Hydrodynamic factors for linear and star polymers on lattice under the theta condition

Monte Carlo calculations were made to evaluate the intrinsic viscosity [η] and hydrodynamic radius R_H along with the mean square radius of gyration 〈S²〉 for linear and star polymers with the arm number f=3, 4, 6, and 8 on a simple cubic lattice. For the hydrodynamic calculation, Zimm's method based on the rigid-body approximation was used. The ensemble averages were taken according to the Boltzman factor with the contacting energy between segments, which was chosen to be 0.275 for the theta condition, multiplied by the number of contacts among the chain. The ratios g_η≡[η]_star/[η]_linear and g_H≡(R_H)_star/(R_H) _linear calculated agreed with experimental data for theta solvent systems within 3.5 and 2.5%, respectively, where the subscripts describe the structure of polymer chain. The hydrodynamic factors Φ and ρ defined by [η]M/(6〈S²〉)^3/2 and 〈S ²〉^1/2/R_H, respectively, with the molecular weight M obtained from the simulation for linear and star polymers with f=4 and 6 were also close to experimental values. It was concluded that most of the error of analytical theories, which fail to predict hydrodynamic properties for star polymers, comes from the preaveraging approximation of the Oseen tensor.