Structure of the square-shoulder fluid

Exact equilibrium properties of square-well and square-shoulder disks in single-file confinement

This study investigates the (longitudinal) thermodynamic and structural characteristics of single-file confined square-well and square-shoulder disks by employing a mapping technique that transforms the original system into a one-dimensional polydisperse mixture of nonadditive rods. Leveraging standard statistical-mechanical techniques, exact results are derived for key properties, including the equation of state, internal energy, radial distribution function, and structure factor. The asymptotic behavior of the radial distribution function is explored, revealing structural changes in the spatial correlations. Additionally, exact analytical expressions for the second virial coefficient are presented. The theoretical results for the thermodynamic and structural properties are validated by our Monte Carlo simulations.

Nonconventional Phases of Colloidal Nanorods with a Soft Corona

Using computer simulations, we investigate the phase behavior of hard-core spherocylinders with a length-to-diameter ratio L/σ=5 and coated by a soft deformable corona of length λ/σ=1.35. When quasi-two-dimensional layers are formed in smectic and solid phases at low temperatures, the competition between the two intrinsic length scales of the parallel aligned particles leads to the stabilization of different in-plane lattices of nonconventional symmetry, including low-density hexagonal, square, and high-density hexagonal crystals, as well as an intriguing dodecagonal quasicrystal. Our Letter opens up the opportunity to control the assembly of anisotropic nanoparticles into structures with preengineered symmetry-dependent physical properties.

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.

Temperature expansions in the square-shoulder fluid. II. Thermodynamics

In Paper I [O. Coquand and M. Sperl, J. Chem. Phys. 152, 124112 (2020)], we derived analytical expressions for the structure factor of the square-shoulder potential in a perturbative way around the high- and low-temperature regimes. Here, various physical properties of these solutions are derived. In particular, we investigate the large wave number sector and relate it to the contact values of the pair-correlation function. Then, the thermoelastic properties of the square-shoulder fluids are discussed.

Low-Temperature Crystal Structures of the Hard Core Square Shoulder Model

In many cases, the stability of complex structures in colloidal systems is enhanced by a competition between different length scales. Inspired by recent experiments on nanoparticles coated with polymers, we use Monte Carlo simulations to explore the types of crystal structures that can form in a simple hard-core square shoulder model that explicitly incorporates two favored distances between the particles. To this end, we combine Monte Carlo-based crystal structure finding algorithms with free energies obtained using a mean-field cell theory approach, and draw phase diagrams for two different values of the square shoulder width as a function of the density and temperature. Moreover, we map out the zero-temperature phase diagram for a broad range of shoulder widths. Our results show the stability of a rich variety of crystal phases, such as body-centered orthogonal (BCO) lattices not previously considered for the square shoulder model.

Predicting the structure of fluids with piecewise constant interactions: Comparing the accuracy of five efficient integral equation theories

We use molecular dynamics simulations to test integral equation theory predictions for the structure of fluids of spherical particles with eight different piecewise-constant pair-interaction forms comprising a hard core and a combination of two shoulders and/or wells. Since model pair potentials like these are of interest for discretized or coarse-grained representations of effective interactions in complex fluids (e.g., for computationally intensive inverse optimization problems), we focus here on assessing how accurately their properties can be predicted by analytical or simple numerical closures including Percus-Yevick, hypernetted-chain, and reference hypernetted-chain closures and first-order mean spherical and modified first-order mean spherical approximations. To make quantitative comparisons between the predicted and simulated radial distribution functions, we introduce a cumulative structural error metric. For equilibrium fluid state points of these models, we find that the reference hypernetted-chain closure is the most accurate of the tested approximations as characterized by this metric or related thermodynamic quantities.

Singular value decomposition of the radial distribution function for hard sphere and square well potentials

We compute the singular value decomposition of the radial distribution function g(r) for hard sphere, and square well solutions. We find that g(r) decomposes into a small set of basis vectors allowing for an extremely accurate representation at all interpolated densities and potential strengths. In addition, we find that the coefficient vectors describing the magnitude of each basis vector are well described by a low-order polynomial. We provide a program to calculate g(r) in this compact representation for the investigated parameter range.

An improved first-order mean spherical approximation theory for the square-shoulder fluid

The theory, which utilizes an exponential enhancement of the first-order mean spherical approximation (FMSA) for the radial distribution functions of the hard-core plus square-well fluid, is adopted to study the properties of the simplest model of the core-softened fluids, i.e., the hard spheres with a square-shoulder interaction. The results for structure and thermodynamic properties are reported and compared against both the Monte Carlo simulation data as well as with those obtained within the conventional FMSA theory. We found that in the region of low densities and low temperatures, where the conventional FMSA theory fails, the exponential-based FMSA theory besides being qualitatively correct also provides with a notable quantitative improvement of the theoretical description.