Dynamic multiple scattering theory of the Huggins coefficient for discrete Gaussian chains. II. Numerical computations of the frequency dependence and steady state limit

Numerical calculations are presented for the frequency dependent Huggins coefficient based on the formal derivation provided in paper I using the dynamical multiple scattering theory for discrete Gaussian chains. The calculations employ fast Fourier transform methods and confirm the analytic complexity of this frequency dependence as previously anticipated from our calculations of the concentration dependence of the normal mode autocorrelation function. The harmonic spring model is considered because this simple limit is amenable to closed form solution, displaying the frequency dependence of the relaxation rates and providing a useful check on the difficult numerical computations for higher numbers n of beads. The steady state Huggins coefficient is also calculated with carefully optimized Gauss–Laguerre quadrature methods which permit extrapolation to n→∞. The calculated steady state value of 0.33 lies below experimental data for theta solutions, and an extensive discussion of the experimental data is provided to understand the discrepancy. One major factor, suggested by Schrag, arises from a strong concentration dependence of the individual bead friction coefficient.