Limitations of heterogeneous models of liquid dynamics: very slow rate exchange in the excess wing

For several molecular glass formers, the nonlinear dielectric effects (NDE's) are investigated for the so-called excess wing regime, i.e., for the relatively high frequencies between 10(2) and 10(7) times the peak loss frequency. It is found that significant nonlinear behavior persists across the entire frequency window of this study, and that its magnitude traces the temperature dependence of the activation energy. A time resolved measurement of the dielectric loss at fields up to 480 kV/cm across tens of thousands of periods reveals that it takes an unexpectedly long time for the steady state NDE to develop. For various materials and at different temperatures and frequencies, it is found that the average structural relaxation with time scale τα governs the equilibration of these fast modes that are associated with time constants τ which are up to 10(7) times shorter than τα. It is argued that true indicators of structural relaxation (such as rate exchange and aging) of these fast modes are slaved to macroscopic softening on the time scale of τα, and thus many orders of magnitude slower than the time constant of the mode itself.