Modeling the structure and thermodynamics of multicomponent and polydisperse hard-sphere dispersions with continuous potentials.

A model system of identical particles interacting via a hard-sphere potential is essential in condensed matter physics; it helps to understand in and out of equilibrium phenomena in complex fluids, such as colloidal dispersions. Yet, most of the fixed time-step algorithms to study the transport properties of those systems have drawbacks due to the mathematical nature of the interparticle potential. Because of this, mapping a hard-sphere potential onto a soft potential has been recently proposed [Báez et al., J. Chem. Phys. 149, 164907 (2018)]. More specifically, using the second virial coefficient criterion, one can set a route to estimate the parameters of the soft potential that accurately reproduces the thermodynamic properties of a monocomponent hard-sphere system. However, real colloidal dispersions are multicomponent or polydisperse, making it important to find an efficient way to extend the potential model for dealing with such kind of many-body systems. In this paper, we report on the extension and applicability of the second virial coefficient criterion to build a description that correctly captures the phenomenology of both multicomponent and polydisperse hard-sphere dispersions. To assess the accuracy of the continuous potentials, we compare the structure of soft polydisperse systems with their hard-core counterpart. We also contrast the structural and thermodynamic properties of soft binary mixtures with those obtained through mean-field approximations and the Ornstein-Zernike equation for the two-component hard-sphere dispersion.

Soft representation of the square-well and square-shoulder potentials to be used in Brownian and molecular dynamics simulations.

The discrete hard-sphere (HS), square-well (SW), and square-shoulder (SS) potentials have become the battle horse of molecular and complex fluids because they contain the basic elements to describe the thermodynamic, structural, and transport properties of both types of fluids. The mathematical simplicity of these discrete potentials allows us to obtain some analytical results despite the nature and complexity of the modeled systems. However, the divergent forces arising at the potential discontinuities may lead to severe issues when discrete potentials are used in computer simulations with uniform time steps. One of the few routes to avoid these technical problems is to replace the discrete potentials with continuous and differentiable forms built under strict physical criteria to capture the correct phenomenology. The match of the second virial coefficient between the discrete and the soft potentials has recently been successfully used to construct a continuous representation that mimics some physical properties of HSs (Báezet al2018J. Chem. Phys.149164907). In this paper, we report an extension of this idea to construct soft representations of the discrete SW and SS potentials. We assess the accuracy of the resulting soft potential by studying structural and thermodynamic properties of the modeled systems by using extensive Brownian and molecular dynamics computer simulations. Besides, Monte Carlo results for the original discrete potentials are used as benchmark. We have also implemented the discrete interaction models and their soft counterparts within the integral equations theory of liquids, finding that the most widely used approximations predict almost identical results for both potentials.

Thermodynamics, static properties and transport behaviour of fluids with competing interactions.

Competing interaction fluids have become ideal model systems to study a large number of phenomena, for example, the formation of intermediate range order structures, condensed phases not seen in fluids driven by purely attractive or repulsive forces, the onset of particle aggregation under in- and out-of-equilibrium conditions, which results in the birth of reversible and irreversible aggregates or clusters whose topology and morphology depend additionally on the thermodynamic constrictions, and a particle dynamics that has a strong influence on the transport behaviour and rheological properties of the fluid. In this contribution, we study a system of particles interacting through a potential composed by a continuous succession of a short-ranged square-well (SW), an intermediate-ranged square-shoulder and a long-ranged SW. This potential model is chosen to systematically analyse the contribution of every component of the interaction potential on the phase behaviour, the microstructure, the morphology of the resulting aggregates and the transport phenomena of fluids described by competing interactions. Our results indicate that the inclusion of a barrier and a second well leads to new and interesting effects, which in addition result in variations of the physical properties associated to the competition among interactions.