Ad ances in Colloid and In e ace Science 302 (2022) 102620
A ailable online 3 Ma ch 2022
0001-8686/© 2022 The Au ho s. Published by Else ie B.V. This is an open access a icle unde he CC BY license (h p://c ea i ecommons.o g/licenses/by/4.0/).
His o ical Pe spec i e
A b oad pe spec i e o pa icle-laden luid in e aces sys ems: om
chemically homogeneous pa icles o ac i e colloids
Edua do Guzm´
an
a
,
b
,
*
, Fe nando Ma ínez-Ped e o
a
,
**
, Ca les Cale o
c
,
d
, A mando Maes o
e
,
,
F ancisco O ega
a
,
b
, Ram´
on G. Rubio
a
,
b
,
*
a
Depa amen o de Química Física, Facul ad de Ciencias Químicas, Uni e sidad Complu ense de Mad id, Ciudad Uni e si a ia s/n, 28040 Mad id, Spain
b
Unidad de Ma e ia Condensada, Ins i u o Plu idisciplina , Uni e sidad Complu ense de Mad id, Paseo Juan XXIII 1, 28040 Mad id, Spain
c
Depa amen de Física de la Ma `
e ia Condensada, Facul a de Física, Uni e si a de Ba celona, A enida Diagonal 647, 08028 Ba celona, Spain
d
Ins i u de Nanoci`
encia i Nano ecnologia, IN2UB, Uni e si a de Ba celona, A enida, Diagonal 647, 08028 Ba celona, Spain
e
Cen o de Fısica de Ma e iales (CSIC, UPV/EHU)-Ma e ials Physics Cen e MPC, Paseo Manuel de La dizabal 5, 20018 San Sebas i´
an, Spain
IKERBASQUE—Basque Founda ion o Science, Plaza Euskadi 5, 48009 Bilbao, Spain
ARTICLE INFO
Keywo ds:
Pa icle
luid in e aces
con ac angle
dynamics
ac i e pa icles
heology
ABSTRACT
Pa icles adso bed o luid in e aces a e ubiqui ous in indus y, na u e o li e. The wide ange o p ope ies
a ising om he assembly o pa icles a luid in e ace has s imula ed an in ense esea ch ac i i y on shed ligh
o he mos undamen al physico-chemical aspec s o hese sys ems. These include he mechanisms d i ing he
equilib a ion o he in e acial laye s, apping ene gy, speci ic in e -pa icle in e ac ions and he esponse o he
pa icle-laden in e ace o mechanical pe u ba ions and lows. The unde s anding o he physico-chemis y o
pa icle-laden in e aces becomes essen ial o aking ad an age o he pa icle capaci y o s abilize in e aces o
he p epa a ion o di e en dispe sed sys ems (emulsions, oams o colloidosomes) and he ab ica ion o new
econ igu able in e ace-domina ed de ices. This e iew p esen s a de ailed o e iew o he physico-chemical
aspec s ha de e mine he beha io o pa icles apped a luid in e aces. This has been combined wi h
some examples o eal and po en ial applica ions o hese sys ems in echnological and indus ial ields. I is
expec ed ha his in o ma ion can p o ide a gene al pe spec i e o he opic ha can be exploi ed o esea che s
and echnologis non-specialized in he s udy o pa icle-laden in e aces, o o expe ienced esea che seeking
new ques ions o sol e.
1. In oduc ion
Adso p ion and sel -assembly o nanopa icles and mic opa icles a
luid in e aces a e widely exploi ed phenomena on di e en echno-
logical and indus ial pu poses. This may be unde s ood conside ing ha
luid in e aces p o ide a sui able en i onmen o he quasi-2D
con inemen o pa icles, which esul s ex emely use ul o guiding
he ab ica ion o so and econ igu able in e ace-domina ed de ices
[1,2]. In ac , pa icle-laden in e ace has been used as suppo o no el
applica ions which ange om he s abiliza ion he s abiliza ion o
dispe sed sys ems, including emulsions (Picke ing emulsions o bijels),
oams, liquid ma bles o colloidosomes, o he p oduc ion o no el
nanopo ous memb anes o il a ion o encapsula ion [3–6] and he
ab ica ion o unc ional ma e ials wi h di e en elec ical, op ical, o
magne ic p ope ies [7–9]. The accumula ion, and quasi-2D con ine-
men , o colloids a luid in e aces leads o he eme gence o comple ely
new beha io s and p ope ies, e.g., in iguing 2D phase ansi ions o
anomalous heological esponses. These canno be easily explained in
e ms o he physico-chemical concep s adi ionally used in he
desc ip ion o hei 3D coun e pa s, and equi e o conside he mo-
dynamics aspec s ac ing a he molecula scale wi h mechanical ones
ope a ing a he mic oscale o e en la ge dis ances, which a e s ongly
de e mined by he cha ac e is ics o he pa icles and he na u e o he
luids composing he in e ace [10,11]. The dis inc i e ea u es o
pa icle-laden in e aces wi h espec o hose s abilized wi h su ac-
an s, can be unde s ood conside ing ha : (i) pa icles a e equen ly
* Co esponding au ho a : Depa amen o de Química Física, Facul ad de Ciencias Químicas, Uni e sidad Complu ense de Mad id, Ciudad Uni e si a ia s/n, 28040
Mad id, Spain.
** Co esponding au ho .
E-mail add esses: [email p o ec ed] (E. Guzm´
an), [email p o ec ed] (F. Ma ínez-Ped e o), [email p o ec ed] (R.G. Rubio).
Con en s lis s a ailable a ScienceDi ec
Ad ances in Colloid and In e ace Science
jou nal homepage: www.else ie .com/loca e/cis
h ps://doi.o g/10.1016/j.cis.2022.102620
Recei ed 4 Decembe 2021; Recei ed in e ised o m 22 Feb ua y 2022; Accep ed 23 Feb ua y 2022
Ad ances in Colloid and In e ace Science 302 (2022) 102620
2
chemically iso opic objec s (Janus pa icles and pa chy colloids a e
excep ions ha in oduce some speci ici ies); (ii) pa icles do no end o
agg ega e in bulk o o m well-de ined sup amolecula sys ems such as
micelles, and (iii) mos o he adso bed pa ices ha dly unde go
deso p ion o bending p ocesses [12–15]. The abo e aspec s, oge he
wi h he e ec o colloidal in e ac ions be ween pa icles, some o hem
a ising speci ically a in e aces, o be ween he pa icles and he in-
e aces, de e mine he adso p ion kine ics and sel -o ganiza ion o
adso bed pa icles [16–18].
The unde s anding o phenomena in ol ing he in e ac ions o pa -
icles wi h luid in e aces has ad anced signi ican ly since he seminal
s udies o Ramsdem [19] and Picke ing [20], in which some o he mos
undamen al aspec s unde lying he physico-chemis y o pa icle-laden
luid in e aces we e in oduced. Nowadays, he de elopmen o new
syn hesis ou es, which ha e enabled he con olled ab ica ion o many
ypes o pa icles ha di e in shape, size ( anging om a ew nano-
me e s o se e al mic ome e s) o su ace chemis y has opened new
a enues on he unde s anding o he physico-chemical beha io o
pa icle-laden in e aces [21]. Con olling he physicochemical and
s uc u al cha ac e is ics o pa icles also g ea ly expands he phenom-
ena a ising om adso p ion and pa icle assembly a luid in e aces,
while allowing he beha io o pa icle-laden luid in e aces o be
modula ed almos a will [16]. On he o he hand, in he las yea s ha
he unde s anding he undamen al aspec s o pa icle adso p ion/
deso p ion a luid in e aces, such as he dynamics o binding, equi es
expe imen s ha moni o he mo ion o con ollable pa icles du ing he
p ocess [22]. Ne e heless, he e a e many aspec s o he beha io o
pa icle-cha ged luid in e aces ha emain unclea , which con inues o
s imula e he esea ch aimed o he unde s anding o he p ocesses o
pa icle adso p ion a luid in e aces and he physico-chemical p op-
e ies o he esul ing laye s, such as hei esponse agains mechanical
s esses.
The las decade has been ui ul in ad ancing he knowledge o
pa icle-laden in e aces, as e lec ed in he nume ous published e iews
on speci ic aspec s o his ype o sys ems, e.g., con ac angle [23–25],
mechanical esponse [11,26–35], he dynamics o pa icles apped a
luid in e aces [36,37], ac i e and ex e nally ac ua ed pa icles [8,38],
he in e ac ion o pa icle laye s wi h biological in e aces [39,40] o he
de elopmen o pa icula applica ions (s abiliza ion o emulsions and
oams, in e ace-domina ed de ices o p e en ion o co ee- ing e ec )
[1,2,5,14,15,18,41]. This e iew a emp s o p o ide an in eg a i e
iew o he beha io o pa icle-laden luid in e aces ha may help
esea che s and echnologis s in he unde s anding o undamen al and
applica i e aspec s o his ype o sys ems.
2. A b ie app oach o he adso p ion and sel -o ganiza ion o
pa icles a luid in e aces
This sec ion ies o p o ide a desc ip ion o he wo p ocesses ha
a e indispensable in he o ma ion o any pa icle-laden luid in e ace,
ega dless o he speci ic na u e o he colloidal objec s o he luid
in e ace: (i) he anspo o colloidal pa icles o he in e ace, and (ii)
he b each o he in e ace as a esul o pa icle p o usion. As soon as
he pa icles en e in o con ac wi h he in e ace, hei pene a ion in o
he in e ace is mainly d i en by he educ ion o con ac a ea be ween
he wo luid phases, which leads o he minimiza ion o he un a o able
luid/ luid in e ac ions and he educ ion o he o al ee ene gy o he
sys em [13]. This ene gy educ ion in u n con ibu es o gua an ee he
in e acial s abiliza ion.
2.1. In e ac ion be ween pa icles and he in e ace
Pa icle-in e ace in e ac ions can be expec ed o be ele an as soon
as he pa icle is anspo ed o he icini y o he in e ace. Since mos o
he pa icles o in e es hold su ace cha ges ha lead o he eme gence
o elec ical double laye o ces, and bo h he wa e / apo and wa e /
non-pola luid in e aces exhibi a nega i e e ec i e cha ge [42], he
adso p ion o nega i e cha ged pa icles a he luid in e ace is expec ed
o occu e y slowly, o does no occu [43], while he adso p ion o
posi i ely cha ged pa icles is usually s ongly a o ed, al hough he
di usion p ocess can be e y slow. Fu he mo e, as he pa icles
app oach he in e ace made up o luid wi h di e en dielec ic con-
s an , hey expe ience epulsi e image cha ge epulsions and o he
con inemen e ec s, ha dis o he elec ical double laye o he pa -
icles nea he in e ace [43–45]. In ac , when a cha ged colloidal
pa icle app oaches o he in e ace be ween luids ha ing e y di e en
alues o dielec ic cons an s, a new ype o elec os a ic in e ac ion
eme ges. This can be a ionalized conside ing ha a pa icle wi h a
de ined cha ge close o he in e ace (a a dis ance d) pe cei es a o ce
equi alen o ha wha would be expec ed o i s in e ac ion wi h a
simila pa icle placed in he o he phase a simila dis ance o he
in e ace, i.e., he pa icle and he image pa icle a e sepa a ed by a
dis ance 2d [46]. Fo cha ged pa icles suspended in wa e nea an
in e ace wi h ai o oil, he image cha ge in e ac ions a e always
epulsi e, independen ly o he sign o he pa icle cha ge. This allows
modula ing he adso p ion by a ying he ionic s eng h o he dispe -
sion [47], because he inc ease o he elec oly e concen a ion sc eens
he elec os a ic epulsion be ween he pa icles and he in e ace. On
he o he side, when he sign o he image cha ge is opposi e o ha o
he pa icle, he in e ac ion esul s a ac i e.
Mo eo e , sho ange an de Waals pa icle-in e ace in e ac ions
a ise om he combina ion o h ee di e en con ibu ions (i) in-
e ac ions be ween pe manen dipoles (Keesom in e ac ions); (ii) in-
e ac ions be ween pe manen and induced dipoles (Debye
in e ac ions), and (iii) in e ac ions in ol ing luc ua ing dipoles (Lon-
don in e ac ions). The o e all in e ac ion can be pa ame e ized in e ms
o he Hamake cons an s o he h ee ma e ials, i.e., hose ha compose
he pa icle and he wo luids. Thus, o a smoo h and chemically ho-
mogeneous sphe ical pa icle o adius R comple ely imme sed in one o
he luids ( luid 1), bu placed e y close o he luid in e ace, i is
possible o de ine he Hamake cons an o he in e ac ion be ween he
solid pa icle and he second luid ( luid 2) h ough a e y hin laye o
luid 1, A
P12
, as ollows [47]
AP12 ≈(
APP
√−
A11
√)(
A22
√−
A11
√)(1)
whe e A
PP
, A
11
and A
22
a e he Hamake cons an s o he pa icles, and
luids 1 and 2, espec i ely. No e ha A
P12
is always posi i e, so he an
de Waals pa icle-in e ace in e ac ions a e always a ac i e [48]. The
di e en con ibu ions o he Hamake cons an A
P12
can be ela ed,
using Li shi z’s heo y, o he dielec ic pe mi i i y
ε
and e ac i e
indices o he wo luid and he pa icles [49]. Conside ing dielec ic
media wi h iden ical adso p ion equency (
ν
e
), i is possible o ob ain
he ollowing app oxima e exp ession,
AP12 ≈3
4kBT(
ε
P−
ε
1
ε
P+
ε
1)(
ε
2−
ε
1
ε
2+
ε
1)+3h
ν
e
8
2
√(n2
P−n2
1)(n2
2−n2
1)
n2
P+n2
1
√
n2
2+n2
1
√(
n2
P+n2
1
√+
n2
2+n2
1
√)(2)
E. Guzm´
an e al.
Ad ances in Colloid and In e ace Science 302 (2022) 102620
3
whe e h is he Planck’s cons an ; and
ε
i
and n
i
a e, espec i ely, he s a ic
(ze o- equency) dielec ic cons an s, and he e ac i e indices in he
isible ange, and k
B
and T he Bol zmann cons an and he absolu e
empe a u e, espec i ely. He e, he sub-indexes P, 1 and 2 e e o he
pa icle and he luids 1 and 2. In Equa ion 2, he i s e m accoun s o
he Keesom and Debye con ibu ion, and a e always lowe han ¾k
B
T
[48,49], while he second e m inco po a es he con ibu ion o London
in e ac ions, which is commonly he mos signi ican .
2.2. Adso p ion dynamics o pa icles o he luid in e ace
The di e en anspo mechanisms ha p omo e he app oach o
mic on-sized pa icles om a bulk phase o he luid in e ace can be
classi ied in o (i) spon aneous (including B ownian di usion, sedimen-
a ion o lo a ion) o (ii) ex e nally igge ed ( ield-induced o hyd o-
dynamically guided) [35,36,50–52]. When di usion is he main
mechanism, g a i y o en plays an impo an ole due o he pa icle
densi y. In he dilu e egime, whe e in e ac ions be ween pa icles can
be neglec ed, he e minal eloci y o pa icle se ling is de e mined by a
balance be ween he g a i a ional and iscous o ces. Acco ding o he
S okes' law [53], he e minal eloci y o he alling pa icles is gi en by
S =2R(
ρ
p−
ρ
1)g
9
η
(3)
whe e
ρ
p
and
ρ
1
a e he densi ies o he pa icles and he luid phase,
espec i ely, g is he g a i a ional accele a ion and
η
he dynamic is-
cosi y. The compe i ion be ween g a i y and di usion is e alua ed by
means o he P´
ecle numbe , a dimensionless numbe which e alua es
he a io o con ec i e o di usi e anspo de ined as
Pe =R S
D(4)
He e, D is he bulk di usion coe icien o he pa icles. P´
ecle
numbe assumes alues abou 0.1 o silica pa icles o 1
μ
m suspended
in wa e , whe eas pa icles o 10
μ
m p esen s a P´
ecle numbe almos 4
o de s o magni ude highe . The e o e, i is clea ha he inc ease o he
pa icle size may a o he ballis ic mo emen o he pa icles o e
di usi e anspo [29].
I g a i a ional o ces can be neglec ed, Pe <<1, and di usion occu s
in he absence o adso p ion ba ie s and ex e nal low ields, pa icles
anspo o he in e ace can be desc ibed by a Fickian-like di usion
law, in a simila manne o he desc ip ion o molecula su ac an
adso p ion de eloped by Wa d-To dai [45]. Thus, he mass anspo
a e is gi en by
∂
c(x, )
∂
=D
∂
2c(x, )
∂
x2(5)
wi h c( , x) being he bulk concen a ion, x he dis ance o he luid
in e ace and he di usion ime, espec i ely. Assuming an ini ially
homogeneous pa icle bulk concen a ion c(x, 0) =c
∞
, hen he
bounda y condi ion o he adso p ion kine ics is gi en by
∂
Γ
∂
=D[
∂
c(x, )
∂
x]x=0
(6)
whe e Γ( ) is de ined as he ime-dependen in e acial excess o pa i-
cles adso bed a he in e ace, and Γ(0) =0. Thus, aking he Wa d-
To dai app oach unde condi ions o i e e sible adso p ion and
wi hou he p esence o any adso p ion ba ie , and conside ing a
comple e deple ion o he pa icles con ained in he sublaye and small
change o he bulk concen a ion, i.e., c(∞, ) → c
∞
, he combina ion o
Equa ions (5) and (6) leads o [45]
Γ( ) = 2c∞
D
π
√(7)
Howe e , he p esence o elec os a ic ba ie s be ween he pa icles
in he bulk phase and he luid in e ace is e y common and equi es an
ex ension o he amewo k desc ibed abo e (see Fig. 1). The e ec o
he elec os a ic ba ie on he ime e olu ion o he su ace concen-
a ion can be app oxima e by including an e ec i e di usi i y [54]
Γ( ) = − 2c∞ΔEp
De
π
√(8)
whe e ΔE
p
is he educ ion in in e acial ene gy associa ed wi h he
sc eening o he luid– luid in e ace and D
e
is he e ec i e di usion
coe icien , de ined as
De =Dexp(−ΔEba ie
kBT)(9)
wi h ΔE
ba ie
being he heigh o he ene gy ba ie o he ene ge ic
landscape eme ging o adso p ion o a pa icle o a luid in e ace [54].
On he o he hand, Schwenke e al. [50] ound ha he adso p ion
kine ics is also slowed down wi h he inc ease o in e acial co e age in
ag eemen wi h he esul s by Deshmukh e al. [35]. The la e epo ed
he exis ence o wo dis inc egimes in he ime e olu ion o he
adso p ion o mic ogel pa icles a wa e / apo in e aces: (i) a sho -
e m egime, whe e adso p ion is con olled by di usion, and (ii) a
long- e m slowe egime, limi ed by he inc ease in co e age and he
associa ed s e ic ba ie . This is simila o wha was ound o he
adso p ion o se e al su ace ac i e wa e -soluble polyme s, whe e a
i s ini ial as di usion o he molecules om he solu ion o he sub-
su ace is ollowed by a eo ganiza ion o he molecules, which is limi ed
by he s e ic hind ance induced by he adso bed molecules and d i es
he equilib a ion o he in e acial laye [55].
2.3. The meaning o he in e acial ension o pa icle-laden in e aces
Fluid in e aces a e commonly conside ed o be in he molecula
scale, wi h hei densi y p o ile being analy ically desc ibed by a
hype bolic- angen unc ion [56,57]. Howe e , in mos o he cases, he
size o he pa icles is much bigge han he in e ace wid h, which does
no allow one o use he classical mic oscopic desc ip ion o explaining
he dec ease o he in e acial ension o clean luid/ luid in e ace γ
12
as
esul o he pa icle apping a he in e ace [2]. Ins ead, i is usually
desc ibed in e ms o he dec ease o he ee ene gy associa ed wi h he
educ ion o he con ac a ea be ween he wo luid phases [58–61].
Conside ing a pa icle cons i u ed by a ma e ial ha ing he same in e -
acial ension wi h bo h luid phases, i is expec ed ha i s adso p ion a
he in e ace occu s because i leads o a dec ease o he di ec con ac
Fig. 1. Simpli ied ep esen a ion o he ene ge ic landscape eme ging o
adso p ion o a pa icle o a luid in e ace. The ene gy ba ie ΔE
ba ie
usually
inc eases wi h he in e acial co e age due o he inc ease o he elec ical
po en ial and, hus he Debye leng h. Rep in ed om Deshmukh e al. [35],
Copy igh (2015), wi h pe mission om Else ie .
E. Guzm´
an e al.
Ad ances in Colloid and In e ace Science 302 (2022) 102620
4
be ween he wo luids, wi hou any addi ional ene ge ic cos s due o he
con ac o he pa icles wi h he luids [40].
The abo e pic u e equi es a desc ip ion o he in e acial ension
using a mac oscopic pe spec i e, which conside s ha he su ace en-
sion o a pa icle-laden in e ace is no uly a he modynamic magni-
ude, and should be de ined as an e ec i e one [2,13]. Thus, he
educ ion o he e ec i e in e acial ension is due o he eme gence o a
2D la e al p essu e Π, o igina ed om an in ica e balance be ween he
en opy and in e -pa icle in e ac ions, which coun e ac s he con ac-
ion o he in e acial a ea associa ed wi h he in e acial ension. This
leads o a dec ease o he in e acial ension γ=γ
12
-Π, as he in e acial
packing o he pa icle-laden in e ace inc eases, which is measu able
using some o he common me hodological app oaches used o in e -
acial ension e alua ion [2,13,61–65].
Fu he analysis o he change o he in e acial ension wi h he
apping o pa icles poin ou ha he educ ion o he a ea be ween he
wo luids is di ec ly co ela ed o he in e acial excess o pa icles, Γ,
and, consequen ly, o he o al numbe o pa icles, N, which leads o a
de ini ion o he e ec i e in e acial ension o a pa icle-laden in e -
ace as
γ=(
∂
Gγ
∂
A)Γ=(
∂
Gγ
∂
A)N,T,p
(10)
The apping o a pa icle o a luid/ luid in e ace is associa ed wi h
an ene gy change ΔE
p
, which leads o a educ ion o he in e acial
ension ΔE
p
/A. The e o e, he e ec i e in e acial ension o he
pa icle-laden luid/ luid in e ace in absence o any con ibu ion o he
in e -pa icle in e ac ions, i.e., a low in e acial excess concen a ion, is
de ined by [66]
γ=γ12 −Π(Γ)(11)
wi h Π(Γ) =Γ|ΔE
p
|.
2.3.1. The modynamics model o desc ibing pa icle-laden luid in e aces
The de ini ion o he in e acial ension o a pa icle-laden in e ace
as an e ec i e magni ude makes i di icul o ob ain a physically
insigh ul he modynamic desc ip ion o such sys ems. The de ini ion o
he in e acial ension o a pa icle-laden in e ace as an e ec i e
magni ude makes i di icul o ob ain a physicaly insigh ul he mo-
dynamic desc ip ion o such sys ems. This makes i necessa y o conside
he ole o he in e ac ions be ween he pa icles apped a he in e ace
and be ween he pa icles and he in e ace, oge he wi h he we ing
and he chemical po en ial o he pa icles [2,31,32]. Howe e , his is
no i ial o pa icle apped a luid in e aces, because, unlike mo-
lecula species, he pa icle size is e y di e en om ha o he sol en
molecules [67], so, a new he modynamic amewo k is needed.
Hende son [68] p oposed he i s he modynamic desc ip ion o
pa icle-laden luid in e ace, conside ing ha he in e acial ilm was
composed o a 2D colloidal luid o ha d disc-shaped pa icles, in which
only he ole o he olume in e ac ions was conside ed. Howe e , his
model did no p o ide a ealis ic pic u e because i did no include he
changes on he su ace p essu e a low in e acial co e age due o long-
ange elec os a ic in e -pa icle epulsions. The simpli ica ion adop ed
in he p e ious model was pa ially o e come by he one in oduced by
Binks [68], who combined Volme and an de Waals equa ions we e
combined. This model accoun s o he absence o la e al in e ac ions
be ween pa icles a low packing densi y and sho - ange la e al in-
e ac ions be ween hem a high packing densi y, espec i ely. Besides,
i includes wo addi ional assump ions: (i) he beha io o he pa icles is
eminiscen o ha expec ed o a su ac an molecule, and (ii) he a ea
occupied by he adso bed pa icle a he luid in e ace is he a ea p o-
jec ed by he adso bed pa icle on he luid in e ace, i.e., i s geome ical
a ea. Howe e , his model did s ill no conside he ole o in e ac ions
be ween pa icles a long sepa a ion dis ances, so i con inued o p o ide
un ealis ic p edic ions on he dependence o he in e acial ension wi h
he packing densi y. Finally, he di e en leng h-scales in ol ed in
pa icle-laden and su ac an -laden in e aces we e an addi ional
con ibu ion o he ailu e o he model, ha p edic ed changes in he
su ace p essu e only a high alues o he in e acial co e age (50-70%
o he o al in e acial a ea when he monolaye was composed o small
pa icles, diame e <1nm).
A mo e ealis ic he modynamic desc ip ion o pa icle-laden luid
in e aces was p oposed by he g oup o Mille [69,70]. They ex ended
hei p e ious wo k on he he modynamic desc ip ion o p o ein-laden
luid in e aces [71] by including speci ic aspec s enabling o a
desc ip ion o he beha io o pa icles apped a he luid in e ace.
Acco ding o his model, he in e acial p essu e o he pa icle-laden
in e ace is gi en by
Π=kBT
ω
0[ln(1−
ω
A)+(
ω
A)]−Πcoh (12)
whe e
ω
/A and
ω
0
a e he ac ion o a ea co e s by pa icles and he
a ea o a single pa icle, espec i ely, and Π
coh
is he cohesion p essu e, a
pa ame e ha accoun s o he con ibu ion o he in e -pa icle in-
e ac ions o he packing o he pa icle-laden in e ace. Applica ion o
he abo e model p o ides a sui able desc ip ion o he change in in e -
acial ension wi h packing densi y, ega dless o he chemical na u e
and dimensions o he pa icles in ques ion, e en when he in e acial
co e ages is a om a close-packed s a e.
Mo e ecen ly, Hua e al. [72] in oduced an al e na i e model ha
accoun s o : (i) he impac o he educ ion o he con ac line be ween
he wo luid phases on he in e acial ension, and (ii) he in e -pa icle
in e ac ions. The con ibu ion o he educ ion o he con ac line on he
su ace p essu e due o pa icle adso p ion, Π
p
, was ob ained in e ms o
he pa icle densi y a he luid in e ace, whe eas he con ibu ion
associa ed wi h he in e -pa icle in e ac ions, Π
p-p
, was assessed,
assuming a linea addi i i y Π =Π
p
+Π
p-p
, by e alua ing he change o
he in e acial p essu e o he 2D pa icle-laden in e ace. Thus,
combining hese con ibu ions wi h he F umkim model [57], which
conside s he non-ideali y o he in e ac ions, and assuming he mody-
namic equilib ium, whe e he Gibbs ela ionship is ul illed, he in e -
acial p essu e is gi en by he ollowing exp ession [73]
Π= − kBTΓ∞[ln(1−ϑ)− 0.5Kϑ2](13)
whe e Γ
∞
and K a e he in e acial excess concen a ion o a close-
packed pa icle-laden in e ace and an in e -pa icle in e ac ion con-
s an , espec i ely. He e, ϑ=Γ/Γ
∞
ep esen s he in e acial co e age, i.
e., he a ini y o he pa icles o he in e ace.
Finally, G oo and S oyano [74] p oposed a model ha in oduces
he dependence o he in e -pa icle in e ac ions on he in e acial
co e age densi y in he es ima ion o he in e acial p essu e. Acco ding
o his model, he la e is desc ibed by
Π=4kBT
π
d2[byZ
λ−b2ϑ2](14)
whe e d accoun s o he ange o he long- ange in e ac ions, Z is he
comp essibili y ac o [74], (λ)
1/2
λ
√is he e ec i e diame e o he
pa icles, and b and b
2
a e pa ame e s accoun ing o he in e -pa icle
in e ac ions. This model has been success ully applied on he desc ip-
ion o he collec i e beha io o so pa icles adso bed a luid in-
e aces [75].
2.4. We abili y o pa icles a a luid in e ace
The chemical aniso opy o su ac an s, i.e., he exis ence o wo
moie ies wi h di e en pola i ies and di e en a ini y o luid phases,
is he main d i ing o ce o hei a achmen o luid in e aces. The
en opic penal y associa ed wi h he educ ion o he deg ee o eedom
in he o ien a ion o he su ac an molecules, is coun e balanced by a
E. Guzm´
an e al.
Ad ances in Colloid and In e ace Science 302 (2022) 102620
5
a o able en halpic con ibu ion, hus educing he Gibbs ee ene gy o
he sys em. Howe e o desc ibing he en apmen o smoo h, sphe ical
and chemically iso opic pa icles a a luid in e ace, pa icle we a-
bili y plays he essen ial ole [29]. En apmen o a pa icle a a luid
in e ace is only possible when he di e ence be ween he ene gies o
he pa icle dispe sed in one o he bulk phases and ha o he pa icle
apped a he luid in e ace exceeds he ene gy associa ed wi h he mal
agi a ion k
B
T. Assuming ha he pa icle is small enough o neglec
g a i a ional o ces, he ene gy o a pa icle, whose cen e is loca ed a
an a bi a y dis ance z o he in e ace, is gi en by [1,25]
E(z) =
π
R2γ12[(z
R)2+2(γP2−γP1
γ12 )(z
R)+2(γP2+γP1
γ12 )−1](15)
whe e γ
P1
and γ
P2
a e he in e acial ensions be ween he solid pa icles
and he wo luid phases. Fig. 2 shows he dependence o he ene gy o a
pa icle as a unc ion o z
0
=z/R, wi h z
0
=1 and z
0
=-1 co esponding
o a pa icle comple ely imme sed in he luid 1 and 2, espec i ely, and
z
0
=0 o a pa icle placed in he in e acial plane.
The equilib ium posi ion z
0min
, which co esponds o a pa icle
mos ly imme sed in luid 1 (0<z
0min
<1) o 2 (−1 <z
0min
<0), is placed
a he dis ance whe e he ee ene gy is minimized, i.e.,
∂
E/
∂
z =0, and is
gi en by [76]
zmin
0=γP1−γP2
γ12
R(16)
A his poin , he equilib ium condi ion o he o ces ac ing a he
con ac line can be de ined in e ms o he h ee cha ac e is ic in e acial
ensions, he in e ac ion be ween he pa icle and bo h luids and be-
ween he wo luid phases, simpli ies o he Young-Dup e equa ion
0=γP1−γP2−γ12cosθ (17)
He e, he con ac angle, θ, is de ined as he angle be ween he plane
angen o he pa icle’s su ace and he in e ace a he line whe e he
in e ace mee s he solid, as shown in Fig. 3 [77].
Unde hese condi ions, he equilib ium con ac angle is comple ely
de e mined by he h ee su ace ensions
cosθ =γP1−γP2
γ12
(18)
F om he p e ious equa ion, i ollows ha he pa icle adso bs a he
luid in e ace only when he ollowing inequali y is me [13,25]
|γP2−γP1|<γ12 (19)
Hence, he con ac angle plays he same ole as he hyd ophilic-
lipophilic balance (HLB) o molecula su ac an s [12,23], i.e., a
pa ame e ha p o ides in o ma ion on he p e e en ial pa i ioning o
pa icles be ween he wo luid phases, and esul s om he di e en
in e ac ion o he pa icles wi h he wo luid phases [10,12,78].
I is possible o desc ibe he apping o colloidal pa icles a a luid
in e ace in e ms o he in ica e balance o in e ac ions, e.g., an de
Waals, pola and elec os a ic in e ac ions, and hyd odynamics o ces
ha con ibu e o in e acial equilib ium [48,49]. Fo example, in
cha ged pa icles he ee ene gy pe uni o a ea, associa ed wi h he
o ma ion o he elec ic double laye , ΔF
DL
, leads o a change o he
su ace ee ene gy γ
1P
=γ
1P,0
+ΔF
DL
[79], whe e γ
1P,0
is he su ace
ension a he poin o ze o ne cha ge. In oducing he abo e co ec ion
in o Equa ion (18), he ollowing exp ession is ob ained
cosθ =cosθ0−ΔFDL
γ12
(20)
Conside ing ha in mos cases he double laye o ms spon aneously,
ΔF
DL
<0. The e o e, a smalle pa i ioning o he cha ged pa icles
be ween he wo media is expec ed han o an uncha ged pa icle. I one
o he luids is wa e , pa icles a e conside ed as hyd ophilic when θ <
90◦, and hey emain mainly subme ged in wa e , while pa icles a e
conside ed hyd ophobic when θ >90◦, and hey a e p edominan ly
subme ged in he non-aqueous phase. The case in which he pa icles
show a simila p e e ence o bo h luid phases is he so-called neu al
we ing and is cha ac e ized by a con ac angle o 90◦(see Fig. 4).
Fo sphe ical and pe ec ly smoo h pa icles, i is possible o ind a
simple geome ical ela ion connec ing he con ac angle and he p o-
usion heigh h o he pa icle in o he less pola phase,
Fig. 2. F ee ene gy o a sphe ical colloidal pa icle (R =50 nm) as a unc ion o
i s cen e ela i e o he hexadecane/wa e in e ace. The in e acial ensions
a e γ
12
=53.5 mN/m, γ
P1
=28.5 mN/m and γ
P2
=14.2 mN/m. Rep in ed om
Balla d e al. [25], Copy igh (2019), wi h pe mission om The Royal Socie y
o Chemis y.
Fig. 3. Idealized ep esen a ion o he posi ion o a pa icle apped a an
a bi a y luid/ luid in e ace. θ and R ep esen he con ac angle, o ela i e
we abili y o he pa icle by he in e ace, and pa icle adius, espec i ely; γ
P1
and γ
P2
a e he in e acial ensions be ween he solid pa icle and he wo luid
phases, and γ
12
he in e acial ensions co esponding o he luid in e ace.
Adap ed om Da ies e al. [77], Copy igh (2014), wi h pe mission om
Ame ican Ins i u e o Physics.
Fig. 4. Schema ic showing he ela i e posi ion o a colloidal pa icle in ela-
ion o he in e acial plane as a unc ion o i s con ac angle. Rep in ed om
Maes o e al. [80], Copy igh (2019), wi h pe mission om The Royal Socie y
o Chemis y.
E. Guzm´
an e al.
Ad ances in Colloid and In e ace Science 302 (2022) 102620
6
θ=cos−1[1−h/R](21)
F om equa ion (15), he ene gy change associa ed wi h he ans-
e ence o a pa icle om a luid phase o i s equilib ium posi ion, i.e. he
so-called apping ene gy, is gi en by [81]
ΔEp= −
π
R2
γ12 (γ12 − (γP1−γP2))2(22)
which o sphe ical pa icles can also be de ined in e ms o he con ac
angle as
ΔEp= −
π
R2γ12(1±cosθ)2(23)
whe e he ±signs in he b acke indica e he posi ion o he pa icles in
ela ion o he in e acial plane. Acco ding o Equa ion (23) pa icle
apping a luid in e aces s ongly depends on size. Fig. 5 shows he
dependence o he en apmen ene gy on he con ac angle, calcula ed
wi h Equa ion (23), o wo colloidal pa icles wi h di e en sizes, 10 nm
and 1
μ
m, a an a bi a y luid in e ace wi h γ
12
=50 mN/m.
The ene ge ic landscape, esul ing om he analysis o he con ac
angle and size dependences o he apping ene gy, shows ha he la e
la gely exceeds he he mal ene gy k
B
T in mos o he cases [82].
The e o e, he adso p ion o mic on-sized pa icles o a luid in e ace
can be conside ed as an i e e sible p ocess, wi h ypical apping en-
e gy alues in he ange be ween 10
6
k
B
T and 10
7
k
B
T. Fo he
men ioned mic opa icles, adso p ion is e e sible only a e y low
alues o he luid/ luid in e acial ension γ
12,
and/o o cosθ ~ 1. On
he o he hand, in pa icles wi h sizes smalle han 10 nm he apping
ene gy is o he o de o se e al k
B
T. This sugges s ha o pa icles wi h
a e y small size, he low alue o he apping ene gy can lead o a
he mal-ac i a ed escape o he pa icles om he in e ace. Hence,
small nanopa icles exhibi an adso p ion-deso p ion equilib ium like
ha ound in con en ional molecula su ac an s, polyme s and p o eins
[83]. Fig. 6 shows he dependence o he de achmen ene gy (-ΔE
p
) on
he pa icle adius o he apping o colloidal pa icles a an oil/wa e
in e ace wi h γ
12
=50 mN/m, and a ixed alue o θ =90◦. The esi-
dence ime o pa icles a he luid in e ace is educed wi h he dec ease
o he cha ac e is ic size o he adso bed pa icles, which explains he
acili a ed displacemen o small nanopa icles om he in e ace by he
adso p ion o pa icles wi h bigge size [84].
In mos cases, mic o-sized pa icles a e i e e sibly adso bed, so ha
he pa icles can only mo e eely wi hin he in e acial plane. The ex-
is ence o la e al mobili y o he pa icles allows hei ea angemen in
a di usi e manne o a e he applica ion o ex e nal s imuli, which lays
he ounda ion o he ab ica ion o new ma e ials ha can be econ-
igu ed by adjus ing he pa icle in e ac ions/o ganiza ion a he luid
in e ace [17,37]. This scena io la gely di e s om he one s ablished
when pa icles a e se on liquid/solid in e aces [16], o e en when
pa icles a e in he icini y o a luid in e ace bu wi hou ac ually being
adso bed [85]. The posi ion o pa icles apped a luid in e aces un-
de goes luc ua ions ela i e o he in e acial plane, when he in e a-
cial and he mal ene gies a e compa able, and de o ma ions induced by
in e ace capilla y wa es [84,86]. Howe e , he mo ion o adso bed
pa icles along he di ec ion pe pendicula o he luid in e ace induces
he eme gence o capilla y o ces ha p omo e he ees ablishmen o
he equilib ium posi ion [87].
The en apmen o a colloidal pa icle in he in e acial plane sepa-
a ing wo luid phases equi es ha he in e acial ension o ces can
o e come he ac ion o g a i y [81]. The balance be ween hese wo
con ibu ions is ypically de ined in e ms o he Bond o E¨
o os numbe
Bo =Δ
ρ
g2R
γ(24)
whe e Δ
ρ
deno es he di e ence be ween he densi y o he pa icle and
he luid. I should be no ed ha he g a i a ional con ibu ion only is
ele an o pa icles o se e al mic ome e s. Fo pa icles smalle han
10
μ
m, Bo assumes alues well below uni y, and hence he con ibu ion
o in e acial ension o ces becomes dominan [88,89].
I should be no ed ha he e e sible/i e e sible cha ac e o he
a achmen o pa icles o he luid in e ace, oge he wi h he alue o
he con ac angle ha e an impo an impac on di e en physicochem-
ical aspec s associa ed wi h po en ial applica ions o pa icle-laden in-
e aces. Among hem, he o ganiza ion o he pa icles a he in e ace,
he s eng h and na u e o he in e pa icle in e ac ions, he ic ion
coe icien alues in mic o heology expe imen s, o he esponse o
pa icle-laden luid in e aces o ex e nal mechanical de o ma ions, ha
go e n he abili y o pa icles o s abilize emulsions and oams
[27,64,78,80,86,90–93].
2.4.1. E ec o line ension and pa icle oughness in he we ing o pa icles
o luid in e aces
The con ibu ions o he pa icle oughness and/o he line ension o
he we ing p ope ies o he pa icles limi he applicabili y o Equa ion
(18) o p o ide an app op ia e desc ip ion o pa icle en apmen a
luid in e aces [94]. The line ension is caused by he imbalance
Fig. 5. T apping ene gy o wo colloidal pa icles wi h R =1
μ
m (a) and R =
10 nm (b), a a luid in e ace wi h γ
12
=50 mN/m, as unc ion o he con ac
angle. Please, no e he di e ences on he ene gy scales. Rep in ed om Guzm´
an
e al. [34], Copy igh (2021), wi h pe mission om Ins i u e o Physics.
Fig. 6. Dependence o he de achmen ene gy a 298 K o a pa icle adso bed
a a plana oil/wa e in e ace (γ
12
=50 mN/m) a a ixed con ac angle θ =
90◦. No e he low ene gies o pa icles wi h adii smalle han 0.5 nm (close o
ha o molecula su ac an s). Adap ed om Binks [12], Copy igh (2002), wi h
pe mission om Else ie .
E. Guzm´
an e al.
Ad ances in Colloid and In e ace Science 302 (2022) 102620
7
be ween he in e molecula o ces ha ope a e wi hin he h ee-phase
con ac line [95], and can be posi i e o nega i e, wi h a magni ude in
he ange be ween 1-100 pN [25]. The ela i e impo ance o i s
con ibu ion can be assessed in e ms o a dimensionless numbe de ined
as
Li =
τ
γ12L(25)
whe e
τ
and L a e he line ension and he leng h o he con ac line,
espec i ely [96]. The ole o he line ension in he we ing o pa icles
can be included by modi ying he Young’s equa ion wi h he co ec ion
p oposed by B esme and Qui ke [97], who in oduced a dependence
be ween bo h in e acial and line ensions on he con ac angle o
sphe ical smoo h pa icles as ollows
γP1−γP2
cosθ −γ12 = −
τ
Rsinθ (26)
I ollows om he abo e exp ession ha he line ension in luences
he we abili y o pa icles only o sizes below 20 nm [10,18,98–100].
Following a gumen s analogous o hose de eloped in sec ion 2.4, bu
including he con ibu ion associa ed wi h he line ension, he ene gy
change associa ed wi h he en apmen o a pa icle a he luid in e ace
can be de ined as
ΔEp=γ12cosθ∞2
π
R2(1−cosθ)+2
τπ
Rsinθ −
π
R2γ12cos2θ(27)
whe e θ
∞
is he con ac angle p o ided by he Equa ion (18). When
pa icles a e in condi ions o mechanical and he mal equilib ium, wi h
(
∂
ΔE
P
/
∂
θ)
T
=0, hey a e in he posi ion dic a ed by he con ac angle
cosθ =cosθ∞[1−
τ
Rγ12]−1
(28)
I should be no ed ha he minimiza ion o he line ensionmodi ies
he we abili y o non-sphe ical pa icles and hei o ien a ion a he
in e ace [88,89,96]. Fo θ → 90◦, i.e., in e media e we ing condi ions,
i is possible o neglec he ole o line ension, and Equa ion (28) be-
comes Equa ion (18). In such condi ions, he line ension applies almos
angen ially o he in e ace, and he e o e i s impac on he posi ion o
he pa icles in ela ion o he in e icail plane becomes almos negli-
gible [13,25]. When he con ac angle di e s signi ican ly om 90◦, he
pe pendicula componen o he line ension assumes a ela i ely high
alue, becoming maximum o θ → 0◦and θ → 180◦[101], which leads
o a posi i e con ibu ion o he ene gy change associa ed wi h he
apping o he pa icle.
The assyme y o he shape and oughness o he pa icles inc ease
he a io be ween he con ac line and he cha ac e is ic dimension o
he pa icles [98], also modi ying he we ing p ope ies o colloidal
pa icles by luid in e aces [61,102], especially when he oughness o
he pa icles is high and hei size is small [103]. This modi ica ions
we e s udied heo e ically by Nonomu a and Komu a [103] using he
Cassie–Bax e model, associa ed o he eme gence o pinning–depinning
o he in e ace along he con ac line.
2.4.2. Tuning he con ac angle o pa icles a a luid in e ace
The in e acial o ganiza ion o he pa icles wi hin he in e ace can
be modula ed by al e ing he we abili y o he pa icles (see Fig. 7), and
consequen ly he in e pa icle in e ac ions.
Many physical and chemical ools a e cu en ly a ailable o modi y
he we abili y o colloidal pa icles and une hei in e acial o gani-
za ion. The mos widesp ead s a egy o modi y he abili y o pa icles o
emain apped a he luid in e ace is he addi ion o di e en chemical
addi i es, e.g., su ac an s, polyme s, sal s o e en low molecula weigh
compounds (e.g., alcohols), o he pa icle dispe sion. These molecula
species can deco a e he pa icle su ace h ough non-elec os a ic, e.g.,
hyd ogen bonds, elec os a ic o an de Waals in e ac ions
[51,58,60,61,102,104–108].
Fo ins ance, due o a complex in e play be ween hyd ophobic and
non-co alen elec os a ic in e ac ions, i is possible o modi y he
we abili y o he pa icles in si u by modi ying he amoun o su ac an
added in he dispe sion con aining he colloidal pa icles, o in he
second luid [109]. The g adual addi ion o su ac an s usually esul s in
he appea ance o di e en su ac an s uc u es and he p og essi e
inc ease in pa icle hyd ophobici y. The maximum deg ee o pa icle
hyd ophobiza ion is usually ound o su ac an concen a ions high
enough o ensu e neu aliza ion o he su ace cha ge o he pa icles.
Any u he inc ease o he su ac an concen a ion beyond he iso-
elec ic poin usually leads o ehyd a ion o he pa icles. The dec ease
in con ac angle is usually due o he o ma ion o a su ac an bilaye on
he su ace o he pa icles h ough hyd ophobic in e ac ions be ween
he alkyl ails o he su ac an molecules. This app oach was explo ed
by Maes o e al. [80] and Binks e al. [110], who added wo di e en
ypes o alkyl ime hylammonium b omide su ac an s (hexadecyl-
ime hylammonium b omide, CTAB and dodecyl ime hylammonium
b omide, DTAB) o dispe sions con aining silica nanopa icles o une
he assembly o silica nanopa icles a he wa e /s eam in e ace. Binks
e al. [111] ex ended he possibili y o modi ying he we abili y o silica
pa icles by he addi ion o a wo ails su ac an (didecyldime hy-
lammonium b omide). Ob iously, he impac o he addi ion o su ac-
an s on he we abili y o pa icles is de e mined by he chemical na u e
o he pa icles. Deleu ence e al. [112] s udied he modi ica ion o
hyd ophobic anionic polys y ene and hyd ophilic silica pa icles wi h a
ca ionic su ac an . They ound ha polys y ene pa icles unde wen a
Fig. 7. Ske ch showing he e ec o he we abili y o he pa icles on hei o ganiza ion a a luid in e ace. Rep in ed om Ga bin e al. [93], Copy igh (2012), wi h
pe mission om Else ie .
E. Guzm´
an e al.
Ad ances in Colloid and In e ace Science 302 (2022) 102620
8
s ong change in hei con ac angle. Howe e , he con ac angle o silica
pa icles was no signi ican ly modi ied, al hough he e was a s ong
modi ica ion o he pa icle cha ge. Ano he example o he s ong
impac o he addi i es on he in e acial p ope ies o pa icles can be
ound in he wo k by Pe in e al. [113]. They demons a ed ha he
addi ion o die hylene glycol monobu yl e he o sil e nanopa icles
leads o a s ong modi ica ion o he abili y o pa icles o adso p ion a
bo h luid/ luid and luid/solid in e aces, which can be exploi ed in he
ab ica ion o elec onic de ices by ink-je p in ing [114].
On he o he hand, i is also possible o ob ain a well-con olled
modi ica ion o pa icle we abili y by i e e sible co alen bonding o
speci ic coa ing ligands o he pa icle su ace [115]. Fo ins ance,
silaniza ion o silicon dioxide pa icles, wi h a educ ion in he pe -
cen age o su ace ee silanol g oups om 34% o 20%, leads o an
inc ease in he alue o he pa icle con ac angle a he wa e / apo
in e ace by a ac o o wo. [116] Thus, pa icles wi h he highes hy-
d ophobici y ( hose wi h 20% o ee silanol g oups) p esen a con ac
angle o 113◦, whe eas his dec eases o hyd ophilic pa icles ( hose
wi h 34% o ee silanol g oups) down o 55◦. Simila ly, g a ing poly
(glyce ol-monome hac yla e) chains on o he su ace o polys y ene
la ex pa icles modi ies hei con ac angle a he luid in e ace [117].
The pa icle we abili y con ol de eloped in ecen yea s has s im-
ula ed signi ican esea ch e o s on he a ional design o we abili y-
con olled pa icles, and in pa icula o he design o colloidal pa i-
cles wi h asymme ic we ing p ope ies, e.g., Janus pa icles and pa chy
colloids [29,118,119].
2.4.3. Expe imen al me hods o he e alua ion o he con ac angle o
pa icles apped a luid in e aces
Since he e is no s anda d app oach o de e mine he con ac angle o
pa icles a luid in e aces, ega dless o hei dimensions, shape and
mo phology, i s de e mina ion emains a challenge [120–122]. A p e-
sen , he e a e di e en expe imen al echniques designed o a di ec o
indi ec de e mina ion o he con ac angle o isola ed pa icles adso bed
a he in e ace o he luid (o i s assemblies). These me hods a e usually
classi ied in o h ee di e en g oups: (i) indi ec measu emen s; (ii)
di ec measu emen s o mul iple pa icles (ensemble me hods); and (iii)
di ec measu emen s o indi idual pa icles, in which he posi ion o he
pa icle cen e is esol ed ela i e o he in e acial plane
[23,24,123,124]. Indi ec me hods he mean alue o he con ac angle
o he pa icle apped in a luid in e ace by measu ing a p ope y
associa ed wi h i . In single pa icle me hods, colloids a e di ec ly
isualized by di e en ypes o mic oscopies (op ical, elec on, a omic
o ce...), so he minimum pa icle size ha can be obse ed depends on
he speci ic echnique. These me hods a e usually ee o assump ions
and allow he de ec ion o any in e ace he e ogenei y. Howe e , hey
equi e imaging o a la ge numbe o pa icles o ensu e good s a is ics
o con ac angle de e mina ion. On he o he hand, ensemble ap-
p oaches allow de e mining a e y accu a e mean con ac angle, wi h
e y good s a is ics, by measu ing he mac oscopic p ope ies o he
sys em, e en in smalle objec s. Howe e , he use o his ype o me hods
does no gi e di ec ly in o ma ion abou he possible he e ogenei y o
he pa icle con ac angle, i.e., he possible a ia ion o he con ac angle
be ween indi idual adso bed pa icles esul ing om sub le changes on
hei chemis y, size o mo phology (shape and oughness).
2.4.3.1. Indi ec me hods. The analysis o he p o ile o a sessile d ople
deposi ed on he su ace o a la subs a e, ha has he same chemical
na u e as he pa icles apped a he luid in e ace, is an indi ec
me hod commonly used o es ima e he con ac angle [125]. Howe e ,
he assump ion ha his angle coincides wi h he pa icle con ac angle
ails in mos cases because i does no conside he ole o cu a u e,
oughness and line ension.
The pa icle con ac angle a he luid in e ace can also be de e -
mined h ough he analysis o in e acial p essu e-a ea iso he ms (Π-A)
o pa icle-laden luid in e aces. Two di e en me hods ha e been
desc ibed o such pu pose: (i) he analysis o he a ea exclusion induced
by he pa icles in a second componen , usually a su ac an , and (ii) he
e alua ion o he iso he m collapse p essu e. The i s me hod is based
on he analysis o he a ea displacemen exhibi ed by he Π-A iso he ms
o an insoluble su ac an when colloidal pa icles a e adso bed simul-
aneously. In his case, he con ac angle is es ima ed by assuming bo h
ha he we abili y o he pa icles does no change wi h he p esence o
he su ac an , and ha such displacemen occu s because he pa icles
occupy pa o he in e acial a ea. The la e assump ion implies he
absence o in e ac ions be ween pa icles and su ac an molecules.
O he wise, he a ea shi could mask he expansion o con ac ion o
a ailable a ea associa ed wi h he in e ac ions [126,127]. The second
me hod, exploi ed o a long ime, calcula es he con ac angle by su -
ace p essu e measu emen s and geome ical conside a ions, assuming
ha once he sys em eaches he collapse p essu e, Π
c
, iden i ied by a
kink o la egion in he Π–A iso he m, he pa icles adop a close
packing con igu a ion o ganized in ideal coplana i y [52,128–131]. On
he o he hand, i comp ession p o ides enough ene gy o o ce
deso p ion o he pa icles he collapse p essu e and deso p ion ene gy
can be co ela ed as ollows [128]
ΔEp=Πc
Γc
(29)
whe e Γ
c
is he su ace concen a ion a he collapse poin .
The pendan d op ensiome e is also a echnique o en used o
measu e he binding ene gy o pa icles apped a a luid in e ace. This
echnique moni o s he ime e olu ion o he in e acial ension o a
d ople o he pa icle suspension du ing he spon aneous adso p ion o
he pa icles a he luid in e ace [66]. Thus, neglec ing he exis ence o
in e pa icle in e ac ions a he in e ace, and assuming ha he
maximum packing o he pa icles a he in e ace co esponds o a
pe ec 2D hexagonal a ay, he sa u a ion o he in e acial ension is
ela ed o he adso p ion ee ene gy as
ΔF= − (γ12 −γ)
π
R2/
η
(30)
wi h
η
=0.91 o a close-packed in e ace.
A e y popula al e na i e app oach o indi ec con ac angle
de e mina ion is based on he measu emen o he upwa d eloci y o a
luid, pushed by capilla y p essu e, which is con ained in a capilla y
column illed by a packed bed o pa icles [132,133]. This me hod,
exploi ed o de e mine he con ac angle o pa icles wi h a wide ange
o sizes, shapes and chemical na u e, assumes ha pa icles o m a
bundle o capilla y ubes, o ci cula c oss-sec ion and adius R
eq
. In his
me hod, he con ac angle is assessed using he Washbu n equa ion
[134]
h2
L=γ12Reqcosθ
2
η
(31)
whe e h
L
, and
η
a e he heigh o he liquid column, he ime and he
iscosi y o he ising liquid, espec i ely. Acco ding o Equa ion (31) h
L
is de ined as a unc ion o he expe imen al ime. Howe e , his me hod
is limi ed o he de e mina ion o he con ac angle o a he mono-
dispe se pa icles, which o m bundles whe e he po osi y o he bed o
pa icles is well de ined. Fu he mo e, he Washbu n me hod only p o-
ides in o ma ion o he ad ancing con ac angle, which can be a om
he ue equilib ium si ua ion due o he we ing dynamics.
As al e na i e o he Washbu n me hod, Diggins e al. [135] in o-
duced ano he app oach based on he de e mina ion o he equilib ium
capilla y p essu e o a packed bed o pa icles, ΔP, which can be de ined
as he p essu e equi ed o hinde ing he luid mo ion h ough he
packed pa icles. The la e is ela ed o he con ac angle h ough he
Laplace-Whi e equa ion [136]
E. Guzm´
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Ad ances in Colloid and In e ace Science 302 (2022) 102620
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ΔP=γ12Aϕcosθ
1−ϕ(32)
The main ad an age o his app oach is ha only depends on
expe imen ally accesible pa ame e s, such as he speci ic su ace a ea A,
he olume ac ion o powde ϕ and he luid/ luid in e acial ension
γ
12
.
The use o a o ce ensiome e can also help on he e alua ion o he
we abili y o powde s. This e alua ion is possible by loading a packed
bed o pa icles, hunged om a p ecision balance and hen dipped in o
he liquid. Thus, i is possible o de e mine he con ac angle om he
change de ec ed in he mass when he liquid p og essi ely pene a es
h ough he bed, as ollows
cosθ( ) = m2
η
C
ρ
2γ12 (33)
whe e C is a cons an cha ac e is ic o he ma e ial and m he a ia ion o
he mass a a gi en embedding ime [137]. I is should be s essed ha
he di e en app oaches in oduced o eplacing he con en ional
Washbu n me hod can be only used o ob aining he ad ancing con ac
angle.
Ano he app oach used o de e mine he con ac angle is based on
he use o a hea - low calo ime e o measu e he ene gy change-
associa ed wi h he mixing o solid pa icles and a liquid [138]. In his
me hod, he con ac angle is ela ed o he en halpy o imme sion,
h ough he modynamic conside a ion, as ollows
cosθ =−KT −hi
γ12
(34)
whe e K is gi en by he empe a u e change associa ed wi h he im-
me sion o he pa icles in he luid phase, and h
i
is he change o
en halpy associa ed wi h such imme sion. This app oach equi es he
use o wo calo ime ic cells: he i s one illed wi h d ied powde , and
he second emp y one used as e e ence. The expe imen al e alua ion o
he con ac angle elies o he equilib a ion o bo h chambe s wi h
liquid, and he de e mina ion o he di e ences on he changes o
he mal ene gy du ing he we ing p ocess. This me hod is commonly
used o pa icle apped a liquid/ apo in e aces, wi h he con ac
angle o pa icles a liquid/liquid in e aces being ob ained by combi-
na ion o he da a ob ained o he indi idual liquid/ apo in e aces.
Howe e , he equi ed assump ions o link imme sion en halpy and
con ac angle ha e limi ed he applicabili y o his app oach.
A las indi ec al e na i e used o de e mine he con ac angle elies
on he use o he A omic Fo ce Mic oscope (AFM). In his me hod, he
con ac angle is es ima ed by measu ing he o ce-dis ance cu e due o
he in e ac ion be ween a colloidal p obe and a liquid bubble [139]. This
is possible because du ing a achmen and de achmen o he colloidal
pa icle om he in e ace, i is possible o ob ain in o ma ion o
di e en pa ame e s, including he jump-in and de achmen posi ion,
he de achmen o ce and he wo k adhesion, which allows es ima ing
bo h he ad ancing and eceding con ac angles o pa icles bigge han
2–3
μ
m. The use o AFM o de e mining he con ac angle is a ex emely
sensi i e me hodology which is a ec ed by speci ic de ails o he pa icle
su ace, e.g. su ace opog aphy and chemis y, which can esul in
displacemen s o he con ac line o local pinning. Fu he mo e, he
complexi y o he me hodology makes i di icul o ob ain a de ailed
s a is ical analysis om AFM measu emen s, e en hough his echnique
p o ides impo an in o ma ion ela ed o he mechanics o he we ing
o pa icles.
2.4.3.2. Di ec me hods o pa icle ensembles
2.4.3.2.1. Immobiliza ion me hodologies. A e y popula app oach
o de e mining he con ac angle o pa icles apped a luid in e aces
elies on he immobiliza ion o pa icles a he in e ace, commonly by
eezing [122] o gelling [140], ollowed by an analysis o he
immobilized su aces by using a high- esolu ion mic oscopy (elec on
mic oscopy o AFM). Cu en ly, he e is a b oad ange o immobiliza ion
s a egies ha allow ob aining in o ma ion on he con ac angle o
pa icles a luid in e aces, wi h hei main ad an ages a ising om he
possibili y o e alua e many pa icles om a single measu emen .
Ne e heless, hei applica ion appea s limi ed by he signi ican in e -
ace manipula ion, which may modi y he loca ions o he pa icles,
induce pa icle de o ma ions o change he composi ion o he sys em.
The i s and p obably mos popula me hodology based on pa icle
immobiliza ion is he so-called gel apping echnique (GTT). I was
o iginally designed o he e alua ion o he con ac angle o mic o-
pa icles a a luid/ luid in e ace by hei ans e ence o a solid ma ix,
allowing hei di ec isualiza ion by using Scanning Elec on Mic o-
scopy (SEM) [140]. I was quickly ex ended o he de e mina ion o he
con ac angles o nanopa icles apped a luid in e aces by using AFM
o imaging [99,120]. In he GTT, a pa icle ilm is p epa ed a he
in e ace be ween a luid and an aqueous solu ion o a gellan, main-
ained a a empe a u e abo e i s gelling empe a u e. The empe a u e
is hen educed o o ce he gela ion and he pa icles a e apped in hei
ixed posi ion a he in e ace. This allows he monolaye o be ans-
e ed o a poly(dime hylsiloxane) (PDMS) eplica, whe e he ela i e
posi ion o he adso bed pa icles can be di ec ly de e mined by mi-
c oscopy. F om he images i is possible o es ima e he con ac angle by
a simple geome ical analysis. Thus, i is possible o de e mine he
con ac angle o pa icles wi h sizes in he ange 100 nm-100
μ
m,
apped a bo h liquid/ apo and liquid/liquid in e aces
[102,120,140]. Despi e i s appa en simplici y and accu acy (con ac
angle can be de e mined wi h a a iabili y o 3-5◦), he use o GTT ap-
pea s limi ed due o he di e en aspec s. Fi s , he gellan is a non-
su ac an ac i e molecule wi h a cha ac e is ic leng h o 10 nm. This
can lead o apping he e ogenei ies which makes di icul y o p o ide a
de ini ion o he con ac line when pa icles wi h a diame e below 100
nm a e conside ed. Fu he mo e, he aplica ion o high empe a u es
limi s he applicabili y o GTT o non- ola ile luids, and can induce
de o ma ion on he pa icles [141].
Vogel e al. [142] in oduced an al e na i e o con en ional GTT
based on he addi ion o bu ylcyanoac yla e o he in e ace h ough he
apou phase. The o ma ion o a poly(bu ylcyanoac yla e) ma ix, ia
an anionic polyme iza ion p ocess ha s a s upon he con ac o he
p ecu so bu ylcyanoac yla e wi h he aqueous phases p omo es he
apping o he colloids a he wa e / apou in e ace. This app oach
also c ea es a solid eplica o he in e ace ha can be used o he
e alua ion o he equilib ium posi ions o he colloids, using high es-
olu ion mic oscopy.
A mo e sophis ica ed immobiliza ion me hodology combines eeze-
ac u e (F eSCa) and shadow-cas ing c yo-Scanning Elec on Mic o-
scopy (SEM) [122]. This me hod elies on he immobiliza ion o he
pa icles a he luid in e ace by a as i i ica ion, helped by he ac ion
o p opane je eeze , ha aps he pa icles a he luid in e ace
wi hou any signi ican he mal con ac ion. The ob ained sample a e
la e ac u ed and uni-di ec ionally coa ed wi h a me al laye a a well-
de ined il angle
α
, and hen he con ac angle o he pa icles is
de e mined om he images ob ained using c yo-SEM, using simple
geome ical assump ions [111,122,143]. This is possible because he
p esence o a pa icle-laden laye a a la in e ace appea s as a weak
ac u e plane, and allows he exposu e o he immobilized pa icles.
Thus, he oblique me al deposi ion cas s he shadow o he pa icle
p o uding om he in e ace. The measu emen o he leng h o he
shadow and he p ojec ed heigh make i possible he calcula ion o he
p o uding heigh h, and consequen ly he con ac angle, knowing he
alue o he shadowing angle
α
and he geome y o he pa icles [144].
The use o he F eSCa coupled wi h c yo-SEM imaging allows e alua ing
ela i ely la ge egions o pa icle-laden in e aces, which allows an
accu a e e alua ion o he exis ence o we ing he e ogenei ies a he
in e ace. Fu he mo e, his me hod o e s a high accu acy and lexi-
bili y o he de e mina ion o con ac angles o pa icles a wa e /oil
E. Guzm´
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Ad ances in Colloid and In e ace Science 302 (2022) 102620
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in e acial plane, is mainly de ined by he we ing p ope ies o he
pa icles [206]. Howe e , hei adso p ion can lead o local de-
o ma ions o he luid in e ace a ound he pa icles, hus leading o
long- ange capilla y imme sion o ces. Roughness and/o chemical
he e ogenei ies on he su ace o he adso bed pa icles su ace p omo e
he o ma ion o a non-smoo h, wa y o i egula ly shaped, h ee phase
con ac lines, de o med enough o p omo e s ong capilla y in e ac ions
[10,40,207].
The capilla y in e ac ion be ween wo iden ical neighbo ing sphe -
ical colloids can be exp essed h ough an e ec i e po en ial [207]
Ecapilla y(R) = − 12
π
γ12Κ2ζ 4
R4(56)
whe e ζ is a ac o ha de ines he dependence o he capilla y in e -
ac ion on he pa icle o ien a ion and K a unc ion accoun ing o he
de o ma ion ampli ude o he in e ace.
The de o ma ion o he in e ace, and hus he s eng h and dominan
mode o capilla y o ces, can be modi ied by he applica ion o elec ic o
magne ic ields [208], o he addi ion o di e en addi i es (sal s, su -
ac an s, o polyme s), ha allow ine- uning o pa icle we abili y and
in e acial ensions. The adso p ion o cha ged colloids a a luid in e -
ace be ween non-pola and pola luids p omo es ex a in e acial de-
o ma ions. These de o ma ions a e p oduced by he e ical in e acial
elec ic o ce di ec ed owa ds he luid wi h highe dielec ic cons an ,
esul ing om he combina ion o any ex e nal e ical o ce ac ing on
he colloid and an inhomogeneous s ess ield. The la e p esen s
di e en componen s o he abo e and below he luid in e ace, which
a e induced by he elec ic dipola ield o he pa icles, and can be
desc ibed in e ms o he Maxwell p essu e enso [10]. These condi ions
lead o he elec odipping and elec ocapilla y o ces ha in ol e mul-
iple o single pa icles, espec i ely [18,205]. I should be no ed ha
elec ocapilla y and elec odipping o ces can induce in e acial de-
o ma ions ha a e o en compa able o hose esul ing om he ac ion
o g a i y on in e aces laden wi h la ge pa icles [78].
When he capilla y in e ac ions engage a la ge numbe o pa icles,
hey can induce sel -assembly h ough he so-called “Chee ios” e ec ,
simila o ha wha is obse ed in ce eal bowls [88]. The e o e, he
con ol o capilla y in e ac ions, by adjus ing he shape o we ing
p ope ies o he pa icles, can be used in he ab ica ion o complex
in e acial s uc u es [188]. I he appa en weigh o he adso bed
species becomes la ge han he in e acial o ces, which is o en he case
o monolaye s wi h a high in e acial co e age, he collec i e e ec s
may modi y he simple pai wise in e ac ions, de e mining he de o -
ma ion o he su ounding in e ace. This a ec s he o ganiza ion o
pa icles a he in e ace such ha he en i e agg ega e sinks o he
hea ie phase (“collec i e sinking mechanism”) [192,209].
4.2.2. Hyd odynamic in e ac ions
Capilla y o ces a e no he only con ibu ion o he ene ge ic land-
scape eme ging in pa icle-laden luid in e aces appea ing as esul o
he p esence o he in e ace, wi h he hyd odynamic in e ac ions,
s imula ed by he mo ion o he pa icles h ough he iscous media,
being s ongly dis o ed by he pa icle adso p ion. The adso bed pa -
icles mo e in an o e damped egime, in which he applied o ces and
o ques a e cons an ly balanced by hei iscous coun e pa s. The low
gene a ed by he andom o di ec ed mo ion o he adso bed pa icles,
which can be modi ied by he possible p esence o o he pa icles o
objec s and su aces, anspo s ene gy h ough he wo media and can
be desc ibed by he linea ised S okes equa ions. The e o e, apa om
o he possible di ec in e ac ions, he pa icles always exhibi sol en -
media ed o ces which, unlike he in e ac ions desc ibed abo e,
canno be desc ibed by a po en ial. Complex and indi ec hyd odynamic
in e ac ions ha e a enso cha ac e , as hey a e s ongly de e mined by
he shape, o ien a ion and ela i e eloci y o he agen s in ol ed.
These in e ace-media ed hyd odynamic in e ac ions con ol he
s ee ing o swimme s along de ined ajec o ies [210], hei a ac ion
owa ds he in e ace [211], he ci cula pa h ound in he mo ion o
Esche ichia coli [212], can be exploi ed on he anspo o ca gos along
luid in e aces [9], o he ec i ica ion o o a ion in o ansla ional
mo ion [213], whe e he local low induced by he slip bounda y con-
di ion imposed by he liquid-ai in e ace di e ed om he one gene -
a ed by he s ick bounda y condi ion cha ac e is ic o a solid wall. On
he o he hand, he balance be ween a ac i e in e ac ions and hyd o-
dynamic epulsi e in e ac ions eme ging be ween o a ing disks,
loa ing a a liquid/ai in e ace, leads o he assembly o dynamic la -
ices [214]. The ela i e impo ance o he hyd odynamic in e ac ions is
gi en by he capilla y numbe
Ca =
η
p
γ12
(57)
whe e
p
is he pa icle eloci y. I is commonly accep ed ha o Ca <1,
he ole o he hyd odynamics in e ac ions may be neglec ed [40,208].
4.3. Ex e nally ac ua ed in e ac ions
The adso p ion o pa icles a a luid in e ace is associa ed wi h a
es ic ion o hei mobili y wi h espec o he in e acial plane. How-
e e , in-plane mobili y is no limi ed, and in p inciple pa icles a e ee
o mo e wi hin he in e acial plane [215]. This mo ion can be boos ed
by he mechanical de o ma ion o he in e ace, which can induce
changes on he in e acial a ea (dila a ional de o ma ions) o shape
(shea de o ma ions). So, hese pe u ba ions can be exploi ed in he
con ol o he in e acial assembly o he modula ion o 2D phase an-
si ions, which allows o adjus almos a will di e en mechanical, op-
ical o elec onic p ope ies [104,216,217]. The applica ion o
magne ic o elec ic ields leads o simila e ec s when conside ing as-
semblies o esponsi e pa icles and is also a e y powe ul ool o
uning he assembly o colloids a luid in e aces [7,208,218]. When
adso bed pa icles espond app eciably o he applica ion o a magne ic
ield, while dispe si e luids do no show a s ong esponse, he p esence
o he in e ace has essen ially no e ec on he na u e o he magne ic
in e ac ion be ween he pa icles. Howe e , he mobili y cons ain s
imposed by he high adso p ion ene gy o ce he pa icles o es ic
hei mo ion o he adso p ion plane. Consequen ly, he angle o appli-
ca ion o he ex e nal ield becomes a undamen al pa ame e de e -
mining he esponse o he pa icle monolaye . Al e na i ely, he
applied ield can be used only o o ce he o a ion o he pa icles along
he axes pa allel o he con ining su ace, which is s ongly hampe ed by
he occu ence o in e acial pai s. The induced o a ion can be used o
change he ex en and na u e o capilla y in e ac ions a will [10,97].
An al e na i e way o modula e he in e ac ions be ween pa icles,
and hus he o ganiza ion o pa icle assemblies a luid in e aces, is by
modi ying he en i onmen al condi ions (pH, empe a u e o ionic
s eng h). Fo example, changing en i onmen al condi ions has p o en
o be a e y powe ul ool o con olling he assembly o mic ogel
pa icles a luid in e aces [35,75,182].
5. Chemically iso opic pa icles a luid in e aces
As de eloped p e iously, he su ace chemis y o pa icles in-
luences he sel -assembly o pa icles a he luid in e aces [75]. This
esul s om he speci ic we ing p ope ies o he pa icles [117], he
shape o he con ac line and/o he in e -pa icle in e ac ions ope a ing
be ween he adso bed pa icles [219]. In pa icula , chemical he e o-
genei ies on he pa icle su ace can lead o an undula ed con ac line.
Fu he mo e, he p esence o su ace cha ges on he pa icles may
modi y he elec os a ic and capilla y con ibu ions o he in e -pa icle
in e ac ions [219], and consequen ly he sel -assembly o pa icles a he
luid in e aces. The e o e, he impo ance o he su ace chemis y on
he con ol o he p ope ies o pa icle-laden luid in e aces makes
E. Guzm´
an e al.
Ad ances in Colloid and In e ace Science 302 (2022) 102620
17
necessa y o dis inguish be ween a leas h ee di e en si ua ions: (i)
chemically iso opic pa icles; (ii) pa icles capped wi h ligands, and (iii)
chemically aniso opic pa icles. This sec ion ocuses on he in e acial
beha io o chemically iso opic pa icles.
5.1. Ha d pa icles a luid in e aces
Colloidal ha d pa icles a e a ca ego y including a b oad ange o
pa icles wi h di e en chemical na u e (polyme ic, me allic, me al
oxide compounds o ce amic), which p esen as main cha ac e is ic ha
hei maximum de o ma ion upon apping a he in e ace emains on a
leng h scale much smalle han hei diame e , and hence hey beha e a
he in e ace as solid-impene able objec s o neighbo ing pa icles.
This p ope y de e mines he maximum packing ha hese pa icles can
achie e a he luid in e ace.
5.1.1. Sphe ical pa icles
The equilib ium apping o chemically iso opic sphe ical pa icles
a luid in e aces is cha ac e ized by he exis ence o a single ene gy
minimum, de e mined by he in e acial ension, pa icle size and con-
ac angle, which also ule on he o ganiza ion and p ope ies o he
adso bed assemblies.
5.1.1.1. In e acial o ganiza ion. The unde s anding o he o ganiza ion
and sel -assembly o colloidal pa icles a luid in e aces equi es o
conside bo h he dis ibu ion o he pa icles wi hin he quasi-2D luid
in e ace, and he posi ion o he pa icles wi h espec o he in e acial
plane, i.e., con ac angle o he pa icles o imme sion heigh . Bo h as-
pec s a e s ongly co ela ed o he complex in e ac ions ha occu
be ween pa icles bo h h ough he bulk and he luid in e ace [220].
Fo ins ance, Zang e al. [221] epo ed ha he change in he we a-
bili y o he adso bed nanopa icles allows uning he packing o he
s uc u es o med a he luid in e ace, and consequen ly he in e acial
mo phology, in ag eemen wi h s udies by di e en au ho s [64,80]. In a
di e en wo k, he inc ease o he hyd ophobici y o pa icles was
desc ibed as he d i ing o ce o o a ansi ion om loose-packed o
close-packed a ays o pa icles [61], which appea s s ongly co ela ed
o he complex in e play o in e ac ions occu ing be ween pa icles
bo h in he bulk and upon apping a he luid in e ace [220].
Bonales e al. [222] s udied he sel -assembly o polys y ene sul a e
la ex pa icles, wi h a b oad ange o diame e s (in he ange 1.0-5.7
μ
m)
a wa e /oil in e aces (in pa icula a wa e /oc ane in e aces). They
ound ha he inc ease o he in e acial co e age d o e he eme gence
o ansi ions be ween phases wi h di e en deg ee o o de ing as was
also ound o nanopa icles [221]. I should be no ed ha he ansi-
ions be ween he di e en phases we e no ind independen o he
pa icle dimensions, and only a shi o he c i ical densi y o he onse
on a speci ic phase was obse ed wi h he change o he pa icle size.
These inding we e in acco dance wi h he esul s ob ained by Pa olini e
al [223] in a simila wo k. Fig. 10 epo s a se o op ical mic oscopy
images co esponding o polys y ene sul a e la ex pa icles
mic opa icles o di e en sizes apped a he wa e /oc ane in e ace, a
di e en su ace densi ies, oge he wi h he co esponding Fas Fou ie
T ans o m (FFT) o he images.
The images ob ained using an op ical mic oscope shows ha he
inc ease o he densi y o he pa icles apped a he luid in e ace
enhances he o de wi hin he monolaye , in such a way ha should be
conside ed as eminiscen o ha wha happens in adi ional 3D sys-
ems. The inc ease o he in e acial o de is also e lec ed in he FFT
images (see inse s in he op ical mic oscope images). The luid phases,
bo h gas-like and liquid-like ilms, a e cha ac e ized by a andom dis-
ibu ion o poin s in he FFT images. The hexa ic phase, and mo e
clea ly he solid one, shows he o ma ion o well-de ined hexagonal
a ays o do s in he FFT images as he monolaye densi y inc eases. The
au ho s ob ained u he in o ma ion ela ed o he o ganiza ion o he
pa icles a he luid in e ace by calcula ing he s uc u e ac o . Thus,
a low in e acial co e age, he gas-like cha ac e o he monolaye was
e idenced om an ini ial inc ease o he alue o he s uc u al ac o
om 0 o 1, ollowed o a egion o cons an alue. The inc ease o he
in e acial co e age pushes he monolaye s o he onse on he liquid-
like phase. This p esen s a s uc u e ac o cha ac e ized o he p es-
ence o a ew oscilla ions which unde go an exponen ial damping wi h
he inc ease o he sepa a ion be ween pa icles. This may be conside ed
he esul o he weakening o he posi ional o de wi h he inc ease o
he sepa a ion be ween pa icles. The e o e, he gas-like and liquid-like
monolaye s a e cha ac e ized by he absence o o ien a ional and posi-
ional o de . The o de in hexagonal 2D solid is e idenced by he p es-
ence o a na ow and in ense peaks ollowed by ano he se o peaks,
which appea s a he posi ion expec ed o a hexagonal a ay. The
hexagonal 2D a ays p esen posi ional and o ien a ional o de s. On he
o he side, he hexa ic phase p esen s only o ien a ional o de , appea -
ing as an in e media e s a e be ween a liquid-like sys em and a pe ec ly
o de solid-like one as is p edic ed o he KTHNY heo y [224]. Bonales
e al. [225] also explo ed he in e acial o ganiza ion o mix u es
monolaye s composed o pa icles ha ing di e en sizes. They ound
ha independen ly o he size di e ence be ween he pa icles he in-
clusion o pa icles o di e en size p omo es diso de , and he s oichi-
ome y in he mix u e de e mines he eme gence o a es ed glassy s a es
o polyc ys alline egions, leading o an in e acial o ganiza ion which
appea s as in e media e be ween hose wha co espond o each indi-
idual se o pa icles.
Rahman e al. [226] analyzed he possible co ela ions exis ing be-
ween he in e -pa icle in e ac ions and he di e en phases eme ging
in pa icle-laden in e aces as he co e age inc eases. They ound ha
he o de a he in e ace is dependen on he s eng h o he in-
e ac ions. Weakly epulsi e o s ongly a ac i e in e ac ions p omo e
he o ma ion o diso de ed phases, whe eas he eme gence o a s ong
epulsion be ween he pa icles a he in e ace is associa ed wi h he
o ma ion o a highly o de ed hexagonal a ay. The o ma ion o he
hexa ic phase occu s when he epulsi e and a ac i e o ces a e
coun e -balanced.
The impo an ole o he in e ac ions in he o ganiza ion o pa icles
Fig. 10. Images and FFT images o cha ged polys y ene sul a e la ex mic opa icles apped a he wa e /oc ane in e ace. F om le o igh : mic opa icles wi h
diame e o 2.9
μ
m; mic opa icles wi h diame e o 5.7
μ
m; mic opa icles wi h diame e o 1.6
μ
m, and mic opa icles wi h diame e o 1.0
μ
m. Adap ed om
Bonales e al. [222], Copy igh (2011), wi h pe mission om Ame ican Chemical Socie y.
E. Guzm´
an e al.
Ad ances in Colloid and In e ace Science 302 (2022) 102620
18
a luid in e aces was also e ealed by he esul s ob ained by Reynae
e al. [227]. They ound ha he modula ion o he elec os a ic and
capilla y in e ac ions, by adding elec oly e o su ac an , may induce
he agg ega ion o pe cola ion o pe ec ly o de ed monolaye s o med
by polys y ene sul ona e la ex mic opa icles adso bed a he wa e /
decane in e ace. Thus, unde condi ions cha ac e ized by s ong
capilla y and/o hyd odynamics in e ac ions, pe cola ion can occu ,
esul ing in he o ma ion o ne wo ks o med by pa icles o min chains
ha span he bounda ies o he in e ace [130]. The eme gence o
pe cola ion in pa icle-laden in e aces o e s a e y in e es ing ool o
modula ing he mechanical esis ance o he ilm [228].
5.1.1.2. In e acial heology. The adso p ion o pa icles o luid in-
e aces is widely used in he design and op imiza ion o new ma e ials
and echnological p ocesses [65,70,183,229], e.g., phase ans e
ca alysis, encapsula ion, enhanced oil eco e y o emulsi ica ion and
oaming [230]. In pa icula , hese sys ems can be in oduced o con ol
he hicknesses o ilms in coa ing lows [231,232], he dispe sion o
su ace wa es [30,233], he dynamics and hicknesses o sp eading ilms
[113,234] and he li e ime o oams and emulsions [235–237]. The
la e occu s because he adso bed pa icles induce an addi ional ene -
ge ic ba ie o he coalescence o d ople s and bubbles, due o elec-
os a ic o s e ic epulsions, which slow o s op he hinning o liquid
ilms. [238]. These p ocesses a e also go e ned by he dynamics o he
sys em, since he pa icles ad ec ed by ilm hinning in oduce g adien s
(Ma angoni s esses) ha oppose ilm d ainage [239]. On he o he
hand, pa icles apped a luid in e aces can induce excess su ace
iscosi y, elas ici y o iscoelas ici y ha delays o modi ies he ilm
hinning [235]. The e o e, he unde s anding o he mechanisms
in ol ed in he elaxa ion o pa icle-laden in e aces a e a mechanical
de o ma ion is a p oblem wi h a ma ked mul idisciplina y cha ac e
[240–242]. In his amewo k, in e acial heology explo es he de o -
ma ion and low ha occu a in e aces when mechanical pe u ba ions
a e applied o hem.
The in e acial esponse o pa icle-laden luid in e aces is cha ac-
e ized by he su ace p essu e, which is opposed o he su ace ension
and con ibu es o he in-plane de o ma ions o he in e acial plane,
dila ions ha cause changes in he ma e ial a ea, and shea s esses ha
induce changes in shape, gene a ed by he coupling be ween he lows
occu ing a he in e ace and hose o he bulk. On he o he hand,
unde speci ic s ess condi ions, complex luid in e aces exhibi ou -o -
plane de o ma ions ha push he monolaye s o pa s o he monolaye s
ou o he in e acial plane (splaying o bending), inducing phenomena
such as buckling o he monolaye , expulsion o ma e ial in o he bulk o
he o ma ion o mul ilaye s. Fig. 11 displays an idealized image o he
di e en ypes o de o ma ion ha a pa icle-laden in e ace can un-
de go as esul o he applica ion o a mechanical s ess.
The s udy o he heological esponse o a pa icle-loaded in e ace
equi es conside a ion o he ole o he modynamic and hyd odynamic
in e ac ions be ween he pa icles and he su ounding luids. The so-
lu ion o his complex p oblem is only s aigh o wa d when he me-
chanical esponse o he bulk luids is decoupled om ha o he
in e ace, i.e., when he mechanical esponse o he luid phases is
negligible wi h espec o ha co esponding o he in e acial laye
[235,243]. I he abo e condi ion is ul illed, he de o ma ion o a
pa icle-loaded luid in e ace can be conside ed he esul o wo con-
cu en p ocesses ha go e n he mechanical p ope ies o he in e ace:
(i) he change o he size and/o shape o he luid in e aces, and (ii) he
de o ma ion o he in e acial laye . Hence, he ene gy inpu equi ed o
he in e acial de o ma ion can be exp essed as
σ
ij =γδij +Τij (57)
whe e δ
ij
is he K onecke del a and
σ
ij
he in e acial s ess enso , ha is
comp ised by wo con ibu ions: (i) he in e acial ene gy, which is
ela ed o he ene ge ic cos o he exis ence o a luid in e ace wi h a
ixed a ea. This con ibu ion also includes any adso p ion/deso p ion
phenomena, ha modi y he in e acial ension, and (ii) he Ma angoni
s esses esul ing om he exis ence o spa ial su ace ension g adien s.
The second con ibu ion, he so-called aniso opic enso (Τ
ij
), includes
he ene ge ic cos associa ed wi h he de o ma ion o he pa icle laye
[2,244].
5.1.1.2.1. In e acial dila ional heology. The apping o pa icles a
luid in e aces does no in luence only o he in e acial ension, bu also
leads o an inc ease o he esis ance o comp ession ha is cha ac e ized
by he in e acial dila ional iscoelas ic modulus
ε
[27]. This magni ude
p o ides in o ma ion on changes in su ace ension as a esul o he
modi ica ion o he a ea a ailable o he dis ibu ion o he pa icles,
which can be de e mined om he empo al e olu ion o he su ace
p essu e δΠ( ) as esul o he change o he in e acial a ea δA( ) upon
he applica ion o an uniaxial s ess [245]
δΠ( ) = Π( )− Π0=
∂
Π
∂
AδA = −
ε
( )u( )(58)
He e, u( ) and
ε
( ) a e he empo al e olu ion o he comp essional
s ain and dila ional iscoelas ic modulus, espec i ely, and Π( ) and
Π
0
he empo al e olu ion o he su ace p essu e and he ini ial su ace
p essu e, espec i ely. The ime dependence o he iscoelas ic dila-
ional modulus is gi en by
ε
( ) = − A0(
∂
Π
∂
A)T
(59)
and ha o he comp ession s ain by
u( ) = δA
A0(60)
Fig. 11. Idealized ep esen a ion o he di e en ypes o
de o ma ion ha can appea a pa icle-laden in e aces as
esul o he applica ion o a mechanical s ess. (a) Equilib ium
pa icle-laden in e ace cha ac e ized by i s alues o su ace
ension γ and su ace p essu e Π. (b) Pa icle-laden in e ace
subjec ed o dila ional (le panel) and shea ( igh panel)
de o ma ions, cha ac e ized by su ace dila ional elas ici y
ε
’
and iscosi y κ, and shea elas ici y G’ and iscosi y
η
S
,
espec i ely. (c) Pa icle-laden in e aces subjec ed o ou -o -
plane de o ma ions ( om op o bo om): buckling (cha ac-
e ized by he bending elas ici y κ
b
), expulsion o ma e ial o
he bulk, and mul ilaye o ma ion. Adap ed om Ga bin [26],
Copy igh (2019), wi h pe mission om Else ie .
E. Guzm´
an e al.
Ad ances in Colloid and In e ace Science 302 (2022) 102620
19
Conside ing a luid laye unde equilib ium condi ion, he limi alue
o he dynamic modulus a ze o equency can be de ined as he s a ic
modulus in e ms o he Gibbs elas ici y
ε
0
as
ε
( )→
ε
0=Γ(
∂
Π
∂
Γ)eq
(61)
whe e Γ=1/A is he in e acial concen a ion. Fo an oscilla o y de o -
ma ion o small-ampli ude and cha ac e is ic equency
ω
, he complex
dila ional iscoelas ic modulus is de ined as
ε
(
ω
) =
ε
´
(
ω
)+i
ω
κ(
ω
)(62)
whe e he eal pa
ε
’(
ω
) is he s o age modulus o in e acial dila ional
elas ici y and he imagina y pa
ε
”(
ω
) =
ω
κ(
ω
) he loss modulus. He e, κ
ep esen s he su ace dila ional iscosi y. The abo e de ini ion o he
iscoelas ic in e acial dila ional modulus conside s ha he s ess
associa ed wi h he in e acial de o ma ion can change bo h he
adso p ion s a e o he pa icles and he in e acial s uc u e. Unde
hese condi ions, he modi ica ion o he in e acial a ea can p omo e
o he di e en elaxa ion p ocesses, wi h di e en cha ac e is ic ime-
scales [36,229,246,247].
One o he i s a emp s o shed ligh on he esponse o pa icle-
laden luid in e aces o dila ional de o ma ions was made by Mille
e al. [247]. They p o ided a heo e ical desc ip ion o he elaxa ion
mechanisms eme ging in pa icle-laden in e aces upon he applica ion
o a dila ional s ess ollowing a simila app oach o ha was p e iously
epo ed o he desc ip ion o he dila ional heology o p o eins and
p o eins–su ac an sys ems [65,248]. This allows desc ibing he dila-
ional esponse o pa icle-laden in e aces in e ms o he in o ma ion
p o ided by he adso p ion iso he ms. Despi e he in e es in ob aining
models ha combine equilib ium in o ma ion wi h dynamic one, he
abo e model was no u he ex ended, mainly because o he di icul ies
associa ed wi h de e mining a ue equilib ium iso he m.
The pa icle we abili y is p obably he mos impo an pa ame e o
de ining he apping o pa icles a luid in e ace, and hence he con-
ac angle o he pa icles may modi y decisi ely he pe o mance o
pa icle-laden in e ace agains dila ional s esses as was demons a ed
by Sa ouane e al. [249]. They s udied he heological esponse agains
dila ion o monolaye s o umed silica nanopa icles a he wa e / apo
in e ace using measu emen s o he damping o capilla y wa es in he
equency ange 200–1000 Hz), and ound he exis ence o impo an
co ela ions be ween he in e acial mo phology and he in e acial
heological esponse. The elas ic componen o he dila ional isco-
elas ic modulus was ound o inc ease wi h he pa icle hyd ophobici y
and he in e acial co e age, whe eas he loss modulus emained almos .
This leads o a si ua ion in which he comp essibili y modulus o hy-
d ophilic pa icles apped a he wa e / apo in e ace eme ges close o
0, inc easing i s alue up o alues close o 200 mN/m wi h he inc ease
o he hyd ophobici y o he pa icles. This igidi ica ion media ed o
he pa icle hyd ophobici y may be unde s ood conside ing a densi i-
ca ion o he in e acial laye coupled o he s eng hening o in-
e ac ions be ween he pa icles a he in e ace [250]. Ki by e al. [251]
showed ha he in e -pa icle in e ac ions play a e y impo an ole on
he con ol o he in e acial mechanical esponse. They ound ha he
sc eening o he elec os a ic epulsion be ween pa icles leads o a
s ong hys e esis on he dila ional esponse o he pa icle-laden in e -
ace, which may be explained conside ing he o ma ion o igid
incomp essible ilms a he in e ace media ed o he agg ega ion o he
pa icles.
Sa ouane e al. [249] also ound ha he s o age modulus appea s
always highe han he loss one, i espec i ely o he pa icle hyd o-
phobici y and he in e acial co e age. Zang e al. [252] enla ged he
equency ange explo ed by Sa ouane e al. [249], including da a co -
esponding o he low equency ange. This s udy p o ides in o ma ion
on he elaxa ion p ocesses eme ging a he in e ace as esul o he
applica ion o he dila ional s ess. Thus, i was ound ha he eo ga-
niza ion o he pa icles a he in e ace leads o a elaxa ion p ocess
wi h a cha ac e is ic ime o abou 1000 s. The impo ance o his
elaxa ion p ocess was ound o inc ease as he pa icle hyd ophobici y
dec eases, which may be unde s ood conside ing he educ ion o he
in e acial co e age, and hence he educ ion o he s e ic hind ance
associa ed wi h he eo ganiza ion o he pa icles a he in e ace which
a o s he mo ion o pa icles a he in e ace.
The esponse agains dila ion o pa icle-laden in e ace o med by
polyme pa icles p esen s some di e ences wi h he abo e discussed o
silica nanopa icles as i was epo ed by Kobayashi and Kawaguchi
[253]. These di e ences may be asc ibed o he pa ial de o mabili y o
he polyme pa icles. Kobayashi and Kawaguchi [253] showed ha he
dila ional esponse o la ex pa icles a he wa e / apo in e ace p e-
sen ed a mos ly iscoelas ic cha ac e , independen ly o he s ain a e.
Fu he mo e, he elas ic and iscous dila ional moduli unde go an in-
c ease wi h he in e acial co e age up o each a c i ical alue a a
su ace p essu e o abou 15 mN/m, and hen bo h s a o dec ease
s eeply. This may be explained conside ing he eme gence o ou -o -
plane de o ma ions (buckling) o he monolaye upon he applica ion
o he dila ional s ess, which leads o a dis o ion o he quasi-2D o -
ganiza ion o he pa icle-laden in e ace. Analyzing he equency de-
pendences o he iscoelas ic moduli, i was possible o obse e he
eme gence o a ansi ion om a luid-like beha io o a solid-one as he
in e acial packing densi y inc eases, which ag ees wi h he s uc u al
pic u e ex ac ed om he s udies by Bonales e al. [222]. The e o e, he
dila ional heological esponse may be conside ed s ongly dependen
on he speci ic egion o he phase diag am analyzed [222,253,254]. I is
wo h o s ess ha he igidi y o sp ead laye s appea s in mos o he
cases highe han ha ob ained o pa icle-laden in e aces wi h he
same in e acial densi y ob ained upon comp ession o he a ea. This
may be he esul s o he eme gence o non-equilib ium a es ed s a es
which add some addi ional elaxa ion p ocess o he esponse o he
pa icle-laden in e ace agains dila ional s esses [252].
The unde s anding o he in e acial o ganiza ion- heological
esponse co ela ions in pa icle-laden in e aces we e u he
explo ed by del Rio e al. [255], con i ming he impo ance o he na u e
o he monolaye , i.e., i s phase, on he con ol o he dila ional isco-
elas ic modulus o pa icle-laden in e ace. Fu he mo e, hei esul s
con i med he inding by Sa ouane e al. [249] in ela ion o he mainly
elas ic cha ac e o he monolaye s, i.e., he s o age modulus appea s
highe han he loss one. The s o age modulus was ound o inc ease
wi h he in e acial co e age wi hin he egion o low su ace p essu e o
he iso he m, whe eas he loss modulus appea s simila o ha expec ed
o he p is ine wa e / apo in e ace. This esul s om he con ibu ion
o he elec os a ic epulsion be ween he pa icles apped a he luid
in e ace. Fu he mo e, when he in e acial co e age is pushed beyond
a h eshold alue, he s o age modulus unde goes a sha p inc ease up o
a alue close o 350 mN/m, which can be explained conside ing he
o ma ion o a close-packed pa icle ilm a he in e ace, as was e i-
denced by using B ews e Angle Mic oscopy (BAM). I is wo h
men ioning ha he sc eening o he elec os a ic in e ac ion, i.e., in
p esence o weak epulsi e elec os a ic in e ac ions, he s o age
modulus can each alues close o 600 mN/m, which is he esul s o he
minimiza ion o he numbe o de ec s emaining in he close-packed
monolaye [256]. I should be no ed ha eme gence o ou -o -plane
de o ma ions a he highes alues o he su ace p essu e makes d op-
ping bo h he s o age and loss moduli in ag eemen wi h he esul s
p e iously epo ed by Kobayashi and Kawaguchi [253]. On he o he ,
he heological esponse agains dila ion o la ex monolaye s can be
conside ed quali a i ely simila o pa icles adso bed a bo h wa e /
apo and wa e /oil in e aces [254,256].
The size o he pa icles is a e y impo an pa ame e o be
conside ed when he heological esponse agains dila ional s esses o
pa icle-laden in e aces is analyzed. Vella e al. [257] epo ed ha he
Young’s modulus o monolaye s monodispe se pa icles wi h he same
E. Guzm´
an e al.
Ad ances in Colloid and In e ace Science 302 (2022) 102620
20
chemical na u e a luid in e aces is in e sely p opo ional o he size o
he pa icles.
I should be no ed ha he in e acial dila ional lows induced in
common labo a o y expe imen s a e smalle han hose wha a e ex-
pec ed in indus ial p ocesses. This was demons a ed by Hilles e al.
[258], who explo ed he dila ional esponse o la ex pa icles a he
wa e /oc ane in e ace agains oscilla o y de o ma ions wi h di e en
de o ma ion ampli udes and ound ha pa icle-laden in e aces p esen
a e y na ow egion o low s ain in which he in e acial esponse
appea s as linea .
5.1.1.2.2. In e acial shea heology. The exis ence o bulk low can
induce he eme gence o in e acial shea de o ma ions a pa icle-laden
in e ace in ol ing mass and momen um anspo [216]. Fo shea
de o ma ions, he ampli ude and ime e olu ion a e no coupled o any
o he o he in e acial modes [259]. This leads o a si ua ion in which is
possible o p o ide a de ini ion o he shea elas ici y co esponding o
an in-plane shea de o ma ion as a cons an ha de ines he p opo -
ionali y be ween he applied s ain (u
xy
) and he s ess (
σ
xy
). In a solid
like- ilm, conside ing a Hookean-like beha io , he shea elas ici y is
gi en by
σ
xy
=Gu
xy
. On he o he side, he beha io o luid-like laye s is
domina ed by he iscous cha ac e o he laye , and he shea s ess can
be exp essed as
σ
xy =
η
Sduxy
d (63)
whe e du
xy
/d and
η
S
a e he s ain a e and he in e acial shea is-
cosi y, espec i ely. In mos o he sys ems he iscoelas ic pa ame e s
(G,
η
S
) a e highe when he sys em p esen s s ong in e ac ions be ween
he pa icles, which can be explained by conside ing he low induced in
he su ace elemen s as esul o he ene gy equi ed o o e come
in e acial in e ac ions [27]. Fo an oscilla o y de o ma ion, he com-
plex shea modulus G
*
is de ined as
G*(
ω
) = G
´
(
ω
)+iG
´
´
(
ω
) ≡ G'+i
ωη
S(64)
wi h G’ and G” being he s o age o shea elas ic, and loss moduli,
espec i ely. Fo expe imen s in which he ampli ude o he oscilla o y
de o ma ions a ixed equency
ω
emains small, i is possible o de ine
he shea iscosi y as G”=
ωη
S
.
The s udy o he esponse o pa icle-laden luid in e aces o shea
has gained impo ance in ecen yea s, especially because o he impli-
ca ion o he shea p ocess in di e en aspec s ela ed o he s abili y o
emulsions and oams [28,36,247]. This has s imula ed signi ican
esea ch wo k a emp ing o un a el he co ela ions ha a ise be ween
he in e acial mic o-s uc u e and he shea esponse o pa icle-laden
luid in e aces, wi h in e -pa icle in e ac ions playing a key ole in
modula ing hese co ela ions [260]. I should be no ed ha he di e -
ences be ween he in e -pa icle in e ac ions ha a ise when he pa i-
cles a e dispe sed in bulk and a luid in e aces gi e ise o impo an
di e ences in he shea ing beha io o 3D pa icles suspensions and
hei in e acial coun e pa s [261].
The seminal wo k on he cha ac e iza ion o pa icle-laden in e aces
agains shea s esses was done by Cicu a e al. [262]. They compa ed
he beha iou o polys y ene la ex pa icles (3
μ
m o diame e ) a he
wa e /decane in e ace wi h ha o β-lac oglobulin laye s. While he
in e acial heological esponse o he pa icle monolaye s p esen ed a
mainly iscous cha ac e (G′′ >G′), he β-lac oglobulin laden in e ace
u ned ou o be mainly elas ic. The di e ence can be a ibu ed o he
possibili y ha he p o ein unde goes de o ma ion and comp ession
p ocesses when shea de o ma ions a e applied. A low co e age, he
esponse agains shea was ound o be domina ed by he iscous
con ibu ion, which can be conside ed eminiscen o wha is expec ed
o liquid-like ilms. On he o he hand, i was ound ha he isco-
elas ici y o pa icle-laden in e ace unde goes a sha p inc ease o
su ace co e age abo e 75-80% as a esul o pa icle jamming. This
ag ees quali a i ely wi h he indings by Yu e al. [263] o monolaye s
o silica pa icles. In he limi ing condi ions, a highe co e ages, he
esponse is domina ed by he elas ic con ibu ion, and he monolaye s
can be conside ed as solid-like ilms.
I should be no ed ha he ansi ion om iscous-like o solid-like
beha iou can be modula ed by changing he ionic s eng h, i.e., by
modi ying he in e -pa icle in e ac ions. The inc ease o he ionic
s eng h does no signi ican ly modi y he dependence o he iscoelas ic
moduli on he in e acial co e age. Howe e , he ansi ion om iscous
o elas ic-like beha iou occu s a lowe alues o he in e acial
co e age as he ionic s eng h inc eases, which can be unde s ood
conside ing ha he sc eening o he elec os a ic epulsions be ween
pa icles a ou s in e acial agg ega ion [263].
The ole o in e acial co e age in he esponse o pa icle-laden luid
in e aces o shea s esses was also analysed by Impe iali e al. [264].
They showed ha he eo ganiza ion abili y o he pa icles plays a
cen al ole in con olling he in e ace esponse agains shea , which
quali a i e ag ees wi h he esul s o Ba man and Ch is ophe [265] o
polys y ene la ex a wa e / apo in e ace. They used a double-walled
in e acial shea heome e ha allowed cha ac e iza ion o he in e -
acial mic os uc u e, and ound a ansi ion om shea hinning
beha iou , cha ac e ized by he b eakup o pa icle clus e s, o one o
yielding wi h inc easing in e acial co e age. The o igin o his ansi-
ion was a ibu ed o di e ences in he mechanism o iscous s ess
dissipa ion. The occu ence o yielding a in e acial co e ages well
below ha co esponding o in e acial jamming, sugges ed ha he
solid-like beha iou can occu p io o eaching close-packing o jam-
ming condi ions. In addi ion, he au ho s ound ha monolaye s wi h
high in e acial co e age can unde go a shea -induced o de ing
phenomenon.
Ba man and Ch is ophe [265] ound ha inc easing in e acial
co e age educes he ange in which he heological esponse is linea ,
wi h he co e age dependence o he iscoelas ic shea modulus being
desc ibed in e ms o a powe law. The abo e s udies we e ex ended,
leading o he conclusion ha he iscoelas ic esponse o pa icle-laden
in e ace is go e ned by cons ains on pa icle mo ion. These cons ains
we e associa ed wi h he in e -pa icle capilla i y a ac ion and he
caging-e ec s eme ging om he local mic o-s uc u e. Fu he mo e,
Ba man and Ch is ophe [266] epo ed he impo an ole o meso-
s uc u al o ganiza ion in de e mining he elas ici y and yield. They
ound ha he o ma ion o aligned domains o hexagonally packed
pa icles gi es ise o elas ic-like pa icle ilms, and ha dec easing
domain size leads o in e acial lows and iscous-like beha iou .
The s udy o he e ec o he in e acial packing on he esponse o
pa icle-laden in e aces agains shea s esses was ex ended by Rey-
nae e al. [267]. They p o ided u he e idence o he in luence o
in e -pa icle in e ac ions in modula ing he in e acial heological
esponse, showing ha pa icle agg ega ion leads o an in e acial shea
esponse eminiscen o ha ound in bulk coun e pa s. This ag ees
quali a i ely wi h he esul s ob ained by Wijmans and Dickinson [268]
using B ownian dynamics simula ions. The ole o he in e -pa icle in-
e ac ions in he esponse o pa icle-laden in e aces o shea s esses
was also s udied by Bel amo e al. [247]. They ound ha he exis ence
o s ong la e al in e ac ions be ween he pa icles p omo es he eme -
gence o in e acial yield s ess, and ha he elas ic modulus and he
yield s ess inc ease en old when he in e acial co e age inc eases
om 0.47 o 0.88. Fo in e acial co e ages below 0.64 he iscoelas ic
modulus was almos negligible, while abo e ha h eshold he isco-
elas ic modulus o he pa icle ilms inc ease. Fo in e acial co e ages in
he ange 0-75-0.80 he iscoelas ic modulus eached a pla eau, which
was a ibu ed o he eme gence o in e acial jamming.
Mun z and Thijssen [269] ha e ecen ly del ed in o he co ela ions
be ween he s uc u e o pa icle-laden in e aces and hei heological
beha iou . Fo his pu pose, hey s udied poly(me hyl me ac yla e)
pa icles a wa e /dodecane in e aces using a shea heome e coupled
o a con ocal mic oscope. The esul s ob ained showed ha , a low
su ace co e age, he pa icle-laden in e ace beha es as a wo-
E. Guzm´
an e al.
Ad ances in Colloid and In e ace Science 302 (2022) 102620
21
dimensional New onian luid, which unde goes agg ega ion when a
shea s ess abo e a h eshold alue is applied. The inc ease in in e a-
cial co e age leads o an in e acial beha iou domina ed by he elas ic
con ibu ion, and abo e he yield s ess, he in e ace unde goes plas ic
de o ma ion.
As was men ioned abo e, pa icle oughness plays a e y c i ical ole
in he en apmen o pa icles a luid in e aces and hus in hei
in e acial o ganiza ion. Hence, i is necessa y o conside i s impac on
he esponse o pa icle-laden in e ace upon he applica ion o shea
s esses. The ole o he pa icle oughness in he shea esponse o he
pa icle-laden in e aces is closely co ela ed o he in e acial co e age
[270], which can be explained in e ms o in e -pa icle ic ion [271].
A low in e acial co e age, he in e acial shea iscosi y o he pa icle-
laden in e aces dec eases as he su ace oughness inc eases, while he
esponse is he opposi e as jamming app oaches [272].
This beha iou can be unde s ood conside ing he apping o he
pa icles a me as able posi ions as esul o he con ac line pinning
[273]. The eme gence o con ac line pinning may lead o a si ua ion in
which pa icles beha e e y di e en ly o ha wha was expec ed
conside ing hei we abili y, i.e., hyd ophilic pa icles may beha e
upon apping a luid in e aces as hyd ophobic ones, and he la e as
hyd ophilic ones. This o e s he possibili y o s abilizing bo h wa e -in-
oil and oil-in-wa e by using a single ype o pa icles, wi hou needing
any change o i s we abili y. The e o e, i is clea ha he shea
esponse o pa icle-laden in e aces appea s s ongly in luenced by he
hyd ophilic-lipophilic balance o he pa icles. Sa oune e al. [249]
con i med such pic u e. They s udied monolaye s o umed silica pa -
icles ha ing di e en hyd ophobici y deg ees, and ound ha he in-
c ease o he hydophobici y o pa icles o a simila alue o he
in e acial co e age leads o monolaye s wi h highe alues o he shea
elas ic and iscous moduli. The pa icle monolaye s we e ound o
p esen a beha io go e ned mainly by he elas ic con ibu ion o
pa icles wi h a low hyd ophobici y deg ee, becoming pu ely iscous
when he hyd ophobici y deg ee is high. Thus, a c oss-o e be ween
elas ic and iscous ilms was ound, i.e., a gel poin (G’ =G”), o pa -
icles wi h an in e media e we abili y which a e apped a he luid
in e ace wi h a con ac angle a ound 90◦. The abo e s udies we e
ex ended by Zang e al. [90,252,274], who explo ed he e ec o he
pa icle hyd ophobici y on he esponse agains shea s esses. They
s udied monolaye s o umed silica pa icles a he wa e / apo in e -
ace, and did no ind any dependence o he elas ic modulus on he
s ain ampli ude when he la e was small. Fu he mo e, an elas ic
modulus wi h alues en imes highe han he iscous one was ound.
On he o he side, Zang e al. [90,252,274] epo ed he possible
appea ance o a mel ing ansi ion o pa icle monolaye s when he
s ain ampli ude o e comes a h eshold alue (yield s ess). Unde such
condi ions, he loss modulus eaches i s maximum alue, whe eas he
s o age modulus d ops. The esponse o he pa icle-laden luid in e ace
o he applica ion o small de o ma ions o low equency e idences a
iscous cha ac e , whe eas o de o ma ions o high equency he
beha io becomes mainly elas ic. Fu he mo e, a quasi-linea depen-
dence o he elaxa ion ime on he shea a e was ound. This may be
conside ed analogous o ha wha is ound in 3D so s solids, and may be
explained conside ing he educ ion o he cha ac e is ic ime o he
s uc u al elaxa ion ha occu s because o he inc ease o he s ain-
a e ampli ude [275], in ag eemen wi h he esul s epo ed by Van-
deb il e al. [276].
A u he impo an aspec o be conside ed, o he esponse o
pa icle-laden luid in e aces o he applica ion o shea s esses is
ela ed o he analysis o i s ime e olu ion. Fo elucida ing his aspec ,
K ishnaswamy e al. [277] s udied, by using shea heology, he
adso p ion kine ics o sil e nanopa icles (in he ange 10-50 nm) a
oluene/wa e in e aces by using shea heology, and ound an inc ease
o bo h he s o age and loss moduli wi h ime. This is due o he densi-
ica ion o he monolaye du ing he adso p ion p ocess. Fu he mo e,
upon in e acial equilib a ion i was ound ha he pa icle-laden
in e ace has a beha io ha p esen s some eminiscence o ha wha
may be expec ed o a 2D glassy ma e ial, wi h he shea esponse
depending s ongly on he s ain ampli ude. On he o he side, he use o
s ain sweep measu emen s e idenced a shea hickening beha io o G”
upon de o ma ions wi h a la ge s ain ampli ude, whe eas no de-
pendences o G’ on he s ain ampli ude we e epo ed up o he shea
hickening poin . Fu he mo e, i was ound ha he shea hickening
may be desc ibed using a powe -law in which he exponen s o
desc ibing he s o age and loss moduli assumed alues o 2 and 1,
espec i ely. The beha io ound o sil e nanopa icles may be
conside ed e y di e en o ha o gold nanopa icles a he wa e /
apo in e ace [278]. The la e shows a beha io eminiscen o a gel-
like sys ems unde going s ain induced so ening. Fu he mo e, o gold
nanopa icles he heological esponse does no p esen any dependence
on he applied s ain o alues below a h eshold co esponding o 0.1%,
and hen he s o age modulus d ops. On he o he side, he iscoelas ic
moduli can be desc ibed as a unc ion o he in e acial co e age using a
powe law wi h an exponen a ound 0.65. This seems a eminiscence
om ha wha is ound in pe cola ing sys ems [246].
5.1.1.2.3. Ou -o -plane de o ma ion. The de o ma ion o pa icle-
laden luid in e aces upon he applica ion o la ge comp essional
s esses may induce he eme gence o elas ic ins abili ies in he mono-
laye , which leads o ou -o -plane de o ma ions o he quasi-2D pa icle
laye [11,26]. This may be explained conside ing he eme gence o
di e en ypes o phenomena in pa icle-laden in e aces upon
comp ession. An ini ial comp ession o he pa icle-laden luid in e ace
leads o he o ma ion o close-packed ilms, which can unde go in and
ou -o -plane de o ma ion upon u he comp ession. This esul s in
monolaye buckling, expulsion o ma e ial om he in e ace o mul i-
laye mul ilaye o ma ion [279].
The buckling in pa icle-laden in e aces occu s when he su ace
p essu e is high enough o cause a d opping o he e ec i e in e acial
ension down o a quasi-null alue. Howe e , unde speci ic condi ions
he expulsion o pa icles om he in e acial laye may be a o ed wi h
espec o he buckling. This may be a ionalized conside ing he di -
e ences exis ing be ween he apping ene gy ΔE
p
, and he mechanical
wo k equi ed o comp essing he in e ace dW=ΠdA. This allows one
o conside ha he expulsion o pa icles om he in e ace is only
possible when he wo k associa ed wi h he comp ession exceeds o he
apping ene gy. The e o e, i is possible o de ine a bounda y condi ion
which de ines he expulsion o pa icles as W=ΔE
p
. This p o ides a
de ini ion o he o ce balance associa ed wi h he pa icle expulsion as
[280]
Π=γ12(1±cosθ)2(65)
I should be s essed ha he abo e exp ession does no include he
ole o he in e acial in e ac ions, which may modi y he de o ma ion
p o ile. Thus, he p esence o a ac i e in e -pa icle in e ac ions may
induce he o ma ion o elas ic solid-like ilms, in which he eme gence
o pa icle expulsion upon comp ession is no possible [93].
Leahy e al. [281] ound ha he comp ession o monolaye s o med
o gold nanopa icles beyond he close packing leads o he olding o
he monolaye ollowed by he o ma ion o mul ilaye s. The wa e-
leng h o he w inkles allows ob aining in o ma ion ela ed o he
bending modulus o he pa icle monolaye s and mul ilaye s by applying
he elas ici y heo y. The eme gence o w inkles on pa icle-laden in-
e aces was asc ibed by Vella e al. [257] o he o ma ion o pa icle
clus e s a he luid in e ace, which allows conside ing ha he
comp ession o pa icle-laden in e aces beyond he collapse leads o an
elas ic beha io cha ac e ized by a buckling leng h de ined as
λ=
π
[4
3(1−ϑ)(1− P)]1/4
2Rlc
√(66)
whe e
ν
P
ep esen s he Poisson a io, which p o ides in o ma ion abou
he de o ma ion o he in e ace ollowing he di ec ion pe pendicula o
E. Guzm´
an e al.
Ad ances in Colloid and In e ace Science 302 (2022) 102620
22
he di ec ion o applica ion o he s ess. In his pa icula case, he
Poisson a io e alua es he abili y o he in e ace o unde going ou -o -
plane de o ma ions. I should be no ed ha he abo e model p o ides a
good desc ip ion o he in e acial beha io o pa icles wi h diame e s
in he mic ome e ange (abo e 1
μ
m). Howe e , o smalle pa icles, i
p o ides an unde es ima ion o he buckling wa eleng h, which may be
he esul o a high bending elas ici y, κ
b
[282]. In he case o monolaye s
o aniso opic pa icles, he comp essi e s ess can be eleased by hei
in e acial ea angemen s, which may induce a lipping ansi ion upon
comp ession. Fu he comp ession o bucked pa icle-laden in e aces
may esul in he expulsion o some pa icles o one o he adjacen luid
phases [283].
Mos o he phenomena occu ing a pa icle-laden in e aces when
he monolaye is comp essed beyond he collapse may be modula ed by
changing he pa icle con ac angle [284]. This may be unde s ood
conside ing he impo an con ibu ion o he in e -pa icle in e ac ion
on he con ol o he in e acial mic os uc u e and heological esponse.
Thus, hyd ophilic pa icles lead o he o ma ion o luid-like pa icle-
laden in e aces which may unde go an i e e sible collapse wi h a
no iceable expulsion o pa icles om he in e ace o he bulk. On he
o he side, solid-like ilms o med by hyd ophobic pa icles p esen a
high comp essional elas ici y due o he s eng h o he cohesi e in-
e ac ions be ween pa icles. This commonly leads o he eme gence o a
e e sible collapse h ough he o ma ion o w inkles and olds. This can
be unde s ood conside ing he a es o he mechanisms guiding he
expulsion o pa icles om he monolaye o he bulk luids as esul o
in e -pa icle in e ac ions wi h a ac i e o igin.
5.1.2. Aniso opic pa icles a luid in e aces
The abo e discussion has been ocused on he analysis o he
beha io o sphe ical o nea ly sphe ical pa icles apped a luid in-
e aces. Howe e , he adso p ion o pa icles may be modula ed by he
chemical and geome ical cha ac e is ics o he pa icles [285,286],
which has s imula ed he in e es o s udying he in e acial beha io o
pa icles wi h aniso opy in hei shape o in hei chemis y [287,288].
5.1.2.1. Chemically homogeneous non-sphe ical pa icles. The shape
aniso opy o pa icles p esen s a key ole in he a achmen o pa icles
o he luid in e ace. This is clea conside ing ha , whe eas o sphe ical
pa icles he posi ion in ela ion o he in e acial plane can be de ined
exclusi ely by he con ac angle, he analysis o he apping o non-
sphe ical pa icles, including ellipsoids, dumbbells o cylinde s, need
o conside bo h he shape and we abili y o he pa icles [289,290].
Pa icles wi h a ela i ely high deg ee o aniso opy, i.e., pa icles wi h a
la ge aspec a io, adso b commonly a luid in e aces o ien ing hei
majo axes pa allel o he luid in e ace. Fig. 12 is a ske ch showing he
o ien a ion o pa icles wi h di e en aspec a ios (S
I
) apped a luid
in e ace. I should be no ed ha he aspec a io p o ides a ela ionship
be ween he wo main adiuses o he aniso opic pa icles.
The exis ence o di e en possible con igu a ions o he apping o
a speci ic ype o pa icles a a luid in e ace in luences he balance o
in e acial in e -pa icle in e ac ions, which in u n modi ies he as-
sembly o pa icles a he in e ace, and consequen ly he p ope ies o
he pa icle laye s. On he o he side, he abili y o pa icles wi h
aniso opic shape o emain apped a he luid in e ace is s ongly
dependen on hei geome ies. A c i ical aspec a io exis s beyond
which he adso p ion o aniso opic pa icles becomes uns able. The
eme gence o adso p ion ins abili ies esul s om he high alues o he
line ension [10]. The co ela ions be ween he line ension and he
aspec a io ha e d i en impo an esea ch e o s ying o op imize
he adso p ion o di e en aniso opic pa icles, e.g., ca bon nano ubes,
a luid in e aces. Thus, o pa icles wi h simila olume, he apping
ene gy changes acco ding o he ollowing o de disks> ods>sphe es.
On o he side, he maximum di e ences o he apping ene gy in
ela ion o ha wha a e ound o sphe ical pa icles can be ound a he
ex eme we ing condi ions, i.e., close o 0 and 180 deg ees [291].
Fo cases in which he we ing condi ions a e ul illed, ensu ing he
a achmen o chemically homogeneous bu geome ically aniso opic
pa icles o he luid in e ace, i is possible o ind a de o ma ion o he
luid in e ace in he icini y o he pa icles, ha leads o a ac i e
capilla y in e ac ions ha o e come he epulsi e elec os a ic con i-
bu ions [188]. Fu he mo e, he sho - ange in e ac ions, e.g., an de
Waals o s e ic, a e also s ongly modi ied as esul o he shape
aniso opy o pa icles [10].
The impac o he shape aniso opy on he assembly was e idenced
om he wo k by Loude e al. [187]. They explo ed he assembly o
mic on-sized pa icles wi h ellipsoidal shape a a luid in e ace, and
ound ha he asymme ic dis ibu ion o he in e ac ions wi hin he
in e ace leads o he associa ion o he pa icles in open b anched ag-
g ega es o pa icles which ends o be o ien ed o ming pa icle chains
as a esul o he di ec ionali y o he in e ac ions [287]. This beha iou
is e y di e en o ha wha is ound o sphe ical colloids apped a
luid in e aces which o m well-de ined close-packed ilm s uc u es
[222]. The di e ences on he in e acial assembly o pa icles esul ing
om he speci ic pa icle shape should be asc ibed o he capilla y in-
e ac ions. Thus, non-sphe ical pa icles in e ac h ough long- ange
capilla y in e ac ions wi h quad upola o igin, which exceed by
se e al imes he he mal ene gy (k
B
T), leading o a complex in e acial
assembly [10,187,287,288]. In pa icula o ellipsoidal pa icles ap-
ped a he wa e / apou in e ace, he quad upola in e ace de o ma-
ion cha ac e ized by dep ession and ascension o he in e ace a ound
he ip and side egions, espec i ely lead o he assembly o side- o-side
o ip- o- ip s uc u es as was epo ed by Loude e al. [309]. The
quad upola de o ma ion o he in e ace was also epo ed o he
adso p ion o cylind ical pa icles a bo h wa e / apou and wa e /oil
in e aces [188,292]. Thus, o cylinde -like pa icles apped a luid
in e aces, he in e ace de lec s upwa d on he plana end su ace and
downwa d a ound he sides. The p ominen in e acial de o ma ion on
he end su aces leads o he o ma ion o linea chain-like s uc u es.
The abo e di e ences on he o ganiza ion o aniso opic pa icles a
luid in e aces depending on hei shape a e due o he e y di e en
ene ge ic landscapes [292]. Thus, he side- o-side chains ob ained om
he assembly o ellipsoidal pa icles p esen a ce ain deg ee o lexi-
bili y, whe eas he end- o-end con igu a ions ob ained om he as-
sembly o cylind ical pa icles p esen a high igidi y. This con i ms he
impo an di ec ional cha ac e o he capilla y in e ac ions in mono-
laye s o aniso opic pa icles a luid in e aces. The abili y o sel -
o ganizing o aniso opic pa icles can lead o a ich in e acial phase
beha iou , including he o ma ion o iso opic, 2D nema ic, 2D smec ic
and 3D nema ic phases, as was e idenced by Kim e al. [293] o BaC O
4
nano ods and by He n´
andez-L´
opez e al. [294] o ca bon nano ubes.
The di e ences in he assembly induced by he aniso opic shape also
a ec s he in e acial esponse agains mechanical s esses. Madi ala
e al. [289] explo ed he in e acial beha io o ellipsoidal pa icles
Fig. 12. Ske ch ep esen ing he adso p ion o di e en chemically homoge-
nous pa icles wi h di e en deg ee o shape aniso opy apped a luid in-
e aces. Rep in ed om Pa k and Lee [285], Copy igh (2014), wi h pe mission
om Sp inge -Na u e.
E. Guzm´
an e al.
Ad ances in Colloid and In e ace Science 302 (2022) 102620
23
made o polys y ene a wa e /decane and wa e / apo in e aces, and
ound ha he assembly o he pa icles a he luid in e aces may be
uned by changing he elec os a ic in e ac ions wi hin he sys ems. This
leads o he o ma ion o a angemen s o indi idual pa icles coexis ing
wi h linea agg ega es a wa e /decane in e aces, and lowe -like ag-
g ega es a wa e / apo one. The di e en o ganiza ion o he pa icles
depending on he na u e o he in e ace leads o e y di e en esponses
upon he applica ion o shea s esses. This ag ees wi h he gene al
pic u e ha co ela es he in e acial packing and he mechanical
esponse o he pa icle-laden luid in e aces. In pa icula , ellipsoidal
pa icles a he wa e /decane in e ace beha e as an elas ic sys em, wi h
i s iscoelas ic modulus inc easing wi h he in e acial co e age. Such
inc ease was ound o be go e ned by a s ong inc ease o he elas ic
componen o he shea modulus. I should be no ed ha he impo ance
o he elas ic componen on he beha io o ellipsoidal pa icles is jus
he opposi e si ua ion ha wha epo ed by Cicu a e al. [262] o
sphe ical pa icles, which may be due o he exis ence o e y di e en
elaxa ion mechanisms [283]. Fu he mo e, on he con a y o ha wha
was ound o sphe ical pa icles, ellipsoidal pa icles apped a a luid
in e ace can unde go buckling p ocesses when he in e acial co e age
is ela i ely high. The e o e, i is possible o assume ha he di e ences
on he heological esponse due o he shape aniso opy o pa icles may
be unde s ood conside ing he b oad ange o in e acial packings ha
can appea o non-sphe ical pa icles. This is s ongly co ela ed o he
speci ic deg ee o aniso opy o he conside ed pa icles, which modi ies
he balance o in e acial in e ac ions, and hence changes he agg ega-
ion pa e n and in e acial heology o he pa icle-laden in e ace. The
e ec o he mo phology o he pa icles on he esponse o he in e ace
upon he applica ion o shea s esses was ex ended by B own e al.
[271]. They s udied pa icles wi h di e en aspec s a ios, and ound a
shea hickening phenomenon independen o he aniso opy deg ee o
he pa icles. Howe e , he aniso opy becomes a c i ical pa ame e o
con olling he jamming o he pa icles a he luid in e ace. Thus, he
inc ease o he deg ee o he aniso opy o he pa icles educes he
h eshold alue o he co e age o he onse o he jamming egion. On
he o he side, i has been epo ed ha he asymme y o he pa icles
may induce he o ma ion o kine ically apped ilms, which modi ies
he shea lows a he in e ace [295,296].
5.1.2.2. Chemically aniso opic pa icles. The in e es in exploi ing
chemically aniso opic pa icles o s abilizing in e aces was o igina ed
om he Nobel Lec u e o Pie e-Gilles de Gennes, in which he use o
colloidal pa icles wi h wo sepa a ed egions wi h di e en chemical
na u e, he so-called Janus pa icles, was p oposed o eplacing mo-
lecula su ac an s [297]. Howe e , he ad ances in he syn he ic ou es
used o he ab ica ion o colloidal pa icles has allowed o in oduce
o he ypes o chemical aniso opic pa icles, e.g., dumbbells, pa chy
colloids o shape aniso opic Janus pa icles [118].
The adso p ion o sphe ical Janus pa icles ies o ensu e he ene gy
minimiza ion condi ion. This leads o a si ua ion in which pa icles wi h
wo symme ic domains o di e en we abili y adso b o he luid
in e ace in such a way ha each domain is pai ed wi h i s p e e ed
luid phase, i.e., he phase o highe a ini y, and hei apping occu s
wi h he Janus bounda y pinned a he in e ace. This means ha pa -
icles ha ing a non-pola domain and a pola one will adso b o wa e /
oil in e aces wi h he non-pola and pola egions placed in con ac wi h
he oil and he aqueous phases, espec i ely. This con o ma ion leads o
he la ges dec ease o he in e acial ene gy [298]. Fu he mo e, he
adso p ion o Janus colloids in which he domains o di e en we a-
bili y a e no symme ic, i.e., p esen di e en size also adop s he
con igu a ion a he luid in e ace ha allows minimizing he in e acial
ene gy, which may no co espond o he pinning o he Janus bounda y
a he in e ace [299]. I should be s essed ha he apping ene gies o
Janus colloids a luid in e ace can be se e al imes highe (up o 3- old
highe ) han ha co esponding o homogeneous pa icles [300].
Acco ding o he abo e discussion, he equilib ium posi ion o Janus
pa icles a luid in e aces may be p edic ed using simila app oach o
ha used abo e o de ining he con ac angle (see Sec ion 2.4) [301].
Howe e , he dual chemis y o Janus pa icles makes necessa y o
de ine wo con ac angles, he i s one in ela ion o he pola phase θ
P
and he second one in ela ion o he non-pola phase θ
A
[299]. This
allows de ining a deg ee o amphiphilici y o a Janus pa icle as Δθ =
(θ
A
−θ
P
)/2. Thus, i is possible o de ine he Janus bounda y using he
angle
α
, which is placed a 0 and 180 deg ees o pola and non-pola
pa icles, espec i ely, whe eas o pa icles wi h wo pa ches o he
same size assumes a alue o 90◦[302]. The e o e, i is possible o
modi y he amphiphilici y o Janus pa icles by changing he we abili y
o each pa ch, i.e., modi ying θ
P
and θ
A
, o he alue o he Janus
bounda y
α
. Thus, assuming he absence o o a ion o Janus pa icles a
he in e ace, he equilib ium con ac angle may lead o up o h ee
di e en equilib ium posi ions de ined o hei equilib ium con ac
angle θ
E
. Fig. 13a-c epo s di e en si ua ions o he equilib ium po-
si ions o di e en Janus pa icles in ela ion o hei chemically ho-
mogeneous coun e pa s [301,302].
The abo e discussion cla i ies he o ien a ion o sphe ical Janus
pa icles upon he adso p ion o luid in e aces. Howe e , he si ua ion
is less clea when Janus pa icles wi h aniso opic shapes (ellipsoids,
dumbbells o cylinde s) a e conside ed in which he aniso opy p o ides
ex a deg ees o eedom o modi ying he o ien a ion o he pa icles
upon he adso p ion a he luid in e ace, which in luences signi ican ly
he in e ac ion be ween pa icles a he in e ace [303]. I has been e-
po ed ha Janus pa icles wi h la ge aspec a ios adso b p e e en ially
in a il ed con igu a ion, i.e., wi h he Janus bounda y pa allel o he
in e ace. Howe e , he inc ease o he we abili y di e ences be ween
he wo domains o he Janus pa icle may induce he adso p ion in an
up igh o ien a ion o maximize he con ac be ween each egion and i s
p e e ed luid phase. On he o he hand, o pa icles wi h domains o
simila we abili y, i is possible o ind he coexis ence o up igh and
il ed o ien a ions, which may be conside ed as a me as able o ien a ion
a a seconda y ene gy minimum [303]. The e o e, he o a ional
eedom o Janus pa icles eme ges as an essen ial aspec go e ning
hei s abili y a luid in e ace [286,298,302]. This was con i med by
Bon and Cheung [304] using Mon e Ca lo simula ion. They epo ed ha
neglec ing he o a ional eedom o Janus pa icles a he in e ace
unde es ima es he apping ene gy. Fu he mo e, di e en s udies
demons a ed he ole o he amphiphilici y o he Janus pa icles on
hei o ien a ion a luid in e aces [190,298]. The adso p ion o
dumbbells is mo e s aigh o wa d because he na ow neck hinde s he
seconda y ene gy minimum, which limi s he possibili y o abso b in he
il ed con igu a ion [303]. The exis ence o his p e e ed di ec ion o
he adso p ion was e idenced by he con ac angle measu emen s by Isa
e al. [305]. The si ua ion o he adso p ion o pa chy colloids is anal-
ogous o ha wha appea s o dumbbells, wi h hei adso p ion
occu ing in a p e e en ial o ien a ion de ined o he opening angle o
he pa ches [199,306]. Fig. 13d shows an example o he di e en o i-
en a ions ha can eme ges o Janus pa icles o which a combina ion
o shape and chemical aniso opies exis s.
The abo e discussion has e idenced he impo ance o aniso opies
on de e mining he equilib ium posi ion o pa icles a luid in e aces.
Howe e , a mo e de ailed analysis allows e idencing ha he equilib-
ium posi ion o Janus pa icles is de ined o he balance be ween shea -
and capilla i y induced o ques. The o me eme ges om he shea
o ces occu ing a he pa icle su ace, whe ea he la e a e a esul o
he p e e en ial we ing o he pa icles o one o he luid, and he
equilib ium o ien a ion o Janus pa icles is gi en o he poin in which
he ne o que assumes a null alue [118].
5.1.2.2.1. In e -pa icle in e ac ions. The con ac angle pinning o
Janus pa icles apped a luid in e aces leads o i egula de-
o ma ions o he in e ace which induce a ac i e in e ac ions be ween
pa icles [298]. This is because in e -pa icle in e ac ions a e go e ned
by he minimiza ion o he in e acial ene gy, which equi es a educ ion
E. Guzm´
an e al.
Ad ances in Colloid and In e ace Science 302 (2022) 102620
24
o he con ac a ea be ween he wo luids. Thus, he educ ion o he
in e -pa icle dis ance be ween pa icles placed a he in e ace wi h
di e en o ien a ions leads o he o e lapping o he in e acial dis o -
ions, which leads o s ong capilla y in e ac ions. On he o he side, o
pa icles ha ing simila o ien a ion angles, he in e acial de o ma ions
do no o e lap and hence he in e acial ene gy inc eases as pa icles a e
close . This leads o s ong epulsions be ween pa icles, which con as
wi h he si ua ion o pa icles wi h opposi e o ien a ion angles. As a
consequence, he app oaching o pa icles wi h opposi e o ien a ion
angles ongly dec eases he in e acial ene gy, hus inducing he o -
ma ion o capilla y b idges as esul o he s ong a ac i e in e ac ions
be ween pa icles [290].
The abo e pic u e may be also applied o he desc ip ion o he
in e -pa icle in e ac ions o pa chy pa icles apped a luid in e aces
[306]. Thus, o hyd ophilic pa icles con aining hyd ophobic pa ches, a
capilla y a ac ion may be expec ed upon app oaching. Howe e , he
si ua ion changes when he pa ches o he app oaching pa icles p esen
di e en amphiphilici y. In his case, he menisci o he pa icles appea
de lec ed in opposi e di ec ion which is ansla ed in in e -pa icle
epulsion.
5.1.2.2.2. In e acial heology
5.1.2.2.2.1. Dila ional heology
The esponse agains dila ional s esses o Janus pa icles apped a
luid in e ace has been explo ed o di e en ypes o Janus colloids,
and many imes he esul s ha e been pu in compa ison wi h hose wha
we e ound o chemically homogeneous pa icles. Kadam e al. [307]
s udied he esponse o di e en bio unc ionalized silica Janus nano-
pa icles a he wa e / apo in e ace, and ound ha he elas ici y in-
c eases in ela ion o monolaye s o ba e silica, wi h he elas ic modulus
appea ing o monolaye s o some speci ic Janus pa icles up o six- old
highe han ha wha was ound o ba e silica. The inc ease o he
elas ic con ibu ion o monolaye s o Janus pa icles in ela ion o
monolaye s o non-Janus coun e pa s was con i med by Fe n´
andez-
Rod íguez e al. [308] o monolaye s o polyme ic Janus pa icles. They
s udied he comp essional elas ici y o such pa icles a bo h wa e /
apou and wa e /decane in e aces, and ound ha Janus pa icles
leads o monolaye s wi h highe comp essional elas ici y han hose o
homogeneous pa icles, which may be asc ibed o he abili y o Janus
pa icles o o m pa icle ne wo ks a he in e ace. Fu he mo e, an
inc ease o he dila ional s o age and loss moduli wi h he inc ease o he
in e acial co e age was epo ed. Raza i e al. [302] expanded he
abo e s udies in ela ion o he in e acial dila ional esponse using
Janus pa icles o di e en deg ee o amphiphilici y. They ound ha he
inc ease o he amphiphilici y o he Janus pa icles leads o an inc ease
o hei abili y o emaining apped a he wa e / apou in e ace, and
enhances he elas ici y o he pa icle-laden in e ace. Fu he mo e, i
was ound ha monolaye s o highly amphiphilic Janus pa icles un-
de go a e e sible collapse h ough in e acial bucking wi h a educed
numbe o pa icles expelled o he subphase a e successi e comp es-
sion/expansion cycles. On he o he side pa icles wi h low amphiphi-
lici y unde go an i e e sible collapse upon comp ession. This di e ence
on he heological esponse may be asc ibed o he di e ences on he
o ien a ion o pa icles a he luid in e ace. Thus, pa icles wi h low
amphiphilici y appea apped a he luid in e ace wi h a andom
o ien a ion, whe eas hose wi h high amphiphilici y a e placed a he
in e ace in such a way ha hey ha e pai ed hei di e en egions wi h
he mo e a ou able luid.
5.1.2.2.2.2. Shea heology
The s udy o he esponse o Janus pa icles agains shea s esses is
cu en ly a e y ac i e esea ch ield [29]. Yin e al. [309] explo ed he
heological esponse o silica-based Janus nanoshee s a wa e /oil in-
e aces by means o equency sweep expe imen s pe o med a small
s ain ampli ude (a ound 1%), and ound a s ong inc ease o he
in e acial iscosi y up o 1000 mN∙s∙m
-1
. Fu he mo e, he inc ease o
he shea a e up o 2.5 ad/s esul s in a educ ion o he in e acial
iscosi y ollowed by a pla eau egion, which may be a ionalized in
e ms o a dis up ion o he in e acial ne wo k.
Rez an alab e al. [310] explo ed he esponse o in e acial laye s o
Janus pa icles a luid in e aces agains shea ing by calcula ions using
a mul icomponen La ice-Bol zmann me hod, which allows he s udy o
Fig. 13. Equilib ium posi ion o Janus pa icles a luid in e aces. (a) Equilib ium con ac angle de ined o he con ac angle o he non-pola phase. (b) Equilib ium
con ac angle de ined o he Janus bounda y. (c) Equilib ium con ac angle de ined o he con ac angle o he pola phase. (d) Impac o shape and chemical
aniso opies. Rep in ed om Co eia e al. [29], wi h pe mission om MDPI unde A ibu ion License C ea i e Common 4.0 (2021).
E. Guzm´
an e al.
Ad ances in Colloid and In e ace Science 302 (2022) 102620
25
he in e acial o de ing induced upon shea ing o monolaye s o
di e en sizes and in e media e in e acial co e age (in he ange 32-
65% o he o al in e acial a ea). They ound ha he capilla y induced
in e ac ions eme ging om he o e lapping o he in e acial de-
o ma ions induced by he shea low induced he o ma ion o pa icle
chains aligned in he di ec ion no mal o he shea de o ma ion, inde-
penden ly o he cha ac e is ic o he pa icle-laden in e ace, i.e., he
ype o pa icles and he in e acial co e age. The chain-like s uc u es
emain in ac upon he emo al o he low ield, wi h he only modi-
ica ion being associa ed wi h he o a ion o he pa icle o adop ing an
up igh o ien a ion. Rez an alab e al. [311] ex ended hei s udies o
unde s anding he combined ole o chemical and shape aniso opies in
he beha iou o Janus pa icles a luid in e aces agains shea s esses.
They ound he exis ence o wo o a ional dynamics (smoo h il and
umbling), which depends on he pa icle shape, deg ee o amphiphi-
lici y and shea a e. Despi e he exis ence o wo ype o dynamics, all
he pa icles each a s eady-s a e o ien a ion a he in e ace which de-
pends on an in ica e balance be ween o ques induced by shea and
capilla i y. The e o e, i is possible modula e he o ien a ion o Janus
pa icles a luid in e ace by con olling he shea a e and he su ace
chemis y o he pa icles.
Fu he s udies on he shea induced assembly o Janus pa icles a
luid in e aces we e pe o med by Pai a e al. [312]. They ound ha
aniso opic Janus pa icles exhibi umbling beha iou upon he appli-
ca ion o shea s esses ha allows o e coming he capilla y o ques.
This leads o he o ma ion o a Janus an ipa allel con igu a ion o
s acked agg ega e shee s. Wang e al. [313] s udied he co ela ion be-
ween he in e acial mo phology and he shea esponse o Janus pa -
icles o poly( inylidene luo ide)/poly(L-lac ide) a luid in e ace, and
ound ha he ob ained ilms p esen a high elas ici y (se e al imes ha
co esponding o homogeneous pa icles) and low in e acial ension.
This solid-like beha iou was asc ibed o he o ma ion o o de ed a ays
o Janus pa icles a he luid in e ace.
5.2. So pa icles
A pa adigm o so colloidal pa icles a e hose made up by mic ogels
(i.e., chemically c oss-linked polyme s o ming ne wo ks o colloidal
size) ha can unde go swelling in liquid en i onmen s. The deg ee o
swelling depends on he densi y o c oss-linking and he sol en quali y
[314]. Mic ogel pa icles ha e p ope ies ha can be conside ed in e -
media e be ween hose co esponding o colloidal pa icles, and hose
ha a e expec ed o polyme chains [35,314].
The mos common mic ogel pa icles a e hose ob ained om poly
(N-isop opyl ac ylamide) (PNIPAM), a he mosensi i e polyme ha
unde go a e e sible swelling/sh inking ansi ion a a empe a u e
a ound o he physiological empe a u e o he human body [315,316].
In some cases, i is possible o add some co-monome s ha change hei
ioniza ion s a e by pH changes, e.g., ac ylic o me hac ylic acid, which
allows ob aining pH esponsi e mic ogels [317].
The dual cha ac e o he mic ogels plays a e y impo an ole in
hei apping a luid in e ace. On one side, hey a e pa icles and
hence hey emain apped a he luid in e ace e y s ongly. On he
o he side, hey p esen a polyme cha ac e which a o s hei a ach-
men om dispe sion o he luid in e aces [35]. The e o e, he so ness
is no a limi a ion o he adso p ion o pa icles a luid in e ace.
Howe e , i in oduces a compe i ion be ween he bulk elas ici y and
su ace ension, which leads o he pa icle s e ching a he luid
in e ace. This leads o a change o he ene ge ic landscape associa ed
wi h he apping o he pa icles a he in e ace, which is cha ac e ized
by an inc ease o he apping ene gy [75,182,318]. Fu he mo e, he
de o mabili y o he pa icles enhances he con ibu ion o he capilla y
in e ac ions and educes ha co esponding o he di ec in e ac ions
[319]. This esul s in he o ma ion o in e acial mesos uc u es, which
can be exploi ed o he s abiliza ion o dispe sed sys ems, mainly
emulsions [320–323]. The enhancemen o he con ibu ion o he
capilla y in e ac ions o he global balance o he in e ace may be un-
de s ood conside ing ha he capilla y in e ac ions a e ela ed o he
de o ma ion o he in e ace upon pa icle adso p ion. The e o e, he
modi ica ion o he we ing p ope ies o so pa icles as esul o he
change o hei con o ma ion may induce e y di e en con ibu ion o
he capilla y o ces in such a way ha depends on he speci ic size o he
pa icles [324]. This leads o a deg ee o p opaga ion o he pa icle in
each phase depending on he quali y as sol en o he speci ic luid,
esul ing in e y di e en de o ma ion p o iles o he luid in e ace. In
ac , o small pa icles he ole o he capilla y o ces can be conside ed
almos negligible, and he in e acial beha io is eminiscen om ha
expec ed o monolaye s o polydispe se so disks, whe eas monolaye s
o big pa icles unde go s ong a ac i e capilla y o ces, appea ing
clus e ing be ween he pa icles om he lowes alues o he in e acial
co e age.
5.2.1. T apping o so pa icles a luid in e aces
The apping o so pa icles a luid in e aces, bo h wa e / apo
and wa e /oil, is aimed o educe he in e acial ene gy be ween he wo
luids, simila ly o ha wha happens o ha d pa icles [325]. Howe e ,
he so ness o mic ogels allows i s de o ma ion upon adso p ion a in-
e aces, which de e mines wo main aspec s o he in e acial o gani-
za ion o he mic ogels a he in e ace: (i) he su ace ac i i y o mos
mic ogels induce ha in con ac wi h he in e ace, mic ogels can appea
s e ched ou a he in e ace o maximize he in e acial co e age, and
(ii) mic ogels p o udes in o he wo luid phases acco ding o hei
espec i e a ini ies. The la e esul s in an asymme ic dis ibu ion o
he mic ogels be ween he wo phases. I should be no ed ha he
ex ension o he in-plane de o ma ion and he asymme y ac oss he
in e ace depends on he speci ic s uc u e o he mic ogel and he na-
u e o he luid phases [326].
Di e en s udies ha e e idenced ha mic ogels a in e aces be-
ween a pola luid and a non-pola one adop “ ied-egg” mo phologies.
These esul om he lowe c oss-linking o he ex e nal egion o he
mic ogel (co ona) in ela ion o he inne one (co e), which de e mines a
highe de o mabili y [143,318,323,327]. I should be s essed ha he
bulk elas ici y o he mic ogels eme ges as a es ic ion o hei de o -
ma ion upon adso p ion a he luid in e ace. This may be unde s ood
conside ing he balance be ween wo con ibu ions: (i) educ ion o he
in e acial ene gy be ween wo immiscible luids, and (ii) he elas-
ocapilla y leng h L
EC
=γ
S
/E de ined as he a io be ween he su ace
ension o he solid γ
S
and i s Young’s modulus E [318]. Thus, pa icles
wi h adius la ge han he elas ocapilla y leng h can be conside ed
e ec i ely as non-de o mable pa icles, and only sligh de o ma ions
close o he con ac line may be expec ed. On he o he side, o pa icles
wi h adius smalle han he elas ocapilla y leng h, pa icles beha e
almos as a liquid.
I may be expec ed ha he de o ma ion o so pa icles upon
adso p ion a a luid in e ace can appea s ongly dependen on he
in e acial co e age. A low co e age, he adso p ion o he pa icles
occu s wi h he pa icles adop ing a s e ched-ou con o ma ion a he
in e ace. This may be unde s ood conside ing ha such con o ma ion
ensu es he maximiza ion o he ac ion o in e acial a ea occupied by
he pa icles. This in oduces a a o able en opic con ibu ion, allowing
o e coming he ene gy penal y associa ed wi h he elas ic de o ma ion
o he pa icle. Unde he abo e condi ions, he majo po ion o he
pa icles emains imme sed in he pola phase, and only a e y small
ac ion appea s p o uding o he non-pola phase [328]. On he o he
side, he inc ease o he in e acial co e age leads o a si ua ion in which
he pa icles a he in e ace s a o ouch each o he . This d i es he
collapse o pa icles a he in e ace, educing he con ibu ion o he
elas ic ene gy [35]. The abo e pic u e can be in e p e ed conside ing
ha a low co e age, mic ogels can appea o ming ei he monolaye s
esembling a liquid-like s a e o clus e s media ed h ough capilla y
in e ac ions [327,329]. On he o he side, he inc ease o he co e age
induces a c ys alliza ion o he mic ogels o ming a hexagonal a ay
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c ys alli es [383]. In all hese p ocesses, he applied ield plays he ole
o an e ec i e in e se empe a u e.
I he applied ield is o ien ed pa allel o he in e ace, he induced
magne ic momen s a e nea ly coplana wi h he con ining su ace and
he pa icles o m apped s uc u es aligned along he imposed di ec-
ion, wi h complexi y depending on he applied ield s eng h and
monolaye concen a ion [385]. A in e media e pa icle densi y and
ield ampli ude, he equilib ium s a e consis s o linea agg ega es o one
pa icle hickness. The eme ging in e ac ions be ween he induced
linea agg ega es depend on he dis ance be ween hem, bu also on he
chain leng hs and he ela i e displacemen along he chain di ec ion.
Howe e , in mos possible con igu a ions, he magne os a ic po en ial
be ween wo pa allel chains p esen s a minimum a ac ion along he
la e al di ec ion a sho ange, when he wo chains a e almos in
con ac , ollowed by an ene gy ba ie and a epulsion egion a long
ange. The ene ge ic ba ie is loca ed a a cha ac e is ic leng h, he
escape dis ance, which inc eases wi h chain leng h [386]. As he a ea
ac ion inc eases, he chains a e close oge he , so some o hem a e
o ced oge he by a zippe mechanism and o m o de ed hexagonal
bundles o zippe ed chains, in which he pa icles o adjacen chains a e
a anged ou o egis e by a dis ance o adius [385].
Til ing he applied ield wi h espec o he con ining su ace can
ans o m he hexagonal o de o he loa ing c ys als in o me as able
s uc u es wi h o he plana c ys al symme ies, such as oblique,
cen e ed- ec angula , ec angula and squa e la ices [383], and p o-
mo e he unzipping o chains la e ally agg ega ed [211]. The unzipping
p opaga ion is consis en wi h an A henius p ocess, in which one o he
cons i u ing pa icles jumps o e an ene gy ba ie , be o e en aining
adjacen pa icles in he chain. Th oughou his p ocess, he chains
main ain hei in eg i y as hey con inue sepa a ing along he pe pen-
dicula di ec ion. The subsequen inc ease in he slope o he applied
ield esul s in he pa ial agmen a ion o he chains, he g adual
sepa a ion o he monome s, and inally he ab up colloidal explosion.
In his sys em, he di e en disman ling mechanisms a e e e sible and
a e mainly go e ned by he il angle, bu a e also s ongly in luenced by
he mal ene gy, pa icle con ac angle and local magne iza ion [387].
When he numbe o adso bed pa icles is small, hen he pa icles o m
ini e agg ega es, ha can be used in he s udy o bo de and con ine-
men e ec s [209,218]. Due o he supe -pa amagne ic cha ac e o he
componen s, all he desc ibed s uc u es a e s able only unde he
p esence o he ex e nal ield, while immedia ely disin eg a e due o
he mal luc ua ions once he applied ield is swi ched o .
7.1.1.3.2. Dynamic sel -assembly o adso bed magne ic pa icles.
Floa ing magne ic pa icles ha e been widely used in he bo om-up
ab ica ion o no el and dispa a e dynamic sel -assemblies, s ongly
de e mined by he size and magne ic cha ac e o he pa icles, he ge-
ome y and dynamics o he applied ield, and he heological p ope ies
o he comp ising luids. In pionee ing wo k, G zybowski e al. used
millime e -sized magne ic disks adso bed on a liquid-ai in e ace, and
o a ing synch onously wi h he applied ield, o s udy he o ma ion o
a ious dynamic s uc u es [214]. The la e , esul ing om he equi-
lib ium be ween hyd odynamic epulsion and a e aged magne ic
a ac ion, we e s ongly de e mined by he geome y and chi ali y o
he spinne s [388]. In a di e en wo k, o a ing e omagne ic mic o-
discs wi h cosinusoidal edge-heigh p o iles, con ined by an ex e nally
applied magne ic po en ial and subjec ed o a apidly o a ing ield,
we e assembled and disassembled in di e en con igu a ions dic a ed by
he di ec ionali y o capilla y in e ac ions, which we e ul ima ely
de e mined by he p o ile o he pa icles and he o a ional speed o he
applied ield [389]. Snezhko e al. epo ed snake-like s uc u es o med
by an i e omagne ically aligned segmen s, hemsel es composed o
e omagne ic mic o loa e s. These objec s sel -assemble dynamically,
upon applica ion o an oscilla ing ield pe pendicula o he ai /wa e
in e ace, h ough coupling be ween su ace wa es gene a ed a he
luid in e ace and magne ic in e ac ions [365]. A he liquid-liquid
in e ace, he oscilla ing chains gene a ed a hyd odynamic low in
bo h media ha p omo ed he o ma ion o as e -like s uc u es, o ga-
nized in 2D pe iodic a ays a su icien ly high su ace concen a ions.
When ene gized wi h an in-plane al e na ing ield, he pa icles o med
monolaye s o equal-sized spinne s, single-pa icle- hick linea agg e-
ga es, and pulsed clus e s [390].
Unde low equency plana o a ing ields Melle e al. showed using
a mic oscopic model ha pa amagne ic mic opa icles on a plane
o med o a ing chains o gi en leng h and shape as a balance o mag-
ne ic dipola in e ac ions and hyd odynamic d ag [391,392]. Abdi e al.
ex ended he analysis o high equency ields, whe e — hey showed—
he chains b eak and can o m clus e s, using compu e simula ions o a
mic oscopic model in he o e damped egime wi h hyd odynamics
ea ed in he a - ield app oxima ion [393]. In hese high equency
condi ions, he applica ion o in-plane o a ing ields a he con ining
in e ace induces an a ac i e in e ac ion be ween adso bed magne ic
pa icles, which ul ima ely p omo es dynamic sel -assembly in o ini e
hexagonal la ices. Unde ex e nal magne ic ields o a ing on he plane
o a luid- luid o solid- luid in e ace a high equencies, pa amagne ic
colloids we e shown o o m 2D s uc u es wi h di e en mo phology
depending on he pola iza ion o he ex e nal ac ua ion, as a ionalized
in e ms o e ec i e a e aged pa icle-pa icle in e ac ions. Ci cula ly
pola ized ields we e shown o o m iso opic clus e s —ca pe s— and
c ys als o o a ing pa icles [394], whe eas ellip ically pola ized ields
can gene a e bo h chains and ca pe s depending on he ellip ici y o he
ac ua ion [394]. The inclusion o a componen pe pendicula o he
con ining bounda y induces he ansi ion om plana ca pe s o sepa-
a e chains, capable o anspo ing passi e cha ges h ough he low
gene a ed by he o a ing cons i uen s [211].
7.1.1.3.3. Magne ic in e acial swimme s. Some o he dynamic sel -
assemblies, o med om he equilib ium o iscous, ine ial, capilla y,
and magne ic o ces, can be used as models o nume ous in iguing is-
sues, such as he o ganiza ion in biological s uc u es o he anspo o
ma e in he low Reynolds numbe egime [395]. In bulk, he main
s a egies a e based on local gene a ion o low ields h ough o ced
o a ion o non-pe ec ly symme ic objec s, helical shapes in mos de-
signs ha mimic some exis ing na u al sys ems, he o o- ansla ion
coupling s a egy desc ibed abo e, and he con olled ac ua ion o
lexible ilamen s. On he o he hand, con olled anspo o mic o-
pa icles along luid in e aces has adi ionally been induced h ough
s a egies ha make use o au o-pho esis, capilla i y phenomena, o
spa ial symme y b eaking. Fo example, he in e acial snake and as e
s uc u es desc ibed abo e spon aneously b eak spa ial symme y a
ela i ely high ield equency, inducing unbalanced su ace lows ha
lead o p opulsion and can be used o anspo passi e cha ges. A low
equency, i is he p esence o a nea by non-magne ic objec ha in-
oduces he imbalance o he gene a ed luxes necessa y o p opulsion
[396]. In as e s, he la e can be gene a ed by applying an in-plane
magne ic ield, which p omo es he o ma ion o asymme ic ex ended
objec s [365].
Using a di e en s a egy, Lumay e al. exploi he balance be ween
ield-induced dipole epulsion and capilla y a ac ions o gene a e
p opulsion [209]. In he p oposed design, h ee magne ic millime e
sphe es adso bed on a plana wa e -ai in e ace we e ene gized by bo h
a e ical ield and an in-plane oscilla ing ield, so he h ee sphe es o m
a sequence o iangula con igu a ions ha sa is y he ime e e sibili y
b eakdown equi ed in he low Reynolds egime. A mode a e alues o
he Reynolds numbe , he ene gized a ays o med by pa icles o
di e en sizes ollow a non- ecip ocal de o ma ion sequence, as he one
desc ibed by he Naja i-Goles anian mic oswimme [397]. La ge mag-
ne ocapilla y a ays showed me ach onal wa es a he pe iphe y when
subjec ed o a p ecessing magne ic ield [398]. Recen ly, Fei e al.
applied s a ic o ime- a ying ields o o ce magne ic Janus pa icles
adso bed on cu ed luid in e aces o mo e o he zones whe e he
magne ic momen s align pa allel o he ield [399].
O he al e na i e p opulsion s a egies do no ely on he use o
hyd odynamic in e ac ions. In hese, adso bed o non-adso bed colloids
E. Guzm´
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a e anspo ed by he ac ion o a mo ing magne ic po en ials gene a ed
by a a ie y o sel -assembled s uc u es o magne ic pa icles. The
adso bed magne ic colloids can be collec i ely anspo ed ac oss
modula ed ene gy landscapes gene a ed by dynamic sel -assembled
monolaye s o di e en ly sized pa icles, loca ed a di e en posi ions
wi h espec o he in e ace [9]. On he o he hand, he sub le balance
be ween magne ic and iscous o ques allows he anspo o he sub-
me ged colloids unde s aigh acks o adso bed pa icles, which
unc ion as i hey we e mic oassembly lines o Ty olean a e ses
[400].
7.1.2. Dielec ic colloidal pa icles adso bed a a luid- luid in e ace unde
he ac ion o an ex e nal elec ic ield
The esponse o adso bed colloidal pa icles a a luid in e ace o an
elec ic ield depends on he s eng h and equency o he ield, as well
as on he dielec ic p ope ies, elec ical conduc i i y and geome y o
bo h he pa icles and he su ounding media [401]. The use o an
elec ic ield o manipula e colloids and induce sel -assembly has some
ad an ages, compa ed o magne ic ield, since he s eng h and e-
quency o he o me a e mo e unable, bo h spanning on se e al o de s
o magni ude. Howe e , elec ic ields, especially DC ields, can cause
Fa adaic eac ions and elec ical b eakdown ha can deg ade he sam-
ple [402]. Mo eo e , he implied esul s a e mo e di icul o in e p e ,
as he elec ic ield in e ac s wi h pa icles, he su ounding media and
mobile and immobile cha ges [403] -conside , o example, he
con o e sial discussion a ound he long- ange in e ac ion desc ibed by
Nikolaides e al. [404] and A eya d e al. [189]. To a oid, a leas
pa ially, hese impedimen s, high- equency AC elec ic ields a e o en
p e e ed [405].
In he p esence o a uni o m elec ic ield, cha ged pa icles su -
ounded by an elec oly e a e pushed by he ield owa ds he opposi ely
cha ged elec ode, in a p ocess called elec opho esis [406]. I he
applied ield is no uni o m, which can be p omo ed o s essed by he
p oximi y o he luid in e ace, and he dielec ic cons an o he pa -
icle is di e en om ha o he su ounding media, hen he pa icle
expe iences a dielec opho e ic o ce esul ing om he elec ic s ess
ac ing on he pa icle su ace [407]. In addi ion, pa icles exhibi dipole-
dipole in e ac ions ha p omo e he o ma ion o ield-induced chains,
bundles and 2D la ices a luid in e aces, while aniso opic pa icles
unde go ield-induced alignmen [405]. A low equency, he in e ac-
ion be ween he applied ield and he pola iza ion o he ionic double
laye s su ounding he pa icles can also gi e ise o nonlinea elec o-
osmo ic lows [408]. All eme ging phenomena ha e been widely used
o gene a e con ollable Janus d ople s [406], o sepa a e pa icles on
he su ace o d ople s [406], in he des abiliza ion o Picke ing emul-
sions, o o deso b pa icles om luid in e aces [409]. On he o he
hand, he applied ield can induce ee cha ge accumula ion a in e aces
and local elec ical s esses, coupled o in e ace de o ma ion and low
gene a ion o ei he luid [410]. These elec ohyd odynamic lows ha e
also been used ex ensi ely in he collec ion and anspo o adso bed
pa icles a luid in e aces [402,405]. When cha ged pa icles adso bed
a a luid in e ace a e upon he in luence o an ex e nal elec ic ield, he
in e ace de o ms ia he elec o-dipping o ce ha eme ges om he
in e ac ion be ween he su ace cha ge o he pa icles and he wo
media. The e ical componen o his o ce, posi i e o nega i e
depending on he dielec ic cons an and pa icle con ac angle, is
balanced by in e acial ension [411], while he la e al in e ac ion be-
ween wo adso bed pa icles is always epulsi e [412].
To ou knowledge, all s udies conce ning adso bed dielec ic pa i-
cles subjec ed o he ac ion o ex e nal elec ic ields ha e been pe -
o med on Picke ing d ople s, bu none o hem ha e been ca ied ou on
plana cha ged in e aces. Only in he elec ocapilla y wa e echnique is
an ex e nal AC elec ic ield applied locally h ough a kni e-edge elec-
ode placed jus abo e he in e ace. Howe e , he ield is no used he e
o a ange o anspo adso bed colloidal pa icles, bu o exci e he
luid in e ace in a Langmui ough, and measu e he heological
p ope ies o he laden pa icle in e aces [30]. In a simila expe imen al
se up, ecen ly designed by Jia e al., he applica ion o he ex e nal ield
igge s cha ge injec ion, allowing modula ion o he cha ge-induced
epulsi e o ce, along wi h he co esponding e e sible induc ion o
he epulsion-domina ed colloid assembly o dispe sion o agg ega ed
pa icles [413].
7.1.3. Ac i e pa icles
Ac i e sys ems, hose ha can con e con e chemical [414],
he mal [415], o elec omagne ic [416] ene gy in o mechanical p o-
pulsion, a e p esen a a wide ange o scales, in assemblies o li ing
o ganisms such as bac e ial colonies and bi d locks o in collec i i ies o
a i icial componen s. In he las decade, he manipula ion o ac i e
colloids has gene a ed signi ican expe imen al and heo e ical a en-
ion, because he s udy o sel -p opelled mic opa icle suspensions opens
he doo o he unde s anding o sys ems a om equilib ium and o he
de elopmen o dis up i e echnologies. The sel -p opulsion capabili y
o syn he ic chemical powe ed ac i e colloids is suppo ed by di e en
mechanisms, om induced-cha ge elec opho esis [408], o bubble
p opulsion [417], o ca aly ic local eac ions and sel -pho esis [380]. In
au opho esis, a chemical eac ion is ca alyzed a he pa icle su ace,
leading o he gene a ion o asymme ic g adien s ( he mal, su ace
ension, ionic and/o chemical) a ound he pa icles. The occu ence o
hese g adien s, which may be coupled o each o he and/o induced by
an ex e nal ield, such as a ligh sou ce, ul ima ely leads o he mo e-
men o he pa icle ela i e o he solu ion, due o he ac ion o pho e ic
o ces and he igge ing o hyd odynamic lows [418]. These induced
lows can also be used o gene a e long- ange hyd odynamic a ac ions
ha igge he assembly o mic oscale pa icles [372]. In hese expe -
imen s, he inhe en asymme y o Janus mic obeads, sphe es consis ing
o wo di e en (chemically o he mally) ac i e and passi e ma e ial
aces, is o en used o p omo e a p e e ed di ec ion o mo ion.
Ac i e pa icles ha e po en ial applica ions in he enginee ing o
sma lab-on-a-chips, in he anspo o d ugs [419], cells [420], pol-
lu an s [421] o ca goes [422], in he de ec ion o chemicals as well as in
he s udy o ac i e c ys als and glasses [423]. In hese sys ems, indi-
idual pa icle ac i e mo ion is coupled o B ownian o a ional di u-
sion, simila o wha is obse ed in un-and- umble sys ems, while he
collec i e beha io exhibi s a a ie y o complex phenomena, such as
local clus e ing [424], mel ing o clus e s [425], swa ming [416], ac i e
sel -assembly [426] as well as seg ega ion o ac i e and passi e species
[427], mimicking on many occasions he collec i e beha io s exhibi ed
by many biological sys ems. All hese phenomena can be o some ex en
con olled using magne ic [361] and op ical ields [428] o by modi-
ying he swimme geome y. Ensembles o ac i e pa icles dispe sed in
a luid, nea ixed obs acles [429] o a solid-liquid in e ace [430],
whe e pa icles exhibi alignmen in e ac ion [431] and ci cula a-
jec o ies [432], ha e been widely s udied in he las yea s, and
nume ous e iews o he subjec can be ound in he li e a u e [380].
7.1.3.1. Ac i e pa icles adso bed a luid in e aces. Fluid- luid in-
e aces a e o en igno ed in mos undamen al esea ch, e en hough
hey a e p esen in many eal sys ems. Howe e , he dynamics o pho-
e ic colloids is pa icula ly sensi i e o he p oximi y o solid and liquid
in e aces [8,38]. P oximi y o a luid in e ace induces o ien a ion o
he ac i e pa icles la e ally and p opulsion pa allel o he in e ace,
allowing o a obus guidance mechanism along he luid in e ace
[433], while es ic ing o a ion ou o he swimming plane [434]. The
hyd odynamic in e ac ion wi h he luid- luid bounda y a o s he
appea ance o ci cula ajec o ies, like hose obse ed o solid in-
e aces, bu in he e e se di ec ion [362].
When apped a a luid in e ace, ac i e Janus pa icles exhibi
s ongly enhanced pe sis ence leng h and eloci y, compa ed o hose
obse ed in he bulk [418], due o he implici cons ain s o pa icle
eo ien a ion, slowed down due o local pinning o he h ee-phase
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con ac line [185,430]. The abo e cons ic ions lead, in some cases, o
ci cula ajec o ies ha de ia e signi ican ly om andom ec ilinea
mo ion by B ownian o a ional mo ion [435]. Since he o a ion o he
pa icles abou he axes angen o he in e ace is s ongly hinde ed by
local pinning o he h ee-phase con ac line and he capilla y o ces, he
mo ion o ac i e Janus pa icles is s ongly de e mined by he as ened
o ien a ion o he pa icle wi h espec o he luid in e ace, esul ing in
he e ogeneous popula ions o non-mo ing and mo ing pa icles [430].
The ac i i y o adso bed pa icles o en induces local su ace ension
g adien s, which gi e ise o Ma angoni s esses. Ma angoni su e s use
ex e nal ene gy inpu s o chemical eac ions o c ea e local g adien s o
empe a u e and su ac an concen a ion, p opelling hemsel es a high
eloci y owa d egions o highe su ace ension, along di ec ions
pa ially de e mined by he symme y o su e s [418]. In p inciple,
Ma angoni na iga ion equi es asymme ies in he su ace ension
g adien o he in e ace a ound he pa icles. Howe e , e en symme ic
pa icles exhibi apid ansla ional and o a ional mo ions when placed
a a wa e -ai in e ace, gene a ed by a con ec i e ins abili y ha p o-
okes he spon aneous up u e o he ini ial axial symme y. In he
abo e sys ems, he p opulsion mechanism is s ongly dic a ed by he
deg ee o exposi ion o he ca aly ic su ace o aqueous phase [418]. The
in e play be ween mo ili y, capilla y in e ac ions and induced Ma -
angoni lows p omo es in some sys ems ins abili y and up u e o hin
ilms [436], while in o he s i a o s he exis ence o sel -assembled
dynamic and s a iona y s a es [437,438]. In ano he ype o expe i-
men s, whe e mic o-sized loa ing objec s a e illumina ed wi h ligh , he
applied adia ion is adso bed by he Janus pa icles and con e ed in o
mechanical wo k hanks o he coupling be ween he empe a u e and
su ace ension g adien s. The mic o-machines powe ed h ough his
mechanism ha e he ad an age o being long-li ed and easily swi ch-
able, while he linea and angula eloci ies a e easily con olled by he
lase powe and he su ac an concen a ion a he in e ace [418].
7.2. Theo y and simula ion o dynamic sel -assembly
The sel -assembly o colloidal pa icles a liquid-liquid in e aces can
occu as a esul o a wide ange o p ocesses and in e ac ions, bo h in
equilib ium and ou o equilib ium. F om a heo e ical s andpoin , sys-
ems in he modynamic equilib ium ha e been ho oughly s udied o e
many yea s and a e unde s ood using classical concep s o he mody-
namics and s a is ical physics, equi ing he minimiza ion o he
app op ia e he modynamic po en ial o he sys em. A leas in p inci-
ple, he knowledge o in e pa icle in e ac ions allows us o p og am he
mos s able s uc u es ha will be spon aneously o med by sel -
assembly.
He e we ocus ou a en ion on he heo e ical desc ip ion o ag-
g ega ion p ocesses a in e aces ha occu ou o he modynamic
equilib ium, be i by ac ua ion wi h ex e nal ields o due o collec i e
p ocesses s emming om indi idual consump ion o ene gy om he
en i onmen . A common gene al heo e ical amewo k which dic a es
he eme gence o such sel -assembled s uc u es and hei p ope ies is
s ill missing. In sea ch o a deepe unde s anding o such phenomena,
on he one hand mic oscopic models ha e been de eloped o analyze
and cha ac e ize non-equilib ium s uc u es. On he o he hand,
nume ous in es iga ions ha e been de o ed o ind a he modynamic
p inciple o cha ac e ize he eme gence o s eady s uc u es ou o
equilib ium.
7.2.1. Sel -assembly unde ime-dependen ex e nal ields
In he p e iously no ed wo k o G zybowski and co-wo ke s [214],
he dynamic s uc u es o med by o a ing e omagne ic disks a a luid
in e ace we e explained as a p ocess go e ned by he equilib ium be-
ween magne ic pa icle a ac ion and hyd odynamic epulsion wi h
ine ial e ec s [439]. These sys ems we e also in es iga ed using
magne o-hyd odynamic models de ined h ough bounda y alue p ob-
lems [440]. The me hod uses he Na ie -S okes equa ion, which
includes mul i-body in e ac ions exe ed on he luid due o he o a ions
o magne ic pa icles. The nume ical solu ion o he model pe mi ed he
calcula ion o he ene gy dissipa ion a es o he sel -assembled s eady
s a es o o a ing pa icles. In Re . [441], he sole e ec o hyd ody-
namics on he collec i e beha io o spinning discs was s udied wi h he
help o simula ions o luid pa icle dynamics, a echnique ha allows o
p ope ly accoun o hyd odynamic in e ac ions be ween pa icles. The
au ho s concluded ha hyd odynamics alone can gene a e a ich phase
beha io o spinne s, including a luid s a e, clus e ing, hexa ic o de ing
and glassy s a es [441]. The o ma ion o clus e s o spinning magne ic
pa icles a liquid-liquid in e aces was also in es iga ed using La ice
Bol zmann simula ions, which p ope ly accoun s o he hyd odynamics
(o an incomp essible low) gene a ed by he o a ing pa icles [442].
Using his echnique, hey demons a ed ha hyd odynamics can cause
he sepa a ion in o a pa icle- ich egion and a pa icle-poo egion
[442]. G¨
o ze and Gomppe analyzed he e ec s o con inemen on he
assembly and dynamics o magne ic discs d i en by a o a ing ield using
mul ipa icle collision dynamics simula ions, which na u ally includes
bo h hyd odynamics and he mal e ec s [443,444].
As men ioned p e iously, Snezhko e al. [365,396,445] also
demons a ed ha he coupling be ween he collec i e esponse o
e omagne ic colloidal pa icles unde al e na ing magne ic ields and
he su ace wa es gene a ed a liquid-ai in e aces is esponsible o he
o ma ion o dynamical sel -assembled dynamical pa e ns. The s uc-
u e and dynamics o such s uc u es was heo e ically desc ibed
h ough bo h a con inuum phenomenological app oach and also a
mic oscopic model which couple he dynamics o su ace wa es wi h he
Na ie -S okes equa ions o he low [445]. I was shown la e on ha
such s uc u es could be used as sel -p opelling agen s [396]. The
anspo on sel -assembled dynamical s uc u es was also s udied in he
wo k by Ma ínez-Ped e o e al. [446], whe e B ownian dynamics
simula ions we e used o in es iga e he dynamics o wo ypes o
supe pa amagne ic pa icles o di e en size in a luid- luid in e ace
unde p ecessing ields. The au ho s demons a ed ha unde such
ac ua ion, sel -assembled la ices o med by one ype o pa icle could be
c ea ed and, simul aneously, anspo o he o he ype could be
es ablished om node o node o he la ice.
7.2.2. Clus e ing and phase sepa a ion o ac i e pa icles
So a , he heo e ical modelling o ac i e pa icle sys ems used o
s udy hei collec i e eme ge ging e ec s, e.g., sel -assembly, has been
mos ly done conside ing highly simpli ied models. In hese models,
hyd odynamic in e ac ions a e o en neglec ed o conside ed in an
e ec i e manne , and in mos cases he sys ems conside ed a e es ic ed
o mo e on a plane. Howe e , some o he conclusions d awn om hese
s udies should be gene al, in he sense ha hey should be applicable o
p ocesses whe e such es ic ions a e no imposed, and ha e been used
o p edic and in e p e expe imen al beha io o ac i e pa icles a
liquid in e aces.
The sole capaci y o pa icles o sel -p opel was shown o induce he
o ma ion o dynamic clus e s (li ing c ys als), e en i hei mu ual in-
e ac ions a e epulsi e and no alignmen in e ac ions a e included
[447–450]. This is e lec ed in long-li ed densi y luc ua ions and
anomalous clus e ing. While a sys em o N passi e pa icles in a olume
V exhibi s numbe luc ua ions o ΔN ~ √ N, he numbe luc ua ions in
ac i e pa icle sys ems scales as ΔN ~ N
α
, whe e
α
can become o o de 1
in wo dimensional sys ems [451,452]. The p inciple o such clus e
o ma ion can be explained quali a i ely. Ac i e pa icles ollow a
di usi e dynamics wi h long pe sis ence leng h in absence o o he
pa icles. When hey collide wi h o he pa icles hei eloci y is educed
due o excluded olume in e ac ion, since i impedes mo ion induced by
he ac i e o ce. I he cha ac e is ic ime o eo ien and escape om he
collision is la ge han he cha ac e is ic ime o encoun e ano he
pa icle clus e ing will occu .
In ac , sel -mobili y alone was shown o induce he sepa a ion o
pa icles in o a dense and dilu e luid phases (Mo ili y Induced Phase
E. Guzm´
an e al.
Ad ances in Colloid and In e ace Science 302 (2022) 102620
35
Sepa a ion, MIPS). This a he mal ansi ion was sugges ed by Tailleu
and Ca es [447] using heo e ical a gumen s on a one-dimensional
sys em and la e on i was shown using compu e simula ions o discs
mo ing in a 2D plane [448–450]. Expe imen al e idence o clus e ing
and phase sepa a ion o such ac i e sys ems was gi en la e on
[453,454]. The na u e o he ansi ion o he mobili y induced phase
sepa a ed s a e has been widely in es iga ed om a heo e ical pe se-
pec i e [447,455–461]. In case o ac i e b ownian pa icles wi h no
alignmen in e ac ions, he p essu e exe ed by he sys em was
demons a ed o be a s a e unc ion independen o he in e ac ion wi h
he walls [455–457], and p essu e- olume non-equilib ium phase dia-
g ams we e ob ained. The MIPS ansi ion was ound o sa is y he
cha ac e is ic p ope ies o an equilib ium i s -o de liquid-gas phase
ansi ion [461]. The o igin o phase sepa a ion was a ibu ed o me-
chanical [455,456] and di usi e ins abili ies [447,459,460]. To con ol
he size o he dynamic clus e s, sys ems o ac i e b ownian pa icles
mo ing on a plane and in e ac ing h ough a sho ange a ac ion and a
long- ange so epulsion ha e been s udied using compu e simula ions
[462].
In p ac ice, mos ac i e and ac ua ed pa icles used in expe imen
de elop aligning in e ac ions bo h wi h o he pa icles and he con aine
walls. These can be o igina ed, o example, om hyd odynamic in-
e ac ions [463], s e ic in e ac ions o geome ically aniso opic pa -
icles [464], o elec os a eic in e ac ions [416]. Such in e ac ions can
lead o he eme gence o swa ming collec i e mo ions o pa icles, as
demons a ed by analysis o he Vicsek model [465] and gene alized
e sions o i . In hese models, he di ec ion o an ac i e pa icle is
de e mined by he a e age di ec ion o he neighbo ing pa icles and a
phase ansi ion is ob ained a high enough concen a ions om a luid
o iso opically di ec ed pa icles o a s a e whe e all pa icles mo e in
he same di ec ion in he o m o bands [466,467]. Solon and co-wo ke s
demons a ed ha sys ems o ac i e pa icles wi h aligning in e ac ions
canno be desc ibed by an equa ion o s a e, since he p essu e ha hey
exe depends on he speci ic na u e o he in e ac ion wi h he wall,
which is no a unc ion o s a e [457,458]. This esul e idences he
di icul y o building a gene al heo y o desc ibe he mac oscopic ou -
o -equilib ium beha io o ac i e pa icle sys ems.
7.2.3. Seeking a p inciple o non-equilib ium sel -assembly
In equilib ium, he sel -assembly o a subse o pa icles o he sys em
occu s as a p ocess o minimize he o e all ee ene gy. Fo sel -assembly
p ocesses ou o equilib ium he e is a cons an ene gy dissipa ion and
en opy p oduc ion and in gene al he e is no a he modynamical po-
en ial which becomes a minimum a s eady s a es. In his con ex , he
ques o a gene al he modynamic c i e ion o p edic he e olu ion o
non-equilib ium sys ems and iden i y s eady s a es —in pa icula sel -
assembled s a es— has mo i a ed a g ea numbe o in es iga ions
o e he yea s.
In analogy o he second law o he modynamics, Onsage p oposed
he p inciple o leas dissipa ion o unde s and he e olu ion o non-
equilib ium sys ems [468]. Buil upon he seminal wo k o Rayleigh,
Onsage o mula es his a ia ional p inciple in e ms o a dissipa ion
unc ion which con ains he a e o change o en opy and he hyd o-
dynamic dissipa ion. Onsage ’s p inciple has been e y in luen ial o e
he yea s, wi h ecen applica ions being discussed [469].
Based on Onsage ’s wo k, P igogine in oduced he minimal en opy
p oduc ion heo em o unde s and s eady s a es ou o he mal equi-
lib ium. This heo em asse s ha in sys ems ou o equilib ium he a e
o p oduc ion o en opy is a minimum [470]. In dynamical sel -
assembled s a es o pa icles, his heo em would cons ain he
possible s uc u es in he s eady s a e o hose which dissipa e he leas
amoun o ene gy and consequen ly minimize he a e o en opy p o-
duc ion. The heo em is de i ed in he linea egime whe e Onsage ’s
ecip ocal ela ions hold, and unde he assump ion o local he mody-
namic equilib ium [470]. Howe e , mos o non-equilib ium s eady
s uc u es, including hose o pa icles a in e aces unde ime-
dependen ac ua ions, occu a om he mal equilib ium and he he-
o em canno be applied. In pa icula , G zybowski and co-wo ke s
s udied expe imen ally how dissipa ion dic a es he selec ion o gi en
non-equilib ium s uc u es o o a ing magne s a an in e ace, and
concluded ha he sys em does no always e ol e in o he leas dissi-
pa i e s uc u e, minimizing he en opy p oduc ion as he minimum
en opy p oduc ion claims. Ra he , hey obse ed he exis ence o
al e na i e mo e dissipa i e s uc u es al hough wi h a p obabili y
which decays exponen ially wi h he dissipa ion a e [471]. To unde -
s and s eady s a es a om equilib ium whe e local he modynamic
equilib ium canno be applied, E ans and Ba anyai p oposed an al e -
na i e app oach in e ms o an al e na i e a ia ional p inciple [472],
al hough i was ound o be only app oxima ely alid [473]
O he app oaches ha e a emp ed o desc ibe non-equilib ium s a-
iona y s a es using ex ensions o he concep o en opy. Dewa in es-
iga ed he eme gence o non-equilib ium sel o ganiza ion p ocesses
using Jaynes’ o malism o s a is ical mechanics [474,475], based on he
pa h in o ma ion en opy S
I
= − ∑
Г
p
Г
log p
Г
. He e,
Г
ep esen he
mic oscopic phase-space pa hs, wi h p obabili y p
Г
, and he sum ex ends
o all possible pa hs [474,475]. A a d o mula ed a heo y o desc ibe
non-equilib ium s a iona y s a es in oducing a second en opy o
ansi ion en opy, de ined in e ms o he numbe o molecula con-
igu a ions associa ed wi h a ansi ion be ween mac os a es a a gi en
ime [476]. The au ho hen a gues ha he nonequilib ium s eady
s a es o sys ems unde ixed he modynamic g adien s a e de ined by
he maximiza ion o his en opy, p o iding he op imum a e o change
o lux in a gi en sys em.
Recen ly, A ango-Res epo e al. [477,478] in es iga ed he o ma-
ion o sel -assembled s uc u es unde non-equilib ium condi ions.
They show ha he a chi ec u e o he o med s uc u es is de e mined
by he en opy p oduc ion in he p ocess o o ma ion. Fu he mo e,
hey demons a e ha such s uc u es a e cha ac e ized by being
ex eme alues o he en opy p oduc ion as a unc ion o a s uc u al
pa ame e , and es hei indings agains expe imen al esul s o gela-
ion p ocesses and o Liesgang ing o ma ion [477]. The same au ho s
p oposed a c i e ion o iden i y he o ma ion o sel -assembled s uc-
u es unde nonequilib ium condi ions [478]. They p opose an e ec i e
po en ial unc ion which akes in o accoun he ene gy equi ed o
change he con igu a ion o he sys em and i s s a iona y p obabili y.
Using a phenomenological app oach, hey de e mine ha he e ec i e
po en ial becomes a minimum a he s a iona y s uc u es o med by
sel -assembly in nonequilib ium condi ions. The c i e ium is success-
ully es ed agains expe imen s o Liesgang ings o ma ion and also
agains expe imen s o sel -assembly o colloidal pa icles a in e aces
unde ime-dependen ield ac ua ions. In pa icula , hey show ha he
minimiza ion o he e ec i e po en ial can p edic he mos s able
s uc u e gi en an ex e nal ac ua ion [478].
8. Po en ial applica ions o pa icle-laden luid in e aces
Colloidal pa icles con ined a luid in e aces o e many oppo u-
ni ies on he design o ma e ials. F om a p ac ical pe spec i e, he s a-
biliza ion o in e aces by using pa icles allows ob aining emulsions and
oams wi h enhanced s abili y in ela ion o hose s abilized by molec-
ula and polyme su ac an s. The combina ion o quasi-2D con inemen
o pa icles adso bed a luid in e aces wi h he ad ances in he syn-
hesis o new colloids, makes possible o ake ad an age o he mic o-
scopic complexi y o colloidal in e ace-domina ed ma e ials o he
design o new unc ional ma e ials wi h unable mac oscopic p ope ies,
which can open new a enues in di e en echnological applica ions
[44].
The con olled and guided exploi a ion o pa icle-laden luid in-
e aces equi es add essing he ela ionship exis ing be ween di e en
co ela ed aspec s, such as he cha ac e is ics o he pa icles, he deg ee
o adso p ion, he s uc u e o he eme ging assemblies and hei mag-
ne ic, elec ical o heological p ope ies. Some examples o he
E. Guzm´
an e al.
Ad ances in Colloid and In e ace Science 302 (2022) 102620
36
po en ial applica ions o pa icle-laden in e aces a e gi en in his sec-
ion, while mo e speci ic de ails can be ound in he li e a u e
[1,2,41,285].
8.1. Pa icles a luid in e aces o he s abiliza ion o emulsions and
oams
The co ela ion be ween he in e acial p ope ies o pa icle-laden
luid in e aces, and hei abili y o s abilize emulsions and oams
eme ges as a e y impo an issue in di e en echnological and in-
dus ial ields, anging om he design and manu ac u e o new ood
and cosme ics p oduc s o was ewa e o oil eco e y ea men s
[19,20,100,237]. The use o pa icle-laden luid in e aces o he s a-
biliza ion o dispe sed sys ems is widesp ead because hey p o ide no el
heological p ope ies o he luid in e ace. As a consequence, hey
imp o e long- e m s abili y in oams and emulsions because o he
educ ion o he in e acial a ea upon he quasi-i e e sible apping o
pa icles, and he mechanical s abili y p o ided by he o ma ion o a
igid p o ec i e shell o e laying he ex e nal su ace o d ople s o
bubbles, which con ibu e o hinde , a leas pa ially, he di e en
des abiliza ion p ocesses occu ing in dispe sed sys ems, e.g., c eaming
(o sedimen a ion), loccula ion, coalescence, and Os wald ipening
[14,479]. The e o e, i is possible o assume ha he s abili y and
p ope ies o emulsions and oams a e closely co ela ed o he in e a-
cial and mechanical p ope ies o single pa icula e in e aces, and ha
he laye s o adso bed pa icles help o dampen he ex e nal mechanical
pe u ba ions and hus con ibu e o minimize des abiliza ion and
up u e e en s o dispe sed sys ems [100,280].
Cu en ly i has become ob ious ha he inc ease o he su ace
densi y o pa icles adso bed a luid in e aces is c i ical o he
enhancemen o he s abili y o emulsions and oams [295,480]. P o-
cesses such as jamming and clogging o colloidal monolaye s may induce
an a es o he in e acial dynamics, which in u n minimizes he
coa sening p ocesses due o he educ ion o he in e acial ension, and
enhances he in e acial s abili y. The s abili y o emulsions and oams is
also associa ed wi h he heological p ope ies o he laye s
[58,59,236,237,481]. Thus, a high in e acial co e ages, s ong in e -
pa icle in e ac ions end o p omo e he o ma ion o pa icle-laden
in e aces wi h a mainly elas ic beha io , con olling he ilm hinning
phenomena [482]. Acco ding o he Gibbs c i e ia, which de ine he
s abili y o dispe sed sys ems in e ms o he a io be ween he in e a-
cial ension and elas ici y, emulsions and oams a e s able only when
ε
’
>γ/2. Howe e , his c i e ion only applies o emulsions and oams
o med by sphe ical d ople s o bubbles [236].
The close co ela ion be ween s abili y and su ace heology was
con i med by Sulli an and Kilpa ick [483], who ound ha he o -
ma ion o igid, s agnan pa icle ilms ia he o ma ion o pa icle
b idges, especially when he in e acial co e age is ela i ely low, e-
sul s in dispe sed sys ems wi h inc eased s abili y. Besides, he o ma-
ion o pa icle zips be ween close in e aces helps d ople s o bubbles o
agg ega e o ming s able locs, a oiding, a leas pa ially, he coales-
cence phenomena [238,480]. The inc ease o bo h he shea iscosi y
and he dila ional moduli also plays an impo an ole in he con ol o
he d ainage phenomena, which a e especially ele an o he s abili y
o oams [296]. The impac o he la e is clea ly shown in he s udies by
Ce an es-Ma ínez e al. [481]. They ound ha he esis ance agains
comp essi e s esses p esen ed by pa icle-laden luid in e aces mini-
mizes sh inkage o small bubbles and imp o es oam s abili y. Despi e
he ex ensi e esea ch e o s on seeking co ela ions be ween he
dila a ional heological p ope ies o pa icle-laden in e aces and hei
abili y o dispe sed sys em s abiliza ion, he cu en unde s anding is
a om clea , as e idenced by he s udies by San ini e al.
[4,60,61,107]. They ound no co ela ion be ween he s abili y o
dispe sed sys ems and he heological esponse o he single in e aces. A
simila conclusion was eached a when luid in e aces a e s abilized
wi h laye s o silica nanopa icles deco a ed wi h palmi ic acid
[61,106]. The abo e mix u e leads o he o ma ion o e y igid in-
e aces, wi h e y high alues o dila ional iscoelas ic modulus (>100
mN/m). Howe e , his is no enough o ensu e he s abiliza ion o he
oams [61]. A di e en s udy showed no co ela ion be ween he s a-
bili y o emulsions s abilized by he abo e men ioned mix u es and he
p ope ies o he single wa e /oil in e ace [106].
The po en ial ole o he dila a ional modulus in con olling he
s abili y o oams and emulsions is in e ed om he abo e discussion, a
leas unde some expe imen al condi ions. Howe e , he shea modulus
also plays a e y impo an ole on he s abili y o dispe sed sys ems,
mainly due o i s co ela ion o he in e acial s uc u e and packing
[276,289]. B ugge e al. [320] ound ha emulsions s abilized using
poly(N-isop opylac ylamide) pa icles we e s able only when he
pa icle-laden in e ace exhibi ed an elas ic cha ac e , whe eas iscous
in e aces, wi h high G” alues, we e easily des abilized. This coincides
wi h he apid des abiliza ion shown by asphal ene-s abilized emulsions
[484]. Appa en ly, he inc ease o he in e acial shea iscosi y en-
hances he coalescence a e (on he o de o seconds) be ween d ople s
in close con ac , whe eas he coalescence is hinde ed when he d ople s
a e coa ed by a laye wi h a mic os uc u e domina ed o he elas ic
p ope ies o he single in e aces. The di e ences in he coalescence
a e obse ed as a unc ion o he iscoelas ic p ope ies o single in-
e aces a e commonly ela ed o he exis ence o a high shea yield
s ess (~10
4
Pa), which in u n is closely co ela ed o he ilm shea
yield poin and he ilm hickness. The inc ease o he elas ic s i ness
p e en s he mobili y and up u e o he pa icle laye , and hence he
o ma ion o a solid-like ilm may in oduce an ene ge ic ba ie agains
coalescence.
The mo phology and size dis ibu ion o he d ople s and bubbles can
be modula ed by changing he size o con ac angle o he adso bed
pa icles. These pa ame e s also play a e y impo an ole on he con-
ol o he s abili y o emulsions and oams. I should be s essed ha he
s abiliza ion o emulsions and oams equi es pa ial we ing o he
pa icles o bo h luid phases. This leads o he o ma ion o oil/wa e
dispe sions in he case o hyd ophilic pa icles (θ <90◦), whe eas wa e /
oil dispe sions a e o med when he in e ace is s abilized by hyd o-
phobic pa icles (θ >90◦). The change o he pa icle we abili y by he
addi ion o su ac an can be used in he modula ion o he s abili y o
emulsions and oams [243] as demons a ed Binks e al. [111]. They
ound ha mix u es o silica nanopa icles and a bica ena y ca ionic
su ac an can s abilize di e en ypes o emulsions, wi h he su ac an
concen a ion being he con ol pa ame e dic a ing he ansi ion be-
ween he di e en emulsion ypes. In hese mix u es, he deg ee o
hyd ophobici y o he pa icles, and consequen ly hei con ac angle a
he luid in e ace, a ies as esul o hei associa ion wi h he su ac-
an molecules, wi h he in e sion poin appea ing in dispe sions s a-
bilized wi h pa icles o simila a ini y o bo h in e aces, i.e., o θ =
90◦[100]. The addi ion o a low su ac an concen a ions is no enough
o modi y signi ican ly pa icle hyd ophobici y, which emains mainly
hyd ophilic wi h a con ac angle lowe han 90◦. Hence, he s abiliza ion
o oil in wa e (o/w) emulsions should be expec ed, while he inc ease o
he su ac an concen a ion enhances he pa icle hyd ophobici y,
esul ing in a apping o he pa icles a he in e ace wi h θ >90◦, and
hence he o ma ion o wa e in oil (w/o) emulsions is ound. Fu he
inc eases in su ac an concen a ion lead o he e-hyd ophiliza ion o
he pa icles, which leads again o he o ma ion o o/w emulsions
[485]. Simila ansi ions we e ound by using chemically modi ied
pa icles [486]. The modi ica ion o he pa icle we abili y has been
also exploi ed o modula ing oam s abili y [487,488]. Howe e , o he
bes o ou knowledge, he s udy o he ansi ion om aqueous oams o
ee aqueous d ople s su ounded by a pa icle shell, e.g., d y wa e o
liquid ma bles, has no been sys ema ically done, e.g., by changing he
hyd ophobici y o he pa icles. Howe e , he e is s ong e idence o
he o ma ion o d y wa e and liquid ma bles by he use o hyd ophobic
pa icles [489,490].
Fig. 17 shows an idealized pic u e o he possible co ela ions
E. Guzm´
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Ad ances in Colloid and In e ace Science 302 (2022) 102620
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exis ing be ween he con ac angle o pa icles apped a luid in e ace
and he in e acial cu a u e in ela ion o he s abiliza ion o wa e /
apo in e aces.
I should be no ed ha he exis ence o a non-uni o m we ing o he
pa icles a he in e ace modi ies he in e acial ene ge ic landscape,
which can change he abili y o pa icles o s abilizing emulsions and
oams [102,207,272]. Fu he mo e, he de o ma ion o he con ac line
p omo ed by he weigh o la ge adso ba es may in oduce an addi ional
con ibu ion o he des abiliza ion o he dispe sed sys ems as esul o
he g a i a ional o ces [186].
Pa icle-s abilized oams and Picke ing emulsions ha e been widely
used as empla es o he manu ac u e o solid po ous ma e ials, he so-
called solid oams. This ype o sys ems can be ob ained om he
dispe sed p ecu so sys ems ollowing wo di e en app oaches: (i)
sin e ing and d ying he we sys em, o (ii) di ec solidi ica ion o he
bulk liquid phase [487,491]. Gonzenbach e al. [488] exploi ed hese
s a egies o ob ain solid oams using p ecu so liquid oams s abilized
by mix u es o pa icles and di e en sho -leng h su ac an . A simila
app oach was ollowed by Zabiegaj e al. [3,4] o he ab ica ion o
pa icle s abilized solid oams using ca bon and alumina pa icles.
Alumina-based aqueous oams we e also used by San os e al. [492] in
he p epa a ion o mac opo ous e ac o y ce amics by adding calcium
alumina e cemen as a binde . The addi ion o he binde allows
educing he ime equi ed o se ing he solid s uc u e, imp o ing i s
mechanical s eng h. Simila esul s we e ound by Finhana e al. [493].
8.2. Colloidosomes
Colloidosomes a e solid capsules o med by a shell o densely packed
pa icles wi h hei size anging om he sub-mic ome e scale o
millime e scale. They ha e as main p ope ies hei con ollable
pe meabili y and mechanical s eng h [2,494]. The mos common
me hodology o he ab ica ion o colloidosomes is based on he as-
sembly o colloidal pa icles in o emulsion d ople s ha a e locked
oge he by sin e ing o elec os a ic binding o opposi ely cha ged
polyelec oly es, a oiding he des uc ion o he shell by ans e ing
hem o a di e en luid [2,40].
Dinsmo e e al. [494] p epa ed colloidosomes by sel -assembly o
ca boxyla ed polys y ene la ex mic opa icles on he su ace o oil-in-
wa e and wa e -in-oil o emulsions d ople s. A e he assembly o he
pa icles on he su ace o he d ople , hey we e bound by hea ing he
sys em jus abou he glass ansi ion o polys y ene (a ound 105◦C).
Du ing his s ep, glyce ol was added o he aqueous phase o p e en
wa e e apo a ion. The high empe a u e equi ed o sin e ing becomes
a majo d awback in he p epa a ion o colloidosomes, which can be
pa ially o e come by using pa icles wi h a lowe glass ansi ion [495].
The sin e ing p ocess can also be pe o med locally by hea ing using
lase i adia ion, as demons a ed L´
opez-de-Luzu iaga e al. [496]. By
sel -assembly o sphe ical gold nanopa icles a he in e ace o oleic
acid (OA) nanod ople s o med in n-hexane, ollowed by lase i adia-
ion, hey ab ica ed plasmonic gold colloidosomes wi h collec i e
plasmonic abso p ions unable in su ace, size and shape.
The assembly o opposi ely cha ged polyelec oly es on pa icles has
also been exploi ed o p epa e colloidosomes and a oid he use o high
empe a u es. Go don e al. [497] used his me hodology o he as-
sembly o la ex pa icles in oluene/wa e sys ems by in oducing poly
(L-lysine) in o he aqueous phase. Du ing he assembly, he poly(L-
lysine) chains adso b on he la ex su ace, which allows locking hem
in a supe s uc u e. The o med colloidosomes we e s ong enough o
wi hs and he osmo ic s esses ha occu du ing hei ans e ence o a
di e en sol en . Ano he possibili y o ix he pa icles in colloidosomes
is he use o polyelec oly e mul ilaye s ob ained by he Laye -by-Laye
(LbL) me hod [498,499].
Colloidosomes can be also ob ained using an in e nal phase con-
aining a gelling agen . Gela ion o he in e nal phase o wa e -in-oil
colloidosomes gene a es a solid-like s uc u e, which p o ides he col-
loidosomes enough s abili y and s uc u al s eng h o p e en hei
collapse upon sol en exchange p ocesses [500]. Cay e e al. [500]
ab ica ed colloidosomes h ough he assembly o amine- unc ionalized
polys y ene la ex on wa e d ople s con aining aga ose dispe sed in
sun lowe oil a 70◦C. A e wa ds, he gela ion o he aqueous d ople s
ook place by educing he empe a u e om 70 o 20◦C. The gelling
agen can be eplaced by wax o ob ain solid capsules. This equi es
p epa ing wax-in-wa e emulsions s abilized by colloidal pa icles, a
high empe a u e, and hen he ob ained dispe sions mus be cooled
down o c ys allize he oil phase [299].
The s abili y o he colloidosomes can be imp o ed by polyme iza-
ion a e hei p epa a ion, wi hin o on he su ace o he Picke ing
p ecu so emulsions, which a o s he pa icle en apmen a he
in e ace. This app oach was ollowed by Chen e al. [501] on he
p epa a ion o pa a in in wa e emulsions s abilized by unc ionalized
silica pa icles in such a way ha a om ans e adical polyme iza ion
(ATRP) can be induced on hei su ace. Thus, a e p epa ing he
Picke ing emulsions, a polyme iza ion p ocess was induced by he
addi ion o 2-hyd oxye hyl me hac yla e in he medium, which allows
ob aining colloidosomes c oss-linked by a poly(hyd oxye hyl me hac-
yla e) ne wo k. An al e na i e app oach is o pe o m he polyme iza-
ion inside he d ople s by including inyl monome s. This s a egy was
used by Bon e al. [502], who s abilized d ople s con aining s y ene and
di inylbenzene, using poly(me hyl me hac yla e) pa icles as eac o s
o he copolyme iza ion p ocess. This p ocedu e allowed he o ma ion
o colloidosomes wi h sizes in he ange o 5-30
μ
m ein o ced by a
polys y ene co e. P ecipi a ion o a p e o med polyme in he inne co e
o he Picke ing emulsion can be exploi ed as an al e na i e o poly-
me iza ion, as was demons a ed by Cay e e al. [503]. They p epa ed
oil-in-wa e emulsions s abilized wi h silica and gold pa icles. In his
wo k, a linea poly(me hyl me hac yla e) was dissol ed in he oil phase,
a mix u e o dichlo ome hane/n-hexadecane. A e p epa ing he
emulsions dichlo ome hane was e apo a ed, a 40◦C. As he polyme is
less soluble in hexadecane han in he mix u e, he e apo a ion induced
i s p ecipi a ion on he inne walls o he capsules, blocking he ino -
ganic pa icles a he in e ace. The educ ion o he amoun o polyme
leads o a deg ada ion o he mechanical p ope ies o he ob ained
colloidosomes [504]. In he li e a u e, he e a e many o he examples
ollowing simila me hods o imp o e he s abili y o he colloidosomes
ob ained [505].
The me hodologies discussed abo e, designed o imp o e he me-
chanical s eng h o colloidosomes, o en in ol e hea ing s eps ha
should be a oided in ce ain applica ions, e.g., encapsula ion o bio-
logical compounds. This limi a ion may be o e come by choosing pa -
icles sui able o ob aining a co alen ly c oss-linked s uc u e a oom
Fig. 17. (a) Idealized ep esen a ion o he pa icle posi ion a he wa e / apo
in e ace as a unc ion o he we abili y. (b) Bending beha io o pa icle-laden
luid in e aces as unc ion o he pa icle con ac angle. Rep in ed om Yu
e al. [491], Copy igh (2021), wi h pe mission om Else ie .
E. Guzm´
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Ad ances in Colloid and In e ace Science 302 (2022) 102620
38
empe a u e [506]. The e a e many examples in he li e a u e o col-
loidosomes ein o ced by chemical c oss-linking. This idea was used by
C oll e al. [507] o he ab ica ion o colloidosomes upon he assembly
o poly-(di inylbenzene-al -maleic anhyd ide) mic osphe es a an oil/
wa e in e ace, ollowed by c oss-linking ia amide o ionic bonds. In
he o ma ion o mic ocapsules, he leng h o he c oss-linke is c i ical,
as low molecula weigh species a e o en oo small o span he gap
be ween adjacen pa icles. Co alen c oss-linking was also used in he
ein o cemen o colloidosomes o med by quan um do s [508]. Ska
e al. [509] ob ained c oss-linked CdSe/ZnS capsules by a ing-opening
me a hesis polyme iza ion o no bo nene a ached o he quan um do s,
which allows he quan um do s o be a es ed in a supe s uc u e a
oom empe a u e. Ano he s a egy used o exploi ionic c osslinking
was de eloped by A umugan e al. [510] o he ab ica ion o magne ic
colloidosomes s abilized wi h FeP pa icles. He e, complexa ion o
e py idine e he ed o he pa icle su ace wi h Fe(II) me al ion lead o
nanopa icle ne wo ks a he liquid−liquid in e ace.
Sha h e al. [511] p epa ed he mo-sensi i e colloidosomes by c oss-
linking p ima y amine unc ionalized PNIPAM pa icles wi h glu a al-
dehyde. These colloidosomes unde go a s ong educ ion o he size wi h
he inc ease o he empe a u e. The combina ion o co alen c oss-
linking and s e ic s abiliza ion is also e y popula , as e idenced he
s udy by Walsh e al. [512]. They ab ica ed colloidosomes o poly-
s y ene la ex s abilized by he adso p ion o poly(e hylene imine) qua-
e nized wi h 4- inylbenzyl chlo ide, which can be c oss-linked by using
di e en bis-epoxy polyme ic c oss-linke s. A simila app oach was
ollowed o he ab ica ion o colloidosomes by using di e en o gano-
clays [513,514] and silica pa icles [515]. Yuan e al. [516] epo ed
ano he design ha combined co alen c oss-linking wi h s e ic s abi-
liza ion, by deco a ing polys y ene pa icles wi h a poly(2-
dime hylaminoe hyl me hac yla e)-poly(me hyl me hac yla e) diblock
copolyme . The la e can be c oss-linked a he oil/wa e in e ace
hough a qua e niza ion p ocess, using 1,2-bis(2-iodoe hyloxy)e hane.
8.3. Co ee ing supp ession
Pa icles homogeneously dispe sed wi hin liquid d ople s may lead
o he o ma ion o ing-like deposi s upon e apo a ion o he sol en ,
esul ing in he so-called co ee- ing e ec [113,234]. The o ma ion o
his ype o deposi s is o en undesi able in applica ion such as inkje
p in ing, and he ab ica ion o mic o- and nanos uc u es, o coa ings,
whe e a mo e homogenous deposi ion o he ma e ial is equi ed
[517–524]. In he las yea s, he use o colloidal pa icles apped a
wa e / apo in e aces has been e y common o a comple e supp es-
sion, o pa ial mi iga ion, o he o ma ion o he co ee- ings when
sessile d ople s a e d ople s a e e apo a ed [48,149]. This is he esul o
he compe i ion be ween adso p ion a he luid/ luid in e ace and a
he solid/ luid in e ace occu ing du ing d ople e apo a ion. The e-
o e, by modula ing he p ope ies o he pa icles dispe sed wi hin he
e apo a ing d ople i is possible o modi y hei adso p ion o he in-
e aces in ol ed, which in u n p o ides a la ge deg ee o con ol o e
he mo phology o he deposi s ob ained. The la e is he esul o an
in ica e balance be ween pa icle−pa icle, pa icle− luid/ luid in e -
ace, and pa icle−subs a e in e ac ions [338].
The e a e se e al me hodological app oaches enabling he educ ion
o he co ee- ing e ec in he deposi ion d ople s con aining colloidal
pa icle suspensions. Bigioni e al. [525] con olled he o de o he sel -
assembled pa icle a ay on he solid su ace by pushing he pa icles
owa ds he luid/ luid in e ace. This was possible by a combina ion o
a apid e apo a ion o he sol en , as e han he di usion o he pa -
icles in he bulk, which a o s pa icle seg ega ion owa ds he liquid/
apo in e ace, and he appea ance o a ac i e capilla y in e ac ion
be ween pa icles once hey each o he luid in e ace. This leads o he
he o ma ion o pa icle ne wo k wi h a high deg ee o long- ange
o de , p e en ing pa ially he deposi ion o he co e- ing on he solid
su ace. Selec i e seg ega ion o he pa icles owa ds he luid in e ace
can be also s imula ed by he use o a mix u e sol en /co-sol en [526].
The combina ion o wa e wi h a co-sol en , wi h highe apo p essu e,
leads o seg ega ion o he co-sol en nea o he liquid/ apo in e acial
egion, which a o s he anspo o hyd ophobic pa icles o he
liquid/ apo in e ace whe e hey sel -assemble in o an o de ed a ay.
Su ac an -media ed in e ac ions can be also be exploi ed o modula e
he deposi ion pa e ns o pa icles on solid su aces [338]. In his case,
i was possible o adjus he elec os a ic and hyd ophobic pa i-
cle−pa icle, pa icle−in e ace, and pa icle−subs a e in e ac ions o
c ea e deposi s wi h e y di e en mo phologies, om ings o disks.
The use o pa icles wi h high hyd ophobici y (deco a ed wi h in e -
media e concen a ion o opposi ely cha ged su ac an s) leads o he
o ma ion o deposi s wi h he highes homogenei y, which is associa ed
wi h he o ma ion o a skin o colloidal pa icles a he wa e / apo
in e ace du ing e apo a ion. On he o he side, he deposi ion o pa -
icles deco a ed wi h e y low and e y high su ac an concen a ions
(highly hyd ophilic pa icles) esul s in he o ma ion o ing-like
deposi s.
Ano he possibili y o he supp ession o he co ee- ing e ec s,
p oposed by Li e al. [527], is based on he cap u e and sel -assembly o a
apidly descending liquid/ apo in e ace. This me hod equi es he use
o an en i onmen al chambe , designed o allow con ol o he em-
pe a u e and he ela i e humidi y. High empe a u e e apo a ion hin-
de s he deposi ion in he bo de o he h ee-phase con ac line,
p omo ing he o ma ion o homogeneous deposi s. This happens
because a high empe a u e he a e o descen o he liquid/ apo
in e ace is as e han he di usion o he colloidal pa icle, which a-
o s ha a pa o he pa icles can be e ained by he luid in e ace.
Thus, he jamming o he pa icles a he luid in e ace leads o an
enhancemen o he in e acial iscosi y in ela ion o ha o he bulk,
which in oduces an addi ional esis ance o he capilla y ou low and
leads o he o ma ion o uni o m deposi s.
Pa icle shape aniso opy can be also exploi ed o modula e he
mo phology o he deposi s ob ained upon e apo a ion [528]. Sphe ical
o sligh ly de o med colloidal pa icles a e usually anspo ed e y
e icien ly o he h ee-phase con ac line because o he e apo a ion-
d i en capilla y low, whe eas ellipsoidal pa icles a e deposi ed ho-
mogeneously du ing sol en e apo a ion. This di e ence is due o he
ac ha ellipsoidal pa icles can be en ained owa ds he edge o he
e apo a ing d ople s due o he ou wa d capilla y low, un il hey a e
apped by he descending liquid/ apo in e ace, whe e hey unde go
s ong a ac i e in e -pa icle o ce. These phenomena a e accompa-
nied by a s ong inc ease o he in e acial iscosi y, associa ed wi h he
adso p ion o ellipsoidal pa icles ha in oduces an addi ional esis-
ance o he ou wa d capilla y low. In colloidal suspensions o sphe ical
pa icles, he si ua ion changes signi ican ly, as he pa icles can be
deso bed om he descending in e ace due o he weakness o he in e -
pa icle a ac ion. The abo e mechanism based on he balance be ween
capilla y and hyd odynamic o ces, is qui e gene al. Thus, in sys ems
whe e he in e acial o ces a e g ea e han he hyd odynamic ones, he
o ma ion o s able pa icle ne wo ks a he in e ace is a o ed and,
he e o e, hei mig a ion owa ds he h ee-con ac line is hinde ed. On
he con a y, when he hyd odynamic o ces o e come he capilla y
o ces, he pa icles a e easily anspo ed o he con ac line, whe e hey
o m he e ogeneous deposi s [529].
Pa hasa a hy e al. [530] explo ed he e apo a ion o d ople s o
highly dilu ed suspensions con aining pa icles o diame e s om 3 o 10
mic ons o s udy he pa e n o ma ion on solid subs a es. They s a ed
ha he p ocess is go e ned by he combined e ec o g a i y and
in e acial hyd odynamic o ces, such ha when he g a i y d i en
deposi ion exceeds capilla y d i en anspo , i is possible o supp ess
he co ee ing o ma ion. They also ound he exis ence o a ansi ion in
he mo phology o he e apo a i e pa e ns, om mono- o mul ilaye s,
wi h he inc ease o he pa icle diame e and he ini ial pa icle con-
cen a ion o he suspension. Fu he mo e, hey desc ibed an o de -
diso de ansi ion, which disappea s a ela i ely high pa icle
E. Guzm´
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Ad ances in Colloid and In e ace Science 302 (2022) 102620
39
concen a ions. This ansi ion was s ongly de e mined by he o gani-
za ion o he pa icles a he edge o he deposi s.
A mo e ecen app oach o minimizing he co ee- ing e ec
in ol ed he di ec sp eading o pa icles a he liquid/ apo in e ace o
he e apo a ing d ople . This leads o a si ua ion in which he pa icles
can assemble a he in e ace du ing he e apo a ion enabling he o -
ma ion o a uni o m ilm. This occu s in h ee s eps: (i) sp eading o he
pa icles a he su ace o he e apo a ing d ople ; (ii) assembly o he
pa icles a he liquid/ apo in e ace, and (iii) se ling o he pa icle
ilm on o he subs a e upon e apo a ion. This app oach can be
exploi ed o he ab ica ion o low in e acial ensions inks con aining
colloidal pa icles and a high in e acial ension liquid, e.g., wa e o
e hanol/wa e mix u es [531,532].
Recen ly, Na h and Ray [533] demons a ed he powe o he la ice
Bol zmann me hod o p edic he 3D-mic os uc u es ob ained a e
e apo a ion o d ople s con aining nanopa icles. Fo P´
ecle numbe
abo e he uni y, non-uni o m co ee ing deposi s a e ob ained in he
icini y o he pinning egions. Besides, he inc ease o he pa e n di-
mensions and he di e ence be ween he pa e n and subs a e su ace
ene gies lead o he o ma ion o deposi s wi h s e eoscopic
mo phologies.
8.4. Fluid in e aces laden wi h ac i e/ac ua ed pa icles
Laden luid in e aces o unable colloids a e p omising candida es
o designing new sma ma e ials wi h ema kable p ope ies. Fo
example, Picke ing emulsions s abilized wi h magne ic pa icles can be
des abilized a will simply by app oaching a magne o applying a ho-
mogeneous magne ic ield. [368,399], and magne ic needles can be used
as p obes o heological cha ac e iza ion o luid in e aces [184].
Guided mo ion o ac i e and ac ua ed adso bed pa icles can be used in
he anspo o adso bed ma e a he mic oscale, in con ined en i-
onmen s, in he enhancemen o mass anspo o in he modula ion o
in e acial p ope ies. Howe e , chao ic lows gene a ed a low Rey-
nolds numbe s by dispe sions o ac i e colloids [534] can also be ha -
nessed o p omo e mixing in he mic oscale o in wa e emedia ion.
Al hough he up ake o hese eme ging applica ions in comme cial
echnologies is s ill low, we an icipa e ha adso bed ac i e colloids will
soon be egula ly employed in mic o- and nano luidic de ices and a he
luid in e aces inhe en in all li ing o ganisms, and ha ou -o -
equilib ium assemblies will be used as pilo ed ca ie s o p ecise and
a ge ed in e acial d ug anspo a biological luid in e aces, such as
o al mucosa and sali a, ea ilms o hose s abilised by lung su ac an s
[535].
9. Concluding ema ks
The impac o pa icle-laden luid in e aces in di e en p oblems
wi h in e es o academia and indus y has s imula ed o esea che s
wi h e y di e en backg ounds o deepen on he unde s anding o he
main o ces d i ing he assembly o colloidal mic o- and nano-pa icles
a luid in e aces as well as o he physico-chemical beha io o he
ob ained laye s. This is essen ial o opening new a enues allowing he
explo ai ion o he powe o pa icle-laden luid in e aces in applica-
ions, e.g., he ab ica ion o in e ace-domina ed sys ems such as oams,
emulsions and hin ilms. Also econ igu able de ices, o he modula ion
o p ocesses wi h echnological in e es , e.g. ink-je p in ing, whe e he
b oken symme y o luid in e aces becomes an ideal pla o m o he
con ining o ma e ials o ab ica e ma e ials wi h educed dimension-
ali y will bene i om pa icle laden in e aces. The e o e, he analysis
o di e en aspec s allowing he modula ion o he assembly o pa icles
a he in e ace, mainly he pa icle we abili y and he in e -pa icle
in e ac ions, and he unde s anding o he esponse o pa icle-laden
in e ace upon he applica ion o ex e nal s imuli (mechanical, he -
mal, magne ic o elec ic) become o pa amoun impo ance.
The beha io o pa icle-laden luid in e aces is go e ned by a
complex in e play be ween he indi idual and collec i e beha io o he
apped colloids which con e no el mechanical (shea and dila ional)
and unc ional p ope ies o he luid in e ace. These p ope ies eme ge
s ongly dependen on he speci ic chemis y, mop hology, we abili y
and cha ge o he conside ed colloids as well as on he modi ica ion o
hei su ace by addi ion o su ac an s o co alen binding o o he ypes
o molecules. Nowadays, he e is a easonably good unde s anding on
he beha io o single ha d pa icles a luid in e aces. Howe e , he
cu en knowledge on he beha io o so pa icles as well as o pa icle-
media ed in e ac ions and he collec i e beha io o pa icle-laden luid
in e aces emain ela i ely poo . The e o e, i is necessa y o mo e he
esea ch on pa icle-laden in e aces o such opics. In ac , he in-
e ac ions a e esponsible o he abili y o pa icle o mig a ing, being
dispe sed o assembly a he in e ace, esul ing in speci ic o de ed
s uc u es which in u n de ine he mechanical beha io o he pa icle-
laden in e ace. This is e y impo an because de ines he high s abili y
o Picke ing emulsions and pa icle-s abilized oams. Fu he mo e, he
dynamical beha io o pa icles apped a luid in e aces also equi es
u he s udies. In ac , colloid adso bed a luid in e aces show e y
di e en mo ion pa hways han colloids in he bulk. The cha ac e iza-
ion o he dynamical aspec s a e no only impo an i sel , and he po-
en ial applica ion o pa icles as mic o heological aces equi es o
unde s and he mo ion o indi idual pa icles. On he o he side, he
unde s anding o he dynamics o pa icle-laden in e aces becomes e y
impo an because hey play a e y impo an ole on he beha io on
ac i e colloids apped a luid in e aces. These o e s e y in e es ing
dynamic beha io and phase ansi ions which dese eds u he
a en ion.
This e iew has ied o p esen a b oad pe spec i e o he s udy o
pa icle-laden in e ace, which makes his e iew an excellen guide o
esea che s and echnologis add essing o i s ime p oblems ela ed
o pa icle-laden in e ace as well as o expe ienced esea che ying o
exploi he whole po en ial o pa icle-laden luid in e aces o opening
new a enues in nanoscience and nano echnology.
CRediT au ho ship con ibu ion s a emen
Edua do Guzm´
an: Concep ualiza ion, Me hodology, So wa e, Da a
cu a ion, W i ing – o iginal d a , W i ing – e iew & edi ing, In es i-
ga ion, Visualiza ion, Funding acquisi ion. Fe nando Ma ínez-
Ped e o: Concep ualiza ion, Me hodology, So wa e, Da a cu a ion,
W i ing – o iginal d a , W i ing – e iew & edi ing, In es iga ion,
Visualiza ion, Funding acquisi ion. Ca les Cale o: W i ing – o iginal
d a , W i ing – e iew & edi ing, In es iga ion. A mando Maes o:
W i ing – o iginal d a , W i ing – e iew & edi ing, In es iga ion.
F ancisco O ega: Supe ision, Valida ion, W i ing – e iew & edi ing,
Resou ces, In es iga ion, Funding acquisi ion. Ram´
on G. Rubio: Su-
pe ision, Valida ion, In es iga ion, W i ing – e iew & edi ing, Re-
sou ces, P ojec adminis a ion, Funding acquisi ion.
Decla a ion o Compe ing In e es
The au ho s decla e no con lic o in e es . The unde s had no ole in
he design o he s udy; in he collec ion, analyses, o in e p e a ion o
da a; in he w i ing o he manusc ip , o in he decision o publish he
esul s.
Acknowledgemen s
This wo k was unded by MICINN unde g an s PID2019-105343GB-
I00 and PID2019-106557GB-C21, and by EU in he amewo k o he
Eu opean Inno a i e T aining Ne wo k-Ma ie Sklodowska-Cu ie Ac ion
NanoPaIn (g an ag eemen 955612). We hank Pa icia Guisado-
Ba ado o he help in adap ing Fig. 3.
E. Guzm´
an e al.
Ad ances in Colloid and In e ace Science 302 (2022) 102620
40
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