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() is that it depends on through the combinations -i j-1, where j are the matrix fluctuation times. For a single-exponential relaxation, we obtain the relation K(-1)=K0(-i-1), where K0 is the effective force constant of the static (-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 Ansa$iumltze, which are shown to be obeyed by the EMA for sufficiently small fluctuation times. We find that the dynamic fluctuation effects become dominant for small enough and are manifested (as 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.