Mode coupling corrections tot he Onsager coefficient as determined by light scattering of critical concentration fluctuations from polymer mixtures

Abstract

We report static and dynamic light-scattering experiments of an almost symmetric polymer mixture made up from polydimethylsiloxane (PDMS), N=260 and polyethylmethylsiloxane (PEMS), N=340 with N being the degree of polymerization. The mixture exhibits an upper critical solution temperature T c≃57°C with a critical composition φ C, PEMS=0.465. The measurements were performed in a broad temperature range in the one-phase region between −0.7<ɛ<−2.5 with ɛ=T−T c/T. From measurements of the mutual diffusion coefficient \(\tilde D\)and the static structure factor S(q=0), the Onsager coefficient \(L(q) = \tilde DS(q = 0)\)was calculated. It is related to W 0, a microscopic frequency, given by the Rouse diffusion coefficient D R 0 =W 0/N via L=φ(1−φ)W 0. We have basically found that for values of the correlation length ς of concentration fluctuations smaller than the coil size, W 0 behaves according to Rouse theory, but in the hydrodynamic regime, where one probes the slow diffusive dynamics of concentration fluctuations with wavelengths larger than the size of the polymer coil and the correlation length, W 0 tends to accelerate as T → T c. Using the mode-mode coupling prediction that in the cited regime W 0 is proportional to ς we have removed the apparent discrepancy.