STATISTICAL-MECHANICS OF VULCANIZATION AND THE SPONTANEOUS EMERGENCE OF STATIC-DENSITY FLUCTUATIONS

We present a statistical-mechanical analysis of a system of randomly c ross-linked macromolecules, focusing on the emergence of random static -density fluctuations as the solidification transition is approached. In mean-field theory the problem can be formulated in terms of a singl e macromolecule in an effective random potential. The distribution of the random potential, which must be calculated self-consistently, dete rmines all moments of the static-density fluctuations. We find that th e solidification transition occurs when an infinite network of cross-l inked macromolecules is formed, and that a sequence of nonlinear densi ty response functions diverges simultaneously at this transition.