Temperature Dependence of the Structural Relaxation Time in Equilibrium below the NominalTg: Results from Freestanding Polymer Films

Abstract

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 α-relaxation time of the polymer in nanoconfinement, tau_alphanano(T), much shorter than tau_alphabulk(T) in the bulk. The consequence is avoidance of vitrification at and below the bulk glass transition temperature, Tg_bulk, on cooling, and the freestanding polymer thin film remains at thermodynamic equilibrium at temperatures below Tg_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_alphanano(T) becomes the same or almost the same as the JG beta-relaxation time tau_betabulk(T) of the bulk glass-former at equilibrium and at temperatures below Tg_bulk. Taking advantage of being able to obtain tau_betabulk(T) at equilibrium density below Tg_bulk by extreme nanoconfinement of the freestanding films, and using the CM relation between tau_alphabulk(T) and tau_betabulk(T), we conclude that the Vogel−Fulcher−Tammann−Hesse (VFTH) dependence of tau_alphabulk(T) cannot hold for glass-formers in equilibrium at temperatures significantly below Tg_bulk. In addition, tau_alphabulk(T) does not diverge at the Vogel temperature, T0, as suggested by the VFTH-dependence and predicted by some theories of glass transition. Instead, tau_alphabulk(T) of the glass-former at equilibrium has a much weaker temperature dependence than the VFTHdependence at temperature below Tg_bulk and even below T0. This conclusion from our analysis is consistent with the temperature dependence of tau_alphabulk(T) found experimentally in polymers aged long enough time to attain the equilibrium state at various temperatures below Tg_bulk