AMORPHOUS SOLID-STATE OF VULCANIZED MACROMOLECULES - A VARIATIONAL APPROACH

We present a microscopic theory of the transition to and properties of the amorphous solid state of a system of vulcanized (i.e., randomly c rosslinked) macromolecules. Our approach invokes a variational hypothe sis for the random static density fluctuations characterizing this sol id state. The variational parameter is the inverse monomer localizatio n length, which is zero in the liquid state and increases continuously as the mean number of crosslinks exceeds a critical value. The emerge nt solid is a homogeneous isotropic elastic medium, whose elastic modu li we compute near the transition.