Cell theory for glass-forming materials and jamming matter, combining free volume and cooperative rearranging regions

We investigate the statistical mechanics of glass-forming materials and jamming matter by means of a geometrically driven approach based on a revised cell theory. By considering the system as constituted of jammed blocks of increasing sizes, we obtain a unified picture that describes accurately the whole process from low densities to limit densities at the glass/jamming transition. The approach retrieves many of the aspects of existing theories unifying them into a coherent framework. In particular, at low densities we find a free volume regime, based on local relaxation process, at intermediate densities a cooperative length sets in, where both local and cooperative relaxation process are present. At even higher densities the increasing cooperative length suppresses the local relaxation and only the cooperative relaxation survives characterized by the divergence of the cooperative length, as suggested by the random first order theory. Finally a relation between the cooperative length and the hyperuniform length is also suggested.