Self-concentrations and effective glass transition temperatures in polymer blends

In a miscible polymer blend the local environment of a monomer of type of A will, on average, be rich in A compared to the bulk composition, φ, and similarly for B; this is a direct consequence of chain connectivity. As a result, the local dynamics of the two chains may exhibit different dependences on temperature and overall composition. By assigning a length scale (or volume) to particular dynamic mode, the relevant 'self-concentration' φ_s can be estimated. For example, we associate the Kuhn length of the chain, l_K, with the monomeric friction factor, ζ, and thus the composition and temperature dependences of ζ should be influenced by φ_s calculated for a volume V approx. l_K³. An effective local composition, φ_eff, can then be calculated from φ_s and φ. As lower T_g polymers are generally more flexible, the associated φ_s is larger, and the local dynamics in the mixture may be quite similar to the pure material. The higher T_g component, on the other hand, may have a smaller φ_s, and thus its dynamics in the mixture would be more representative of the average blend composition. An effective glass transition temperature for each component, T_g^eff, can be estimated from the composition-dependent bulk average T_g as T_g(φ_eff). This analysis provides a direct estimate of the difference in the apparent T_g's for the two components in miscible blends, in reasonable agreement with those reported in the literature for four different systems. Furthermore, this approach can reconcile other features of miscible blend dynamics, including the asymmetric broadening of the calorimetric T_g, the differing effects of blending on the segmental relaxation times of the two components, and the failure of time-temperature superposition.