Classical Liquids in Fractal Dimension

TL;DR

This paper introduces fractal liquids with particles and configuration space of non-integer dimension, exploring their thermodynamics and correlations through simulations and analytical methods, relevant for complex porous and gel systems.

Contribution

It generalizes classical liquids to fractal dimensions, providing a new model and analytical tools for studying liquids in fractal geometries.

Findings

Fractal hard spheres on percolating lattices match simulation data

Fractal Percus-Yevick equation accurately predicts properties

Model applicable to porous media and gel-confined liquids

Abstract

We introduce fractal liquids by generalizing classical liquids of integer dimensions $d = 1, 2, 3$ to a fractal dimension $d_f$. The particles composing the liquid are fractal objects and their configuration space is also fractal, with the same non-integer dimension. Realizations of our generic model system include microphase separated binary liquids in porous media, and highly branched liquid droplets confined to a fractal polymer backbone in a gel. Here we study the thermodynamics and pair correlations of fractal liquids by computer simulation and semi-analytical statistical mechanics. Our results are based on a model where fractal hard spheres move on a near-critical percolating lattice cluster. The predictions of the fractal Percus-Yevick liquid integral equation compare well with our simulation results.