Theory of relaxation dynamics in glass-forming hydrogen-bonded liquids

We address the relaxation dynamics in hydrogen-bonded supercooled liquids near (but above) the glass transition, measured via broadband dielectric spectroscopy (BDS). We propose a theory based on decomposing the relaxation of the macroscopic dipole moment into contributions from hydrogen-bonded clusters of s molecules, with s(min) < or = s < or = s(max) . The existence of s(max) is translated into a sum rule on the concentrations of clusters of size s . We construct the statistical mechanics of the supercooled liquid subject to this sum rule as a constraint, to estimate the temperature-dependent density of clusters of size s . With a theoretical estimate of the relaxation time of each cluster, we provide predictions for the real and imaginary parts of the frequency-dependent dielectric response. The predicted spectra and their temperature dependence are in accord with measurements, explaining a host of phenomenological fits like the Vogel-Fulcher fit and the stretched exponential fit. Using glycerol as a particular example, we demonstrate quantitative correspondence between theory and experiments. The theory also demonstrates that the alpha peak and the "excess wing" stem from the same physics in this material. The theory also shows that in other hydrogen-bonded glass formers the excess wing can develop into a beta peak, depending on the molecular material parameters (predominantly the surface energy of the clusters). We thus argue that alpha and beta peaks can stem from the same physics. We address the BDS in constrained geometries (pores) and explain why recent experiments on glycerol did not show a deviation from bulk spectra. Finally, we discuss the dc part of the BDS spectrum and argue why it scales with the frequency of the alpha peak, providing an explanation for the remarkable data collapse observed in experiments.