Cluster approach to the phase transitions from fluid to amorphous solids: gels, glasses and granular materials

Based on various results present in the literature, we elaborate a unifying cluster percolation approach to interpret the dynamical arrest occurring in amorphous materials such as those of the gel, glass and granular variety. In the case of the sol-gel transition, this cluster approach predicts scaling laws relating dynamical exponents to critical random percolation exponents. Interestingly, in the mean-field such relations coincide with those predicted by the schematic continuous mode coupling theory, known as model A. More appropriate to describe the molecular glass transition is the schematic discontinuous mode coupling theory known as model B. In this case a similar cluster approach and a diffusing defect mechanism predicts scaling laws, relating dynamical exponents to the static critical exponents of the bootstrap percolation. In finite dimensions, the glass theory based on the random first order transition suggests that the mode coupling theory transition is only a crossover towards an ideal glass transition characterised by the divergence of cooperative rearranging regions. Interestingly, this scenario can also be mapped onto a mixed order percolation transition, where the order parameter jumps discontinuously at the transition, while the mean cluster size and the linear cluster dimension diverge. A similar mixed order percolation transition seems to apply to the jamming transition as well.