Critical phenomena in colloid-polymer mixtures: Interfacial tension, order parameter, susceptibility, and coexistence diameter

Vink, R. L. C.; Horbach, Jürgen; Binder, Kurt

doi:10.1103/physreve.71.011401

Cited by 65 publications

(108 citation statements)

References 36 publications

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“…The same difficulty would occur if we would use η col , η pol as variables in a simulation of a colloid-polymer mixture in equilibrium, but there Figure 1(a) provides for a more convenient alternative, e.g. one records the probability distribution P (η col ) at fixed η r p , finding the end-points of the tie line in Figure 1(a) from the peaks of that distribution, and analyzing the merging of the peaks near criticality in terms of a finite size scaling analysis 36 . In the following, we study a model of Vicsek-like interactions between active particles.…”

Section: Model and Methodsmentioning

confidence: 99%

“…The continuous Asakura-Oosawa model, which is used as a basis for the active model discussed here, belongs to the Ising universality class 36 . In three dimensions one would thus expect β = 0.3269 (6) 59 .…”

Section: Critical Exponent βmentioning

confidence: 99%

“…Studies with active particles often consist of active and passive particles, e.g., motile bacteria in a polymer background [30][31][32] . The model we study here is a variation of the well known Asakura-Oosawa (AO) model [33][34][35][36][37][38] , which consists of two particle types, colloids and polymers. In our active model, the colloidal particles become self-propelled with Vicsek-like interactions 22,25 .…”

Section: Introductionmentioning

confidence: 99%

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Estimation of the critical behavior in an active colloidal system with Vicsek-like interactions

Trefz

Siebert

Speck

et al. 2017

The Journal of Chemical Physics

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We study numerically the critical behavior of a modified, active Asakura-Oosawa model for colloid-polymer mixtures. The colloids are modeled as self-propelled particles with Vicsek-like interactions. This system undergoes phase separation between a colloid-rich and a polymer-rich phase, whereby the phase diagram depends on the strength of the Vicsek-like interactions. Employing a subsystem-block-density distribution analysis, we determine the critical point and make an attempt to estimate the critical exponents. In contrast to the passive model, we find that the critical point is not located on the rectilinear diameter. A first estimate of the critical exponents β and ν is consistent with the underlying 3d-Ising universality class observed for the passive model.

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Section: Model and Methodsmentioning

confidence: 99%

Section: Critical Exponent βmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Estimation of the critical behavior in an active colloidal system with Vicsek-like interactions

Trefz

Siebert

Speck

et al. 2017

The Journal of Chemical Physics

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“…and Vrij 125 (henceforth referred to as "AO model"), well suited for Monte Carlo simulation studies 34,[126][127][128][129][130][131][132] . In this model, colloids are simply described as hard spheres of radius R c while polymers are soft spheres of radius R p .…”

mentioning

confidence: 99%

Capillary condensation in cylindrical pores: Monte Carlo study of the interplay of surface and finite size effects

Winkler

Wilms

Virnau

et al. 2010

The Journal of Chemical Physics

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When a fluid that undergoes a vapor to liquid transition in the bulk is confined to a long cylindrical pore, the phase transition is shifted (mostly due to surface effects at the walls of the pore) and rounded (due to finite size effects). The nature of the phase coexistence at the transition depends on the length of the pore: For very long pores the system is axially homogeneous at low temperatures. At the chemical potential where the transition takes place fluctuations occur between vapor-like and liquid-like states of the cylinder as a whole. At somewhat higher temperatures (but still far below bulk criticality) the system at phase coexistence is in an axially inhomogeneous multi-domain state, where long cylindrical liquid-like and vapor-like domains alternate. Using Monte Carlo simulations for the Ising/lattice gas model and the Asakura-Oosawa model of colloid-polymer mixtures the transition between these two different scenarios is characterized. It is shown that the density distribution changes gradually from a double-peak structure to a triple-peak shape, and the correlation length in axial direction (measuring the equilibrium domain length) becomes much smaller than the cylinder length. The (rounded) transition to the disordered phase of the fluid occurs when the axial correlation length has decreased to a value comparable to the cylinder diameter. It is also suggested that adsorption hysteresis vanishes when the transition from the simple domain state to the multi-domain state of the cylindrical pore occurs. We predict that the difference between the pore critical temperature and the hysteresis critical temperature should increase logarithmically with the length of the pore.

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“…In the approach pioneered by the Hansen group in Cambridge [38,[73][74][75][76][77], the 'polymer as soft colloids' model is adopted; the simulation of sufficiently large systems is facilitated by a coarse-grained approach in which the polymer-polymer interactions are incorporated using an effective potential that acts between the centres of mass of the chains. Vink and Horbach [78] have also introduced 'cluster moves' that allow tractable simulation of the AO and related models using grand canonical Monte Carlo [70,[79][80][81]. An alternative approach to simulate large systems has been lattice Monte Carlo, using an explicit (monomer) description of the polymers ( [36,82]).…”

Section: Introductionmentioning

confidence: 99%

Fluid–fluid coexistence in an athermal colloid–polymer mixture: thermodynamic perturbation theory and continuum molecular-dynamics simulation

et al. 2015

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Using both theory and continuum simulation, we examine a system comprising a mixture of polymer chains formed from 100 hard-sphere (HS) segments and HS colloids with a diameter which is 20 times that of the polymer segments. According to Wertheim's first-order thermodynamic perturbation theory (TPT1) this athermal system is expected to phase separate into a colloid-rich and a polymer-rich phase. Using a previously developed continuous pseudo-HS potential [J. F. Jover, A. J. Haslam, A. Galindo, G. Jackson, and E. A. Muller, J. Chem. Phys. 137, 144505 (2012)], we simulate the system at a phase point indicated by the theory to be well within the two-phase binodal region. Molecular-dynamics simulations are performed from starting configurations corresponding to completely phase-separated and completely pre-mixed colloids and polymers. Clear evidence is seen of the stabilisation of two coexisting fluid phases in both cases. An analysis of the interfacial tension of the phase-separated regions is made; ultra-low tensions are observed in line with previous values determined with square-gradient theory and experiment for colloid-polymer systems. Further simulations are carried out to examine the nature of these coexisting phases, taking as input the densities and compositions calculated using TPT1 (and corresponding to the peaks in the probability distribution of the density profiles obtained in the simulations). The polymer chains are seen to be fully penetrable by other polymers. By contrast, from the point of view of the colloids, the polymers behave (on average) as almost-impenetrable spheres. It is demonstrated that, while the average interaction between the polymer molecules in the polymer-rich phase is (as expected) soft-repulsive in nature, the corresponding interaction in the colloid-rich phase is of an entirely different form, characterised by a region of effective intermolecular attraction.

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Critical phenomena in colloid-polymer mixtures: Interfacial tension, order parameter, susceptibility, and coexistence diameter

Cited by 65 publications

References 36 publications

Estimation of the critical behavior in an active colloidal system with Vicsek-like interactions

Estimation of the critical behavior in an active colloidal system with Vicsek-like interactions

Capillary condensation in cylindrical pores: Monte Carlo study of the interplay of surface and finite size effects

Fluid–fluid coexistence in an athermal colloid–polymer mixture: thermodynamic perturbation theory and continuum molecular-dynamics simulation

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