Finite-temperature critical point of a glass transition

We generalize the simplest kinetically constrained model of a glass-forming liquid by softening kinetic constraints, allowing them to be violated with a small finite rate. We demonstrate that this model supports a first-order dynamical (space-time) phase transition, similar to those observed with hard constraints. In addition, we find that the first-order phase boundary in this softened model ends in a finite-temperature dynamical critical point, which we expect to be present in natural systems. We discuss links between this critical point and quantum phase transitions, showing that dynamical phase transitions in $d$ dimensions map to quantum transitions in the same dimension, and hence to classical thermodynamic phase transitions in $d+1$ dimensions. We make these links explicit through exact mappings between master operators, transfer matrices, and Hamiltonians for quantum spin chains.Comment: 10 pages, 5 figure

Temperature Dependence of the Structural Relaxation Time in Equilibrium below the NominalTg: 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 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