Equilibrium properties of strongly confined fluids

TL;DR

This work develops and applies an exact theoretical framework for equilibrium properties of strongly confined fluids, focusing on quasi-one-dimensional (Q1D) systems where single-file constraint and transverse confinement induce strong anisotropy. The central advance is a mapping that translates Q1D problems into exactly solvable one-dimensional mixtures (monocomponent, discrete mixtures, and polydisperse limits), yielding closed expressions for thermodynamic quantities, the full radial distribution function, and the anisotropic pressure tensor. The framework is applied to hard-core, square-well, square-shoulder, and anisotropic hard-body models, uncovering phenomena such as zigzag ordering, structural crossovers, and distinct longitudinal/transverse thermodynamics, all validated against Monte Carlo and molecular dynamics simulations. The results illuminate how dimensionality governs fluid behavior under extreme confinement and provide a robust, adaptable tool for predicting structure and thermodynamics in nanoconfined fluids with potential experimental realizations in nanopores and channels. The work also maps out avenues for extending the theory to mixtures, wall interactions, and continuous orientational degrees of freedom, with open-source code enabling reproducibility and broader use in the community.

Abstract

The statistical-mechanical study of the equilibrium properties of fluids, starting from the knowledge of the interparticle interaction potential, is essential to understand the role that microscopic interaction between individual particles play in the properties of the fluid. The study of these properties from a fundamental point of view is therefore a central goal in condensed matter physics. These properties, however, might vary greatly when a fluid is confined to extremely narrow channels and, therefore, must be examined separately. This thesis investigates fluids in narrow pores, where particles are forced to stay in single-file formation and cannot pass one another. The resulting systems are highly anisotropic: motion is free along the channel axis but strongly restricted transversely. To quantify these effects, equilibrium properties of the confined fluids are compared with their bulk counterparts, exposing the role of dimensionality. We also develop a novel theoretical framework based on a mapping approach that converts single-file fluids with nearest-neighbor interactions into an equivalent one-dimensional mixture. This exact isomorphism delivers closed expressions for thermodynamic and structural quantities. It allows us to compute the anisotropic pressure tensor and revises definitions of spatial correlations to take into account spatial anisotropy. The theory is applied to hard-core, square-well, square-shoulder, and anisotropic hard-body models, revealing phenomena such as zigzag ordering and structural crossovers of spatial correlations. Analytical predictions are extensively validated against Monte Carlo and molecular dynamic simulations (both original and from the literature), showing excellent agreement across the studied parameter ranges.

Figures (10)

• Figure 1: Visual representation of particles in different geometries: (a) a bulk system exhibiting isotropic translational invariance in all directions; (b) a confined system with translational invariance only along the longitudinal axis; (c) an ultraconfined system in which particles are restricted to move solely along the longitudinal direction.
• Figure 2: Schematic representation of the convolution property from Eq. \ref{['eq:convolution']} for a system of length $L$ where periodic boundary conditions have been applied, enforcing $x_{N+1}=x_1+L$.
• Figure 3: Schematic representation a 1D system of $N$ particles, including a visual description of the variables necessary to evaluate the configurational partition function $\Delta_C$. Periodic boundary conditions enforce $x_{N+1}=x_1+L$.
• Figure 4: Visual example of mixtures where particles interact only through hard-core volume exclusion: (a) a binary mixture of additive particles and (b) a binary mixture of negative nonadditive particles.
• Figure 5: Schematic illustration of the convolution property [Eq. \ref{['eq:convolutionmixture']}] for a ternary mixture ($M=3$). The summation over species in Eq. \ref{['eq:convolutionmixture']} is shown explicitly, indicating that the particle at position $x_2$ might belong to any of the three species. Periodic boundary conditions impose $x_{N+1}=x_1+L$.