Associate 1995-96

Paul M Goldbart


Dynamical Properties of Randomly Crosslinked Macromolecular Networks

As Charles Goodyear discovered in 1839, when he first vulcanized rubber, a viscous liquid of macromolecules becomes solid when sufficient random crosslinking is performed. Before vulcanization, the long, flexible rubber macromolecules can wander throughout the container, so that if the sample is sheared, the macromolecules flow, ultimately relaxing the restoring force. Vulcanization has the effect of permanently binding together random pairs of atoms, thus converting the system into an extended, random macromolecular network and, as a result, the macromolecules are no longer free to flow, instead becoming localized, like the atoms of simple solids. In contrast with simple solids, however, the formation of a crystalline macromolecular solid is frustrated by the random locations of the crosslinks and the impenetrability of the macromolecules. Thus, the emergent solid is an equilibrium amorphous solid, in which the atomic positions are random: unlike simple solids, in which the atoms form in a regular array, a snapshot of this amorphous solid would not distinguish it from a liquid.

In collaboration with Professor Annette Zippelius (Universität Göttingen, Germany), Professor Goldbart has recently developed a microscopic theory that describes the static (i.e., equilibrium) properties of the unusual amorphous solid state of randomly crosslinked macromolecular matter. As an Associate in the Center for Advanced Study, he plans to construct a comprehensive microscopic theory of the dynamical (i.e.., nonequilibrium) properties of randomly crosslinked macromolecular matter, from lightly vulcanized liquids through to heavily vulcanized solids. Such a development, which would represent important progress in the theory of macromolecular materials, is intended to provide a first-principles explanation of the remarkable viscoelastic behavior of such materials, which in addition to being of fundamental interest in basic research, is also of enormous technological and biological importance.