Implicit function theorem and Jacobians in solvation and adsorption

Seishi Shimizu; Nobuyuki Matubayasi

doi:10.1016/j.physa.2021.125801

Implicit function theorem and Jacobians in solvation and adsorption

Seishi Shimizu, Nobuyuki Matubayasi

Chemistry

Research output: Contribution to journal › Article › peer-review

Abstract

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 language	English
Article number	125801
Journal	Physica A: Statistical Mechanics and its Applications
Volume	570
Early online date	1 Feb 2021
DOIs	https://doi.org/10.1016/j.physa.2021.125801
Publication status	Published - 1 May 2021

Bibliographical note

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10.1016/j.physa.2021.125801

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©2021 Elsevier B.V.All rights reserved.This is an author-produced version of the published paper. Uploaded in accordance with the publisher’s self-archiving policy.
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Cite this

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