Mass transport across liquid-liquid interfaces are a crucial part of many biochemical and industrial processes. Despite the need for mechanistic descriptions of transport between liquid phases, molecular-level understanding of phase transfer processes is lacking. The main reason is the challenging problem of characterizing structural features at locally heterogeneous interfaces. Limited studies to date have used molecular simulations to investigate transport of water by extractant molecules such as tri-n-butyl phosphate (TBP). They observed that ion transport is assisted by the formation of water “fingers” that trail the ion as it departs the aqueous interface. Further, TBP-assisted water transport through molecular-scale “protrusions” of water was observed at the water-(TBP+n-hexane) interface. A comprehensive investigation of protrusion-type interfacial features accompanying solute transport is necessary for a statistical mechanical description of the reaction pathways. We propose a computational framework to identify protrusions as well as surface roughness features at liquid-liquid interfaces. We first capture water-water and water-amphiphile molecular interactions using tools from graph theory. Second, employ methods from computational geometry to generate a spatial representation of the instantaneous liquid-liquid interface. We then employ concepts from geometric measure theory to directly identify protrusions in this interface. The concept of flat norm is employed to identify volumes filling in candidate protrusions at varying scale factors. This step involves the solution of multiple linear programming problems, which are carried out in a parallel fashion. Certain geometric features of each candidate protrusion are then evaluated to yield a probability of the feature being an actual protrusion. Our framework automatically identifies a small set of features with the highest probabilities of being protrusions. We demonstrate our framework on various instances of TBP-assisted water transport in reactions. But the framework is quite general, and is applicable to any system with a liquid-liquid interface.

Characterizing Interfacial roughness and protrusions in liquid-liquid Interfaces using graph theory and geometric measure theory

Macromolecular Chemistry: The Second Century

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ACS Spring 2020 National Meeting & Expo

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