ANALYSIS OF THE DYNAMIC STRUCTURE FACTOR FOR SEMIDILUTE SOLUTIONS OF POLYISOBUTYLENE

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