Understanding Constraint Release in Star/Linear Polymer Blends

In this paper, we exploit the stochastic slip-spring model to quantitatively predict the stress relaxation dynamics of star/linear blends with well-separated longest relaxation times and we analyze the results to assess the validity limits of the two main models describing the corresponding relaxation mechanisms within the framework of the tube picture (Doi's tube dilation and Viovy's constraint release by Rouse motions of the tube). Our main objective is to understand and model the stress relaxation function of the star component in the blend. To this end, we divide its relaxation function into three zones, each of them corresponding to a different dominating relaxation mechanism. After the initial fast Rouse motions, relaxation of the star is dominated at intermediate times by the skinny tube (made by all topological constraints) followed by exploration of the fat tube (made by long-lived obstacles only). At longer times, the tube dilation picture provides the right shape for the relaxation of the stars. However, the effect of short linear chains results in time-shift factors that have never been described before. On the basis of the analysis of the different friction coefficients involved in the relaxation of the star chains, we propose an equation predicting these time-shift factors. This allows us to develop an analytical equation combining all relaxation zones, which is verified by comparison with simulation results.