Dielectric and mechanical relaxation in liquids and glasses; transition from effective medium to percolation treatments

Abstract

The general proportionality of the dielectric relaxation peak frequency to the dc conductivity in glasses implies the relevance of the “percolation” of pair processes; the critical rate defining percolation of pair processes is proportional to both the loss peak frequency, ω c, and the dc conductivity. The critical rate w c = ω c is that rate at which interconnected pathways of macroscopic length appear such that relaxation between all individual pairs on the path occurs within times τij≤ w −1 c . The physics of mechanical relaxation that surfaces slip past one another requires a separation of such “percolation” paths of order r o where r o is a typical hopping length. This requires inclusion of rates significantly slower than w c = ω c (past critical percolation) making the dc viscosity and (by analogy with dielectric response) the relaxation peak frequency ω p involve a slower relevant relaxation time. Consequently the viscosity rises more rapidly than the resistivity, and the mechanical relaxation peak is broader than the dielectric relaxation peak in the percolation regime (after the viscosity has risen about 5 orders of magnitude).