A cage model of liquids supported by molecular-dynamics simulations .2. The stochastic-model

The cage variables describing solute-solvent interactions have been introduced in part I of the work. Moreover, the equilibrium distribution and the relaxation times for both solute and cage variables were derived from the analysis of a molecular dynamics (MD) simulation of liquid argon. In the second part of the work, a stochastic model for the cage is developed on the basis of these informations. The model is characterized by a particular choice for the set of independent stochastic variables and for the evolution operators describing each elementary process. Accurate solutions are derived numerically, while analytical solutions are obtained by separating the cage frame rotations from fast variables like the solute velocity. The calculation of correlation functions allows the comparison with MD results. A substantial agreement is found except for the displacement between solute and cage center. The examined cage model, because of its simple structure, allows a straightforward analysis of the effects of the solvent cage and, in particular, of the distribution of cage frequencies describing the dispersion in the strength of solute-solvent interactions.