POLYMERS IN SOLUTIONS - PRINCIPLES AND APPLICATIONS OF A DIRECT RENORMALIZATION METHOD

The configurational properties of long polymers in solution can be conveniently studied by using a direct renormalization method, recently introduced by the author. This method is described here in detail and applied to the two-parameter model. The indices gamma , v and omega are calculated directly to second order in epsilon equals 4 minus d, where d is the space dimension. As expected, these expansions coincide with the expansions of the indices gamma , v and omega of the zero-component Landau-Ginzburg-Wilson field theory. The formalism may describe monodisperse or polydisperse ensembles and leads directly to scaling equations. The second virial coefficient, expressed in terms of a scaling length which is the end to end distance of an isolated polymer, has been exactly calculated, for a monodisperse system to second order in epsilon . The ratio of the radius of gyration to the end to end distance is calculated to first order in epsilon ; the result obtained is in agreement with the value calculated by T. Witten and L. Schafer using field theory. The dependence of the expansion factor and of the virial coefficient, with respect to the interaction in the cross over domain, are studied to order epsilon **2. An expression is also given for the entropy of an isolated chain.