Gibbsian interpretation of Langmuir, Freundlich and Temkin isotherms for adsorption in solution

IF 1.2 4区材料科学 Q4 MATERIALS SCIENCE, MULTIDISCIPLINARY

Philosophical Magazine Letters Pub Date : 2022-06-20 DOI:10.1080/09500839.2022.2084571

Lei Lu, Chongzheng Na

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引用次数: 5

Abstract

ABSTRACT Adsorption is a physicochemical phenomenon important in both natural and engineering processes. In the research and practice of adsorption equilibrium, a long-standing challenge is how to reconcile the classical models proposed by Gibbs, Langmuir, Freundlich, and Temkin for interpreting experimentally obtained adsorption isotherms. Here, we show that the Langmuir, Freundlich, and Temkin isotherms can be derived from the Gibbs equation under different conditions for the change of surface energy (a.k.a. surface tension) by adsorption. When the change of surface energy is predominantly controlled by the change of chemical potential with negligible contribution from the change of internal energy and entropy, the Gibbs equation can be integrated to give the Langmuir isotherm. When changes of internal energy and entropy are no longer negligible, the integration of the Gibbs equation gives the Freundlich and Temkin equations, according to a change of surface energy either independent or linearly dependent on the adsorption capacity. These results indicate that the classical models share the common mechanism of phase equilibrium described by the Gibbsian thermodynamics, thereby providing novel insights for their application.

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溶液中吸附的Langmuir, Freundlich和Temkin等温线的gibbian解释

摘要吸附是一种在自然和工程过程中都很重要的物理化学现象。在吸附平衡的研究和实践中，一个长期存在的挑战是如何调和Gibbs、Langmuir、Freundlich和Temkin提出的用于解释实验获得的吸附等温线的经典模型。在这里，我们证明了Langmuir、Freundlich和Temkin等温线可以从吉布斯方程中导出，在不同条件下，吸附引起的表面能（也称为表面张力）的变化。当表面能的变化主要由化学势的变化控制，而内能和熵的变化贡献可以忽略不计时，吉布斯方程可以积分得到朗缪尔等温线。当内能和熵的变化不再可以忽略时，吉布斯方程的积分给出了Freundlich和Temkin方程，根据表面能的变化，独立于或线性依赖于吸附容量。这些结果表明，经典模型具有吉布斯热力学所描述的相平衡的共同机制，从而为其应用提供了新的见解。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Philosophical Magazine Letters 物理-物理：凝聚态物理

CiteScore

2.60

自引率

0.00%

发文量

审稿时长

2.7 months

期刊介绍： Philosophical Magazine Letters is the rapid communications part of the highly respected Philosophical Magazine, which was first published in 1798. Its Editors consider for publication short and timely contributions in the field of condensed matter describing original results, theories and concepts relating to the structure and properties of crystalline materials, ceramics, polymers, glasses, amorphous films, composites and soft matter. Articles emphasizing experimental, theoretical and modelling studies on solids, especially those that interpret behaviour on a microscopic, atomic or electronic scale, are particularly appropriate. Manuscripts are considered on the strict condition that they have been submitted only to Philosophical Magazine Letters , that they have not been published already, and that they are not under consideration for publication elsewhere.