Thermodynamic mechanism for solution phase chiral amplification via a lattice model

We formulate a two-dimensional lattice model to study the equilibrium phase behavior of a ternary mixture composed of two enantiomeric forms of a chiral molecule and a nonchiral liquid solvent. Numerical solution of the model invoking the mean-field approximation of statistical mechanics allows the calculation of a ternary phase diagram. A prominent feature of the phase diagram is the appearance of a mirror-image pair of triple points involving coexistence of a liquid phase enriched in one of the enantiomers with two solid phases: a racemic and an enantiopure crystal. Thus, over broad ranges of initial composition, including liquid mixtures containing almost equal amounts of the two enantiomers, the equilibrium state of the system produces liquid-phase chiral amplification. The calculations predict that chiral amplification is favored at low temperatures, and by strengthening those molecular interactions that stabilize the racemic crystal. The phase behavior that we obtain is qualitatively identical to that reported in a recent experimental study of solutions of amino acids, aimed at probing the liquid-phase control of asymmetric catalysis. Those results, and the present calculations that provide molecular-level insight into their underlying causes, suggest a possible thermodynamic scenario for the liquid-phase emergence of chiral imbalance in a prebiotic and presumably nearly racemic world.