BEYOND FLORYS THEORY - A COMPUTER-AIDED PHENOMENOLOGY FOR POLYMERS

Extending the histogram method of Ferrenberg and Swendsen to the probl em of a SAW in a bad solvent, we obtain a new expression for the free energy of such a system, which fits very properly the numerical result s of our Monte Carlo simulations. The basic difference with Flory's th eory lies in the reference system: instead of considering random walks (RW) we start with self-avoiding walks (SAW) for which we already pro posed a model expression for the distribution of the radius of gyratio n. This distribution is universal for any class of homo- or heteropoly mers and contains all the information concerning the excluded volume p roblem. For homopolymers we consider the standard case where attractiv e nearest neighbours interactions simulate a bad solvent At a given ra dius of gyration r we compute the density of states P(r, m) for an int eracting self avoiding walk (ISAW) as a function of its number of cont acts m. We build a microscopic phenomenology for P(r, m) based on a fa ctorisation procedure: P(r, m) is split into an a priori probability P (r) of finding a SAW with a given r, and a conditional probability P(m /r) of finding such a conformation with m contacts. A complete scaling is given for P(r) whereas P(m/r) is found to be well approximated by a gaussian distribution. Scaling laws for the first two cumulants of P (m/r) are exhibited from a finite-size scaling analysis. The theta-poi nt temperature is recovered along with its dependence on the polymer l ength and the free energy of the globule phase is well reproduced. Thi s approach is shown to be generalizable to heteropolymers by merely re placing m by u, the energy per monomer, and computing the density of s tates P(r, u) at a given r. The case of sequenced and random copolymer s is examined with special attention to polyampholytes.