Filler-induced strengthening is ubiquitous in materials science and is particularly well-established in polymeric nanocomposites. Despite having similar constituents, colloidal gels with solid filling exhibit distinct rheology, which is of practical interest to industry (e.g., lithium-ion batteries) yet remains poorly understood. We show, using experiments and simulations, that filling monotonically enhances the yield stress (i.e., strength) of colloidal gels while the elastic modulus (i.e., stiffness) first increases and then decreases. The latter softening effect results from a frustrated gel matrix at dense filling, evidenced by a growing interphase pressure. This structural frustration is, however, not detrimental to yielding resistance. Instead, fillers offer additional mechanical support to the gel backbone via percolating force chains, decreasing the yield strain at the same time. We develop a mechanistic picture of this phenomenology that leads us to a novel “filler-removal protocol,” making possible individual control over the strength and brittleness of a composite gel.

1.
Royall
,
C. P.
,
M. A.
Faers
,
S. L.
Fussell
, and
J. E.
Hallett
, “
Real space analysis of colloidal gels: Triumphs, challenges and future directions
,”
J. Phys.: Condens. Matter
33
,
453002
(
2021
).
2.
Bonn
,
D.
,
M. M.
Denn
,
L.
Berthier
,
T.
Divoux
, and
S.
Manneville
, “
Yield stress materials in soft condensed matter
,”
Rev. Mod. Phys.
89
,
035005
(
2017
).
3.
Sprakel
,
J.
,
S. B.
Lindström
,
T. E.
Kodger
, and
D. A.
Weitz
, “
Stress enhancement in the delayed yielding of colloidal gels
,”
Phys. Rev. Lett.
106
,
248303
(
2011
).
4.
Bantawa
,
M.
,
B.
Keshavarz
,
M.
Geri
,
M.
Bouzid
,
T.
Divoux
,
G. H.
McKinley
, and
E.
Del Gado
, “
The hidden hierarchical nature of soft particulate gels
,”
Nat. Phys.
19
,
1178
1184
(
2023
).
5.
Keshavarz
,
B.
,
D. G.
Rodrigues
,
J.-B.
Champenois
,
M. G.
Frith
,
J.
Ilavsky
,
M.
Geri
,
T.
Divoux
,
G. H.
McKinley
, and
A.
Poulesquen
, “
Time–connectivity superposition and the gel/glass duality of weak colloidal gels
,”
Proc. Natl. Acad. Sci. U.S.A.
118
,
e2022339118
(
2021
).
6.
Rose
,
S.
,
A.
Prevoteau
,
P.
Elzière
,
D.
Hourdet
,
A.
Marcellan
, and
L.
Leibler
, “
Nanoparticle solutions as adhesives for gels and biological tissues
,”
Nature
505
,
382
385
(
2014
).
7.
Ubbink
,
J.
, “
Soft matter approaches to structured foods: From ‘cook-and-look’ to rational food design?
,”
Faraday Discuss.
158
,
9
35
(
2012
).
8.
E. Del
Gado
,
D.
Fiocco
,
G.
Foffi
,
S.
Manley
,
V.
Trappe
, and
A.
Zaccone
, “Colloidal gelation,” in Fluids, Colloids and Soft Materials (John Wiley & Sons, Ltd, New York, 2016), Chap. 14, pp. 279–291.
9.
Manley
,
S.
,
H. M.
Wyss
,
K.
Miyazaki
,
J. C.
Conrad
,
V.
Trappe
,
L. J.
Kaufman
,
D. R.
Reichman
, and
D. A.
Weitz
, “
Glasslike arrest in spinodal decomposition as a route to colloidal gelation
,”
Phys. Rev. Lett.
95
,
238302
(
2005
).
10.
Patrick Royall
,
C.
,
S. R.
Williams
,
T.
Ohtsuka
, and
H.
Tanaka
, “
Direct observation of a local structural mechanism for dynamic arrest
,”
Nat. Mater.
7
,
556
561
(
2008
).
11.
Hsiao
,
L. C.
,
R. S.
Newman
,
S. C.
Glotzer
, and
M. J.
Solomon
, “
Role of isostaticity and load-bearing microstructure in the elasticity of yielded colloidal gels
,”
Proc. Natl. Acad. Sci. U.S.A.
109
,
16029
16034
(
2012
).
12.
Wang
,
Y.
,
M.
Tateno
, and
H.
Tanaka
, “
Distinct elastic properties and their origins in glasses and gels
,”
Nat. Phys.
20
,
1171
1179
(
2024
).
13.
Lu
,
P. J.
,
E.
Zaccarelli
,
F.
Ciulla
,
A. B.
Schofield
,
F.
Sciortino
, and
D. A.
Weitz
, “
Gelation of particles with short-range attraction
,”
Nature
453
,
499
503
(
2008
).
14.
Koumakis
,
N.
,
E.
Moghimi
,
R.
Besseling
,
W. C. K.
Poon
,
J. F.
Brady
, and
G.
Petekidis
, “
Tuning colloidal gels by shear
,”
Soft Matter
11
,
4640
4648
(
2015
).
15.
Gibaud
,
T.
,
N.
Dagès
,
P.
Lidon
,
G.
Jung
,
L. C.
Ahouré
,
M.
Sztucki
,
A.
Poulesquen
,
N.
Hengl
,
F.
Pignon
, and
S.
Manneville
, “
Rheoacoustic gels: Tuning mechanical and flow properties of colloidal gels with ultrasonic vibrations
,”
Phys. Rev. X
10
,
011028
(
2020
).
16.
Wei
,
M.
,
M. Y.
Ben Zion
, and
O.
Dauchot
, “
Reconfiguration, interrupted aging, and enhanced dynamics of a colloidal gel using photoswitchable active doping
,”
Phys. Rev. Lett.
131
,
018301
(
2023
).
17.
Omar
,
A. K.
,
Y.
Wu
,
Z.-G.
Wang
, and
J. F.
Brady
, “
Swimming to stability: Structural and dynamical control via active doping
,”
ACS Nano
13
,
560
572
(
2019
).
18.
Muhammed Shameem
,
M.
,
S.
Sasikanth
,
R.
Annamalai
, and
R.
Ganapathi Raman
, “
A brief review on polymer nanocomposites and its applications
,”
Mater. Today: Proc.
45
,
2536
2539
(
2021
).
19.
Spanoudakis
,
J.
, and
R. J.
Young
, “
Crack propagation in a glass particle-filled epoxy resin
,”
J. Mater. Sci.
19
,
473
486
(
1984
).
20.
Moosberg-Bustnes
,
H.
,
B.
Lagerblad
, and
E.
Forssberg
, “
The function of fillers in concrete
,”
Mater. Struct.
37
,
74
81
(
2004
).
21.
Ganesan
,
V.
, and
A.
Jayaraman
, “
Theory and simulation studies of effective interactions, phase behavior and morphology in polymer nanocomposites
,”
Soft Matter
10
,
13
38
(
2014
).
22.
Mahaut
,
F.
,
X.
Chateau
,
P.
Coussot
, and
G.
Ovarlez
, “
Yield stress and elastic modulus of suspensions of noncolloidal particles in yield stress fluids
,”
J. Rheol.
52
,
287
313
(
2008
).
23.
Jiang
,
Y.
,
S.
Makino
,
J. R.
Royer
, and
W. C. K.
Poon
, “
Flow-switched bistability in a colloidal gel with non-Brownian grains
,”
Phys. Rev. Lett.
128
,
248002
(
2022
).
24.
Li
,
Y.
,
J. R.
Royer
,
J.
Sun
, and
C.
Ness
, “
Impact of granular inclusions on the phase behavior of colloidal gels
,”
Soft Matter
19
,
1342
1347
(
2023
).
25.
Jiang
,
Y.
, and
R.
Seto
, “
Colloidal gelation with non-sticky particles
,”
Nat. Commun.
14
(
1
),
2773
(
2023
).
26.
Ferreiro-Córdova
,
C.
,
G.
Foffi
,
O.
Pitois
,
C.
Guidolin
,
M.
Schneider
, and
A.
Salonen
, “
Stiffening colloidal gels by solid inclusions
,”
Soft Matter
18
,
2842
2850
(
2022
).
27.
Jia
,
D.
,
H.
Cheng
, and
C. C.
Han
, “
Interplay between caging and bonding in binary concentrated colloidal suspensions
,”
Langmuir
34
,
3021
3029
(
2018
).
28.
Jia
,
D.
,
J. V.
Hollingsworth
,
Z.
Zhou
,
H.
Cheng
, and
C. C.
Han
, “
Coupling of gelation and glass transition in a biphasic colloidal mixture—From gel-to-defective gel-to-glass
,”
Soft Matter
11
,
8818
8826
(
2015
).
29.
Duduta
,
M.
,
B.
Ho
,
V. C.
Wood
,
P.
Limthongkul
,
V. E.
Brunini
,
W. C.
Carter
, and
Y.-M.
Chiang
, “
Semi-solid lithium rechargeable flow battery
,”
Adv. Energy Mater.
1
,
511
516
(
2011
).
30.
Mohraz
,
A.
,
E. R.
Weeks
, and
J. A.
Lewis
, “
Structure and dynamics of biphasic colloidal mixtures
,”
Phys. Rev. E
77
,
060403
(
2008
).
31.
Dellatolas
,
I.
,
M.
Bantawa
,
B.
Damerau
,
M.
Guo
,
T.
Divoux
,
E.
Del Gado
, and
I.
Bischofberger
, “
Local mechanism governs global reinforcement of nanofiller-hydrogel composites
,”
ACS Nano
17
,
20939
20948
(
2023
).
32.
Das
,
D.
,
T.
Kar
, and
P. K.
Das
, “
Gel-nanocomposites: Materials with promising applications
,”
Soft Matter
8
,
2348
2365
(
2012
).
33.
Park
,
J. H.
,
S. H.
Sung
,
S.
Kim
, and
K. H.
Ahn
, “
Significant agglomeration of conductive materials and the dispersion state change of the Ni-rich NMC-based cathode slurry during storage
,”
Ind. Eng. Chem. Res.
61
,
2100
2109
(
2022
).
34.
Larsen
,
T.
,
J. R.
Royer
,
F. H. J.
Laidlaw
,
W. C. K.
Poon
,
T.
Larsen
,
S. J.
Andreasen
, and
J. D. C.
Christiansen
, “
Controlling the rheo-electric properties of graphite/carbon black suspensions by ‘flow switching’
,”
Rheol. Acta
63
,
283
289
(
2024
).
35.
Pradeep
,
S.
,
P. E.
Arratia
, and
D. J.
Jerolmack
, “Origins of complexity in the rheology of soft earth suspensions,” arXiv:2312.15092[cond-mat.soft] (2023).
36.
Suratwala
,
T.
,
M.
Hanna
,
E.
Miller
,
P.
Whitman
,
I.
Thomas
,
P.
Ehrmann
,
R.
Maxwell
, and
A.
Burnham
, “
Surface chemistry and trimethylsilyl functionalization of Stöber silica sols
,”
J. Non-Cryst. Solids
316
,
349
363
(
2003
).
37.
Thompson
,
A. P.
,
H. M.
Aktulga
,
R.
Berger
,
D. S.
Bolintineanu
,
W. M.
Brown
,
P. S.
Crozier
,
P. J.
in’t Veld
,
A.
Kohlmeyer
,
S. G.
Moore
,
T. D.
Nguyen
,
R.
Shan
,
M. J.
Stevens
,
J.
Tranchida
,
C.
Trott
, and
S. J.
Plimpton
, “
LAMMPS—A flexible simulation tool for particle-based materials modeling at the atomic, meso, and continuum scales
,”
Comput. Phys. Commun.
271
,
108171
(
2022
).
38.
Though still weaker than the hydrophobic attraction in experiments ( 10 2 k B T), we confirm that such a value causes irreversible bonding and is sufficient to produce a fractal gel network, similar to that resulting from stronger attraction.
39.
Viehman
,
D. C.
, and
K. S.
Schweizer
, “
Theory of gelation, vitrification, and activated barrier hopping in mixtures of hard and sticky spheres
,”
J. Chem. Phys.
128
,
084509
(
2008
).
40.
Eberle
,
A. P. R.
,
R.
Castañeda-Priego
,
J. M.
Kim
, and
N. J.
Wagner
, “
Dynamical arrest, percolation, gelation, and glass formation in model nanoparticle dispersions with thermoreversible adhesive interactions
,”
Langmuir
28
,
1866
1878
(
2012
).
41.
Colombo
,
J.
, and
E.
Del Gado
, “
Stress localization, stiffening, and yielding in a model colloidal gel
,”
J. Rheol.
58
,
1089
1116
(
2014
).
42.
Stukowski
,
A.
, “
Visualization and analysis of atomistic simulation data with OVITO—The open visualization tool
,”
Model. Simul. Mater. Sci. Eng.
18
,
015012
(
2009
).
43.
Differing from conventional creep test, we do not equilibrate the sample (by either replacing with a fresh sample or applying the rejuvenation-recovery protocol) between each imposed stress-step, because of the limited amount of samples and aging effects.
44.
Cabriolu
,
R.
,
J.
Horbach
,
P.
Chaudhuri
, and
K.
Martens
, “
Precursors of fluidisation in the creep response of a soft glass
,”
Soft Matter
15
,
415
423
(
2019
).
45.
Shih
,
W.-H.
,
W. Y.
Shih
,
S.-I.
Kim
,
J.
Liu
, and
I. A.
Aksay
, “
Scaling behavior of the elastic properties of colloidal gels
,”
Phys. Rev. A
42
,
4772
4779
(
1990
).
46.
Kao
,
P.-K.
,
M. J.
Solomon
, and
M.
Ganesan
, “
Microstructure and elasticity of dilute gels of colloidal discoids
,”
Soft Matter
18
,
1350
1363
(
2022
).
47.
Petekidis
,
G.
, and
N. J.
Wagner
, “Rheology of colloidal glasses and gels,” in Theory and Applications of Colloidal Suspension Rheology, Cambridge Series in Chemical Engineering, edited by N. J. Wagner and J. Mewis (Cambridge University, Cambridge, 2021), pp. 173–226.
48.
Barwich
,
S.
, and
M. E.
Möbius
, “
The elastic response of graphene oxide gels as a crumpling phenomenon
,”
Soft Matter
18
,
8223
8228
(
2022
).
49.
Roy
,
S.
, and
M. S.
Tirumkudulu
, “
Micro-mechanical theory of shear yield stress for strongly flocculated colloidal gel
,”
Soft Matter
16
,
1801
1809
(
2020
).
50.
Meyer
,
E. E.
,
K. J.
Rosenberg
, and
J.
Israelachvili
, “
Recent progress in understanding hydrophobic interactions
,”
Proc. Natl. Acad. Sci. U.S.A.
103
,
15739
15746
(
2006
).
51.
Santos
,
A. P.
,
D. S.
Bolintineanu
,
G. S.
Grest
,
J. B.
Lechman
,
S. J.
Plimpton
,
I.
Srivastava
, and
L. E.
Silbert
, “
Granular packings with sliding, rolling, and twisting friction
,”
Phys. Rev. E
102
,
032903
(
2020
).
52.
Guazzelli
,
É.
, and
O.
Pouliquen
, “
Rheology of dense granular suspensions
,”
J. Fluid Mech.
852
,
P1
(
2018
).
53.
Gravelle
,
A. J.
, and
A. G.
Marangoni
, “
A new fractal structural-mechanical theory of particle-filled colloidal networks with heterogeneous stress translation
,”
J. Colloid Interface Sci.
598
,
56
68
(
2021
).
54.
Zhang
,
S.
,
E.
Stanifer
,
V. V.
Vasisht
,
L.
Zhang
,
E.
Del Gado
, and
X.
Mao
, “
Prestressed elasticity of amorphous solids
,”
Phys. Rev. Res.
4
,
043181
(
2022
).
55.
Sorichetti
,
V.
,
V.
Hugouvieux
, and
W.
Kob
, “
Structure and dynamics of a polymer-nanoparticle composite: Effect of nanoparticle size and volume fraction
,”
Macromolecules
51
,
5375
5391
(
2018
).
56.
Tsurusawa
,
H.
,
S.
Arai
, and
H.
Tanaka
, “
A unique route of colloidal phase separation yields stress-free gels
,”
Sci. Adv.
6
,
eabb8107
(
2020
).
57.
Zhang
,
H.
,
W.
You
,
F.
Bian
, and
W.
Yu
, “
Heterogeneous percolation in poly(methylvinylsiloxane)/silica nanocomposites: The role of polymer–particle interaction
,”
Macromolecules
55
,
8834
8845
(
2022
).
58.
The quantitative difference may result from the difference in interaction range and contact mechanics.
59.
Tian
,
B.
,
X.
Liu
,
C.
Yu
,
F.
Gao
,
Q.
Luo
,
S.
Xie
,
B.
Tu
, and
D.
Zhao
, “
Microwave assisted template removal of siliceous porous materials
,”
Chem. Commun.
(
11
),
1186
1187
(
2002
).
60.
Poon
,
W.
, and
M.
Haw
, “
Mesoscopic structure formation in colloidal aggregation and gelation
,”
Adv. Colloid Interface Sci.
73
,
71
126
(
1997
).
61.
van Doorn
,
J. M.
,
J. E.
Verweij
,
J.
Sprakel
, and
J.
van der Gucht
, “
Strand plasticity governs fatigue in colloidal gels
,”
Phys. Rev. Lett.
120
,
208005
(
2018
).
62.
Nabizadeh
,
M.
,
F.
Nasirian
,
X.
Li
,
Y.
Saraswat
,
R.
Waheibi
,
L. C.
Hsiao
,
D.
Bi
,
B.
Ravandi
, and
S.
Jamali
, “
Network physics of attractive colloidal gels: Resilience, rigidity, and phase diagram
,”
Proc. Natl. Acad. Sci. U.S.A.
121
,
e2316394121
(
2024
).
63.
Dokholyan
,
N. V.
,
Y.
Lee
,
S. V.
Buldyrev
,
S.
Havlin
,
P. R.
King
, and
H. E.
Stanley
, “
Scaling of the distribution of shortest paths in percolation
,”
J. Stat. Phys.
93
,
603
613
(
1998
).
64.
Tsurusawa
,
H.
, and
H.
Tanaka
, “
Hierarchical amorphous ordering in colloidal gelation
,”
Nat. Phys.
19
,
1171
1177
(
2023
).
65.
Keene
,
M. T. J.
,
R.
Denoyel
, and
P. L.
Llewellyn
, “
Ozone treatment for the removal of surfactant to form mcm-41 type materials
,”
Chem. Commun.
(
20
),
2203
2204
(
1998
).
66.
Ghaedi
,
H.
, and
M.
Zhao
, “
Review on template removal techniques for synthesis of mesoporous silica materials
,”
Energy Fuels
36
,
2424
2446
(
2022
).
67.
Zhang
,
X.-Z.
,
D.-Q.
Wu
, and
C.-C.
Chu
, “
Synthesis, characterization and controlled drug release of thermosensitive IPN–PNIPAAm hydrogels
,”
Biomaterials
25
,
3793
3805
(
2004
).
68.
Xie
,
M.
,
Y.
Sun
,
J.
Wang
,
Z.
Fu
,
L.
Pan
,
Z.
Chen
,
J.
Fu
, and
Y.
He
, “
Thermo-sensitive sacrificial microsphere-based bioink for centimeter-scale tissue with angiogenesis
,”
Int. J. Bioprint
8
(
4
),
599
(
2022
).
69.
Farjami
,
T.
, and
A.
Madadlou
, “
An overview on preparation of emulsion-filled gels and emulsion particulate gels
,”
Trends Food Sci. Technol.
86
,
85
94
(
2019
).
70.
Gravelle
,
A. J.
, and
A. G.
Marangoni
, “
Effect of matrix architecture on the elastic behavior of an emulsion-filled polymer gel
,”
Food Hydrocoll.
119
,
106875
(
2021
).
71.
Torre
,
K. W.
, and
J.
de Graaf
, “
Structuring colloidal gels via micro-bubble oscillations
,”
Soft Matter
19
,
2771
2779
(
2023
).
72.
Saint-Michel
,
B.
,
G.
Petekidis
, and
V.
Garbin
, “
Tuning local microstructure of colloidal gels by ultrasound-activated deformable inclusions
,”
Soft Matter
18
,
2092
2103
(
2022
).
73.
Müller
,
F. J.
,
L.
Isa
, and
J.
Vermant
, “
Toughening colloidal gels using rough building blocks
,”
Nat. Commun.
14
(
1
),
5309
(
2023
).
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