Thermodynamic properties of quasi-one-dimensional fluids

TL;DR

This paper develops a perturbative method to calculate thermodynamic and structural properties of quasi-one-dimensional hard-sphere fluids, linking them to an effective one-dimensional rod model with explicit two- and three-body interactions.

Contribution

It introduces a novel perturbative approach to analyze confined fluids, explicitly deriving effective multi-body potentials and connecting 3D behavior to a 1D rod model.

Findings

Explicit expressions for pressure, surface tension, and density profiles.

Validation of the approach through comparison with Monte Carlo simulations.

The method captures the jamming transition singularity.

Abstract

We calculate thermodynamic and structural quantities of a fluid of hard spheres of diameter $\sigma$ in a quasi-one-dimensional pore with accessible pore width $W $ smaller than $\sigma$ by applying a perturbative method worked out earlier for a confined fluid in a slit pore [Phys. Rev. Lett. \textbf{109}, 240601 (2012)]. In a first step, we prove that the thermodynamic and a certain class of structural quantities of the hard-sphere fluid in the pore can be obtained from a purely one-dimensional fluid of rods of length $ \sigma$ with a central hard core of size $\sigma_W =\sqrt{\sigma^2 - W^2}$ and a soft part at both ends of length $(\sigma-\sigma_W)/2$. These rods interact via effective $k$-body potentials $v^{(k)}_\text{eff}$ ($k \geq 2$) . The two- and the three-body potential will be calculated explicitly. In a second step, the free energy of this effective one-dimensional fluid is calculated up to leading order in $ (W/\sigma)^2$. Explicit results for, e.g. the perpendicular pressure, surface tension, and the density profile as a function of density, temperature, and pore width are presented presented and partly compared with results from Monte-Carlo simulations and standard virial expansions. Despite the perturbative character of our approach it encompasses the singularity of the thermodynamic quantities at the jamming transition point.