Star polymer dynamic moduli

The case of star/linear blends is a challenging one, because the description of constraint release that works best for pure star polymers is dynamic dilution, while for pure linear polymers, double reptation , or some variant of it, seems to be the better description. However, Milner, McLeish and coworkers [23] have developed a rather successful theory for the case of star/ linear blends. In the Milner-McLeish theory, at early times after a step strain both the star branches and the ends of the linear chains relax by primitive-path fluctuations combined with dynamic dilution, the latter causing the effective tube diameter to slowly increase with time. Then, at a time corresponding to the reptation time of the linear chains, the tube surrounding the unrelaxed star arms increases rather quickly, because of the sudden reptation of the linear chains. The increase in the tube diameter would be very abrupt, if it were not slowed by inclusion of the constraint release-Rouse processes, which leads to a square-root-in-time decay in the modulus (see Section 7.3). With this formulation, the Milner-McLeish theory yields very favorable predictions of polybutadiene data for star/linear blends see Fig. 9.13, where the parameters have the same values as were used for pure linears and pure stars. 

Block Ionomers. The block ionomers to be discussed are of AB or ABA type, in which one of the blocks is ionic (eg, sodium methacrylate) and the other consists of nonionic units (eg, polystyrene). While ionic block copolymers in a micelle form in both aqueous and nonaqueous solutions have been studied extensively (99-101,130,131), the viscoelastic properties of block ionomers in bulk have not received much attention (132-137). If the short ionic blocks formed micelle-like aggregates, which were surrounded by nonionic blocks, the viscoelastic properties of the diblock ionomers would be very similar to those of stars or polymers of low molecular weight (136). Thus, above the Tg of the nonionic blocks, as the temperature increased the modulus dropped rapidly with a very short rubbery plateau. For example, in a dynamic mechanical study, it was found that a homopolymer containing 490 styrene units showed a Tg at ca 115°C, and started to flow at ca 150°C. However, in the case of a diblock ionomer containing 490 styrene units and 40 sodium methacrylate ionic units showed a Tg at ca 116°C, and flow behavior was observed above ca 165°C, which was only 15°C higher than that of nonionic polystyrene (135). 

---