REPTATION OF A POLYMER-CHAIN IN AN IRREGULAR MATRIX - DIFFUSION AND ELECTROPHORESIS

A simple version of the reptation theory of motion of polymer chains through random matrices is extended by adding a free energy of interaction between the moving chain (the ''probe'') and the matrix. This free energy is assumed to depend on the position of the probe and to fluctuate randomly as the probe moves. The electrophoretic mobility and diffusion constant of the probe are calculated by numerical integration of the diffusion equation. It is found that the probe sometimes falls into low-free-energy states that act as temporary traps. These traps can dramatically slow the motion of the probe, depending on the values of the interaction free energy and a possible external field, if any. The dependence of the diffusion constant on probe size N changes from the classical reptation N-2 at small N to an exponential dependence at large N. The electrophoretic mobility has a more complex behavior that depends on the strength of the electric field. With low fields the mobility shows the classical N-1 at small N, is markedly depressed at intermediate N, and becomes classical again at large N. (With sufficiently high fields the behavior is classical at all N.) The depression at intermediate N can make the mobility depend very steeply on size over a short range of sizes and can also produce ''band inversion'', where larger probes move faster than smaller ones. In the region of the depression the migrating band can be greatly broadened.