We explore the dynamical and mechanical characteristics of an evolving gel in diffusing wave spectroscopy (DWS) and rheometry, aiming to assess how the gel evolution impacts the creep response of the system. Our gel is formed by inducing the aggregation of thermosensitive colloids by a variation in temperature. We find experimental evidence that the long time evolution of this gel is due to two distinct processes: A coarsening process that involves the incorporation of mobile particles into the network structure and an aging process that triggers intermittent rearrangement events. While coarsening is the main process governing the evolution of the elastic properties of the gel, aging is the process determining structural relaxation. The combination of both processes in addition to stress hardening governs the creep behavior of the gel, a creep behavior that is determined by three distinct contributions: an instantaneous elastic, a delayed elastic, and a loss contribution. The systematic investigation of these contributions in recovery experiments provides evidence that losses and delayed elastic storage have a common origin, both being due to intermittent local structural relaxation events.

1.
Liu
,
A. J.
, and
S. R.
Nagel
, “
The jamming transition and the marginally jammed solid
,”
Annu. Rev. Condens. Matter Phys.
1
,
347
369
(
2010
).
2.
Lu
,
P. J.
, and
D. A.
Weitz
, “
Colloidal particles: Crystals, glasses, and gels
,”
Annu. Rev. Condens. Matter Phys.
4
,
217
233
(
2013
).
3.
Zaccarelli
,
E.
, “
Colloidal gels: Equilibrium and non-equilibrium routes
,”
J. Phys. Condens. Matter
19
,
323101
(
2007
).
4.
Cates
,
M. E.
,
M.
Fuchs
,
K.
Kroy
,
W. C. K.
Poon
, and
A. M.
Puertas
, “
Theory and simulation of gelation, arrest and yielding in attracting colloids
,”
J. Phys. Condens. Matter
16
,
S4861
S4875
(
2004
).
5.
Zia
,
R. N.
,
B. J.
Landrum
, and
W. B.
Russel
, “
A micro-mechanical study of coarsening and rheology of colloidal gels: Cage building, cage hopping, and Smoluchowski's ratchet
,”
J. Rheol.
58
,
1121
1157
(
2014
).
6.
Conrad
,
J. C.
,
H. M.
Wyss
,
V.
Trappe
,
S.
Manley
,
K.
Miyazaki
,
L. J.
Kaufman
,
A. B.
Schofield
,
D. R.
Reichman
, and
D. A.
Weitz
, “
Arrested fluid-fluid phase separation in depletion systems: Implications of the characteristic length on gel formation and rheology
,”
J. Rheol.
54
,
421
438
(
2010
).
7.
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
).
8.
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
).
9.
Meakin
,
P.
, “
Formation of fractal clusters and networks by irreversible diffusion-limited aggregation
,”
Phys. Rev. Lett.
51
,
1119
1122
(
1983
).
10.
Poon
,
W. C. K.
,
A. D.
Pirie
, and
P. N.
Pusey
, “
Gelation in colloid-polymer mixtures
,”
Faraday Discuss.
101
,
65
76
(
1995
).
11.
Verhaegh
,
N. A. M.
,
D.
Asnaghi
,
H. N. W.
Lekkerkerker
,
M.
Giglio
, and
L.
Cipelletti
, “
Transient gelation by spinodal decomposition in colloid-polymer mixtures
,”
Physica A
242
,
104
118
(
1997
).
12.
Weitz
,
D. A.
, and
M.
Oliveria
, “
Fractal structures formed by kinetic aggregation of aqueous gold colloids
,”
Phys. Rev. Lett.
52
,
1433
1436
(
1984
).
13.
Zaccarelli
,
E.
,
P. J.
Lu
,
F.
Ciulla
,
D. A.
Weitz
, and
F.
Scortino
, “
Gelation as arrested phase separation in short-ranged attractive colloid-polymer mixtures
,”
J. Phys. Condens. Matter
20
,
494242
(
2008
).
14.
Puertas
,
A. M.
,
M.
Fuchs
, and
M. E.
Cates
, “
Dynamical heterogeneities close to a colloidal gel
,”
J. Chem. Phys.
121
,
2813
2822
(
2004
).
15.
Puertas
,
A. M.
,
M.
Fuchs
, and
M. E.
Cates
, “
Dynamical heterogeneities in an attraction driven colloidal glass
,”
J. Non-Cryst. Solids
352
,
4830
4834
(
2006
).
16.
Dibble
,
C. J.
,
M.
Kogan
, and
M. J.
Solomon
, “
Structure and dynamics of colloidal depletion gels: Coincidence of transitions and heterogeneity
,”
Phys. Rev. E
74
,
041403
(
2006
).
17.
Dibble
,
C. J.
,
M.
Kogan
, and
M. J.
Solomon
, “
Structural origins of dynamical heterogeneity in colloidal gels
,”
Phys. Rev. E
77
,
050401
(
2008
).
18.
Andrade
,
E. N. D.
, “
On the viscous flow in metals, and allied phenomena
,”
Proc. R. Soc. A
84
,
1
12
(
1910
).
19.
Chen
,
M. W.
, “
Mechanical behavior of metallic glasses: Microscopic understanding of strength and ductility
,”
Annu. Rev. Mater. Res.
38
,
445
469
(
2008
).
20.
Fielding
,
S. M.
,
P.
Sollich
, and
M. E.
Cates
, “
Aging and rheology in soft materials
,”
J. Rheol.
44
,
323
369
(
2000
).
21.
Struik
,
L. C. E.
,
Physical Aging in Amorphous Polymers and Other Materials
(
Elsevier Science Ltd
,
Amsterdam
,
1978
).
22.
El-Awady
,
J. A.
, “
Unravelling the physics of size-dependent dislocation-mediated plasticity
,”
Nat. Commun.
6
,
5926
(
2015
).
23.
Miguel
,
M. C.
,
A.
Vespignani
,
M.
Zaiser
, and
S.
Zapperi
, “
Dislocation jamming and Andrade creep
,”
Phys. Rev. Lett.
89
,
165501
(
2002
).
24.
Caton
,
F.
, and
C.
Baravian
, “
Plastic behavior of some yield stress fluids: From creep to long-time yield
,”
Rheol. Acta
47
,
601
607
(
2008
).
25.
Coussot
,
P.
,
H.
Tabuteau
,
X.
Chateau
,
L.
Tocquer
, and
G.
Ovarlez
, “
Aging and solid or liquid behavior in pastes
,”
J. Rheol.
50
,
975
994
(
2006
).
26.
Grenard
,
V.
,
T.
Divoux
,
N.
Taberlet
, and
S.
Manneville
, “
Timescales in creep and yielding of attractive gels
,”
Soft Matter
10
,
1555
1571
(
2014
).
27.
Siebenburger
,
M.
,
M.
Ballauff
, and
T.
Voigtmann
, “
Creep in colloidal glasses
,”
Phys. Rev. Lett.
108
,
255701
(
2012
).
28.
Lidon
,
P.
,
L.
Villa
, and
S.
Manneville
, “
Power-law creep and residual stresses in a carbopol gel
,”
Rheol. Acta
56
,
307
323
(
2016
).
29.
Brenner
,
T.
,
S.
Matsukawa
,
K.
Nishinari
, and
R.
Johannsson
, “
Failure in a soft gel: Delayed failure and the dynamic yield stress
,”
J Non-Newtonian Fluid Mech.
196
,
1
7
(
2013
).
30.
Gopalakrishnan
,
V.
, and
C. F.
Zukoski
, “
Delayed flow in thermo-reversible colloidal gels
,”
J. Rheol.
51
,
623
644
(
2007
).
31.
Landrum
,
B. J.
,
W. B.
Russel
, and
R. N.
Zia
, “
Delayed yield in colloidal gels: Creep, flow, and re-entrant solid regimes
,”
J. Rheol.
60
,
783
807
(
2016
).
32.
Lindstrom
,
S. B.
,
T. E.
Kodger
,
J.
Sprakel
, and
D. A.
Weitz
, “
Structures, stresses, and fluctuations in the delayed failure of colloidal gels
,”
Soft Matter
8
,
3657
3664
(
2012
).
33.
Sprakel
,
J.
,
S. B.
Lindstrom
,
T. E.
Kodger
, and
D. A.
Weitz
, “
Stress enhancement in the delayed yielding of colloidal gels
,”
Phys. Rev. Lett.
106
,
248303
(
2011
).
34.
Dingenouts
,
N.
,
C.
Norhausen
, and
M.
Ballauff
, “
Observation of the volume transition in thermosensitive core-shell latex particles by small-angle X-ray scattering
,”
Macromolecules
31
,
8912
8917
(
1998
).
35.
Fournet
,
G.
, and
A.
Guinier
,
Small Angle Scattering of X-Rays
(
John Wiley & Sons
,
New York
,
1955
).
36.
Halperin
,
A.
,
M.
Kroger
, and
F. M.
Winnik
, “
Poly(N-isopropylacrylamide) phase diagrams: Fifty years of research
,”
Angew. Chem. Int. Ed. Engl.
54
,
15342
15367
(
2015
).
37.
Guo
,
H. Y.
,
S.
Ramakrishnan
,
J. L.
Harden
, and
R. L.
Leheny
, “
Gel formation and aging in weakly attractive nanocolloid suspensions at intermediate concentrations
,”
J. Chem. Phys.
135
,
154903
(
2011
).
38.
Rueb
,
C. J.
, and
C. F.
Zukoski
, “
Viscoelastic properties of colloidal gels
,”
J. Rheol.
41
,
197
218
(
1997
).
39.
Zaccone
,
A.
,
J. J.
Crassous
, and
M.
Ballauff
, “
Colloidal gelation with variable attraction energy
,”
J. Chem. Phys.
138
,
104908
(
2013
).
40.
Kantor
,
Y.
, and
I.
Webman
, “
Elastic properties of random percolating systems
,”
Phys. Rev. Lett.
52
,
1891
1894
(
1984
).
41.
DeRooij
,
R.
,
D.
Vandenende
,
M. H. G.
Duits
, and
J.
Mellema
, “
Elasticity of weakly aggregating polystyrene latex dispersions
,”
Phys. Rev. E
49
,
3038
3049
(
1994
).
42.
Romer
,
S.
,
H.
Bissig
,
P.
Schurtenberger
, and
F.
Scheffold
, “
Rheology and internal dynamics of colloidal gels from the dilute to the concentrated regime
,”
Europhys. Lett.
108
,
48006
(
2014
).
43.
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
).
44.
Weitz
,
D. A.
, and
D. J.
Pine
,
Dynamic Light Scattering
(
Oxford University
,
New York
,
1993
).
45.
Viasnoff
,
V.
,
F.
Lequeux
, and
D. J.
Pine
, “
Multispeckle diffusing-wave spectroscopy: A tool to study slow relaxation and time-dependent dynamics
,”
Rev. Sci. Instrum.
73
,
2336
2344
(
2002
).
46.
Cipelletti
,
L.
,
H.
Bissig
,
V.
Trappe
,
P.
Ballesta
, and
S.
Mazoyer
, “
Time-resolved correlation: A new tool for studying temporally heterogeneous dynamics
,”
J. Phys. Condens. Matter
15
,
S257
S262
(
2003
).
47.
Duri
,
A.
,
H.
Bissig
,
V.
Trappe
, and
L.
Cipelletti
, “
Time-resolved-correlation measurements of temporally heterogeneous dynamics
,”
Phys. Rev. E
72
,
051401
(
2005
).
48.
Scheffold
,
F.
,
S. E.
Skipetrov
,
S.
Romer
, and
P.
Schurtenberger
, “
Diffusing-wave spectroscopy of nonergodic media
,”
Phys. Rev. E
63
,
061404
(
2001
).
49.
Krall
,
A. H.
, and
D. A.
Weitz
, “
Internal dynamics and elasticity of fractal colloidal gels
,”
Phys. Rev. Lett.
80
,
778
781
(
1998
).
50.
Cipelletti
,
L.
,
L.
Ramos
,
S.
Manley
,
E.
Pitard
,
D. A.
Weitz
,
E. E.
Pashkovski
, and
M.
Johansson
, “
Universal non-diffusive slow dynamics in aging soft matter
,”
Faraday Discuss.
123
,
237
251
(
2003
).
51.
Crassous
,
J.
, and
A.
Saint-Jalmes
, “
Probing the dynamics of particles in an aging dispersion using diffusing wave spectroscopy
,”
Soft Matter
8
,
7683
7689
(
2012
).
52.
Snabre
,
P.
, and
J.
Crassous
, “
Multispeckle diffusing wave spectroscopy of colloidal particles suspended in a random packing of glass spheres
,”
Eur. Phys. J. E
29
,
149
155
(
2009
).
53.
Krall
,
A. H.
,
Z.
Huang
, and
D. A.
Weitz
, “
Dynamics of density fluctuations in colloidal gels
,”
Physica A
235
,
19
33
(
1997
).
54.
Kamp
,
S. W.
, and
M. L.
Kilfoil
, “
Universal behaviour in the mechanical properties of weakly aggregated colloidal particles
,”
Soft Matter
5
,
2438
2447
(
2009
).
55.
Koumakis
,
N.
, and
G.
Petekidis
, “
Two step yielding in attractive colloids: Transition from gels to attractive glasses
,”
Soft Matter
7
,
2456
2470
(
2011
).
56.
Manley
,
S.
,
B.
Davidovitch
,
N. R.
Davies
,
L.
Cipelletti
,
A. E.
Bailey
,
R. J.
Christianson
,
U.
Gasser
,
V.
Prasad
,
P. N.
Segre
,
M. P.
Doherty
,
S.
Sankaran
,
A. L.
Jankovsky
,
B.
Shiley
,
J.
Bowen
,
J.
Eggers
,
C.
Kurta
,
T.
Lorik
, and
D. A.
Weitz
, “
Time-dependent strength of colloidal gels
,”
Phys. Rev. Lett.
95
,
048302
(
2005
).
57.
Bissig
,
H.
,
S.
Romer
,
L.
Cipelletti
,
V.
Trappe
, and
P.
Schurtenberger
, “
Intermittent dynamics and hyper-aging in dense colloidal gels
,”
PhysChemComm
6
,
21
23
(
2003
).
58.
Puertas
,
A. M.
,
M.
Fuchs
, and
M. E.
Cates
, “
Aging in attraction-driven colloidal glasses
,”
Phys. Rev. E
75
,
031401
(
2007
).
59.
Duri
,
A.
, and
L.
Cipelletti
, “
Length scale dependence of dynamical heterogeneity in a colloidal fractal gel
,”
Europhys. Lett.
76
,
972
978
(
2006
).
60.
Durian
,
D. J.
,
D. A.
Weitz
, and
D. J.
Pine
, “
Multiple light-scattering probes of foam structure and dynamics
,”
Science
252
,
686
688
(
1991
).
61.
Chung
,
B.
,
S.
Ramakrishnan
,
R.
Bandyopadhyay
,
D.
Liang
,
C. F.
Zukoski
,
J. L.
Harden
, and
R. L.
Leheny
, “
Microscopic dynamics of recovery in sheared depletion gels
,”
Phys. Rev. Lett.
96
,
228301
(
2006
).
62.
Cipelletti
,
L.
,
S.
Manley
,
R. C.
Ball
, and
D. A.
Weitz
, “
Universal aging features in the restructuring of fractal colloidal gels
,”
Phys. Rev. Lett.
84
,
2275
2278
(
2000
).
63.
Gao
,
Y.
,
J. H.
Kim
, and
M. E.
Helgeson
, “
Microdynamics and arrest of coarsening during spinodal decomposition in thermoreversible colloidal gels
,”
Soft Matter
11
,
6360
6370
(
2015
).
64.
Teece
,
L. J.
,
M. A.
Faers
, and
P.
Bartlett
, “
Ageing and collapse in gels with long-range attractions
,”
Soft Matter
7
,
1341
1351
(
2011
).
65.
Baravian
,
C.
, and
D.
Quemada
, “
Using instrumental inertia in controlled stress rheometry
,”
Rheol. Acta
37
,
223
233
(
1998
).
66.
Ewoldt
,
R. H.
, and
G. H.
McKinley
, “
Creep ringing in rheometry or how to deal with oft-discarded data in step stress tests!
,”
Rheol. Bull.
76
,
4
6
(
2007
).
67.
Divoux
,
T.
,
C.
Barentin
, and
S.
Manneville
, “
From stress-induced fluidization processes to Herschel-Bulkley behaviour in simple yield stress fluids
,”
Soft Matter
7
,
8409
8418
(
2011
).
68.
Gibaud
,
T.
,
D.
Frelat
, and
S.
Manneville
, “
Heterogeneous yielding dynamics in a colloidal gel
,”
Soft Matter
6
,
3482
3488
(
2010
).
69.
Colombo
,
J.
, and
E.
Del Gado
, “
Stress localization, stiffening, and yielding in a model colloidal gel
,”
J. Rheol.
58
,
1089
1116
(
2014
).
70.
Argon
,
A. S.
, “
Delayed elasticity in inorganic glasses
,”
J. Appl. Phys.
39
,
4080
4086
(
1968
).
71.
Gueguen
,
Y.
,
V.
Keryvin
,
T.
Rouxel
,
M.
Le Fur
,
H.
Orain
,
B.
Bureau
,
C.
Boussard-Pledel
, and
J. C.
Sangleboeuf
, “
A relationship between non-exponential stress relaxation and delayed elasticity in the viscoelastic process in amorphous solids: Illustration on a chalcogenide glass
,”
Mech. Mater.
85
,
47
56
(
2015
).
72.
Trachenko
,
K.
, “
Slow dynamics and stress relaxation in a liquid as an elastic medium
,”
Phys. Rev. B
75
,
212201
(
2007
).
73.
Petekidis
,
G.
,
D.
Vlassopoulos
, and
P. N.
Pusey
, “
Yielding and flow of sheared colloidal glasses
,”
J. Phys. Condens. Matter
16
,
S3955
S3963
(
2004
).
74.
Uhlherr
,
P. H. T.
,
J.
Guo
,
C.
Tiu
,
X. M.
Zhang
,
J. Z. Q.
Zhou
, and
T. N.
Fang
, “
The shear-induced solid-liquid transition in yield stress materials with chemically different structures
,”
J. Nonnewtonian Fluid. Mech.
125
,
101
119
(
2005
).
You do not currently have access to this content.