Interpretation of dynamic scattering from polymer solutions

Abstract

The theoretical results available for the interpretation of the dynamic scattering from polymer solutions have been re-examined. The scattering law S( q, t) is formulated using the eigenfunction expansion method and the linear response theory. All previously known exact expressions of S( q, t) for a single unperturbed Gaussian chain have been re-derived using the first method to demonstrate the interrelationships among the various approaches to calculation of S( q, t). The results are cast into new forms which, in many cases, are more convenient for both numerical and analytical discussions. The infinite chain results are obtained from the exact closed expression of S( q, t) for ring polymers as a special case as N → ∞. Questions like the effect of the draining parameter on the shape of S( q, t), the positive definiteness of the diffusion tensor, and the possibility of measuring the eigenvalue of the first internal mode through light scattering, have been included in the discussions. A new method has been proposed for the interpretation of the dynamic scattering experiments in terms of the initial slope, Ω, of In S( q, t). The quantity Ω can also be identified as the first cumulant of S( q, t). The advantage of this method is that Ω(q) can be calculated for all q values as a function of temperature and concentration by combining the linear response theory and the blob model of chain statistics. Consequently, one is not restricted to the asymptotic small- and intermediate- q regions in order to interpret the scattering experiments. The analytical and numerical results giving Ω(q) under various conditions have been presented. Using infinite chain results it is shown that Ω acts as a characteristic frequency in the sense that in both the small- and intermediate- q regions, In S( q, t) can be scaled to a q-independent shape function when time is expressed as Ωt. This property facilitates the measurement of Ω from S( q, t)-data using a known shape function. The feasibility of the method has been demonstrated using light scattering data on polystyrene in toluene in the transition region between small- and intermediate q-regions.