MONTE-CARLO SIMULATION OF MANY-ARM STAR POLYMERS IN 2-DIMENSIONAL GOOD SOLVENTS IN THE BULK AND AT A SURFACE

A Monte Carlo technique is proposed for the simulation of statistical properties of many-arm star polymers on lattices. In this vectorizing algorithm, the length of each arm l is increased by one, step by step, from a starting configuration with l = 1 or l = 2 which is generated directly. This procedure is carried out for a large sample (e.g., 100,000 configurations). As an application, we have studied self-avoiding stars on the square lattice with arm lengths up to l(max) = 125 and up to f = 20 arms, both in the bulk and in the geometry where the center of the star is adsorbed on a repulsive surface. The total number of configurations, which behaves as N approximately l-gamma-G-1 mu-fl, where mu = 2.6386 is the usual effective coordination number for self-avoiding walks on the square lattice, is analyzed, and the resulting exponents gamma-G = gamma(f) and gamma-s(f) for the bulk and surface geometries are found to be compatible with predictions of Duplantier and Saleur based on conformal invariance methods. We also obtain distribution functions for the monomer density and the distance of the end of an arm from its center. The results are consistent with a scaling theory developed by us.