Branching random graph model of rough surfaces describes thermal properties of the effective molecular potential

TL;DR

This paper introduces a novel random branching tree model to describe rough surfaces and their influence on fluid thermodynamics, revealing hierarchical geometry impacts at low temperatures.

Contribution

It presents a new mathematical framework using random branching trees to analyze the effect of hierarchical random solid geometries on fluid interface energy.

Findings

Hierarchical structure significantly affects interface energy at low temperatures.

Model predictions align with Monte Carlo simulation results.

Approach applicable to various quenched disorder systems on random graphs.

Abstract

Fluid properties near rough surfaces are crucial in describing fundamental surface phenomena and modern industrial material design implementations. One of the most powerful approaches to model real rough materials is based on the surface representation in terms of random geometry. Understanding the influence of random solid geometry on the low-temperature fluid thermodynamics is a cutting edge problem. Therefore this work extends recent studies bypassing high-temperature expansion and small heterogeneity scale. We introduce random branching trees whose topology reflects the hierarchical properties of a random solid geometry. This mathematical representation allows us to obtain averaged free energy using a statistical model of virtual clusters interacting through random ultrametric pairwise potentials. Our results demonstrate that a significant impact to fluid-solid interface energy is induced by the hierarchical structure of random geometry at low temperature. These calculations coincide with direct Monte Carlo simulations. Due to the study's interdisciplinary nature, the developed approach can be applied to a wide range of quenched disorder systems on random graphs.