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.
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