Glass transition-related thermorheological complexity in polystyrene melts

Abstract

The relaxation-modulus G( t) functional forms covering the whole time range are given by incorporating a stretched exponential for the structural-(glassy-) relaxation process into the extended reptation theory ( ERT; for entangled systems) or the Rouse theory ( for entanglement-free systems). The creep compliance J ( t) curves of two entangled ( A and B) and one entanglement-free ( C) polystyrene samples ( Plazek) as well as the viscoelastic spectra G*(omega) of four entanglement-free polystyrene samples ( Inoue et al) have been quantitatively analyzed in terms of the given G( t) functional forms. In such quantitatively successful analyses, the ERT or the Rouse theory works as the frame of reference in both the line shape and timescale. The thermorheological complexity in the J ( t) curves is explained naturally and precisely by the temperature dependence of the energetic-interaction-derived structural relaxation being stronger than that of the entropic ERT or Rouse dynamics in a simple way. Structural-relaxation times tau(S)(=18s' K') of all the studied samples are equally well separated into two decoupled quantities: the structural- growth parameter s' and the frictional factor K' ( for the Rouse Mooney or Rouse modes of motion). The separation is fundamentally a clean-cut process: s' is determined entirely by the line shape of J ( t) or G*(omega) while K' is calculated from the timescale shifting factor obtained from the superposition of the calculated curves onto the measured. The glassy- relaxation strength A(G)(f) and the stretching parameter beta extracted from the J ( t) and G*(omega) results over the glassy- relaxation region are in good agreement. The glass-transition temperature T-g is defined as corresponding to tau(S) = 1000 s for all the studied samples. The tau(S), s' and K' data points of samples A, B and C extracted from their J ( t) curves individually fall closely on the same curves when expressed as a function of Delta T = T - T-g, revealing a T-g-related universality within the polystyrene system, entangled or not. The revealed universality confirms the previously derived conclusion that the ERT and the Rouse theory have the same footing at the Rouse-segmental level. Representing important physical features of the universality, the length-scale of the structural relaxation increases as Delta T diminishes and reaches the value of similar to 3 nm at Delta T = 0 ( or at T-g) for all three samples, A, B and C. Extracted from the G*(omega) results, the tau(S), s' and K' data of samples with molecular weights just below and well below entanglement molecular weight M-e ( 13 500) are found to deviate more from the respective universal curves with decreasing molecular weight. Deviation is estimated to start occurring at M-w = 12 000.