Description and molecular interpretations of anomalous compositional dependences of the glass transition temperatures in binary organic mixtures

The present study explores the applicability of a three-parameter equation: Tg = φ1Tg,1 + (1 − φ1)Tg,2 + φ1(1 − φ1)[a0 + a1(2φ1–1) + a2(2φ1–1)2] (where φi and Tg,i are, respectively, the weight fraction and the glass transition temperature of the ith neat component), recently proposed for describing the Tg vs. composition dependencies in miscible binary polymer blends and copolymers (Brostow et al. Mater. Lett. 62 (2008) 3152 [16]). Its efficacy is postulated here also for mixtures of polymers with low molecular mass organics (solvent, plasticizer or semicrystalline drug molecule phases) and very strongly/weakly associating polymer blends, including interpolymer complexes. Binary systems where entropic factors overcome the enthalpic ones were also considered. For several complicated (asymmetric or sigmoid) dependencies a description with better accuracy was achieved, compared to the common theoretical or semi-empirical functional forms, some of which require parameters that are not always readily available to the experimentalist or contain a superfluous number of fitting parameters. First- (linear) or second-order (parabolic) polynomial dependencies are established among its prime parameter a0 and “interaction terms” of common Tg(φ) functions, which are used as semi-quantitative measures of the strength of intermolecular interactions (e.g., parameter kGT of Gordon–Taylor, b of Jenckel–Heusch, and q of Kwei). Changes in the shape of the Tg(φ) plots, and the corresponding ai fitting parameter estimates, are discussed in relation to important physicochemical phenomena and properties of the mixtures, such as, the strength of the hetero-contact forces and their composition dependence, irregular excess free-volume effects, as well as nanoscale effects arising from variation of components molecular mass, chains’ branching or organization in crystalline phases.