Classical Liquids in Fractal Dimension

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.

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• Calculating particle pair potentials from fluid-state pair correlations: Iterative Ornstein-Zernike Inversion
• Radial distribution function for hard spheres in fractal dimensions: A heuristic approximation
• Residual Multiparticle Entropy for a Fractal Fluid of Hard Spheres
• Connectedness percolation of fractal liquids