Monte Carlo simulation and self-consistent field theory for a single chain on a diamond lattice

Abstract

Monte Carlo simulations of self‐avoiding walks with nearest‐neighbor attractions have been performed on a diamond lattice for n≤210, where n is the number of steps. The data are compared with the scaling analysis of Daoud and Jannink and de Gennes, and, as found by previous simulation studies, a crossover exponent greater than the theoretical value is required for a good fit in the good solvent regime, though the theory works much better on the poor solvent side. For good solvent conditions it was found that the results do not accord too well with two‐parameter theory, and the theoretical expression of Muthukumur and Nickel fit the data rather poorly. The Domb–Barrett interpolation formulas fit somewhat better. This lends weight to the view that lattice corrections to two‐parameter theory are important. Finally the results are compared with a self‐consistent field theory over the whole range of solvent conditions. Provided an n‐dependent excluded volume parameter was used, fair agreement for many properties could be obtained for both good and poor solvents.