Interpretation of dynamic scattering from polymer solutions

Abstract

The theoretical results availabTe for the i,nte,rpretatio~ of the dynamic scattering from polymer soJutions have been re,examined. The scattering law S~/, 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 cl~ain 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 ~nfi~i~e ~hain results are obtained from the exact closed expression of S(q, t) for ring polymers as a special .case as N ~ oo. 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, ,Q,, of In S(q, t). The quantity ~ can also be identified as the first cumulant ofS(q, t). The advantage of this method is that ~Q(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 ~2(q) under various conditions have been presented. Using infinite chain results it is shown that 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 ~,t. This property facilitates the measurement of ~ 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.

Dynamics of star-burst dendrimers in solution in relation to their structural properties

“…Not preaveraging the Oseen tensor just leads to a renormalization of the prefactors from 1/(6 )Ϸ0.053 to 0.063 and from 0.071 to 0.079 for -and good solvent conditions, respectively. 26,27 Independent of the solvent quality, the q 3 dependence is preserved.…”

Simple Derivation of the First Cumulant for the Rouse Chain

“…The central quantities of interest in these studies are the dynamic structure factor (DSF) and its first cumulant Γ, approximate formulas which have been obtained already in the classic de Gennes' work forty years ago [3]. Later, Akcasu et al [4] derived closed expressions for the first cumulant both in the free-draining limit and with hydrodynamics included, but these formulas are too complicated to be used in the interpretation of experimental data. As discussed in the recent paper [5], they are given as summations over the number of beads in the chain and produce simple results only in the limit of large scattering vectors.…”

Translational diffusion of polymer chains with excluded volume and hydrodynamic interactions by Brownian dynamics simulation

“…Both light scattering experiments [12][13][14][15] and first-principles Molecular Dynamics (MD) simulations 16,17 show that the difference must be quite small such that it is below resolution. In the case of MD, the main difficulty is the fact that the "shorttime" limit of Kirkwood theory is of course not the exact t → 0 limit, but rather a time regime where the local motions of the particles in their "cages" (or the momenta) have already relaxed completely, while the conformational degrees of freedom of the chain must at the same time be considered as completely unrelaxed.…”