Temperature Dependence of the Structural Relaxation Time in Equilibrium below the Nominal T-g: Results from Freestanding Polymer Films

When the thickness is reduced to nanometer scale, freestanding high molecular weight polymer thin films undergo large reduction of degree of cooperativity and coupling parameter n in the Coupling Model (CM). The finite-size effect together with the surfaces with high mobility make the a-relaxation time of the polymer in nanoconfinement, tau(nano)(alpha)(T), much shorter than tau(bulk)(alpha)(T) in the bulk. The consequence is avoidance of vitrification at and below the bulk glass transition temperature, T-g(bulk), on cooling, and the freestanding polymer thin film remains at thermodynamic equilibrium at temperatures below T-g(bulk). Molecular dynamics simulations have shown that the specific volume of the freestanding film is the same as the bulk glass-former at equilibrium at the same temperatures. Extreme nanoconfinement renders total or almost total removal of cooperativity of the alpha-relaxation, and tau(nano)(alpha)(T) becomes the same or almost the same as the JG beta-relaxation time tau(bulk)(beta)(T) of the bulk glass-former at equilibrium and at temperatures below T-g(bulk). Taking advantage of being able to obtain tau(bulk)(beta)(T) at equilibrium density below T-g(bulk) by extreme nanoconfinement of the freestanding films, and using the CM relation between tau(bulk)(alpha)(T) and tau(bulk)(beta)(T), we conclude that the Vogel-Fulcher-Tammann-Hesse (VFTH) dependence of tau(bulk)(alpha)(T) cannot hold for glass-formers in equilibrium at temperatures significantly below T-g(bulk). In addition, tau(bulk)(alpha)(T) does not diverge at the Vogel temperature, T-0, as suggested by the VFTH-dependence and predicted by some theories of glass transition. Instead, tau(bulk)(alpha)(T) of the glass-former at equilibrium has a much weaker temperature dependence than the VFTH-dependence at temperature below T-g(bulk) and even below T-0. This conclusion from our analysis is consistent with the temperature dependence of tau(bulk)(alpha)(T) found experimentally in polymers aged long enough time to attain the equilibrium state at various temperatures below T-g(bulk).