Dynamics and thermodynamics of the liquid state (T < T_g) of amorphous polymers

Abstract

A B S T R A C TThe liquid state behavior of the following atactic polymers has been reviewed: the alkyl and cycloalkyl methacrylates; polyisobutylene; polybutadiene, its random copolymers with styrene and acrylonitrile, and S-B diblocks; polystyrene; and the poly-cuolefins C3, C5, and C Just as T manifests itself through time-dependent (relaxational) and thermodynamic (transition) effects, so also does a T > T transition (relaxation) found generally in the range of 1.1 t o 1.3 T but mostly near 1 . 2 T This is designated as TQQ, a liquidl-liquid transition. T a~ is found, usually by a variety of dynamic, thermodynamic, and probe methods, in all of the above classes of polymers plus iso-PMMA, which also has a weak T < T o r T relaxation. With increasing syndiotactic content, PMMA's reveal strengthening T and T processes. Relaxation maps plotting log frequency-T TQQ. tion enthalpy about half that at T when both are observed some 50-100°K above their very low frequency values. Probe methods 6' g g g g' 2 g P P QQ-1 a r e presented for PBD and PIB, showing both T and g The latter exhibits non-Arrhenius behavior with an activag 461 Copyright 0 198 1 by Marcel Dekker, Inc. Downloaded by [Tulane University] at 09:04 05 January 2015 462 BOYER such as IR, "C-NMR, ESR with spin probes, depolarization of fluorescence, and thermally stimulated current seem unusually well suited to studies of the liquid state. The earliest concept of a TPL is that of Ueberreiter in 1943; the earliest experimental evidence is the torsion pendulum data of Schmieder and Wolf on PIB in 1953 and PMMA in 1957. TLP is inherently weak comparedto T and its strength is polymer specific, being relatively strong in PIB, weak in PBD. TLp is compared with the "slow process"of F e r r y and co-workers, ascribed t o slippage of dangling entanglements. TPQ occurs also below the entanglement molecular weightMc.Modern statistical methods such a s regression analysis are used to analyze T > T data for the presence o r absence of weak transitions, especially V-T and C -T data. The possibility of artifacts in some methods makes it imperative to search for T P p by many alternate methods, It is shown that isothermal V -P plots are more revelatory of TLL than a r e isobaric V-T plots. The use of Wood's variation of the Tait equation relating bulk modulus and pressure is useful in some cases for locating liquid state relaxations. Preliminary estimates of d(TQP)/dP, presented for PnBMA, P(cyclohexy1 MA) and a-PS, a r e in the range of 50-70 K/kbar, i.e. , 2-3 times the well known values for dT dP. A phase dualism hypothesis by Frenkel and Baranov suggests that TPL represents competition between segment-segment (liquid-like) behavior and the tendency of the macromolecule t o act as a gas at high temperature, Melt elasticity measurements on PS reveals a molecular weight dependent transition which appears to be TPQ ,The enthalpy of activation decreases by a factor of two from below to above TPp. The term "thermodynamic" in the title signifies use of quasi-equilibrium typ...

Free volume dependence of polymer viscosity

“…It is noteworthy that the crossover transition at ca. 1.2T g falls within the range of the so-called liquid-liquid transition temperature, T LL T g ¼ 1:2 AE 0:1, described by Boyer (1977Boyer ( , 1980aBoyer ( ,b, 1985Boyer ( , 1987as:"T LL is a molecular level transition-relaxation associated with the thermal disruption of segmentsegment contacts". Initially, Boyer considered T LL to be a third order thermodynamic transition (Boyer 1980a,b), the idea accepted by several researchers, while others suggested a dynamic nature (Patterson et al 1976), or denied its existence (Plazek 1982;Plazek andGu 1982,C h e ne t al.…”

“…For example, molecular weight distribution (MWD) affected the magnitude of the a 1 slope. Furthermore, within wide range of T and P (e.g., 1<T/T g <1.6, where T g is the glass transition temperature), some liquids undergo a secondary liquid-liquid transition, T tr T g ¼ 1:20 AE 0:05 (Boyer 1977(Boyer , 1980a(Boyer ,b, 1985(Boyer , 1987. To superimpose the viscosity data below and above T tr different characteristic pressure reducing parameters of Eq.…”

Free Volume in Molten and Glassy Polymers and Nanocomposites

“…Similarly, at T > T g there are several transitions, of which the one at T T /T g ≈ 1.2 ± 0.1 is the easiest to detect [Utracki, 2007a]. Coincidently, within these limits, Boyer [1977Boyer [ , 1980Boyer [ , 1985Boyer [ , 1987 postulated the presence of a liquid-liquid transition temperature, T LL . Other mechanisms based on molecular modeling and/or NMR measurements postulate the existence of the crossover transition temperature, T c /T g ≈ 1.2 ± 0.1, separating the regions of structural and segmental relaxations where liquid exists as an assembly of particles enclosed in cages formed by their neighbors [i.e., mode-coupling theory (MCT)] [Götze and Sjögren, 1988;Kisliuk et al, 2000;Paul, 2004;Casalini and Roland, 2005].…”

“…One cannot argue that the difference between T g and T c stems from different measuring methods (e.g., involving either a different quenching rate or test frequency). The T c transition temperature coincides with Boyer's liquid-liquid transition temperature, T LL /T g = 1.20 ± 0.05 [Boyer, 1977[Boyer, , 1980[Boyer, , 1985[Boyer, , 1987 and with Ngai's T B crossover temperature [Ngai, 2000[Ngai, , 2003. In short, for decades, T g and a transition temperature secondary to it, T c ≈ T B ≈ T LL , has been observed on the same function (e.g., viscosity or dielectric relaxation versus T) [Patterson et al, 1976;Murthy, 1990Murthy, , 1993.…”

“…The glass transition temperature (T g ) separates the vitreous from the molten state; it is a freezing-unfreezing temperature of micro-Brownian motion involving 20 to 50 carbon atoms of the main chain [Boyer, 1977[Boyer, , 1980[Boyer, , 1985[Boyer, , 1987. The more recent twinkling fractal theory (TFT) postulates that upon cooling of a molten polymer, dynamic percolating fractal structures are formed [Wool, 2008a,b;Wool and Campanella, 2009].…”