Phase diagram and structure of colloid-polymer mixtures confined between walls

TL;DR

This study uses advanced Monte Carlo simulations to explore how confinement between walls affects phase separation in colloid-polymer mixtures, revealing a gradual shift from 2D to 3D critical behavior and non-monotonic critical packing fractions.

Contribution

It provides the first detailed simulation analysis of confined colloid-polymer mixtures, demonstrating the crossover of critical behavior and validating theoretical scaling predictions.

Findings

Critical behavior transitions from 2D to 3D Ising universality with increasing film thickness.

Critical colloid packing fraction approaches bulk value non-monotonically as confinement decreases.

Density profiles and pair distribution functions reveal wall effects on phase behavior.

Abstract

The influence of confinement, due to flat parallel structureless walls, on phase separation in colloid-polymer mixtures, is investigated by means of grand-canonical Monte Carlo simulations. Ultra-thin films, with thicknesses between $D=3-10$ colloid diameters, are studied. The Asakura-Oosawa model [J. Chem. Phys. 22, 1255 (1954)] is used to describe the particle interactions. To simulate efficiently, a ``cluster move'' [J. Chem. Phys. 121, 3253 (2004)] is used in conjunction with successive umbrella sampling [J. Chem. Phys. 120, 10925 (2004)]. These techniques, when combined with finite size scaling, enable an accurate determination of the unmixing binodal. Our results show that the critical behavior of the confined mixture is described by ``effective'' critical exponents, which gradually develop from values near those of the two-dimensional Ising model, to those of the three-dimensional Ising model, as $D$ increases. The scaling predictions of Fisher and Nakanishi [J. Chem. Phys. 75, 5875 (1981)] for the shift of the critical point are compatible with our simulation results. Surprisingly, however, the colloid packing fraction at criticality approaches its bulk ($D \to \infty$) value non-monotonically, as $D$ is increased. Far from the critical point, our results are compatible with the simple Kelvin equation, implying a shift of order 1/D in the coexistence colloid chemical potential. We also present density profiles and pair distribution functions for a number of state points on the binodal, and the influence of the colloid-wall interaction is studied.