Monte Carlo studies of two measures of polymer chain size as a function of temperature

Monte Carlo simulations of single polymer chains with both excluded volume and nearest-neighbor interaction energies are discussed. Two measures of chain size are obtained in the simulation, the radius of gyration of the polymer chain and the inverse radius of the polymer chain. Both of these are reported as a function of temperature, or interaction energy, and chain length,N. The possibility of estimating the fractal dimensions of these measures from the Monte Carlo data is discussed in the context of two different interpolation functions for the temperature dependence of the fractal dimensions. The approach to the fractal dimension as a function of chain length,N, is studied. It is suggested that the approach to fractal dimension of the measures of chain size of polymers is slow, perhaps a fractional power itself.