Microscopic theory of the jamming transition of harmonic spheres

Ludovic Berthier (1) , Hugo Jacquin (2) , Francesco Zamponi (3)

1 L2C - Laboratoire Charles Coulomb
2 MSC - Matière et Systèmes Complexes
3 LPTENS - Laboratoire de Physique Théorique de l'ENS [École Normale Supérieure]

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.

Domains: Disordered Systems and Neural Networks [cond-mat.dis-nn]; Statistical Mechanics [cond-mat.stat-mech]

Ludovic Berthier, Hugo Jacquin, Francesco Zamponi. Microscopic theory of the jamming transition of harmonic spheres. Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, 2011, 84, pp.051103. ⟨10.1103/PhysRevE.84.051103⟩. ⟨hal-00643045⟩