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

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 AsakuraOosawa 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 → ∞) 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.

Wall–particle interactions and depletion forces in narrow slits

“…μ c ). Hence, μ c Similar observations are also found for a polymer-colloid size ratio of q = 0.8 [47,49]. That is, the binodal shrinks and capillarity condensation are enhanced by decreasing L. In these works the authors employed the grand-canonical ensemble (μ c μ p VT), so the number of polymer coils and colloidal particles fluctuates inside the slit.…”

“…On the contrary, π/2 ≤ θ b π produces a decay of the slit chemical potential and capillarity condensation appears at certain thermodynamic conditions. The qualitative correctness of this macroscopically deduced expression holds for microscopic systems and even for strong confinement [45,47]. As an example we focus attention on the capillarity condensation case of an AO mixture.…”

“…[49] and references therein). When considering a permeable wall for the polymer coils [45] (but not for the colloids) or a sufficiently large energetic penalty for colloids close to the surface [47,49], the situation reverses. That is, the polymer coils adsorb onto the walls and the colloidal particles concentrate at the slit midplane.…”

Statics and dynamics of colloid-polymer mixtures near their critical point of phase separation: A computer simulation study of a continuous Asakura–Oosawa model

“…In view of this wealth of experimental data on static and dynamic behavior relating to liquid-vapor type phase separation in colloid-polymer mixtures, it is also desirable to provide a detailed theoretical understanding of these phenomena. In fact, many static aspects (including the understanding of the phase diagram and bulk critical behavior 20,21,22 , interfacial fluctuations 23 and interface localization transitions 24,25 , capillary condensation/evaporation 25,26,27,28,29,30 and wetting 31,32,33,34 ) can all be understood by the simple Asakura-Oosawa (AO) 7,8,9 model, at least qualitatively. In this model colloids and polymers are described as spheres of radius R c and R p , respectively.…”

“…It allows for various elegant analytical approximations 11,32,33,34,35 as well as for efficient Monte Carlo simulation techniques 20,21,22,23,24,25,26,27,28,29,30,31 . However, the assumption that polymers do not interact with each other at all makes the AO model unsuitable for studying dynamical aspects of colloid-polymer mixtures.…”