with the sq uare of t he sca ttering ve ctor:
𝑔 1 ( 𝜏 ) = e −𝛤∙𝑡 = e − 𝐷∙𝑞 2 ∙𝑡 .
eq. 71
A more acc urate and more common method to calc ulate Γ is proposed by Fr isken known as the Cumu-
lant-ana l ysis method : 95
𝑔 1 ( 𝜏 ) = ex p (−𝛤 ( 𝜏 − 𝜇 2
2! 𝜏 2 + 𝜇 2
3! 𝜏 3 … ) ) ,
eq. 72
with μ 2 / Γ 2 i s the sec ond order polydispersity index. T he t hird order polydi spersity index is only nec es-
sary if the system contain h ighly polyd isperse par ticles.
Note that , the z - aver age diff usion coe fficie nt is obt ained if the sys tem is very dilute (no mul t i sca t tering,
no particle int era ction through colli si on or electr ostatic int er action is present ). Then , the t ra nsl ational
diffusion can be derive d into a hydrodyna mic radius R H over t he S TO KES -E I NSTE IN equation:
𝐷 = 𝑘 ∙𝑇
6∙π∙𝜂 ∙𝑅 H ,
eq. 73
with k t he Bo ltzmann c onstant , T the te mpe rature , η the vi scosity of the solvent . To c alcula te the hydro-
dynamic radius from multiple ang le measur ements the diffusion coef ficient was calc ulated from slope
of the deca y rate Γ ver sus q 2 .
2.3.8 Static l i gh t sca t tering
The scatter ing of s tatic light is compar able to t hat of X -ra ys and neutron sca ttering. Ther efor e, the in-
tensity at a certa in amount of t he q -vector ca n be calc ulated from the count ra te of the sa mple, solvent
and toluene via the Rayleigh re lation: 96
27
𝐼 ( 𝑞 ) = 𝐶𝑅 sample
𝐼 mon,sample − 𝐶 𝑅 H2O
𝐼 mon,H2O
𝐶𝑅 Tol
𝐼 mon, Tol ∙ 𝑅 Tol ,
eq. 74
with the count ra te (nu mber of scattere d ligh t , abbrevia ted as CR ) for the sample CR sample , wate r CR H 2 O
and CR toluene .
I ( q ) is plott ed versus q 2 , wher e the amo unt of forwa rd scatter ing I 0 and the R G can be calculate d us ing
the Guinier approximati on, 96 ,8 8 Fr om the forwa rd scatter ing I 0 the mol ec ular weight can be calcula ted
via:
𝑀 W
app = 𝐼 0
𝐾 ∙𝑐 g ,
eq. 75
with the knowledge of the mass conce ntration c g [g/mL] and optical constant K = [2π(d n /d c ) n sol ] 2 /( λ 4 N A )
including the ref rac tive index incre ment d n /d c for the specific sol vent, the re fra ctive index of t he solvent
n sol and the Avogadr o constant N A .
28
2.3.9 Quartz c ry st al microbalance with dissipati on (QCM- D)
Figure 16 : a) Sche mati c c ross se ction of a 2D QCM-D - meas urement cell with QCM-D c hip, b) 3D pictur e of a
QCM-D chip , c ) sc hematic quar t z cryst al deform a tion , d) r e sonances observed when a c r ystal sh ow no parti cle
adsorpt ion (blue) or a p article l a yer adsor bs (r ed). e ) E xample of t he rin g-down method , w here the dri vi ng vol t age
is int ermitten t ly sw itch ed off and th e d e cay of th e osc il l ation is moni tored. T he decay is much s t rong er for cryst al
with the pa r ticl e layer. f) Correspon ding Δ f a nd Δ D valu es a s a f unction of t ime for strong and w ea k adsor bing
NPs. 97
The re exist se vera l w ays to mea sure ma terial prope rties at inter fac es. In the conte xt of biocompati bil i ty,
biosensors, b i omater ial st udies, nanotoxicit y invest i gati on, a nd b iom ater ial de velopment interfa ce stud-
ies are complic ated for surfac e sensiti ve analyz ing technique s . Those sys tem s are usually s trongly hy-
dra ted and t hey consis t of eithe r i solated, fre quently polydisperse , obje cts (e.g . , surfac e-adsorbed pro-
teins, lipo somes or nanoparticle s) or some di ffuse continuous layer s (poly m er brushes , hy drogels). 97
Poor densi ty con trast betwe en the bulk wa ter and the strongly hydra t ed i nterf a ce makes the investigati on
of such int er fac es with most (e.g., opti ca l) t ec hniques d i ff icult , and if a contra st betwe en inter face s ex-
ist s, using X-ra ys or neutrons for exa mple, the ana lysis of those int er fac es can be challenging and re-
quires a huge know ledge of information about most pa rameter s for a rea sonable data interpre t ation or
appr oximation . Then, the use of acoustic wave s such as quartz cr ystal mi cr obalanc e with dissipat i on
(a bbrevia ted QCM-D) has a huge advanta g e because there is a contra st in terms of ac oustic wave be-
twee n bulk aque os soluti on and the m ate rial at the int erface . 97 The technique is base d on the inverse
piezoe l ec tric proper ty by defor mation of the quartz crystal once excite d by a voltage . If an alterna ting
voltage is applied , obviously the crystal can be deform ed in two oppos ite direc t ions resulting in an os-
cillation usua lly at the resonanc e freque ncy or m ultip les (so called over tone n umber) of the crystal
f c = 4.95 MHz, wh ich is in the fre quenc y ra nge of acoust ic wave s. There are s eve ral ways to perfor m a
QCM-D measure ment. One of them is t he ring-down method, which is develope d by R ODAL et al. re-
fe rre d to a quartz crysta l microbala nce with dissipa tion (QCM-D) . 98 The princip le of t he measur ement
29
is t o rec ord the volt age di re ctly after the exter nal driv ing voltage i s turned off allowing the piez o t o
dec ay. Then fr om the measur ed voltage the exa ct resonanc e fre quenc y and ene rgy loss known as Г (the
halfw idth of t he bandwidth – ab breviated bandwidth) pe r overtone numbe r ca n be calc ulated. Г is relate d
with the resona nce fr equenc y l ea ding to the dissi pati on D = 2 Г / f C . In a typica l m ea surement the exc ita-
tion and rec ording a re periodica l i n ve ry short t i mesca le s and t hen in a usual measure ment, the fr equenc y
and di ssipat ion shift Δ f and Δ D per overtone num ber are recor ded as function of the tim e. Now i n simple
ca se if someth ing adsorbs at the i nterf ace of t he crystal to air or solvent t he mass and ener gy loss in-
cr ease s and leads to a Δ f a nd Δ D change over t i me or vi ce versa for case of desor ption. Prior to eac h
measur ement, the resonanc e freque ncy and energy dissipation of each indi vi dual crysta l must be rec-
orde d in t he desire d bul k mediu m (air , solvent, water , v iscous solvent) as th is is strongly depe nding on
the surrounding mediu m. As a rule of thumb, the visc osi ty strongly causes additiona l dissipation . But
not on ly surr ounding bulk liquid cause s d issi pat ion , al so the adsorbe d materia l at the int er fac e can in-
cr ease the ener gy loss of t he perpe ndicular propa gating wave s. Then, data i nterpr etation is m uch more
complex bec ause t hese cha nges ar e rela ted to the thickn ess a nd ela stic prope rties of a dsorbed fil ms . The
most conside rable si mple adsorpti on layer is a rigid one (F igure 17a)), where the adsorbed mass m QCM
is proportio nal to Δ f :
𝑚 ads
𝐴 = 𝑚 QCM = − 𝐶
𝑛 ∙ Δ𝑓 ,
eq. 76
with C the cr ystal constant , n the overtone numbe r and Δ f the freque ncy shi ft , i . e ., known as the well -
established Sauerbr ey re lation. 9 9 Latter is valid in l im ite d si tuat i on in first approxi m ation for t hin and
rigid layer s. It allows the dete rmination of the l aye r thickne ss t layer once the dens ity of the l aye r ρ layer is
known with:
𝑡 l ayer = 𝑚 QCM
𝜌 layer .
eq. 77
If one do es not know the adsorption behavior of the system t he follow i ng approa ch is proposed by
seve ral authors, wher e Δ f and Δ D shi ft ca n be read from the initial and equilibra ted state a nd tra nsfer red
into mass densit ies per uni t area using a us ing a kin d of modi fied Sauerbr ey equa tion for unknown
adsorbe d films in firs t approxima tion cons i der ing so called fluid effe cts withi n: 97 ,100
𝑚 ads
𝐴 = 𝑚 QCM = − 𝐶
𝑛 ∙ ( Δ𝑓 + 𝑓 c ∙ Δ𝐷
2 ) ,
eq. 78
wher e C is t he crystal cons tant C ~ 17 ng/cm², n the over tone number ( n = 5), f C the resona nce freque ncy
of the crystal f C = 4.95 MHz, Δ f a nd Δ D the fr equenc y and dissi pat ion shif t.
Much more complex systems as illustra ted in F igure 17 b – d make the data int er preta tion more difficult
bec ause t he additional energy l oss of per pendicular propaga ting wave s influence s st rongly t he measure d
fre quency shifts and then QCM -D is strongly overe sti m ating the mass of adsorbe d layer . The adsorption
model of par tially rigid domains linke d b y a s ubst rate ( e.g. pol y m er ) can be analyze d by the Sauerbr ey
re lation if surface cover age of rigid domain s i s l ar ge en ough. 97 The ca se visualized in c) illustrates as a
model of nu merous ho mogenous d iffuse layers with polymer brushes being t he m o st co mm on. 97 Us ually
for t hose soft f ilms Δ D > 0 Q CM -D becomes sens i tive t o mecha nical and viscoelastic proper ties. These
prope rties are commonly repre sented by the co mplex shear modulus G = G *+ iG * *, wher e G * is t he
shea r modulus descr ibing material prope rties and G ** is the l o ss modulus desc ribing viscous energy
dissipation as a function of t he freque ncy ωη . G * and G ** vary wit h the angular freque ncy of def or-
mation ω in orders of seve ral magnitudes, respe ctivel y. Thus, d iffer ent overtone num ber s c an show
diffe rent Δ f and Δ D values. Ther e is an existi ng fitt in g m odel that can ca lculated the l aye r thi ckne sses
or mass adsorbe d of visc o-elastic films assuming unifo rml y distributed mass density but should be ap-
plied car efully beca use it contains 5 indiv i dual para met ers like the area l m ass density , the shear mo dul i
30
G * and G ** and the fre quency depe ndents of the moduli. 97 Details about t he m odel can be rea d
elsew ere . 97
Figure 17 : a – d show dif fe r ent t yp es of a dsor bed la y er. The wa ve l ength of the st a nd ing wave is sche mati cally
depict ed al wa ys below t h e adsorbed layer . T he rela tionship between fil m and pro pagat i ng w ave s is show n sch e-
matical ly as w e ll . Films wh ic h do not abso lutely diss ipate e nerg y a re shown in a ) and b) , a nd films wh ich do
dissipa te energ y a re show n i n c) an d d) How ev er films i n a) and c) hav e a homoge nous d i str i bu ti on and t h at
depict ed in b) a nd d ) shows t hat o f d i screte particl es. L ayers in a) and b) can b e analyzed w i th t h e Saue rbrey
relation. The layer i n c) has to b e an al y zed with t he visco elastic m o de l. Th e l ayer i n d) illustr ates d iscret e na-
nosized obje ct of sphe rical shap e and the relat ionsh ip betwe en film and prop agating waves is influen c ed by the
partic le shape, NP to surfa ce link a ge an d surf ace cov erage . 97
The last i s shown i n Figure 17 d) il lustrating film s of discrete nano sized obj ec ts at i n t er fac es. These
contains objects like adsorbed proteins , liposomes, v iruses and nanopa rticles. The fre quency response
of nanopar ticle films ca n be transforme d in ma ss densit i es using S aue rbre y re l ation , if surfac e c overage
values are lar ge and cor responding Δ f varianc es as a f unction of the over tone number s are low . 97 But
the Sauer brey relation brea ks down, if the surfa ce cov er age values are low. Then t he t ra nsfer is m ore
complex, be cause indiv i dual N Ps contain a frequenc y de pendent oscillation mot ion re laying to ph ysi ca l
and mecha nical proper ties of adsorbe d nano s ized obje cts and surrounding trappe d li quid . 97 Both men-
tioned phenomena are a result of the crystal oscill atio n prope rties and are desc ribed further in detail.
The first one i s the oscil l ation o f adsorbed NPs in para llel d irection to the crystal o scillation , wh ich is
a function of sha pe and surfa ce to N P link age . The exte nt of the oscilla tion depe nds on the contact ar ea
betwe en linker (gr een a rea F igure 17d)) and surface. For example cubic NPs oscill ate less t han spherica l
ones, which could be mea sured 10 1 , 10 2 and proofe d by finite element mater ial (FEM) sim ulations s howing
that the ene rgy dissipation r esults from the rocking mo t i on of adsorbe d NP s. 10 3 Th e sec ond one is the so
mentioned fr actional trapped liquid s urrounding NPs (F igure 18 blue marke d are as), which dec rea ses
with i ncr easing surfa ce cove r age , due to overlap gain o f adjac ent wa ter layer . 97 , 10 1 , 10 2 Especially , at low
and m oder ate surfac e coverage QCM -D st rongly overe stimate the adsorbe d m ass but wi t h incre asing
surfa ce coverage the mass calculation becomes more acc urate until re aching the full surfa ce covera g e .
31
Then the Sauer brey re lation becomes valid , due to adso rbed layer change s from discre te nanosize d ob-
jects int o more over “homogenous” rigid layer, respe ct i vely. The fra ctional trappe d l iquid is no t co m -
par able with the hyd ration shell and depends on t he sur face covera ge and shape of such nanosized ob-
jects. 9 7 An empirical mode l assu mes that the sha pe and the thickness of the water coat around e ach
adsorbe d par ticles to be constan t, which has proven re marka bly successf ul quan t itativel y reproduc i ng
re sult s. 97, 10 1, 10 2
Figure 18 : a ) and b ) Sch eme of t he t r apped l iquid as a fu nctio n of the surf ace coverag e . c ) measu re d trapp e d liquids
as a func ti o n of the fraction a l cov erage f or d iffe r ent nanosi zed ob ject of d iffe r ent shapes. Cowp e a mosaic virus
(CPMV ) → Avid i n → cho le r a tox in B 5 sub unit ( CT B 5 ) th e shape fro m spheric al lik e cha nges into more elong a te
structure an d corresp onding mass overesti mation o f QCM-D decreases f rom CPMV → Avi di n → CTB 5 . CPMV
have a d i ame te r of 28 nm . 97, 10 1 , 10 2 Figure c) re printed with permission fro m ref erenc e 97.
Howe ver for ß < 1 Q CM- D c an overe stim ate the adsorb ed mass by a fac t or of 5 – 10 times and measur es
the sum of the masses of adsorbe d nano sized o bjects a nd t ra pped water : m ads = m NP + m H2O . 9 7 The prin-
cipal approa ch to calc ulate the fr a ctional trapped liquid coef ficie nt H is to compare the adsorbe d mass
m QCM of the Q CM -D expe riment with that obtaine d by another surfa ce sensitive technique , for example
AF M yielding m AFM : 97
1 − 𝐻 = 𝑚 AFM
𝑚 QCM .
eq. 79
2.3.10 Fraction t rap ped liquid calculation for NP s in this work
Related to exper iments done in this work m AFM wa s me asured on the same quar tz crystal direc tly after
the QCM-D measur ement . There fore, particle dec orated cr ystal from a QCM -D measur ement wer e
rinsed with Millipore wa ter, removed care fully from the QCM -D instrument and gently dried on air
without b low drying . QC M -D measure m ents c onfirm th at rinsing the mea surement cha mber with wa ter
does not remove adsorbed NPs. Before H is unknown va lues for adsorbe d m ass via QCM - D m QCM was
ca lculated with eq. 78:
𝑚 QCM = − 𝐶
𝑛 ∙ ( Δ𝑓 + 𝑓 c ∙ Δ𝐷
2 ) .
eq. 78
Afte r the QCM-D measur ement the de cora t ed crysta ls wer e measur ed w ith AF M using tapping mode a t
four differ ent spots on the surfa ce with a mea sure ment area of 25 μm². The absorbed m ass via AF M
measur ements m AFM was ca lculated by counting the part icles for each spot using the software image J . 10 5
All par ticle num ber s N were aver aged and normalized to the unit area A S to obtain t he particle densit y
and corr esponding m AFM :
32
𝑚 AFM = 𝑚 NPs
𝐴 s = 𝑁 ∙ 𝑀 W
𝑁 A
𝐴 S ,
eq. 80
w ith A S as unit are a, molecula r weight of individual pa rti cle s M W , t otal mass of adsor bed NP s m NPs ,
number of partic les N and Avogadro constant N A .
Figure 19 : L eft: r ec o rde d Δ f and Δ D for ov ertone numb e rs 3 – 11 from a QCM-D m easure m ent for a) SiO 2 @NH 2
and c) S iO 2 @PDM AEMA wi th 3.0 w t% graft ed po lymer , R ight: c or respon ding examp le AFM h ei gh t imag e s of
the sa me crys tal in air b) SiO 2 @NH 2 -N Ps and d) SiO 2 @PD MAEMA.
H w as de t er mined for “ strongly adsor bing” N Ps (such a s SiO 2 @PDMAEMA with 3 .0 w t% gr afte d pol-
ymer d = 50 nm and SiO 2 @NH 2 ( d = 50 – 140 nm) . Onc e H i s known the m ass of absor bed NPs can be
ca lculated wit h eq. 87 ( page 39 ) for a ll Q C M-D me asur ements for the specif ic ove rtone nu mber ( n = 5).
Corre cted values of m QCM t o m ads from eq. 87 wit h previously ca lculated H result in corr esponding low
surfa ce coverage values ( β = 10 – 30 %) for al l N Ps. Int rinsi ca lly , we assume here a homogeneous N P
distribution (strong particle-par ticle repulsion at pH 4) on the surfac e i n water while the AF M heigh t
images measure d in the dried st ate indicate a clustering tendenc y . In gene ral, QC M-D data of p ol ymer
gra fted NPs exhibit much higher values for the dissip ation , whe re the po l ymer of brush grafted NP s
ca using tende ntially bigger di s sipation shi ft s . It m ight be attributed to s urfa ce t o Si O 2 @ PDMAEMA
linkage, where the polyme r is acting similar t o a spring . As we did obs erve no differ ence of H betwee n
har d and pol ymer graf ted N Ps, we ass umed the same to apply for N P s wit h differ ent degre e of polyme r
gra fting. In contra ry, H is s trongly size depe ndent and decrease s progre ssively w it h increa sing NP size
(see Table 1). Limitation s of t his calc ulation approa ch are the surfac e coverage depende ncy assuming
that H is similar for i ndi vidual given particle size, i rr espec tive of polymer grafting having no overlap
re gime of the li qu i d coa t. But as the data yi eld relative ly low surfac e covera ge values ( β = 10 – 30 %),
wea k or no overlap of adjacent li quid coats can be expec ted. Sample s with lowe r surfa ce cover ag e values
33
may have a highe r H as cor rec ted and then m ad s may sti ll be sli gh tly over estimated. Nonethe less , over-
estimation should be rather sm all and can be considere d within measur ement inacc urac i es. In contra ry ,
cal cula ted values for m ad s for low charge d NPs (high p H values) may be un dere stim ate d as overla pping
of liquid coats of high ly pac ked particle s s hould be con sidered.
34
Table 1: Samp l e t yp e, amount of gr a ft ed pol y mer p g raft , diame t er d NP of th e silic a core and m o lecular we i ght of the M W,N P of th e N Ps, fr equenc y and dissip ations shifts
for t he 5 th ov ertone nu mber Δ f /5 and Δ D /5, m Q CM cal culate d from eq. 78, cal culated m A FM fro m AFM h ei g ht ima ges (eq. 80) , pa r t icl e densiti es from QCM -D and
AFM measurem ent s N Q CM a n d N A FM , and t he tr apped liquid coat of pa r ticl es H .
Samp le
p graft
d NP
M W, NP
Δ f /5
Δ D /5
m QCM
m AFM
N QCM
N AFM
H
wt%
nm
g/mol
Hz
10 – 6
ng/cm²
ng/cm²
1/um²
1/um²
–
SiO 2 @NH 2
–
50
8.69 ∙ 10 7
225
8.1
3685
726 (101)
255
50 (7)
0.803 (11 4 )
SiO 2 @PD MAEMA
3.0
50
8.99 ∙ 10 7
325
27.3
4384
853 (64)
281
54 (4)
0.813 (59)
SiO 2 @NH 2
–
70
2.06 ∙ 10 8
250
10 .0
3950
1141 (111)
89
33 (3)
0.711 (63)
SiO 2 @NH 2
–
140
2.12 ∙ 10 9
635
50 .0
8960
4045 (410)
20
9 (1)
0.640 (60)
35
2.3.11 Surface coverage calculati on
Figure 20 : T op and si de v i ew of c losely h exagon a l d e nse pac ke d n anopart icle. I mportan t v a lu es for p article nu m -
ber densi ty or surfa ce cover a g e rat io calcu lation.
With the kn owledge of the molecular we i ght of the NPs the particle nu mber de nsi ty per unit are a ca n be
ca lculated with following equa tion:
𝑁
𝐴 s [ NP
μm 2 ] = 𝑚 ads ∙𝑁 A
𝑀 W .
eq. 81
Assuming spher ical cor e shell nanopa rticles as polymer gra fted N P s and ass umi ng the hexagona l dense
pac king as the highest mono layer packing possibil ity for spher ical particle s the are a of one hexa gon A H
is : 24
𝐴 𝐻 = 6∙𝑅 H
2
√ 3 .
eq. 82
With the hydrodynam i c ra dius R H t he s urfa ce covera g e β was calcula ted by m u l tiplying the num ber
density of t he par ticles with the hexagona l s urfa ce of one NP with nor m aliza tion to the uni t ar ea:
𝛽 = 𝑁 ∙𝐴 H
𝐴 S .
eq. 83
2.3.12 ζ -potential
An index how st rong similar char ged nano s ized obj ec t are st abi li ze d in sol ution corre lates wit h their
ef fective surfac e charge density or potential. The sur fac e charge lea ds to an elec trostatic repulsion,
which kinetica lly hinder s pa rticles from c luster ing (agglomera tion) – a result of a total surf ace area
ene rgy gain from the thermodyna mic aspect due to a tt ra ctive vdW intera ction betwee n particles of
equa lly composed mater ial. It is yet im po ss ible to mea sure t he exac t surface potenti al of char ged sur-
fa ces in liqu id. How eve r, t he s urfa ce charge correlate s with t he ζ -potential – a value which can be easily
obtained from elec t rophore t ic mobili t y me asure ments.
36
Figure 21 : S chemati c ov e rv ie w of left: surroun di ng ion distribut ion o f ne gativ ely c h arged NP and ri gh t: corr e-
sponding po tential as a funct i on of the p article surfa ce. T h e d a rk line marks t he S te rn lay er, the orange dott ed l ine
marks th e s l ipp ing pl ane and th e g reen l ine that of the Gou y - Chapman- length.
A charge d surface cr ea tes a capacitor in sol ution and conseque nt ly t he surfac e is balanc ed by co- and
counter ions neutralizing their ef fec tive net charge . How ever, ions are not uniformly distribu ted wi th
incre asing dist ance from t he surfac e, wher e the t otal ion cloud can be divi ded into two main l aye rs:
- An i nner la yer, c alled Ste rn or Helmhol tz layer, whe re i ons ar e str ongly bo und a nd in molecular
contac t with the par ticle surfa ce (counter i ons are l oc ked in pl ac e). A t this region t he charge
potential decays l inear ly towards the bulk sol u tion. 5
- An outer l aye r as diffuse laye r where m obile ions cre ate a diffuse ion cloud due to therma l
fluctua tions descr ibed by t he Bo lt zma nn dis tribution. It is ca l led as e lectr ic double laye r, wher e
the surfac e potential Ψ surfa ce deca ys exponentia l ly to the potential of the bulk solution Ψ ∞ . The
cha racteristic l ength of the ele ctric doubl e l aye r is called t he Gouy-Chapman length and depends
on the surfac e potential and ionic stre ngth of the bulk solut ion . The doub le layer is separa t ed
into two layer s of less mobile ions in the inner layer a nd rather mo bile ions in the ou t er layer .
The border betwee n t hose two l aye rs is t he h ydrodynamic shea r or slipping pl ane . 5 , 10 6
To measure a potentia l of nanos i ze d obj ec ts in solution one has to measure the ele ctrophore t ic mob ility
μ e , whic h can be done by applyi ng an alterna ting pot ential in a s olution with dispersed N P s. Then,
cha rged NPs with a t o tal net char ge (e ither posi tive or negative) move to the op posi te ly char ged elec-
trode. F urthermor e, counter ions in t he inne r l aye r follo w t he NP m ovement and ions in the oute r layer
moves to the oppo site ele ctrode . The velocity of those particle s is mea sured by Lase r Doppler Veloci-
metry – a technique similar to a dynamic l ight scattering exper iment calc ulating the NP velocity from
time resolve d i n t ensity fluctu ation s of scatter ed light. I t is note worthy, that the particle veloci ty corr e-
lates with the St okes-Eins tein equa tion and thus with t he hydrodynamic siz e. The extend of the hydro-
dynamic size in an elec trophore tic mobility measure m ent is compar able to the d istance at t he sl ipp ing
plane. Thus , the po tential can neve r be measure d at the surfac e but at the slipping plane wh ich is per
def init ion t he distance whe re the surf ac e pote ntial Ψ surf ac e dec ays to the ζ -potential Ψ zeta = ζ . Th e elec tro-
phore tic m obility is linked as a function of veloci ty v of the particles and applied elec tric field E : 10 6
𝜇 𝑒 = 𝑣
𝐸 ,
eq. 84
and ca n be transf err ed int o the ζ -potential :
37
𝜁 = 3𝜂 𝜇 𝑒
2𝜀 0 𝜀 r 𝑓( 𝜅 𝑅 P ) ,
eq. 85
with the Henry func tion f ( κR ), vi scos i ty of the solvent η and t he permittivity of fr ee space and sol vent
ε 0 and ε r . The Henr y func tion is influence d by the radiu s of the particle R NP and the Debye length κ – 1 .
For l ar ge particle s in a mediu m w ith high ionic strength ( κR NP >>1) , the Henr y function goes to 1 . 5 and
eq. 85 reduc es t o ζ = ημ e / ε 0 ε r , which is known as the Smoluchowski approximati on . For s mall objects
in low ionic stre ngt h solutions the henry function goes to 1 and t hen the ζ -potent ial can be expresse d
with ζ = 3 ημ e / 2 ε 0 ε r .
Neither our nanoparticle s can be considere d as small p articles, nor our particles are dispersed in h igh
ionic strength so lutions. Thus , a pre cise approxima tion is difficult . Never theless, we conse quent l y use d
the Smoluchowski approximation in this work
3 Experi mental part
3.1 Nanoparti cle synthe sis
3.1.1 Materials
Ace t one, ac etic ac id, acryl amide , 3-a m inopropyl t rieth oxy silane (A PTS), 2 -bromo-2-me thylprop ionyl
bromide (BI BB ), chloroform , ethyl ace tate, copper (I)bromide (99. 99 %), d ichloromethane (DC M),
disodium hydrogen phosphate , L -lysine, Ludox H S40 silica nanoparticles, hydroc hloric acid, methanol ,
N , N -d im ethylam ino -e thyl-methacr ylate (DMAE MA), N , N , N ׳ , N ״ , N ״ – penta methyl di ethylene triamine
(PMDETA) , phosphorpento xide, po tassium chloride, sodium chloride, sodium dodecyl sulfa te (SDS),
sodium hydrox ide, tert -bu t yl-methac rylate ( t BuMA), t et raethyl ortho silicate (TEOS), tolue ne, trifluoro-
ac etic acid (TFA), and wer e purchase d f rom Si gma Al drich and used without furthe r purification. 1 ,2-
dioleoyl- sn -glyce ro-3-phosphocholine (DOPC) a nd 1,2-dimyrist oy l - sn -glyc ero-3- phosphate (sodium
salt) (DMPA) wer e obt aine d from NOF corpora tion without further purific ation. Anhydrous ethyl ac e-
tate was prepar ed by mixing “w et sol vent “wit h phosph orpentoxide in a m ass ratio of 5:1 and evapora t-
ing t he ethyl ac etate af ter 15 minutes of expos ure time . This anhydrous ethyl aceta te was stored with a
molecular sieve (5 Å). Millipore water was taken from a Millipore syste m having a resistivity h i gher
than 18 MΩ cm . D 2 O for t he S AN S measur ements was obtained from Euriso t op (Gif -sur- Yvette,
Fr ance) in 99. 9% isotopic puri t y.
3.1.2 Method s
Light scatter i ng (DL S and S LS) wa s m ea sured s imult aneously on an ALV/ CGS -3 ins trument (ALV,
Lange n, Ger many) at 25 °C. I ntensity fluctuation s wer e rec orded by an ALV 500/E mu l tip le- τ corr elator
of mea surement angles of 40°-120° i n 5° steps . The dec ay ra te Γ was ca lculated by fitting t he corre lation
func tions with t he cu mul ant method . 95 T he di ff usion co eff icient was calc ulated from slope of the decay
ra te Γ ver sus q 2 , then transfor med into a hydrodynami c ra dius R H with Stokes Einstein equation . F or
SLS t he scattering intens i ty at a ce rtain q -vec tor was cal culate d from the count rate of the samp l e, so lvent
and toluene. I ( q ) is plotted versus q 2 , wher e the amoun t of for war d scatte ring I 0 and the R G can be cal-
culate d using t he Guinier approxi mation . Fr om the forwa rd scatter ing I 0 the molecular we ight was ca l-
culate d vi a eq. 75. The ref rac t ive index increme nt d n /d c was calcula ted f rom refle ctive index measure-
ments at diffe rent concentr ations for NP solution and has an ave rage value for SiO 2 -N P and
SiO 2 @PDMAE MA-NPs d n /d c = 0 .0755 mL/g.
Tra nsmiss ion mea sureme nts we re re corde d a t λ = 632 nm using a UV-Vis ca ry instrument . De nsiti es of
self-synthe sized PDMAEMA solution (same re ac tion c ondit ions exc ept the y wer e not surfa ce ini tiated,
but the po lymerization wa s d one in sol ut ion) we re measure d a t seve ral conc entrations wi th a densi meter
38
(DMA 4500 from An ton P aa r) . From these values we deduced the specific density of the polyme r chains
in solution.
Titration were perfor med wit h a commerc ial Ti t ra ndo i nstrument (Me trohm) by measur ing the pH as a
func tion of the added volume of 0. 1 M HC l or NaO H stock solutions . The poly mer conce ntration wa s
adjusted to 1 wt% and the star ting pH was set to pH = 2 for PDMAEMA and pH = 12 for PMAA . The
degr ee of ionization β was calcula ted via:
𝛽 = 𝑉 PH −𝑉 EP , 2
𝑉 EP ,1 − 𝑉 EP ,2 ,
eq. 86
with adde d volu me of s tock solution at the m ea sured pH V pH , the vo l ume at t he first equiva lence point
V EP,1 (neutra l ization of excess acid or base) and the vol um e at t he sec ond equivale nce point V EP,2 (neu-
traliza t ion of po l ymer) .
TGA wa s per forme d usi ng TA Instruments Q50 V6 . 7 Build 203 instru ment ove r a te mpera ture range of
25 – 800 °C In a typical m ea surement previously fre eze dried samples wer e hea ted i n a synt hetic air en-
vironment over a temper ature range of 20 – 700 ° C and a temper ature ramping rate of 10 °C/m in.
SAXS measureme nts were perfor med at ESRF i n Grenoble on the ID02-beamline with a sam ple to de-
tector distance (SDD) of 10 m and an X-ra y wave l ength of λ X-r ay = 0.0996 n m re sult ing in a q -range of
0.0067 – 1 nm – 1 . The sca ttering length densit i es we re calculated using the NIST ca lculator. The mol ec ular
weight of the silica core wa s ca l culate d from the fo rwar d scattering I 0 with the de nsity of sili ca
ρ SiO2 = 2.2 g/ cm 3 , the scattering length dens ity contra st Δ η of sil ica to wa ter. 10 7
Time-Re solved SAXS measure ments (t r-SAXS) were perf ormed on ID02 at the Europe an S ynchr otron
Radiation Fac ilit y (ESRF) in Grenoble . Me asure m ents w ere st ar ted after t he delay time ( t delay ~ 8.5 ms)
and m onitored over t hre e minutes with a very hi gh t i me resolution and then in a lowe r resolution ti ll
minute 10 . Ea ch exper iment wa s re peated at le ast onc e to achieve a good repr oducibility. The sample to
detec t or distances S DD is set to SDD = 10 m and the X- ray wavele ngth i s adjusted to λ X-ray = 0.0996 n m
re sult ing i n a q -range of 0.0067 – 1 nm – 1 . The scattering was rec orded on a FReLoN (Fa st R ea dout, Low
Noise) Koda k C CD detector. The input field is 100 mm x 100 mm, has a nominal dynam ic range of 16
bit with 4 x 4 binning (512 x 512 pixel) and a rea d-out ra te of 5 frame s/s and with expo sure t i mes of
100 ms . All sca ttering pat terns wer e corre cted for elec t ronic background, detector ef ficienc y and elec-
tronic eff ects of t he CCD detector i n a s tandar d proc edure at the ES RF. T he scatter ing length densitie s
wer e ca lculated using the website provided from NIST . 10 7
Small a ngl e neut ron scattering (SAN S ) was measure d at MLZ in Mun ich on the Instrument KW S -1 108
and ILL in Grenoble on the inst rument D11 with a wavelength sprea d of 10% and 20% . Thre e configu-
ra tions were used with wave l ength λ 0 = 5 . 0 Å for SDD = 1. 5 and 8 m and λ 0 = 10 Å with S DD of 20 m
for KWS-1and λ 0 = 4 . 5 Å for SDD = 1, 8 and 20 m for D11 in order to cove r a q -r ange of 0. 015 – 1 nm -1 .
Tra nsmiss ions were measure d for bot h wave lengths at a SDD of 8 m. In all scatte ring data the int ensi t ies
wer e divided by tra nsmission a nd sa mple th i ckne ss (1 mm) corr ecte d for the scatte ring of t he e mp ty cell
and normalize d to the scatter ing of water. The scattering intensity was approximated us ing eq. 40 . For
P ( q ) the sca ttering intens ity of t he spherica l cor e of the NPs was describe d by a sphere for m factor fit
while data for the po lymer gra fted NPs were fi tted wi th a core-shell form fac tor with spherica l s ym -
metry, where the scatter ing length density of the shell η shell is describe d by t he vol u m e frac tion of so l vent
containe d in the shell and η sh ell decays expone ntially to the scattering length density of the solvent η solv
(see 2. 3.5 ). S welling of t he pol ymer shell at the core radius R C for η sh ell by t he solvent i s desc ribed by.
For samples, where aggrega tion took plac e we furthe r e mpl oyed a fra ctal m o del introduce d by Teixe ira
et al. (eq. 66 ) to desc ribe such aggl om er ates. 90 Samp les prepar ed for SANS wer e prepa re d with a
39
V D2O / V H2 O ratio 0. 58 / 042 to match the contra st of the silica cor e later, i . e ., at con trast match condi t ions
(C M) and wit h a V D2 O /V H2O ratio 0.8/0.2 for “full con trast conditions”. SLD values calc ulated using
NIST calc ulator with density of silica ρ SiO2 = 2. 2 g/ cm ³. F or calc ulating the absolu te SLD value s for the
polyelec trolyte a net degre e of ioni za tion of a singl e polye lectrolyte chain was measure d via titration
and rea d at pH4 for PDMAEMA α B,DMAEMA = 0.97 and at pH 9 for PMAA α B,PMAA = 0.90 and assumed
to be equal as i n a polymer brush, wh ich in rea lit y is more complicate d. 75 De nsity of PMAA was as-
sumed as structura l similar pol ymer PMMA, wh ich ha ve a measur ed densit y of ρ MAA = 1.19 g/cm ³. 10 9
Density of PDMAEMA was measure d with a value of ρ DMAEM A = 1 . 19 g/cm³.
Data analysis wa s done using t he softwar e pac kage of SasFit. 89
Zeta potentia l measureme nt s wer e perf ormed at 25 °C on the zeta Sizer-Nano series (Malvern inst ru-
ments, Wor ceshire , UK) opera ting wi th a 4mW He Ne l a ser (633 n m). The sa mple s we re equilibra ted 30
sec onds and measure d 3 t imes with 30 runs per measure ment. Aver aging the value from all runs leads
to ζ -po tential, which is u sed for furthe r discussion.
Atomic force microscopy Visualiza t ion of surfac es w as perf ormed using a commer cial atomic f orce mi-
cr oscope (Nano- scop e V, B ruker , Santa Barba ra, C A, E sca nner) at room t empe rature i n air usin g the
tapping m ode with triangular Si 3 N 4 cantileve rs (Digital Instrument s) with a spri ng constant of 40 N/m
oper ating at 5% offset from the ca ntilever re sonanc e fre quency for NP dec orated surfa ce s or i f for a
visualization of a SLB at a spring constant of 0.6 N/ m . P rior fre shly pre pare d surfac es were rinsed with
Milli pore w ater tre ated with the plasma cle ane r a t medium power f or 2 min, rinse d with Millipore w ater
aga in, and finally blow dried with N 2 . Supported lipid bi laye rs decor ated with N P s were pre pared by
dropping v iew droplets of di ff ere nt solution with addi tional re mov ing of supernatant fr om surfac e in
following order si mila r to a t ypical QC M -D m ea surement: PBS (1 X ), vesicles (0.1 w t%), PBS (1 X ),
wate r pH 4 , NP solutio n, Millip ore and drying on air. T he he ight and phase dif fer ence s wer e de t er mined
from cr oss-sectional analysis of the t wo d iffer ent locations.
Quartz crystal microb al ance wi t h dissipation (QCM-D) m ea sureme nts were performed on a four-c ham-
ber Q-Se nse E4 i nstrument f rom Biolin Scient i fic usi ng Q-Se nse SiO 2 c oated crystal ( QSX 3 03) a nd Q-
Sense Au-c oated cr ystal (QSX 300). Adsorption expe riments wer e perf ormed by first collecting fre -
quenc y and dissi pati on shift , Δ f and Δ D respe ctively , from 3 rd ti ll 11 th overtone number. B ef ore each
measur ement t he resonanc e fr equenc y of t he crystal was first collected i n air and then in bubble free
PBS (1 X ) sol u t ion . Δ f and Δ D values wer e recor ded as l ong as needed to rea ch the equilibra ted state.
Solut i on transport into the m ea suring chambe r was d one usi ng an ult ra prec ise peristaltic pump at a
flowra t e of 100 µ L/min exce pt differ ently mentione d . Always when t he solu tion had to be change d , the
flow was shortly interrupted to avoid air bubble soakin g into the t ubing syste m. B ef ore ea ch measure-
ment the quartz crystals wer e wa shed with Mil l ipore wa ter, then trea ted with a plasma clea ner for 2 min,
rinsed wit h Millipore water and final l y b low dried w ith N 2 . After fin ishi ng the measure ment, the crysta ls
wer e directly incubate d i n sol u t ions wi t h adjusted t emp era ture T = 50 °C for 13 min plus 2 mi n of son-
ication in the foll owing order : Hellma nx III (3 wt%), S D S (2 wt%), ace tone and Millipore water keeping
the cr ystal always wet exce pt for the final step than blow dried with N 2 . For calc ulating the adsorbed
mass from QCM- D mea surements a modi fied S aue rbre y relation was used from Δ f and Δ D values i n
equilibrate d st ate alwa ys for 5 th ove rtone nu mber: 97 – 10 4
𝑚 ads = − 𝐶
𝑛 ∙ ( 𝛥𝑓 + 𝑓 C ∙ Δ𝐷
2 ) ∙ ( 1 − 𝐻 ) ,
eq. 87
with f C being the re sonance freque n cy of the crystal f C = 4 . 95 MHz , C t he crystal con-
stant C ~ 17 ng/cm 2 , n the over tone number n = 5 and H the frac tional trapped liquid coe ffic ient. The
40
adsorbe d m ass data was t ra nsfer red into particle nu mb er densities and from t hat we calcula ted surfac e
cove rage values (see cha pter 2. 3.10 and 2. 3 . 11).
Phosphate buffere d s aline ( PBS , 1X) solution are typ ically prepar ed by d issolving 8. 00 g NaCl , 0. 20 g
KCl, 1 . 42 g Na 2 HPO 4 and 0.24 g KH 2 PO 4 in 1 L Millipo re water . The pH was che cked with pH electr ode
and had a usual value of 7.4. If no t , the pH was adjus ted with adding 1 M Na OH solution . 1 10
Vesicle preparation fo r Q C M-D measurem ents : T he de sired mass of DOP C was weight into g lass v ials
and mixed w ith 10 mL methanol and chlorofor m m i xtu re ( V / V = 1/1). Then a desire d volume of a stock
solution of chlorof orm m ethanol and DMPA mixture ( c = 1 mmol) was added, t he mixture was v igor-
ously sti rr ed and trea t ed in sonication bath for two min utes. Afte r the complete solvent evapor ates the
dried lipid mixture was dissol ved in 10 m L of P BS solution (P B S 1X) and adjusted t o a conce ntration
of 0.2 wt%. The sol u t ion was then extruded 30 t imes through pore filte rs (ce llulose a ceta te) of first
400 nm and then 100 n m in d iameter usi ng the comme rcia l extruder fr om Avanti Polar Lipids. T he
vesicle sol ution was t hen di l uted to the conce ntration of c = 0. 1 wt% wit h PB S (1x) and used as a st ock
solution. Stock solutions were stored at T = 8 ° C , u sed w ithin t wo wee ks and equili bra ted to RT bef ore
ea ch measure m ent.
Vesicle preparation for t ime resolved SAXS measureme nts First DOP C wa s scaled in gl as vial and solved
with 5 mL methano l -chlor oform mixture ( V / V = 1/1) . T hen a desire d vo lume of a s t ock solution of chlo-
rofor m-methanol-DMPA mixture ( c = 1 mM) wa s adde d into t he DOP C mix ture, v i gorously s tirred and
trea ted in sonication bath for two minute s. If vesicle w ere l abe lled by a dye, now 100 μL of a Nil -Red-
ethanol solu tion c dye = 0.1 g/ mL were added. After the complete sol vent eva porates the dried lipid m ix-
ture was dissolved in Millipore wate r sol ution and the conce ntration is adjusted t o c lipi d ,total = 0.2 wt% .
Unilamellar vesicles were prepa red from aqueos l ipid mixture by extrus ion through po l yca rbonate mem-
bra nes (Wha tman® nominal pore size 400 nm, for dy e labelled vesicle t he pore size is 800 nm). The
solution is extrude d 30 tim es to obtain a suspension of monodisperse ves i cle s ( P DI < 0.2 , measur ed by
DLS and a m ea n gyration radius of R G = 160 ± 5 nm , me asured by S LS)
Microsc ope pictures wer e taken with a com mercia l C ar l Zeiss Axio Imager A1. Samples wer e mea sured
in transmission and fluor esce nt mode and rec orded with a CCD. Fluor esce nt samples we re m ea sured
with a reflec t ion m ode usin g a comme rcial cutoff filter set from Zeiss (fil t er set 15) . Filter set 15 have a
bea m spl itte r FT at λ BS = 580 n m , an exc i tat i on range from λ ex = 546 – 558 nm and an emiss i on ra nge
from λ em = 590 – 800 nm. The dye N ile Red was embe dded into the ves icles wi th an excitati on wa ve-
length λ ex = 553 nm and emis sion the wave length of λ em = 636 nm. NP-vesic les samp les wer e mixed in
the desired ratio , equi l ibrate d for 4 0 min deposit on the gl ass sl ide a nd c overe d with a cover slip. A tot al
magnifica t ion of 1 000 x wa s calculate d.
41
3.1.3 Si O 2 - NP -synth esis
Figure 22 : S cheme of l ys i ne c atalyze d syn the s is fro m T EOS to SiO 2 - NPs. 34
For exa ct re producible results similar stirr er should be used due t o t he influence i n t he nuclea tion and
growing prope rties of the si l ica nanopa rticles as a res ult of the convec tion prope rties in the rea ction
mixture. Fa ster stirr ing rate re duces the effe ctive NP siz e. A 250 mL round bottom flask was used and
stirrer m etric es are :
- length: 2 cm
- diame ter: 0. 5 cm
In a 250 mL round bot to m flask L -ly sine was dissolved i n 100 g of wate r and mixture wa s hea ted up to
the desire d tempera ture. 15 g TEO S were added drop-w ise within 10 m i n to the solut ion and the mi xture
was stirred for a given t i me at gi ven specific s tirrer speed (Table 2). F or purifica tion the dispersion was
dialyze d 6 times aga inst 5 L Milli pore wate r. 34
Table 2: Show n a r e the p aram eter for t he d e sired si z e of the Si O 2 - NP .
partic le diamet er
d nm
reaction time
h
T
°C
stirrer sp e ed
RPM
m (L-lysin)
g
50-60
36
90
270
0.062
70
40
90
250
0.062
140
27
105
100
0.074
NP with diameter of approximate ly 17 nm we re com m er cially available as Ludox HS40 sil ica nanopa r-
ticles. They were di alyz ed 10 times against 5 L Mil lipor e water and st ore d at 8 °C.
42
3.1.4 Si O 2 @NH 2 - NP -synthes is
Figure 23 : Shown i s th e su rface modif ication to SiO 2 @NH 2 . 34
To a Si O 2 di spersion ( d = 17 – 1 40 n m ) a mixture of AP TS a nd a cetic acid w as a dded drop-wise at 70 °C
within 10 minute s and the n t he m ixture was stirre d at 70 °C for 16 h ( Table 3). For purifica t ion t he
aque os S iO 2 @NH 2 disper sion were dialyzed 5 time s against 5 L Mi l lipore wate r (pH 4 pre adjusted with
ac etic acid) . 34
Table 3: Show n a r e the p aramet ers for the amin o surf ace m o dification with A P TS
d NP
nm
C (SiO 2 )
wt%
m (APTS)
g
m (ace tic ac id)
g
17
1.43
1.3
4
50
1.28
1.3
4
70
1.34
1.3
4
140
3.00
1.3
4
3.1.5 Si O 2 @Br-NP s ynthes is – intr o ducti on of sur fa ce in i tiator
Figure 24 : Shown i s th e su rface in itiated modif ication with 2-bromo-2-m e th ylpropion yl bromid e (BIBB) . 34
For prepar ing the po lymeriza tion initiator on the nanop article surfa ce Si O 2 @NH 2 - NPs we re transf err ed
into tol uene using aze otropic di s tillation of water. In a typic al distillat i on proce dure a round bottom flask
with 70 mL of aqueous SiO 2 @NH 2 - NP -di spersion w as mixed w ith 30 mL of toluene a nd 100 mL anhy-
drous ethyl ace tate, condensing the ethyl ac etate over the steam pressure ( T ~ 40 °C) of tol uene and
wate r unti l all of the water disappea red in the round bottom flask . In the di st ill atio n proce ss continuous
sonication in a sonication bath was appl ied. If nece ssary 100 mL anhydrous ethy l ace t ate (in t otal one
nee d around 1 L) wa s adde d i nto the roun d bottom flask and af ter eva porating all of the wate r and et hyl
ac etate t he desired NP conce nt ration in toluene wa s adjusted and the sample trea ted 20 mi nutes wi t h
sonication using a sonication bath and sonication tip fin ger (pulse ti me 2 s, pause t i me 5 s). 34
In a protec ting atmospher e (N 2 ) a solution of 0 .5 mL BIBB in 1 mL toluene was added drop-wise i nto a
mixture of 60 mL toluene , 15 mL triethyl amine and Si O 2 @N H 2 which was cooled under a water ice d
bath and t he mixt ure was vigorou sl y st irred (RPM = 400 with big stirrer ) for 16 h. After adding B IB B
the t empe rature of the wate r ice bath was slowly adjus ted to RT. For purifica tion the brown SiO 2 @Br
mixture was d ilut ed with MeO H ( V = 30 mL) , gently centrifuge d (RP M = 2000) and t he super natant
brown sol vent was removed. The brown SiO 2 @Br-N Ps were washed with MeOH followed by gent le
ce ntrifugation. This step ha d to be repe ated se vera l times ( ~ 3 X ) . Fina lly, the particles w ere disper sed in
wate r by a 20 min treatment i n sonication bath and w ith son ication t ip finge r (pul se time: 3 s, pulse
43
bre ak: 5 s) kee pi ng tempera ture below 25 °C . The co ncentr ation was adjusted to c = 0.003 g/mL by
adding MeOH t o the d ispersion r esul t in g in a ye llow S i O 2 @Br-Me OH dispe rsion . The w hole proce dure
was done in a similar fashion for the diffe rent nanopar ticles of 50, 70 and 140 nm diamete r. 34
3.1.6 Polym e rization – p re paration of SiO 2 @PDM AE MA- NP
Figure 25 : Shown i s th e polym e riza tion via ATRP with m on om er DM AEAMA . 34
Wa ter, MeOH and the S iO 2 @ Br dispersion were bubb led with N 2 for 20 min to remove all dissolved
oxygen. I n a 100 m L Schlenk f l ask under prote ctin g a tmosphe re (N 2 ) 55 mg C u(I) Br ( 0. 38 mmoL) we re
adde d quickly. Immediately 20 mL wate r, 13 mL MeO H and 7 mL S iO 2 @ Br dispersion were adde d and
the green/ye llow dispersion was bubble d with nitrog en for 10 m in . The final H 2 O/MeOH ratio is
V H2O / V M eOH = 1/1. Now the desired amount of t he m onomer DMAE MA and 73 μL (0.38 m mol )
PMDETA (ligand) wer e adde d si mult ane ously in to t he Schlenk flask and the gree n mixture was stirre d
for 24 h at RT. Depe nding on the added monomer am ount the color cha nged fr om gree n to blue w ith
the observa tion that more added m ono m er resulted in slow er color cha nge. For purification t he mixture
was centrif uged gently (RPM = 2000) and the exce ss blue solvent was re moved. The orange
SiO 2 @PDMAE MA-NPs containing Cu -mo nomer com plexes were diluted with 40 mL water and dia-
lyzed against 5 L Mill i pore wa ter at pH 4 a dj us ted w ith acetic ac i d. Then SiO 2 @PDMAE MA-NPs we re
disperse d by sonication using a s onication bath (20 min) and a sonication t ip finger (5 min, pul s tim e:
2 s, puls bre ak 5 s) keeping t emper ature below T = 15 °C. Fina lly, the dispersion was filte red with a
5 μ m ce llulose ac etate syringe fi lter and subs eque nt so nicate with tip finger at same cond i tions for one
minute. 34
3.1.7 Polym e rization – p re paration of SiO 2 @PMAA- NP
Figure 26 : Shown i s th e poly meri zation vi a ATRP wit h mon omer t BuMA . 34
The S iO 2 @ B r disper sion i n wate r/MeOH with the Cu(I)Br was prepa red as befor e, but the fina l
H 2 O/MeO H ratio was V H 2 O / V MeOH = 1/ 4 due to the im proved solubility of t -BuMA. Now the desired
amount of t he monomer t - BuMA and 73 μ L (0.38 mmo l) P MDETA wa s adde d simulta neously into the
Schlenk flask and the green mixture was stirred for 24 h. Depending on the amount of added mono mer
the color change d from gree n to blue with t he observatio n that more adde d mo nom er resul t ed i n a s lower
color cha nge. The NP mixt ure was gently centrifuge d ( RP M = 2000) , washed once w ith MeOH, centr i-
fuge d and then dispersed in 20 mL DCM . To the N P -DCM m ixture TFA wa s adde d qui ckly to ac hieve
a V DCM / V TFA = 1/ 1 and the mixtur e was stirred 1 h at 30 0 RPM. For purification NPs was gently ce ntri-
fuge d and d ispersed in DCM aga in (3 x) , t hen wa shed and di sperse d i n water. The aqueous N P -disper-
sion was dialyze d 8 times against Mi l lipore wi t h pre-adjusted to pH 9 usi ng NaOH . Then Si O 2 @ PMAA-
44
NP s wer e d isperse d in a sonication bath (20 mi n) and us ing a sonica tion ti p f inger (5 min, puls ti me: 2 s,
puls bre ak 5 s) kee ping tempe rature below T = 15 °C. T he final dispersion wa s filtered with 5 μm c ellu-
lose ace tate syringe filter and subseque ntly soni cated w it h a tip finger one m inute. 34
Table 4 : Weig ht fractions m for AT RP for poly meriza ti on of DMA EMA and t B uMA, th e th e or e tic al
mass r atio of po l ym er ( for 1 00 % c onv ersion) a n d si lica m (P)/ m (NP ), and measur ed g rafted amoun t
of polym er fro m TGA resul t s corre sp onding to the ma ss of g rafted poly m er m (gr afted) .
d NP
m (P)/ m (S iO 2 )
m (mo no-
mer)
grafted
poly me r
grafted
poly me r
m (P)/ m (S iO 2 )
m (mo no-
mer)
grafted
poly me r
grafted
poly me r
DMA E MA
PMAA
nm
g
wt%
mg
g
wt%
g
50
2.4
0.05
3.0
0.6
4.23
0.07
2.5
0.5
50
3.5
0.09
4.5
1.0
8.46
0.14
3.0
0.6
50
7.7
0.16
5.5
1.2
16.9
0.28
7.5
1.7
50
15.6
0.31
7.0
1.6
25.4
0.43
10.5
2.5
50
38.4
0.79
11.5
2.7
33.9
0.57
13.0
3.1
50
–
–
–
–
42.3
0.71
14.5
3.6
70
2.4
0.05
17.5
4.5
4.23
0.07
4.5
1.0
70
3.5
0.09
20.5
5.4
8.46
0.14
5.5
1.2
70
7.7
0.16
23.5
6.5
16.9
0.28
7.0
1.6
70
15.6
0.31
27.5
8.0
25.4
0.43
7.8
1.8
70
38.4
0.79
28.5
8.4
33.9
0.57
8.0
1.8
70
–
–
–
–
42.3
0.71
13.5
3.3
140
2.4
0.05
27.5
8.0
4.23
0.07
1.5
0.3
140
3.5
0.09
28.0
8.2
8.46
0.14
4.5
1.0
140
7.7
0.16
28.1
8.2
16.9
0.28
5.5
1.2
140
15.6
0.31
31.5
9.7
25.4
0.43
6.5
1.5
140
38.4
0.79
33.5
10.6
33.9
0.57
7.0
1.6
140
–
–
–
–
42.3
0.71
4.5
1.0
m (SiO 2 @B r, d = 5 0 nm ) = 0 .021 g
m (SiO 2 @B r, d = 7 0 nm ) = 0 .021 g
m (S iO 2 @Br , d = 14 0 nm ) = 0 .021 g
m (Cu(I )B r) = 0.0 55 g (0 . 38 m mol)
V (PMDE TA) = 73 μL (0.34 mmo l )
3.1.8 Sample p reparati o n SANS-measu rem ent
For S ANS-samples: Sever al rea ction batche s of pol y m er grafted NP s were comb i ned and condensed
with evapor ation rotator by simultaneously applying co nt inuous sonication to i ncr ease the conce ntration
as much as possi b le. C ondensed NPs were filtere d with a 5 µm cellulose ac etate filter and trea t ed soni-
ca ted (tip finger) for one minute . The remaining solution was diluted with deuterium ox ide to the desired
V D2O / V H2 O ra tio. 34
45
3.1.9 Sy n th esis of SiO 2 @PDM AE MA/FOMA-NPs
Fi gur e 27 : Fluo resc e in O-meth acrylate ( FOMA).
The S iO 2 @ B r disper sion i n wate r/MeOH with the Cu(I)Br was prepa red as befor e, but t he fina l
H 2 O/MeO H ratio was V H2 O / V MeOH = 1/1 . Now the desir ed amount of t he monomer DMAEMA , FOMA
and 73 μ L (0.38 mmol) PMDE TA was added simultane ousl y into the Schle nk flask and t he gree n mix-
ture wa s st irred for 24 h. De pending on the amoun t of adde d monome r the color change d fr om gre en to
blue with the observa tion, that more added m onomer resulted in a slower color c hange. For purif ication
the mixture was centrifuge d gently (RPM = 2000) and the exce ss blue solvent was removed. The orange
SiO 2 @PDMAE MA-NPs containing C u-monomer comple xes was d iluted wit h 40 mL water and dia-
lyzed against 5 L Mil l ipore wate r a t pH 4 a djust ed with ac etic acid. The n Si O 2 @PD MAEMA-NPs we re
disperse d by sonication using a s onication bath (20 min) and a sonication tip finger (5 m i n, puls ti me:
2 s, puls bre ak 5 s) keeping t emper ature below T = 15 °C. Fina lly, the dispersion was filte red with a
5 μ m ce llulose ac etate syringe fi lter and subs eque nt so nicate with tip finger at same cond i tions for o ne
minute.
3.1.10 Poly merization of SiO 2 @PAM-NPs
Figure 28 : Po lymeriza ti o n via AT RP with mon omer ac ryl a mi d e .
The SiO 2 @ Br disper sion in water /MeOH wit h the C u(I) Br was prepa red as befor e. The desired amount
of the monomer acr yl amide is adde d and t he mixture wa s bub bled under n itrogen for 10 min. Now73 μL
(0.38 m mol) P MDETA was added in t o the S chle nk fla sk and the gree n m ixture was stirr ed for 24 h .
Depe ndi ng on the added monomer amount the co lor c hanged from green to blue wit h the ob servation
that more adde d m onom er re sulted in s lower color cha nge. For purif ication t he mix t ure wa s c entrifuge d
gently (RP M = 2000) and the exce ss blue solvent was remove d. The white SiO 2 @PAM-N P s wer e di-
luted with 40 mL water and di alyz ed against 5 L Mill i pore. Then SiO 2 @ P AM-NPs were dispersed by
sonication using a soni ca tion bath (20 min) and a so nication tip finger (5 m in , puls t ime: 2 s, puls bre ak
5 s) keeping tempera ture below T = 15 °C. Finally, th e dispersion wa s filt er ed with a 5 μm cellu l ose
ac etate syringe filter and subseque nt sonicated with tip finger at same conditions for one m inute.
46
4 Res ults and disc ussion
4.1 Nanoparti cles s yn thes is an d an alysi s
4.1.1 Pr ep aration of po lym er modified silica nan op articles
Sil ica nanopar ticles ( Si O 2 -NP s) were synthesize d w it h a modified S TÖBE R m ethod w ith TEOS as pre-
cur sor but using L - lysine as ca t alyst where t he s ize and polydispersity can be well con trolled and tune d
by the rea ction ti me , tempera ture and sti rring speed. 37, 38 We synt hesize d three NPs wi th diameters of
50,70 and 140 nm. Succ essful am i no functionaliza tion was ac hieved with APTS in wate r. 11 1 The am ino
group was then re ac ted with BIBB in order to pl ac e the i n itiator group on the surfa ce . For this rea ction
the NPs had to be transf err ed into toluene due t o t he need of a nonpolar and aprotic sol vent for preve nting
hydrolysis of t he bromide ac id m oi ety . Drying of t he NPs had to be avoided as othe rwise irreve rsibl e
agglomer ation of S iO 2 - NPs could take plac e. Thus, S i O 2 @NH 2 - NPs had to be transf err ed from water
into toluene via az eotropic d i stillation with anhydr ous e thyl ace tate. 34
Howe ver, the numb er of aggrega tes increa ses pa rticularly for t he smallest NPs as sonication ca nnot
sepa rate all aggre gates into single NPs afte r t oluene transf er. The – Br moiety is a good leaving group,
which re nders the s torage of the SiO 2 @Br-NPs in wat er impossible and t o avoid an – B r t o – OH ex-
cha nge the SiO 2 @ Br-NPs had t o be tr ansfe rre d i nto Me OH for the subse quent polyme riza tion, as kee p-
ing the particles in a st able colloida l st ate is only possibl e in a ver y po lar solvent . Nonetheless S iO 2 @Br-
NPs we re coa gulating over time as they exhib it low sur fac e potentials ( ζ ~ – 20 mV measure d in metha-
nol) and have alwa ys to be sonicated short l y before polyme rization.
As a first st ep we cha rac t er ized the ini tially prepar ed SiO 2 -NPs, wher e SAX S shows nicely the marked
monodispersity of the par ticles as well as their systema ti c size variation ( Figure 29). Fitt i ng t he SAXS
cur ves w as done with a model of po lydisperse sphere s (Figur e 29 l ef t). I n our ca se ave rage diameter s of
48.6, 64.8 and 140.6 n m and polydisper sity i ndice s for the diamete rs of 0. 0 86, 0.074 and 0. 07 0 were
deduc ted, re spectively. Ve ry similar fit results we re obt aine d for further modi fica tions steps but the
re duced surfa ce potential and the l owe r polar ity of MeOH compare d to wate r t end to lead to more ag-
glomera tion . As the major obj ec tive was t o obtain stabl e colloidal solution with the smalles t amount of
ag grega ted NPs . Afte r ea ch functionaliz ation all surface modified NPs were analyze d with sca ttering
technique s (LS, SAXS) and addit i onally with ζ -potenti al m ea surements. For SAX S , all data were fitted
using a sphe rical for m fa ctor re specting the par ticle n um ber density and scattering length density of
SLD = 9. 5 ∙ 10 – 4 nm -2 . For all NP s the PDI i s re marka bly low i ndicating that size and polydisper sity are
well controlled via L -lysine modified NP synthesis. Fo r SAXS -measur ements concentr ations wer e ad-
justed t o 0. 2 wt%. Howeve r, we mea sured the exa ct co ncentra t ion afte r t he measure m ent by means of
eva porating the sol vent . The data show, that the small SiO 2 @Br- NPs ( d = 50 and 70 n m) have an addi-
tional upturn i n the low q -regime indi ca ting po ss ible a gglomeration. Thus, we interpr eted a collo idal
stability l os s during solve nt t ra nsfer from polar t o nonpo lar conditi ons as a result of reduc ed ele ctrostatic
stabilization . Attac hing the Br -mo i ety, re action leads to a re duce surf ace potential (ioniza ble NH 2 -mo i-
eties are re placed by uncharge d B r-moities) of less t ha n 25 mV (Ta ble 5), which is usually conside red
to be a threshol d for colloi dal sta bili t y. For the subsequ ent polyme riza tion the majori t y of t h ose aggre -
gates ca n be separa ted int o single NPs again by s onicati on . O nce NPs are cha rged, due to polymer pro-
tonation or deprotonation, l ong time colloidal s table so lut ions can be achieve d as l ong ζ -potent ials are
high. The succ ess of the ami ne functional ization wa s co nfirmed by the cha rge inve rsion f rom a n a nionic
to a cationic sur fac e and a reve rsal to an anionic surfa ce charge once the bromine functionaliza tion had
taken plac e. 34
47
Tabl e 5: Measur ed dat a SiO 2 -, SiO 2 @ NH 2 , SiO 2 @ B r-N Ps; f or light scatt ering: hydr odynamic r ad ii
R
H , appr oximat e d for wa rd s ca tt e ring
I
0 ,L S , weight con centr ation
c
g, LS ,
and mo lec ul ar weight
M
W,L S ; for SAXS: weight concent ratio n
c
g,SAXS , , a pp rox ima ted for ward sca tt e ring
I
0,SAXS , r adius of the core
R
NP , th e po lydisp e rsity index P DI, the
molecul a r w e ig ht
M
W ,SAXS and the ζ -po tential dat a at high c harged condition s. 34
surface
LS dat a
SAX S data
d th e o
modific ation
R H
I 0, LS
c g
M W, LS
R MW
c g, S A X S
I 0, SAXS
R NP
PDI
M W, SAXS
M W,th
ζ
nm
nm
cm – 1
g/L
g/mol
g/L
cm – 1
nm
g/moL
g/mo L
mV
50
– OH
29
5.4 ∙ 10 -3
0.3
6.98 ∙ 10 8
50
2.2
591
24.3
0.086
8.69 ∙ 10 7
7.96 ∙ 10 7
– 54.3
50
– NH 2
34
5.4 ∙ 10 -3
0.5
4.64 ∙ 10 8
44
2.2
595
24.3
0.086
8.75 ∙ 10 7
7.96 ∙ 10 7
+49 .0
50
– Br
73
78 .5 ∙ 10 - 3
0.4
9.11 ∙ 10 9
118
2.3
–
24.4
0.088
–
–
– 24.1
70
– OH
36
10 .7 ∙ 10 - 3
2.0
2.24 ∙ 10 8
34
2.1
1337
32.6
0.074
2.06 ∙ 10 8
1.92 ∙ 10 8
– 46.9
70
– NH 2
37
13.8 ∙ 10 - 3
2.0
2.91 ∙ 10 8
37
2.1
1286
32.5
0.072
1.98 ∙ 10 8
1.91 ∙ 10 8
+43.8
70
– Br
82
17.5 ∙ 10 - 3
3.1
2.40 ∙ 10 8
35
2.2
–
32.6
0.080
–
–
– 21.2
140
– OH
73
49.2 ∙ 10 - 3
1.0
2.26 ∙ 10 9
74
2.2
14440
70.3
0.070
2.12 ∙ 10 9
1.93 ∙ 10 9
– 55.4
140
– NH 2
74
58.1 ∙ 10 - 3
1.0
2.44 ∙ 10 9
76
1.9
12649
70.3
0.073
2.15 ∙ 10 9
1.93 ∙ 10 9
+53.2
140
– Br
74
51 .1 ∙ 10 - 3
1.3
1.71 ∙ 10 9
68
1.8
10766
70.3
0.070
1.93 ∙ 10 9
–
– 20.5
* ζ -potential are taken in h i gh char ged condit i ons; the re fra ctive index incre ment d n /d c measure d for SiO 2 and h as a value for d n /d c = 0.0755 mL / g
48
Figure 29 : Left ) S AXS -data of p ure SiO 2 -NPs . Dots rep resen t d ata po int s a nd dar k lin e a pproxim ated s cattering
intensit y with a spher ical for m factor f i t, Righ t ) SAXS -data o f all NP modific a tions. 34
4.1.2 Polym e rization
Figure 30 : Syn the s is str a tegy for SiO 2 @PD MAEMA and Si O 2 @PMAA - NPs. 34
For pol ymeriz ation, we used a surfa ce initiated ATRP w ith Cu(I)Br as ca talyst and PMDETA as l i g-
and in a m ethanol-wa ter mixture ( V MeOH / V H 2 O = 1:1 for DMAEMA or V Me OH / V H2O = 4:1 for t BuMA)
kee ping the SiO 2 @Br- NP conce ntration low to avoid f usi on of polymer cha ins from diffe rent parti-
cles. P o l ymeriz ations we re ca rrie d out with high mono mer and coppe r to initiator mo lar ra tio and the
monomer conc entration was varie d fr om 2.4 – 122 mM per re a ction batc h, while ke eping temper ature ,
ca talyst and S iO 2 @Br- NPs weight conc entra tion consta nt. Cationic PDMAE MA wa s d irectly synthe -
sized using the mono mer DMAEMA. In contrast, anio nic pol yelec t rolyte brushes were achie ved by
polymeriza t ion of t BuMA and s ubsequent hydroly sis t o yield pol y m ethac ryli c acid brus hes
(SiO 2 @PMAA) .
Afte r t he rea ction polymer coated SiO 2 -NPs wer e trans ferr ed int o water by dialysis, wher e polymers
wer e cha rged due t o the adj usted pH . The pol y mer ch ar ging is a nece ssary step in the purification
proc edure due to ele ctrostatica lly enha nc ed collo i dal s tabilit y , where disper sion then wa s achieve d
via sonication and filtratio n. PMAA can be deprotonat ed (p K a ~ 4.5) 11 2 and typ ically the pH of the
solutions was 9. In con t ra st , the dimethyl amino moi et y of P DMAEMA (p K a ~ 7.6) 1 13 can be proto-
nated leading to a cationic po lymer at pH values lower than 7, wher e we always used ace tic ac id for
the pH adjustment. It should be not ed, that we tried in a si milar fashion to polyme rize neutra l acr yl
amide onto SiO 2 - NPs bu t this always led to substantiall y bi gger aggrega tes. Appar ently charging is a
nec essar y step for keeping the N Ps colloi dal ly stable, th us i t i s intrinsica l ly c hallengin g to obtain such
cor e shell structure s with uncha rged poly mer shells, that do not aggrega te. 34
Polym er graf ted NPs we re studied by sever al t ec hniqu es including sca ttering (l i ght , S AXS, SANS),
ζ – potential measur ements, TGA and TEM ana lysis to g ain deta iled infor mation re gar ding their struc-
ture.
49
4.1.3 Polym e r-modif ied SiO 2 -NPs – variation of polym e r ty pe
Figure 31 : Sh own i s examp le TGA d ata of S iO 2 @PDM AE MA (top; a ) 50 n m, b) 70 n m and c) 140 nm)) and
SiO 2 @PMA A (botto m ; d) 50 nm, e) 70 nm a n d f) 14 0 n m )). 34
Due to the tempera ture inertness of Si O 2 at h igh tempe rature s TGA i s a powerful technique t o deter-
mine the amount of gra fted polyme r on t he NP s. The st udied t em pera ture range was 20 °C to 700 °C ,
wher e the final mass value was rea d at 700 °C. As expec ted, the measure d loss Δ m for SiO 2 @Po lymer-
NPs is much smaller than if 100% of the monomer wou ld ha ve be en conve rted ( theoretical Δ m losses
from 70 – 98 %, de pending o n the mono mer to NP r atio ; Table 6), which i mpl ies that on ly 10 – 40 % of
adde d monom er poly merize onto the surfac e, a conditi o n as normally seen for surfac e poly meriza t ions
by means of ATRP , wher e polymeriz ation eff iciency is expe cted t o be l ow ac cording to heter ogeneous
surfa ce liquid rea ction. 11 4 An interesting observation is that the amount of graf ted pol ymer incre ases
with inc re asing particle size for SiO 2 @ PDMAE MA-NPs (while it is rathe r constant for
SiO 2 @PMAA ). Thi s result is une xpecte d , due to a dec rea se of total surfa ce ar e a with i ncr easing NPs
size one would expec t a reduc ed polymer amo unt for the same grafting densi ty and polymer length.
In ge nera l , t he amount of gra fted po lymer is smaller for S iO 2 @PMAA-NPs than for
SiO 2 @PDMAE MA-NPs , pre sumably as re sult of the ha rsh r eaction c ondi tions in the hydr olysis rea c-
tion when transf orming hydrophobic SiO 2 @P t BUMA-NPs to hydroph ili c S iO 2 @ PMAA-NPs . Durin g
that proce ss so me of t he pol y mer cha ins m ight be clea ved from the core .
Sever al approa che s can be used to ca l culate the m olecula r weight of N Ps and polymer graf ted NPs
using L S , S AN S or SAXS. I n our case we c onsidere d a s m ost ac curate wa y to calc ulate the molecular
weight from a combinat i on of SAXS and TGA, where T GA give s the to t al amo unt of boun d po lym er .
The M W of pol ymer gra fted NPs was calculated by multiplying the M W of the cor e with the polymer
amount obtained from TGA. In addi ti on , the M W of polymer grafte d NPs was measure d by SLS. The
re fractive index inc reme nt d n /d c g of po lym er gra fted N P s i s similar to pure SiO 2 -NPs as t hat is by far
the largest fra ction of t he hybrid N P s. M W value s ca lcul ated fr om SLS ar e te ndentially in goo d agree -
ment wi t h t he resul t s of S AXS+TGA data. Howeve r , da ta exhibit for the smallest NPs a higher M w
from SLS compar ed to SAXS+TGA data i ndicating tha t the sm al l est N Ps have a higher tende ncy for
agglomer ation. In contra ry, for the bigger NPs M W from S LD is s maller compa red to values obta ined
SAXS+TGA data but usually i n the same magni tude. Here we assume that at low concentr ation a
re pulsi ve structure fac tor is still prese nt , which re duces the rea l sca ttering int ensi t y of t he N P s at low
50
q va lues , and a n a ccur ate I 0 est imation vi a eq . 40 is d istor ted. Thu s, tendential ly smaller a pproximated
I 0 values result s in smal l er ca lculated M W values respe ctively. 34
Table 6 . Param eter from the T GA i nv estigat ion for SiO 2 @P DMAEM A a nd SiO 2 @PMA A-NPs :
mono me r concen tration c (mono m er) , expe ct ed mass loss if 100 % mon omer con version would
have tak e n pla ce, T GA t h eo, me asured d a t a mass loss, TGA data, a n d the corresp ondin g conv er-
sion rat e o f the mono m er (c onvers ion = TGA da ta/TGA theo ).
d core
SiO 2 @PDM AEMA
SiO 2 @PM AA
nm
c (mo nomer)
TGA d ata
TGA
theo
conv ersion
c (mo nomer)
TGA
data
TGA
theo
conv er-
sion
mM
%
%
%
mM
%
%
%
50
0.3
3.0
70.4
4.3
0.5
2.5
65.6
3.8
50
0.6
4.5
81.1
5.5
1.0
3.0
79.2
3.8
50
1.0
5.5
88.2
6.2
2.0
7.5
88.4
8.5
50
2.0
7.0
93.7
7.5
3.0
10.5
92.0
11.4
50
5.0
11.5
97.4
11.8
4.0
13.0
93.8
13.9
50
–
–
–
–
5.0
14.5
95.0
15.3
70
0.3
17.5
70.4
24.9
0.5
4.5
65.6
6.9
70
0.6
20.5
81.1
25.3
1.0
5.5
79.2
6.9
70
1.0
23.5
88.2
26.6
2.0
7.0
88.4
7.9
70
2.0
27.5
93.7
29.3
3.0
7.8
92.0
8.5
70
5.0
28.5
97.4
29.3
4.0
8.0
93.8
8.5
70
–
–
–
–
5.0
13.5
95.0
14.2
140
0.3
27.5
70.4
24.9
0.5
1.5
65.6
2.3
140
0.6
28.0
81.1
25.3
1.0
4.5
79.2
5.7
140
1.0
28.1
88.2
26.6
2.0
5.5
88.4
6.2
140
2.0
31.5
93.7
29.3
3.0
6.5
92.0
7.1
140
5.0
33.5
97.4
29.3
4.0
7.0
93.8
7.5
140
–
–
–
–
5.0
4.0
95.0
4.2
Beside TGA we measure d the hydrodynamic ra dius R H of poly m er grafte d NP s and by su btrac ting the
cor e radius we estimate the shell thickness t shell :
𝑡 s hell = 𝑅 H − 𝑅 NP
eq. 88
LS data wa s mea sured at ful ly cha rged c onditio ns for both poly m er s, i . e . , at pH 4 for
SiO 2 @PDMAE MA and at pH 9 for SiO 2 @ P MAA (see Figure 32 ). 34
The results for bot h po lymers dif fer fr om ea ch other . An e xpected shell thickne ss incr ease f or PMAA
ca n be obser ved result i ng from an incre ase of degree of polymeriza tion of gra fted cha ins as a func tion
of the monomer conce ntration. The ref ore, we can control the shell thickne ss simp l y by the employed
t BuMA monome r conce nt ra tion for anionic poly mer gra fted NP s . In contrast, for SiO 2 @PDMAE MA-
NPs show the inte resting and unexpec ted result, that t shell does not inc rea se with incre asing am ount of
gra fted polymer. The only re asona ble int er preta tion is an increa se of the gr af ting density upon in-
cr easing amount of grafte d po lym er . T hat obse rva tion s trongly d iffer s fr om re sults of w orking gr oups
using surface initi ated AT RP, where the grafting dens it y was control led by the initiator density. 11 5
Based on our r esults we a re able to con trol t he graf ting density of the P DMAEMA brush polymer jus t
by the m ono m er conce nt ra tion , while t he shel l thi ckne ss alwa ys rema i ns constant t shell ~ 16 nm. We
assume, that this unexpecte d result has its origin i n th e complexa tion potential of t he pol ymer and
monomer. Onc e a critical degre e of polymeriza tion is re ache d the c hains may tend to chela te the c op-
per by re placing P MDETA wi th PDAEMA and furth er monomer propa gation is no longer po ssi-
ble. 11 6,117 A higher monomer conce ntration i ncr ease s th e probability to grow new cha ins on diffe rent
initi ator moi eties once rema ining cha i ns are alrea dy t r apped. Those com pl exe s can brea k down by
51
cha rging the di methyl amino m oiety of the poly mer. T he char ging is nece ssary beca use it separ ates
the intra and inter particle bridged po l ymer cha i ns and e nhance s the colloi dal sta bilit y due to elec t ro-
static repulsion . For detail s t he rea der is refe rre d t o chapter 4. 1.5. 34
Figure 32 : Righ t ) h ydrodyna m ic radi i R H of polym e r gra f t ed NPs and Le f t) sh e ll thickn esses for d i fferen t core
sizes; ▲: d = 50 nm, ● : d = 70 nm, ■: d = 14 0 n m (fu ll symbo l s: SiO 2 @P DMA EMA, o pen symbo ls:
SiO 2 @PMA A) . 34
52
Table 7: M ass l oss Δ m from T GA (whi ch gives the amount of g r afted poly m er of the nanop a rt icles) , m o lecul ar weight M W from SAXS in combin a tion with T GA
results fro m S LS, hydr odyn amic ra dii R H , sh ell thi ckness e s t shel l , and ζ -p otent ia l v a lu es for SiO 2 @PDM AEMA a nd SiO 2 @ PMA A nanopart icles .
R NP
Δ m
M W
(SAX S+T GA)
M W
(SLS)
R H
t sh e ll
ζ
(pH 4)
Δ m
M W
(SAX S+T GA)
M W
(SLS)
R H
t sh e ll
ζ
(pH 9)
nm
wt%
g/mol
g/mol
nm
nm
mV
wt%
g/mol
g/mol
nm
nm
mV
SiO 2 @PD M AE MA (cati onic)
SiO 2 @P MAA ( anioni c)
24.3
0.0
8.69 ∙ 10 7
2.79 ∙ 10 8
27
0
+49.0
0.0
8.69 ∙ 10 7
2.79 ∙ 10 8
26
0
54.3
24.3
3.0
8.99 ∙ 10 7
1.96 ∙ 10 8
39
13
+50.1
2.5
8.94 ∙ 10 7
1.91 ∙ 10 8
48
24
32.8
24.3
4.5
9.14 ∙ 10 7
1.08 ∙ 10 9
42
16
+44.9
3.0
9.19 ∙ 10 7
1.77 ∙ 10 8
60
35
39.1
24.3
5.5
9.25 ∙ 10 7
2.16 ∙ 10 8
43
17
+51.0
7.5
9.73 ∙ 10 7
2.96 ∙ 10 9
89
65
38.2
24.3
7.0
9.41 ∙ 10 7
2.65 ∙ 10 8
41
16
+52.8
10.5
1.05 ∙ 10 8
2.27 ∙ 10 9
88
63
36.9
24.3
11.5
9.94 ∙ 10 7
2.83 ∙ 10 8
40
17
+51.1
13.0
1.12 ∙ 10 8
2.33 ∙ 10 9
111
86
38.2
24.3
–
–
–
–
–
14.5
1.16 ∙ 10 8
9.67 ∙ 10 8
118
93
39.8
32.4
0.0
2.06 ∙ 10 8
1.64 ∙ 10 8
35
0
+45.7
0.0
2.06 ∙ 10 8
1.64 ∙ 10 8
36
0
46.9
32.4
17.5
2.54 ∙ 10 8
2.36 ∙ 10 8
47
14
+32.3
4.5
2.17 ∙ 10 8
3.35 ∙ 10 8
53
20
39.9
32.4
20.5
2.65 ∙ 10 8
3.23 ∙ 10 8
49
16
+43.2
5.5
2.29 ∙ 10 8
4.62 ∙ 10 8
71
39
48.1
32.4
23.5
2.76 ∙ 10 8
2.55 ∙ 10 8
47
15
+41.8
7.0
2.35 ∙ 10 8
3.47 ∙ 10 8
78
45
41.6
32.4
27.5
2.93 ∙ 10 8
2.93 ∙ 10 8
48
15
+42.4
7.8
2.41 ∙ 10 8
5.72 ∙ 10 8
78
45
47.9
32.4
28.5
2.98 ∙ 10 8
4.04 ∙ 10 8
49
16
+42.2
8.0
2.43 ∙ 10 8
5.20 ∙ 10 8
97
64
40.7
32.4
–
–
–
–
–
–
13.5
2.60 ∙ 10 8
5.11 ∙ 10 8
94
61
49.9
70.3
0.0
2.66 ∙ 10 9
2.26 ∙ 10 9
72
0
+53.2
0.0
2.66 ∙ 10 9
2.26 ∙ 10 9
72
0
55.4
70.3
27.5
3.02 ∙ 10 9
2.91 ∙ 10 8
78
7
+35.8
1.5
2.16 ∙ 10 9
8.87 ∙ 10 8
75
5
48.6
70.3
28.0
3.87 ∙ 10 9
8.27 ∙ 10 8
79
9
+36.8
4.5
2.26 ∙ 10 9
1.96 ∙ 10 9
78
8
35.8
70.3
28.1
3.89 ∙ 10 9
1.05 ∙ 10 8
80
10
+44.4
5.5
2.35 ∙ 10 9
3.23 ∙ 10 9
82
12
44.0
70.3
31.5
4.11 ∙ 10 9
1.10 ∙ 10 9
78
8
+47.4
6.5
2.40 ∙ 10 9
1.20 ∙ 10 10
100
30
42.5
70.3
33.5
4.36 ∙ 10 9
1.27 ∙ 10 9
82
12
+48.3
7.0
2.44 ∙ 10 9
2.09 ∙ 10 9
103
33
42.3
70.3
–
–
–
–
–
–
4.0
2.37 ∙ 10 9
2.31 ∙ 10 9
83
13
44.2
For Δ m l oss the value 0.0 repres ent none graft ed SiO 2 @NH 2 and S i O 2 -NP as re f erenc e for c ationic or anion i c NP s ; R c o re obtained fro m fitt ing resu lt s usi ng a sphe ri cal cor e form
factor fit fro m SAX S for pure SiO 2 - NPs ; light scatteri ng r es ult done in high charg e c ond i tions (SiO 2 @NH 2 a nd SiO 2 @P DMA EMA @pH 4; SiO 2 a nd SiO 2 @PMAA @ pH 9 t shell
calcu la t ed via eq . 88 , Deta il s about M W (SAX S+TGA) show n in appen dix.
53
4.1.4 pH responsible p ro perties
Both polymers ar e pH re sponsive (PMAA, p K a ~ 4 . 3 11 2 and PDMAEMA , p K a ~ 7. 6 11 3 ). P olyme r
cha rging is nece ssary beca use it incre ase s the colloidal stability simply by electrostatic repulsion of
the particle s, wher e the charge density ca n be described by the ζ -potent i al. In additi on, there will be a
steric repulsion of the particle s from the po lymer chain s. For the ca se that the pol y mer is unchar ged
the attrac t ive vdW forc es (they should be pronounce d not only between t he SiO 2 surf ace s and the
polymer cha ins) m ay dominate the st er ic repulsio n force as we alwa y s see NP aggre gation and phase
sepa ration.
The minimum nee ded ζ -potential for colloidal st abi li za tion (marke d as a red dotted l ine) is normal ly
assumed to be around │ ζ min │~ 25 mV , which i s the potential whe re the electrostatic energy of an
eleme ntary cha rge is equa l to the therma l ene rgy kT . P u re SiO 2 -NPs have always a negative potential
in t hi s pH ra nge due to deprotonable OH -moieties on the surf ace . How ever, at pH 4 and 5 the ζ -
potential is above – 25 m V but l ight scattering shows no aggr egation. Anionic SiO 2 @PMAA -NPs have
alwa ys a negative surfa ce potential. The latter rises quic kly from pH 4 t o 6 and beyond the potent i al
is we akly inc rea sing or almost c onstant for a ll amounts of gr afte d polymer (Figure 35) indicating that
cha rge saturation is reac hed at pH 6 and not being a fu nction of the poly mer content . 11 2 In con trary,
the surfa ce potential of cationic SiO 2 @NH 2 and SiO 2 @ P DMAEMA-N Ps is nega tive only in strongly
basic media due to the deprotona t ion of still fre e Si -OH moieties. For ca tioni c NPs if the ζ -po t ential
drops below +25 mV NP s alwa ys coa gulation is seen (light scatter ing data, Figure 33). Indepe ndent
of the amount of gra fted poly mer the ζ -po tential values are close to ea ch other at pH 4 with in expe ri-
mental error indi ca ting that here char ge saturation of the pol ymer is ac hieved. F urthermor e, and dif-
fe rent to S iO 2 @PMAA a hi g her polym er con tent result s in higher values at h i gher pH values, wh ich
may explain , the delaye d pH de pendent aggrega tion with incre asing gra fting density of catanionic
PDMAEMA. 34
Espec ially for the highly graf ted SiO 2 @PDMAEMA- NPs at pH 8 l ig ht scatter ing show s colloida lly
stable solutions . Howeve r, N Ps show agg l omera t ion o ver tim e which is i n good agre ement with the
DLVO- theory wher e w eak electrostatic repulsion stabi l izes NPs kine tically onl y for short time peri-
ods. In con trast at pH 7 SiO 2 @PDMAE MA with higher degree of grafting rema in long time stable as
colloidal solution. NPs are pH re sponsive and ca n be p rec i pitated and di sperse d si mp ly by t he varia -
tion of the pH . We followed the forc ed pre cipitation and dispersion cyc le with turbidity m ea sureme nts.
Once prec ipit ated by changing pH NP s ca nnot d isperse completely bac k by adjusting the pH bac k t o
4 with subseque nt i n t ense m i xing and a cer tain amou nt of aggrega t es re main i n the sol ution. With
ea ch prec ipitation and dispe rsion cycle t he conc entra tion of aggre gates i ncr ease s ( Figur e 34), bu t one
ca n a chieve the i n itial particle c oncentr ation a gain u sing a s oni ca tion t ip finge r. Important to m ention,
that elec trostatic long-range stabili za tion reduce s with ea ch cha rging/d is cha rging step due to concom-
itant i ncr ease of t o tal salt conc entra tion. 34
54
Figure 33 : pH depend e n t valu es for h ydrodyna mic r adii R H (lef t) and ζ -poten tials fo r all S i O 2 @PD MAEMA -
NPs (top d = 50 nm, middle d = 70 n m , botto m, d = 140 n m). 1 ϕ , 2 ϕ i s noti ce d as one (sing le NPs ) a nd two
(aggrega tes) phas e system . If NP s fully p ha se se p arated v alues of h ydrody nami c r adii a re not shown in the 2 ϕ
regime. 34
Figure 34 : a ) Turbidi ty measur ements of SiO 2 @PD MAEM A-NPs after one charg i ng/ d e ch arging cycl e a nd
subsequen t ly a pplied son i cation b) turbidi ty f or s eve r a l pr e ci pi tati on/ disp e rsion cyc le s . 34
55
Figure 35 : pH dep e nd e nt va lues for hydrodyn amic rad ii R H ( left) a n d ζ -p otentials (right) for all S iO2@PMAA-
NPs (top d = 50 nm, middle d = 70 n m , botto m, d = 140 n m). 1 ϕ , 2 ϕ i s noti ce d as one (sing le NPs ) a nd two
(aggrega tes) phas e system . If NP s fully p ha se sep a rate d v a lues of h ydrodyna m ic radi i are not shown in the 2 ϕ
regime. 34
56
Also the h igher the polymer density of SiO 2 @PDMAE MA-NPs, the less sens iti ve ar e the NPs to the
adde d electr olytes (NaCl) wh i ch i s in g ood agr eeme nt with theore t ical pre dictions fr om Pi ncus for
polyelec trolyte brushes anchore d at surfac es. 69 Light sc attering data exhibi t (Figure 36) a mean hy-
drodyna mic radius gain (aggr ega tion gain) wit h incre asing salt conce ntration but S iO 2 @ P DMAEMA-
NPs wi t h the highest am ount of grafted polymer do not aggre gate until a salt concentr ations of
c NaCl = 50 mM. 34
Figure 36: Hydro dynamic radii R H for SiO 2 @PD MAEMA - NPs with d = 50 nm as a funct ion of t he amoun t of
grafted polym er for diff e rent ionic strengt hs (N aCl ) at 25 °C. 34
4.1.5 Complexa tion Beh a vio r o f SiO 2 @PDM AEM A- NPs
Figure 37: SiO 2 @PDM AEMA-N Ps wi t h core size of d NP = 50 n m. a) L eft ) NPs a re sep a ra te d from r eaction
mixture by ce n t rifuga t ion wit h subseq ue n t m e thano l w ash ing (2 X) a nd fina l tr ansfer into M i llipor e wa t er (neu-
tral condit i ons). Righ t ) NPs dialy z ed i n ace tic acid -w ater so l ution (pH 4) with subs equ ent soni c atio n treatme nt. 34
Afte r the rea ction SiO 2 @PD MAEMA-NPs were purifi ed by wa sh ing the remaining m onomer from
the NPs awa y with methanol and finally the NPs wer e transfe rred into Millipore wa ter solution. Just
by optical observa tion S iO 2 @PDMAE MA-NPs have an intense ora nge color and with increa si ng
amount of graf ted poly mer a brown t in t becomes i ncr ea singly obser vable. The intense color disa p-
pea rs, and a clea r tr anspare nt sol ution is formed once the NPs we re dialyze d at lower (~ pH 4, ace tic
ac id), and then t he NPs can easily be di spersed by son ic ation. We assume , that the ora nge color has
its origi n in the complexa tion of c opper(I ) by t he polyme r. Onc e a certa in degr ee of pol ymeriz ation is
re ached the chain will st ar t to chelate the coppe r by re placing the li gand PMDETA w ith the polyme r
PDAEMA. The chain there by dea ctivates t he i nitia tor a nd t her efor e further monomer propaga tion on
that cha in is no longer possible . The rema ining monome r is more likely to be i nvol ved i n s tarting a
new cha in o n the surfa ce of the S iO 2 -NP and growth of new chains on yet dormant initiator mo ie ties
takes plac e. As an outcome the grafting density incre ases with incre asing monomer conce ntration.
57
Figure 38 : a ) Sche m atic descr i ption of the c hela ti ng r e act ion of PDM AEMA, that repl aces PMD ETA i n the
comple xation of Cu + . PDM AEMA can ch elate op t o s ix co or dination positions of the c opp er c omple x. Pr e sum-
ably the chel ating is not favored until 4 or mor e co ordinat ion posit ions w ill b e o cc up i ed by the amino mo i ety of
PDM AEMA. O nce c h e lated the chain wi ll co ntrac t and the n further m ono mer propaga ti on is im p e d ed and n o
longer possibl e o n t he same c h a in due to steri c repu lsion b) 1 – 3) Shows sk etch of the m ono m er propag a t ion
until the criti cal degre e of po l ymeri zation is reach ed a nd then 4) due to ste r i c re p ul sio n new chai ns begin t o
propagat e. 34
Presumably both copper specie s, Cu(I) and Cu (II), will be chela ted by the polymer. But just by op t ica l
inspection we th ink , that Cu(I ) complexed more probab ly than Cu(I I) otherw ise we would see a light
blue color as re ported by Kava kl ı et al. 1 16 Due to the ve ry hi gh copper /monom er t o ini t iator ratio the
trapping of copper w ill have a wea k influence of the K ATRP shi ft fr om ac t ive to dormant st ate (no te
that the tota l disso lved coppe r conc entra tion re duce s constantly with incre asing re action time) . In
principa l, up to 6 coordina tion sites ca n be occupie d b y the poly mer. Howe ver , entropica lly it might
be favor ed if only four dimethy l amino moietie s of one polymer chain will complex t he copper . That
allows for the possibility of addi tional comp lexation of t wo or m ore polym er chains at t he same copper
atom leading int er pol y mer bridging or ever inter NP br idging. That may expla in the strong t urbidity
of those collo idal so luti ons befor e the NP cha rged at l ow pH, there by indicating t hat the strong tur-
bidity re sult s from huge mac roscopic structure s due t o a ggrega tion.
The complex ca n break down by charging the dimethyl amino moie ty of the polymer and t he in tense
ora nge color disappea rs. The protonate d amino groups will no longer be able to complex and instea d
elec t rostatica lly st abilize d col l oidal sol ut ions are form ed. Howeve r , the corre ct choice of the acid i s
important as the counter ions types has a signif icant influ enc e on the brush confor mation and cha rging.
The polyelec t rolyte brush cha rging and the copper re moval by d ialyzing the brush gra fted NPs is
much m ore effe ctive with following acids from left to rig ht: C H 3 C OOH > HCl > HBr and is i n t he
good agree m ent with re sults from Vlac hy et al based o n the Hofmeis t er ser ies. 11 8
To confir m our hypothe sis of the grafting density incr ease being mediated by the copper complexatio n
by P DMAEMA we stud ied the copper concentra t ion as a function of the amount of graf ted polym er .
Higher amounts of poly mer corr elate with more cha i ns per particle and thi s is proportional t o the
amount of copper which ca n be complexed. Drying t he SiO 2 @ PDMAEMA@Cu-agglomer ates with-
out further purifica tion and a subsequent combined S E M -EDX analysis of those agglomer ates kee ping
X-r ay ir radia tion area constant conf irms a n incr ease d copper amount with increa si ng gr afted pol ymer
(F igure 39d). The normaliz ed count rate Cu K α and K β t o S i conf irms our hy pothesis of t he influence
of copper on the gra fting densi t y (F igure 39 e) . 34
58
Figure 39 : a – c ) SEM- i mages of SiO 2 @PDMA EMA @ Cu- aggrega te s with the small e st core sizes d NP = 50 n m
for differ ent amou nt s of gr a fted polyme r: a) 4. 5, b) 5 .5 and c )11. 5 wt%. V isualizat i on of the exc i tation a rea fo r
local EDX- analysis as d a rk re c tangl es. Th e area w as tri ed to be kept consta nt as muc h as possib l e . d) Show the
corresp onding EDX spec tra of SiO 2 @PDMA EMA @Cu - agg regates for differ ent amoun ts o f gr afted po lymers
and e) norma lized Cu K α and K β v ersus the Si count r ate as a funct ion of graft ed p ol y mer. 34
In addition, i n some TEM-pictures those coppe r comple xes may be obser ved and interpr eted as ran-
dom dark dots with in t he polyme r shell. All samples fr om TEM analysis were purified using dialy si s
but i n the minority of core-shell structure s the cha rging of the polyme r may be incomple te. Nonethe -
less, the ma jority of t hose N P s show a perf ec t cor e-shell structure w ithout dark dot s as can be seen in
cha pter 4.1. 6 . Those dots resul t from l ess ele ctron beam transmissi on having t he origin from heavy
eleme nts with a hi gh electr on densi ty , where t he only r easona ble source lea ds to copper. 34
Figure 40: TE M -images of SiO 2 @ PDM A E MA-N Ps of d = 50 nm wi th di f ferent a m ou nts of gra f t ed poly m er. a)
referen c e sa mple as c ore-shel l -NP s (SiO 2 @PDMA E MA wi th 5.5 w t% graft) w i th out Cu-com plexes , wh e re t he
poly me r can be seen as a ligh t grey shell su rround ing t h e SiO 2 -core. b – d) sampl es showi ng occasiona l d ark ar ea s
within the po lymer shell. For clar ificatio n the dark are as ar e mark ed wit h arrows . 34
59
4.1.6 Transmission electro n microscopy analysi s
Figure 41 : T EM p ictures of SiO 2 @PD MA EMA-NPs with c o re dia m eter d NP = 50 nm: a) a nd b) c ) As a r eferen ce
SiO 2 -NP s. SiO 2 @PDMA EMA a t diff e rent polym er grafts : d ) 3.0 wt %; e ) 5.5 wt %; f) 7.0 w t%; g ) 11.5 wt% .
For a bett er dist inction b e tw een po lymer and SiO 2 the contra st was e nh anced usin g the softw are Imag e J. 34
In Figur e 41 – Figure 43 are TEM pic tures of S iO 2 @ Poly mer-NPs shown . For a bette r view the contrast
was m odified to d ist in guish the SiO 2 core (dark) fr om the polymer shell (gr ey). The prese nce of cor e -
shell SiO 2 @Polymer ca n be observed. As expec ted, po lymers i n dried are collapse d and have much
smaller shell th icknesses compare d in a queous solution. S imilar to pr evious d iscussed results the pol-
ymer shell thickne ss of Si O 2 @ P DMAEMA-N Ps is constant (mean dry polymer thickne ss of
t shell,dry ~ 6 nm) a lthough t he gr afte d a mount of polyme r inc rea ses. I n c ontrary, f or S iO 2 @PMAA-N Ps
is a m ea gre polymer she ll thi ckne ss gain w i th ra isi ng gr afte d amount of polym er per NP ca n be ob-
serve d ( t shell,dry ~ 3 – 10 n m). In all pictures N P s exhibit aggre gation. Howe ver, li ght scattering confirms
single particles thus, observe d particle agglomera t ion r esults from drying ef fec ts from sample prepa -
ra tion. Furthe rmore, polymer fusion of some single particle s (Figur e 41a) and b)) i ndica te the com-
bined of the c hain -c hain radic al te rmination of poly meri za tion of two nea rby pa rticles as an unwa nted
side reac t ion of an AT RP but the ma jority of NP s have a m ore over spher ical core shell morpho logy.
60
Figure 42 : La r ger SiO 2 @ PDM AEMA-N Ps w i th d i fferen t a m ount of gra f ted poly m er . T op : d NP = 70 nm: poly-
mer graf ti ng content: b) 17 . 5 w t%, c) 20.5 wt %, d) 23.5 wt%, e) 28 . 5 w t%; botto m : d NP = 140 nm: polym er
grafting co ntent : b ) 27.5 wt% , c) 28 wt %, d) 3 1 . 5 w t%, e) 33.5 wt% ; a) S iO 2 as re f e r ence and from b → e t he
amount of gra f ted polym er i n c r ea ses . For a better distin ctio n bet w ee n poly mer a n d SiO 2 the c o ntrast was e n-
hanced using t he softw are Imag e J. 34
Figure 43 : L arger S iO 2 @PMAA -NPs wit h d ifferen t a moun t of gr afted poly me r . Top: d NP = 70 n m: poly me r
grafting cont ent: b) 4.5 wt %, c) 3.0 wt %, d) 13 .0 wt%, e) 14.5 wt%; b ottom : d NP = 140 n m: polymer grafting
content : b) 1 . 5 wt%, c ) 4.5 wt%, d) 6.5 w t%, e) 7 . 0 wt%; a) SiO 2 as refe rence and fr om b → e the amount of
grafted poly m er incre ases. For a b etter distinc tion be tween polym er and SiO 2 t h e contr a st w a s modifi ed usi ng
the softw a re I m age J. 34
4.1.7 Anal y sis o f polym er graft e d NPs via SANS
SANS mea surements allowed to obtain detailed st ruc tur al information on the po l ymer structure . We
per formed an exter nal contrast variation (using H/D wa t er ) to m atch com pletely t he silica core and
there fore onl y see the polymer shell. We measure d cationic and anionic brush graf ted NPs w ith the
smallest core si ze d NP = 50 nm at constant pH 4 or 9, r espec tively. Prior i nto discussing t he S A NS -
data we estim ate the absolute values of the sca ttering le ngth densi t y of all com pounds .
4.1.7.1 Sca tte ri ng l ength d ens ity valu es es ti ma tion
Due t o the de- a nd protona tion potential of both polyele ctrolytes the e xac t η po lym e r is d i ffic ult to c alcu-
late in absolu te prec ision. Howeve r, we estimated η polym er as most as po ss ible for P DMAEMA and
PMAA for absol ute values at differ ent contrast condi tions.
61
Figure 44 : Shown is t h e prot onation equi li br ium f or PDMA EM A in a H 2 O/D 2 O mi xture.
Fr om the SLD calculator provided from NIST η values are calc ulated: 107
η PDMAEMA = 0.945 ∙ 10 – 4 nm – 2
η PDMAEMA,H + = 0. 75 2 ∙ 10 – 4 nm – 2 (proto nated)
η PDMAEMA,D + = 1. 21 6 ∙ 10 – 4 nm – 2 (deuter ated)
We used H 2 O/D 2 O mixture s, so an H t o D exc hange ca n occ ur. Depe nding on t he solvent ra tio, now
assuming D 2 O/H 2 O ( V / V = 0 .58/ 0 . 42), the aver age η PDMAEM A,H + ,D + was assumed to be g i ven as:
𝜂 PD MAEMA H + ,D + = 𝑉% H + ∙ 𝜂 PDMAEMA H + + 𝑉 % D + ∙ 𝜂 PDMA EMA D +
eq. 89
𝜂 PD MAEMA H + ,D + = 0. 58 ∙ 1. 216 ∙ 10 – 4 nm −2 + 0. 42 ∙ 0 . 752 ∙ 10 – 4 nm −2 = 1. 0211 ∙ 10 – 4 nm − 2
Due to very high counte r ion conc entra tion in the brush , the degr ee of protonatio n in a brus h i s lowe r
than in solution . Here we assume 97% degre e of ionizati on at pH 4 (p K a PDMAEMA ~ 7. 4) so t he re sulting
SLD at pH 4 is:
𝜂 PD MAEMA H + ,D + = 0. 97 ∙ 1. 0211 ∙ 10 – 4 nm −2 + 0. 03 ∙ 0. 945 ∙ 10 –4 nm −2 = 1. 0188 ∙ 10 –4 nm −2
eq. 90
Same calcula tion s we re done for PMAA, assu ming a de gree of ioni za tion of 0.9 for PMAA brushes .
Note, t hat degre e of ionization within the polymer brus h is di ffe rent t o the degree of i onization in the
bulk solution. 75 The scattering densi ties are sum marize d for diffe rent solvent conditions in Table 8.
Table 8 : Scat te r i ng length d e nsi ties of used p olymers in d i fferent solven t cond i tions with high o r
low degr e e of ioniz ation .
mater ial
Sum formu l a a dded
in NIS T
ρ [g/cm 3 ]
D 2 O/H 2 O
( V / V )
SLD [n m – 2 ] ∙ 10 – 4
SiO 2
SiO 2
2.2
–
3.4750
PDM AEMA (protona ted, D 2 O)
C 7 H 13 NO 2 D
1.19
0.80/0.2 0
1.1178
PDM AEMA (protona ted, CM)
C 7 H 14 NO 2
1.19
0.58/0.4 2
1.0188
PDM AEMA (deproto nated , dry)
C 7 H 13 NO 2
1.19
–
0.9450
PMA A (proto nated , D 2 O)
C 4 H 5 O 2 D
1.19
0.80/0.2 0
1.9856
PMA A (proto nated , CM)
C 4 H 6 O 2
1.19
0.58/0.4 2
1.8003
PMA A (deproton ated, D 2 O)
C 4 H 5 O 2
1.19
–
1.6736
PMA A (deproton ated, CM)
C 4 H 5 O 2
1.19
–
1.6578
D 2 O/H 2 O ( V / V = 0.8/0 .2)
–
1.08
–
5.0034
D 2 O/H 2 O ( V / V = 0.58/ 0.42)
–
1.05
–
3.4748
Full contra st condit ion ( V D2 O / V H 2 O = 0.8/0.2); contra st matc h conditions (CM) ( V D2 O / V H2 O = 0.58/0.4 2)
The density of the polymer wa s est imated by mea suring the density of self -synthe sized PDMAE MA
solution (same re ac tion conditi ons exc ept they wer e not surfa ce initiated, but the po lym er ization too k
62
place in so luti on) at sever al conce ntrations and approxi mat ed t o pure po l ymer fr om the linear extra p-
olation with the density for P DMAEMA ρ PDMAEMA = 1.19 g/cm³ . 34
The value s for η we re used to ca lculate the scatte ring in tensit ies .
Figure 45: Lef t) measure d d ensity of PDMA EMA as a func t io n of th e weigh t c oncen t ration ; r ight) D egree of
ioniza ti on of PDA E MA a nd PMAA . 34
The degre e of ion ization was obt ained via ti tratio n of both polymer s. P MAA sodi um sal t is a com-
merc ial polym er (Si gma Aldrich) with a molecula r weight of 5100 g/moL (degr ee of polymeriz a-
tion = 51). The self-synthesize d PDMAEMA was taken, wher e m olec ular weight and degree of
polymeriza t ion are unknown . 34
4.1.7.2 SANS of pur e SiO 2 - NP
Prior into model ing the poly mer graf t ed N P s the values of the silica core such as size and polydisper -
sity wer e calc ulated using a sphere form factor fit. The radius of the silica core and i ts polydispe rsity
wer e t ake n from the SANS data of the pure SiO 2 -NPs in full contra st using a spherical form fac tor
given by R NP = 24.3 , 32. 6 and 70 .3 nm and P DI = 0.11, 0 . 11 and 0.12, which wer e kept constant for
furthe r modeling.
Figure 46 : SA NS data (dots) of pur e s ilica n anop articles w ith corr esponding sph ere f orm factor f it (dark line) . 34
63
4.1.7.3 Core-shell-form fa ctor
Figure 47 : Shown is a) a c ar toon of poly m er graf t ed NPs, where uniqu e pol y mer c h ains have differ ent c hain
lengths r esulting in a s chem atic e xp onenti a l pol y mer dens it y dec r eas e wi th i ncreasi ng s urf ace d i stan ce. b ) Sc a t-
tering leng t h density η pro fi le for a sph erical core-sh e ll for m factor mode l wi th di fferent de caying sh e ll prof iles
(purple (t o p): η shel l profile for V D 2O / V H 2 O = 0 .80/0.2 0 a s an e xam p le for full contrast condit ions and da r k (bo t-
tom): η shell profi le fo r V D2O / V H2O = 0.58/0 . 48 as a n e xa mple for CM- c ond i tion, c ) sch ematic c o nt r ast cartoon
relat ed t o the purp le and dark η shell profi l e a n d i n d) neutron count r ate (SD = 20 m) plot te d a s a functio n the
volu me fraction of D 2 O. 34
The obtained SAN S data are di splayed in F igure 48 f or SiO 2 @PDMAE MA with 5. 5 wt % grafted
polymer and in Figure 51 as well as Figure 53 and Figu re 54 and S iO 2 @ PMAA systems i n Figure 52
and Figur e 55 . Look i ng at the data displaye d in Figur e 48, one fin ds, that in bulk contra st ( Figure
48a) one see s very well t he form fa ctor oscillation that indica t es the high monodispersit y of the NPs,
while in t he pol ymer contr ast (contra st m atch , Figure 48c) one see s a m ono t onous decr ease of the
sca ttering int ensity t hat is stee per than a q − 2 law as would be expe cted for a simple shell structu re .
Howe ver, e specially the polymer contrast is ver y sui t ed for ga ining informa tion rega rding the scatter -
ing l ength distribut ion in the polyme r shell and there fore about the polymer density profile. In litera -
ture, a sigmoida l segment density profi le is desc ribed for poly mer brushes i n good so lvent cond itions
anc hored at flat surf ace s (for deta ils see chapter 1.2.7. 3). 7 6 Howeve r, with i ncr easing curva t ure t he
segment density is expe cted to decay expone nt ially t ow ard the continuum in good sol vent conditio ns
for t he pol ymer density . 77 – 82 W e use d a sphe rica l core -shell form fac tor w here the si ze , polydispersity
and scattering length density of the core η core were fixe d by the values obta ined from approxi mated
sca ttering intens it y of pure S iO 2 -NPs by u sing a spherical form fa ctor model . For the sc attering length
density of t he shel l variation we empl oyed as d iffer ent functions of the di s tance l inea r, re verse expo-
nential or an expone ntial re lation. ( Figure 47) . The dec ay of t he scatte ring lengt h density of the shell
η shell is desc ribed by t he par amete r α wh ile the volume frac tion at the core radius X C and shell t h i ckne ss
X shell influenc es η shell , R c and η shell , R c+ t s hell , i . e . , lat ter is set to 1 assuming fully deca yi ng η sh ell to η solv e nt . 89
To test the valid i ty of an exponential deca ying scatte rin g l ength densi t y within the shel l , the data was
fitted by kee ping the inte nsit y at low q constant for the three diffe rent shell types: cons tant ( α = –∞),
linear ( α = 0) a nd e xponent ial ( α > 0) η s hell deca y towards t he solve nt. T he volume fr action of w ater a t
the core radius X C increa ses wit h constant shell > linear shell > exponential shell. Thus, we have in
total two free para meter s with α descr ibing the vol u m e fra ction deca y and X C for adjusting the scat-
tering i ntensity to the int ensit y of the data in t he l ow q -regime otherwise we would increa se the amount
of the polymer in the shell with constant she ll > l i nea r shell > exponent i al shell. A ll o ther par ameter s
wer e fixed. Diff ere n ce s from the approximation and t he data can be observed in the hi gh q regime
( q = 0 . 2 – 1 nm – 1 ) afte r subtra cting the bac kground. 34 For c ontrast ma tch ( CM) a nd full contra st condi-
tions t he expone ntial shell approxi mates mo st acc urately the measure d da ta a s seen from the re si duals
which bec ome smallest for the expone ntial approxi mation (Figure 48).
64
Figure 48 : Compar ison of th e di fferent sc a tteri ng l eng th d ens ity p rofiles f or th e e xamp le o f SiO 2 @PD MAEMA
with 5.5 wt % of gr afted poly m er. a) sc atter ing data (dots) wit h differ e nt m odels of t h e sh ell profi les (lines) a nd
b) co rre spo nding r esiduals in in CM-condi ti o ns a nd c) s c att e r ing d a ta (dots) with diff e rent mod el s (lines) and d)
corresp onding r esiduals in full co ntrast co ndit ions. 34
For further data modeling to m inimize the degre es of fre e par amete rs previous obt ained results are
re specte d in the approximat ion for examp l e the est imat ed shell thi ckne ss bu t some tole ranc es i n t he
shell thi ckne ss were allowed. The scattering cur ves lo ok a lmost identical but t her e is evidence for
aggr egation seen in low q -regime, whe re t he i ntensity i ncre ases further . Ther ef ore, we employed a
fra ctal model i ntroduce d by Teixeira et al. to acc ount for that. 90 For all polyme r graf ted samples α
typically has pos itive values of 3 – 10 and desc ribes an e xponential η shell deca y (see Figur e 49, Table 9
and Table 10). F or SiO 2 @PMAA the volume frac tion at the core is r emar kable constant with inc rea s-
ing polym er gra fting but α i ncr ease s respectively. In contra ry and di ff e re nt to the anionic NPs for
SiO 2 @PDMAE MA the volume fra ction of the solvent a t the core surfa ce X C decr ea ses with i ncr easing
amount of grafte d po l ymer and thus confirming an incre ase of the graf ting density . C om paring the fit
re sult s from bo t h contrast t he absolute values diffe r but show t he same trend towards incre asing po l -
ymer gra fting (Figure 49, Table 9 and Table 10) . Simi lar trends can be observed from the data for
bigger nanopa rticles ( d = 70 and 140 nm) respec tively . In gener al, at CM conditions we see only a q –
2 depe ndenc y over the whol e q -ra nge for the scattering i ntensity, wher e the theore t ical oscillation of
the shell form fac tor is completely s mear ed out due t o instru mental s mear ing and in reality , have a
more complex for m fa ctor, where also additional polyd ispersity of par amete rs is prese nt. 34
65
Figure 49 : F it param eters from SANS m od e ling for SiO 2 @P DMAEMA a nd S iO 2 @PM AA core-sh ell st ructures
( d = 50 n m ) i n contr a st match η co re = η s olvent ( ▲ S iO 2 @PDM AEMA, ● SiO 2 @PMAA ) and full c on trast condi-
tions η core < η s olvent ( △ SiO 2 @PDMA EMA, ○ SiO 2 @PMAA ) ; Plo tted a re the a) radius o f t he core -sh el l NPs R ,
b) volum e fra ction at th e core X C , c ) the ex ponenti al d iffuse parameter α versus th e amount of gr afted poly m e r.
Note th at at 0 wt % is the core radius of p ure sil ica nan oparti cles. 34
In par allel to modeling the core-she ll structure s , we d i d some model fr ee analysis. In full contrast
conditions we s ubtracte d the sca t tering intensity of the Si O 2 -NPs from that of the SiO 2 @Po lym er da ta
to gain a p seudo shell-form factor (Figure 50a,b; this is neglec ting all scatter ing cross-terms and there -
fore can only be conside red t o be a very rough approxi mation of the rea l ly sca ttering of the polymer
shell). Direc tly observable for anionic samples the mi ni ma ar e shifted towards lower q -values wit h
incre asing pol y mer graf ting, wh ich is in good agree m ent with the LS data, and indic ates an i ncr eas-
ingly thi cke r polymer shell. In comparison for catio nic NPs the first mi ni mum re mains remar kably
constant at q = 0 . 126 nm – 1 . Thus, th is is a direc t confirma tion for t he incre ase of shell thickness for
the anionic versus cation i c NPs, wher e the she l l thic kn ess i s al m ost constant. The aver age radius of
the S iO 2 @PD MAEMA shell ca n be c alculated (using a thin shell form factor ) wit h
R = π/ q min = 2 4.92 nm indicatin g that t he m ass aver age of the shell is rather cl ose to t he core radius .
Figure 50 : a, b) SANS i n t ens it y of co re shel l s tructur es after subtr a ctin g the sca ttering intensi ty o f t he SiO 2 -
NPs. 34
66
Table 9 : sum marized v al u e s fro m SAN S d ata m o del i ng for SiO 2 @PDMA EMA and
SiO 2 @PMA A-NP s at both contr a st c on di tions for d = 50 n m. For the fo rm f ac tor: po lymer graft
content X polymer , w eight conc e ntr ation c g , particle number d ens it y 1 N , sh e ll t hickn e ss t shell , po ly me r
volu me fra c tion at th e core ra d ius X C , expo ne n tial de cay rate α , for th e st ructure factor: rad i us of
individu a l sca tterer R i n d , cut off si ze R f and f ract al dimens i on coefficien t D f .
SiO 2 @PD MAEMA @ pH4
X poly mer
c g
1 N
t sh e ll
X C
α
R ind
R f
D f
wt%
g/L
cm – 1 ∙ n m – 2
nm
nm
nm
η core = η solvent
3.0
3.4
0.219
9.6
0.54
4.01
32
108
2.95
5.5
4.0
0.252
14.2
0.49
3.90
36
128
2.73
7.0
3.4
0.212
14.2
0.42
4.39
37
120
2.89
11.5
4.2
0.252
15.5
0.37
2.35
40
141
2.43
η core < η solvent
3.0
1.3
0.090
9.5
0.55
4.78
35
106
2.27
5.5
2.4
0.149
13.5
0.50
5.50
40
128
2.50
7.0
2.1
0.129
13.8
0.46
5.46
–
–
–
11.5
3.2
0.195
15.4
0.37
4.74
39
110
2.80
SiO 2 @PM AA @ pH 9
η core < η solvent
2.5
2.0
0.133
13.3
0.45
2.82
40
121
2.70
7.5
2.6
0.160
19.8
0.48
6.65
43
110
2.63
11.5
2.1
0.127
23.0
0.45
8.85
–
–
–
13.5
2.9
0.172
29.2
0.47
12.96
34
130
2.88
η core < η solvent
2.5
1.3
0.085
13.6
0.45
5.49
38
120
2.60
7.5
1.4
0.085
19.8
0.48
8.85
44
150
2.30
11.5
1.5
0.091
24.0
0.45
11.78
40
122
2.89
13.5
1.0
0.062
29.8
0.47
16.10
50
194
2.87
67
Figure 51 : SiO 2 @PDMA EMA f or d = 50 nm at a,b) η core = η s o l vent a nd c,d) η core < η solve n t condi t io ns at pH 4. The
data is shown i n absolute scale (left) and for b e tter legibi lit y shifted wi th a cumu l ativ e factor of 10 for e ach
scatter ing c urv e (ri g ht). Mod e l ed sc attering in tensit ies a re sho wn as dark l i ne s for poly me r grafted nan opa r t icl es
and as a red line for si l ica na n opa r ticles. Da ta measur e d at K WS -1. 34
68
Figure 52: S iO 2 @PMA A for d = 50 nm a t a,b) η core = η solvent and c, d) η core < η s olvent cond itions at pH 4. The dat a
is s hown i n absolute s cale (lef t) and for b e tter legibi lity s hifte d w ith a cu m u l ativ e factor of 10 f or each sca ttering
curve (right) . Mod eled scat te r ing intensit ies are show n a s dar k l ines for poly m er gra fted nanopa rticl es an d a s a
red line for silica nanop articles . D ata me asured at KWS- 1. 34
69
Figure 53 : SiO 2 @PDMA EMA f or d = 70 nm at a,b) η core = η s o l vent a nd c,d) η core < η solve n t condi t io ns at pH 4. The
data is shown i n absolute scale (left) and for b e tter legibi lit y shifted wi th a cumu l ativ e factor of 10 for e ach
scattering c urv e (ri g ht). Mod e led sc a tter i ng in t ens ities are sho wn a s dark l ines for pol y m er gra f ted nan oparti cles
and as a red l ine for si l ica nanopar t icl es . Da ta measur e d at D 11. 34
70
Figure 54: SiO 2 @ PDM A E MA for d = 140 n m at a, b) η co re = η solvent and c,d) η core < η solvent c ond itions at pH 4.
The d ata is show n in a bsol ute scale (left) a nd fo r be tter l e gibi li ty shifted w ith a c umula ti v e fa ctor of 1 0 for each
scatter ing c urv e (ri g ht). Mod e l ed sc attering in tensit ies a re sho wn as dark l ine s for pol y mer graf ted nanopar ticles
and as a red l ine for si l ica nanopar t icl es. 34
71
Figure 55 : SiO 2 @PMAA f or d = 140 n m at a , b) η co re = η s olvent and c ,d) η c ore < η solvent conditions a t pH 4 . The da t a
is s hown i n absolute s cale (lef t) and for b e tter le g i bili ty shif t ed w it h a c u mula tive fa c tor of 10 f or e a ch s cattering
curve (right) . Mod eled scat te r ing intensit ies are show n a s dark lines for poly m er gra fted nanopa rticl es an d a s a
red line for silica nanop articles . 34
72
Table 10 : su mmarized va l ues fr om SAN S da ta mod eling for SiO 2 @PDMA EMA a nd
SiO 2 @PMA A-NP s at both contr a st condi t ions for d = 70 and 140 nm . For th e fo rm f actor : poly-
mer graf t content X poly mer , we ight conce ntration c g , particl e num b er densit y 1 N , sh e l l th ickness
t sh e ll , p olymer vo lume fra c tion a t t h e core radius X C , expon enti al decay rate α , for the str ucture
factor: r a dius of ind ividua l sc a tter er R ind , cu t off size R f and f ractal d imensio n coef ficient D f .
X poly mer
c g
1 N
t sh e ll
x C
α
R ind
R f
D f
wt%
g/L
cm – 1 ∙nm – 2
nm
nm
nm
SiO 2 @PD MAEMA @ pH 4
d = 70 n m
η core = η solvent
22.0
5.8
0.109
10.6
0.55
4.43
46
171
2.63
28.0
4.8
0.089
13.1
0.50
4.87
49
165
2.78
32.0
5.2
0.090
14.9
0.45
5.32
50
143
2.73
33.0
6.4
0.117
16.1
0.34
4.60
50
143
2.50
η core < η solvent
17.5
2.8
0.053
10.7
0.55
13.00
48
177
2.72
23.5
2.5
0.045
13.0
0.50
13.00
48
128
2.64
27.5
2.4
0.042
14.1
0.46
13.00
51
155
2.90
28.5
3.3
0.057
16.1
0.38
13.00
52
194
3.12
SiO 2 @PD MAEMA @ pH 4
d = 140 n m
η core = η solvent
17.5
1.4
0.0024
12.5
0.50
1.65
–
–
–
23.5
1.8
0.0031
14.2
0.48
1.75
–
–
–
27.5
1.4
0.0023
15.4
0.43
2.03
–
–
–
28.5
2.6
0.0043
15.6
0.30
1.07
–
–
–
η core < η solvent
32.0
0.7
0.0012
12.1
0.54
6.00
–
–
–
33.0
0.6
0.0010
14.1
0.48
6.60
–
–
–
36.0
0.7
0.0011
14.5
0.42
6.00
–
–
–
38.0
1.1
0.0018
15.1
0.30
5.00
–
–
–
SiO 2 @PMA A @ pH 9
d = 140 n m
η core = η solvent
6.0
3.9
0.0083
12.3
0.51
2.43
–
–
–
10.0
4.8
0.0099
18.4
0.52
6.95
–
–
–
11.0
5.2
0.0106
25.2
0.48
8.35
–
–
–
11.5
5.4
0.0109
29.0
0.52
13.63
–
–
–
η core < η solvent
1.5
2.1
0.0045
11.2
0.51
6.78
–
–
–
4.5
2.8
0.0058
18.9
0.52
7.64
–
–
–
5.5
2.7
0.0055
26.0
0.50
9.65
–
–
–
6.5
2.6
0.0053
29.3
0.51
14.50
–
–
–
73
4.1.8 Degraft i ng dif ficul tie s
Figure 56 : D egrafting s t ra te gy with HF.
To determine the graf ting density of the polymer brush es gra fted onto the surfa ces of those nanopa r-
ticles we t ried to clea ve t he chains from t he surfac e. Mild clea ving agents for examp l e T BAF failed
to cleave P DMAEMA in wa ter, so we decided to use HF which succ essfully etche d t he S iO 2 -core
from t he N Ps. Imp ortant cons i der able side produc ts ar e SiF 4 , wh i ch is highly water soluble and still
re maining fluoride ani ons. Latter had to be deac t ivated by adding a saturate d Ca C l 2 solution into the
mixture leading to an im mediate CaF 2 precipitate by subseque nt separ ation with a gentle centr ifuga-
tion while keeping t he supernata nt solutio n. Drying of the superna tant soluti on wa s absolute ly avoided
as SiF 4 is very toxic in gaseous sta te. Thus, the strong acidic aque ous sol u tion (~ pH 0.5 – 1) was t hen
neutra lized by addi ng an excess am ount of sodi u m hydr oxide and at pH 8 we saw by optical inspection
a precipitation of “soft and less dense” m ate rial indica ti ng the expe cted polym er P D MAEMA. The
polymer was separa ted from the superna tant sol ution washed with water as we know that at basic
conditions the pol ymer should be le ss soluble. F or SiO 2 @ PMAA the pH adjusting s tep w as ne glecte d
bec ause at that pH range PMAA should be completely protonated. Then the polymer wa s dried with
the aim to transfe r the polymer to organi c so lvents suc h as THF, which is com m only used as fluid
phase i n a typical SEC -mea surement. Howeve r, ju st by opt ical i nspec tion of the dried polymer t he
mater ial showed high dense w i th solid material prope rties ind icating a huge content of salt. Thus ,
bef ore dissol ving our expe cted polyme r i n THF we ana lyzed the solid material by IR and EDX indi-
ca ting, that the m ajority of the material is related to Ca / Na and Cl, those elements having the origin
from the nec essar y purification’s st eps. Particular coun terions for clea ved polym er (PDMAEMA →
Cl, PMAA → Ca) show the highest count ra tes in the EDX -mea sureme nts. Howeve r, some of the
counter ions prefe r to be l oca ted closely at hi gh ly char ged polymer chains and once the pol y m er i s
elec t roneutr al i t re markably leads to addi t ional salt prec i pitation (polymer sal t comple x) which then,
and this i nexplica ble, cannot be remove d w ith furthe r w ashing c ycles with wate r or diffe rent solvents.
Additionally, the dense materia l wa s t hen mi xed with di ffere nt solvents (me thanol , etha nol, THF,
toluene) with t he aim to separ ate t he pol y m er from the s alt but af ter drying t he super natant no polyme r
could be measure d with IR or EDX-spectrosc opy as we l l.
74
Figure 57 : Sh own are EDX- sp ectra of “cl eaved p ol y mer -salt- compl e x ” for left: SiO 2 @PDM AEMA and righ t
SiO 2 @PMA A.
Figure 58 : Pi c ture take n from camera imp lemente d in the EDX i nstr ument for SiO 2 @PMA A.
75
4.1.9 Dy e lab eling o f SiO 2 @PDM AE MA-NPs
Fi gur e 59 : Fluo res cein O-meth acrylate ( FOMA) .
One attra ctive metho d to func tionalize polyele ctrolyte b rushes with a dye can be done b y i mplemen t-
ing s mall amou nt of l u minesce nt repe ating units w ithin t he p o lymer chain backbone. Thus , i n order
to label t he cor e shell nanoparticle s w it h 50 nm di ame ter we dec ided to propa gate DMAEMA and
fluore scein O methac rylate (F OMA) simultaneously , whe re the FO MA content varies betw een 1 –
10 m ol% . We kept the total amoun t of monomer constant, which corre sponds to a monome r to silica
ra tio of 38 . 4 and thus to the highest amount of gra ft ed polym er st udied i n thi s work . Dye labe ling of
SiO 2 @PMAA- NPs was not successful, presumably du e to the har sh rea ction conditi on in the hydro-
lyzation ste p from t Bu MA i nto P MAA . Fluore scein has an excitation w avele ngth maximum at
λ ex = 490 nm. The fluoresc ent spectrum is st rongly pH s ensitive , wh ich is in good agree m ent with data
pre sented in Figure 60 . Al l samp le show an emission m aximum a t λ em = 518 and c onfirms the success
of the i mplementatio n of t he dye within the polymer she ll. At pH 4 a str ong reduc ed emis sion int ens it y
compar ed to pH 6 can be seen. Furthe rmore, data exhibit an increa sed i ntens it y with increa si ng FOMA
content.
Figure 60 : Fluor e sc ent intensi t y as a fu nction o f w avelength f or S iO 2 @PDM A E MA-N Ps a t left) pH 4 and right)
pH 6. The FOMA con te n t is show n in mol%. Me asur emen ts wer e p erformed o n NP so l ution conc ent r ation of
c NP ~ 0.05 w t%.
76
4.1.10 Poly mer mod ification on smaller NPs with diamete r o f 17 nm
Rece ntly Michél et al. i nvest igated the i n t er action of s mall hard nanopar ticles (NP d i amete r 17 nm)
with ve sicles of dia meter around 50 nm. 24 To compar e the inter action of s oft na noparticle wi t h r esult s
from the li tera ture, it mo tivated us to do a surfa ce ini tia t ed ATR P on commercia l Ludox HS40 si lic a
NPs . The size and polydispersi ty of bare si lica-N Ps wa s determined via SAX S and show a radius of
R NP = 8. 4 nm wi th a PDI of 0. 206.
Figure 61 : SAXS-da t a of com m erci al Ludox HS40-NPs. Data me asured wi t h SAXS ess mc2 instrum e nt.
Surfac e modifica tion and surfa ce polymeriz ation wa s d one in a simi lar fashion a s pre sented in Figure
30, wher e ATR P was do ne with Cu(I) Br as ca talyst and P MDETA as liga nd in MeOH water mix ture
( V / V = 1:1) kee ping the SiO 2 @Br-N P conce ntration lo w to avoid fusion of poly mer chains from t wo
or more particles. Polymeriza tions were car ried wit h high molar ratio of monomer t o i n i tiator mole-
cules and the mono m er conc entration wa s varie d fr om ( c = 2 . 4 – 122 m m ol/L) per reac tion batch kee p-
ing tempera ture, catalyst and S iO 2 @ Br-NPs concentr a tion constant. Afte r the rea ction the polymer
coa ted S i-NPs wer e transfe rre d into wate r using dialysi s. We employ ac ryl amide and D MAEMA as
monomers. Polym er coated particle were ana lyzed by sca t tering (light, SAX S ), ζ – pote ntial measur e-
ments and TGA analysis .
Figure 62 : Cart oon of polyme r graf t ed NP s wi th core diam eter of 17 n m .
77
For both m on omers the am ount of grafted po l ymer ca n be controlled via the mo nomer conc entration
(F igure 62 a) and b)). Note, that data i s prese nted as a ra tio of adde d mass of m onomer versus the
mass of silica nanopar ticle. Acr yl amid yi eld s a water soluble non ioni c polyme r on t he N P surfac e
(SiO 2 @P AM , (Figure 62) . With increa sing m ono m er co ncentra tion, the ζ -potential of t he SiO 2 @ PAM
dec reases (Figure 63) and confirms t he success of the c ontrol over the amou nt of graf ted polyme r via
the monomer conc entration . In contra st, P DMAEMA re sults a ca tioni c polymer at sol u tion pH 4 ,
wher e the ζ - potential va lues a re consequently posi ti ve , si milar t o re sults pr esente d in 4 .1.4. 34 T he size
of cor e shell structure s was dete rmined via light sca tteri ng and value for R H are huge compar ed to bare
N Ps (see Figure 63), i ndicating aggl omeration . Howeve r, data exhibit s maller R H values for the
SiO 2 @PDMAE MA compar ed to SiO 2 @PAM presuma bly due to electrostatic sta bilization . Further -
more, t he extend of R H for S iO 2 @ P DMAEMA is not a function of the amount of graf t ed polymer, in
good ga rment w ith results i n 4. 1 . 4 . In c ontrast , for Si O 2 @ PAM-NPs val ues for R H ar e incre asing with
incre asing monom er conce ntration. We interpre t , that SiO 2 @PAM-NPs show a strong cluster ing ten-
denc y (SiO 2 @PAM have value s for R H = 180 – 230 nm c ompare d to NP core R c = 8.4 nm) . Aggre gates
could not be remove d by filtration , power ful soni ca tion or by deca ntation of the supernata nt solution
(sample solut ion stayed up to 8 h hours).
In summary, the s maller NP s can be polymer coa t ed but one must cons i der st rong aggre gation. In
gene ral, with dec rea si ng c ore di amete r the c lustering te ndenc y incr ea ses. Some of the a ggre gates may
vanish once a po l yelec t rolyte is gra fted on the NP surfac e.
Figure 63 : Fo r SiO 2 @ Pol ymer modifi ed NP wi th core diam eter of 17 n m. re l a ti v e m ass los s as a fun ction of th e
temper at u re f or a) SiO 2 @PA M-NP s and b) SiO2 @ PDM AE MA-NP s. c) hy drodyn amic ra d ii, d) ζ -p otent ial va l -
ues at pH solut i on 4.
78
4.2 Mem brane – NP i nte r action
Figure 64 : Top left: mo lecular stru ct ur e of th e zwitterion ic D OPC and anio nic DMPA phospho l ip ids employ ed
for a n ionic v e sicle formation v ia e xt rusion . Top r ight: cartoo n o f SiO 2 -NPs used in this st udy wh i ch are diff er-
ently surfa ce modifi e d by a nionic ( – OH) , c ationic ( – NH 2 ) moieti e s or brush grafted polyelec trolyt e ( –
PDM AEMA). B ottom : cartoon of combi ning the inter action with m od el me mbranes and the NPs . The spont a -
neous form a tion of a suppor t ed l ipi d bilayer from a vesicl e s ol ution on a sil ica sur face and it s inter action wi t h
the NPs was studied i n situ vi a the QCM-D t echn i qu e .
The centra l part of the work was the investigation of t he int er action betwe en model membrane s as
anionic supported lipid bilayers (SL B) and cationic po lymer grafted o r surfac e modi fied sili ca N P s.
Polym er graf ted NPs ar e intere sti ng bec ause t he parameter “sof tness” , controlled by the poly mer shell
via a systemat ic variation of t he gra fting dens ity modulate s t he eff ective softness c ontrol , there by
modulating the additional st eric repulsio ns in the syste m (see chapte r 4 .1.3). The N P char ge densit y
bec omes tunable by t he graf ting density or pH as the amino group is positively cha rged under ac idic
conditions and bec omes more neutral at higher pH (see chapter 4. 1.4) . We varie d the amount of graf ted
polymer (here it has to be not ed that at large r amount of polymer does not mean necessa rily longer
polymer chains), b ut an increa si ng graf t ing densi ty, pH, charge density of the S L B , and t he conce n-
tration of the SL Bs in orde r to gain a compre hensive un der standing of th is system .
An attrac tive method to analyze t hese in tera ctions i s t h e quartz crysta l microba lance wit h diss ipation
monitoring (Q CM -D). A huge advantage of t hat tec h ni que is a reliable and quick confirmati on of
supported lipid bilaye r formation on a substrate by a typica l time depe ndent fre quenc y Δ f and dissi-
pation shift Δ D patter n. 11 9 ,1 20 The subse quent N P adsorption ca n be ea sily studied i n situ via QCM -D,
wher e we have a 2D model syste m. In addition, in our expe riments the S L B charge density was ad-
justed b y t he ratio of zwitter ionic and an ionic phospho l ipids DOP C and DMPA. In our exper i ments
we varied then syste matically the siz e of the conta ctin g NPs, their sur fac e char ge, a nd by the poly mer
modification als o the surfa ce and the softness of the polymer shell .
79
4.2.1 Spon tane ou s su p ported lipid bilayer fo rm ation
Figure 65 : T o p: QCM-D- measure ments for supp orted lipid bi layer form a tion for d i fferen t charge d ve si cles
(black frequen cy shif t and r ed dissi pation shi ft). Bot tom: Po ssible inte raction mech a nis m after su ccessful SLB
formati on f or le f t ) DOPC/DM PA 98 / 02 mol% or rig ht) DOP C/ DMPA 95/05 m o l%.
The mechanism of the SLB formation is described in detail elsewhe re. 119 ,1 20 How ever , spontane ous
SLB formation is favor ized if t he vesicles size and t he electrosta tic interac tion betwee n t he vesicles
and the surfa ce is reduce d as much as p ossi b l e. Fur thermore , the proper choice of the surfac e i s im-
portant, where the most probable spont ane ous S LB form ation i s observe d on S iO 2 surfa ce in liter ature .
Thus, w e used vesicle s w ith a di ame ter of 100 nm disper sed i n a P B S solut ion (1x pH = 7. 4 ,
I S = 0.1713 m ol/L) with a conc entra tion of c vesicle = 0.1 wt%. Experimenta l evidence shows, that the
cha rge density of l ipid ratio i s important for a sub sequent vesic le adsorption on an alrea dy formed
SLB (see Figure 65). Lipid ra tios below the DMP A c ontent of 3 mol% show a transiti on between
adsorbing vesicle s and not adsorbin g vesicles. Howe ve r, adsorbed vesic les c an be rin sed from the
surfa ce by washing the measure ment cha mber with P B S but t he SLB remains st able on the surfac e .
The mean measure d fr eque ncy shi ft for our membrane sys tem is Δ f SLB = – 26 ± 2 Hz and leads to a
thickness via the Saue rbre y relation: 99
∆𝑑 = − 𝐶
𝑛∙𝜌 SLB ∙ ∆𝑓 ,
eq. 76
wher e the thickness d = 4 .50 ± 0. 34 nm of the li pid m embra ne wa s ca lculated with the density of
phospholipids ρ SLB = 1 .01 g/cm³ 121 and is in g ood a gree ment w ith liter ature va lues. 135 The d issipation
shift is low and the S L B ca n be assumed as a rigid laye r, whe re the Sauer brey re lation is val i d .
80
4.2.2 Variation of polym er de nsity an d c ha rge d e nsit y o f SLB
Figure 66 : Exa mple Q CM- D me asureme nt; Δ D (top) a nd Δ f shift s ( bottom) for sev eral s teps: I – III descr ibe the
SLB forma ti o n wi th subse que n t buffer ch a ng e . The new freq ue ncy shif t at III serv e as new base line for fur t her
mass calcul ation for NP adsorp tion. St ep IV shows NP injec t ion into the c h amber , sa mples with huge am ount
of polym er absor b less co m par ed to l ess amoun t of grafted polym er or S iO 2 @NH 2 .
The cha rge density of the NPs is control led by the graf ting densi t y and pH, i . e . , at h igher solution pH
PDMAEMA or amino moieties of SiO 2 @NH 2 - NPs bec om e d is char ged, which reduce s their ef fec tive
surfa ce potential. I n t he first step we wor ked at pH 4, whe re the poly mer brush is l ar gely c harge d (and
DOPC is neutra l, wh ile DMP A is singl e cha rged) and wit h Millipore wate r as sol vent , t her eby being
at very low ion ic st re ngt h . T he surfac e char ge density of the su pported lipid bilayer was var ied from
0 – 10 mol%.
The QCM -D results summar ized i n F igure 67 and Fig ure 70 gi ve t he amount of at tache d NPs as a
func tion of the amo unt of po lymer containe d in t he NP s , s how some i ntere st ing trends. Initia lly , wi th
incre asing polym er amount, more NPs adsorb onto t h e S LBs (as this incre ase i s small the nu mber
density of adsorbe d N Ps decr ease s with incr easing pol ymer grafting), a t rend o ne may expec t as one
incre ase s simpl y t he char ge density on the NP surfa ce and thereby its ability to in tera ct wit h t he op-
positely char ged S LBs . An importa nt observation here is, t hat for a pure DOPC SL B no adsorptio n
takes pl ac e for t he s maller N P s ( d = 50 nm) , which ind ic ates that her e the a dsorption proc ess i s dri ven
by electrostatic i ntera ctions. In contra st, for the l ar ger NPs ( d = 70 nm) no such effe ct is see n, wh ich
might be at tributed to the fac t , that here the surfa ce is more flat and there fore the interac tion with the
flat SLB surfac e is in genera l st ronge r. 5 Ver y interesting is, that almost n o differ enc e is observed when
81
incre asing t he S L B cha rge density by going from 2 to 10 mol% DMPA , but that might be l inked to
the fac t that the S L B charge seems to be inhomo geneously distributed .
Figure 67: C alcu lated ma ss fr om QCM-D measur ements (eq . 87) a) d = 50 n m, d) d = 70 nm; cal culated p a rtic le
numb er densi t y N / A s (eq . 81 ) b) d = 50 nm, e) d = 70 nm; calculat ed surfa ce c o ve r age valu es β (eq. 82 and eq.
83) c) d = 50 n m and f) d = 70 nm .
Howe ver, the most i ntere sting finding is that N Ps adsor pti on is drastically re duced for higher amounts
of graf ted pol ym er , and then basica l ly no adsor ption is o bserve d (F igure 67) . Thi s is a ver y i nt er esting
observa t ion as i t shows a very distinct depende nce of the bind in g of the polyme r m o di fied N P s as a
func tion of the gra fting density and this i s occur ring as a rather sharp transition . This observa t ion from
QCM-D could be confirme d by AFM mea surements on differ ent samples. For the NPs with d = 50 n m
Figur e 68 shows de nsely packe d surfac es for SiO 2 @ NH 2 NPs and those for low polymer content ,
while almost bare SLBs ar e see n for high polymer grafting. Obvious l y, there i s a critica l polymer
gra fting density above which the te ndenc y for binding t o t he SL B surfa ce is l ar gely suppressed. This
threshold is at ~ 5.5 wt% PDMAEMA for the sma ller N Ps ( d = 50 nm) and incre ases to ~ 27 w t % for
the large r NPs ( d = 70 n m). It is intere sti ng t o note, tha t t her e is even good quantitative agre ement
betwe en the re sults derived from QCM -D and AF M (Figure 69). In addition, the surfa ce cove rage β
is h igher f or the large r NPs, t here by c onfirming the f act, tha t bi nd ing tende ncy inc rease s with incre as-
ing particle s ize.
82
Figure 68 : AFM height images of ca ti o nic NPs on S LB (DO PC/DMP A = 95/05 mol%) .
Figure 69 : Co mpa r i son of th e par ticle number densit y pe r unit a rea N NP a s a func t ion the amou nt of gr a fted
poly me r for parti cle di a m eter d = 50 nm. AF M and QCM-D m easure me n t w e r e done on dif ferent surfac es.
This be havior may be rationalize d by t he fa ct tha t less curve d N Ps have a bigge r conta ct a rea with the
flat SLBs. The lacking adsorptio n for m ore de nsely graf ted N Ps can be e xplained, that for a too dense
gra fting t he polymer char ges of the NPs ar e no longe r able to effe ctively intera ct wi th the opposite
cha rges of the S LB (as the brush is now dense and t here fore has l itt le flexib il ity) and here then the
83
steric re pulsion induced by the pol ymer cha ins do m inat es (see F igure 70). An im portant poi nt i s also
that once adsorbed NPs rema in rema rkably strongly adsorbe d on the interf ace , as flushing the m ea s-
ure ment chamber with wa ter does not re move them, but NP s are rapidly removed from the surf ac e
with a S D S solution (1 wt%, see Figure 66; here it may be assumed that the SD S simply repla ces the
nega tively charge d NPs). That could be succe ssfully co nfirmed via AFM just by comparing the height
and phase images of sa mples contain ing SLB with and w ithout adsorbe d NPs ( Figure 71 , Figur e 72) .
Obviously, i t is not a fast dyna mic equi librium or a ful ly irreve rsibl e b inding of the NPs at the S LB
surfa ce , as otherwise t he wa ter injection would allow t o remove t he N P s dispersed due to such an
equilibrium .
Figure 70: Surfa c e cover age β ca lcul ated from QCM -D m ea s ure m ents for ca ti o nic SiO 2 @NH 2 (0 w t% graf ted)
and SiO 2 @PDM AEMA-N Ps a t pH 4 for bot h core sizes (left d = 50 nm and right d = 70 nm) pl o tted as a fun c tion
of the amou nt of graft e d polym e r (~ grafti ng dens i ty). b) car toon of the i n teraction of SiO 2 @PD MAEMA n a-
noparti c le s of d i fferen t grafting d ensiti e s w ith suppor ted li p id bilayers . Red do ts r e pr esent the counter ions dis-
tributed along th e backbon e of fully i onized polye lectrolyt e b rush. ( i ) a nd (ii) il lustrat es the NP a pproach at the
surface, wh ere t h e NPs ha v e (i ) l ow gr afting dens it y and ( ii) high graf ti n g dens ity of the poly m er dens ity.
Acc ording to li tera ture phospholipids o f diffe re nt comp ounds usual l y te nd to f orm domain s of a c om-
pound rich phase . 11 9 Both compou nd ric h phase s ca n b e imaged, i f one doma in slight l y diff ers in the
height (heigh t re trace ) or in mecha ni ca l proper ties (pha se retra ce). At roo m temper ature DMPA i s in
the gel state lea ding to a thic ker and stiffe r membrane c ompare d to D OPC. The bes t w ay to i mage t he
SLB is by us ing cantileve rs wi t h a very soft spring con stant (~0 .6 N/m), howeve r NPs can be better
imaged with ca ntil eve rs of highe r spring cons tant (~40 N/m). As expe cted SLB shows domains of
rich DOPC flui d sta tes and of rich DM P A gel sta te D MP A dom ains have undefined shape str ucture
and vary in a wide size range. Especia lly a strong contrast in t he phase image between DOPC and
DMPA c an be seen if usin g a sof t ca ntile ver. H oweve r, artifa cts of doubling N P s a re observe d, due to
the soft ca ntil eve r. But we ca n conf irm the prese nce of SLB after NP adsor p tion from Figure 71 and
Figur e 72 by interpre tation t he height diffe renc e (usually ~ 1 nm) of marke d cr oss section and pha se
84
images. D MPA domain s may be se en better from the ph ase image as wea kl y incr eased shiny do mains
if using a stif f cantileve r or with a bet ter contra st if using a soft cantileve r.
Figure 71: Left) D OPC/DM PA 95 / 05 mo l% AFM he ight measur e ment in a i r, Right) DOPC /DMPA
95/05 mo l%@SiO 2 @PDMA EMA-NP s with 3. 0 wt% grafted am ou nt of poly m er, Phas e Image, DMP A dom ains
can be a ssume d as shi ne a r eas .
Figure 72 : AFM measu rements i n dried c on ditions: AFM hei ght (a , c) and p ha se im ag es (b, d) of top pur e SLB
(DOP C/DMP A 95 /05 m o l%) a nd botto m S i O 2 @PDMA E MA -NPs on s a m e SLB w ith 4.5 w t % gr afted poly mer.
Gel domains (DMPA ) a r e a rou nd one n m hi gh er t h en fl u id doma ins of DO PC . Go od c on t ras t betw e en both
domains can b e s e en i n phase image .
SDS as a surf actant is an anionic surfac e-a ctive material. For bare NPs it may adsorb on the silica
surfa ce by char ging them high ly nega tive. Thus , whil e SDS adsor bs on the surfa ce QCM -D recor ds a
85
fre quency reduce and strong dissipation increa se ( Figure 66). But at a critical surfac tant adsorption ,
these anionic NPs (c harge maybe also conve rted from absorbe d SDS ) im mediate ly desorbs int o t he
bulk sol ut ion. The ca se of poly m er grafted nanoparticl es is m uch more compl icated, but SD S may
pene trate int o the brush inter ior and re place s anionic c ounterions with SDS. Due to t he presenc e of
the alkyl chains the l oca l vdW force s betwee n polyelectrolyte chains and surfac tant m olecule s leads
to bridges betwee n adjac ent pol yelec t rolyte chains. Macrosc opely the brush layer collapses and the
soft pr operties of t he brush laye r are de cre asing. Thi s ma y be in reasona ble a greeme nt with the Q CM -
D data, wher e the fre quenc y response for all polyme r grafted NPs show first an i ncre asing mass ad-
sorption ( –Δ f increa se, F igure 66). In contrast, the en ergy dissipation re duces we akly (F i gure 66) .
Again, at a crit ical surfac tant ratio NP s are immediate ly desorbing . In any ca se the binding tendenc y
of adsorbe d N P s is re duces by S DS due net cha rge of the NPs and p lanar surfa ce is anionic resultin g
from adsorbe d SDS. The n there i s a strong elec trostatic repulsion a nd a n e nergy gain may result fr om
desorbing NPs
86
4.2.3 Variation of the c harge d e nsit y of the NPs v ia the pH
Figure 73 : E xampl e me asuremen t for S LB -SiO 2 @ PD MAEM A-NPs with 1 1.5 w t% po l ym er gr a fting at d iffe r ent
pH values .
As ne xt step we inve stiga ted the influenc e of t he NP c h arge de nsity (contr ollable via pH) while keep-
ing the char ge densit y of the S L B constant at a ra tio of DOPC/DM PA 95/5 mol% . Cationi c NP s are
highly oppositely cha rged at acidic conditions (pH 4) but the char ge density is reduce d with i ncr easing
pH until t he isoelectr ic point (IEP) is rea che d and afte rwa rds t hey bec ome ch arged aga in (see Figur e
74b), bu t now nega tively l ike the SL B . At the same time their colloidal stabi l ity i s r educe d around t he
IEP a nd t his the more lowe r the de gre e of po lymer gr af ting (Figure 74a) . In contra st t he a nionic Si O 2 -
NPs become s impl y more and more nega tively cha rged with incre asing pH (see Figure 74b) .
The QCM-D data (F igure 74c and d) exhibit an increa s ed adsorption of cationic NPs w ith incre asing
pH (dec reasing NP charge ), which indic ates that this effect is not purely of electrosta tic nature. In
contra st, for the anionic bare SiO 2 -NPs t he absorption is dire ctly decr easing. That result in first ap-
proximation is co mpletely unexpecte d as one would expe ct especia lly for diss i mil ar cha rged surfa ce
a cha rge driven adsorpt ion t owa rds lowe r so l ution pH va lues. Def initely, for Si O 2 @PDMAEMA-N Ps
we obser ve a systematic trend of bet ter adsor bing NP s a s conse quence of incr ea sing pH. An explana -
tion may be that the latera l elec t rostatic re pulsion of si mi lar cha rged adsorbe d NPs becomes reduc ed
for less charge d particles. As observed in chapte r 4.2 .2 the adsorption is less wit h inc rea sing amount
of graf ted polymer.
87
Sim i lar results for brush gra fted SiO 2 @PDMAE MA-NP s with 15 nm cor e diamete r had bee n observe d
bef ore from Ril ey et a l. whe re particles at pH 5 show w eake r a dsorption a ffinity c ompare d to pH 9 on
planar anionic surfa ces (oxidized si licon waf ers) . 12 2 , 12 3 Also Jing et al. obse rved for ca rboxyl function-
alize d poly(styrene )-NPs a reduc ed NP adsorpt ion pote ntial wi th decr easing ioni c strength . 124 Phase
sepa rate d NPs w ere in jected into t he m ea suring c hambe r but surpr isi n gl y those samples do no t adsorb
at all. Howeve r, for ef fec t ive adsorption the pre sence of i ndiv idually disperse d NPs is requir ed.
Figure 74 : Vari a tion of pH for cationi c ally modifi ed and bare NPs wit h c or e diamet er of 50 nm . a ) hydrod ynami c
radius R H b) correspond ing ζ -po te n t ials, c) adsorb ed mass per area , d) su rface c o verage β.
88
4.2.4 Effect of NP concentration on the ad sorpti on p r o cess
Figure 75 : Exam ple measure ment of SL B int eraction wi th Si O 2 @PDMA EMA-NPs w it h 23.5 wt% g rafted po l-
ymer at pH 4 on differ e nt NP con c entra tions.
As next step we investigated the influenc e of the NP conc entra tion while keeping solution pH and
cha rge density of t he phospholip id membrane constant at a l ipi d ratio of DO P C/DMPA 95/5 mol% .
We studied the surfac e cove rage for ca tioni c Si O 2 @NH 2 and SiO 2 @PDMAE MA-NP wi t h m o der ate
and high graf t ing dens it ies for both core si ze s ( d = 50 a nd 70 nm). Obtaini ng the equil ibrium state is
mainly a functio n of the conce ntration and it is ac hieved m uch m ore slowly for reduce d conce nt ra tion,
wher e the cha r ac teristic tim es incre ases fr om seve ral seconds to se vera l hours (see F igure 75 and
Figure 78 a) .
As expecte d, data for NP s with high gra fting densities Δ f and Δ D do not cha nge with increa sing N P
conc entra tion, ther eby indic ating, t hat the NP adsor ption i s re lated to N P proper ties and is not a func-
tion of t he c oncentra tion. Ve ry similar behavior is seen f or Si O 2 @NH 2 , w here the sl igh t incr ease may
be attributed to t he rising conc entra tion, but t he adsorp tion pat tern cannot be describe d wi t h a Lang-
muir model . Howeve r, the p ure SiO 2 @NH 2 par ticles show alre ady at ver y low conce ntrations a rela -
tively high bi nd i ng, indica ting a much higher binding affinity compar ed to the polyc ation modi fied
SiO 2 -NPs.
In contrast, for modera te graf ting densities one observ es a very peculiar conce ntration depende nce,
wher e first a m ar ked increase of adsorption takes place , which is foll owed by m ar ked reduc t ion of
surfa ce c overage for higher c oncentra tions. Th is is a very st ra nge be havior, that occ urs exa ctly f or the
89
gra fting densities whe re in chapte r 4.2 . 2 we ha d seen the tra nsiti on from adsorp tion to non-adsorption
(F igure 76). Appa rently here the adsorption conditio ns depend subt ly on pre cise conditions. O ne may
spec ulate, t hat one m ay have the ef fec t during the Q CM-D expe rim ent. Higher the conc entration leads
to higher number of collisions of d i sperse d NPs with alr eady adsorbe d NP s and this may be a sufficient
proba bili ty of re moving these we akly bound N P s from the S L B s.
Figure 76 : Sh own are sur face cov era g e β for cation ic NPs on th e SLB wit h DOPC/D MPA 95/05 mol% for
differen t core si z es Left) d = 50 n m , Right) d = 70 nm.
Both cor e si ze s have similar trends , but it is conf irmed , that bigger NPs adsorb m ore st rongly than
smaller ones. In addit ion, the sharpness of the t ra nsiti on is l ess prono unced, in agre ement with t he
observa t ions for the depende nce on polymer graf ting. It is def initely int er esting , that particle s with
polymer graf ting densi t y i n the t ra nsit ional regime of ad sorption t o non-adsorptio n show a decre asing
adsorption af finity with increa sing conce ntration. In or der to exc lude , tha t this is due to changes of
the state of the NPs in bul k, we mea sured the hydrodyn amic radius R H as a func tion of the conce ntra-
tion. We o bserved, within mea surement i nac curac i es, t hat the R H of c ore- shell-NP i s constant (see
Figur e 77). We further investigated the effe ct of the fl ow velocity , wh ich was re duced from 100 t o
15 μ L/ min, wit h the in tere sting result of incre ase d surfa ce cove rage β for high concentr ations for the
lower flow rate samples (see Figure 78c and d). Thi s observa t ion supports our explanation t hat t he
adsorbe d layer of NPs is perturbe d by the flowing NPs , tha t collide wit h adsorbe d NP s during the
QCM-D exper iment.
Figure 77 : R H as a fun c tion of the SiO 2 @PDM AEMA-NP wi th 23.5 wt% gr a fted polym e r.
90
Figure 78 : a ) C harac teristi c times for reaching the equilib rium a t di ff erent conc entrat ions for studi e d NPs . b)
For SiO 2 @N H 2 and SiO 2 @PDM AEMA with 23.5 wt% grafting ( d = 70 n m ): mass con c entr a t ion on a SiO 2
surface c ) S i O 2 @PDMA EMA wi t h 23.5 wt% g rafting flow r ate of 100 μL /min a t NP concen trations and d) fl ow
rates of 15 μL /mi n and 100 μL /min a t hig h con c entra tions .
The equilibration time was calcula ted via a simple expo nential decay:
Δ𝑓 ( 𝑡 ) = (Δ𝑓 0 − Δ𝑓 eq ) ∙ ex p (− 𝑡 𝜏 ) + Δ𝑓 eq ,
eq. 91
wher e Δ f ( t ) is the resona nce fre quency at any tim e t , Δ f 0 at the resona nce fre quency at the begin ning
of NP adsor ption and Δ f eq the resona nce fr equenc y at th e equilibrium.
As menti oned ear l ier the equilibrium st ate is m ainly a function of the concentr ation . Consequently ,
the data was fit ted w ith a s impl e expone nt ial f it func tion with e q. 91 and is shown in Figure 79. La tt er
do not fi t the measure d data in absolute prec i sion , but it is a good approximatio n t o show the marke d
incre ase of the equi librated s tate with decre asing N P co ncentra tion. Howeve r, on a closer look on the
ra w data displ aye d in Figure 79 , espec i ally for the low NP conce ntrations, one sees first a linear re la-
tionship between the resona nce fr eque ncy re sponse an d the tim e until a tra nsiti on p oint i s rea ched .
Beyond this transit ion poin t the fr equenc y respons e fo llow proba bly a simple expone ntial decay un t il
the equil ibrium is re ache d (Figure 79). For highe r con centra tions the simple expone ntial decay ap-
proximates the data better for the total equilibra tion time τ compare d to the data of lower NP conce n-
tration. T his observa tion can be seen for bare and polyme r grafte d NP s.
91
Figure 79 : Examp le d ata of the e qu ilibriu m stat e for NP dia m eter of 70 nm. a ) SiO 2 @NH 2 and b)
SiO 2 @PDM AEMA with 23.5 w t % graft ed. NP a dso rption on SL B (DOPC/DM PA 95/5 mol%). For a b etter
view S LB ads orption no t shown and data is normaliz ed to t h e beginn i ng of NP adsorp t ion. D a ta fitt ed wi th e q.
91 and fit curves are shown as shor t dark do t s.
One would expe ct for t he equi li bra tion time a conce ntration depende ncy as τ ~ 1/ c 2 due t o simple
diffusion of N Ps . But the plot of τ as a function 1/ c 2 sh own in F igure 80 conf irm not a li nea r depend-
enc y. Also, if only diff usion influenc e the magni tude of τ , po lymer grafte d NP s should adsor b l onger
compar ed to bar e NPs (Diff usion coef ficient; D bare,NP ~ 7 .7 um 2 / s; D P DMAE MA,NP ~ 5.1 um 2 /s.) B ut
measur ements show , a rever sed behavior (see Figure 78 and Figure 80) Thu s, the adsor ption proce ss
is probably n ot only mediate d fr om the di ffusio n of the NP s. In any ca se t he proc ess of adsorption is
ra ther complex and see ms t o be a function of many pa ramete rs likewise the concentr ation, pol y m er
content and l iquid flow, respe ctively.
Figur e 80 : Equilibration time pl otted as a functi on of 1/ c 2 . For a better vi ew 1/ c 2 axis is shown in l og
sca le.
92
4.2.5 Variation of the ty pe o f the flat substrate
Figure 81 : e xa mple QCM D me a sure ment on Au surf a ce . T he Au surfac e was fre sh l y tre ated with the plasm a
clean er; Δ D (top) a nd Δ f shif t s (b ottom) for sev e ra l s te ps : I H 2 O at pH 4, II NP injectio n int o t h e cham ber,
samples w it h huge a m oun t of po l y me r abso rb less compar ed t o less a mount of graft ed poly mer or SiO 2 @NH 2 .
Figure 82 : Cont a ct angles f or diff erent Au@SAM surfaces: a ) Au@NH 3 + ; b) Au ; c) Au@ CH 3
As a next st ep we we re intere sted i n the effe ct of the ty pe of substrate on which the SL B was for med
on t he ove rall adsor ption proc ess f or the differ ently modifie d N Ps. F or this purpose, diff er ent surf aces
such as SiO 2 , a ni on i c Au sur fac e ( fre sh plasma tre atme nt), ca tioni c Au@N H 3 + , and ve ry hydr ophobic
surfa ce s of the Au@CH 3 were prepa red. The diffe rent functionaliza tion was done by depos i ting the
desire d self-a ss embled monolayer (SAM) on a pure gold surfac e. F urthermor e, the anionic gold sur-
fa ce was made by trea ting the surfa ce with p lasma cle aning immedia tely before the measur ement. The
succ ess of the functionaliza tion was studi ed via conta ct angle measure m ents. 12 5 In tot al , we have a
93
broa d variety of di ffe rent surfac e types, which are inor ganic, metal lic, elec troneutra l, str ong hydro-
phobic and equally or differ ently cha rged compar ed to the N P char ge . These surfa ces do not have a
SLB adsorbed but result s from NP interac t ion are compared also with re sults from NP -SL B in tera c-
tions .
As expec ted, both N P s do not adsorb on equa lly cha rged surfa ce s . El ec trostatic interac tion has a cer -
tain i nfluenc e in N P adsorp tion, whe re equally charge d surfa ces lead to repulsive elec trostatic int er -
ac tions compar ed to anion ic surfac es, where one has ele ctrostatic attrac tion. Appare ntly, elec trostatics
is a domi nat ing ef fec t here. Surprisingly smaller NPs do not tend t o adsorb neither on S iO 2 nor on
zwitter ionic SLB but in gene ral small NPs adsorb less t han bigger ones. The highest NP density can
be observe d on Au surfa ces for both size s. Surprisingly the NPs adsorb strong ly on hydrophob ic sur-
fa ces.
Figure 83 : SiO 2 @P D MA EMA-NPs on differ e nt surfac es me asured a t pH 4 a ) d NP = 50 n m; b) d NP = 70 nm .
4.2.6 Variation of the NP size
In this chapte r we s tudy t he N P a dsorpt ion as a func t ion of cor e size on anio ni c go ld surfac es at a cidic
solution condi t ions (pH 4). As for all core sizes t he ty pi ca l trend of re duce d NP adsorption affinity
with increa sing amoun t of gra fted poly mer can be obs erve d. The bi ggest N Ps have the h ighest ad-
sorbed mass resulting from the hea vier m ass of ea ch p ar ticle. But calcula ted surfa ce covera ge con-
firms the hi ghest surfac e cover age value for NPs w i th a di ame ter of 70 nm . In gener al, one has her e a
re latively si m ilar behavior as seen bef ore for t he SL Bs.
Figure 84: SiO 2 @ PD MAEMA-N Ps adsorption stud y as a fun c tion of the graftin g densi t y and NP core s ize: Left:
mass adsorb ed vs the nor malized graft e d pol y mer; Right : sur face cov e rage vs the norma lized gr a fted polym er .
94
4.3 Properties o f SiO 2 @PD MAEMA -NPs brushes
Our expe rimental data exhibi t, t hat the grafting density has a strong influence for soft NP membrane
intera ction . Here it is intere sti ng , which brush regi me at which graf ting dens it y is prese nt for cationic
NP s wi th polyele ctrolyte grafting . Thu s , we estima ted the graf ting density of Si O 2 @PDMAEMA-NP s
with core diamete rs of 50 and 70 nm and compare d to t heore tical results pre sented in re fer ence 6 4 .
To e st ima te the gr af ting density , first the M W of s ingle c hain was es t imated under the assump tion, that
the contour length L of one po l yelec t rolyte is equa l to t he shell thickness t shell . 12 2 It assumes, t hat the
brush is fully ionized (pH 4, p K a PDMAEMA = 7 .4), w her e the polymer backbone is f ully elongate d .
Then mathema tically M W, ch ain can be expr essed:
𝑀 W, ch ain = 𝑡 she ll
𝑎 ∙ 𝑀 W ,DMAEMA ,
eq. 92
with M W,DMAEMA = 157.21 g/ mol and a as the length of one repea ting unit and has a value of
a = 0 .25 nm. 12 2
Now the graf ting dens ity σ can be calculate d with th e knowledge of chains per N P N ch ai n and N P
surfa ce ar ea A NP :
𝜎 = 𝑁 chain
𝐴 NP ,
eq. 93
wher e N ch ain is the ratio of molecular weight of graf t ed polymer per N P M W ,P a nd m olecula r weight of
one single chain M w,cha in :
𝑁 c hain = 𝑀 W , P
𝑀 W, chain .
eq. 94
While M W, P is ca lculated in chapter 4. 1 . 3 in detail the grafting densi ty ca n be estimate d for
SiO 2 @PDMAE MA-NPs and is sum mariz ed in Table 11 .
Table 11 : t h e nano pa r t icle core radi us R C , the hyd rodynam i c radius R H , the she ll thi ckne ss t shell ,
the m olec ular wei ght o f cor e -sh e ll s tructures M W,NP+P , of pure polym er p er NP M W,P , of s ingle
poly me r cha in M W,C , chai ns p er NP , the gr afting densit y σ a n d the nega ti v e square of t h e co ntour
length L of polye lectrolyt e brushes
R C
R H
t sh e ll
grafted
poly me r
(TGA)*
M W, NP+P
(core + po l-
ymer)
M W, P
(poly me r
per NP)
M W, C of
single
chain
N chain
σ
L – 2
nm
nm
nm
wt%
g/mol
g/mol
g/mol
1/nm²
1/nm²
24.3
–
–
0
8.69 ∙ 10 7
–
–
–
–
–
24.3
39
13
3.0
8.99 ∙ 10 7
2.96 ∙ 10 6
8888
333
0.05
0.006
24.3
42
16
4.5
9.14 ∙ 10 7
4.51 ∙ 10 6
10412
433
0.06
0.004
24.3
43
17
5.5
9.25 ∙ 10 7
5.57 ∙ 10 6
11162
499
0.07
0.003
24.3
41
16
7.0
9.41 ∙ 10 7
7.21 ∙ 10 6
10098
714
0.10
0.004
24.3
40
17
11.5
9.94 ∙ 10 7
1.25 ∙ 10 7
9674
1289
0.17
0.003
32.6
–
–
0
2.06 ∙ 10 8
–
–
–
–
–
32.6
47
14
17.5
2.42 ∙ 10 8
4.84 ∙ 10 7
8719
5553
0.42
0.005
32.6
49
16
20.5
2.48 ∙ 10 8
5.90 ∙ 10 7
9820
6007
0.45
0.004
32.6
47
15
23.5
2.54 ∙ 10 8
7.04 ∙ 10 7
8830
7976
0.60
0.004
32.6
49
16
27.5
2.62 ∙ 10 8
8.73 ∙ 10 7
9692
9003
0.68
0.004
32.6
49
16
28.5
2.64 ∙ 10 8
9.18 ∙ 10 7
9928
9244
0.69
0.004
*Samples w ith 0 wt% are the values for bar e silica nan oparticle s
95
Fr om Zhulina and Rubinstein the requireme nt for ch arge d m ushroom regime for polyelec trolyte
brushes of plana r surfa ce i s, that the gra fting density σ is much bigger then the reciproc al square of
the contour length L of the polye lectrolyte chains as σ << L – 2 . 64 Here i t is ass umed t o be sim i lar on
cur ved surfac es.
The data clea rly show, that for all sys tems studied: σ > L – 2 . Especia lly NPs wi th the smallest amou nt
of graf ted polymer ha ve an a lmost one m agnit ude bigge r σ t hen L – 2 . Thu s, we conc lude, that the poly-
elec t rolyte l aye r is conseque nt ly in the os motic brush regime at all grafting densi ties. Furthe rmore,
the assumption tha t t sh ell is i ndepe ndent of t he graf ting density, is in g ood agree ment wit h theoretica l
pre dictions from the liter ature . 6 4
Bigger par ticles have re lative high grafting densi ties a nd are close at the transition t o quasi neutra l
re gime σ ~ 1/nm 2 . 64 Her e the brush net charge is almost neutral due t o eq. 19 , where the majority of
counter ions are located i n the brush interior (The gra ftin g density scales with the rec i proc al of esca ped
counter ions σ ~ 1 /Δ n , see follow ing cha pter). This m ay e xplain t he tendentiall y big ger adsorption af -
finity of bigger N P s also on neutra l supp orted lipid b ila yers as di scussed previously .
4.4 Electr ostatic con ditions
Beca use of t he low i onic st re ngth of the bulk solution at pH 4 ( c ion = 1 .4 ∙ 10 – 4 m o l /L from conduc t ivity
measur ements) resulting i n a Debye length κ – 1 ~ 25 nm ) and probably relative hig h grafting dens i ties
of the NP s we assume an osm otic brush regime for o ur poly mer m odified NPs (see c hapter 4. 3) .
Howe ver, acc ording to Zhulina et al . the net cha rge of the planar pol yele ctrolyte brushe s is no t exactly
ze ro a nd the c om pensa ting counter ions (Δ n pe r c hain) e scape f rom the brush and for m a Gouy− Chap-
man layer of thi ckne ss λ . But the majority of counte rions are l oca ted within the brush and the net
number of esca ped counter ions per uni t area for planar surfa ce can be estimated wit h: 64
𝜎Δ𝑛 ≃ 1
𝜆 B 𝐻 0 ,
eq. 19
with σ the graf ting de nsity, Δ n number of escape d co unterions, the B jerr um length λ B = 0 .7 nm in
aque ous solut ion and H 0 t he brush th ickness. 64 For estimate d graf ting densiti es prese nted in cha pter
4.3 values for Δ n are summar ized in Table 12. Furthe rmore, t he resulti ng surfa ce pot ential Ψ b rush at
brush layer thickness were calc ulated using the graha m equation. 5 The charge density and corre spond-
ing Ψ brush at the brush layer thickness are at any grafting density high but decr easing with increa si ng
gra fting density . Calcula ted values of Ψ brush are in good agree ment with m ea sured ζ -potent i als. 34
Table 12 : gra f ting dens it y σ , brush th i ckn ess H 0 , es c ap ed counter ions Δ n , a nd s ur face p otent ia l a t
the brush layer thi ckne ss Ψ brush
d = 50 nm
d = 70 nm
σ
H 0
Δ n
Ψ brush
σ
H 0
Δ n
Ψ brush
nm
nm
e / nm 2
mV
nm
nm
e /n m 2
mV
0.05
13
2.2
329
0.42
14
0.2
216
0.06
16
1.5
309
0.45
16
0.2
205
0.07
17
1.2
298
0.60
15
0.2
194
0.10
16
0.9
283
0.68
16
0.1
184
0.17
17
0.5
252
0.69
16
0.1
183
e = 1.602 ∙ 10 – 19 C, d e tails a b out t h e ca lcul at i on o f the Ψ brush are pr e sented in th e app endix
Note, that ionic strengt h is rel atively low a nd t hus surf a ce poten tials are hi g h. S maller v al u es for Ψ brush should
be exp ected wi t h inc reasing ionic streng t h. 5
96
The upper disc ussed phenomenon is re lated to pl ana r surfa ce where the segment density prof ile of
polymer brushes is usua lly s igm o i dal f or good solvent c onditions. The c urvatur e of spheric al poly mer
brushes causes t he segment density profile t o dec ay mor e r apidly awa y (expone ntial) from the grafting
surfa ce c ompared t o pla nar pol y m er brushe s (see c hapter 1.2.7.3 and 4.1 . 7 . 3). Than scaling prope rties
may differ somew hat and one would expe ct higher Δ n va lues t han gi ven by eq. 19 for spher ical com-
par ed to pl ana r po lyelectr olyte brushes . In any case wit h incre asing grafting densit y, we expe ct an
incre ase of the counter ion conc entra tion of such cor e-shell structure s, which ca n become reduc ed by
incre asing the pH wh il e kee ping the graf ting consta nt a s illustra ted in Figur e 85a .
In t hi s part we explain our hypothesis of particle surfac e i ntera ction whe n NPs appr oach the p lanar
SLB surfa ce . Intuitively one woul d expec t that opposite ly cha rged NPs always tend to adsor b on sur-
fa ces, but data show a decre ase of NP density with inc rea s ing char ge density/ gra fting density. Here
one has to consider, that the net forc e a NP expe rienc es upon appr oaching the surfac e is gi ven by the
sum of t he elec trostatic forc e F П of two over lapping e lectr ic double laye rs, the osmo tic for ce of brush
interior counter ions F П,inter i or , the attrac t ive vdW force , and the steric repuls ion force of overlapping
polyelec trolyte cha ins: 5
𝐹 net = 𝐹 П + F П,interio r + 𝐹 vdW + 𝐹 st eric .
eq. 95
It is in t er esting t o note , t hat the higher steric repulsio n at hi gher grafting dens i ty is appa rently not
exc lusively re spons ib le for t he non -a dsorption seen in Figure 74 (chapte r 4.2. 3) . The more h ighl y
gra fted NPs at h igher solution pH (none ionized brus h) become incre asingly adsorbe d (Figur e 74 ,
page 87). This is defini tely a surprising beha vior. In co ntrast , at low so lution pH only N P s wit h low
gra fting densiti es do adsorb . The ref ore, we hypot hesiz e t hat the i ntera ction of brush graf ted NPs i s
also sub stantially influe nce d by the electrosta tic inter ac tions, but not just in the simple sense of ac-
counting for the to tal cha rge of the NPs. For bare particle s the elec trostatic intera ction can be descr ibed
by the DLV O the ory. F or gr afte d NPs t he e l ec trostatic i nterac t ion is muc h m ore c om plicate d but may
be simpl ified by taking the exte nded radius of the polymer brush as char ged rigid sphere s (in reality
should be consider ed as soft ones). A s describe d b y Zhulina et al., the cha rge build -up from esc ape d
counter ions from the brush, w hich c rea te a c apacitor wi th c hara cter istic Gouy-Chapman l ength λ out-
side the brush and the resulting cha rge is proport ional t o e Δ n . We may now assu me, that t h i s cha rge
cr eate s a proportional surfac e potential ψ locate d at the position R + t shell , whic h dec ays with the char-
ac teristic length λ towar ds the bulk solution . 64
For surfac es of differ ent charge densities or potent i als the i ntera ction po tential m ay have a maxi m um
or mi nimum, typically at distance below κ – 1 . Howe ver, ions will still be t ra pped betwee n those sur-
fa ces, due to maintain i ng the ele ctrone utrality between surfa ce and t he ions in the elec tric double
layer . This is known as the os moti c limit, wh i ch applie s to any systems, wher e ions remain confine d
or trappe d between two surfa ces as they approa ch ea ch other. 5
97
Figure 85 :a) Sch eme of S i O 2 @PDMA EMA- NPs b ) Mode l of approac hing NP on opposi tely c harged surf ace s
top) high count e r ion conce ntrat ion , botto m) low cou nter ion conce ntration. The c ou nter ion c on centratio n c ion
is a func t ion of d egree of ioni z ation of the poly electrol yte an d t h e gr afting densi t y. T he str ength of F Π d epe n ds
on c i on , and of F vdW on t h e NP si z e and mater ia l (for de tails see c hapte r 4.4. 2 ) Mod e l i ll ust rates t he inter actio n
for S iO 2 PDMA EMA-NP s but i s a lso val id for b are SiO 2 a n d SiO 2 @ NH 2 -NPs un der assumpt ion of an electr ic
double la y e r . 5
98
For the situation of two plana r surfac es that are scree ned by a 1:1 elec trolyte and for constant char ge
intera ction t he pre ssure as a function distanc e is gi ven by: 5,12 6
𝛱 ( 𝐷 ) = 𝜌 ∞ ∙ 𝑘𝑇 ∙ [ 2 √ 1 + ( 𝑧𝑒 ( 𝜓 1 +𝜓 2 ) : 𝑘𝑇
exp ( 𝜅𝐷 /2 ) −exp ( − 𝜅𝐷 /2 ) ) 2 − { 𝑧𝑒 ( 𝜓 1 −𝜓 2 ) : 𝑘𝑇 } 2 ∙exp ( − 𝜅𝐷 )
1+ ( 𝑧𝑒 (𝜓 1 +𝜓 2 ) : 𝑘𝑇
exp( 𝜅𝐷 /2)− exp (− 𝜅𝐷 /2) ) 2 − 2 ] .
eq. 96
Her e ψ 1 and ψ 2 are the potentia l of the first and second sur fac e (approximating the N P surfac e as being
flat), z i s the valency of the electr olyte, e the element ary cha rge, D the sepa ration dis tance , к – 1 the
Debye length, k the Bo l tzmann cons tant and T the t e mpera ture and ρ ∞ a s t he conc entra tion of the
elec t rolyte in units of numbe r density. The pre ssure can cha nge si gns depending on condi t ions and is
per definition attra ctive wi th negative si gn and repul sive with a positi ve si gn . F or large separa tion
distance s eq. 96 reduc es to Π ( D ; κD ⨠ 1) = 2 εε 0 ψ 1 ψ 2 ex p( – κD ) and t hus attra ctive inter ac tions are for
oppositely cha rged surfa ce s present. For close approac h ( D → 0) the pressure goes to
Π ( D → 0) = +│( ψ 1 + ψ 2 ) kT / zeD │, which is alwa ys posi tive and thus repuls i ve . 5
The pressure acc ording to eq. 96 as a functi on of the dist ance for SiO 2 @ PDMAEMA-NPs ( d = 50 nm)
and 11.5 wt% p olymer graf ting was c alcula ted a nd is sh own in Figure 86 . The surfa ce potential of t he
NPs was approximated by expe rimental ζ -potentials . The interac t ion is attrac tive at large separ ation
(50 – 60 nm) but cha nges sign usuall y beyond the Deb ye length , whe re the osmo tic limit be comes
significant. Then ther e is an osmotic repulsio n even for oppositely cha rged surf ace s if charge re gula-
tion and van der Waa l s attra ction ar e not considere d. With decre asing NP cha rge density (incr ea sing
pH) and decr easing к – 1 the pri m ar y m inim u m and the c orresponding osmotic limit is shifte d t owar ds
smaller sepa ration d istance s. This m ea ns , that the attr ac tion and re pulsion go to sm aller separa t ion
distance s upon re ducing N P surfa ce charge de nsiti es , bu t if the NP surfac e c harge density is hi gh ( low
pH) ther e is a l o ng ra nge repulsion that appe ars at a r ound ~10 nm . Th is re pulsion at low pH may
explain the vanish ing adsor ption of the se highly cha rged par ticles compare d t o their be havior at high
solution pH. Howeve r, rela ted to our expe riments κ – 1 d ecrease with incre asing pH due to an inc rease
of the ionic s trength from pH adj ustment. Thus , the osmotic l i mit at pH 4 should be shifted t owa rds
smaller sepa ration di stance s at the same ionic st re ngth concentr ation , wh ich would l ikely enta il an
eve n st ronger NP adsorption, i n reasona ble agre ement with observations from Ji n g et al. 12 4 W e obvi-
ously worke d in low ioni c strength sol ut ion as much as possibl e due to NP s aggrega te st ronge r wit h
incre asing ionic stre ngth. Especially, NP s with s mall polymer densit i es ar e very sensit i ve to ionic
strength (see F igure 36).
99
Figure 86: Osmotic pre ssur e П as a fun ction of t h e separ ation d istanc e D c alcu l ated from eq. 96 respe c ting
differen t D ebye l engths from pH adj us t m ent and surf ace poten tial ( a s ζ -pot entia ls, se e ch apter 4 . 1 .4 ) of t he
nanop articles ψ 2 (for) Surf ace potentia l ( ζ -potentia l) of th e S L Bs ψ 1 w it h poten t ial values fro m Table 13 . Not e
that κ – 1 decre ase with increasing pH (incr ea sin g s a l t concen tration due t o pH adjus tment, si mulat ion of meas-
uremen t cond i tions).
Table 13 : Shown is the pH of the NP solu tion, t h e ion str eng th of the bu lk solution c ion obtained
from electropho retic mobi l ity m ea su remen ts, th e numbe r den sit y of ions ρ ∞ , and the zeta po tenti al
of t h e NPs ζ - NPs and vesi cles ζ -ves .
pH
κ – 1
c ion
ρ ∞
ζ -ves
ζ - NP
ζ - NP
SiO 2 @PD MAEMA
SiO 2 @NH 2
nm
∙ 10 – 4
mol/L
1/m³
mV
mV
mV
4
25.7
1.4
8.43 ∙ 10 22
-14.6
51.1
49.0
5
13.0
5.9
3.54 ∙ 10 23
-17.4
45.4
33.0
6
12.0
6.9
4.13 ∙ 10 23
-18.3
31.2
12.4
7
11.8
7.0
4.22 ∙ 10 23
-20.6
16.4
10.4
ζ = – 35 m V ζ -p otent ia l fr om suppor te d lipi d bil ayers → ζ - po t entia l of vesi c les → k e pt co nstan t
z = 1 → 1 : 1 el ectrolyt e with ace tate as anion and H 3 O + or N a + as cation
ε 0 = 8.854 ∙ 10 – 12 C/(V ∙ m)
ε r = 7 8 (w ater)
ρ ∞ = c ion ∙ N A 1/m 3
k T = 4.11 ∙ 10 – 21 J with T = 29 8 K
4.4.1 Oth er p os si ble i nt erac tions influencing the surface covera ge
Once NPs are i n molecular c ontact wit h the surf ac e the net c harge of the dec orate d surf ac e is inverte d ,
which rende rs it more difficult for furthe r NPs t o rea ch the s urfa ce. Also , the electrosta tic repulsion
of similar cha rged N Ps explains t he relatively l ow surf ac e cove rage observe d. Acc ordingly, we ob-
serve re lative low surface cove r age values for highly c harge d NP s compare d to l ess cha rged NP s,
which are i n good agre ement with result s from R IL EY an d coworke rs 12 2, 12 3 and J IN G and cowor kers. 12 4
Not discussed yet b ut not to exclude, is the influence of the polymer densi ty of such core-shell struc-
tures. Beca use polyelec trolyte brushes of core-she ll-NPs are in t he osm otic regime , the steric repulsion
100
of contra cted polymer cha ins and the result ing pressure of counter ions wit h i n the brush leads to strong
re pulsi on of SiO 2 @PDMAE MA -NPs if D c or e-surface is sm aller than the shell thickness t shell ~ 16 nm. The
re pulsi ve potentia l increa ses with increa sing graf ting d ensit y or in ot her words the adhesion energy
gain while adsorbing reduce s with increa sing pol y m er density (unless attrac tive vdW forc es would
start playing a si gnifica nt role). For c ollapsed polye lectrolyte brushes ( high solution pH) the potent ial
of t he osm ot ic pressure m ediate d by counterions withi n and outside of t he brush basically vanishes
and SiO 2 @ PDMAEMA-NP s wi th high poly m er de nsiti es ca n a dsorb on f l at surf ac e in neutra l solvent
conditions . But the st er ic repulsion of contr acte d “elec t roneutra l” polym er chains (high pH) is insen-
sitive to pH so higher graf ting densities shou ld lead to l ower adsorption affinity and t hus to lower
surfa ce cov er age, i n reasonable agreement with the dat a (Figure 74). C once rning the hi gher surfa ce
cove rage of adsorbed bigger NPs ( d = 70 nm) we think, t hat it result s from incre ased net vdW attrac -
tion due to increa sed particle size. 5 In any case vdW inte ractions betwe en phospholipid b ilayers and
the Si O 2 -NP core are expecte d t o be large and shou ld p lay a significant role her e. 5
4.4.2 VdW-d epen den ce o f ad sorpti on fo r di ff ere n t surfaces
For a spherica l particle of t he radius R NP Argento and Fre nch describe d a gener al expr ession for the
vdW forc e nea r a planar surfa ce: 5
𝐹 vdW = − d𝑊
d𝐷 = −2𝐴 𝑅 NP
3
2 ( 2𝑅 NP +D ) 2 𝐷 2 ,
eq. 97
and simplifies i n t he li mit of sm al l d istances (D ≪ R NP ) to:
𝐹 vdW = −2𝐴 𝑅 NP
8𝐷 2 ,
eq. 98
with D as the se para tion dist anc e and A the Hama ker constant.
Figure 87: Cartoon of a three-co m pon e nt system to d e scr ibe the non retard ed H a m aker co nstant A 1 3 2 for medi a 1
and 2 int erac ting across 3. In this stu dy, medium 1 re p resent the s il i ca core for bare and cor e -shell NPs r e spe c-
tively . No te, th at for core sh el l NPs t h is m odel poor l y d e scr ibes real i stic valu e s, due to th e poly me r a mount i s
neglec te d in t his mode l. Mediu m 2 is t he p l anar surfa ce and t he magn it ud e of A 22 is a funct ion of th e materia l.
Mediu m 3 corr e sponds t o t h e so lvent a nd i s se t fo r w at e r in t hi s stu dy.
In the L i fshitz t heor y the vdW forc es re sults pri m ar ily fr om inducing di poles . The strength of the force
may often depend on t he objec t size, net char ge, ele ctri c dipole mom ent or the elec tric polariza bilit y
of the mo lecules/mate rial. Thu s , the stre ngth of vd W for ce ca n be expre ssed by t he Hamaker c onstant
A and is at t he end a material prope rty . Mate rials with a high po l ar ization aff init y (meta ls) usually
have high values for A . Further more , A is s t rictly never truly cons tant at any sepa ration and decr ea ses
progre ssively a s D inc rea ses. How ever , for simplifica t i on it is a ssume d to be constant a s a funct ion of
the dist anc e. To est imate A for a thre e component syste m, A 132 i s de fined as the no nreta rded Hamaker
constant for media 1 and 2 inter acting acr oss 3 and can be appr oximate with (Figure 87): 5
101
𝐴 132 ≈ ( √ 𝐴 11 − √ 𝐴 33 ) ∙ ( √ 𝐴 22 − √ 𝐴 33 ) ,
eq. 99
wher e A 11 and A 33 ar e alwa ys t he values f or S iO 2 of the NP s, wate r and A 22 re prese nts t he planar
surfa ce material ( membra ne, SiO 2 , Au, A u@CH 3 ). Not e, tha t combini ng rela tions are only applicable
when vdW force s dominate the i ntera ction but they br ea k down on mater ials w ith a high diele ctric
constant such as water, which always l ea ds to sm aller Ha maker constant t han the rea l value. Non e-
theless, re l ative values ca n be compare d with ea ch ot her due to ke eping A 33 a lways as a constant
par ameter but absolute va l ues may diff er from re al va l ues. F rom Ta ble 14 al l nece ss ar y hama ker con-
stant values use d i n this work ar e summ ar ized. 5
Table 14 : no nretard ed h amak e r co nstants for two id entical me di a A 22 and app roximate d for m edia
1 a n d 2 i ntera ct ing a cros s 3 a s A 132 calcu l a te d via eq. 99
Materia l
A 22
A 132 (SiO 2 -H 2 O-m aterial)
∙ 10 – 20 J
∙ 10 – 20 J
H 2 O
3.70
0.00
SiO 2
6.50
0.39
Membr ane (S L B)
12.0
0.96
Au
50.0
3.22
*Au@CH 3
5.20
0.22
*Au@NH 3 +
5.20
0.22
*SAM adsorbed at the surf a ce, th us h exa d ecan e w as used to approxim a te the carb on cha in ba ckbone
As one can see from Figure 88 with incre asing A 1 32 for diff er ent surfac e types, the surfa ce cove rage β
incre ase s for strong adsorbing N P s. Note, t hat the A u@NH 3 + surfac e is st rong ly re pulsive due to
equa lly cha rged surfaces. Additionally, t he hama ker constant of t he Au@ CH 3 surfac e seems to be
much bi gger ; here we may consider the i nfluenc e of t h e gold to approximat e more acc urate A 132 for
Au@CH 3 particle inter action.
Figure 88 : Le f t: Surface cover a g e v alues as fu nction of the surf ace t yp e for st rong adsor bing NPs wi th
d = 50 n m . Add i t ional p l otted t he A 132 c onst a n t as a functio n of the surfa ce t ype (blu e); Right: Ca l cula te d vdW
force as NP-A u sur face inte raction at a NP-surface distanc e of 5 nm. In c omp arison pl o t ted t h e amoun t of graft e d
poly me r for the lowes t g ra f ti ng d ensity for SiO 2 @PD MA EM A as func ti o n of t he NP si z e.
4.4.3 DLVO int erac tion
The total i ntera ction of surfa ce s must inc lude t he van d er Waa ls and elec trostatic i ntera ction . Unlike
to the elec trostatic in terac t ion, the vdW i ntera ction is mostly insensiti ve t o the elec trolyte conce rtation
and sol ut ion pH and in firs t approximat i on conside rable as constant . With pressur e (for ce /unit area )
of the vdW inter action: 5
102
𝑃 vdW = − 𝐴 132 ∙ 𝜋
6 ∙ 1
𝐷 3 ,
eq. 100
wher e D is the separ ation dista nce and A 132 the hamak er constant for a 3 component system, the net
pre ssure (force/ unit are a) according to t he sum of eq . 96 and eq. 100 as a func tion of the di s tance is
ca lculated for SiO 2 @N H 2 and Si O 2 @ P DMAEMA- NPs ( d = 50 nm) with 11 .5 wt% polymer grafting
in Figure 89. The surfac e potentials we re approximated f rom ζ -potentials . Value s for diffe rent sol ution
pH of the NPs and SLB are taken from Table 13. Valu es for differ ent m ate rial ar e shown in F igure
89 . For bar e particles the electrostatic interac t ion ca n b e desc ribed by the DLVO the ory. For graf ted
NPs the electrosta tic int er action i s more complicated but m ay be sim p l ified by t aking t he extended
ra dius of t he polymer brush as char ged rigid sphe res (in reality sh ould be considere d as soft ones).
Charge buil d-up from the borde r of t he s hell thi ckne s s a nd below the she ll thickness, t he os motic
pre ssure is assumed to be constant due t o brush i nteri or counterions . Fur ther, t he pressure of vdW
intera ction P vdW is assumed to be a func tion of t he si lic a core surfac e of the NPs and t hat of the oppo-
site planar surfa ce. In this calc ulation the influence of the polyelec trolyte brush is not consi dered but
may enhanc e t he attractive vdW int er action. In t o t al t hi s is a very s impl e model of exp laining t he
intera ction of S iO 2 @ P DMAEMA-NPs with p lanar surfac e and poorly describe realist ic conditions,
howeve r ca l culate d pressure s ar e informa tive . F urther not explained but not t o exclude, is the not
consider ation of t he attrac t ive electr ostatic for ces betwe en si ngle char ged polyelectrolyte chains and
cha rged plana r surface once in molecular contac t (local linkage of cha ins). 5
In Figure 89a t he DLVO pressure of SiO 2 @NH 2 -N Ps is shown for an assumed SLB b ilayer with ζ -
potentials values for t he lipi d ratio of DOPC/DMPA = 95/ 05 mol% as a function of the sol ut ion pH
(see Table 13) . At sol u t ion pH 4 the pressure is attractive at long d istances but pea ks into repul sive
values (primary maximum) below the Debye length κ – 1 = 25 nm, known as the force ene rgy barrier .
Beyond the forc e energy barr ie r, it is t he vdW force dominated re gime, and the surfac e i s strongly
attra cted to the oppo sit e surfa ce. With decre asing sol ut ion pH the forc e ener gy barr ier vanishes and
NPs wi th lower cha rge ar e stronge r attra cted to the surf ac e, in r ea sonable agre ement wi th re sults fr om
cha pter 4. 2.3. The net forc e of SiO 2 @PDMAEMA-N Ps with t he highe st amount of grafte d polyme r
show a similar trend (F i gure 89b) and the de t ailed elec t rostatic interac t ion is di scussed in cha pter 4.4 .
The interac t ion shows a seconda ry mi nimum at large s epar ation (50 – 60 nm) and thus is attrac tive at
long di stance s, bu t cha nges sign usua lly beyond the De bye length and pea ks to the force barrie r (os-
motic limit) . Wit h decre asing NP char ge density (incre asing pH) and dec rea sing к – 1 t he secondar y
minim u m and the corre sponding force barrie r i s shifted t owa rds smaller separ ation dista nces . How-
eve r, t he magnitude of the forc e barrie r beginning fr om t he shell t h i ckne ss reduce s with incr easing
solution pH and values for t he for ce bar rier a re within the first 5 nm of po lymer layer penetration
consider ed to be constant . C ompare d to bare Si O 2 @NH 2 -NP t he force ener gy barr ier is much s tronger,
which reduc es t he bindi ng affinity of such polyme r grafte d NPs compare to bare sili ca NPs. An in-
cr easing polymer density lea ds to an incr ease of t he co unterion density and thus to an incre ase of the
forc e barrier, which is in good agr eeme nt with the data.
103
Figure 89 : Os motic pressur e P = (fo rce/ area) by applyi ng D L VO theory for two flat sur faces as a f unction of
the separa tion d istanc e (NPs assum ed to be f lat) Top: the int eraction is shown as a fu nction of the so l ut ion pH
for the suppor te d lipi d bil aye r (DO PC/DMP A 95/ 05 mol% ) a ) SiO 2 @NH 2 -N Ps, b ) SiO 2 @PD MA EMA- NPs
with 11.5 w t% po l ym er gr a fting , bottom : the inter a ction is sh own a s a fun ct ion of t h e surface at cons tant solutio n
pH = 4 c) SiO 2 @NH 2 -NPs, d) S i O 2 @PD MAEM A-NPs with 1 1.5 wt% polym e r graft ing. Pot entia l v al u e s are ζ -
potenti al values and for c and d values for diff e rent p la n ar surface s are assum e d and show n in the le g e nd .
Ham ake r c onst ants are take n f rom T able 14 . Not e, t hat the o smotic pressur e for po lymer grafted NPs assu med
to consta nt at t shell and not b e ing a fun ction of D . T hus , it is a very si mple model of the re al ity a nd do no t descr i be
the press ure in r ealis tic c on ditions appropri a te. How ever, c al culated force sh ows the strong rep ulsive press ure
of poly m er graf te d c o m pared to bar e NPs below th e she ll t h ickness . In any case brush interio r counte ri ons and
polyelectr ol y te chai ns leads to r e puls ive pr essure at low s e paration di st ances.
In Figure 89c and d is the DLVO pressure calcula t ed for Si O 2 @N H 2 and S iO 2 @ P DMAEMA-N Ps
assuming d iffer ent sur fac e materia ls a t fully ionize d NPs (pH 4). The pressure is prim ar ily influence d
by the surfa ce charge of the opposite surfa ce and the material, i . e . , the magnitude of the van der Waa ls
attra ction i s a function of the non-re tardet Ha maker constant A 132 . C onseque ntly, t he for ce ene rgy
bar rier is bigger for SiO 2 @ PDMAEMA-NPs compare d to SiO 2 @NH 2 -N Ps, and NPs with a huge
amount of polyme r do not adsor b . Calculat ions show , that t he for ce ene rgy barrier fo r the equa l ly
cha rged Au @NH 3 + surfa ce has t he hig hest value and theore tical pre dication clea rly conf irms that
elec t rostatic repulsion protects NPs from adsorption. Th e lowest forc e ener gy barrier is for the anionic
Au -surfa ce media ted f rom the h ighest surfa ce potential and the biggest Ha maker consta nt , whe re N Ps
adsorb t he st ronge st o nto the Au-surfa ce. For the di fferent surfac es the force ener gy barriers are in
betwe en t hose two extre mes, indica t ing t hat the ad sorption affinity of the NP s incre ases wit h
Au@N H 3 + → Au@CH 3 → SiO 2 → SL B → Au, in rea so nable agree ment with data from chapte r 4. 2 . 5 .
Howe ver, data exhibit strong adsorption for Au@ CH 3 but theore t ical ca lculation predicts a modera te
adsorption. Probably t he forc e ener gy barr ier is not strong enough or the Au somehow increa ses the
Hama ker consta nt , wher e particle s with low amo unt of graf ted polymer will adsorb rather strong ly at
104
the surfa ce. Note, that the surfa ce is approximated to be fla t. In reality , values for the pre ssure should
be smaller as the surfac e covera ge of spherica l N Ps all ows an ea sier excha nge of counter ions with
the bulk solution. Thu s , the os moti c l imi t shoul d be rea ched at smaller separa t ion di stance s as calc u-
lated from eq. 96 .
4.4.4 Con ce nt rati on de pen den ce of ads orpt i on
The conc entra tion depende nt results for NPs wit h mode rate polymer densities ar e clear ly surprising .
Just from our results we postulate, t hat the t o t al ene rgy o f adhesion decr eases upon incre asing po lymer
density. P article s with a h igh amount of polymer do not adsorb bec ause E ad ≪ kT resul t ing from strong
steric and elec trostatic repulsion at sma ll separa t ion di s tance s. In contra st , partic les without polym er
provide enough adhe sion ene rgy: E ad ⨠ kT due to elec t rostatic attrac t ion and lac king steric re pulsion
at small separa tion d i stance s. Tha t expla in s t he trend for higher par ticle number densities for har d
SiO 2 @NH 2 compa red t o SiO 2 -PDMAEMA- NP s. Inter esti ng are particle s with inter mediate graf ting
densities, where E ad ~ kT resulting in weakly bound pa rticles at t he surfac e, which should easily af-
fe cted by a dditi onal fac tors. The nanopartic le a dsorptio n is a dy namic pr ocess de pending on the com-
petition of t he af finity of i nd i vidual par ticle to adsor b versus the particle -par ticle interac tions. The
latter is conce nt ration and proba bly shear depende nt . The flow of t he bulk solution i s par allel t o t he
interfa ce and wea kly bound par ticles may feel the l on g range electrosta tic repulsion of i dent i ca lly
cha rged particles and theref or e alre ady adsorbe d particles are pushed awa y in a par allel direc tion from
the surfac e. Thus , particles disperse d i n the bulk so lution are able t o “grind” particle s from the inte r-
fa ce in a k ind of “sa nd paper effe ct” , which i s contro l led by t he shear ra te and NP conce ntration.
Higher shea r ra tes a nd NPs conc erta tion incre ase t he “p ushing potential” for a dsorbed NPs . How ever ,
this eff ec t af fec ts only weakly bound par ticles , whi le strongly bound Si O 2 @NH 2 - NPs w i ll re main on
the surfa ce. This appea rs to be a plausible expla nation a s the eff ect is cle arly depende nt on flow rate ,
being re levant for high ( V solven t = 100 μ L/min) but m uc h l ess at low flow rates ( V solv e nt = 15 μL/min)
(see Figure 78d, page 90 ).
105
4.5 Adsorp tion kinet ics
Fi gur e 90 : Cartoo n o f mixing NPs wi th v e s i cl es. a) t w o se para te sol utions of eith er NPs and ves i cl es wi ll be
quickly mi x e d t og ethe r . b) NP s inter ac t with t he v esicl e s a nd m ay adsorb o n t he v esicl e sur face du e to elec-
tro static a ttr action. c) d e corat ed vesi cle s , thei r su rf ace charg e is conv erted.
Previously the sta tic beha vior was discussed in detail. At least as imp ortant is the kinetics of t he nano-
par ticle/membrane intera ction, as i n colloidal sys tems one may have lar gely reta rded struc tural for-
mation. It may depend on the colloidal stab i lity of the components i nvolved. The funda mental kinetics
of the inte rac t ion of nanoparticle s with a phospholipid bi layer , as a model system for cell membrane s,
has poorly been studied yet and s o far , little information is known. This m otivated us to s tudy t he kinetic s
of the N P adsorpt ion on p hospholipid vesicles. Ma inly we used cationic SiO 2 @NH 2 a nd
SiO 2 @PDMAE MA-NPs wi t h a poly mer coating of 5. 5 wt%. The vesicle char ge wa s anionic and their
cha rge density was controlled by the ratio of zwit terionic and anion ic pho spholi p i ds DOPC and DM P A
employed similar as introduce d in cha pter 4.2 ff.
Figure 91: a) Sc attering intens i ty as a func t ion of t h e s c atte ring vect or fr om stati c light s cattering e x perim ent for
vesicles w it h 0 mo l % DMPA con te n t , data w as f it t ed using t he Gu i nier Appr oxima tion to cal culate the ra d ius of
gyration R G of t he vesicl e s. N ote th at for v esicl es t h e R G i s equal to the radius; b) R G plo tt ed as a func t ion of t he
DMP A conten t for d ifferen t ly c harged ves icles.
Beca use the si ze of the NPs ( d ~ 50 + 32 nm) is huge the corre spondi ng vesicle size should st ill be larger .
Thus, the desire d size of t he ve sicles wa s c hosen to be b igger a nd w as prac tically a chieve d v ia e xtrusio n
106
using pore fil ters in a diamete r of 400 nm . Thi s yields in vesicles with a m ea n diameter of around
320 nm, wh ich was confirmed v i a stat ic light scatter ing (F igure 91).
The NP-membrane intera ction was followed by t he st o pped flow technique, where the int er action (ad-
sorption or repuls ion) was m ea sured wi th time resolve d X-ray and t ra nsmi s sion measure ments (light) .
Prior int o discus s ing the theore tical ba ckground of the measure ment, we brie fly e xplain the m ixing pro-
ce dure of the stopped flow tec hnique.
Figure 92 : Sch ematic overvi ew of a stop ped f low t echn i que in c o m binat ion wi t h a t ime reso lved X-r ay measur e-
ment. A s tructural simil ar i nstr ument ation setup is for ti me resolved t u rbidity m eas uremen ts.
Small volumes of a solution are injected from high per for mance syringe system with a high eff icienc y
mixing proce dure and the samp le passes through a measure ment flow cell ( Figure 92). The flow is ab-
ruptly st opped by a shutter (so ca lled hard stop) t rigger ed elec tronically, which allows the observa tion
of the mixed syste m at l ea st after 1 ms (depe ndi ng on the flow-ra te) si nce the mixi ng time. Structural
cha nges can be detec t ed by ti me resolved tra nsmi ssion, fluore scenc e, conductivity or in or der to obtain
more st ruc tural information even with t ime resolved SAXS, SANS measure m ents. We st u died the s truc-
tural cha nges via transm i ssion ( l ight) and SAX S measur ements.
If NP s adsorb on a vesicle surfa ce, they mimic the shape of vesicles cre ating d ecora t ed vesicles as de-
picted in Figur e 93 . Such s tructure s scatter the l ight muc h stronger and t he tim e resolve d turbid ity in-
cr ease gi ves informa tion about the kinetics of NP adsor ption onto the vesicle s . Henc e light gives an
over all picture about t he aggrega tion, structura l details about the N P adsorption can be obt ained via ti me
re solved S AX S m ea sureme nts. While t he acc urate form fac tor as i llustra t ed Figure 93 a i s complex to
model (sma ll spherica l core -shell par ticles on a bigge r spherica l shell), such structur es in first appr oxi-
mation may be assumed as a shell-shell formation . The n the scattere d int ensi t y as func tion of the sca t-
tering vector q may be descr ibed by a shel l -shell form fac tor. Fur ther, respec ting the scattering l ength
densities of a l l c ompone nts t he majority of the sca t tered inte nsity results from the NP c ore a nd the shell-
shell form fa ctor can be si mp lified in a shell form fac tor as shown in Figure 93b . Then, for the fre shly
mixed NP vesicle mixture t he scattering i ntensi t y as a function of the scatter ing vector q may be de-
scribe d by a spheric al form fac tor approximation. B ut with incre asing time t he int ensi t y in the low q -
re gime i ncr ease s due to N P adsor ption (Figur e 93 d and see chapter 2. 3 .4).
107
Figure 93 : a) Simpl e model of NP adsorp ti on on v e si cl es . A shell for m factor is assum e d for the adsorb ed NP s on
the surf a ce. b) s a m e mode l resp ecting t he s ca tte ring c on trast for X- ra ys of sin gle co m pon ent s . c) sc atter ing length
densities r elated t o X-r a y, d) s i mula t ed sc attering pat te rn of the v esicle NP mixtu re at the i n i tial time, re d a rrow
indica te s the oscil lation min im u m of t he spher ical for m f act or, e) s imulated scat tering i n t ensity , if NPs adsorb at
the v esicle assum i ng a sh e ll for m fa c tor, wh ere the n et S L D is a su m of adsorb ed NPs p er she ll v olume (s imula ti on
details are pr esented in App endix . S i m ulation e x hibit an i ncrease of t he i nt ensity i n the low q -r e gime compar ed t o
the SAX S p a ttern pres ented in d), red a rrows indi cate the sc a ttering of t h e aggre gated s tructur e i n the l ow q -regi me
and t h a t of t h e pur e NPs from the first oscillat ion m in imum . R ed dotted l in e indi c ates the minimu m of the measured
q -range in th is study.
First , we present the static SAXS data of all NPs and vesicles in Figure 94 . T he data of the bare
silica NPs can be approximated with a sphe re f orm factor f it , which res ults in a co r e radius
R = 26 nm and a PD I = 0.08. The cationic core-s hell SiO 2 @PDMAEMA- NPs shows some ag-
gregates, but in reas onable agreement with the data reported in the chapter 4 .1. 7 . Note , that f or
the stopped flow measurement NPs had to be resynthesized and dif fer slightly in the size from
the particles described there . The magnitude of the scattering intensity o f the v es icles is very
low and confirms that the contrast between vesicles and water bulk solution is low .
108
Figure 94 : Scatt ering da ta of vesi c les , SiO 2 and SiO 2 @PD MAEMA-NP s, l ef t: log -log-pl ot, ri gh t: For a be tter
compar i son for t he in tensity inc r e as e t he d a ta is p l ot ted as a Krat ky-Po rod-plot ting style. A logari thmi c plott ing is
depict ed in th e app endix.
4.5.1 Time resolv e d s catteri n g measurem en ts
Figure 95 : Shown is an exa m ple time reso l v ed SAX S measu re ment . Fo r a bet te r view data plo tted Kratky-Porod
plotting style.
In Figure 95 ar e shown exa mple measurements of time resolved S AXS data of hi gh l y negative ly charge d
Si O 2 -N Ps (pH 9) and positi vely c har ged SiO 2 @PDMA EMA-NPs with 5 . 5 wt% of gra fted polymer ( pH
5) . F or bare S iO 2 -NPs data exhib it in the low q -regime a constant intensity over time . In gene ral, SiO 2 -
NPs do not adsor b on vesicles surfa ce at pH 9 for cha rg ed and uncharge d vesicles, so further NP -mem-
bra ne inte rac tion was not study into detail anymore . Pro bably SiO 2 - NP do no t adsorb on vesicle s due t o
elec t rostatic re pulsion of similar charge d comp ounds . For cationic brush gra fted N P s an intensity i n-
cr ease in the low q-r egime over the t im e is pre sent. The int er action was stud ied in deta il with eit her har d
SiO 2 @NH 2 or soft S iO 2 @PD MAEMA-NPs w it h 5 .5 w t% of grafte d polymer . We varied two i m portant
par ameter s. The first is the i nfluenc e of li p i d charge density s impl y by the ratio of DO PC and D MP A ,
wher e higher DMPA content i ncr ease s t he vesicle char ge density, respe ctively. The sec ond is t he influ-
enc e of the NP conce nt ra tion, where the data is normali ze d to particle nu m ber densi t y of the vesicles as
[NP]/[V es] ratio. St ruc tural information of the aggre gati on N agg was obtained from S AXS data. By doi n g
so the exper imental N agg was estimated by dividin g the forwa rd sca ttering I 0 of the final ver sus the ini tial
state via eq. 49, where I 0 was approximated via the G uinier approxima tion (e q. 50). 88 The theoretica l
[NP]/[V es] ratio is compar ed wit h experimenta l value of N agg and is shown in Figure 96c and d . How-
eve r, estim ate d N agg do not incre ase as strong as one would expe ct for t he t heor etical values (dar k marked
line) and shows that the N agg is not a functio n of the NP conce nt ra tion or the ve sicle char ge densit y . This
109
is i n rea sonable agr eeme nt wi th adsorp tion studie s v i a the quar tz crystal microbala nce with dissipa tion
(see cha pter 4.2. 2), where surfac e covera ge values for the smalles t NPs in high char ge conditio ns are
not extendin g ove r 20 % . Fur ther the ave rage gyratio n radius R G show an i ncr ease from the initi al
R G,0 = 157 ± 4 nm to final R G,f = 180 ± 20 nm and confi rms the si ze gain of the bare into dec orate d ves-
icle. No te, t hat for the highest [NP]/[ Ves] ratio a repul sive struc ture factor may be prese nt , wher e the
Guinier appr oximation may not be valid anymore .
Figure 96 : a ) Exam ple data of the initial and fina l s t ate , b) R G of decor a ted and pure vesicl es, c, d) est imated N agg
from forwa rd s c attering I 0 .
110
Table 15 : m e asur e d in t ens ity I a t q = 6 .6∙10 – 3 nm -1 f or in itial and fin a l stat e. A p proxim a t ed intensi t y
I 0 for ini ti a l and fina l state, cal culated aggrega tion number N a g g and gyr ation radius at t he fi n al st ate
R G
DOP C/ DMP A = 98/02 m ol%
[NP]/[Ves]
I ( q = 6.6 ∙ 10 – 3 nm -1 )
initial state
(da ta)
I ( q = 6.6 ∙ 10 – 3 nm -1 )
final state
(da ta)
I 0
initial state
(ap pro xima ted)
I 0
final state
(ap pro xima ted)
N ag g
R G
cm – 1
cm – 1
cm – 1
cm – 1
nm
10.42
452
835
600 (53)
9000 (990)
15 (2)
187 (5)
6.14
462
702
1020 (167)
8000 (1310)
7.8 (1)
196 (9)
4.86
400
625
1200 (181)
6500 (990)
5.4 (1)
189 (9)
2.21
492
720
980 (92)
4000 (376)
4.0 (1)
168 (5)
1.96
325
410
800 (43)
3500 (472)
4.3 (1)
175 (8)
1.74
225
327
780 (85)
3200 (491)
4.1 (1)
178 (13)
0.79
202
257
500 (77)
3000 (467)
6 (1)
192 (10)
DOP C/ DMP A = 90/10 mol%
[NP]/[Ves]
I ( q = 6.6 ∙ 10 – 3 nm -1 )
initial state
(da ta)
I ( q = 6.6 ∙ 10 – 3 nm -1 )
final state
(da ta)
I 0
initial state
(ap pro xima ted)
I 0
final state
(ap pro xima ted)
N ag g
R G
cm – 1
cm – 1
cm – 1
cm – 1
nm
38.2
300
800
480 (67)
800 (110)
1.7 (1)
169 (5)
17.3
512
1198
816 (89)
10000 (1097)
12.3 (1)
211 (11)
10.4
608
842
960 (94)
9000 (885)
9.4 (1)
185 (6)
6.14
490
728
784 (81)
7000 (744)
8.9 (1)
181 (5)
4.86
403
600
640 (61)
5500 (611)
8.6 (1)
178 (6)
3.47
390
525
624 (43)
3200 (330)
5.1 (1)
182 (6)
1.74
252
321
400 (55)
2800 (304)
7.0 (1)
178 (5)
1.04
180
220
288 (41)
2000 (293)
6.9 (1)
183 (7)
0.79
61
121
96 (14)
1000 (149)
10.4 (1)
173 (7)
0.3
42
63
64 (53)
60 (8)
0.9 (1)
178 (8)
111
4.5.2 Adso rption rate for cati on ic NP s wit h ani onic v esicles
Figure 97 : I ( q = 0 . 0063 nm – 1 ) as a functi on of th e time on diff erent c h a rged v e sic le s , a) DOP C/DMP A 98/02
mol%, b) DOPC/D MPA 90/10 m ol%, tr a nsm ission as a funct ion of th e t ime c) DOPC/DM PA 97/03 m ol%, d)
DOP C/ DMP A 95/05 mol %; da ta fitted v i a eq. 101 and th e f it is shown a s a dar k l ine. For a b e tter view f or c) and
d) t h e t i me scal e is p resente d in log sc ale and sh own in the A ppe nd ix.
Yet discussed i s the aggr egation behavior of NP -ve sicle mixture s vi a tr-SAXS-data. The measur ements
for anionic vesicles with ca tionic hard and sof t NPs -ves icles mixture w il l be discussed . For the ana lysis
of the time resolve d -SAXS experiment the sca ttering i ntensity was follow ed at q = 6 . 6 ∙ 10 – 3 nm – 1 , i . e .
at the l ow q limit of the e xperiment, a s her e one expe cts to see the ove rall size of the a ggregate s pre sent.
In these experiments char ged vesicles with 2 and 10 mol% DMPA conte nt wer e st ud i ed. Additional ly,
we studied trans mi ssio n measure m ents for the same Si O 2 @PDMAEMA-NPs for di ffe rent vesicle sur-
fa ce charged densities (3 and 5 mo l% DMPA content) and for Si O 2 @NH 2 - N P s. In bo th measur ements
technique s, we observe at ver y l ow and ver y high NP c oncentra tion no i n tensity changes over the time ,
i . e . , the number of dec orated vesicle s is too low to detec t or so high that the sca ttering i ntensi ty resul ts
mainly f rom sing l e d isperse d N Ps. I n be tween these e xt r emes the intens ity cha nges w ith incr easing ti me
and is fi t ted wi th an exponential functi on :
112
𝐼 ( 𝑡 ) = 𝐼 0 ∙ exp ( 𝐴 ∙ 𝑡
𝜏 ads ) + 𝐼 end { 𝐴 = 1 ( SAXS )
𝐴 = −1 (tu rbitdity) ,
eq. 101
which allow us t o calc ulate chara cter istic t ime constan t τ ad s requir ed t o rea ch t he equilibrium. In both
ca ses one observe d an increa sing eff ec tive mass of the scatter ing objects, either by the increa sing scat-
tering intensity in SAXS or the reduce d transmi ssion in light. This incre asing mass then can simply be
attributed by the nanopa rticles at t ac hing to the vesic les.
Figure 98 : τ ads v alues for differ ent c h arge d ves i cles from bo th measur ements (SAX S a nd turbidi ty) fo r cationi c
NPs (po lymer coated a nd u ncoat ed), lines guid e s t h e tr end a nd represen t no li n e ar fitti ng, le f t: τ ads values for t h e
[NP]/[Ves]-r atio and b) ch arge r atio Z = [N + /N – ].
In gener al, SiO 2 @NH 2 -N Ps have much smal ler τ ad s than the Si O 2 P DMAE MA-NPs ind icating the parti-
cles wit hout a po lym er fa vorizes stronger t o a dsorb a t t he ve sicle surfa ce. Da t a exhibit two main trends.
The first one i s a decre ased decay to t he equi li brium with incre asing charge density of t he vesicle s, due
to a mplified e lectrostatic attraction . This interpre tation may be c onfirmed if the data is pl otted as a func -
tion of the char ge ratio Z = N + / N – , wher e a linea r behavior betwe en τ a d s and Z i s obser ved.
The second tre nd is an incre ase of the de cay wit h increa si ng [N P]/[Ve s]-ra tio. In f irst approximation the
re sult i s completely unexpec ted but once NPs adsorb on a vesicle surf ac e t he surfa ce net char ge is in-
ver ted f rom a nionic ve sicles to ca tioni c dec orate d vesicles. Fur ther NP a dsorption is re ndered and leads
to a n incr ease in the de ca y rate . To c onfirm the c harge conversion hypothesis, we mea sured t he electro-
phore tic mobi l ity of NP-vesicle mixtures to calc ulate th eir re spective ζ -potentia l. In Figure 99 data s how
highly nega tive potential s for pur e vesicle s, bu t bec omes more neutral with incre asing N P conc entra tion
and is inve rted afte r critical [NP]/[Ve s] ratio. The char ge inversion is fa st er for lower cha rged vesicles
compar ed to higher cha rged vesicles.
113
Figure 99 : ζ -pot ential for ves i c le - NP -mix t ures a s a fu nction of a) [NP] /[Ves] r a tio (No t e, that [NP]/[V e s] = 0 cor-
respond pure v esicl e so lution) , b) as a fu nc tion of th e ch arge ratio Z .
4.5.3 Visual insp ec tion of Vesicles NP m ixt ures
Figure 100 : Mo lecu la r formul a for N ile- R e d.
Not yet discus sed but n ot t o exclude is the observa t ion of the NP-membrane intera ction on a mac roscopic
sca le. Thus, we stud ied our ve sicles via op tical micr osc opy. P reviously r eporte d vesic les a re in compa r-
ison to the resolut i on limit for an optica l mi cr oscope t o s mall . Thu s, we pre pare d highly anionic vesicles
in a diameter of 800 nm vi a extrusio n and embedded t h e dye Nil-Red i n t o t he bilayer membra ne. Note ,
that N P s are beyond the resolution limit and not marked with a dye . The vesicles ar e at the boa rder of
the resolution limit but can be seen as sphe rica l objects in the transpa rent and fluore scent mode (F igure
101) . We recor ded picture s of differ ent NP -vesicle m ix tures after 40 mi nute s since the mixing time. In
c and d a re S iO 2 -NP s wi th ves i cle s m ixed, where the solution shows spher ical vesicles i ndicating no N P
adsorption, i n re asonable agree m ent with tr -SAX S me asure ments . In contra ry, for dissimilar char ged
compounds (Figure 101) macrosc opic st ructur es of und efine d shape s in size range fr om 10 – 80 µ m are
pre sent, where the bigge st structures are seen for ca tionic NP s withou t any pol ym er grafting. Data ex-
hibit for NPs wit h polym er graf ting st ill occ asional si ngle vesicles . The mac roscopic st ructur es may
re sult from t he low surfac e char ge ( ζ < 25 mV < kT ) as shown i n Figure 99, wh i ch leads to sl ow aggre -
gation and finally to phase sepa ration after longer t i me . Howe ver, not to exclude is the possibili ty , tha t
such dec orate d vesicles m ay break and for m dom ains of lamellar l ike phases w it h embedde d NP s in
betwe en, where the NPs ac t as bridg i ng agent betwe en tw o or more b i layer s.
114
Figure 101 : Microscop y pict ures o f ves i cle NP mixtures , L eft: t rans mi ss ion mode ; Right : f luoresce nt mode with
excitation w avelength λ ex = 520 n m and emissi on w avelength of λ em = 54 0 nm .
115
4.5.4 Discu ssi on of kinetic meas urements
In total, the intera ction i s primarily of ele ctrostatic natu re, where S iO 2 -NPs do not adsorb at the vesicle
surfa ce due to e lectr ostatic r epulsion . For di ss imil ar cha rged surfa ce the aggre gation number s of ve sicle
NP -mi xtures ar e low, presumab ly due to m utual repulsi on of similar char ged NPs on t he vesicle s urfa ce ,
in rea sonable agr eeme nt wit h results from cha pter 4.2.3 . Howe ver , with increa sing NP conc entra tion t he
adsorption rate increa ses at a constant vesic le surface ch arge density . This result s from the surfa ce
cha rge inversion of pure anionic vesicle i nto cationic decora t ed vesicles . The latter re pel s further ap-
proa ching cationic NPs from t he surfac e aw ay. The surf ac e cha rge conver sion is faster for lower c harged
vesicle s compare d to higher char ged vesicle s. Thus, th e adsorption kinetics i ncr ease s with incre asing
vesicle charge density and clea rly confirm s , that the pri m ar y i nfluenc e of the inte rac tion is m ediate d by
elec t rostatic intera ction. For NPs with grafted po l yele ctrolyte, t he p olyelec trolyte la yer lea ds to tenden-
tially bi gger adsorption rates. The attrac tive forc es ma y be co mpeted by addi tional repulsion force s
mediated from steric intera ction of the cha ins and the osmot ic pre ssure of counterions , respe ctively. The
exc hange of counterions wit h t he bulk solution and the reorde ring of polyelectrolyte chains may nee d
time whi l e approa ching at the surfac e and slows t he ads orption.
Fur ther, in a first approximat ion both nanosize d obj ec ts need to di ff use t hrough the solvent bef ore they
get i n m o l ec ular contac t for a succ essful NP adsorptio n on the vesicle surf ac e . Here i t is particula r i n-
tere sting, i f t he proc ess of NP adsorpti on is d iffusion limited. For a succe ss ful adsorption one equivale nt
of NP and one equivale nt of vesic le rea ct into a NP- vesicle structure and the rea ction rate R is de-
scribe d: 127
𝑅 = 𝑘 12 ,r ∙ [ NP ] ∙ [Ves] ,
eq. 102
wher e k 12 ,r is the re action rate constant, [NP] the nanop article conc entra tion and [Ves] the vesicle con-
ce ntration. From the eq. 102 the reac tion ra te depe nds on N P and vesicle conce nt ra tion and is per defi-
nition a second order rea ction, whe re k 12 ,r may depe nd on t he diffusion of vesicles. Latter relate s to the
ac tivation ener gy E A via t he Arr henius equation:
𝑘 12 ,𝑟 = 𝑘 12 ∙ 𝑒𝑥𝑝 (− 𝐸 𝐴
𝑘𝑇 ) ,
eq. 103
with k as Bolt zma nn constant , T = 298.15 K t he tempera ture, k 12,r the measure d rate cons tant abbre viated
from the deca y tim e τ ads and the initial nanopar ticle con centra tion [NP] 0 , τ ad s = ( k 12 ,r ∙ [Ve s] 0 ) – 1 , and k 12 as
the rate constant for the di ffusion limited case equal t o t he preexpone nt ial fre quent fac tor . Unde r as-
sumption of Sm o l uchowski diffusion the rate constant k 12 c a n be calculate d via: 127
𝑘 12 = 4𝜋 ∙ ( 𝐷 𝑣𝑒𝑠 + 𝐷 𝑁𝑃 ) ∙ 1
∫ 𝑒𝑥𝑝 ( 𝑈
𝑘𝑇 ) ∙ 𝑑𝑟
𝑟 2
∞
𝑑 12 ,
eq. 104
wher e d 12 = R v es + R NP is the co lli si on diameter, D v es and D NP are the diffusion coeff i cients of vesicles
and NPs. Under assumpt ion that the re is no intera ction ener gy ( U = 0 J) between vesicle s and NPs the
term ∫ exp ( 𝑈
𝑘𝑇 ) ∙ d𝑟
𝑟 2
∞
d 12 si mplif ies i n t o 1/ d 12 and lea ds t o the simple expre ss ion for k 12 : 127
𝑘 12 = 4𝜋 ∙ ( 𝐷 𝑣𝑒𝑠 + 𝐷 𝑁𝑃 ) ∙ 𝑑 12 .
.
eq. 105
Both values for the diffusion coef ficie nts were ca lculated via the Stokes Eins tein Rela tion. For vesicles
( R = 160 nm) and S iO 2 @NH 2 - N P s ( R ~26 n m) k 12 is 2. 56 ∙ 10 – 17 m³/s and for SiO 2 @PD MAEMA
( R ~ 42 nm) k 12 i s 1. 78 ∙ 10 – 17 m³/s .
Now to compare the reac tion rate R f rom experimenta l data versus t heor etical calc ulations we furthe r
ca lculate R at the initial t ime t = 0 s, her e denoted as R 0. The re action rate R for a chemica l reac tion is
116
per def initi on the c oncentra t ion c hange per time ( R = d c /d t ) a nd so fa r pr ese nted in this st udy in un its of
1/(m 3 ∙ s) . Adsorpt ion rate τ a d s was obtained fr om experimental data by approximat i ng the data with a
simple exponential deca y model acc ording to eq. 101 . To ca lculate R 0 fr om approximate d functio n, the
slope at t = 0 s ca n be inter prete d as R 0 and the derivate of eq. 101 leads to:
d𝐼 ( 𝑡 )
d𝑡 = 𝐼
𝜏 ads ∙ exp ( 𝑡
𝜏 ads ) ,
eq. 106
wher e I is the intensity at any time t . N eglec ting t he del ay time of the s topped f low instru ment ~ 8.5 ms ,
the int ensi t y I 0 at t = 0 s corre lates onl y from si ngle NPs and vesicles and i s proportiona l main l y to t he
initi al conc entra tion of N Ps. Thus I 0 ~ [ NP ] 0 and eq . 10 6 can be transfe rre d int o:
𝑅 ( 𝑡 = 0 ) = d𝑐 ( 𝑡 =0 )
d𝑡 = [ NP ] 0
𝜏 ads ∙ exp ( 𝑡 0
𝜏 ads ) = 1
𝜏 ads ∙ [ NP ] 0 ,
eq. 107
with [ NP ] 0 as t he in iti al c oncentra t ion of t he na nopart icles, and τ a ds = ( k 12 ,r ∙ [ Ves] 0 ) – 1 as the mea sured
adsorption rate. The initial conce ntration [ NP ] 0 in the measure m ent chamber is well known and can be
ca lculated from t he ratio and the vol u m e, conc entra tion of both (vesicle and NPs) injected stoc k so lu-
tions. Details about this calcula tion are shown i n the appendix. The t heor etica l value of R 0 is ca lculated
via eq. 102 by insertin g for the conce ntration the initi al conce ntration ([NP] = [N P] 0 , [V es] = [Ve s] 0 )
and rate constant k 12 . Experimenta l and t heor etical values for R 0 are shown in Figure 102 .
Figure 102 : a) R 0 as a func t ion of t he nanopar ticle t o vesic l e ratio. b) A ctivatio n Energ y as a f unction of [NP] / [Ves]
ratio. L i nes show the t h eoreti cal activat ion e nergy for di ff usio n limited s i tuat ion for bare and poly mer gr afted NPs .
Consecutively, theore tical values are higher compare d t o m ea sured values for R 0 and differ in orde r of
2 magnitude . Surpris i ngly, theoretica l values predict a maxi m um of the reac t ion rate at a [NP]/[Ve s]
ra tio of 5, where values for experimenta l data we akly de crease with incr easing [NP]/[Ve s] ra tio . Values
for R 0 are sm aller for polymer grafte d NPs compare d to bare NPs. This in rea sonable agree m ent due to
the smaller diffusion coef ficient lea d t o weake r collu sions per tim e. Further more, we ca lculated the
ac tivation ener gy E A . We assu me un der perfe ct adsorpti on , no re pulsive or at trac tive inte rac t ion betwee n
NPs and vesicles but on ly considering the diffusion li mit ation , t hat k 12 ,r is equal t o the preexpone nt ial
fre quent fa ctor k 12 a nd E A = 0 kJ/mol . De t ail s a re shown in appendix 9.6 . Thus , the c ompa rison betwe en
value for E A for the diff usion li mit at ion ( E A = 0 k J/mo l) and e xperimental va l ues ( E A > 0 kJ/mol) abbre -
viated from the deca y τ ads clear ly show , that the reac t io n is probably not diffusion limited, wher e both
NPs-types show l ar ger values for E A ~ 10 kJ/mol . This may explain the l ar ge di ff ere nces in t he initial
re action rate in order of 2 magnitude , where theore tical values for R 0 expec t muc h faster equil ibration
times (~ τ ads ~ 10 m s) c ompa red to measur ements of ( ~ τ a d s ~ 2 s). Thu s , t he net i nterac t ion is not ze ro a nd
not ea ch collision leads to a succe ssful bi nding . Then, E A is probably not zero and the magnitude o f E A
might be attribu ted from fol lowing physical reasons:
117
- 1 : The elec trostatic interac tion betwe en oppositely char ged NPs and vesicles influence s E A . The
elec t rostatic attraction be t wee n oppos itely charge d c ompounds exte nd s t he ef fe ctive inter action
diameter due to lo n g ra nge elec trostatic attrac t ion. An incre ase of the surfac e pot ential Ψ s of
vesicle s or NPs increa ses the effe ctive interaction diam eter due to the Gouy -Chapman-lengths
from elec tric double layer s i ncre ases. Thus , we hypoth esis t hat E A ( Ψ s ) and decr ea ses when Ψ s
incre ase s. It seems to be pl ausib le whe re exper imental data (F igure 98) confirms a dec rea se of
E A with incre asing surfac e cha rge of the vesicles.
- 2 The osm otic limit m ay reduc e the coll ision rate betw een NPs and ves icles and thus i ncr ease
E A . Then the reac t ion rate is much s maller as theore tic al values predic ts. T hi s may probably
have the major i nfluenc e and l ea ds to diff er ences from exper imental versus theoretica l values
of R 0 in orders of two magnitude s. As discusse d in chapt er 4. 4 (page 95) highly opposite char ged
surfa ce may undergo the o smotic limit in close molecu lar contact (small sepa ration distanc es) .
The osmotic pre ssure of oppos itely cha rged surfa ce mediated from competing double layer re-
duce the probability of mol ec ular contact collisions, w hich i s a function of surrounding coun-
terions respe ctively. This eff ec t is enhanc ed for po lymer grafte d NPs, where st er ic eff ects of
polyelec trolyte chains and brush interior counter ions l eads to stronger repuls i ve for ces com-
par ed to bare NPs, i . e ., i n rea sonable agr eeme nt with th e data displ aye d in Figure 98 .
- 3 : The previou sl y mentioned “re action/adsorption” co nditi ons assume a single NP adsorpti on
on a single vesicle. But i n prac tice m u l tiple NPs can adsorb on a si ng l e vesicle , respe ctively .
Then for one vesicle t he NP adsorpt ion may be explain ed as a multi-c hain rea ction, wher e eac h
individual NP adsorp ti on can be consider ed as a single reac tion. Eac h si ngle rea ction has a dif-
fe rent ra te constant k 12 ,r and latter decre as es constantly w ith incre asing NP adsorpt ion . The phys-
ical re ason is a long ra nge elec t rostatic repuls iv e in tera ction of equa lly cha rged dec ora ted vesi-
cles wit h approa ching NPs (c harge c onversion of vesicl es, see Figur e 99) and thus t he repulsive
potential inc rea ses E A with incr ease d num ber of adsor bed NPs . This seems t o plausible con-
firmed fr om time resolved experimenta l data (se e Figure 98).
To summarize , theore tical values for R 0 diffe r fr om experimenta l values in an order of 2 ma gnitudes and
should predict much faster equilibrations ti me if only considering Smoluchow ski diffusion . Vesicle s
and NPs may get fast in close contact mediated from d iff usion, but t he approa ch in to molecula r contact
in sm all separ ation distanc es is sl owe d from differe nt physi ca l re asons likewise the osmotic l i mit of
oppositely charged surfa ces and t he surfa ce charge i nver sion of decor ated vesicle s , which incre ases the
ac tivation ene rgy E A for bi nding. So fa r f rom our inter pretation, the i ntera ction is primar ily mediated of
elec t rostatic intera ction and pure diffusion limi tat i on can be excluded as much fa ste r reaction rate s
should be observed.
118
5 Conclus ion
5.1 Pr ep ara tion of nan oparti cles (NP s) modifie d w it h d if ferent p oly-
mer sh ells
In the main par t of th is work we studied the inter ac tion of phospholipid membrane s with nanopar ticles ,
which wer e surface modified anionica lly and cationica lly by either a functional group or gra ft ed poly-
elec t rolyte brush. For that purpose, we syn thesized well-def ined si lica and sil ica-polye lectrolyte nano-
par ticles, whose core size (24 – 70 nm) and po lymer shel l ca n be varied sy stematica lly, and these hybrid
NPs show pH-re sponsive beha vior, a s for the poly mer shell weak polyele ctrolytes we re chose n.
Polym er ization was done by a surfac e-initiated atom tr ansfe r radica l polym er ization (ATRP) . As cati-
onic polym er we emp loyed PDMAEMA and for the an ionic poly mer PMAA , where the latte r was ob-
tained afte r hydrolysis of the in i tially formed P t BMA. The amount of attache d polymer was con trolled
by t he amoun t of added monomer in the reac tion batch . C harging of t he NPs is nece ss ar y to have col-
loidal st abili ty i n wa ter and to i n hi bit agglome ration in solu tion. Th is mea ns t hat up on re ducing the
cha rge density, inc rea sing pH for P DMAEMA and dec rea sing pH for PMAA, one observe s agglo mer-
ation and precipitat ion in t he samples .
The obtained hybr id N P s were then cha rac teriz ed in detail by thermogr avimetric ana lysis (TGA ), static
and dynamic light scatter ing (SLS , DLS) , and sma ll - angle neutron sca ttering ( SANS). For ani oni c
brushes t he shell th ickness is simpl y c ontrolled by the monom er conc entration a s typica l ly ob serve d for
living radica l pol y meriz ation. In contra st for the cation i c NPs the shell thickness is independent of the
amount of added monomer and appar ently t he gra fting density is determined v ia the monomer conce n-
tration. We assu me, that t he unexpe cted result i s due to complexa t ion potential of PD MAEMA , which
may che late coppe r at a certa in degree of po lymeriza tion und further monomer propaga tion on t hat chain
is not possible anym ore .
SANS data shows, that t he polymer density profile of t he shell is best describe d by an exponentially
dec aying polymer density. As expec ted, the shell is lar gely swollen by solvent but the model ling also
clea r ly confir ms the constant thickness of t he PDMAE MA shell seen befor e by light scatter ing, where
the shell simp ly bec omes denser with i ncr easing poly me r content.
5.2 Phospholi pid mem bran e i nt er act ion
We st udied the in tera ction betwee n NP s with gra fted polym er and bilaye rs membrane s o n either f lat
supported lipid bilayer s of oppos ite charge usi ng quartz cr ystal m icroba lance with dissipation monit or-
ing (QCM-D) and AFM, and for spherical vesicles with the same l ipid composi tion by using ti me re-
solved SAXS and transm i ssion measure ments. F or the e xperiments o n the SLB i ntera ction we control led
the char ge density of the particle s either by the grafting density of the polye lectr olyte brush at constant
pH or by pH while keeping the grafting de nsit y const ant. The cha rge density of the membra ne was
alwa ys controlled by the mixing ratio betwee n nonion ic DOPC and anionic DMPA. For the ti me re-
solved exper iments we st udied the i nfluenc e of t he NP concentr ation and t he charge density of the ves-
icles.
QCM-D expe riments show, that the cha rge density of S LBs does n ot have a strong infl uence on the
adsorption, once t he S LBs are charge d (and thi s become s even less pronounced for large r NPs). For t i me
re solved-SAXS and light transmi ssion m ea sureme nts t he charge density i nfluenc es t he adsorption ki-
netics. Even for highly cha rged par ticles the surfa ce cover age value s ar e not ver y h i gh, pre sumably due
to t heir m utual repulsion at the interfa ce , and in goo d a gree ment with liter at ure. A gene ral trend is, that
119
incre asing the N P char ge either by the graf ted polymer o r by sol ut ion pH leads to lower surfac e cove ra g e
values. The i ntera ction is arising mainly from electr ostat ic NP -NP repulsion of adsorbe d sim i lar cha rged
par ticles and the char ge inver sion of t he net charge of de cora ted surfa ce s , which re pels further approa ch-
ing NPs fr om the surfac e awa y. The cha rge conve rsion can be confirmed from ζ -pote ntia ls mea sure-
ments of NP-vesic le mix t ure s or from re sul ts of time -re sol ved measur ements, wher e the time f or rea ch-
ing t he equilibrate d state of the adsorption incre ased wi t h increa sing N P conce ntration.
The electrostatic int er action is main ly influenc ed by the counter ion conc entra tion of t he pa rticles , w here
the osmot ic limit is rea ched a t longer separation distanc es be twee n the S LBs and the s pheric al N Ps. We
could proof, that alre ady adsorbed NPs cannot be re move d from the interfa ce wit h acidic water (good
solvent condi t ions for cationic NPs) but they rapid ly d esorbing with S D S sol ut ion. SD S adsorbs at all
interfa ces by reducing the ef fec tive binding tendenc y of the N Ps between the planar sur fac e pr esumably
due to electrostatic re pulsion.
As most int er esting outcome , the adsorption of NPs on phospholipid bilaye rs bec omes eff ectively re-
duce d by a sufficiently dense pol y m er brush and that f or strongly oppos itely cha rged particle s and b i -
layer s. Without a polyme r layer such particle s adsorb strongly whil e with incre asing graf ting densit y
one observe s a marke d and sudden decr ea se of adsorpti on, o nce a cer tain gra fting dens i ty i s surpassed.
Time resolved measur ements showe d t hat the pol ymer layer re duce s their effe ctive adsorption kinetics
compar ed t o N Ps without a pol y mer layer. Th is critical amount of grafte d polymer increa ses wit h in-
cr easing size of the NPs. Howeve r, int er estingly t he adsorption t hen becomes somewha t enhanc ed aga in
upon inc rea sing s olution pH , i . e ., ef fe ctively r educing t he e l ec trostatic inte rac tion, w hich is another sur -
prising e ffe ct. F inally, we a l so obser ved for t he Q CM-D e xperiments, these weakly adsorbe d NP s i n t he
borde r region of t hi s t ra nsition ar e also marke dl y af fec ted by t he conce ntration . With i ncr easing NP
conc entra tion data exhibit a substantial re duction of ad sorpti on. Th is thir d surprising effe ct appar ently
depe nds on the shear ra te and i s attributed to a col lisi o n eff ec t in which at hig her flow rate and concen-
tration simply more adsorbe d particles bec ome hit and the reby re moved f rom the surfa ce.
In summa ry it can be st ated, t hat po lymer modification of si lic a nanopar t icles is a very powerf ul tool t o
control their abil ity to bind to pho spholipid b ilayers, w here t he gra fting density is eve n overcoming the
elec t rostatic attra ction in duced by having opposi tely c harge d surfa c es. S eve ral surprising effe cts ar e
observe d , that ca n be explained by the inte rplay of e l ec tr ostatic, s teric , and van der Wa als forc es and for
wea kl y bound N P s even she ar for ces play a signific ant r ole.
6 Outlook
The herby prese nted results gene rate seve ral intere sting questions, which should be answe red in futur e
studies. First one is the i nfluenc e of the ionic strength, as intera ction in most rea list ic simula tion for the
field of nanotoxicity s hould be done i n hi g h ionic streng t hs solution ( c ion ~ 15 0 mM). Related t o the field
of nanotoxicit y the adsorption of such hybrid NP s sh ould be pre vented as much as possible , i . e . we
proofe d that the NP adsor ption in sal t f re e solut i ons c an be dec rea sed by the density of the pol ym er shell
eve n for electr ostatic attrac t ion. The rea son is the stron g osmotic and st er ic re pulsion mediated by the
osmotic pressure due t o the pre sence of the counterio ns of t he po l yelec trolyte inter ior and exte rior .
Howe ver, ionic st re ngth plays an important role as the electr ostatic long-ra nge i n t er action reduc es to
small distanc es with i ncr ea sing salt conce ntration (Debye scree ni ng length κ < 1 nm for c ion ~ 150 mM).
Fur thermore , the conf ormation of such polyelectrolyte l aye rs change s from the osmotic into the salted
re gime. Thus, we expe ct, that our N P s will t hen adsorb much st ronge r compare d t o salt free sol utions .
Nonethe less, the influenc e of polymer density i s impor ta nt to st udy , i . e ., it m ight be particula r inter esting
to synthesize NPs wi th hi gher polymer densities or thic ker pol ymer layers to extend t he amount of steric
intera ction, respec tively.
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