Phase Transitions Affected by Molecular Interconversion

If a binary liquid mixture, composed of two alternative species with equal amounts, is quenched from a high temperature to a low temperature, below the critical point of demixing, then the mixture will phase separate through a process known as spinodal decomposition. However, if the two alternative species are allowed to interconvert, either naturally (e.g. the equilibrium interconversion of enantiomers) or forcefully (e.g. via an external source of energy or matter), then the process of phase separation may drastically change. In this case, two phenomena could be observed: either phase amplification, the growth of one phase at the expense of the other, or microphase separation, the formation of nongrowing (steady-state) microphase domains. In this work, we generalize the mean-field Cahn-Hilliard theory of spinodal decomposition to include molecular interconversion of species and describe the physical properties of systems undergoing phase amplification or microphase separation. We show that the condition for phase amplification occurs if the equilibrium interconversion rate is faster than the diffusion rate and the rate of forceful racemization (provided by an interconversion energy source), while arrested microphase separation occurs if the rate of forceful racemization is faster than the equilibrium interconversion and diffusion rate. The growth of the phase domain for these two phenomena are characterized through the temporal evolution of the structure factor, which exhibits a crossover from the early stages of spinodal decomposition to nucleation. We show that the presence of a source of energy or matter drives the system into a nonequilibrium state with the possibility of forming dissipative structures.