Charge fluctuations from molecular simulations in the constant-potential ensemble

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 f...

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Bibliographic Details
Published in:Physical chemistry chemical physics : PCCP 2020-05, Vol.22 (19), p.148-1489
Main Authors: Scalfi, Laura, Limmer, David T, Coretti, Alessandro, Bonella, Sara, Madden, Paul A, Salanne, Mathieu, Rotenberg, Benjamin
Format: Article
Language:English
Subjects:
Capacitance
Capacitors
Computer simulation
Electrodes
Electrolytes
Mathematical analysis
Physics
Quadratic forms
Statistical mechanics
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Summary: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. Statistical mechanics of constant-potential molecular simulations yields a new fluctuation-dissipation relation for the differential capacitance.
ISSN:1463-9076
1463-9084
DOI:10.1039/c9cp06285h