How Deep is Your DES? A Numerical Framework for Ideal Eutectic Prediction in Multicomponent Mixtures

Abstract

Abstract Here, we present a simple and computationally efficient procedure to determine the eutectic temperatures of ideal binary, ternary, and higher-order mixtures, providing a quantitative reference for evaluating deep eutectic solvent (DES) behavior. In the DES literature, ternary systems are often simplified as pseudo-binaries by fixing the molar ratio of two components and varying only the third along a fixed-composition line (isopleth). Although this reduces the experimental effort, it restricts liquidus mapping to a single compositional pathway and may fail to identify the global ideal eutectic. In contrast, our implementation solves the classical ideal liquidus equations for all components, assuming Raoult-law ideality and pure, mutually immiscible solid phases. Using pure-component melting temperatures and molar fusion enthalpies, the method enables multidimensional liquidus-surface mapping. The root-finding implementation was verified against analytical symmetric-mixture solutions, independent 80-digit calculations, a MATLAB implementation, permutation tests, 3,521 stress-test systems, and published benchmarks. All stress-test systems converged, and published ideal eutectic temperatures were reproduced within 0.7 K. Application to literature-reported binary and ternary mixtures further showed that comparison with the global ideal eutectic combines an apparent local thermal deviation with a nonnegative ideal-composition penalty. The framework therefore provides a transparent and extensible ideal-equilibrium baseline for multicomponent eutectic screening.