Convective constraint release with chain stretch: Solution of the Rouse-tube model in the limit of infinite tubes

Abstract

This article derives a constitutive equation for entangled polymer melts and solutions, including the effects of convective constraint release (CCR) and chain stretch. It uses a model for CCR based upon the conjecture that constraint release events produce local hops of the tube, giving rise to a dynamical equation similar to the Rouse model. This equation is solved in the limit of infinite tubes. Although the solution in this limit ignores chain-end effects, the method presented has the following advantages; (i) it is less computationally expensive to implement than a full “finite chain” solution, (ii) it retains separate variables for chain stretch and tube orientation, allowing for straightforward modification of the equations to include different stretch dynamics, and (iii) it allows the possibility of smoothly changing the characteristics of the tube (such as tube diameter) upon deformation. In the latter context, this article explores the consequences of possible changes to the tube characteristics (tube diameter, persistence length, and CCR hop length) in response to chain stretch. It is found that the CCR-stretch equations are highly sensitive to the nature of the tube upon deformation, and in particular to the lower lengthscale cutoff used to describe the CCR process. The effect of CCR on chain stretch is explicitly derived from the microscopic model. The behavior of the constitutive equations is described for steady states under shear and startup under steady shear (where the results are compared against experiment).