Rheology and Tube Model Theory of Bimodal Blends of Star Polymer Melts

Abstract

Experiments on solution-cast blends of two anionically synthesized monodisperse star-shaped polyisoprene molecules of widely different molecular weight exhibit a very rich rheological behavior. The time-dependent moduli are exponentially dependent on the relative volume fraction of each species. This work models these new features by extending existing theories for monodisperse melt of star polymers to the blend of two monodisperse star polymers with different molecular weight, keeping the same chemistry. The theory is based on the tube model with constraint release for star polymers in both an approximate and then a more exact level. The latter, with its treatment of nonactivated as well as activated breathing modes, is able to account quantitatively for the huge range of blend rheologies. With no extra parameters, it is able to account qualitatively for relaxation times and entire relaxation functions that vary over many orders of magnitude on blending.

Rheology of Polydisperse Star Polymer Melts: Extension of the Parameter‐Free Tube Model of Milner and McLeish to Arbitrary Arm‐Length Polydispersity

“…As the formalism is applicable to star polymer melts with arbitrary arm-length polydispersity we have shown that for a monodisperse distribution it reduces to that of the original PFTM, while for a bimodal distribution we recover the theory of Blottière et al [10] for bimodal star blends. For the particular case of a Flory distribution, we could derive analytical expressions for both the universal relaxation potential U(z), Equation (46), and the concentration of unrelaxed material c(z), Equation (47).…”

“…This expression is a generalization, applicable to arbitrary molecular weight distributions (see Appendix A), of expressions (17) and (18) in the paper by Blottière et al [10] on bimodal blends of star polymers. Because there one has w(m) :…”

“…For star polymer melts, it is in particular the effect of polydispersity in the molecular weight of the arms that one is looking for. This problem has been considered both experimentally and theoretically by Blottière et al [10] for the special case of a bimodal blend of two monodisperse star polymers sharing the same chemistry. Their extension of the PFTM is clearly able to quantitatively describe the great diversity in rheological behavior one encounters for these blends, and without additional parameters is able to qualitatively account for relaxation times and entire relaxation functions varying over many orders of magnitude with degree of blending.…”

Tube theory of entangled polymer dynamics

“…Predictions of the resulting theory for G ¤ …! † and data from [277] are given in ®gure 33, together with a comparison spectrum of a linear monodisperse PI. Both the relaxation times and the detailed forms of the response function clearly vary exponentially with the relative fraction of the two components, yet the two-parameter theory captures the complete behaviour.…”

Prediction of linear viscoelastic properties for polydisperse mixtures of entangled star and linear polymers: Modified tube-based model and comparison with experimental results

“…This explains why many recent studies [3,[16][17][18][19] have been devoted to the prediction of LVE for ideal model molecules, mainly monodisperse stars, H-shaped or POM-POM molecules and combs. Some studies on simple mixtures of star architectures [20] or mixtures of stars with linear chains [21,22] or asymmetric stars [23] have been published also. For the analysis of more complex structures, two main molecular approaches have been proposed.…”