Estimating the surface composition of a liquid mixture may seem like an easy task at first, but the calculations are not always so straightforward. Combining two liquids together generates complex interactions that may involve breaking and remaking intermolecular bonds. Any energetic change during this process can lead to ‘non-ideal’ behaviors—circumstances strikingly different from theories based on pure ‘ideal’ liquids.
Martin Tjahjono and Marc Garland at the A*STAR Institute of Chemical and Engineering Sciences have now developed a model that can accurately predict surface chemical concentrations for ideal and non-ideal binary mixtures of aqueous and organic liquids. The model is useful for a variety of applications, ranging from synthetic chemistry to heat engineering. The key to this approach is a new equation that answers a fundamental question: how best to express the physical concept of molecular volume at the surface?
Binary liquid surfaces are dynamic places that undergo constant concentration changes due to evaporation, meaning that experimental measurements of composition are not easy to perform. Instead, researchers have to use theoretical models to gauge effects like surface enrichment. However, many of these formulas are based on ideal liquid assumptions, like nearly spherical molecular shapes and the formation of finite monolayers.
Tjahjono and Garland devised a different calculation method based on a parameter called ‘parachor’ that mathematically connects surface tension—a direct measure of the cohesive energy present at the interface—to molecular volume, which measures size and molecular interactions. “These are two important physical properties for characterizing molecular compositions at the interface,” says Tjahjono. “Parachor relates these two properties and therefore can be used to effectively describe surface composition.”
While parachor models have existed for almost a century, their use has been limited due to the inexactness of describing surface molecular volume. The researchers turned to density, a factor proportional to volume, to solve this problem. In the bulk of a binary liquid, density can be measured exactly as a function of composition. Surface densities are harder to determine, but Tjahjono and Garland realized that they can be deduced mathematically in a way similar to the bulk, leading to a new surface molecular volume expression.
The modified parachor model performed flawlessly and produced theoretical surface compositions that closely matched known experimental data, no matter how non-ideally the binary liquid behaved. Using the model, the researchers resolved significant surface enrichments effects in organic hydrocarbon–water mixtures—a finding that could have implications in real-world engineering problems, notes Tjahjono.
The A*STAR-affiliated researchers contributing to this research are from the Institute of Chemical and Engineering Sciences.