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

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Abstract
The 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-α-olefins C3, C5, and C6. Just as Tg manifests itself through time-dependent (relaxational) and thermodynamic (transition) effects, so also does a T < Tg transition (relaxation) found generally in the range of 1.1 to 1.3 Tg but mostly near 1.2 Tg. This is designated as Tℓ, a liquid1-liquid2 transition. Tℓ 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 > Tg or Tβ relaxation. With increasing syndiotactic content, PMMA's reveal strengthening Tβ and Tℓ processes. Relaxation maps plotting log frequency-T−1 are presented for PBD and PIB, showing both Tg and Tℓ. The latter exhibits non-Arrhenius behavior with an activation enthalpy about half that at Tg when both are observed some 50–100° K above their very low frequency values. Probe methods such as IR, 13C-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 Tll 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. Tℓ is inherently weak compared to Tg and its strength is polymer specific, being relatively strong in PIB, weak in PBD. Tll is compared with the “slow process” of Ferry and co-workers, ascribed to slippage of dangling entanglements. Tll occurs also below the entanglement molecular weight Mc. Modern statistical methods such as regression analysis are used to analyze T < Tg data for the presence or absence of weak transitions, especially V-T and Cp -T data. The possibility of artifacts in some methods makes it imperative to search for Tℓ by many alternate methods. It is shown that isothermal V-P plots are more revelatory of Tℓ than are 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(Tℓ)/dP, presented for PnBMA, P(cyclohexyl MA) and a-PS, are in the range of 50–70 K/kbar, i.e., 2–3 times the well known values for dTg/dP. A phase dualism hypothesis by Frenkel and Baranov suggests that Tℓ represents competition between segment-segment (liquid-like) behavior and the tendency of the macromolecule to act as a gas at high temperature. Melt elasticity measurements on PS reveals a molecular weight dependent transition which appears to be Tℓ. The enthalpy of activation decreases by a factor of two from below to above Tℓ. The term “thermodynamic” in the title signifies use of quasi-equilibrium types of data to detect the Tll relaxation process. We do not wish to imply that Tℓ is an equilibrium process. Indeed, it behaves like a third-order transition.