Implicit function theorem and Jacobians in solvation and adsorption

Seishi Shimizu, Nobuyuki Matubayasi

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The use of Jacobians in chemical thermodynamics has focused chiefly on explicit functions. We generalize this powerful method to incorporate implicit functions. Considering a slight deviation from equilibrium, governed by the Gibbs-Duhem equations, is demonstrated to simplify the theories of preferential solvation and adsorption significantly. Since these deviations are zero at equilibrium, implicit function theorem can be applied by postulating their differentiability. A generalization to multiple component solutions is straightforward by virtue of Jacobians and the implicit function theorem.
Original languageEnglish
Article number125801
JournalPhysica A: Statistical Mechanics and its Applications
Early online date1 Feb 2021
Publication statusPublished - 1 May 2021

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