LATTICE-VIBRATIONS IN TIME-FLUCTUATING PERCOLATION NETWORKS - APPLICATION TO BRILLOUIN-SCATTERING FROM GLASSES AND LIQUIDS

A model of lattice vibrations in a percolation network which is stochastically fluctuating in time is treated within the effective-medium approximation (EMA). This work generalizes previous studies on vibrations in static percolation networks, which are characterized by phonon-fracton crossover, to the dynamical regime. Our result for the frequency-dependent effective force constant K(omega) is that it depends on omega-through the combinations omega-i-tau(j)-1, where tau(j) are the matrix fluctuation times. For a single-exponential relaxation, we obtain the relation K(omega,tau(-1)) = K0(omega-i-tau(-1)), where K0 is the effective force constant of the static (tau(-1) = 0) medium. We calculate the effect of lattice renewal on the dispersion relation and on the dynamical structure factor, for which we analyze separately the frequency-dependent linewidth and sound velocity. For the latter quantities, we also provide scaling Ansatze, which are shown to be obeyed by the EMA for sufficiently small fluctuation times-tau. We find that the dynamic fluctuation effects become dominant for small enough tau and are manifested (as tau-decreases) first as a nonuniform broadening and later as a "motional narrowing" of the dynamical structure factor line. The implications of our results on Brillouin scattering from glass-forming polymer melts and polymer electrolytes are discussed.