Analysis of the dynamic structure factor for semi-dilute solutions of polyisobutylene

The equation for polymer concentration fluctuation derived from Onuki's equations of motion is coupled with Onuki's postulate for the partial stresses generated by concentration fluctuation to formulate the dynamic structure factor S(q,t) [t is time and q the magnitude of the scattering vector]. The actual calculation is made for systems in which the elastic relaxation modulus L(t) is given by a linear combination of n exponential functions. It is shown that the corresponding S(q,t) consists of n + 1 exponential functions of time, and that the relative strengths and decay rates of these functions are related by a set of algebraic equations to the diffusion coefficient and cooperative diffusion coefficient, as well as the parameters characterizing L(t). These equations for n = 2 are used to analyze dynamic light scattering data on semidilute solutions of a polyisobutylene fraction in isoamyl isovalerate (Theta solvent) and n-heptane (good solvent). The results give the instantaneous moduli of the solutions which are well compared with the rubbery plateau moduli from viscoelastic measurements, and the friction coefficients which are identical for both solvents when compared at comparable polymer concentrations. (C) 1998 Elsevier Science Ltd. All rights reserved.