Like dissolves like: how like need they be? A statistical field theory for polar liquids and their mixtures

We have been taught the empirical “like-dissolves-like” rule in secondary school chemistry classes, but how like must the solvents be? This question does not yet have a good quantitative answer because of the difficulty in finding a general description for mixture interactions. Here, we present a theory for polar liquids and their mixtures, developed using a statistical field approach. This approach allows us to avoid the use of ad hoc mixing rules, and thus provides a more holistic description of liquid mixtures. The resulting theory consists of simple algebraic expressions for the free energy and the dielectric constant of the liquid, based on just the dipole moments and the sizes of the constituent liquid molecules. Without the use of any adjustable parameters, the theory very well predicts the miscibility for a variety of liquids, thus provides a quantification for the well-known empirical “like-dissolves-like” rule.