Microscopically based calculations of the free energy barrier and dynamic length scale in supercooled liquids: The comparative role of configurational entropy and elasticity

摘要

We compute the temperature-dependent barrier for alpha-relaxations in severalliquids, without adjustable parameters, using experimentally determinedelastic, structural, and calorimetric data. We employ the random first ordertransition(RFOT) theory, in which relaxation occurs via activatedreconfigurations between distinct, aperiodic minima of the free energy. Twodifferent approximations for the mismatch penalty between the distinctaperiodic states are compared, one due to Xia and Wolynes, which scalesuniversally with temperature as for hard spheres, and one due to Rabochiy andLubchenko, which employs measured elastic and structural data for individualsubstances. The agreement between the predictions and experiment issatisfactory, given the uncertainty in the measured experimental inputs. Theexplicitly computed barriers are used to calculate the glass transitiontemperature for each substance---a kinetic quantity---from the static inputdata alone. The temperature dependence of both the elastic and structuralconstants enters the temperature dependence of the barrier over an extendedrange to a degree that varies from substance to substance. The lowering of theconfigurational entropy, however, seems to be the dominant contributor to thebarrier increase near the laboratory glass transition, consistent with previousexperimental tests of the RFOT theory using the XW approximation. In addition,we compute the temperature dependence of the dynamical correlation length, alsowithout using adjustable parameters. These agree well with experimentalestimates obtained using the Berthier et al. procedure. Finally, we find thetemperature dependence of the complexity of a rearranging region is consistentwith the picture based on the RFOT theory but is in conflict with theassumptions of the Adam-Gibbs and "shoving" scenarios for the viscous slowingdown in supercooled liquids.