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.

Constant Potential and Constrained Charge Ensembles for Simulations of Conductive Electrodes.

Constant potential method molecular dynamics simulation (CPM MD) enables the accurate modeling of atomistic electrode charges when studying the electrode-electrolyte interface at the nanoscale. Here, we extend the theoretical framework of CPM MD to the case in which the total charge of each conductive electrode is controlled, instead of their potential difference. We show that the resulting thermodynamic ensemble is distinct from that sampled with a fixed potential difference but they are rigorously related as conjugate ensembles. This theoretical correspondence, which we demonstrate using simulations of an ionic liquid supercapacitor, underpins the success of recent studies with fixed total charges on the electrodes. We show that equilibration is usefully sped up in this ensemble and outline some potential applications of these simulations in the future.

ELECTRODE: An electrochemistry package for atomistic simulations.

Constant potential methods (CPMs) enable computationally efficient simulations of the solid-liquid interface at conducting electrodes in molecular dynamics. They have been successfully used, for example, to realistically model the behavior of ionic liquids or water-in-salt electrolytes in supercapacitors and batteries. CPMs model 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, which includes a constrained charge method and a thermo-potentiostat. The ELECTRODE package also contains a finite-field approach, multiple corrections for nonperiodic boundary conditions of the particle-particle particle-mesh solver, and a Thomas-Fermi model for using nonideal 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 coaxial 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.

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

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 a 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 speedup 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.