Alladi Ramakrishnan Hall

Entanglements in Polymer Liquids: From monodisperse melts to binary blends

Sathish K Sukumaran

Yamagata University

Similarly to entangled ropes, polymer chains can slide past but not cut through each other. These topological constraints, the so-called entanglements, dominate the viscoelastic properties of high molecular weight polymeric liquids. Tube models of polymer dynamics and rheology are based on the idea that entanglements confine a chain to small fluctuations around a primitive path, which follows the coarse-grained chain contour. To establish the microscopic foundation for these highly successful phenomenological models, we have introduced a method for characterising the "topological state" of computer-generated long-chain polymer melts and solutions in terms of the primitive path mesh and obtained parameter-free, quantitative predictions for the plateau modulus. These predictions agree with experiment for all major classes of synthetic polymers [1,2].
The next level of complexity is that of binary blends, a miscible mixture of two different polymers. Their dynamics and rheology exhibit several unique features due to the dynamical heterogeneity induced by the composition fluctuations and remain poorly understood [3]. Therefore, the first step would be to understand the structure of entanglements in these blends, starting with the nature of the mixing rules for the plateau modulus or equivalently, in the context of the tube model, the tube diameter. Early work (see [3] and the references therein) suggested that a harmonic mixing rule provides an adequate description of the experiments. However, recent work by Watanabe and coworkers [3-5] on a blend of Poly(isoprene) and Poly(tert-butylstyrene) has clearly demonstrated qualitative deviations from the harmonic mixing rule.
Motivated by the differences in the molecular characteristics of the two component polymers in the blend, we considered two types of blends: (1) blends of polymers that differ only in their stiffness and (2) blends of polymers that differ only in their monomer size. We found that, in both cases, the topological analysis yielded just one tube diameter for the blend. However, the mixing rules for the two cases were qualitatively different. Case (1) yields a harmonic mixing rule similar to earlier work [3]. This mixing rule can be understood by a direct extension of the packing ansatz for monodisperse melts [5]. On the other hand, the simulation results for case (2) are well described by an ad-hoc mixing rule proposed Watanabe and coworkers.

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1570 (2011).
[5] Y. Matsumiya, N. Rakkapao and H. Watanabe, Macromolecules 48, 7889 (2015).