We present a systematic investigation of the structure and dynamic properties of model soft–hard colloidal mixtures. Results of a coarse-grained theoretical model are contrasted with rheological data, where the soft and hard colloids are mimicked by large star polymers with high functionality as the soft component and smaller stars with ultrahigh functionality as the hard one. Previous work by us revealed the recovery of the ergodicity of glassy soft star solutions and subsequent arrested phase separation and re-entrant solid transition upon progressive addition of small hard depletants. Here, we use different components to show that a small variation in softness has a significant impact on the state diagram of such mixtures. In particular, we establish that rendering the soft component more penetrable and modifying the size ratio bring about a remarkable shift in both the phase separation region and the glass-melting line so that the region of restored ergodicity can be notably enhanced and extended to much higher star polymer concentrations than for pure systems. We further rationalize our findings by analyzing the features of the depletion interaction induced by the smaller component that result from the interplay between the size ratio and the softness of the large component. These results demonstrate the great sensitivity of the phase behavior of entropic mixtures to small changes in the molecular architecture of the soft stars and point to the importance of accounting for details of the internal microstructure of soft colloidal particles for tailoring the flow properties of soft composites.
REFERENCES
1.
S.
Asakura
and F.
Oosawa
, “Interaction between particles suspended in solutions of macromolecules
,” J. Polym. Sci.
33
, 183
–192
(1958
).2.
A.
Vrij
, “Polymers at interfaces and the interactions in colloidal dispersions
,” Pure Appl. Chem.
48
, 471
–483
(1976
).3.
S.
Ramakrishnan
, M.
Fuchs
, K. S.
Schweizer
, and C. F.
Zukoski
, “Entropy driven phase transitions in colloid–polymer suspensions: Tests of depletion theories
,” J. Chem. Phys.
116
, 2201
–2212
(2002
).4.
S. A.
Shah
, Y.-L.
Chen
, K. S.
Schweizer
, and C. F.
Zukoski
, “Viscoelasticity and rheology of depletion flocculated gels and fluids
,” J. Chem. Phys.
119
, 8747
–8760
(2003
).5.
R.
Tuinier
and H.
Lekkerkerker
, Colloids and the Depletion Interaction
(Springer Netherlands
, 2011
).6.
K.
Binder
, P.
Virnau
, and A.
Statt
, “Perspective: The Asakura Oosawa model: A colloid prototype for bulk and interfacial phase behavior
,” J. Chem. Phys.
141
, 140901
(2014
).7.
R. S.
Hoy
and G. S.
Grest
, “Entanglements of an end-grafted polymer brush in a polymeric matrix
,” Macromolecules
40
, 8389
–8395
(2007
).8.
J. B.
Hooper
, K. S.
Schweizer
, T. G.
Desai
, R.
Koshy
, and P.
Keblinski
, “Structure, surface excess and effective interactions in polymer nanocomposite melts and concentrated solutions
,” J. Chem. Phys.
121
, 6986
–6997
(2004
).9.
U. K.
Sankar
and M.
Tripathy
, “Dispersion, depletion, and bridging of athermal and attractive nanorods in polymer melt
,” Macromolecules
48
, 432
–442
(2015
).10.
K.
Dawson
, G.
Foffi
, M.
Fuchs
, W.
Götze
, F.
Sciortino
, M.
Sperl
, P.
Tartaglia
, T.
Voigtmann
, and E.
Zaccarelli
, “Higher-order glass-transition singularities in colloidal systems with attractive interactions
,” Phys. Rev. E
63
, 011401
(2001
).11.
K. N.
Pham
, A. M.
Puertas
, J.
Bergenholtz
, S. U.
Egelhaaf
, A.
Moussaid
, P. N.
Pusey
, A. B.
Schofield
, M. E.
Cates
, M.
Fuchs
, and W. C. K.
Poon
, “Multiple glassy states in a simple model system
,” Science
296
, 104
–106
(2002
).12.
T.
Eckert
and E.
Bartsch
, “Re-entrant glass transition in a colloid-polymer mixture with depletion interactions
,” Phys. Rev. Lett.
89
, 125701
(2002
).13.
A. M.
Puertas
, M.
Fuchs
, and M. E.
Cates
, “Comparative simulation study of colloidal gels and glasses
,” Phys. Rev. Lett.
88
, 098301
(2002
).14.
A. M.
Puertas
, M.
Fuchs
, and M. E.
Cates
, “Simulation study of nonergodicity transitions: Gelation in colloidal systems with short-range attractions
,” Phys. Rev. E
67
, 031406
(2003
).15.
J.
Bergenholtz
, W. C. K.
Poon
, and M.
Fuchs
, “Gelation in model colloid-polymer mixtures
,” Langmuir
19
, 4493
–4503
(2003
).16.
K. N.
Pham
, S. U.
Egelhaaf
, P. N.
Pusey
, and W. C. K.
Poon
, “Glasses in hard spheres with short-range attraction
,” Phys. Rev. E
69
, 011503
(2004
).17.
F.
Sciortino
and P.
Tartaglia
, “Glassy colloidal systems
,” Adv. Phys.
54
, 471
–524
(2005
).18.
E.
Zaccarelli
, “Colloidal gels: Equilibrium and non-equilibrium routes
,” J. Phys.: Condens. Matter
19
, 323101
(2007
).19.
E.
Zaccarelli
and W. C. K.
Poon
, “Colloidal glasses and gels: The interplay of bonding and caging
,” Proc. Natl. Acad. Sci. U. S. A.
106
, 15203
–15208
(2009
).20.
E.
Lázaro-Lázaro
, J. A.
Perera-Burgos
, P.
Laermann
, T.
Sentjabrskaja
, G.
Pérez-Ángel
, M.
Laurati
, S. U.
Egelhaaf
, M.
Medina-Noyola
, T.
Voigtmann
, R.
Castañeda-Priego
, and L. F.
Elizondo-Aguilera
, “Glassy dynamics in asymmetric binary mixtures of hard spheres
,” Phys. Rev. E
99
, 042603
(2019
).21.
P.
Germain
and S.
Amokrane
, “Glass transition and reversible gelation in asymmetric binary mixtures: A study by mode coupling theory and molecular dynamics
,” Phys. Rev. E
100
, 042614
(2019
).22.
J.
Dzubiella
, A.
Jusufi
, C. N.
Likos
, C.
von Ferber
, H.
Löwen
, J.
Stellbrink
, J.
Allgaier
, D.
Richter
, A. B.
Schofield
, P. A.
Smith
, W. C. K.
Poon
, and P. N.
Pusey
, “Phase separation in star-polymer–colloid mixtures
,” Phys. Rev. E
64
, 010401
(2001
).23.
A. M.
Kulkarni
, A. P.
Chatterjee
, K. S.
Schweizer
, and C. F.
Zukoski
, “Depletion interactions in the protein limit: Effects of polymer density fluctuations
,” Phys. Rev. Lett.
83
, 4554
(1999
).24.
K. J.
Mutch
, J. S.
van Duijneveldt
, and J.
Eastoe
, “Colloid–polymer mixtures in the protein limit
,” Soft Matter
3
, 155
–167
(2007
).25.
D.
Truzzolillo
, D.
Marzi
, J.
Marakis
, B.
Capone
, M.
Camargo
, A.
Munam
, F.
Moingeon
, M.
Gauthier
, C. N.
Likos
, and D.
Vlassopoulos
, “Glassy states in asymmetric mixtures of soft and hard colloids
,” Phys. Rev. Lett.
111
, 208301
(2013
).26.
D.
Marzi
, B.
Capone
, J.
Marakis
, M. C.
Merola
, D.
Truzzolillo
, L.
Cipelletti
, F.
Moingeon
, M.
Gauthier
, D.
Vlassopoulos
, C. N.
Likos
, and M.
Camargo
, “Depletion, melting and reentrant solidification in mixtures of soft and hard colloids
,” Soft Matter
11
, 8296
–8312
(2015
).27.
M. C.
Merola
, D.
Parisi
, D.
Truzzolillo
, D.
Vlassopoulos
, V. D.
Deepak
, and M.
Gauthier
, “Asymmetric soft-hard colloidal mixtures: Osmotic effects, glassy states and rheology
,” J. Rheol.
62
, 63
–79
(2018
).28.
M.
Watzlawek
, C. N.
Likos
, and H.
Löwen
, “Phase diagram of star polymer solutions
,” Phys. Rev. Lett.
82
, 5289
(1999
).29.
M.
Laurati
, J.
Stellbrink
, R.
Lund
, L.
Willner
, D.
Richter
, and E.
Zaccarelli
, “Starlike micelles with starlike interactions: A quantitative evaluation of structure factors and phase diagram
,” Phys. Rev. Lett.
94
, 195504
(2005
).30.
D.
Vlassopoulos
and M.
Cloitre
, “Tunable rheology of dense soft deformable colloids
,” Curr. Opin. Colloid Interface Sci.
19
, 561
–574
(2014
).31.
T.
Gibaud
and P.
Schurtenberger
, “A closer look at arrested spinodal decomposition in protein solutions
,” J. Phys.: Condens. Matter
21
, 322201
(2009
).32.
V.
Testard
, L.
Berthier
, and W.
Kob
, “Influence of the glass transition on the liquid-gas spinodal decomposition
,” Phys. Rev. Lett.
106
, 125702
(2011
).33.
D.
Marzi
, C. N.
Likos
, and B.
Capone
, “Coarse graining of star-polymer–colloid nanocomposites
,” J. Chem. Phys.
137
, 014902
(2012
).34.
C. N.
Likos
, “Depletion interactions on soft colloids: Glass formation, melting and demixing
,” in Proceedings of the International School of Physics `Enrico Fermi’, Course CXCII on `Soft Matter Self-Assembly'
(IOS Press
, 2016
), Vol. 193, pp. 57
–80
.35.
J.-P.
Hansen
and I. R.
McDonald
, Theory of Simple Liquids: With Applications to Soft Matter
(Academic Press
, 2013
).36.
J.
Stellbrink
, J.
Allgaier
, and D.
Richter
, “Dynamics of star polymers: Evidence for a structural glass transition
,” Phys. Rev. E
56
, R3772
(1997
).37.
G.
Foffi
, F.
Sciortino
, P.
Tartaglia
, E.
Zaccarelli
, F. L.
Verso
, L.
Reatto
, K. A.
Dawson
, and C. N.
Likos
, “Structural arrest in dense star-polymer solutions
,” Phys. Rev. Lett.
90
, 238301
(2003
).38.
M.
Gauthier
and A.
Munam
, “Synthesis of 1, 4-polybutadiene dendrimer- arborescent polymer hybrids
,” Macromolecules
43
, 3672
–3681
(2010
).39.
S. T.
Milner
, M.-D.
Lacasse
, and W. W.
Graessley
, “Why χ is seldom zero for polymer- solvent mixtures
,” Macromolecules
42
, 876
–886
(2009
).40.
B. J.
Berne
and R.
Pecora
, Dynamic Light Scattering: With Applications to Chemistry, Biology, and Physics
(Courier Corporation
, 2000
).41.
C.
Pellet
and M.
Cloitre
, “The glass and jamming transitions of soft polyelectrolyte microgel suspensions
,” Soft Matter
12
, 3710
–3720
(2016
).42.
D.
Parisi
, D.
Truzzolillo
, V. D.
Deepak
, M.
Gauthier
, and D.
Vlassopoulos
, “Transition from confined to bulk dynamics in symmetric star–linear polymer mixtures
,” Macromolecules
52
, 5872
–5883
(2019
).43.
D.
Parisi
, J.
Ruiz-Franco
, Y.
Ruan
, C. Y.
Liu
, B.
Loppinet
, E.
Zaccarelli
, and D.
Vlassopoulos
, “Static and dynamic properties of block copolymer based grafted nanoparticles across the non-ergodicity transition
,” Phys. Fluids
32
, 127101
(2020
).44.
A.
Wilk
, S.
Huißmann
, E.
Stiakakis
, J.
Kohlbrecher
, D.
Vlassopoulos
, C. N.
Likos
, G.
Meier
, J. K. G.
Dhont
, G.
Petekidis
, and R.
Vavrin
, “Osmotic shrinkage in star/linear polymer mixtures
,” Eur. Phys. J. E
32
, 127
–134
(2010
).45.
N. J.
Wagner
and J.
Mewis
, Theory and Applications of Colloidal Suspension Rheology
(Cambridge University Press
, 2021
).46.
A.
Imhof
and J. K. G.
Dhont
, “Experimental phase diagram of a binary colloidal hard-sphere mixture with a large size ratio
,” Phys. Rev. Lett.
75
, 1662
(1995
).47.
M.
Daoud
and J. P.
Cotton
, “Star shaped polymers: A model for the conformation and its concentration dependence
,” J. Phys.
43
, 531
–538
(1982
).48.
C. N.
Likos
, H.
Löwen
, A.
Poppe
, L.
Willner
, J.
Roovers
, B.
Cubitt
, and D.
Richter
, “Ordering phenomena of star polymer solutions approaching the θ state
,” Phys. Rev. E
58
, 6299
(1998
).49.
L. J.
Fetters
, D. J.
Lohse
, and R. H.
Colby
, “Chain dimensions and entanglement spacings
,” in Physical Properties of Polymers Handbook
(Springer
, 2007
), pp. 447
–454
.50.
A. D.
Dinsmore
, A. G.
Yodh
, and D. J.
Pine
, “Phase diagrams of nearly-hard-sphere binary colloids
,” Phys. Rev. E
52
, 4045
(1995
).© 2021 Author(s). Published under an exclusive license by AIP Publishing.
2021
Author(s)
You do not currently have access to this content.