Modulating the interaction potential between colloids suspended in a fluid can trigger equilibrium phase transitions as well as the formation of non-equilibrium “arrested states,” such as gels and glasses. Faithful representation of such interactions is essential for using simulation to interrogate the microscopic details of non-equilibrium behavior and for extrapolating observations to new regions of phase space that are difficult to explore in experiments. Although the extended law of corresponding states predicts equilibrium phases for systems with short-ranged interactions, it proves inadequate for equilibrium predictions of systems with longer-ranged interactions and for predicting non-equilibrium phenomena in systems with either short- or long-ranged interactions. These shortcomings highlight the need for new approaches to represent and disambiguate interaction potentials that replicate both equilibrium and non-equilibrium phase behavior. In this work, we use experiments and simulations to study a system with long-ranged thermoresponsive colloidal interactions and explore whether a resolution to this challenge can be found in regions of the phase diagram where temporal effects influence material state. We demonstrate that the conditions for non-equilibrium arrest by colloidal gelation are sensitive to both the shape of the interaction potential and the thermal quench rate. We exploit this sensitivity to propose a kinetics-based algorithm to extract distinct arrest conditions for candidate potentials that accurately selects between potentials that differ in shape but share the same predicted equilibrium structure. The algorithm selects the candidate that best matches the non-equilibrium behavior between simulation and experiments. Because non-equilibrium behavior in simulation is encoded entirely by the interparticle potential, the results are agnostic to the particular mechanism(s) by which arrest occurs, and so we expect our method to apply to a range of arrested states, including gels and glasses. Beyond its utility in constructing models, the method reveals that each potential has a quantitatively distinct arrest line, providing insight into how the shape of longer-ranged potentials influences the conditions for colloidal gelation.
REFERENCES
1.
G. K.
Batchelor
, “Transport properties of two-phase materials with random structure
,” Annu. Rev. Fluid Mech.
6
, 227
–255
(1974
).2.
G. K.
Batchelor
, “The effect of Brownian motion on the bulk stress in a suspension of spherical particles
,” J. Fluid Mech.
83
, 97
–117
(1977
).3.
M.
Marcotte
, A. R.
Taherian Hoshahili
, and H. S.
Ramaswamy
, “Rheological properties of selected hydrocolloids as a function of concentration and temperature
,” Food Res. Int.
34
, 695
–703
(2001
).4.
M. A.
Rao
, S. S.
Rizvi
, A. K.
Datta
, and J.
Ahmed
, Engineering Properties of Foods
(CRC Press
, 2014
).5.
Z.
Ma
and J. I.
Boye
, “Advances in the design and production of reduced-fat and reduced-cholesterol salad dressing and mayonnaise: A review
,” Food Bioprocess Technol.
6
, 648
–670
(2013
).6.
K. C.
Taylor
and H. A.
Nasr-El-Din
, “Water-soluble hydrophobically associating polymers for improved oil recovery: A literature review
,” J. Pet. Sci. Eng.
19
, 265
–280
(1998
).7.
B. J.
Maranzano
and N. J.
Wagner
, “The effects of interparticle interactions and particle size on reversible shear thickening: Hard-sphere colloidal dispersions
,” J. Rheol.
45
, 1205
–1222
(2001
).8.
H. A.
Barnes
, “Shear-thickening (‘dilatancy’) in suspensions of nonaggregating solid particles dispersed in Newtonian liquids
,” J. Rheol.
33
, 329
–366
(1989
).9.
R.
Seto
, R.
Mari
, J. F.
Morris
, and M. M.
Denn
, “Discontinuous shear thickening of frictional hard-sphere suspensions
,” Phys. Rev. Lett.
111
, 218301
(2013
).10.
J. L.
Digaum
, J. J.
Pazos
, J.
Chiles
, J.
D’Archangel
, G.
Padilla
, A.
Tatulian
, R. C.
Rumpf
, S.
Fathpour
, G. D.
Boreman
, and S. M.
Kuebler
, “Tight control of light beams in photonic crystals with spatially-variant lattice orientation
,” Opt. Express
22
, 25788
–25804
(2014
).11.
J. A.
Lucey
, M. E.
Johnson
, and D. S.
Horne
, “Invited review: Perspectives on the basis of the rheology and texture properties of cheese
,” J. Dairy Sci.
86
, 2725
–2743
(2003
).12.
D.-W.
Sun
, Thermal Food Processing: New Technologies and Quality Issues
(CRC Press
, 2012
).13.
E.
Dickinson
, “Emulsion gels: The structuring of soft solids with protein-stabilized oil droplets
,” Food Hydrocolloids
28
, 224
–241
(2012
).14.
H. Z.
Cummins
, “Liquid, glass, gel: The phases of colloidal Laponite
,” J. Non-Cryst. Solids
353
, 3891
–3905
(2007
).15.
B.
Ruzicka
and E.
Zaccarelli
, “A fresh look at the Laponite phase diagram
,” Soft Matter
7
, 1268
–1286
(2011
).16.
J. E. G. J.
Wijnhoven
and W. L.
Vos
, “Preparation of photonic crystals made of air spheres in titania
,” Science
281
, 802
–804
(1998
).17.
J. F.
Galisteo-López
, M.
Ibisate
, R.
Sapienza
, L. S.
Froufe-Pérez
, Á.
Blanco
, and C.
López
, “Self-assembled photonic structures
,” Adv. Mater.
23
, 30
–69
(2011
).18.
Z.
Yu
, C.-F.
Wang
, L.
Ling
, L.
Chen
, and S.
Chen
, “Triphase microfluidic-directed self-assembly: Anisotropic colloidal photonic crystal supraparticles and multicolor patterns made easy
,” Angew. Chem.
124
, 2425
–2428
(2012
).19.
J.
Wang
, Y.
Hu
, R.
Deng
, R.
Liang
, W.
Li
, S.
Liu
, and J.
Zhu
, “Multiresponsive hydrogel photonic crystal microparticles with inverse-opal structure
,” Langmuir
29
, 8825
–8834
(2013
).20.
L. J.
Gauckler
, T.
Graule
, and F.
Baader
, “Ceramic forming using enzyme catalyzed reactions
,” Mater. Chem. Phys.
61
, 78
–102
(1999
).21.
J. A.
Lewis
, “Colloidal processing of ceramics
,” J. Am. Ceram. Soc.
83
, 2341
–2359
(2000
).22.
G.
Bonacucina
, M.
Cespi
, M.
Misici-Falzi
, and G. F.
Palmieri
, “Colloidal soft matter as drug delivery system
,” J. Pharm. Sci.
98
, 1
–42
(2009
).23.
M. C.
Koetting
, J. T.
Peters
, S. D.
Steichen
, and N. A.
Peppas
, “Stimulus-responsive hydrogels: Theory, modern advances, and applications
,” Mater. Sci. Eng.: R: Rep.
93
, 1
–49
(2015
).24.
S. C.
Netemeyer
and E. D.
Glandt
, “Percolation behavior of the square-well fluid
,” J. Chem. Phys.
85
, 6054
–6059
(1986
).25.
L.
Mederos
and G.
Navascués
, “Phase diagram of the hard-sphere/attractive-Yukawa system
,” J. Chem. Phys.
101
, 9841
–9843
(1994
).26.
M. A.
Miller
and D.
Frenkel
, “Phase diagram of the adhesive hard sphere fluid
,” J. Chem. Phys.
121
, 535
–545
(2004
).27.
H.
Verduin
and J. K. G.
Dhont
, “Phase diagram of a model adhesive hard-sphere dispersion
,” J. Colloid Interface Sci.
172
, 425
–437
(1995
).28.
A. P. R.
Eberle
, N. J.
Wagner
, and R.
Castañeda-Priego
, “Dynamical arrest transition in nanoparticle dispersions with short-range interactions
,” Phys. Rev. Lett.
106
, 105704
(2011
).29.
A. P. R.
Eberle
, 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
).30.
31.
J.
Klein
, E.
Kumacheva
, D.
Mahalu
, D.
Perahia
, and L. J.
Fetters
, “Reduction of frictional forces between solid surfaces bearing polymer brushes
,” Nature
370
, 634
–636
(1994
).32.
J.
Klein
and E.
Kumacheva
, “Simple liquids confined to molecularly thin layers. I. Confinement-induced liquid-to-solid phase transitions
,” J. Chem. Phys.
108
, 6996
–7009
(1998
).33.
R. R.
Dagastine
, G. W.
Stevens
, D. Y. C.
Chan
, and F.
Grieser
, “Forces between two oil drops in aqueous solution measured by AFM
,” J. Colloid Interface Sci.
273
, 339
–342
(2004
).34.
A. P.
Gunning
, A. R.
Mackie
, P. J.
Wilde
, and V. J.
Morris
, “Atomic force microscopy of emulsion droplets: Probing droplet–droplet interactions
,” Langmuir
20
, 116
–122
(2004
).35.
D. G.
Grier
, “Optical tweezers in colloid and interface science
,” Curr. Opin. Colloid Interface Sci.
2
, 264
–270
(1997
).36.
E. M.
Furst
, “Applications of laser tweezers in complex fluid rheology
,” Curr. Opin. Colloid Interface Sci.
10
, 79
–86
(2005
).37.
K.
Kegler
, M.
Salomo
, and F.
Kremer
, “Forces of interaction between DNA-grafted colloids: An optical tweezer measurement
,” Phys. Rev. Lett.
98
, 058304
(2007
).38.
S. R.
Kline
, “Reduction and analysis of SANS and USANS data using IGOR Pro
,” J. Appl. Crystallogr.
39
, 895
–900
(2006
).39.
C. M.
Jeffries
, J.
Ilavsky
, A.
Martel
, S.
Hinrichs
, A.
Meyer
, J. S.
Pedersen
, A. V.
Sokolova
, and D. I.
Svergun
, “Small-angle X-ray and neutron scattering
,” Nat. Rev. Methods Primers
1
, 70
(2021
).40.
J. C.
Crocker
and D. G.
Grier
, “Microscopic measurement of the pair interaction potential of charge-stabilized colloid
,” Phys. Rev. Lett.
73
, 352
(1994
).41.
M. A.
Bevan
and S. L.
Eichmann
, “Optical microscopy measurements of kT-scale colloidal interactions
,” Curr. Opin. Colloid Interface Sci.
16
, 149
–157
(2011
).42.
A. C. H.
Coughlan
, I.
Torres-Diaz
, H. A.
Jerri
, and M. A.
Bevan
, “Direct measurements of kT-scale capsule–substrate interactions and deposition versus surfactants and polymer additives
,” ACS Appl. Mater. Interfaces
10
, 27444
–27453
(2018
).43.
J.
Schelten
and W.
Schmatz
, “Multiple-scattering treatment for small-angle scattering problems
,” J. Appl. Crystallogr.
13
, 385
–390
(1980
).44.
45.
M. G.
Noro
and D.
Frenkel
, “Extended corresponding-states behavior for particles with variable range attractions
,” J. Chem. Phys.
113
, 2941
–2944
(2000
).46.
F.
Platten
, N. E.
Valadez-Pérez
, R.
Castañeda-Priego
, and S. U.
Egelhaaf
, “Extended law of corresponding states for protein solutions
,” J. Chem. Phys.
142
, 174905
(2015
).47.
F.
Del Río
, E.
Ávalos
, R.
Espíndola
, L. F.
Rull
, G.
Jackson
, and S.
Lago
, “Vapour—Liquid equilibrium of the square-well fluid of variable range via a hybrid simulation approach
,” Mol. Phys.
100
, 2531
–2546
(2002
).48.
G.
Foffi
and F.
Sciortino
, “Extended law of corresponding states in short-range square wells: A potential energy landscape study
,” Phys. Rev. E
74
, 050401
(2006
).49.
E. B.
El Mendoub
, J.-F.
Wax
, I.
Charpentier
, and N.
Jakse
, “Integral equation study of the square-well fluid for varying attraction range
,” Mol. Phys.
106
, 2667
–2675
(2008
).50.
M. C.
Grant
and W. B.
Russel
, “Volume-fraction dependence of elastic moduli and transition temperatures for colloidal silica gels
,” Phys. Rev. E
47
, 2606
(1993
).51.
P. J.
Lu
, 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
).52.
N. A. M.
Verhaegh
, 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
).53.
S.
Buzzaccaro
, R.
Rusconi
, and R.
Piazza
, “‘Sticky’ hard spheres: Equation of state, phase diagram, and metastable gels
,” Phys. Rev. Lett.
99
, 098301
(2007
).54.
E.
Zaccarelli
, P. J.
Lu
, F.
Ciulla
, D. A.
Weitz
, and F.
Sciortino
, “Gelation as arrested phase separation in short-ranged attractive colloid–polymer mixtures
,” J. Phys.: Condens. Matter
20
, 494242
(2008
).55.
T.
Gibaud
, F.
Cardinaux
, J.
Bergenholtz
, A.
Stradner
, and P.
Schurtenberger
, “Phase separation and dynamical arrest for particles interacting with mixed potentials—The case of globular proteins revisited
,” Soft Matter
7
, 857
–860
(2011
).56.
G.
Foffi
, C.
De Michele
, F.
Sciortino
, and P.
Tartaglia
, “Arrested phase separation in a short-ranged attractive colloidal system: A numerical study
,” J. Chem. Phys.
122
, 224903
(2005
).57.
J.
Bergenholtz
and M.
Fuchs
, “Nonergodicity transitions in colloidal suspensions with attractive interactions
,” Phys. Rev. E
59
, 5706
(1999
).58.
M. E.
Helgeson
, S. E.
Moran
, H. Z.
An
, and P. S.
Doyle
, “Mesoporous organohydrogels from thermogelling photocrosslinkable nanoemulsions
,” Nat. Mater.
11
, 344
–352
(2012
).59.
Y.
Gao
, J.
Kim
, and M. E.
Helgeson
, “Microdynamics and arrest of coarsening during spinodal decomposition in thermoreversible colloidal gels
,” Soft Matter
11
, 6360
–6370
(2015
).60.
S. M.
Hashemnejad
, A. Z. M.
Badruddoza
, B.
Zarket
, C.
Ricardo Castaneda
, and P. S.
Doyle
, “Thermoresponsive nanoemulsion-based gel synthesized through a low-energy process
,” Nat. Commun.
10
, 2749
(2019
).61.
Z.
Abbasian Chaleshtari
, H.
Salimi-Kenari
, and R.
Foudazi
, “Interdroplet interactions and rheology of concentrated nanoemulsions for templating porous polymers
,” Langmuir
37
, 76
–89
(2020
).62.
S.
Fenton
, B. K.
Ryu
, P.
Padmanabhan
, T.
Nguyen
, R. N.
Zia
, and M. E.
Helgeson
, “Intersection of percolation, phase separation and glassy behavior sets minimal conditions for gelation of colloidal systems
,” Proc. Natl. Acad. Sci. U. S. A.
(2022
) (unpublished).63.
M. J.
Pagenkopp
and T. G.
Mason
, “Surfactant partitioning in nanoemulsions
,” Langmuir
34
, 10309
–10320
(2018
).64.
J.
Wu
, Y.
Liu
, W.-R.
Chen
, J.
Cao
, and S.-H.
Chen
, “Structural arrest transitions in fluids described by two Yukawa potentials
,” Phys. Rev. E
70
, 050401
(2004
).65.
Y.
Liu
, W.-R.
Chen
, and S.-H.
Chen
, “Cluster formation in two-Yukawa fluids
,” J. Chem. Phys.
122
, 044507
(2005
).66.
M.
Broccio
, D.
Costa
, Y.
Liu
, and S.-H.
Chen
, “The structural properties of a two-Yukawa fluid: Simulation and analytical results
,” J. Chem. Phys.
124
, 084501
(2006
).67.
J.-M.
Bomont
, J.-L.
Bretonnet
, and D.
Costa
, “Temperature study of cluster formation in two-Yukawa fluids
,” J. Chem. Phys.
132
, 184508
(2010
).68.
S.
Plimpton
, “Fast parallel algorithms for short-range molecular dynamics
,” J. Comput. Phys.
117
, 1
–19
(1995
).69.
M. P.
Allen
and D. J.
Tildesley
, Computer Simulation of Liquids
(Oxford University Press
, 2017
).70.
B. J.
Landrum
, 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
).71.
R. N.
Zia
, 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
).72.
P.
Segrè
, V.
Prasad
, A.
Schofield
, and D.
Weitz
, “Glasslike kinetic arrest at the colloidal-gelation transition
,” Phys. Rev. Lett.
86
, 6042
(2001
).73.
A. M.
Puertas
, M.
Fuchs
, and M. E.
Cates
, “Comparative simulation study of colloidal gels and glasses
,” Phys. Rev. Lett.
88
, 098301
(2002
).74.
C.
Gögelein
, G.
Nägele
, R.
Tuinier
, T.
Gibaud
, A.
Stradner
, and P.
Schurtenberger
, “A simple patchy colloid model for the phase behavior of lysozyme dispersions
,” J. Chem. Phys.
129
, 085102
(2008
).75.
E.
Bianchi
, R.
Blaak
, and C. N.
Likos
, “Patchy colloids: State of the art and perspectives
,” Phys. Chem. Chem. Phys.
13
, 6397
–6410
(2011
).76.
H.
Tanaka
, J.
Meunier
, and D.
Bonn
, “Nonergodic states of charged colloidal suspensions: Repulsive and attractive glasses and gels
,” Phys. Rev. E
69
, 031404
(2004
).77.
A.
Furukawa
and H.
Tanaka
, “Key role of hydrodynamic interactions in colloidal gelation
,” Phys. Rev. Lett.
104
, 245702
(2010
).78.
C. P.
Royall
, J.
Eggers
, A.
Furukawa
, and H.
Tanaka
, “Probing colloidal gels at multiple length scales: The role of hydrodynamics
,” Phys. Rev. Lett.
114
, 258302
(2015
).79.
Z.
Varga
, G.
Wang
, and J.
Swan
, “The hydrodynamics of colloidal gelation
,” Soft Matter
11
, 9009
–9019
(2015
).80.
Z.
Varga
and J.
Swan
, “Hydrodynamic interactions enhance gelation in dispersions of colloids with short-ranged attraction and long-ranged repulsion
,” Soft Matter
12
, 7670
–7681
(2016
).81.
R. P.
Mohanty
and R. N.
Zia
, “The impact of hydrodynamics on viscosity evolution in colloidal dispersions: Transient, nonlinear microrheology
,” AIChE J.
64
, 3198
–3214
(2018
).82.
J.
De Graaf
, W. C. K.
Poon
, M. J.
Haughey
, and M.
Hermes
, “Hydrodynamics strongly affect the dynamics of colloidal gelation but not gel structure
,” Soft Matter
15
, 10
–16
(2019
).83.
L. C.
Johnson
, R. N.
Zia
, E.
Moghimi
, and G.
Petekidis
, “Influence of structure on the linear response rheology of colloidal gels
,” J. Rheol.
63
, 583
–608
(2019
).84.
F.
Sciortino
, P.
Tartaglia
, and E.
Zaccarelli
, “Evidence of a higher-order singularity in dense short-ranged attractive colloids
,” Phys. Rev. Lett.
91
, 268301
(2003
).85.
B.
Derjaguin
and L.
Landau
, “Theory of the stability of strongly charged lyophobic sols and of the adhesion of strongly charged particles in solutions of electrolytes
,” Acta Physicochim. URSS
43
, 633
–662
(1941
).86.
E. J. W.
Verwey
, “Theory of the stability of lyophobic colloids
,” J. Phys. Chem.
51
, 631
–636
(1947
).87.
88.
J. G.
Barker
and J. S.
Pedersen
, “Instrumental smearing effects in radially symmetric small-angle neutron scattering by numerical and analytical methods
,” J. Appl. Crystallogr.
28
, 105
–114
(1995
).89.
B. R.
Pauw
, “Everything SAXS: Small-angle scattering pattern collection and correction
,” J. Phys.: Condens. Matter
25
, 383201
(2013
).© 2022 Author(s). Published under an exclusive license by AIP Publishing.
2022
Author(s)
You do not currently have access to this content.
