Critical Casimir interactions and colloidal self-assembly in near-critical solvents

Abstract

A binary solvent mixture close to critical demixing experiences fluctuations whose correlation length, ξ, diverges as the critical point is approached. The solvent-mediated (SM) interaction that arises between a pair of colloids immersed in such a near-critical solvent can be long-ranged and this so-called critical Casimir interaction is well-studied. How a (dense) suspension of colloids will self-assemble under these conditions is poorly understood. Using a two-dimensional lattice model for the solvent and hard disks to represent the colloids, we perform extensive Monte Carlo simulations to investigate the phase behaviour of this model colloidal suspension as a function of colloid size and wettability under conditions where the solvent reservoir is supercritical. Unlike most other approaches, where the solvent is modelled as an implicit background, our model employs an explicit solvent and treats the suspension as a ternary mixture. This enables us to capture important features, including the pronounced fractionation of the solvent in the coexisting colloidal phases, of this complex system. We also present results for the partial structure factors; these shed light on the critical behaviour in the ternary mixture. The degree to which an effective two-body pair potential description can describe the phase behaviour and structure of the colloidal suspension is discussed briefly.

From 2D to 3D: Critical Casimir interactions and phase behavior of colloidal hard spheres in a near-critical solvent

“…We do this by assessing the phase behavior and compare the overall topology of the resulting 3D phase diagram with that of a two-dimensional system. 19,21 This comparison is achieved by calculating the solvent chemical potential difference, ∆µ s , vs colloid packing fraction, η, phase diagrams of the ternary mixture at different reduced temperatures, τ.…”

“…To calculate the phase diagrams, we employ the direct coexistence method 21 in which an elongated box is used to facilitate the formation of an interface between two phases. This allows us to calculate density profiles along the direction normal to the interface, from which the colloid coexistence packing fractions η can be "read off" for a fixed solvent chemical potential, ∆µ s .…”

“…We thus treat the colloids in the canonical ensemble, whereas the solvent is treated grandcanonically; see Ref. 21. Throughout this work, a simulation box with dimensions of 128 × 128 × 256 lattice sites is used; this is large enough to avoid significant finite-size effects.…”

“…19,21 The coexistence curves of the three-dimensional system are broader, mainly due to the fact that the particle surface is proportional to R 2 as opposed to R in 2D; the colloidal particles in 3D are overall adsorbing more strongly for the same value of α. The phase diagrams also exhibit the same trends when decreasing the temperature, τ; the two-phase G-L(X) coexistence region broadens, and the critical point of the ternary system shifts towards the critical point of the pure solvent reservoir.…”

“…This approach fails to capture important elements such as the fractionation of the solvent in the coexisting colloidal phases. In a series of recent studies, [19][20][21] we were able to capture the above-mentioned important elements by using a simple lattice-gas binary solvent model with embedded colloids interacting through first neighbor and excluded volume interactions with the solvent. The model, although simple, contains all the necessary physics to describe the SM interactions between colloids.…”