Critical Casimir Forces and Colloidal Phase Transitions in a Near-Critical Solvent: A Simple Model Reveals a Rich Phase Diagram

Abstract

From experimental studies, it is well known that colloidal particles suspended in a near-critical binary solvent exhibit interesting aggregation phenomena, often associated with colloidal phase transitions and assumed to be driven by long-ranged solvent-mediated (SM) interactions (critical Casimir forces), set by the (diverging) correlation length of the solvent. We present the first simulation and theoretical study of an explicit model of a ternary mixture that mimics this situation. Both the effective SM pair interactions and the full ternary phase diagram are determined for Brownian disks suspended in an explicit two-dimensional supercritical binary liquid mixture. Gas-liquid and fluid-solid transitions are observed in a region that extends well away from criticality of the solvent reservoir. We discuss to what extent an effective pairpotential description can account for the phase behavior we observe. Our study provides a fresh perspective on how proximity to the critical point of the solvent reservoir might influence colloidal self-assembly. DOI: 10.1103/PhysRevLett.114.038301 PACS numbers: 82.70.Dd, 47.57.J−, 64.70.pv, 64.75.Xc Colloidal particles dispersed in a binary solvent mixture have an inherent preference for one of the two solvent species. This is reflected by preferential adsorption of the favored species on the colloid surface, leading to the development of adsorbed films. Such films can mediate an effective interaction between two colloidal particles which is remarkably sensitive to the thermodynamic state of the solvent. Close to the (demixing) critical point of the solvent, the adsorbed film thickness is determined by the correlation length ξ of the solvent [1], and, as first predicted by Fisher and de Gennes [2], the resulting solvent-mediated (SM) interactions are long ranged, with universal scaling properties. An analogy between the confinement of quantum fluctuations of the electromagnetic field [3] and that of thermal composition fluctuations in a near-critical binary solvent led to these (universal) SM forces being referred to as critical Casimir forces [4].Theoretical studies on near-critical fluids confined between a pair of infinitely large planar walls (representing two static large colloids) [4][5][6][7][8], along with direct experimental measurements of the Casimir force [9,10] between a colloid and a wall, have advanced our understanding of the nature of two-body SM interactions. Although experimental investigations of a suspension of colloids go back to the pioneering work of Beysens and Estève [11] (for a very recent experimental study, see [12]), the theory and computer simulation of such systems remain at a primitive stage. Here we use computer simulations of a simple model to understand the strength and range of the SM interactions and the resulting phase behavior of a dense colloidal suspension as a function of the thermodynamic state of the solvent. Computer simulation of colloids in an explicit molecular solvent with a bulk correlation length that diverges upon approac...

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

“…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.…”

“…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.…”

“…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.…”

Hydrodynamics in bridging and aggregation of two colloidal particles in a near-critical binary mixture

“…Guo et al 21 furthermore observed liquid, fcc crystal, and glass phases of the aggregated particles also for ℓ ∼ a ≫ ξ. We mention a number of theoretical papers on this near-critical aggregation [23][24][25][26][27][28][29][30] . In non-critical solvents, on the other hand, the particles often stick and form fractal aggregates due to the attractive van der Waals interaction 31 .…”

“…In recent theories 28,29 , the colloidal particles were assumed to form one-component systems interacting via an attractive solvent-mediated interaction potential (∝ e −r/ξ ) and a repulsive electrostatic potential, where the particle separation r is smaller than ξ in aggregation. Very recently, Edison et al 30 has examined phase behavior of a three-component model on a 2D lattice to obtain aggregation of the third component.…”