Microscopic theory of the jamming transition of harmonic spheres

TL;DR

This paper presents a microscopic mean-field theory for dense soft particle assemblies, analyzing phase behavior, correlation functions, and scaling near the jamming transition at zero temperature, with validation from simulations.

Contribution

It introduces a novel microscopic theoretical framework combining liquid state and replica theories to predict jamming and glass transition phenomena in soft particle systems.

Findings

Predicted phase boundaries and thermodynamic properties.

Derived scaling laws for pair correlations near contact.

Validated predictions with computer simulations.

Abstract

We develop a microscopic theory to analyze the phase behaviour and compute correlation functions of dense assemblies of soft repulsive particles both at finite temperature, as in colloidal materials, and at vanishing temperature, a situation relevant for granular materials and emulsions. We use a mean-field statistical mechanical approach which combines elements of liquid state theory to replica calculations to obtain quantitative predictions for the location of phase boundaries, macroscopic thermodynamic properties and microstructure of the system. We focus in particular on the derivation of scaling properties emerging in the vicinity of the jamming transition occurring at large density and zero temperature. The new predictions we obtain for pair correlation functions near contact are tested using computer simulations. Our work also clarifies the conceptual nature of the jamming transition, and its relation to the phenomenon of the glass transition observed in atomic liquids.