Macromolecules, Vol.42, No.3, 820-829, 2009
Self-Contacts, Self-Concentration, and the Composition Dependence of the Glass Transition Temperature in Polymer Mixtures
Self-concentration, a consequence of chain connectivity, is an important factor in determining the properties of polymer mixtures. It is proposed that self-concentration has two components. First, there is a "covalent connectivity effect", which manifests itself in the probability that a site adjacent to a chosen segment on a chain is occupied by a like or unlike segment; second, there is a "conformational connectivity effect" that is a consequence of a chain bending back on itself through both local and long-range factors that depend on the flexibility of the chain. This latter component is modeled using a contact point approach developed in previous work. If the covalent connectivity effect is treated using a lattice model, there is a cancelation of terms and noncovalent contacts do not contribute to self-concentration in calculating the average properties of polymer blends. Nevertheless, when covalent contacts are included together with conformational self-contacts in order to calculate the composition dependence of the glass transition temperature, an equation corresponding to the self-consistent form of the Lodge-McLeish model derived by Lipson and Milner is recovered. In the systems studied so far, this approach leads to consistent results, with values of self-concentration terms that correspond to what would be expected in terms of connectivity and self-contact parameters determined in previous work. This parameter appears to be a transferable constant that depends on the microstructure, conformation and to some degree the molecular weight of the polymer.