Entanglement Length in Miscible Blends of \textit{cis}-Polyisoprene and Poly(\textit{ptert}-butylstyrene)

In miscible polymer blends, the entanglement length is common for the components, but its changes with the composition $w$ remain unclear. For this problem, this study analyzed viscoelastic data for miscible blends of \textit{cis}-polyisoprene (PI) and poly(\textit{ptert}-butylstyrene) (PtBS), considering the basic feature that the local relaxation is determined only by $w_{\mathrm{PI}}$. On the basis of this feature, a series of unentangled low-$M$ PI/PtBS blends having various $M$ and a given $w_{\mathrm{PI\thinspace }}$were utilized as references for well-entangled high-$M$ PI/PtBS blends having the same $w_{\mathrm{PI}}$, and the modulus data of the references were subtracted from the high-$M$ blend data. For an optimally chosen reference, the storage modulus $G_{\mathrm{e}}' $of the high-$M$ blends obtained after the subtraction exhibited a clear entanglement plateau $G_{\mathrm{N}}$ and the corresponding $G_{\mathrm{e}}''$ decreased in proportion to 1/$\omega $ at high frequencies $\omega $. Thus, the onset of entanglement relaxation was detected. The $G_{\mathrm{N\thinspace }}$values were well described by a linear mixing rule of the entanglement length with the number fraction of Kuhn segments of the components being utilized as the averaging weight. This result, not explained by a mean-field picture of entanglement, is discussed in relation to local packing of bulky PtBS chains and skinny PI chains.