The time-dependent stress relaxation for a Rouse model of a crosslinked
polymer melt is completely determined by the spectrum of eigenvalues of the
connectivity matrix. The latter has been computed analytically for a mean-field
distribution of crosslinks. It shows a Lifshitz tail for small eigenvalues and
all concentrations below the percolation threshold, giving rise to a stretched
exponential decay of the stress relaxation function in the sol phase. At the
critical point the density of states is finite for small eigenvalues, resulting
in a logarithmic divergence of the viscosity and an algebraic decay of the
stress relaxation function. Numerical diagonalization of the connectivity
matrix supports the analytical findings and has furthermore been applied to
cluster statistics corresponding to random bond percolation in two and three
dimensions.Comment: 29 pages, 15 figure
