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Implicit function theorem and Jacobians in solvation and adsorption

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  • Shimizu, Seishi
  • Matubayasi, Nobuyuki

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, can simplify the theories of preferential solvation and adsorption significantly. Since these deviations are zero at equilibrium, the 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.

Suggested Citation

  • Shimizu, Seishi & Matubayasi, Nobuyuki, 2021. "Implicit function theorem and Jacobians in solvation and adsorption," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 570(C).
    • Handle: RePEc:eee:phsmap:v:570:y:2021:i:c:s037843712100073x
    DOI: 10.1016/j.physa.2021.125801
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    References listed on IDEAS

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    1. Shimizu, Seishi & Matubayasi, Nobuyuki, 2018. "A unified perspective on preferential solvation and adsorption based on inhomogeneous solvation theory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 492(C), pages 1988-1996.
    2. Shimizu, Seishi & Matubayasi, Nobuyuki, 2021. "Phase stability condition and liquid–liquid phase separation under mesoscale confinement," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 563(C).
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    Cited by:

    1. Shimizu, Seishi & Matubayasi, Nobuyuki, 2022. "Ensemble transformation in the fluctuation theory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 585(C).

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    1. Shimizu, Seishi & Matubayasi, Nobuyuki, 2022. "Ensemble transformation in the fluctuation theory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 585(C).
    2. Shimizu, Seishi & Matubayasi, Nobuyuki, 2021. "Phase stability condition and liquid–liquid phase separation under mesoscale confinement," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 563(C).

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