金属/溶液界面的熵：热力学框架、理论模型和界面水的作用

doi:10.61558/2993-074X.3601

摘要/Abstract

摘要：

熵是金属/溶液界面双电层的基本热力学性质之一，但其定义、测量方法和理论处理在现有文献中较为分散，且在某些情况下仍存在歧义。本文重新审视了双电层的热力学理论，明确区分并比较了两类熵：过剩熵和形成熵。针对形成熵，在最基本的双电层模型-Gouy-Chapman（GC）模型框架下，验证了两种等价的计算途径。在澄清相关概念和计算方法之后，本文采用改进的Gouy-Chapman-Stern（GCS）模型研究了界面水对双电层形成熵的影响。该模型显式引入了氧端朝向与氢端朝向水分子之间的化学势差，记为δμ。模型计算得到的微分电容和熵与Au(111)电极在水溶液中形成的双电层实验数据进行了对比。结果表明，当未带电表面上水分子更倾向于氧端朝向构型时，最大熵对应的表面荷电（CME）为负值；此外，当δμ随电位变化时，形成熵在CME附近呈现出明显的非对称性。然而，该模型无法同时再现来自两项独立实验研究的电容和熵测量结果，表明模型仍存在不足，或实验数据中可能存在误差。尽管如此，本工作强调了在研究双电层时同步测量电容和熵的重要性。

关键词: 双电层, 过剩熵, 形成熵, 界面水, 最大熵荷电

Abstract:

Entropy is a basic thermodynamic property of the electrical double layer (EDL) at metal/solution interfaces, yet, its definition, measurement, and theoretical treatment are dispersed in the literature, and, in some cases, ambiguous. In this paper, we revisit the thermodynamic theory of EDL, from which two variants of entropy, excess entropy and formation entropy, are obtained and compared. In terms of the formation entropy, two calculation routes are validated in the context of a primitive EDL model, namely, the Gouy-Chapman (GC) model. After clarifying the concepts and calculation routes, we investigate interfacial water effects on the EDL entropy, using a refined Gouy-Chapman-Stern (GCS) model accounting for chemical potential difference between oxygen- and hydrogen-down water molecules, denoted $δ μ$ . The model-derived differential capacitance and entropy are compared with experimental data for the EDL at Au(111) in an aqueous electrolyte solution. The model reveals that the charge of maximum entropy (CME) is negative when water molecules have higher tendency to take oxygen-down configuration at the uncharged surface. Moreover, the formation entropy profile becomes asymmetric around the CME, when $δ μ$ is potential-dependent. However, the model fails to simultaneously reproduce capacitance and entropy measurements on the same system taken from two separate studies, indicating deficiencies of the model or experimental errors. Nevertheless, this work stresses the importance of measuring both capacitance and entropy of EDLs at the same time.

Key words: electrical double layer, excess entropy, formation entropy, interfacial water, charge of maximum entropy

张增明, 梁子西, 黄俊. 金属/溶液界面的熵：热力学框架、理论模型和界面水的作用[J]. 电化学（中英文）, 2026, 32(3): 2515010.

Zeng-Ming Zhang, Zi-Xi Liang, Jun Huang. Entropy of Metal/Solution Interfaces: Thermodynamic Framework, Theoretical Models, and Roles of Interfacial Water[J]. Journal of Electrochemistry, 2026, 32(3): 2515010.

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链接本文: https://electrochem.xmu.edu.cn/CN/10.61558/2993-074X.3601

https://electrochem.xmu.edu.cn/CN/Y2026/V32/I3/2515010

图/表 10

Symbol	Value	Significance
Constants
$k B (J · K$ ^-1 $)$	$1.38 × 10 - 23$	Boltzmann constant
$e 0 (C)$	$1.6 × 10 - 19$	Elementary charge
$N A (m o l$ ^-1 $)$	$6.02 × 10 - 23$	Avogadro constant
$F (C · m o l$ ^-1 $)$	$96485$	Faraday constant
$h (J · s$ ^-1 $)$	$6.626 × 10 - 34$	Planck constant
$ε 0 (F · m$ ^-1 $)$	$8.85 × 10 - 12$	Vacuum permittivity
$ε b (F · m$ ^-1 $)$	$78.5 ε 0$	permittivity of bulk water
$T (K)$	$298$	Temperature
$δ μ 0 (k B T)$	$1$	Water molecule chemical potential difference at pzc
$θ w$	$0.55$	Coverage of adsorbed water molecules
Au(111)-aqueous $H C l O 4$ solution interfaces
$ε 1 (F · m$ ^-1 $)$	$10 ε 0$	permittivity between the electrode and the CAP
$ε 2 (F · m$ ^-1 $)$	$7.5 ε 0$	permittivity between the CAP and the ASP
$ε 3 (F · m$ ^-1 $)$	$35 ε 0$	permittivity between ASP and the OHP
$δ 1 (Å)$	$1.5$	thickness between the electrode and the CAP
$δ 2 (Å)$	$2$	thickness between the CAP and the ASP
$δ 3 (Å)$	$3$	thickness between ASP and the OHP
$N a d (m – 2)$	$1.39 × 1019$	number of adsorption sites
$E p z c, S H E 0 (V)$	$0.30$	potential of zero free charge when $δ μ = 0$
$μ w (C ∙ m)$	$1.85 D$	water molecule dipole moment

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