Multicomponent fluid of hard spheres near a wall

External field-driven property localization in liquids of responsive macromolecules

We explore theoretically the effects of external potentials on the spatial distribution of particle properties in a liquid of explicitly responsive macromolecules. In particular, we focus on the bistable particle size as a coarse-grained internal degree of freedom (DoF, or "property"), σ, that moves in a bimodal energy landscape, in order to model the response of a state-switching (big-to-small) macromolecular liquid to external stimuli. We employ a mean-field density functional theory (DFT) that provides the full inhomogeneous equilibrium distributions of a one-component model system of responsive colloids (RCs) interacting with a Gaussian pair potential. For systems confined between two parallel hard walls, we observe and rationalize a significant localization of the big particle state close to the walls, with pressures described by an exact RC wall theorem. Application of more complex external potentials, such as linear (gravitational), osmotic, and Hamaker potentials, promotes even stronger particle size segregation, in which macromolecules of different size are localized in different spatial regions. Importantly, we demonstrate how the degree of responsiveness of the particle size and its coupling to the external potential tune the position-dependent size distribution. The DFT predictions are corroborated by Brownian dynamics simulations. Our study highlights the fact that particle responsiveness can be used to localize liquid properties and therefore helps to control the property- and position-dependent function of macromolecules, e.g., in biomedical applications.

Structural and thermodynamic properties of hard-sphere fluids

This Perspective article provides an overview of some of our analytical approaches to the computation of the structural and thermodynamic properties of single-component and multicomponent hard-sphere fluids. For the structural properties, they yield a thermodynamically consistent formulation, thus improving and extending the known analytical results of the Percus-Yevick theory. Approximate expressions linking the equation of state of the single-component fluid to the one of the multicomponent mixtures are also discussed.

Anisotropy and memory during cage breaking events close to a wall

The slow dynamics in a glassy hard-sphere system is dominated by cage breaking events, i.e. rearrangements where a particle escapes from the cage formed by its neighboring particles. We study such events for an overdamped colloidal system by the means of Brownian dynamics simulations. While it is difficult to relate cage breaking events to structural mean field results in bulk, we show that the microscopic dynamics of particles close to a wall can be related to the anisotropic two-particle density. In particular, we study cage-breaking trajectories, mean forces on a tracked particle, and the impact of the history of trajectories. Based on our simulation results, we further construct two different one-particle random-walk models-one without and one with memory incorporated-and find the local anisotropy and the history-dependence of particles as crucial ingredients to describe the escape from a cage. Finally, our detailed study of a rearrangement event close to a wall not only reveals the memory effect of cages, but leads to a deeper insight into the fundamental mechanisms of glassy dynamics.

Restoring the consistency with the contact density theorem of a classical density functional theory of ions at a planar electrical double layer

Classical density functional theory (DFT) of fluids is a fast and efficient theory to compute the structure of the electrical double layer in the primitive model of ions where ions are modeled as charged, hard spheres in a background dielectric. While the hard-core repulsive component of this ion-ion interaction can be accurately computed using well-established DFTs, the electrostatic component is less accurate. Moreover, many electrostatic functionals fail to satisfy a basic theorem, the contact density theorem, that relates the bulk pressure, surface charge, and ion densities at their distances of closest approach for ions in equilibrium at a smooth, hard, planar wall. One popular electrostatic functional that fails to satisfy the contact density theorem is a perturbation approach developed by Kierlik and Rosinberg [Phys. Rev. A 44, 5025 (1991)PLRAAN1050-294710.1103/PhysRevA.44.5025] and Rosenfeld [J. Chem. Phys. 98, 8126 (1993)JCPSA60021-960610.1063/1.464569], where the full free-energy functional is Taylor-expanded around a bulk (homogeneous) reference fluid. Here, it is shown that this functional fails to satisfy the contact density theorem because it also fails to satisfy the known low-density limit. When the functional is corrected to satisfy this limit, a corrected bulk pressure is derived and it is shown that with this pressure both the contact density theorem and the Gibbs adsorption theorem are satisfied.

Structure of fluid mixtures near a solute: a density functional approach

The structure of fluid mixtures near a spherical solute is studied using a density functional approach and computer simulation. The input direct correlation function is obtained from integral equation theory with an accurate closure relation. The density and concentration profiles of binary as well as ternary hard-sphere mixtures near a large hard-spherical solute compare quite well with the computer simulation results over a wide range of parametric conditions.

Multicomponent fluid of nonadditive hard spheres near a wall

A recently proposed rational-function approximation [Phys. Rev. E 84, 041201 (2011)] for the structural properties of nonadditive hard spheres is applied to evaluate analytically (in Laplace space) the local density profiles of multicomponent nonadditive hard-sphere mixtures near a planar nonadditive hard wall. The theory is assessed by comparison with NVT Monte Carlo simulations of binary mixtures with a size ratio 1:3 in three possible scenarios: a mixture with either positive or negative nonadditivity near an additive wall, an additive mixture with a nonadditive wall, and a nonadditive mixture with a nonadditive wall. It is observed that, while the theory tends to underestimate the local densities at contact (especially in the case of the big spheres) it captures very well the initial decay of the densities with increasing separation from the wall and the subsequent oscillations.

Weighted correlation approach: an extended version with applications to the hard-sphere fluid

The purpose of this study is to extend the weighted correlation approach (WCA) for inhomogeneous fluids. It now introduces a generic expression to evaluate the single-particle direct correlation function in terms of a series of pair direct correlation functions weighted by different correlation-weight functions and adjustable weight factors. When applied for practical use, however, approximations of the pair direct correlation functions have to be made, together with appropriate definitions of the weighted densities and the choices of the correlation-weight functions. The WCA approach would, then, not only help us to connect and compare different strategies and their underlying assumptions in the density functional approaches, but also enable us to propose and apply density functional theory methods to predict the density profile of, e.g., the hard-sphere fluid confined between a pair of parallel planar hard walls. Numerical results of the extended WCA approach, against the Monte Carlo (MC) simulations in a range of surface separations and bulk densities, suggest that it is capable of representing the fine features of the hard-sphere density distributions. The WCA results also agree well with the calculations from the fundamental measure theory. In addition, the thermodynamic self-consistency of the WCA approach is confirmed by its fairly good agreement with the MC fitted data for the surface tension of a hard-sphere fluid at a planar hard wall. All these tests show that a pure WCA approach can be constructed to investigate the states of ionic hard-sphere fluids.