Fundamental measure density functional theory for nonadditive hard-core mixtures: the one-dimensional case

Ordering properties of anisotropic hard bodies in one-dimensional channels

The phase behavior and structural properties of hard anisotropic particles (prisms and dumbbells) are examined in one-dimensional channels using the Parsons-Lee (PL) theory, and the transfer-matrix and neighbor-distribution methods. The particles are allowed to move freely along the channel, while their orientations are constrained such that one particle can occupy only two or three different lengths along the channel. In this confinement setting, hard prisms behave as an additive mixture, while hard dumbbells behave as a non-additive one. We prove that all methods provide exact results for the phase properties of hard prisms, while only the neighbor-distribution and transfer-matrix methods are exact for hard dumbbells. This shows that non-additive effects are incorrectly included into the PL theory, which is a successful theory of the isotropic-nematic phase transition of rod-like particles in higher dimensions. In the one-dimensional channel, the orientational ordering develops continuously with increasing density, i.e., the system is isotropic only at zero density, while it becomes perfectly ordered at the close-packing density. We show that there is no orientational correlation in the hard prism system, while the hard dumbbells are orientationally correlated with diverging correlation length at close packing. On the other hand, positional correlations are present for all the systems, the associated correlation length diverging at close packing.

Particle-conserving dynamics on the single-particle level

We generalize the particle-conserving dynamics method of de las Heras et al. [J. Phys.: Condens. Matter 28, 244024 (2016)JCOMEL0953-898410.1088/0953-8984/28/24/244024] to binary mixtures and apply this to hard rods in one dimension. Considering the case of one species consisting of only one particle enables us to address the tagged-particle dynamics. The time-evolution of the species-labeled density profiles is compared to exact Brownian dynamics and (grand-canonical) dynamical density functional theory. The particle-conserving dynamics yields improved results over the dynamical density functional theory and well reproduces the simulation data at short and intermediate times. However, the neglect of a strict particle order (due to the fundamental statistical assumption of ergodicity) leads to errors at long times for our one-dimensional setup. The isolated study of that error makes clear the fundamental limitations of (adiabatic) density-based theoretical approaches when applied to systems of any dimension for which particle caging is a dominant physical mechanism.

Deriving the Rosenfeld functional from the virial expansion

In this article we replace the semiheuristic derivation of the Rosenfeld functional of hard convex particles with the systematic calculation of Mayer clusters. It is shown that each cluster integral further decomposes into diagrams of intersection patterns that we classify by their loop number. This extends the virial expansion of the free energy by an expansion in the loop order, with the Rosenfeld functional as its leading contribution. Rosenfeld's weight functions then follow from the derivation of the intersection probability by generalizing the equation of Blaschke, Santalo, and Chern. It is found that the 0-loop order can be derived exactly and reproduces the Rosenfeld functional. We further discuss the influence of particle dimensions, topologies, and geometries on the mathematical structure of the calculation.

Nonadditive penetrable mixtures in nanopores: surface-induced population inversion

We investigate the surface-induced population inversion of the nonadditive penetrable mixtures which exhibits the fluid-fluid demixing transition of the bulk system due to the confinement effect. The result shows that the population inversions are strongly affected by the extra repulsion between unlike species, the mole fraction of species, the width of nanopores, and the nonadditive walls. The extra repulsion between unlike species in a confined system increases the contact density of both species at the wall and promotes the population inversion in nanopores. The population inversion is the typical shift first-order fluid-fluid demixing transition due to the confinement effect in nanopores. The population inversions are only observed in nanopores with finite widths. The population inversion line is shifted toward a higher fluid density with decreasing width of the nanopores and lies slightly in lower density compared with the coexistence curves of the bulk system. The nonadditive wall for the big particles leads to the population inversion in lower density compared with that of the nonadditive wall for the small particles. The population inversion line is terminated at a lower mole fraction.

Nonadditive hard-sphere fluid mixtures: a simple analytical theory

We construct a nonperturbative fully analytical approximation for the thermodynamics and the structure of nonadditive hard-sphere fluid mixtures. The method essentially lies in a heuristic extension of the Percus-Yevick solution for additive hard spheres. Extensive comparison with Monte Carlo simulation data shows a generally good agreement, especially in the case of like-like radial distribution functions.

Binary non-additive hard sphere mixtures: fluid demixing, asymptotic decay of correlations and free fluid interfaces

Using a fundamental measure density functional theory we investigate both bulk and inhomogeneous systems of the binary non-additive hard sphere model. For sufficiently large (positive) non-additivity the mixture phase separates into two fluid phases with different compositions. We calculate bulk fluid-fluid coexistence curves for a range of size ratios and non-additivity parameters and find that they compare well to simulation results from the literature. Using the Ornstein-Zernike equation, we investigate the asymptotic, [Formula: see text], decay of the partial pair correlation functions, g(ij)(r). At low densities a structural crossover occurs in the asymptotic decay between two different damped oscillatory modes with different wavelengths corresponding to the two intra-species hard-core diameters. On approaching the fluid-fluid critical point there is a Fisher-Widom crossover from exponentially damped oscillatory to monotonic asymptotic decay. Using the density functional we calculate the density profiles for the planar free fluid-fluid interface between coexisting fluid phases. We show that the type of asymptotic decay of g(ij)(r) not only determines the asymptotic decay of the interface profiles, but is also relevant for intermediate and even short-ranged behaviour. We also determine the surface tension of the free fluid interface, finding that it increases with non-additivity, and that on approaching the critical point mean-field scaling holds.

One-dimensional model for water and aqueous solutions. IV. A study of "hydrophobic interactions"

The solute-solute pair correlation function and the potential of mean force (PMF) between two hard-rod solutes in two solvents are studied in one-dimensional systems. One solvent consists of particles interacting via square well (SW) potential. The second consists of particles interacting via "hydrogen-bond-like" (HB) pair potential. It was found that the first minimum of the solute-solute PMF at infinite dilution in the two solvents grows deeper as we increase the strength of the solvent-solvent interaction. In the SW (but not in the HB) solvent, we found that the range of solute-solute pair correlation is larger at lower temperatures (or at larger epsilon(BB)/k(B)T). The relevance of this finding to the problem of hydrophobic interactions is discussed.

Exact bulk correlation functions in one-dimensional nonadditive hard-core mixtures

In a recent paper [Phys. Rev. E 76, 031202 (2007)], Schmidt proposed a fundamental measure density functional theory for one-dimensional nonadditive hard-rod fluid mixtures and compared its predictions for the bulk structural properties with Monte Carlo simulations. The aim of this Brief Report is to recall that the problem admits an exact solution in the bulk, which is briefly summarized in a self-contained way.