Relaxation spectra of binary blends: Extension of the Doi-Edwards theory

Abstract

-A molecular model is presented which allows the calculation of the stress relaxation function G for binary blends consisting of two monodisperse samples with arbitrary molecular weights. It extends the Doi-Edwards reptation theory (Doi M. and Edwards S. F., The Theory of Polymer Dynamics (Oxford Press, New York) 1986) to highly polydisperse melts by including constraint release (CR) and thermal fluctuations (CLF), yet making use of the same input parameters. The model reveals an explicit nonlinear dependence of CR frequency in the blend on the blend's molecular weight distribution (MWD). It provides an alternative way to quantify polydisperse systems compared to the widely used "double-reptation" theories. The results of the present model are in a good agreement with the experimental data given in Rubinstein M. and Colby R. H., J. Chem. Phys., 89 (1988) 5291. Copyright c EPLA, 2007The molecular model of Doi and Edwards (DE) [1] proved to be remarkably successful in predicting the rheological response of linear monodisperse polymer melts in the linear viscoelastic regime. Some initial shortcomings in this regime could be eliminated by including a rigorous treatment of thermal fluctuations [2]. However, already in an early stage it was realized that its straightforward extensions to polydisperse systems, such as binary blends, did not adequately describe the observed rheological behavior [3]. This discrepancy between theory and experiment strongly suggested that the fundamental postulate of the DE model that the surrounding network of polymers constitutes a time-independent mean field of topological constraints is not applicable in case of polydisperse materials. It breaks down because a low molecular weight polymer imposing a constraint on a high molecular weight test chain can diffuse away much faster than the test chain reptates. Clearly, any realistic model for polydisperse systems must provide a rigorous treatment of constraint release along with thermal fluctuations.In a number of attempts one has tried to adjust the original DE model through inclusion of constraint release [4][5][6][7]. Most of these extensions led to models, that were mathematically complicated and still had restricted predictive capability and thus limited practical utility. Alternatively to the DE theory, des Cloizeaux and Tsenoglou independently developed a network model [8,9] for linear viscoelastic materials based on the concept of "double reptation". Their formalism allows one to express the stress relaxation function of a polydisperse melt in terms of relaxation spectra of each of its monodisperse components and a so-called "mixing rule". Double reptation theory shows a good agreement with observed data on polydisperse melts with rather narrow molecular weight distribution (MWD). The broader the MWD, the larger the disagreement between theoretical predictions and data. Recently, Mead [10] extended the "double reptation" theory to non-linear flows by introducing convective constraint release and stretch in the model.