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.
References
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
).© 2017 The Society of Rheology.
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