Mean properties and Free Energy of a few hard spheres confined in a spherical cavity
arXiv:1407.4819 · doi:10.1063/1.4896221
Abstract
We use analytical calculations and event-driven molecular dynamics simulations to study a small number of hard sphere particles in a spherical cavity. The cavity is taken also as the thermal bath so that the system thermalizes by collisions with the wall. In that way, these systems of two, three and four particles, are considered in the canonical ensemble. We characterize various mean and thermal properties for a wide range of number densities. We study the density profiles, the components of the local pressure tensor, the interface tension, and the adsorption at the wall. This spans from the ideal gas limit at low densities to the high-packing limit in which there are significant regions of the cavity for which the particles have no access, due the conjunction of excluded volume and confinement. The contact density and the pressure on the wall are obtained by simulations and compared to exact analytical results. We also obtain the excess free energy for N=4, by using a simulated-assisted approach in which we combine simulation results with the knowledge of the exact partition function for two and three particles in a spherical cavity.
arXiv comment11 pages, 9 figures and two tables
References in corpus (7)
- Hard Spheres in Vesicles: Curvature-Induced Forces and Particle-Induced Curvature
- Monte Carlo simulations of the solid-liquid transition in hard spheres and colloid-polymer mixtures
- Bending rigidity and higher order curvature terms for the hard-sphere fluid near a curved wall
- The existence of a bending rigidity for a hard sphere liquid near a curved hard wall: Helfrich or Hadwiger?
- Two hard spheres in a pore: Exact Statistical Mechanics for different shaped cavities
- Statistical Mechanics of Two Hard Spheres in a Spherical Pore, Exact Analytic Results in D Dimension
- An exact formalism to study the thermodynamic properties of hard-sphere systems under spherical confinement