A Theoretical Analysis of Rheodielectric Response of Type-A Polymer Chains

For type-A polymer chains having type-A dipoles parallel along the chain backbone (such as cis-polyisoprene), a theoretical analysis was conducted for the rheodielectric response to relate this response to the chain dynamics. The rheodielectric response in the shear gradient direction (y direction) under steady shear was analyzed on the basis of a Langevin equation. It turned out that the relaxation time is exactly the same for the rheodielectric relaxation function and the end-to-end vector autocorrelation function defined in the shear gradient direction and that the relaxation mode distribution also coincides for these functions at least up to second order of the shear rate (corresponding to the lowest order of nonlinearities of these functions). Consequently, the Green-Kubo theorem holds satisfactorily, and the rheodielectric intensity is proportional to the squared chain size in y direction, < R-y(2)>, averaged over the time-independent conformational distribution function under steady shear. The situation is more complicated under large amplitude oscillatory strain (LAOS) because the conformational distribution function f(LAOS) is synchronized with LAOS to oscillate at the LAOS frequency, Omega. The rheodielectric response under LAOS was found to detect this oscillation of f(LAOS) being coupled with the oscillation of the electric field, E(t) = E(0)sin omega t, and thus, split into a series of components oscillating at frequencies omega and omega +/- beta Omega (beta = 1, 2, ...). Consequently, the rheodielectric intensity under LAOS, evaluated from the component oscillating at (i), is no longer proportional to < R-y(2)>. However, the relative mode distribution and relaxation time of this component can be directly related to those of the end-to-end vector correlation averaged over a nonoscillatory part of f(LAOS). (C) 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 1039-1057, 2009