Limitations of Double Reptation Theory

Let us start by illustrating the conceptual limitations of the double reptation idea. Consider the case of a polymer of high molecular weight at a volume concentration in a matrix of a polymer of much lower molecular weight. This case was considered in Section 6.4.4.2, and we found that the double reptation model predicts two relaxation peaks in G , a peak at a high frequency roughly equal to the inverse of the reptation time, g, of the short chains, and a low-frequency peak, whose frequency is the inverse of half the reptation time, T(Jl/2, of the 

The dashed lines in Fig. 7.2 are the G co) curves for the pure short chains. If these dashed curves are subtracted from the data for the binary blends in Fig. 7.2, the contribution from the long chains is obtained, and this is plotted in normalized form in Fig. 7.3 for several different dilute blends of long chains in short chains [3]. These long-chain contributions to G (D) are 

---