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 crosslinked) macromolecules. Our approach invokes a variational hypothesis for the random static density fluctuations characterizing this solid state. The variational parameter is the inverse monomer localization length, which is zero in the liquid state and increases continuously as the mean number of crosslinks exceeds a critical value. The emergent solid is a homogeneous isotropic elastic medium, whose elastic moduli we compute near the transition.