Disen angling Componen Dynamics in an All-Polyme
Nanocomposi e Based on Single-Chain Nanopa icles by
Quasielas ic Neu on Sca e ing
Jon Maiz,*Es e Ve de-Ses o, Isabel Asenjo-Sanz, Lucile Mangin-Th o, Be nha d F ick,
JoséA. Pomposo, A an xa A be, and Juan Colmene o
Ci e This: Mac omolecules 2022, 55, 2320−2332
Read Online
ACCESS Me ics & Mo e A icle Recommenda ions
ABSTRACT: We ha e in es iga ed an all-polyme nanocomposi e (NC)
consis ing o single-chain nanopa icles (SCNPs) imme sed in a ma ix o linea
chains o hei p ecu so s (25/75% composi ion in weigh ). The SCNPs we e
p e iously syn hesized ia “click”chemis y, which induces in amolecula c oss-
links in he indi idual mac omolecules accompanied by a sligh shi (5−8K)o
he glass ansi ion empe a u e owa d highe alues and a b oadening o he
dynamic esponse wi h espec o he aw p ecu so ma e ial. The selec i e
in es iga ion o he dynamics o he NC componen s has been possible by using
p ope ly iso opically labeled ma e ials and applying quasielas ic neu on sca e ing echniques. Resul s ha e been analyzed in he
momen um ans e ange whe e he cohe en sca e ing con ibu ion is minimal, as de e mined by complemen a y neu on
diff ac ion expe imen s wi h pola iza ion analysis. We obse e he de elopmen o dynamic he e ogenei y in he in e media e
sca e ing unc ion o he NC componen s, which g ows wi h inc easing ime. Local mo ions in he p ecu so ma ix o he NC a e
accele a ed wi h espec o he e e ence bulk beha io , while he displacemen s o SCNPs’hyd ogens show enhanced de ia ions
om Gaussian and exponen ial beha io compa ed wi h he pu e mel o SCNPs. The esul ing a e aged beha io in he NC
coincides wi h ha o he pu e p ecu so , in acco dance wi h he mac oscopic obse a ions by diffe en ial scanning calo ime y
(DSC) expe imen s.
■INTRODUCTION
Resea ch on polyme nanocomposi es, ma e ials composed o
a polyme ma ix wi h embedded fille s, is nowadays o
indus ial and academic in e es .
1,2
The g owing in e es in
applica ions o such ma e ials can be aced back o he
diffe en p ope ies o he final nanocomposi e ma e ial
compa ed o he pu e polyme ma ix. In nanocomposi es,
se e al pa ame e s can be a ied and/o uned o imp o e hei
final p ope ies. No only i is possible o change ma ix
pa ame e s (e.g., chemis y, a chi ec u e, and molecula
weigh ) and/o fille s’pa ame e s (e.g., shape, su ace, and
size), bu also pa ame e s ela ed wi h he final mix u e (e.g.,
composi ion and sol en in e ac ion). Conce ning he fille s,
diffe en classes o nanofille s ha e been used in polyme
nanocomposi es o e he las yea s. Pa icula ly, so-called
polyme nanopa icles,
3−10
in ol ing polyme ic ma e ials, ha e
a ac ed he in e es o many esea ch g oups. This kind o
nanocomposi es, also called all-polyme nanocomposi es, has
he ad an age ha ma e ials can be designed and p epa ed o
which he size and “so ness”o he dispe sed componen s a e
highly unable.
11
A new amily o polyme nanopa icles called single-chain
nanopa icles (SCNPs) has eme ged o e he las yea s.
SCNPs a e unimolecula nano-objec s ob ained by in a-
molecula c oss-linking o indi idual mac omolecula chains
( unc ionalized linea polyme s called “p ecu so s”).
12−15
Se e al s udies ha e been published whe e hese SCNPs
we e blended wi h a linea polyme ma ix o gi e all-polyme
nanocomposi es, and diffe en aspec s o he esul ing mix u es
ha e been in es iga ed. Fo example, di ec expe imen al
obse a ion o he miscibili y was epo ed o SCNPs based
on polys y ene (PS) blended wi h poly( inyl me hyl e he )
(PVME) linea polyme chains.
16
In e es ingly, i was ound a
e y diffe en calo ime ic and dielec ic beha io o PS/PVME
mix u es depending on whe he he PS-componen consis ed
o linea chains o o SCNPs.
17,18
In addi ion, he s uc u al
p ope ies as well as he he mal beha io , he segmen al and
chain dynamics o sys ems based on poly(me hyl me hac y-
la e) (PMMA) SCNPs blended wi h linea poly(e hylene
oxide) (PEO), we e also s udied du ing he las yea s.
19−21
Recei ed: No embe 17, 2021
Re ised: Feb ua y 11, 2022
Published: Feb ua y 28, 2022
A icle
pubs.acs.o g/Mac omolecules
© 2022 Ame ican Chemical Socie y 2320
h ps://doi.o g/10.1021/acs.mac omol.1c02382
Mac omolecules 2022, 55, 2320−2332
Downloaded ia UNIV DEL PAIS VASCO on May 19, 2022 a 13:41:55 (UTC).
See h ps://pubs.acs.o g/sha ingguidelines o op ions on how o legi ima ely sha e published a icles.
Confinemen effec s on he PEO chains we e epo ed. I is
wo h no ing ha bo h amilies o mix u es, composed by
PMMA/PEO and consis ing o PVME/PS, p esen an inhe en
s ong dynamic asymme y (diffe ence in he alues o he
glass ansi ion empe a u e (Tg) o he wo pu e compo-
nen s), ha could, a leas pa ially, be a he o igin o he
peculia phenomenology ound in hese ma e ials. This
dynamic asymme y was absen in he componen s o he
nanocomposi es based on PS in es iga ed in he li e a u e.
22
The e, linea PS chains we e mixed wi h PS−SCNPs. In ha
wo k, he mechanical and he mal beha io o he mix u es
we e in es iga ed, epo ing a educ ion o he iscosi y and he
Tgwi h espec o he linea chains, e en i he Tg- alues o he
wo pu e componen s we e equal. Thus, e en in sys ems whe e
ing edien s in oducing addi ional complexi y o he p oblem
a e minimized, an in iguing phenomenology is ound. In
pa icula , he glass ansi ion phenomenon seems o be
affec ed by he SCNP na u e o one o he componen s. The
glass ansi ion is closely ela ed o he dynamics o he
segmen al o α- elaxa ion; in o ma ion abou he a omic
mo ions in ol ed in his dynamical p ocess is hus o u mos
impo ance o unde s and he obse ed beha io in hese
mix u es. In pa icula , we need o de e mine he mu ual
influence o he componen s in hei a omic mo ions in he α-
elaxa ion egime. This ques ion has been ex ensi ely
in es iga ed in he case o blends o linea chains.
23,24
Bu
li leisknownabou wha happenswhenoneo he
componen s in he mix u e consis s o SCNPs.
19−21
Molecula
dynamics (MD) simula ions can add ess his ques ion, as i
was he case o he wo ks epo ed in he li e a u e o PS-
based nanocomposi es.
25,26
Howe e , om an expe imen al
poin o iew, his is a a he complica ed p oblem, since
componen -selec i e echniques a e equi ed. The quasielas ic
neu on sca e ing (QENS) echnique applied o iso opically
labeled samples is he igh ool o shed ligh on his p oblem
because i di ec ly accesses a omic mo ions o selec ed
componen s in he sys em a he molecula le el. In his
con ex , he aim o his wo k is o in es iga e he phenomenon
o he glass ansi ion and he componen segmen al dynamics
associa ed wi h i in a nanocomposi e consis ing o SCNPs
embedded in a linea -chain ma ix o hei p ecu so s,
combining calo ime y and QENS echniques.
QENS echniques a e based on he ac ha he sca e ing o
a neu on by a nucleus can al e i s momen um and ene gy.
27,28
The momen um ans e dependence o he sca e ed in ensi y
p o ides space esolu ion, and he ene gy dependence, ime
esolu ion, bo h a he mic oscopic le el. The double
diffe en ial sca e ing c oss sec ion ∂2σ/∂Ω∂Ede e mined in
a QENS expe imen is he numbe o neu ons sca e ed in o a
solid angle be ween Ωand Ω+∂Ωwi h an ene gy change ΔE
=ℏω.
29
Elas ic sca e ing occu s when he e is no ene gy
exchange (wi hin he ins umen al esolu ion) be ween he
a oms and he neu ons. In inelas ic sca e ing, neu ons loose
o gain ene gy ela ed o exci a ions in he sample. Quasielas ic
sca e ing
30
gi es ise o b oadening a ound elas ic lines
eflec ing s ochas ic and diffusi e mo ions, elaxa ions, e c. in
he sample.
31
The double diffe en ial sca e ing c oss sec ion con ains
cohe en and incohe en con ibu ions. Cohe en sca e ing
gi es in o ma ion ela ed o collec i e p ope ies, while
incohe en sca e ing is associa ed wi h sel -mo ions. The
espec i e weigh o he cohe en and incohe en con ibu ions
o he o al sca e ing c oss sec ion is de e mined by he
cohe en and incohe en sca e ing leng hs o he nuclei in he
Scheme 1. Schema ic Illus a ion o All-Polyme Nanocomposi e Composi ion
a
a
The samples a e p epa ed by mixing he PTHF p ecu so wi h he PTHF-based SCNPs. The o med nanocomposi e is composed by xP ec/
ySCNPs samples, on selec i ely labeled (x,y)ϵ(h,d) samples. Two kinds o nanocomposi es a e p epa ed in he p esen wo k, he fi s one 75hP ec/
25dSCNPs sample and he second sample was he in e sely labeled one 75dP ec/25hSCNPs. All o he syn hesis me hods and p ocedu es a e
desc ibed in de ail in e s 33 and 34.
Mac omolecules pubs.acs.o g/Mac omolecules A icle
h ps://doi.o g/10.1021/acs.mac omol.1c02382
Mac omolecules 2022, 55, 2320−2332
2321
sample.
31,32
The sca e ing leng h bcha ac e izes he s eng h
o he neu on−nucleus in e ac ion; i depends on he ela i e
o ien a ion o he neu on−nuclea spin pai s and a ies om
one iso ope o ano he . In pa icula , hyd ogen p esen s a huge
incohe en sca e ing c oss sec ion σ(σinc
H≈80 ba n)
compa ed o he cohe en (σcoh
D≈5.6 ba n) and incohe en
(σinc
D≈2.0 ba n) c oss sec ions o deu e ons ( he sca e ing
c oss sec ion σis defined as σ=4πb2). The e o e, deu e a ion
o a gi en moie y o componen in a sample d as ically educes
i s c oss sec ion o neu ons, and he in ensi y sca e ed by he
sample is gene ally domina ed by he incohe en con ibu ion
om he emaining hyd ogens in he sys em (see below). Due
o his capabili y o selec i ely in es iga e componen s in a
complex ma e ial, neu on sca e ing echniques a e ex emely
use ul o s udy he dynamics in nanocomposi e ma e ials.
In he p esen wo k, we s udy a mix u e consis ing o 75 w
% poly( e ahyd o u an) (PTHF)-based linea p ecu so
chains and 25 w % o PTHF SCNPs. Two diffe en samples
a e in es iga ed, whe e he p o ona ed (h) and deu e a ed (d)
moie ies a e in e changed on selec i ely labeled (h/d) samples,
as shown in Scheme 1. In he sample whe e he SCNPs a e
p o ona ed and he p ecu so s a e deu e a ed, he sca e ed
in ensi y in he accessed dynamic window is domina ed by he
sel -a omic mo ions o he hyd ogens in he SCNPs. In he
in e sely labeled sample, we ollow he p ecu so s′hyd ogen
mo ions. Thus, wi h ou QENS expe imen s, we can disce n
how he dynamics o bo h componen s a e mu ually affec ed.
To co e a wide dynamic ange, we ha e combined wo kinds
o QENS spec ome e s, a backsca e ing (BS) and a ime-o -
fligh (ToF) ins umen . The Q- ange accessed (app ox. 0.2 ≤
Q≤2Å
−1,Q: modulus o he sca e ing ec o ; ℏQ:
momen um ans e ) co esponds o ela i ely local leng h
scales o obse a ion ( hese a e in e sely p opo ional o he
Q-scales explo ed). Ou QENS expe imen s a e complemen ed
by diff ac ion expe imen s wi h pola iza ion analysis, o
de e mine he a io be ween cohe en and incohe en diffe -
en ial c oss sec ions in he samples. This allows o disce n in
which egions o Q, B agg-peaks o concen a ion fluc ua ions
a e p esen and we ha e o be cau ious wi h he cohe en
con ibu ion o he sca e ed in ensi y. The aw ma e ials we e
p e iously s udied and published by he au ho s.
33,34
■EXPERIMENTAL SECTION
Ma e ials. B iefly, all chemical eagen s and sol en s we e
ob ained om Sigma-Ald ich (Munich, Ge many), Scha lab (Ba ce-
lona, Spain), and Eu iso op (Sain -Aubin, F ance). The ma e ials used
and he pu ifica ion me hods applied a e published in p e ious
wo ks.
33−35
Syn hesis Me hods. Bo h p o ona ed and deu e a ed syn he ic
ou es employed o p epa e e ahyd o u an (THF) and epichlo -
ohyd in (ECH) (P(THF-co-ECH)) copolyme s ha e been epo ed
in ou p e ious wo ks.
33,34
The syn hesis o single-chain nanopa icles
(SCNPs) was ca ied ou ia coppe (I)-ca alyzed azide alkyne
cycloaddi ion (CuAAc) “click” eac ion. All o he p ocedu es a e
also epo ed in e s 33 and 34. Molecula weigh and polydispe si y
we e 22 kg/mol and 1.24 o he p o ona ed polyme s and 36.5 kg/
mol and 1.20 o he deu e a ed polyme s, espec i ely.
Sample P epa a ion. Two diffe en samples o nanocomposi es
con aining 75 w % o he p ecu so and 25 w % o SCNPs we e
Figu e 1. DSC hea ing scans a 20 K/min a e he p e ious cooling p ocess o p e iously epo ed p o ona ed and deu e a ed p ecu so s and
SCNPs, and he nanocomposi es he e in es iga ed. Tempe a u e e olu ion o he de i a i e o he hea flow o he (b) 75hP ec/25dSCNPs sample
and i s pu e componen s and (c) 75dP ec/25hSCNPs sample and i s pu e componen s. Resul s co esponding o a sample wi h 10% hSCNPs in
90% dP ec a e also shown in (a), dashed line.
Mac omolecules pubs.acs.o g/Mac omolecules A icle
h ps://doi.o g/10.1021/acs.mac omol.1c02382
Mac omolecules 2022, 55, 2320−2332
2322
p epa ed. Blends we e p epa ed by mixing he app op ia e p ecu so
wi h he SCNP sample o p epa e ei he he hP ec/dSCNP o dP ec/
hSCNP mix u e, whe e h ep esen s p o ona ed samples and d
symbolizes deu e a ed ones. Fi s , he p ecu so and he SCNP
mix u es we e s i ed un il he o al dissolu ion in CH2Cl2 o 24 h a
oom empe a u e. Then, each mix u e was d op-cas ed on o he
aluminum fla holde s used o neu on sca e ing expe imen s.
Subsequen ly, he sol en was slowly e apo a ed in a ume hood, and
finally, he samples we e well-d ied in an o en a 343 K o 24 h unde
acuum condi ions. The appea ance o he samples was as ha o a
iscous fluid.
The mal Analysis. Glass ansi ion empe a u es (Tg) we e
s udied by diffe en ial scanning calo ime y (DSC). DSC expe imen s
we e ca ied ou using a TA ins umen Q2000 unde ul apu e
ni ogen flow. Fo each expe imen , a ound 5 mg o he polyme mass
was used, and om he onse o he hea flow jump, he Tg alues
we e ex ac ed. The ollowing p o ocol was applied in all o he
samples s udied. Fi s , he samples we e hea ed up un il 350 K and
kep he e o 3 min o e ase any p e ious he mal his o y. Then, hey
we e cooled down un il 170 K a 20 K/min, and a e wa d, om his
empe a u e, hey we e again hea ed a 20 K/min un il 350 K.
S uc u al Analysis. Neu on diff ac ion wi h pola iza ion
analysis was ca ied ou in a neu on sca e ing expe imen o he
sepa a ion o cohe en and incohe en diffe en ial c oss sec ions.
19,36
The p obabili y o he change o he spin di ec ion o he neu on o
comple ely unpola ized nuclei is 2/3 o sca e ing wi h flip and 1/3
o sca e ing wi hou flip. The ac ha he sca e ed in ensi y wi h
spin flip esul s only om he incohe en pa is used o sepa a e
cohe en and incohe en sca e ing. D7 expe imen s a Ins i u e Laue
Lange in (ILL) in G enoble, F ance,
37
we e ca ied ou whe e
inciden neu on wa eleng h was se o λ= 4.89 Å o co e a Q- ange
om 0.15 o 2.5 Å−1. A Vanadium shee was used o calib a e he
de ec o efficiency, and o he backg ound sca e ing, a combina ion
o an emp y cell and a Cadmium shee was used. In addi ion, a qua z
pla e o he pola iza ion co ec ion was used. The samples we e
s udied a 300 K and fla aluminum cells we e used as sample holde s.
Quasielas ic Neu on Sca e ing (QENS) Analysis. To access a
wide QENS dynamic ange, wo diffe en spec ome e s we e
combined. In his s udy, he backsca e ing (BS) IN16B spec ome e
and he ime-o -fligh (ToF) IN5 ins umen , bo h loca ed a ILL,
we e used.
37
Wi h hem, he Q- ange co e ed was om 0.19 o 1.90
Å−1. The empe a u es in es iga ed we e 285, 320, and 360 K. The
sample hicknesses used in he expe imen s we e calcula ed o each
a ound 90% o ansmission, and fla aluminum cells we e used as
sample holde s. The inciden wa eleng h λwas 6.271 Å o he IN16B
spec ome e , while λ= 5 Å was used o he IN5 ins umen . To
analyze he quasielas ic spec a, he da a we e Fou ie - ans o med o
he ime domain, and hen, a decon olu ion was done om he
ins umen al esolu ion o ob ain he in e media e sca e ing unc ion
in he ime domain S(Q, ). Due o limi ed beam ime, a low-
empe a u e measu emen , ideal o he accu a e no maliza ion o he
decon olu ed esul s, could no be pe o med in all samples
in es iga ed. Spec a ob ained on a Vanadium sample we e used o
pe o m he decon olu ion in he case o IN16B esul s. Misma ches
when pu ing hem oge he wi h he ime-o -fligh da a we e
co ec ed by applying scaling ac o s o he backsca e ing da a.
■RESULTS
We fi s p esen he calo ime ic esul s. In Figu e 1a, he DSC
hea ing scans and Tg alues o he nanocomposi es as well as o
hei pu e componen s (p o ona ed (h) and deu e a ed (d)
p ecu so s and SCNPs) a e shown. Bo h h- and d- p ecu so Tg
alues we e 202 K, while in he SCNPs, hey inc ease up o
210 and 207 K, espec i ely. Independen ly o he iso opic
label, when he composi ion o he nanocomposi e is 75 w %
p ecu so and 25 w % SCNPs, he Tg alue is equal o he
ini ial p ecu so alue (202 K). The simila i y applies no only
o he a e age alue o he glass ansi ion bu also o i s wid h.
This can be be e app ecia ed in he igh panels o Figu e 1,
whe e he de i a i e o he hea flow is compa ed o he
mix u e and i s pu e componen s. Figu e 1b shows hese
unc ions o he 75hP ec/25dSCNPs sample and Figu e 1c o
he in e se labeling.
Mo ing o he neu on sca e ing s udy, we conside fi s he
in o ma ion p o ided by he diff ac ion expe imen s wi h
pola iza ion analysis ha pe mi s he sepa a ion o cohe en
and incohe en con ibu ions o he o al in ensi y. Figu e 2
shows he ela i e con ibu ion o incohe en sca e ing o he
o al diffe en ial c oss sec ion o he wo samples ob ained by
he p ocedu e desc ibed in he Expe imen al Sec ion. The
esul s show ha he incohe en con ibu ion is dominan in all
o he Q- ange in es iga ed. The sample wi h dP ec shows a
highe amoun o cohe en sca e ing bu always below 50%.
The modula ion o he cu es shown in Figu e 2 is due o his
cohe en sca e ing. Since he incohe en diffe en ial c oss
sec ion is Q-independen , he esul s abo e Q≈0.5 Å−1 eflec
he in e se o he s uc u e ac o (cohe en sca e ing). This
shows a main peak in he Q- ange be ween 1 and 2 Å−1
cen e ed a ound 1.4 Å−1 o bo h samples. This peak is well-
known om ea lie X- ay expe imen s; i is commonly named
“amo phous halo”and i is associa ed wi h he in e media e
chain co ela ions.
33,34
The sho - ange o de , hus, seems o
be no modified by he composi ion. The dec ease o he
ela i e incohe en con ibu ion a low-Q- alues (Q< 0.5 Å−1)
is due o he cohe en small-angle sca e ing a ising om he
concen a ion fluc ua ions in he mix u e. We no e ha his
low-Qcohe en con ibu ion is gene ally p esen in mix u es o
iso opically labeled samples. F om he D7 esul s, we can hus
conclude ha in he Q- ange explo ed wi h he cu en QENS
expe imen s, we a e mainly sensi i e o incohe en sca e ing o
he p o ons in he hyd ogena ed componen o he mix u e,
hough he esul s below app ox. 0.5 Å−1and in he ange 1.2
≤Q≤1.7 Å−1a e con amina ed by cohe en con ibu ions.
The QENS esul s a e p esen ed in he ollowing.
In a QENS expe imen , he occu ence o dynamic p ocesses
wi h cha ac e is ic imes wi hin he expe imen al window o
he spec ome e is obse ed as a b oadening a ound he elas ic
line. The elas ic line mani es s when he ene gy exchanged
be ween he sample and he neu ons is ze o o smalle han
he ins umen al ene gy esolu ion. The esolu ion unc ion
R(Q,ω) is de e mined om he sca e ing o a sample whe e all
o he dynamical p ocesses a e ozen wi h espec o he
Figu e 2. Ra io be ween incohe en and o al diffe en ial c oss
sec ions ob ained by D7 a 300 K on samples wi h p o ona ed and
deu e a ed nanocomposi es.
Mac omolecules pubs.acs.o g/Mac omolecules A icle
h ps://doi.o g/10.1021/acs.mac omol.1c02382
Mac omolecules 2022, 55, 2320−2332
2323
accessed dynamic window. As we ha e shown by he
diff ac ion expe imen s wi h pola iza ion analysis, he meas-
u ed signals on ou samples a e domina ed by he incohe en
con ibu ion. The incohe en sca e ing is di ec ly ela ed o
he incohe en sca e ing unc ion Sinc(Q,ω) o he hyd ogens,
e ealing co ela ions be ween he posi ion o a gi en p o on a
diffe en imes in one o he nanocomposi e componen s.
Figu e 3 p esen s ep esen a i e QENS spec a. To compa e
di ec ly da a ob ained om diffe en samples, he cu es a e
no malized o hei alue a ℏω= 0. Resul s a T= 320 K ha e
been chosen o ou ep esen a i e Q- alues in he ange
whe e he cohe en con ibu ion is minimal. A hese Q- alues,
he incohe en signal amoun s o 70−80% o he o al in ensi y
in he 75dP ec/25hSCNPs sample and o abou 90% in he
75hP ec/25dSCNPs sample, as can be seen in Figu e 2.
The wid h o he quasielas ic spec um is ela ed o he
in e se o he cha ac e is ic ime o mo ion p obed by he
ins umen . A all o he empe a u es in es iga ed and in he
Q- ange explo ed, we obse e quasielas ic b oadening. Fo a
gi en empe a u e, as can be obse ed in Figu e 3 o he case
o 320 K, his b oadening becomes mo e p onounced wi h he
inc easing Q- alue, which sugges s he diffusi e-like beha io
o he p o ons. Mo eo e , we can obse e a clea diffe ence
be ween bo h samples, 75hP ec/25dSCNPs and 75dP ec/
25hSCNPs. In gene al, he spec a co esponding o he
75dP ec/25hSCNPs sample a e na owe o all Q- alues,
sugges ing a slowe dynamics o he SCNPs wi h espec o he
linea p ecu so componen in bo h dynamic windows s udied.
In his kind o expe imen ca ied ou in he equency
domain, he ins umen al esolu ion affec s he esul s h ough
con olu ion. Consequen ly, he quan i a i e analysis o he
quasielas ic spec a was based on Fou ie ans o ming he da a
o he ime domain and decon olu ing hem om he
ins umen al esolu ion effec s by di ision. In his way, we
ob ained he in e media e incohe en sca e ing unc ion in he
ime domain Sinc(Q, ). This p ocedu e has also he ad an age
o allowing he di ec combina ion o esul s om diffe en
spec ome e s. In Figu e 4, he esul s o his p ocedu e a e
shown o spec a co esponding o he same ep esen a i e Q-
alues as chosen o Figu e 3. F om Figu e 4a−c, he cu es
co espond o he 75hP ec/25dSCNPs sample a fixed T-
alues o 285 K (Figu e 4a), 320 K (Figu e 4b), and 360 K
(Figu e 4c). F om Figu e 4d− , he esul s a e om he
75dP ec/25hSCNPs sample a he same fixed T- alues o 285
K(Figu e 4d), 320 K (Figu e 4e), and 360 K (Figu e 4 ). The
esul s clea ly show ha he cha ac e is ic ime o hyd ogen
mo ions (which, as a fi s app oxima ion, can be defined as he
ime whe e Sinc(Q, ) decays o 1/e) becomes sho e wi h
inc easing T o a gi en Q- alue, and wi h he inc easing Q-
alue a a gi en empe a u e, as we had p e iously deduced
om he di ec inspec ion o he spec a in he equency
domain. Also, we can app ecia e ha he cu es show a mo e
s e ched unc ional o m han a single exponen ial unc ion.
On he o he hand, he in e media e incohe en sca e ing
unc ions ob ained o he wo nanocomposi e samples a e
compa ed in Figu e 5a wi h bo h pu e p ecu so and SCNP
samples
33
a he same condi ions (a Q- alue o 0.95 Å−1and a
fixed T- alue o 320 K). We can see ha in he pu e mel s he
dynamics o he SCNPs is slowe han ha o he p ecu so ; in
he mix u e, his diffe ence appea s no only o be p esen bu
e en amplified a long imes.
De ia ions om exponen ial beha io a e usually accoun ed
o by Kohl ausch−Williams−Wa s (KWW) o s e ched
exponen ial unc ions SKWW(Q, )
Ä
Ç
Å
Å
Å
Å
Å
Å
Å
Å
Å
Å
Å
Å
i
k
j
j
j
j
j
y
{
z
z
z
z
z
É
Ö
Ñ
Ñ
Ñ
Ñ
Ñ
Ñ
Ñ
Ñ
Ñ
Ñ
Ñ
Ñ
τ
=−
β
S
Q
(,) exp
KWW
s(1)
Figu e 3. No malized IN5 (a−d) and IN16B (e−h) spec a ob ained a 320 K and he diffe en Q- alues indica ed o diffe en nanocomposi es
75hP ec/25dSCNPs (o ange line) and 75dP ec/25hSCNPs (g een line). The do ed line shows he ins umen al esolu ion unc ion.
Mac omolecules pubs.acs.o g/Mac omolecules A icle
h ps://doi.o g/10.1021/acs.mac omol.1c02382
Mac omolecules 2022, 55, 2320−2332
2324
whe e βis he s e ching exponen cha ac e izing he
de ia ions om a single exponen ial and τsis he cha ac e is ic
ime ha depends on bo h Qand empe a u e. The
expe imen ally ob ained in e media e incohe en sca e ing
unc ion can be well desc ibed abo e ≈2 ps in e ms o hese
unc ions
Figu e 4. Fou ie - ans o med and decon olu ed QENS spec a ob ained om IN5 (se s o da a o imes sho e han 10−10 s) and IN16B (se s o
da a o imes longe han 10−10 s) on he 75hP ec/25dSCNPs (a−c) and 75dP ec/25hSCNPs (d− ) samples a he h ee diffe en empe a u es
in es iga ed: 285 K (a, d), 320 K (b, e), and 360 K (c, ) and a ou diffe en Q- alues: 0.57 Å−1(ci cle), 0.95 Å−1(squa e), 1.18 Å−1(up-poin ing
iangle), and 1.72 Å−1(down-poin ing iangle). Solid lines a e Kohl ausch−Williams−Wa s (KWW) fi s wi h he β- alues shown in Table 1 o
he esul s abo e 2 ps.
Mac omolecules pubs.acs.o g/Mac omolecules A icle
h ps://doi.o g/10.1021/acs.mac omol.1c02382
Mac omolecules 2022, 55, 2320−2332
2325
l
m
o
o
o
n
o
o
o
Ä
Ç
Å
Å
Å
Å
Å
Å
Å
Å
Å
Å
Å
Å
i
k
j
j
j
j
j
y
{
z
z
z
z
z
É
Ö
Ñ
Ñ
Ñ
Ñ
Ñ
Ñ
Ñ
Ñ
Ñ
Ñ
Ñ
Ñ
|
}
o
o
o
~
o
o
o
τ
=−+
β
S
Q A
(,) exp BG
inc
s
(2)
He e, p e ac o A accoun s o he decay o he co ela ion
unc ion a sho e imes due o ib a ional and o he as
con ibu ions. A small elas ic con ibu ion (BG) was also
allowed in he fi s, which had a alue o ≈0.02 and <0.05 in all
cases. This componen may accoun o an inaccu a e
sub ac ion o he backg ound in he expe imen , hough i
could also esul om he p esence o some immobile
p o onswi hin he expe imen al windowin he case o
p onounced he e ogeneous beha io . Figu es 4 and 5a shows
ha his unc ion wo ks well o bo h nanocomposi es as well
as o he nea polyme s
33
in he s udied Q- ange.
F om hese fi s, we ob ained he alues o he ampli ude A,
he s e ching exponen β, and he cha ac e is ic imes τsas
unc ions o Qand T. Fo a gi en empe a u e, he β alues
we e sca e ed a ound he a e age alues lis ed in Table 1.We
hen fixed he alue o β o he a e age alue a each
empe a u e and fi ed again he in e media e sca e ing
unc ions, de e mining again he ampli ude Aand he alues
o he cha ac e is ic imes τs. The ampli ude A ollows well a
Debye−Walle ac o -like exp ession A∼exp[−<u2>Q2/3]
wi h he alues o he mean squa ed displacemen <u2> gi en
in Table 1. F om he cha ac e is ic imes τsand he β- alue
used, he a e age cha ac e is ic imes we e calcula ed. In he
case o a KWW unc ion, as exp essed in eq 2, he a e age
cha ac e is ic ime is gi en by ⟨τ⟩=τsΓ(1/β)/β. This ime is
affec ed by he spec al shape and he e o e allows compa ison
o esul s co esponding o unc ions wi h diffe en alues o
he nonexponen ial pa ame e . The esul s on ⟨τ⟩a e collec ed
in Figu es 5b and 6. I has been epo ed ha in he Q- ange
below app ox. 1 Å−1 he cha ac e is ic ime o H-sel -mo ions
in he α- elaxa ion egime o glass- o ming sys ems
33,38−41
ollows a powe law <τ>∝Q−2/βas dic a ed by he Gaussian
p edic ion. This can be a ibu ed o a subdiffusi e-like p ocess.
A high Qs, de ia ions om his Gaussian beha io mani es .
To accoun o hese expe imen al obse a ions (also epo ed
om MD simula ions), he exis ence o an unde lying
dis ibu ion o jumps, gi ing ise o he subdiffusi e egime
a long imes, was p oposed. We emind ha in jump diffusion
Figu e 5. (a) Fou ie - ans o med and decon olu ed QENS spec a o he p ecu so and SCNPs (emp y ci cles) and nanocomposi es ( ull squa es)
a 320 K and Q= 0.95 Å−1. Dashed (p ecu so and SCNPs) and solid (nanocomposi es) lines a e KWW fi s wi h he β- alues shown in Table 1 o
he esul s abo e 2 ps. (b) Sca e ing ec o dependence o he a e age cha ac e is ic ime ⟨τ⟩=τsΓ(1/β)/β o H-sel -mo ions ob ained o he
p ecu so and SCNPs (emp y ci cles) and nanocomposi es (squa es) a 320 K. Lines a e fi s o eq 2. Resul s o nanocomposi es in he ange 1.2 ≤
Q≤1.65 Å−1( ep esen ed by c ossed squa es) ha e been igno ed o he fi o he AJD model. Es ima ed e o ba s a e included o he
nanocomposi e esul s a Q= 0.57, 0.95, and 1.72 Å−1.
Table 1. Values o he Pa ame e s In ol ed in he Anomalous Jump Diffusion (AJD) Fi ing he Homopolyme s and
Nanocomposi e Mix u e Resul s Desc ibed wi h KWW Func ions
sample T(K) <u2>(Å
2)βτ
s,0 (ps) l0(Å)
285 0.44 ±0.02 0.44 ±0.025 37 ±8 0.68 ±0.06
hP ec 320 0.55 ±0.02 0.50 ±0.042 5.8 ±0.7 0.57 ±0.04
360 0.73 ±0.02 0.53 ±0.035 3.1 ±0.3 0.69 ±0.02
285 0.41 ±0.02 0.40 ±0.037 87 ±12 0.73 ±0.03
hSCNPs 320 0.51 ±0.02 0.45 ±0.028 11.6 ±1.2 0.63 ±0.02
360 0.73 ±0.02 0.49 ±0.030 3.6 ±0.4 0.64 ±0.03
285 0.36 ±0.04 0.44 ±0.042 15 ±4 0.63 ±0.05
75hP ec/25dSCNPs 320 0.54 ±0.04 0.50 ±0.053 4.8 ±0.4 0.64 ±0.02
360 0.57 ±0.04 0.53 ±0.030
285 0.30 ±0.04 0.38 ±0.035 51 ±9 0.76 ±0.04
75dP ec/25hSCNPs 320 0.37 ±0.04 0.40 ±0.060 8.9 ±0.6 0.76 ±0.02
360 0.59 ±0.04 0.44 ±0.020 3.5 ±1 0.73 ±0.06
Mac omolecules pubs.acs.o g/Mac omolecules A icle
h ps://doi.o g/10.1021/acs.mac omol.1c02382
Mac omolecules 2022, 55, 2320−2332
2326
models fini e jump leng hs end o cause a bending o he
dispe sion o he diffusi e elaxa ion imes away om he Q−2
law, he la e being alid o simple diffusion a low-Q. The
jump diffusion model
42−44
conside s ha an a om emains in a
gi en si e o a ime τo, whe e i ib a es a ound a cen e o
equilib ium. A e τo, i mo es apidly o a new posi ion
sepa a ed by he ec o l
om i s o iginal si e. I can be
assumed ha in a liquid o diso de ed sys em, jumps ake place
andomly o ien ed, wi h moduli dis ibu ed acco ding o he
unc ion
i
k
j
j
j
j
j
y
{
z
z
z
z
z
=−
ll
l
l
l
() exp
oo
2o(3)
whe e l0is he p e e ed jump leng h. A gene aliza ion o hese
models o he case o subdiffusi e beha io was p oposed by
he anomalous jump diffusion (AJD) model
38,39
ha
in oduces s e ching in he ime-dependen pa o he
in e media e sca e ing unc ion. As a esul , he KWW
unc ion (eq 1) ep esen ing his dynamical p ocess in he
in e media e sca e ing unc ion (eq 2) has a cha ac e is ic
ime gi en by
Ä
Ç
Å
Å
Å
Å
Å
Å
Å
Å
Å
Å
É
Ö
Ñ
Ñ
Ñ
Ñ
Ñ
Ñ
Ñ
Ñ
Ñ
Ñ
τ
τ=+
β
QQl
() 1 1
ss,0
20
2
1/
(4)
In his way, in he limi Qlo→0, he Gaussian app oxima ion is
conse ed, bu now a sublinea inc ease o he mean squa ed
displacemen is ob ained o low-Q- alues; in ha egime, he
Q-dependence o τsis τs(Q)∝Q−2/β. Con e sely, he Q→∞
limi o τsis jus τs,o. The alue o lode e mines he Q- egion
whe e de ia ions om Gaussian beha io s a ( he la ge a e
he jumps in a e age, he smalle is his Q- alue).
This model was applied o he esul s on he pu e
componen s and he wo nanocomposi es in es iga ed (see
desc ip ions in Figu es 5b and 6). To a oid he influence o
cohe en sca e ing, in he fi o he esul son he
nanocomposi es, we did no conside he da a co esponding
o he egion 1.2 ≤Q≤1.65 Å−1, whe e his con ibu ion is
no negligible (see Figu e 2); as can be app ecia ed in Figu es
5b and 6, he imes in his Q- egime show a modula ion ha
p e en s o an accu a e de e mina ion o he alues o he fi
pa ame e s. This model desc ibes well he esul s on he pu e
mel s and he nanocomposi es (see Figu es 5b and 6). The
alues ob ained o he pa ame e s in ol ed in he model (l0
and τs,0) a e lis ed in Table 1. Fo 360 K, a high Q, he decay
o he in e media e sca e ing unc ion o he 75hP ec/
25dSCNPs akes place wi h e y sho cha ac e is ic imes,
ha dly dis inguishable om he fi s as decay below 2 ps;
he e o e, we did no conside he esul s abo e 1.2 Å−1, and
consequen ly, we could no apply he AJD o hese condi ions.
■DISCUSSION
In he pu e mel s, in e molecula c oss-links p oduced by he
“click”chemis y he e employed induce a clea b oadening o
he glass ansi ion phenomenon as moni o ed by DSC, wi h a
shi o he a e age glass ansi ion empe a u e owa d highe
alues. These “mac oscopic”effec s can be app ecia ed in
Figu e 1. B oadening and slowing down effec s a e also
mani es ed in he local a omic dynamics as di ec ly obse ed
by QENS a empe a u es well abo e he espec i e Tg
’s o he
nea samples. This can be seen in Figu e 5 and deduced om
he pa ame e s desc ibing he s e ching and Q-dependence o
he cha ac e is ic imes lis ed in Table 1. Such findings poin o
mo e he e ogeneous dynamics in he SCNPs wi h espec o
he linea p ecu so coun e pa s, cha ac e ized mic oscopically
by longe esidence imes and la ge a e age jump leng hs
unde lying segmen al elaxa ion.
33,34
In ag eemen wi h hese
esul s, ecen MD simula ions on mel s o PS-based SCNPs
ha e ound dynamical he e ogenei y and an inc ease in Tgo
he SCNPs wi h espec o he linea coun e pa s.
45
These
effec s a e amplified wi h he inc easing c oss-linking deg ee.
45
Thus, bo h, DSC and QENS show ha in e nal c oss-links
induce some dynamic asymme y in he pu e componen s o
ou nanocomposi es. In mix u es whe e he componen s ha e a
ma ked dynamic asymme y, as PMMA and PEO, wo glass
ansi ions associa ed wi h each o he componen s a e ound
by DSC.
46
This obse a ion has been epo ed o bo h, blends
o linea polyme s
47
as well as in all-polyme nanocomposi es
made o linea PEO chains as he ma ix and PMMA-SCNPs,
19
o diffe en composi ions including ha he e conside ed (75%
linea ma ix/25% SCNPs). Howe e , he p esence o wo
glass ansi ions is no appa en in he p esen mix u es. We
find ha he glass ansi ion empe a u e o he nanocomposi e
basically coincides wi h ha o he p ecu so ( he majo i y
componen in he nanocomposi e). Bo h, he a e age glass
ansi ion alue and he b oadening o he DSC ace a e
almos indis inguishable om hose in he pu e p ecu so mel
(see Figu e 1). Looking in de ail a he de i a i e o he hea
capaci y (Figu e 1b,c), a e y li le shi o he posi ion o he
maximum and a sligh ly smoo he beha io o he cu e could
be in e ed in he mix u es. Howe e , clea effec s on he glass
ansi ion o he ma ix when SCNPs a e added in his
concen a ion and possible con ibu ions o a diffe en
i ifica ion om he SCNPs, i any, canno be deduced om
ou DSC esul s. We no e ha he mac oscopic dynamic
asymme y in ou samples, diffe ence in glass ansi ion
empe a u es o he homopolyme s, is only abou 5−8K,
Figu e 6. Sca e ing ec o dependence o he a e age cha ac e is ic
ime ⟨τ⟩=τsΓ(1/β)/β o H-sel -mo ions ob ained o 75hP ec/
25dSCNPs (o ange symbols) and 75dP ec/25hSCNPs (g een
symbols) a 285 K (ci cle and squa e), 320 K (up- iangle and
down- iangle), and 360 K (c oss and diamond) (fi s shown in Figu e
4). Lines a e fi s o eq 2 o he 75hP ec/25dSCNPs (o ange lines)
and 75dP ec/25hSCNPs (g een lines), using he β- alues lis ed in
Table 1 o each case. Resul s o nanocomposi es in he ange 1.2 ≤Q
≤1.65 Å−1( ep esen ed by emp y symbols) ha e been igno ed o
he fi o he AJD model. E o ba s ha e been included a Q= 0.57,
0.95, and 1.72 Å−1.
Mac omolecules pubs.acs.o g/Mac omolecules A icle
h ps://doi.o g/10.1021/acs.mac omol.1c02382
Mac omolecules 2022, 55, 2320−2332
2327
i.e., much weake han in he abo e-men ioned PMMA-
SCNPs/PEO nanocomposi es o which he diffe ence was in
he o de o 50 K.
19
The induced effec s migh he e o e be oo
sub le o be esol ed by s anda d DSC expe imen s.
On he con a y, he space/ ime insigh o QENS a he
molecula le el does allow esol ing he mu ual impac o he
componen s in he mix u e. As clea ly shown di ec ly by he
QENS spec a in he equency domain, and, e en mo e
clea ly, in he decon olu ed Fou ie - ans o med in e media e
sca e ing unc ions, a dynamic he e ogenei y is pa en in he
nanocomposi es. This he e ogenei y mainly a ises a imes
longe han some picoseconds, since he alues o he mean
squa ed displacemen in he as dynamics egime <u2> a e no
e y diffe en o bo h componen s (see Table 1). A imes
longe han some picoseconds, he hyd ogens in he SCNPs
mo e in a slowe ashion han he hyd ogens in he p ecu so
(see Figu es 3−6). Also, he mo e p onounced s e ching o
he in e media e sca e ing unc ion o he SCNPs ( eflec ed
by he β alue, see Table 1) sugges s significan ly b oade
dis ibu ions o local mobili ies han in he p ecu so
componen . In addi ion, hei displacemen s show la ge
de ia ions om Gaussian beha io (le us emind ha hese
de ia ions a e quan ified by he fini e jump leng h in oked in
he AJD model, l0). In e ms o he AJD model, we obse e
clea ly longe esidence imes and la ge jump leng hs o he
SCNPs han o he p ecu so (see Table 1). We no e ha in
he mix u e, he diffe ences a e e en s onge han in he
sepa a e componen s. This leads us o discuss he impac o
each o he componen s on he o he one, i.e., he diffe ences
induced wi h espec o he pu e mel beha io .
The influence o he p esence o he SCNPs on he
dynamics o he p ecu so chains mainly consis s o a dec ease
o he esidence ime τs,0. Bo h he shape pa ame e βand he
jump leng h l0a e no app eciably changed, wi hin he
unce ain ies, wi h espec o hose in he pu e p ecu so
(see Table 1). In e es ingly enough, he effec is coun e -
in ui i e, in oducing slowe en i ies leads o speeding up he
local mo ions in he linea chains. MD simula ions on
analogous nanocomposi es as hose he e in es iga ed, bu
based on PS, also epo ed ha he segmen al elaxa ions o he
mel chains a e accele a ed.
25
This effec was a ibu ed o he
he mal de o ma ions o he loose SCNP su ace s uc u es,
based on he compa ison be ween elaxa ions o segmen s
a ound a so SCNP and a igid body SCNP wi h he in e nal
deg ees o eedom a ificially ozen. We also ecall ha i has
been epo ed ha unde confinemen , liquids and polyme s
can show his kind o effec .
48,49
In hose wo ks, ha d
confinemen was induced by a igid su ounding en i onmen .
P ecu so s modi y he dynamics o SCNPs in a e y diffe en
way. Fi s o all, he in e media e sca e ing unc ion o
hyd ogens in he SCNPs in he nanocomposi e becomes e en
mo e s e ched han in bulk, eflec ing much mo e
he e ogeneous dynamics. This effec is clea ly shown in Figu e
7, whe e he esul s on he nanopa icles wi hin he bulk and
he nanocomposi e samples a e di ec ly compa ed o Q= 0.57
Å−1and he h ee empe a u es in es iga ed. We no e ha he
obse a ion o a mu ual influence o he wo componen s in
he dynamics, leading o diffe en beha io om he espec i e
bulk e e ence sys ems, can be conside ed as p oo o
miscibili y a he molecula le el. On he o he hand, while
now he esidence ime emains p ac ically unaffec ed, wi hin
he unce ain ies, he jump leng h shows an inc ease wi h
espec o he bulk. This is a signa u e o s onge de ia ions
om Gaussian beha io in he a omic displacemen s. In he
compa ison o Figu e 5a, we can see ha he main diffe ence
be ween he hyd ogen mo ions o he SCNPs in he
nanocomposi e and in bulk is ound a sho imescales. A
such sho imes, he SCNP beha io seems o be s ongly
modified by he p esence o he as e p ecu so ; appa en ly,
SCNPs ollow he as e majo i y componen a he beginning
o hei elaxa ion. Howe e , he final decay o he in e media e
sca e ing unc ion is e y simila o ha in he SCNP bulk.
This mo e e a ded elaxa ion wi h espec o he linea chains
would be ela ed o he elaxa ion o he in e nal loops in he
SCNPs as a gued o he SCNPs in he bulk.
40,50
We could
also en a i ely sugges he in e pene a ion o he p ecu so
chains wi hin he SCNPs as an explana ion o he obse ed
he e ogenei y enhancemen in he SCNPs’dynamics. Using
coa se-g ained and a omis ic simula ions on PS-based nano-
composi es, i was possible o demons a e infil a ion o
ma ix monome s in o he in e io o he SCNPs.
26
This
finding, suppo ing also expe imen al obse a ions p e iously
epo ed on PMMA/PEO nanocomposi es,
21
leads o a close
co ela ion be ween SCNPs and ma ix chains. Local
en anglemen s p oduced by he linea chains on he SCNP
s ands could gi e ise o mo e he e ogeneous dynamics o he
“fille s”a local leng h scales and o an inc ease o he a e age
leng h o he jumps in ol ed in he sublinea diffusi e egime
o he a oms in he SCNPs.
We may exploi he desc ip ion in e ms o he AJD model
o p o ide a mo e quan i a i e es ima ion o he non-Gaussian
effec s induced, fi s , by in amolecula c oss-linking (mel o
SCNPs e sus mel o p ecu so chains) and, la e , on he
SCNPs by he p esence o he linea chains in he
nanocomposi e. In he amewo k o he AJD model, he
ime-dependen second-o de non-Gaussian pa ame e α2( )
can be calcula ed as
Ä
Ç
Å
Å
Å
Å
Å
Å
Å
Å
Å
É
Ö
Ñ
Ñ
Ñ
Ñ
Ñ
Ñ
Ñ
Ñ
Ñ
α
=
+
τ
β
τ
β
()
()
l
ul
()
72
26
2
o
4
2o
2
2
o
o(5)
Figu e 7. In e media e sca e ing unc ion ob ained o Q= 0.57 Å−1
on he mel o SCNPs (filled symbols) and on he nanocomposi e
wi h he deu e a ed ma ix (emp y symbols), domina ed by he sel -
mo ions o he hyd ogens o he SCNPs in bo h en i onmen s.
Diffe en symbols co espond o he diffe en empe a u es indica ed.
Lines a e fi s o eq 2 wi h he β- alues in Table 1.
Mac omolecules pubs.acs.o g/Mac omolecules A icle
h ps://doi.o g/10.1021/acs.mac omol.1c02382
Mac omolecules 2022, 55, 2320−2332
2328
