Charge fluctuations from molecular simulations in the constant-potential ensemble

Scalfi, Laura; Limmer, David T.; Coretti, Alessandro; Bonella, Sara; Madden, Paul A.; Salanne, Mathieu; Rotenberg, Benjamin

doi:10.1039/c9cp06285h

Title: Charge fluctuations from molecular simulations in the constant-potential ensemble

Journal Article · 13 December 2019 · Physical Chemistry Chemical Physics. PCCP

DOI: https://doi.org/10.1039/c9cp06285h · OSTI ID:1721640

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Sorbonne Univ., Paris (France)
Univ. of California, Berkeley, CA (United States); Kavli Energy NanoScience Institute, Berkeley, CA (United States); Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
Politecnico di Torino (Italy); Ecole Polytechnique Federale de Lausanne (Switzerland). Centre Europeen de Calcul Atomique et Moleculaire (CECAM)
Ecole Polytechnique Federale de Lausanne (Switzerland). Centre Europeen de Calcul Atomique et Moleculaire (CECAM)
Univ. of Oxford (United Kingdom)
Sorbonne Univ., Paris (France); Reseau sur le Stockage Electrochimique de l'Energie (RS2E), Amiens (France)

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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Research Organization:: Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)

Sponsoring Organization:: Agence Nationale de la Recherche (ANR); European Union Horizon 2020; USDOE Office of Science (SC), Basic Energy Sciences (BES)

Grant/Contract Number:: AC02-05CH11231

OSTI ID:: 1721640

Journal Information:: Physical Chemistry Chemical Physics. PCCP, Journal Name: Physical Chemistry Chemical Physics. PCCP Journal Issue: 19 Vol. 22; ISSN 1463-9076

Publisher:: Royal Society of ChemistryCopyright Statement

Country of Publication:: United States

Language:: English

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