Empirical Potential-based Quasi-continuum Theory Research Articles

A multiscale model for charge inversion in electric double layers.

Charge inversion is a widely observed phenomenon. It is a result of the rich statistical mechanics of the molecular interactions between ions, solvent, and charged surfaces near electric double layers (EDLs). Electrostatic correlations between ions and hydration interactions between ions and water molecules play a dominant role in determining the distribution of ions in EDLs. Due to highly polar nature of water, near a surface, an inhomogeneous and anisotropic arrangement of water molecules gives rise to pronounced variations in the electrostatic and hydration energies of ions. Classical continuum theories fail to accurately describe electrostatic correlations and molecular effects of water in EDLs. In this work, we present an empirical potential based quasi-continuum theory (EQT) to accurately predict the molecular-level properties of aqueous electrolytes. In EQT, we employ rigorous statistical mechanics tools to incorporate interatomic interactions, long-range electrostatics, correlations, and orientation polarization effects at a continuum-level. Explicit consideration of atomic interactions of water molecules is both theoretically and numerically challenging. We develop a systematic coarse-graining approach to coarse-grain interactions of water molecules and electrolyte ions from a high-resolution atomistic scale to the continuum scale. To demonstrate the ability of EQT to incorporate the water orientation polarization, ion hydration, and electrostatic correlations effects, we simulate confined KCl aqueous electrolyte and show that EQT can accurately predict the distribution of ions in a thin EDL and also predict the complex phenomenon of charge inversion.

An EQT-based cDFT approach for thermodynamic properties of confined fluid mixtures.

We present an empirical potential-based quasi-continuum theory (EQT) to predict the structure and thermodynamic properties of confined fluid mixtures. The central idea in the EQT is to construct potential energies that integrate important atomistic details into a continuum-based model such as the Nernst-Planck equation. The EQT potentials can be also used to construct the excess free energy functional, which is required for the grand potential in the classical density functional theory (cDFT). In this work, we use the EQT-based grand potential to predict various thermodynamic properties of a confined binary mixture of hydrogen and methane molecules inside graphene slit channels of different widths. We show that the EQT-cDFT predictions for the structure, surface tension, solvation force, and local pressure tensor profiles are in good agreement with the molecular dynamics simulations. Moreover, we study the effect of different bulk compositions and channel widths on the thermodynamic properties. Our results reveal that the composition of methane in the mixture can significantly affect the ordering of molecules and thermodynamic properties under confinement. In addition, we find that graphene is selective to methane molecules.

Langevin-Poisson-EQT: A dipolar solvent based quasi-continuum approach for electric double layers.

Water is a highly polar solvent. As a result, electrostatic interactions of interfacial water molecules play a dominant role in determining the distribution of ions in electric double layers (EDLs). Near a surface, an inhomogeneous and anisotropic arrangement of water molecules gives rise to pronounced variations in the electrostatic and hydration energies of ions. Therefore, a detailed description of the structural and dielectric properties of water is important to study EDLs. However, most theoretical models ignore the molecular effects of water and treat water as a background continuum with a uniform dielectric permittivity. Explicit consideration of water polarization and hydration of ions is both theoretically and numerically challenging. In this work, we present an empirical potential-based quasi-continuum theory (EQT) for EDL, which incorporates the polarization and hydration effects of water explicitly. In EQT, water molecules are modeled as Langevin point dipoles and a point dipole based coarse-grained model for water is developed systematically. The space dependence of the dielectric permittivity of water is included in the Poisson equation to compute the electrostatic potential. In addition, to reproduce hydration of ions, ion-water coarse-grained potentials are developed. We demonstrate the EQT framework for EDL by simulating NaCl aqueous electrolyte confined inside slit-like capacitor channels at various ion concentrations and surface charge densities. We show that the ion and water density predictions from EQT agree well with the reference molecular dynamics simulations.

An EQT-based cDFT approach for a confined Lennard-Jones fluid mixture.

Empirical potential-based quasi-continuum theory (EQT) provides a route to incorporate atomistic detail into continuum framework such as the Nernst-Planck equation. EQT can also be used to construct a grand potential functional for classical density functional theory (cDFT). The combination of EQT and cDFT provides a simple and fast approach to predict the inhomogeneous density, potential profiles, and thermodynamic properties of confined fluids. We extend the EQT-cDFT approach to confined fluid mixtures and demonstrate it by simulating a mixture of methane and hydrogen inside slit-like channels of graphene. We show that the EQT-cDFT predictions for the structure of the confined fluid mixture compare well with the molecular dynamics simulation results. In addition, our results show that graphene slit nanopores exhibit a selective adsorption of methane over hydrogen.

An EQT-cDFT approach to determine thermodynamic properties of confined fluids

We present a continuum-based approach to predict the structure and thermodynamic properties of confined fluids at multiple length-scales, ranging from a few angstroms to macro-meters. The continuum approach is based on the empirical potential-based quasi-continuum theory (EQT) and classical density functional theory (cDFT). EQT is a simple and fast approach to predict inhomogeneous density and potential profiles of confined fluids. We use EQT potentials to construct a grand potential functional for cDFT. The EQT-cDFT-based grand potential can be used to predict various thermodynamic properties of confined fluids. In this work, we demonstrate the EQT-cDFT approach by simulating Lennard-Jones fluids, namely, methane and argon, confined inside slit-like channels of graphene. We show that the EQT-cDFT can accurately predict the structure and thermodynamic properties, such as density profiles, adsorption, local pressure tensor, surface tension, and solvation force, of confined fluids as compared to the molecular dynamics simulation results.

Thermodynamic state-dependent structure-based coarse-graining of confined water

We develop thermodynamic state-dependent single-site isotropic coarse-grained potentials to predict the structure of water confined inside graphene slit-like channels by two multiscale simulation approaches: the coarse-grained molecular dynamics (CG-MD) and the empirical potential-based quasi-continuum theory (EQT). The structurally-consistent coarse-grained potentials for the CG-MD and EQT are systematically determined from the reference all-atom SPC/E water MD (AA-MD) results. For optimization of the CG-MD potentials, the relative entropy based coarse-graining method is used, and for determination of the EQT potentials, we develop a potential of mean force matching scheme. The optimized coarse-grained potentials are found to be dependent on the thermodynamic state. They are evaluated for their ability to predict the density profile of confined water, and it is found that the results obtained by the CG-MD and EQT simulations are in good agreement with the reference AA-MD results.

Coarse-Grained Potential Model for Structural Prediction of Confined Water.

We propose a coarse-grained potential model to predict the concentration and potential profiles of confined water. In this model, we represent one water molecule with one coarse-grained bead, such that the interactions between the coarse-grained beads are given by isotropic two-body potentials. Due to the inherent inhomogeneity of the confined water microstructure, we find that a single spatially uniform coarse-grained water-water potential may not be sufficient to accurately predict the structure of water near the surface. To accurately capture surface effects on the water structure, we add a coarse-grained correction potential between wall atoms and water coarse-grained beads. We use an empirical potential-based quasi-continuum theory (EQT) (J. Chem. Phys.2007, 127, 174701) to derive and evaluate optimal parameters for the coarse-grained potential model. We evaluate the ability of our model to predict the structure of confined water for two different types of surfaces-a silicon slit channel and a graphite slit channel-and show that the results predicted by EQT are in good agreement with all-atom molecular dynamics results across multiple length scales. We also demonstrate that the coarse-grained potential parameters optimized using EQT work well even in the coarse-grained molecular dynamics simulations.

Retraction: An empirical potential based quasicontinuum theory for structural prediction of water [J. Chem. Phys. 131, 184703 (2009)

Retraction: An empirical potential based quasicontinuum theory for structural prediction of water [J. Chem. Phys. 131, 184703 (2009)

A transferable coarse-grained potential to study the structure of confined, supercritical Lennard-Jones fluids

In this paper, we develop a transferable coarse-grained interatomic potential to study the structure of simple (spherical and nonpolar) Lennard-Jones (LJ) fluids confined at supercritical temperatures. The potential is used in empirical potential based quasicontinuum theory, [A. V. Raghunathan et al., J. Chem. Phys. 127, 174701 (2007)] to study the structure of three simple LJ fluids (oxygen, methane, and argon) confined in slitlike geometries. The results obtained using the coarse-grained interatomic potential are found to be in good agreement with those predicted by equilibrium molecular dynamics simulations.

An empirical potential based quasicontinuum theory for structural prediction of water

An empirical potential based quasicontinuum theory (EQT) is proposed to predict the structure, concentration, and various potential profiles of water in confined environments. EQT seamlessly unifies the continuum theory given by the Nernst-Planck equation and the atomistic theory governed by interatomic potentials. In particular, the interatomic potentials describing various interactions in water are directly incorporated into the Nernst-Planck theory. We introduce a new empirical potential to compute electrostatic interactions in water. The results from the EQT formalism are compared with molecular dynamics simulations and a good match is observed for channels with widths ranging from 2sigma(ow) to 20sigma(ow), where sigma(ow) is the water-oxygen Lennard-Jones distance parameter. While molecular dynamics can be limited to small length scales, EQT can be used at various length scales to effectively and accurately capture both the interfacial structure and bulk properties of water making it a robust and fast method that can predict properties in widths ranging from the macroscale down to the nanoscale.