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Register a new userCritical behavior in colloid-polymer mixtures: theory and simulation
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We extensively investigated the critical behavior of mixtures of colloids and polymers via the two-component Asakura-Oosawa model and its reduction to a one-component colloidal fluid using accurate theoretical and simulation techniques. In particular the theoretical approach, hierarchical reference theory [Adv. Phys. 44, 211 (1995)], incorporates realistically the effects of long-range fluctuations on phase separation giving exponents which differ strongly from their mean-field values, and are in good agreement with those of the three-dimensional Ising model. Computer simulations combined with finite-size scaling analysis confirm the Ising universality and the accuracy of the theory, although some discrepancy in the location of the critical point between one-component and full-mixture description remains. To assess the limit of the pair-interaction description, we compare one-component and two-component results.
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We show that the critical behavior of a colloid-polymer mixture inside a random porous matrix of quenched hard spheres belongs to the universality class of the random-field Ising model. We also demonstrate that random-field effects in colloid-polymer mixtures are surprisingly strong. This makes these systems attractive candidates to study random-field behavior experimentally.
As first explained by the classic Asakura-Oosawa (AO) model, effective attractive forces between colloidal particles induced by depletion of nonadsorbing polymers can drive demixing of colloid-polymer mixtures into colloid-rich and colloid-poor phases, with practical relevance for purification of water, stability of foods and pharmaceuticals, and macromolecular crowding in biological cells. By idealizing polymer coils as effective penetrable spheres, the AO model qualitatively captures the influence of polymer depletion on thermodynamic phase behavior of colloidal suspensions. In previous work, we extended the AO model to incorporate aspherical polymer conformations and showed that fluctuating shapes of random-walk coils can significantly modify depletion potentials [W. K. Lim and A. R. Denton, Soft Matter 12, 2247 (2016); J. Chem. Phys. 144, 024904 (2016)]. We further demonstrated that the shapes of polymers in crowded environments depend sensitively on solvent quality [W. J. Davis and A. R. Denton, J. Chem. Phys. 149, 124901 (2018)]. Here we apply Monte Carlo simulation to analyze the influence of solvent quality on depletion potentials in mixtures of hard sphere colloids and nonadsorbing polymer coils, modeled as ellipsoids whose principal radii fluctuate according to random-walk statistics. We consider both self-avoiding and non-self-avoiding random walks, corresponding to polymers in good and theta solvents, respectively. Our simulation results demonstrate that depletion of polymers of equal molecular weight induces much stronger attraction between colloids in good solvents than in theta solvents and confirm that depletion interactions are significantly influenced by aspherical polymer conformations.
We investigate the influence of confinement on phase separation in colloid-polymer mixtures. To describe the particle interactions, the colloid-polymer model of Asakura and Oosawa [J. Chem. Phys. 22, 1255 (1954)] is used. Grand canonical Monte Carlo simulations are then applied to this model confined between two parallel hard walls, separated by a distance D=5 colloid diameters. We focus on the critical regime of the phase separation and look for signs of crossover from three-dimensional (3D) Ising to two-dimensional (2D) Ising universality. To extract the critical behavior, finite size scaling techniques are used, including the recently proposed algorithm of Kim et al. [Phys. Rev. Lett. 91, 065701 (2003)]. Our results point to effective critical exponents that differ profoundly from 3D Ising values, and that are already very close to 2D Ising values. In particular, we observe that the critical exponent beta of the order parameter in the confined system is smaller than in 3D bulk, yielding a flatter binodal. Our results also show an increase in the critical colloid packing fraction in the confined system with respect to the bulk. The latter seems consistent with theoretical expectations, although subtleties due to singularities in the critical behavior of the coexistence diameter cannot be ruled out.
We propose a new coarse-grained model for the description of liquid-vapor phase separation of colloid-polymer mixtures. The hard-sphere repulsion between colloids and between colloids and polymers, which is used in the well-known Asakura-Oosawa (AO) model, is replaced by Weeks-Chandler-Anderson potentials. Similarly, a soft potential of height comparable to thermal energy is used for the polymer-polymer interaction, rather than treating polymers as ideal gas particles. It is shown by grand-canonical Monte Carlo simulations that this model leads to a coexistence curve that almost coincides with that of the AO model and the Ising critical behavior of static quantities is reproduced. Then the main advantage of the model is exploited - its suitability for Molecular Dynamics simulations - to study the dynamics of mean square displacements of the particles, transport coefficients such as the self-diffusion and interdiffusion coefficients, and dynamic structure factors. While the self-diffusion of polymers increases slightly when the critical point is approached, the self-diffusion of colloids decreases and at criticality the colloid self-diffusion coefficient is about a factor of 10 smaller than that of the polymers. Critical slowing down of interdiffusion is observed, which is qualitatively similar to symmetric binary Lennard-Jones mixtures, for which no dynamic asymmetry of self-diffusion coefficients occurs.
An extended theoretical study of interface potentials in adsorbed colloid-polymer mixtures is performed. To describe the colloid-polymer mixture near a hard wall, a simple Cahn-Nakanishi-Fisher free-energy functional is used. The bulk phase behavior and the substrate-adsorbate interaction are modelled by the free-volume theory for ideal polymers with polymer-to-colloid size ratios q=0.6 and q=1. The interface potentials are constructed with help from a Fisher-Jin crossing constraint. By manipulating the crossing density, a complete interface potential can be obtained from natural, single-crossing, profiles. The line tension in the partial wetting regime and the boundary tension along prewetting are computed from the interface potentials. The line tensions are of either sign, and descending with increasing contact angle. The line tension takes a positive value of 10^-14 - 10^-12 N near a first-order wetting transition, passes through zero and decreases to minus 10^-14 - 10^-12 N away from the first-order transition. The calculations of the boundary tension along prewetting yield values increasing from zero at the prewetting critical point up to the value of the line tension at first-order wetting.
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