On Gibbs phase rule for optical enantiomers

Abstract

Exceptions to the usual statement of Gibbs phase rule can occur in systems containing pairs of optical enantiomers or other special symmetries. We examine a modification of the phase rule proposed by Scott and its application to examples in two classes of purported exceptions. For the first class of examples we argue that the usual statement of Gibbs phase rule is in accord with the expected behavior of the system, while for the second we agree that a modification of the rule is required. We obtain a modified rule which gives conventional result when applied to the first class and a modified result in agreement with Scott’s, when applied to the second. In the second class of examples the phase diagram in terms of fields or intensities exhibits more phases meeting at a point or more degrees of freedom for a given number of phases meeting at a point than would be predicted by the usual phase rule. These occur when the P-phase coexistence set is of dimension less than P-1 because of the symmetries present. Even in these cases surface free energy effects favor, in the absence of external bias from the container walls, the reduction of the number of phases to that predicted by the usual Gibbs phase rule. Control of macroscopic variables such as energy, volume, and composition will not prevent such reductions from occurring, although their tendency to occur is a surface effect and the rates may be very low. External bias through special preparation of container walls may be sufficient to overcome this tendency and stabilize the larger number of phases.