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

Contrasting Views of the Electric Double Layer in Electrochemical CO2 Reduction: Continuum Models vs Molecular Dynamics

In the field of electrochemical CO2 reduction, both continuum models and molecular dynamics (MD) models have been used to understand the electric double layer (EDL). MD often focuses on the region within a few nm of the electrode, while continuum models can span up to the device level (cm). Still, both methods model the EDL, and for a cohesive picture of the CO2 electrolysis system, the two methods should agree in the regions where they overlap length scales. To this end, we make a direct comparison between state-of-the-art continuum models and classical MD simulations under the conditions of CO2 reduction on a Ag electrode. For continuum modeling, this includes the Poisson-Nernst-Planck formulation with steric (finite ion size) effects, and in MD the electrode is modeled with the constant potential method. The comparison yields numerous differences between the two modeling methods. MD shows cations forming two adsorbed layers, including a fully hydrated outer layer and a partial hydration layer closer to the electrode surface. The strength of the inner adsorbed layer increases with cation size (Li+ < Na+ < K+ < Cs+) and with more negative applied potentials. Continuum models that include steric effects predict CO2 to be mostly excluded within 1 nm of the cathode due to tightly packed cations, yet we find little evidence to support these predictions from the MD results. In fact, MD shows that the concentration of CO2 increases within a few Å of the cathode surface due to interactions with the Ag electrode, a factor not included in continuum models. The EDL capacitance is computed from the MD results, showing values in the range of 7-9 μF cm-2, irrespective of the electrolyte concentration, cation identity, or applied potential. The direct comparison between the two modeling methods is meant to show the areas of agreement and disagreement between the two views of the EDL, so as to improve and better align these models.

Impedance of nanocapacitors from molecular simulations to understand the dynamics of confined electrolytes

Nanoelectrochemical devices have become a promising candidate technology across various applications, including sensing and energy storage, and provide new platforms for studying fundamental properties of electrode/electrolyte interfaces. In this work, we employ constant-potential molecular dynamics simulations to investigate the impedance of gold-aqueous electrolyte nanocapacitors, exploiting a recently introduced fluctuation-dissipation relation. In particular, we relate the frequency-dependent impedance of these nanocapacitors to the complex conductivity of the bulk electrolyte in different regimes, and use this connection to design simple but accurate equivalent circuit models. We show that the electrode/electrolyte interfacial contribution is essentially capacitive and that the electrolyte response is bulk-like even when the interelectrode distance is only a few nanometers, provided that the latter is sufficiently large compared to the Debye screening length. We extensively compare our simulation results with spectroscopy experiments and predictions from analytical theories. In contrast to experiments, direct access in simulations to the ionic and solvent contributions to the polarization allows us to highlight their significant and persistent anticorrelation and to investigate the microscopic origin of the timescales observed in the impedance spectrum. This work opens avenues for the molecular interpretation of impedance measurements, and offers valuable contributions for future developments of accurate coarse-grained representations of confined electrolytes.

Molecular dynamics simulation study of water structure and dynamics on the gold electrode surface with adsorbed 4-mercaptobenzonitrile

Understanding water dynamics at charged interfaces is of great importance in various fields, such as catalysis, biomedical processes, and solar cell materials. In this study, we implemented molecular dynamics simulations of a system of pure water interfaced with Au electrodes, on one side of which 4-mercaptobenzonitrile (4-MBN) molecules are adsorbed. We calculated time correlation functions of various dynamic quantities, such as the hydrogen bond status of the N atom of the adsorbed 4-MBN molecules, the rotational motion of the water OH bond, hydrogen bonds between 4-MBN and water, and hydrogen bonds between water molecules in the interface region. Using the Luzar-Chandler model, we analyzed the hydrogen bond dynamics between a 4-MBN and a water molecule. The dynamic quantities we calculated can be divided into two categories: those related to the collective behavior of interfacial water molecules and the H-bond interaction between a water molecule and the CN group of 4-MBN. We found that these two categories of dynamic quantities exhibit opposite trends in response to applied potentials on the Au electrode. We anticipate that the present work will help improve our understanding of the interfacial dynamics of water in various electrolyte systems.

Effect of Interlayer Spaces and Interfacial Structures on High-Performance MXene/Ionic Liquid Supercapacitors: A Molecular Dynamics Simulation

The combination of high-capacitance MXenes and wide-electrochemical-window ionic liquids (ILs) has exhibited bright prospects in supercapacitors. Several strategies, such as surficial functionalization and interlayer spacing tuning, have been used to enhance the electrochemical performance of supercapacitors. However, the lack of theoretical guidance on these strategies, including the effects of the microenvironment in the interlayer of confined ILs, hindered the further exploration of such devices. Herein, we performed molecular dynamics simulations to comprehensively investigate the effects of the interlayer space and surface terminations of MXene electrodes on capacity. The results show that the electrical double layer (EDL) structure was found to form on the interface between the MXene electrode and ILs electrolyte by analyzing the ion number density and charge density in the nanometer confined spaces. Under the same potential, the -OH terminations significantly impact the ion orientation in the EDL, particularly near the electrode surface, where cations tend to align vertically, allowing the retention of more cations at the electrode surfaces. Interestingly, such an orientation distribution was decisively from the hydrogen bonds expressed by O-H···O between the -OH termination of MXene and -OH groups of ILs. The differential capacitances of the supercapacitors were calculated by the surficial electron density, and it showed that the capacitance is a nearly one-quarter increase in the 14 Å interlayer spacing compared with that of 10 Å under an applied potential of 2 V. At the same time, the Ti3C2(OH)2 electrode had a higher differential capacitance than the Ti3C2O2 electrode, which possibly originates from the stronger hydrogen bonds to contribute to the vertical aggregation of the cations. Our results highlighted the roles of the interlayer spacing distance and surface terminations of the MXene on the performance of the type of supercapacitor.

Charging and discharging a supercapacitor in molecular simulations

As the world moves more toward unpredictable renewable energy sources, better energy storage devices are required. Supercapacitors are a promising technology to meet the demand for short-term, high-power energy storage. Clearly, understanding their charging and discharging behaviors is essential to improving the technology. Molecular Dynamics (MD) simulations provide microscopic insights into the complex interplay between the dynamics of the ions in the electrolyte and the evolution of the charge distributions on the electrodes. Traditional MD simulations of (dis)charging supercapacitors impose a pre-determined evolving voltage difference between the electrodes, using the Constant Potential Method (CPM). Here, we present an alternative method that explicitly simulates the charge flow to and from the electrodes. For a disconnected capacitor, i.e., an open circuit, the charges are allowed to redistribute within each electrode while the sum charges on both electrodes remain constant. We demonstrate, for a model capacitor containing an aqueous salt solution, that this method recovers the charge-potential curve of CPM simulations. The equilibrium voltage fluctuations are related to the differential capacitance. We next simulate a closed circuit by introducing equations of motion for the sum charges, by explicitly accounting for the external circuit element(s). Charging and discharging of the model supercapacitor via a resistance proceed by double exponential processes, supplementing the usual time scale set by the electrolyte dynamics with a novel time scale set by the external circuit. Finally, we propose a simple equivalent circuit that reproduces the main characteristics of this supercapacitor.

Development of Heteroatomic Constant Potential Method with Application to MXene-Based Supercapacitors

We describe a method for modeling constant-potential charges in heteroatomic electrodes, keeping pace with the increasing complexity of electrode composition and nanostructure in electrochemical research. The proposed "heteroatomic constant potential method" (HCPM) uses minimal added parameters to handle differing electronegativities and chemical hardnesses of different elements, which we fit to density functional theory (DFT) partial charge predictions in this paper by using derivative-free optimization. To demonstrate the model, we performed molecular dynamics simulations using both HCPM and conventional constant potential method (CPM) for MXene electrodes with Li-TFSI/AN (lithium bis(trifluoromethane sulfonyl)imide/acetonitrile)-based solvent-in-salt electrolytes. Although the two methods show similar accumulated charge storage on the electrodes, the results indicated that HCPM provides a more reliable depiction of electrode atom charge distribution and charge response compared with CPM, accompanied by increased cationic attraction to the MXene surface. These results highlight the influence of elemental composition on electrode performance, and the flexibility of our HCPM opens up new avenues for studying the performance of diverse heteroatomic electrodes including other types of MXenes, two-dimensional materials, metal-organic frameworks (MOFs), and doped carbonaceous electrodes.

A simple efficient algorithm for molecular simulations of constant potential electrodes

Increasingly, society requires high power, high energy storage devices for applications ranging from electric vehicles to buffers on the electric grid. Supercapacitors are a promising contribution to meeting these demands, though there still remain unsolved practical problems. Molecular dynamics simulations can shed light on the relevant molecular level processes in electric double layer capacitors, but these simulations are computationally very demanding. Our focus here is on the algorithmic complexity of the constant potential method (CPM), which uses dedicated electrostatics solvers to maintain a fixed potential difference between two conducting electrodes. We show how any standard electrostatics solver-capable of calculating the energies and forces on all atoms-can be used to implement CPM with a minimum of coding. As an example, we compare our generalized implementation of CPM, based on invocations of the particle-particle-particle-mesh routine of the Large-scale Atomic/Molecular Massively Parallel Simulator, with a traditional implementation based on a dedicated re-implementation of Ewald summation. Both methods yield comparable results on four test systems, with the former achieving a substantial gain in speed and improved scalability. The step from dedicated electrostatic solvers to generic routines is made possible by noting that CPM's traditional narrow Gaussian point-spread of atomic charges on the electrodes effectively endows point-like atoms with chemical hardness, i.e., an intra-atomic energy quadratic in the charge.

The hydrogen-bonding dynamics of water to a nitrile-functionalized electrode is modulated by voltage according to ultrafast 2D IR spectroscopy

We report the hydrogen-bonding dynamics of water to a nitrile-functionalized and plasmonic electrode surface as a function of applied voltage. The surface-enhanced two-dimensional infrared spectra exhibit hydrogen-bonded and non-hydrogen-bonded nitrile features in similar proportions, plus cross peaks between the two. Isotopic dilution experiments show that the cross peaks arise predominantly from chemical exchange between hydrogen-bonded and non-hydrogen-bonded nitriles. The chemical exchange rate depends upon voltage, with the hydrogen bond of the water to the nitriles breaking 2 to 3 times slower (>63 vs. 25 ps) under a positive as compared to a negative potential. Spectral diffusion created by hydrogen-bond fluctuations occurs on a ~1 ps timescale and is moderately potential-dependent. Timescales from molecular dynamics simulations agree qualitatively with the experiment and show that a negative voltage causes a small net displacement of water away from the surface. These results show that the voltage applied to an electrode can alter the timescales of solvent motion at its interface, which has implications for electrochemically driven reactions.

Theory and Simulations of Ionic Liquids in Nanoconfinement

Room-temperature ionic liquids (RTILs) have exciting properties such as nonvolatility, large electrochemical windows, and remarkable variety, drawing much interest in energy storage, gating, electrocatalysis, tunable lubrication, and other applications. Confined RTILs appear in various situations, for instance, in pores of nanostructured electrodes of supercapacitors and batteries, as such electrodes increase the contact area with RTILs and enhance the total capacitance and stored energy, between crossed cylinders in surface force balance experiments, between a tip and a sample in atomic force microscopy, and between sliding surfaces in tribology experiments, where RTILs act as lubricants. The properties and functioning of RTILs in confinement, especially nanoconfinement, result in fascinating structural and dynamic phenomena, including layering, overscreening and crowding, nanoscale capillary freezing, quantized and electrotunable friction, and superionic state. This review offers a comprehensive analysis of the fundamental physical phenomena controlling the properties of such systems and the current state-of-the-art theoretical and simulation approaches developed for their description. We discuss these approaches sequentially by increasing atomistic complexity, paying particular attention to new physical phenomena emerging in nanoscale confinement. This review covers theoretical models, most of which are based on mapping the problems on pertinent statistical mechanics models with exact analytical solutions, allowing systematic analysis and new physical insights to develop more easily. We also describe a classical density functional theory, which offers a reliable and computationally inexpensive tool to account for some microscopic details and correlations that simplified models often fail to consider. Molecular simulations play a vital role in studying confined ionic liquids, enabling deep microscopic insights otherwise unavailable to researchers. We describe the basics of various simulation approaches and discuss their challenges and applicability to specific problems, focusing on RTIL structure in cylindrical and slit confinement and how it relates to friction and capacitive and dynamic properties of confined ions.

Molecular understanding of the Helmholtz capacitance difference between Cu(100) and graphene electrodes

Unraveling the origin of Helmholtz capacitance is of paramount importance for understanding the interfacial structure and electrostatic potential distribution of electric double layers (EDL). In this work, we combined the methods of ab initio molecular dynamics and classical molecular dynamics and modeled electrified Cu(100)/electrolyte and graphene/electrolyte interfaces for comparison. It was proposed that the Helmholtz capacitance is composed of three parts connected in series: the usual solvent capacitance, water chemisorption induced capacitance, and Pauling repulsion caused gap capacitance. We found the Helmholtz capacitance of graphene is significantly lower than that of Cu(100), which was attributed to two intrinsic factors. One is that graphene has a wider gap layer at interface, and the other is that graphene is less active for water chemisorption. Finally, based on our findings, we provide suggestions for how to increase the EDL capacitance of graphene-based materials in future work, and we also suggest that the new understanding of the potential distribution across the Helmholtz layer may help explain some experimental phenomena of electrocatalysis.

Constant-Potential Molecular Dynamics Simulations of Molten-Salt Double Layers for FLiBe and FLiNaK

We report the results of constant-potential molecular dynamics simulations of the double- layer interface between molten FLiBe and FLiNaK fluoride mixtures and idealized solid electrodes. Employing methods similar to those used in studies of chloride double layers, we compute the structure and differential capacitance of molten fluoride electric double layers as a function of applied voltage. The role of molten salt structure is probed through comparisons between FLiBe and FLiNaK, which serve as models for strong and weak associate- forming salts, respectively. In FLiBe, screening involves changes in Be-F-Be angles and alignment of the oligomers parallel to the electrode, while in FLiNaK the electric field is screened mainly by rearrangement of individual ions, predominantly the polarizable potassium cation.

ELECTRODE: An electrochemistry package for atomistic simulations

Constant potential methods (CPM) enable computationally efficient simulations of the solid-liquid interface at conducting electrodes in molecular dynamics (MD). They have been successfully used, for example, to realistically model the behavior of ionic liquids or water-in-salt electrolytes in supercapacitors and batteries. The CPM models conductive electrodes by updating charges of individual electrode atoms according to the applied electric potential and the (time-dependent) local electrolyte structure. Here we present a feature-rich CPM implementation, called ELECTRODE, for the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS), which includes a constrained charge method and a thermo-potentiostat. The ELECTRODE package also contains a finite-field approach, multiple corrections for non-periodic boundary conditions of the particle-particle particle-mesh solver, and a Thomas-Fermi model for using non-ideal metals as electrodes. We demonstrate the capabilities of this implementation for a parallel-plate electrical double-layer capacitor, for which we have investigated the charging times with the different implemented methods and found an interesting relationship between water and ionic dipole relaxations. To prove the validity of the one-dimensional correction for the long-range electrostatics, we estimated the vacuum capacitance of two co-axial carbon nanotubes and compared it to structureless cylinders, for which an analytical expression exists. In summary, the ELECTRODE package enables efficient electrochemical simulations using state-of-the-art methods, allowing one to simulate even heterogeneous electrodes. Moreover, it allows unveiling more rigorously how electrode curvature affects the capacitance with the one-dimensional correction.