For physically gelled colloidal suspensions, there are two routes to transform the gel from solid to liquid. One is to raise the temperature, and the other is to increase the shear deformation. In this investigation, we found that the phase boundary of this solid-to-liquid transformation exhibits a surprising Z-shaped curve in the strain-temperature plane. This nonmonotonic feature in phase transition appears to be present in various nanoparticle-filled colloidal gels with significant differences in chemical composition, filler type, structure, particle shape, average diameter, and particle size distribution. By applying the Kraus model to the breakage and restoration of filler networks and comparing our findings to nonequilibrium glassy behavior, we found that this nonmonotonic phenomenon can be theoretically predicted by combining the glassy melting kinetics of filler networks at high temperatures with the viscosity-retarded dissociation between particles at low temperatures.
REFERENCES
1.
Nair
, S. K.
, S.
Basu
, B.
Sen
, M.-H.
Lin
, A. N.
Kumar
, Y.
Yuan
, P. J.
Cullen
, and D.
Sarkar
, “Colloidal gels with tunable mechanomorphology regulate endothelial morphogenesis
,” Sci. Rep.
9
(1
), 1072
(2019
).2.
Lu
, P. J.
, and D. A.
Weitz
, “Colloidal particles: Crystals, glasses, and gels
,” Annu. Rev. Condens. Matter Phys.
4
(1
), 217
–233
(2013
). 3.
Saunders
, B. R.
, and B.
Vincent
, “Microgel particles as model colloids: Theory, properties and applications
,” Adv. Colloid Interface Sci.
80
(1
), 1
–25
(1999
). 4.
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
(7194
), 499
–503
(2008
). 5.
Joshi
, Y. M.
, “Dynamics of colloidal glasses and gels
,” Annu. Rev. Chem. Biomol. Eng.
5
(1
), 181
–202
(2014
). 6.
Sutherland
, D. N.
, “A theoretical model of floc structure
,” J. Colloid Interface Sci.
25
(3
), 373
–380
(1967
). 7.
Lazzari
, S.
, L.
Nicoud
, B.
Jaquet
, M.
Lattuada
, and M.
Morbidelli
, “Fractal-like structures in colloid science
,” Adv. Colloid Interface Sci.
235
, 1
–13
(2016
). 8.
Lu
, P. J.
, J. C.
Conrad
, H. M.
Wyss
, A. B.
Schofield
, and D. A.
Weitz
, “Fluids of clusters in attractive colloids
,” Phys. Rev. Lett.
96
(2
), 028306
(2006
). 9.
Xiong
, W.
, and X.
Wang
, “Nonlinear responses of carbon black-filled polymer solutions to forced oscillatory shear
,” J. Non-Newtonian Fluid Mech.
282
, 104319
(2020
). 10.
Wu
, K.
, J.
Zou
, and X.
Wang
, “Impacts of filler loading and particle size on the transition to linear-nonlinear dichotomy in the rheological responses of particle-filled polymer solutions
,” J. Rheol.
66
(3
), 605
–618
(2022
). 11.
Xiong
, W.
, and X.
Wang
, “Linear-nonlinear dichotomy of rheological responses in particle-filled polymer melts
,” J. Rheol.
62
(1
), 171
–181
(2018
). 12.
Liu
, A. J.
, and S. R.
Nagel
, “Jamming is not just cool any more
,” Nature
396
(6706
), 21
–22
(1998
). 13.
Trappe
, V.
, V.
Prasad
, L.
Cipelletti
, P.
Segre
, and D. A.
Weitz
, “Jamming phase diagram for attractive particles
,” Nature
411
(6839
), 772
–775
(2001
). 14.
Ciamarra
, M. P.
, M.
Nicodemi
, and A.
Coniglio
, “Recent results on the jamming phase diagram
,” Soft Matter
6
(13
), 2871
–2874
(2010
). 15.
O'Hern
, C. S.
, L. E.
Silbert
, A. J.
Liu
, and S. R.
Nagel
, “Jamming at zero temperature and zero applied stress: The epitome of disorder
,” Phys. Rev. E
68
(1
), 011306
(2003
). 16.
Robertson
, C. G.
, and X.
Wang
, “Isoenergetic jamming transition in particle-filled systems
,” Phys. Rev. Lett.
95
(7
), 075703
(2005
). 17.
Wang
, X.
, and C. G.
Robertson
, “Strain-induced nonlinearity of filled rubbers
,” Phys. Rev. E
72
(3
), 031406
(2005
). 18.
Roland
, C. M.
, Chap. 5
, in Viscoelastic Behavior of Rubbery Materials
(Oxford University
, New York
, 2011
).19.
Wang
, X.
, J. E.
Hall
, S.
Warren
, J.
Krom
, J. M.
Magistrelli
, M.
Rackaitis
, and G. G. A.
Bohm
, “Synthesis, characterization, and application of novel polymeric nanoparticles
,” Macromolecules
40
(3
), 499
–508
(2007
). 20.
Wang
, X.
, V. J.
Foltz
, M.
Rackaitis
, and G. G. A.
Böhm
, “Dispersing hairy nanoparticles in polymer melts
,” Polymer
49
(26
), 5683
–5691
(2008
). 21.
Hergenrother
, W. L.
, W. C.
Kiridena
, J. H.
Pawlow
, J. D.
Ulmer
, C. G.
Robertson
, M. C.
David
, and J. D.
Quinn
, “Nanoparticle fillers and methods of mixing into elastomers
,” US Patent 10,407,522 (2019
).22.
Rodewald
, S.
, S. K.
Henning
, and B. E.
Burkhart
, “Process for synthesizing functionalized styrene monomer
,” US patent 6,670,471 (2003
).23.
Won
, Y.-Y.
, S. P.
Meeker
, V.
Trappe
, D. A.
Weitz
, N. Z.
Diggs
, and J. I.
Emert
, “Effect of temperature on carbon-black agglomeration in hydrocarbon liquid with adsorbed dispersant
,” Langmuir
21
(3
), 924
–932
(2005
). 24.
Aoki
, Y.
, and H.
Watanabe
, “Rheology of carbon black suspensions.: III. Sol-gel transition system
,” Rheol. Acta
43
(4
), 390
–395
(2004
). 25.
Aoki
, Y.
, “Rheological characterization of carbon black/varnish suspensions
,” Colloids Surf. A Physicochem. Eng. Asp.
308
(1–3
), 79
–86
(2007
). 26.
Yang
, Y.
, E. A.
Grulke
, Z. G.
Zhang
, and G.
Wu
, “Temperature effects on the rheological properties of carbon nanotube-in-oil dispersions
,” Colloids Surf. A Physicochem. Eng. Asp.
298
(3
), 216
–224
(2007
). 27.
Fuchs
, M.
, and M. E.
Cates
, “Theory of nonlinear rheology and yielding of dense colloidal suspensions
,” Phys. Rev. Lett.
89
(24
), 248304
(2002
). 28.
Tanaka
, T.
, “Gels,” Sci. Am.
244
(1
), 124
–138
(1981
). 29.
Rasool
, N.
, T.
Yasin
, J. Y.
Heng
, and Z.
Akhter
, “Synthesis and characterization of novel pH-, ionic strength and temperature-sensitive hydrogel for insulin delivery
,” Polymer
51
(8
), 1687
–1693
(2010
). 30.
Park
, T. G.
, “Temperature modulated protein release from pH/temperature-sensitive hydrogels
,” Biomaterials
20
(6
), 517
–521
(1999
). 31.
Kabanov
, A. V.
and S. V.
Vinogradov
, “Nanogel networks including polyion polymer fragments and biological agent compositions thereof
,” U.S. Patent 6,696,089 (2004
).32.
Chauveteau
, G.
, R.
Tabary
, M.
Renard
, and A.
Omari
, “Method for preparing microgels of controlled size
,” US Patent 6,579,909 (2003
).33.
Park
, D.
, W.
Wu
, and Y.
Wang
, “A functionalizable reverse thermal gel based on a polyurethane/PEG block copolymer
,” Biomaterials
32
(3
), 777
–786
(2011
). 34.
Kraus
, G.
, “Mechanical losses in carbon-black-filled rubbers
,” J. Appl. Polym. Sci.: Appl. Polym. Symp.
39
, 75
–92
(1984
).35.
Hamaker
, H. C.
, “The London-van der waals attraction between spherical particles
,” Physica
4
(10
), 1058
–1072
(1937
). 36.
Witten
, T.
, M.
Rubinstein
, and R.
Colby
, “Reinforcement of rubber by fractal aggregates
,” J. Phys. II
3
(3
), 367
–383
(1993
).37.
Huber
, G.
, and T. A.
Vilgis
, “On the mechanism of hydrodynamic reinforcement in elastic composites
,” Macromolecules
35
(24
), 9204
–9210
(2002
). 38.
Huber
, G.
, T. A.
Vilgis
, and G.
Heinrich
, “Universal properties in the dynamical deformation of filled rubbers
,” J. Phys.: Condens. Matter
8
(29
), L409
–L412
(1996
). 39.
Heinrich
, G.
, and M.
Klüppel
, “Recent advances in the theory of filler networking in elastomers
,” Adv. Polym. Sci.
160
, 1
–44
(2002
). 40.
Lin
, M. Y.
, H. M.
Lindsay
, D. A.
Weitz
, R. C.
Ball
, R.
Klein
, and P.
Meakin
, “Universality in colloid aggregation
,” Nature
339
, 360
–362
(1989
). 41.
Chiew
, Y. C.
, and E. D.
Glandt
, “Percolation behaviour of permeable and of adhesive spheres
,” J. Phys. A: Math. Gen.
16
, 2599
–2608
(1983
). 42.
Bergenholtz
, J.
, and M.
Fuchs
, “Gel transitions in colloidal suspensions
,” J. Phys.: Condens. Matter
11
, 10171
–10182
(1999
). 43.
Bergenholtz
, J.
, and M.
Fuchs
, “Nonergodicity transitions in colloidal suspensions with attractive interactions
,” Phys. Rev. E
59
(5
), 5706
–5715
(1999
). 44.
Ramakrishnan
, S.
, V.
Gopalakrishnan
, and C. F.
Zukoski
, “Clustering and mechanics in dense depletion and thermal gels
,” Langmuir
21
, 9917
–9925
(2005
). 45.
Somogyi
, B.
, F. E.
Karasz
, L.
Trón
, and P. R.
Couchma
, “The effect of viscosity on the apparent decomposition rate on enzyme-ligand complexes
,” J. Theor. Biol.
74
(2
), 209
–216
(1978
). 46.
Welch
, G. R.
, B.
Somogyi
, J.
Matkó
, and S.
Papp
, “Effect of viscosity on enzyme-ligand dissociation II.: Role of the microenvironment
,” J. Theor. Biol.
100
(2
), 211
–238
(1983
). 47.
Deegan
, R. D.
, R. L.
Leheny
, N.
Menon
, S. R.
Nagel
, and D. C.
Venerus
, “Dynamic shear modulus of tricresyl phosphate and squalane
,” J. Phys. Chem. B
103
(20
), 4066
–4070
(1999
). 48.
Vlassopoulos
, D.
, “Colloidal star polymers: Models for studying dynamically arrested states in soft matter
,” J. Polym. Sci. Part B: Polym. Phys.
42
(16
), 2931
–2941
(2004
). 49.
Kaiser
, A.
, and A. M.
Schmidt
, “Phase behavior of polystyrene-brush-coated nanoparticles in cyclohexane
,” J. Phys. Chem. B
112
(7
), 1894
–1898
(2008
). 50.
Truzzolillo
, D.
, D.
Vlassopoulos
, and M.
Gauthier
, “Thermal melting in depletion gels of hairy nanoparticles
,” Soft Matter
9
(38
), 9088
–9093
(2013
).51.
Mongcopa
, K. I. S.
, R.
Poling-Skutvik
, R.
Ashkar
, P.
Butler
, and R.
Krishnamoorti
, “Conformational change and suppression of the Θ-temperature for solutions of polymer-grafted nanoparticles
,” Soft Matter
14
(29
), 6102
–6108
(2018
). © 2023 The Society of Rheology.
2023
The Society of Rheology
You do not currently have access to this content.