Entanglement Length in Miscible Blends of cis-Polyisoprene and Poly(p-tert-butylstyrene)

The entanglement length a, being equivalent to the plateau modulus G(N) (proportional to M-e(-1) proportional to a(-2)), is one of the most basic parameters that determine the slow dynamics of high molecular weight (M) polymers. In miscible blends of chemically different chains, the components would/should have the common a value. However, changes of a with the blend composition have not been fully elucidated. For this problem, this study conducted linear viscoelastic tests for miscible blends of high-M cis-polyisoprene (PI) and poly(p-tert-butylstyrene) (PtBS) and analyzed the storage and loss moduli (G' and G '') data in a purely empirical way, considering the very basic feature that unentangled and entangled blends having the same composition exhibit the same local relaxation. (From a molecular point of view, this local relaxation reflects the chain motion within the length scale of a.) On the basis of this feature, a series of barely entangled low-M PI/PtBS blends having various component molecular weights and a given composition were utilized as references for well-entangled high-M PI/PtBS blends with the same composition, and the modulus data of the reference were subtracted from the data of the high-M blends. For an optimally chosen reference, the storage modulus of the high-M blends obtained after the subtraction (G(ent)' = G(high-M) (blend)' - G(ref)') exhibited a clear plateau at high angular frequencies omega. The corresponding loss modulus G(ent '') decreased in proportion to omega(-1) at high omega, which characterized the short-time onset of the global entanglement relaxation: A mischoice of the reference gave no plateau of G(high-M blend)' - G(ref)' and no omega(-1) dependence of G(high-M blend)'' - G(ref)'' at high omega, but a survey for various low-M PI/PtBS blends allowed us to find the optimum reference. With the aid of such optimum reference, the entanglement plateau modulus G(N) of the high-M PI/PtBS blends was accurately obtained as the high-omega plateau value of G(ent)''. G(N) thus obtained was well described by a linear mixing rule of the entanglement length a with the weighing factor being equated to the number fraction of Kuhn segments of the components, not by the reciprocal mixing rule utilizing the component volume fraction as the weighing factor. This result, not explained by a mean-field picture of entanglement (constant number of entanglement strands in a volume a(3)), is discussed in relation to local packing efficiency of bulky PtBS chains and skinny PI chains.