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 (Δ<i>H̅</i>_mix) accounted for interspecies interactions and combinatorics provided the entropy contribution (Δ<i>S̅</i>_mix). Later, the excluded volume effects in the combinatorial entropy were introduced. The free energy change due to mixing (Δ<i>G̅</i>_mix) in these models was dominated by Δ<i>H̅</i>_mix, where Δ<i>S̅</i>_mix did not account for the attractive part of interparticle interactions. In this work, we have developed a theoretical formalism, where excess entropy (<i>S̅</i>_mix^e) has been introduced, and both repulsive (excluded volume effects) and attractive parts of interparticle interactions have been systematically incorporated in Δ<i>H̅</i>_mix and Δ<i>S̅</i>_mix contributions. The fit parameter in the present theory (χ_new) is therefore modified by the interspecies interactions through both Δ<i>H̅</i>_mix and Δ<i>S̅</i>_mix. Subsequently, when Δ<i>H̅</i>_mix and Δ<i>S̅</i>_mix for the acetamide + urea mixture were obtained from molecular dynamics simulations and employed as inputs, the present theory predicted endothermic mixing (that is, Δ<i>H̅</i>_mix positive) but is favored and overcompensated by Δ<i>S̅</i>_mix, producing an overall negative Δ<i>G̅</i>_mix. This is in contrast to the predictions from the earlier theoretical approaches, where Δ<i>H̅</i>_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.