We investigate the spatial correlations of microscopic stresses in soft particulate gels using 2D and 3D numerical simulations. We use a recently developed theoretical framework predicting the analytical form of stress–stress correlations in amorphous assemblies of athermal grains that acquire rigidity under an external load. These correlations exhibit a pinch-point singularity in Fourier space. This leads to long-range correlations and strong anisotropy in real space, which are at the origin of force-chains in granular solids. Our analysis of the model particulate gels at low particle volume fractions demonstrates that stress–stress correlations in these soft materials have characteristics very similar to those in granular solids and can be used to identify force chains. We show that the stress–stress correlations can distinguish floppy from rigid gel networks and that the intensity patterns reflect changes in shear moduli and network topology, due to the emergence of rigid structures during solidification.
REFERENCES
1.
E. D.
Gado
, D.
Fiocco
, G.
Foffi
, S.
Manley
, V.
Trappe
, and A.
Zaccone
, “Colloidal gelation
,” in Fluids, Colloids and Soft Materials
(John Wiley & Sons, Ltd.
, 2016
), Chap. 14, pp. 279
–291
.2.
G.
Petekidis
and N. J.
Wagner
, “Rheology of colloidal glasses and gels
,” in Theory and Applications of Colloidal Suspension Rheology
(Cambridge University Press
, 2021
), pp. 173
–226
.3.
K.
Ioannidou
, M.
Kanduč
, L.
Li
, D.
Frenkel
, J.
Dobnikar
, and E.
Del Gado
, “The crucial effect of early-stage gelation on the mechanical properties of cement hydrates
,” Nat. Commun.
7
, 12106
(2016
).4.
V. J.
Anderson
and H. N. W.
Lekkerkerker
, “Insights into phase transition kinetics from colloid science
,” Nature
416
, 811
–815
(2002
).5.
C. P.
Royall
, 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
).6.
M.
Bouzid
, J.
Colombo
, L. V.
Barbosa
, and E.
Del Gado
, “Elastically driven intermittent microscopic dynamics in soft solids
,” Nat. Commun.
8
, 15846
(2017
).7.
S.
Zhang
, E.
Stanifer
, V.
Vasisht
, L.
Zhang
, E.
Del Gado
, and X.
Mao
, “Prestressed elasticity of amorphous solids
,” Phys. Rev. Res.
4
, 043181
(2021
).8.
S.
Zhang
, L.
Zhang
, M.
Bouzid
, D. Z.
Rocklin
, E.
Del Gado
, and X.
Mao
, “Correlated rigidity percolation and colloidal gels
,” Phys. Rev. Lett.
123
, 058001
(2019
).9.
M.
Leocmach
, C.
Perge
, T.
Divoux
, and S.
Manneville
, “Creep and fracture of a protein gel under stress
,” Phys. Rev. Lett.
113
, 038303
(2014
).10.
J.
Colombo
and E.
Del Gado
, “Stress localization, stiffening, and yielding in a model colloidal gel
,” J. Rheol.
58
, 1089
–1116
(2014
).11.
Z.
Filiberti
, R.
Piazza
, and S.
Buzzaccaro
, “Multiscale relaxation in aging colloidal gels: From localized plastic events to system-spanning quakes
,” Phys. Rev. E
100
, 042607
(2019
).12.
S.
Aime
, L.
Ramos
, and L.
Cipelletti
, “Microscopic dynamics and failure precursors of a gel under mechanical load
,” Proc. Natl. Acad. Sci. U. S. A.
115
, 3587
–3592
(2018
).13.
S.
Alexander
, “Amorphous solids: Their structure, lattice dynamics and elasticity
,” Phys. Rep.
296
, 65
–236
(1998
).14.
M. E.
Cates
, J. P.
Wittmer
, J.-P.
Bouchaud
, and P.
Claudin
, “Jamming, force chains, and fragile matter
,” Phys. Rev. Lett.
81
, 1841
(1998
).15.
F.
Radjai
, D. E.
Wolf
, M.
Jean
, and J.-J.
Moreau
, “Bimodal character of stress transmission in granular packings
,” Phys. Rev. Lett.
80
, 61
(1998
).16.
O.
Gendelman
, Y. G.
Pollack
, I.
Procaccia
, S.
Sengupta
, and J.
Zylberg
, “What determines the static force chains in stressed granular media?
,” Phys. Rev. Lett.
116
, 078001
(2016
).17.
H. A.
Vinutha
and S.
Sastry
, “Force networks and jamming in shear-deformed sphere packings
,” Phys. Rev. E
99
, 012123
(2019
).18.
Y.
Wang
, Y.
Wang
, and J.
Zhang
, “Connecting shear localization with the long-range correlated polarized stress fields in granular materials
,” Nat. Commun.
11
, 4349
(2020
).19.
S.
Henkes
and B.
Chakraborty
, “Statistical mechanics framework for static granular matter
,” Phys. Rev. E
79
, 061301
(2009
).20.
X.
Mao
, P. M.
Goldbart
, X.
Xing
, and A.
Zippelius
, “Soft random solids and their heterogeneous elasticity
,” Phys. Rev. E
80
, 031140
(2009
).21.
E.
DeGiuli
, “Field theory for amorphous solids
,” Phys. Rev. Lett.
121
, 118001
(2018
).22.
A.
Lemaître
, “Stress correlations in glasses
,” J. Chem. Phys.
149
, 104107
(2018
).23.
M.
Pretko
, “Generalized electromagnetism of subdimensional particles: A spin liquid story
,” Phys. Rev. B
96
, 035119
(2017
).24.
J. N.
Nampoothiri
, Y.
Wang
, K.
Ramola
, J.
Zhang
, S.
Bhattacharjee
, and B.
Chakraborty
, “Emergent elasticity in amorphous solids
,” Phys. Rev. Lett.
125
, 118002
(2020
).25.
J. N.
Nampoothiri
, M.
D’Eon
, K.
Ramola
, B.
Chakraborty
, and S.
Bhattacharjee
, “Tensor electromagnetism and emergent elasticity in jammed solids
,” Phys. Rev. E
106
, 065004
(2022
).26.
S.
Timoshenko
and J. N.
Goodier
, Theory of Elasticity: By S. Timoshenko and J. N. Goodier
(McGraw-Hill
, 1951
).27.
L.
Landau
, L.
Pitaevskii
, A.
Kosevich
, and E.
Lifshitz
, Theory of Elasticity
(Elsevier Science
, 2012
), Vol. 7.28.
R. P.
Behringer
and B.
Chakraborty
, “The physics of jamming for granular materials: A review
,” Rep. Prog. Phys.
82
, 012601
(2018
).29.
J.
Colombo
and E.
Del Gado
, “Self-assembly and cooperative dynamics of a model colloidal gel network
,” Soft Matter
10
, 4003
–4015
(2014
).30.
M.
Bouzid
and E.
Del Gado
, “Network topology in soft gels: Hardening and softening materials
,” Langmuir
34
, 773
–781
(2018
).31.
M.
Bantawa
, W. A.
Fontaine-Seiler
, P. D.
Olmsted
, and E.
Del Gado
, “Microscopic interactions and emerging elasticity in model soft particulate gels
,” J. Phys.: Condens. Matter
33
, 414001
(2021
).32.
M. G.
Noro
and D.
Frenkel
, “Extended corresponding-states behavior for particles with variable range attractions
,” J. Chem. Phys.
113
, 2941
–2944
(2000
).33.
S.
Plimpton
, “Fast parallel algorithms for short-range molecular dynamics
,” J. Comput. Phys.
117
, 1
–19
(1995
).34.
D. J.
Jacobs
and B.
Hendrickson
, “An algorithm for two-dimensional rigidity percolation: The pebble game
,” J. Comput. Phys.
137
, 346
–365
(1997
).35.
M.
Bouzid
, B.
Keshavarz
, M.
Geri
, T.
Divoux
, E.
Del Gado
, and G. H.
McKinley
, “Computing the linear viscoelastic properties of soft gels using an optimally windowed chirp protocol
,” J. Rheol.
62
, 1037
–1050
(2018
).36.
A. P.
Thompson
, S. J.
Plimpton
, and W.
Mattson
, “General formulation of pressure and stress tensor for arbitrary many-body interaction potentials under periodic boundary conditions
,” J. Chem. Phys.
131
, 154107
(2009
).37.
M.
Bantawa
, B.
Keshavarz
, M.
Geri
, M.
Bouzid
, T.
Divoux
, G. H.
McKinley
, and E.
Del Gado
, “The hidden hierarchical nature of soft particulate gels
,” arXiv:2211.03693 (2022
).38.
R. C.
Arevalo
, P.
Kumar
, J. S.
Urbach
, and D. L.
Blair
, “Stress heterogeneities in sheared type-I collagen networks revealed by boundary stress microscopy
,” PLoS One
10
, e0118021
(2015
).39.
N. Y. C.
Lin
and I.
Cohen
, “Relating microstructure and particle-level stress in colloidal crystals under increased confinement
,” Soft Matter
12
, 9058
–9067
(2016
).40.
A.
Gauthier
, M.
Pruvost
, O.
Gamache
, and A.
Colin
, “A new pressure sensor array for normal stress measurement in complex fluids
,” J. Rheol.
65
, 583
–594
(2021
).41.
J.
Dong
, F.
Turci
, R. L.
Jack
, M. A.
Faers
, and C. P.
Royall
, “Direct imaging of contacts and forces in colloidal gels
,” J. Chem. Phys.
156
, 214907
(2022
).42.
P. M.
Chaikin
, T. C.
Lubensky
, and T. A.
Witten
, Principles of Condensed Matter Physics
(Cambridge University Press
, Cambridge
, 1995
), Vol. 10.© 2023 Author(s). Published under an exclusive license by AIP Publishing.
2023
Author(s)
You do not currently have access to this content.