Dynamic multiple scattering theory of the Huggins coefficient for discrete Gaussian chains. I. Formal derivation of the full frequency dependence
The Huggins coefficient of discrete Gaussian chains is derived from the friction coefficient density tensor to second order in concentration and is formally obtained as a full dynamic multiple scattering expansion. One contribution to the dynamical Huggins coefficient emerges from the single chain term in the multiple scattering expansion, but includes the concentration dependence of the Langevin polymer dynamics to first order in concentration. The other contribution is from the two-polymer multiple scattering term evaluated for the infinite dilution limit dynamics of these two chains. The discrete dynamical multiple scattering theory includes the full dynamics of the interbead scattering factors and therefore enables us to calculate the full frequency dependence of the Huggins coefficient as well as its steady state limit. These quantities are explicitly represented in terms of the single chain Rouse and Zimm eigenvalues and the transformation to Rouse-Zimm normal modes. Numerical evaluations and comparisons with experiment are presented in the accompanying paper.