Numerical path-integration calculation of transport properties of star polymers and theta-DLA aggregates - Mansfield, M.L.; Douglas, J.F. (Condensed Matter Physics, 2002)
Although the calculation of transport properties of complex-shaped particles (Smołuchowski rate constants for diffusion-limited reactions, Stokes friction coefficient, virial coefficients for conductivity, viscosity and other transport properties) is straightforward in principle, the accurate evaluation of these quantities for objects of general shape is a problem of classic difficulty. In the present paper, we illustrate a recently developed numerical path-integration method to estimate basic transport properties of representative complex-shaped objects having scientific and technological interest (i.e., star polymers and diffusion-limited aggregates without excluded volume interactions). The methodology applies to objects of essentially arbitrary shape and its validation for special geometries, where exact results are known, is described in a previous paper. Here we calculate the electrostatic capacity and electrical polarizability tensor of these model branched polymers and then exploit exact and approximate electrostatichydrodynamic property interrelations to estimate the Stokes translational friction coefficient and the virial coefficients for conductivity and shear viscosity (intrinsic conductivity and viscosity, respectively). Dimensionless ratios of these transport properties and equilibrium measures of particle size (radius of gyration) are considered since these ratios are important experimentally in determining macromolecular topological structure and universality class. We also discuss and illustrate the influence of the branching architecture on the equilibrium charge distribution (“equilibrium measure”) of these branched polymers where they are treated as conductors. An unexpected qualitative change in the charge distribution is found with increasing arm number in star polymers that may have important physical consequences.