Equilibrium and non-equilibrium cluster phases in colloids with competing interactions

Abstract

The phase behavior of colloids that interact via competing interactions - short-range attraction and long-range repulsion - is studied by computer simulation. In particular, for a fixed strength and range of repulsion, the effect of the strength of an attractive interaction (ε) on the phase behavior is investigated at various colloid densities (ρ). A thermodynamically stable equilibrium colloidal cluster phase, consisting of compact crystalline clusters, is found below the fluid-solid coexistence line in the ε-ρ parameter space. The mean cluster size is found to linearly increase with the colloid density. At large ε and low densities, and at small ε and high densities, a non-equilibrium cluster phase, consisting of elongated Bernal spiral-like clusters, is observed. Although gelation can be induced either by increasing ε at constant density or vice versa, the gelation mechanism is different in either route. While in the ρ route gelation occurs via a glass transition of compact clusters, gelation in the ε route is characterized by percolation of elongated clusters. This study both provides the location of equilibrium and non-equilibrium cluster phases with respect to the fluid-solid coexistence, and reveals the dependencies of the gelation mechanism on the preparation route.

Origin and detection of microstructural clustering in fluids with spatial-range competitive interactions

“…To determine whether state points are fluid, clustered, or percolating, we calculate cluster size distributions (CSDs), which quantify the probabilistic formation of n-particle aggregates, where particles are considered part of the same aggregate if their centers are within the narrow range of the attractive well. Similar to other studies [14,15,17,18], a system is considered clustered with aggregates of preferred size n * by the presence of a local maxima in the CSD at n * occurring in the range 1 n * N , and is considered percolated (at the level of the box) by a CSD peak comprised of all particles, i.e., n * N . To obtain analytical results for a broader range of potentials, we also derive theoretical thermodynamic and pair structure results via the Ornstein-Zernike (OZ) in-…”

“…This treatment mimics systems for which the short-and long-range aspects of constituent interactions are approximately orthogonal, such as colloids with screening lengths set by particle-solvent interactions and attractions tuned via introduction of depletants [18].…”

“…Various stud- * Contributed equally † truskett@che.utexas.edu ies have demonstrated that the long-range repulsive interaction suppresses macrophase separation-which would occur for strong short-range attractions alone-in favor of IRO structures including clusters [14][15][16][17][18]. However, an ongoing challenge has been to distinguish between generic IRO (i.e., presence of any pre-peak) and clustering specifically, particularly in a way accessible to experiments [12,17].…”

Monte Carlo simulation of kinetically slowed down phase separation

“…From the thermodynamic point of view, long-range repulsion decreases the liquid-vapor critical point [47]. Our simulations are not long enough to equilibrate the system, and we do not deal with equilibrium cluster phases [30], or with small arrested nonequilibrium clusters [10]. We rather simulate large [48], metastable and spherical clusters, where particle exchange between them indicates an ongoing phase-separation, and where the fluid-solid coexistence region seems to be the equilibrium phase in the long-time limit.…”

“…These drops are typically metastable and may be in a liquid, crystalline, or glassy [9] state before they aggregate or dissolve. The properties of the state depend on the interplay between various parameters of the system such as the temperature, strength of the attraction [10], timescale [9], or viscosity of the solvent affecting the diffusion rate [11,5]. For example, crystallization within the drops may precede the aggregation, if the temperature of the quench lies…”