Fully periodic, computationally efficient constant potential molecular dynamics simulations of ionic liquid supercapacitors

Abstract

Molecular dynamics (MD) simulations of complex electrochemical systems, such as ionic liquid supercapacitors, are increasingly including the constant potential method (CPM) to model conductive electrodes at specified potential difference, but the inclusion of CPM can be computationally expensive. We demonstrate the computational savings available in CPM MD simulations of ionic liquid supercapacitors when the usual non-periodic slab geometry is replaced with fully periodic boundary conditions. We show how a doubled cell approach, previously used in non-CPM MD simulations of charged interfaces, can be used to enable fully periodic CPM MD simulations. Using either a doubled cell approach, or a finite field approach previously reported by others, fully periodic CPM MD simulations produce comparable results to the traditional slab geometry simulations with a nearly double speed-up in computational time. Indeed, these savings can offset the additional cost of the CPM algorithm, resulting in periodic CPM MD simulations that are computationally competitive with the non-periodic, fixed-charge equivalent simulations for the ionic liquid supercapacitors studied here.

Molecular insights into capacitive deionization mechanisms inside hydrophobic and hydrophilic carbon nanotube channel electrodes

“…The point charges of electrodes' atoms were considered as a Gaussian charge distribution to make the linear equations of electrodes' charges shown above solvable. The modified implementation of the constant potential 20 introduced by Tee and Searles 21 was used to perform computational efficient constant potential simulation. This updated version introduced various improvements including enabling the use of the PPPM algorithm for the long-range electrostatic interactions.…”

Theory and Simulations of Ionic Liquids in Nanoconfinement

“…Other approaches rely on putting countercharges alongside an electrolyte–electrode interface and adjusting their values each simulation step to reflect metal polarizability. Siepmann and Sprik have introduced variable-charge Gaussian charges, whose magnitude is changed on the fly according to a variational procedure designed to maintain the constant potential on an electrode. ,, This method has been used in several MD simulations studies, particularly for modeling electrodes with complex nanoporous networks, such as carbide-derived carbons. ,,,,− Recently, it has been implemented in the open-source software package Metalwalls. , A similar method has been implemented in the well-known LAMMPS simulation package and more recently extended to fully periodic systems . Most recently, Ahrens-Iwers et al developed a package ELECTRODE for LAMMPS for efficient simulations of solid–liquid interfaces using constant potential method, able to deal with heterogeneous and curved electrodes.…”

Constant Potential and Constrained Charge Ensembles for Simulations of Conductive Electrodes

“…We can now explore thermodynamic relationships between ConP and ConQ configurational ensembles using familiar statistical mechanical tools. We start by defining the ConQ free energy: (15) As usual, the derivative ∂F Q (Q)/∂Q = ⟨∂U Q /∂Q⟩ is the average potential difference: (16) Differentiating again gives an expression for (inverse) differential capacitance, which we label C Q D for now: (17) We write and analyze an explicit expression for C Q D when discussing fluctuations in the ConQ ensemble. Now, categorizing electrolyte configurations by the induced ConP charge Q P (r 3N , Δψ), we have (18) Comparing integrands with eq 13, and using the definition of a probability distribution, we have (19) (up to a normalization constant).…”

“…The Born–Oppenheimer-style charge update procedure reflects how, in reality, charge redistribution occurs instantaneously on the time scale of an MD time step. , In ConP simulations, the charge q P is boldq P ( Δ ψ , b ) = boldO boldC ( b + Δ ψ d ) where C ≡ A –1 is the capacitance matrix, and the electroneutrality projection matrix O keeps the total charge of the system at zero. We include an expression for O in Supporting Information Section 1.1 and refer the reader to refs and for further details. (“P” and “Q” subscripts will denote ConP and ConQ versions, respectively, of identical or closely related physical quantities.)…”