  We propose a dynamic structure of coupled dynamic molecular strings for
supercooled small polar molecule liquids and accordingly we obtain the
Hamiltonian of the rotational degrees of freedom of the system. From the
Hamiltonian, the strongly correlated supercooled polar liquid state is
renormalized to a normal superdipole (SD) liquid state. This scenario describes
the following main features of the primary or a-relaxation dynamics in
supercooled polar liquids: (1) the average relaxation time evolves from a high
temperature Arrhenius to a low temperature non-Arrhenius or super-Arrhenius
behavior; (2) the relaxation function crosses over from the high temperature
exponential to low temperature non-exponential form; and (3) the temperature
dependence of the relaxation strength shows non-Curie features. According to
the present model, the crossover phenomena of the first two characteristics
arise from the transition between the superdipole gas and the superdipole
liquid. The model predictions are quantitatively compared with the experimental
results of glycerol, a typical glass-former.
