Polymers in Random Media and Random Copolymers

The scaling properties of polymer systems with additional random features have been studied by renormalization group techniques. An example is a polymer is a random medium, which may be annealed (e.g. a binary solvent) or quenched (e.g. porous medium). A random medium creates an additional effective interaction between polymer units. The usual analogy between magnetic phase transitions with n=O and polymers appears to run into difficulties with randomness is present. These difficulties have been removed by allowing certain pair interaction variables to have infinite values at the random fixed point. However, physically meaningful difference variables remain infinite. This random fixed point has the same critical exponents as the usual excluded volume fixed point for both annealed and quenched random media. A similar analysis removes difficulties encountered by Kholodenko and Freed in analyzing polyelectrolytes in ionic media. Random copolymers have a third virtual coefficient that is modified by the randomness. Similar instabilities develop. The tricritical exponents describing conditions near the theta point are unchanged from those of homopolymers.