期刊
PHYSICAL CHEMISTRY CHEMICAL PHYSICS
卷 22, 期 19, 页码 10480-10489出版社
ROYAL SOC CHEMISTRY
DOI: 10.1039/c9cp06285h
关键词
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资金
- University of California, Berkeley
- French Agence Nationale de la Recherche (ANR) [ANR-17-CE09-0046-02]
- European Research Council (ERC) under the European Union [771294]
- Agence Nationale de la Recherche (ANR) [ANR-17-CE09-0046] Funding Source: Agence Nationale de la Recherche (ANR)
- European Research Council (ERC) [771294] Funding Source: European Research Council (ERC)
We revisit the statistical mechanics of charge fluctuations in capacitors. In constant-potential classical molecular simulations, the atomic charges of electrode atoms are treated as additional degrees of freedom which evolve in time so as to satisfy the constraint of fixed electrostatic potential for each configuration of the electrolyte. The present work clarifies the role of the overall electroneutrality constraint, as well as the link between the averages computed within the Born-Oppenheimer approximation and that of the full constant-potential ensemble. This allows us in particular to derive a complete fluctuation-dissipation relation for the differential capacitance, that includes a contribution from the charge fluctuations (around the charges satisfying the constant-potential and electroneutrality constraints) also present in the absence of an electrolyte. We provide a simple expression for this contribution from the elements of the inverse of the matrix defining the quadratic form of the fluctuating charges in the energy. We then illustrate numerically the validity of our results, and recover the expected continuum result for an empty capacitor with structureless electrodes at large inter-electrode distances. By considering a variety of liquids between graphite electrodes, we confirm that this contribution to the total differential capacitance is small compared to that induced by the thermal fluctuations of the electrolyte.
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