Excluded volume effect on quasielastic neutron scattering from concentrated polymer solutions

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Abstract
A study is made of the excluded volume dependence of quasielastic neutron scattering from polymer solutions which are concentrated enough that excluded volume interactions are screened for distances comparable to the mean-square-end-to-end vector distance. Both incoherent and coherent scattering are considered as well as the scattering by individual isotopically labeled chains. The theory is developed by employing two different formulations as certain further generalizations will be facilitated from the availability of the two viewpoints. One approach uses the Mori–Zwanzig theory of generalized Brownian motion with the recognition that at low frequencies the memory terms are unimportant for chain dynamics. The hydrodynamic interactions are fully incorporated through the use of a concentration dependent effective bead friction coefficient ν as derived in an accompanying paper, and the screened excluded volume interactions are included for the high concentration limit following Edwards. The coherent scattering cross section contains an additional vρ0k2ν−1 term in the ω−k dispersion relation beyond the usual Rouse (k)4 term, where v is the excluded volume and ρ0 is the monomer number density. The incoherent scattering cross section and the coherent one for scattering by individual labeled chains display the same k4 Rouse dependence, described by de Gennes, but with coefficients that are altered by the excluded volume. The second approach uses a self-consistent Fokker–Planck formalism that was previously developed for the study of turbulence. The theory ignores the effects of entanglements, and the experimental justification for this approximation is provided for chains with molecular weights below a certain critical value.

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