Entropy of Mixing: Contributions from Interparticle Interactions and Its Relevance to Deep Eutectic Solvents

Theoretical modeling of solid-liquid equilibria is critical for choosing the appropriate mixture components and compositions for the formation of deep eutectic solvents (DESs). Earlier theoretical approaches mapped the solid-liquid equilibria of a few DESs in terms of the regular solution theory, where a fit parameter (χ_old) in the enthalpy change (ΔH̅_mix) accounted for interspecies interactions and combinatorics provided the entropy contribution (ΔS̅_mix). Later, the excluded volume effects in the combinatorial entropy were introduced. The free energy change due to mixing (ΔG̅_mix) in these models was dominated by ΔH̅_mix, where ΔS̅_mix did not account for the attractive part of interparticle interactions. In this work, we have developed a theoretical formalism, where excess entropy (S̅_mix^e) has been introduced, and both repulsive (excluded volume effects) and attractive parts of interparticle interactions have been systematically incorporated in ΔH̅_mix and ΔS̅_mix contributions. The fit parameter in the present theory (χ_new) is therefore modified by the interspecies interactions through both ΔH̅_mix and ΔS̅_mix. Subsequently, when ΔH̅_mix and ΔS̅_mix for the acetamide + urea mixture were obtained from molecular dynamics simulations and employed as inputs, the present theory predicted endothermic mixing (that is, ΔH̅_mix positive) but is favored and overcompensated by ΔS̅_mix, producing an overall negative ΔG̅_mix. This is in contrast to the predictions from the earlier theoretical approaches, where ΔH̅_mix provided the required thermodynamic driving force. This is further reflected in the different signs of parameters χ_new (present theory) and χ_old. The present theory can be extended to treat multicomponent mixtures as well.