Comparison of numerical and analytical orientation average methods in polymer light scattering

Publisher Website
Google Scholar
Abstract
We have calculated the Perrin matrix for elastic light scattering by two distinct numerical methods, and we present here a critical comparison. Both methods assume the dipole array model with retarded dipole–dipole interaction between subunits. However, the average over all orientations of the model is carried out differently in the two methods. The conceptually simplest method (and the easiest to program) is rotation by Cartesian matrix (CM) algebra with three-dimensional numerical integration over Euler angles. The second method is based on rotations by Wigner matrix (WM) algebra with analytic integration, and requires an infinite sum in one index which must be truncated. The two methods agree when they are pushed far enough. Both methods require substantial calculation, but the analytic method is shown to be far superior in its convergence properties. Comparing calculations of the whole Perrin matrix of scattering curves (16 curves, 21 scattering angles) in which all curves are computed to 1% accuracy, the CPU times for the numerical integration over Euler angles is about 500 times slower.