Zhehui Jin

Oscillation of Capacitance inside Nanopores

Porous carbons of high surface area are promising as cost-effective electrode materials for supercapacitors. Although great attention has been given to the anomalous increase of the capacitance as the pore size approaches the ionic dimensions, there remains a lack of full comprehension of the size dependence of the capacitance in nanopores. Here we predict from a classical density functional theory that the capacitance of an ionic-liquid electrolyte inside a nanopore oscillates with a decaying envelope as the pore size increases. The oscillatory behavior can be attributed to the interference of the overlapping electric double layers (EDLs); namely, the maxima in capacitance appear when superposition of the two EDLs is most constructive. The theoretical prediction agrees well with the experiment when the pore size is less than twice the ionic diameter. Confirmation of the entire oscillatory spectrum invites future experiments with a precise control of the pore size from micro- to mesoscales.

Solvent Effect on the Pore-Size Dependence of an Organic Electrolyte Supercapacitor

Organic electrolytes such as tetraethylammonium tetrafluoroborate dissolved in acetonitrile (TEA-BF4/ACN) are widely used in commercial supercapacitors and academic research, but conflicting experimental results have been reported regarding the dependence of surface-area-normalized capacitance on the pore size. Here we show from a classical density functional theory the dependence of capacitance on the pore size from 0.5 to 3.0 nm for a model TEA-BF4/ACN electrolyte. We find that the capacitance-pore size curve becomes roughly flat after the first peak around the ion diameter, and the peak capacitance is not significantly higher than the large-pore average. We attribute the invariance of capacitance with the pore size to the formation of an electric double-layer structure that consists of counterions and highly organized solvent molecules. This work highlights the role of the solvent molecules in modulating the capacitance and reconciles apparently conflicting experimental reports.

A classical density functional theory for interfacial layering of ionic liquids

Ionic liquids have attracted much recent theoretical interest for broad applications as environmentally-friendly solvents in separation and electrochemical processes. Because of the intrinsic complexity of organic ions and strong electrostatic correlations, the electrochemical properties of ionic liquids often defy the descriptions of conventional mean-field methods including the venerable, and over-used, Gouy–Chapman–Stern (GCS) theory. Classical density functional theory (DFT) has proven to be useful in previous studies of the electrostatic properties of aqueous electrolytes but until recently it has not been applied to ionic liquids. Here we report predictions from the DFT on the interfacial properties of ionic liquids near neutral or charged surfaces. By considering the molecular size, topology, and electrostatic correlations, we have examined major factors responsible for the unique features of electric-double layers of ionic-liquid including formation of long-range and alternating structures of cations and anions at charged surfaces.

Phase Behavior and Adsorption of Pure Substances and Mixtures and Characterization in Nanopore Structures by Density Functional Theory

Phase behavior in shale remains a mystery because of various complexities and effects. One complexity is from nanopores, in which phase behavior is significantly affected by the interaction between the pore surfaces and fluid molecules. The result is the heterogeneous distribution of molecules that cannot be described by bulk-phase thermodynamic approaches. Statistical thermodynamic methods can describe the phase behavior in nanopores. In this work, we apply an engineering density functional theory (DFT) combined with the Peng-Robinson equation of state (EOS) to investigate the adsorption and phase behavior of pure substances and mixtures in nanopores, and include the characterization of pore structure of porous media. The nanopores are represented by carbon-slit pores each consisting of two parallel planar-infinite structureless graphite surfaces. The porous media are activated carbons and dry coal, each modeled by an array of polydisperse carbon-slit pores. We study the influence of multiple factors on phase transitions of various pure light species and their mixtures in nanopores. We find that capillary condensation and hysteresis are more likely in heavier hydrocarbons, at lower temperatures, and in smaller pores. For pure hydrocarbons in nanopores, the phase change always occurs below the critical temperature and saturation pressure. For mixtures in nanopores, there may be a phase change above the cricondentherm. We characterize the pore structure of porous media to obtain the pore-size distribution (PSD), surface area (SA), and pore volume (PV) on the basis of the measured adsorption isotherms of pure substances. Then, we use the computed PSD to predict the adsorption of mixtures in porous media. There is agreement between the experiments and our predictions. This work is in the direction of phase-behavior modeling and understanding in shale media.

Thermodynamic Modeling of Phase Behavior in Shale Media

In conventional permeable media, once pore volume (PV) is known, the amount of fluid-in-place can be estimated. This is because the fluid is locally homogeneous, pores are generally larger than 100 nm, and surface adsorption is negligible. In shale media, in addition to PV, knowledge of pore-size distribution, total organic content, and chemistry of the rock is required. Fluid molecules in shale media can be found in three different states: (1) free molecules in the pores, (2) adsorbed molecules on the pore surface, and (3) dissolved molecules in the organic matter. Of the three, the first two mechanisms are discussed in the literature. In this work, we compute for the first time the amount of dissolved molecules. To compute the fluids in shale media, we divide the pores into sizes greater than 10 nm and sizes less than 10 nm. In pores greater than 10 nm, the interface curvature affects phase behavior, and fluid phases are homogeneous. Therefore, they can be described by conventional equations of state. Our calculations show that retrograde condensation increases in nanopores; the upper dewpoint increases, and the lower dewpoint decreases. These calculations are supported by experimental measurements. Gas solubility in water and liquid normal decane shows a modest increase with curvature. In pores less than 10 nm, the fluids become inhomogeneous, and the direct use of conventional equations of state cannot be applied even with adjusted critical pressure and temperature. We suggest the use of molecular modeling. A model such as the Langmuir adsorption isotherm is merely a curve fitting of the data. We use available data in shale media, which are mainly limited to excess sorption of methane and carbon dioxide, to compare to our thermodynamic model computations. This is the first attempt to compare measured data in shale and predictions that are based on the integration of molecular modeling and classical thermodynamic modeling.

New Theoretical Method for Rapid Prediction of Solvation Free Energy in Water

We present a new theoretical method for rapid calculation of the solvation free energy in water by combining molecular simulation and the classical density functional theory (DFT). The DFT calculation is based on an accurate free-energy functional for water that incorporates the simulation results for long-range correlations and the fundamental measure theory for the molecular excluded-volume effects. The numerical performance of the theoretical method has been validated with simulation results and experimental data for the solvation free energies of halide (F(-), Cl(-), Br(-), and I(-)) and alkali (Li(+), Na(+), K(+), Rb(+), and Cs(+)) ions in water at ambient conditions. Because simulation is applied only to the particular thermodynamic condition of interest, the hybrid method is computationally much more efficient than conventional ways of solvation free energy calculations.

Flow of methane in shale nanopores at low and high pressure by molecular dynamics simulations

Flow in shale nanopores may be vastly different from that in the conventional permeable media. In large pores and fractures, flow is governed by viscosity and pressure-driven. Convection describes the process. Pores in some shale media are in nanometer range. At this scale, continuum flow mechanism may not apply. Knudsen diffusion and hydrodynamic expressions such as the Hagen-Poiseuille equation and their modifications have been used to compute flow in nanopores. Both approaches may have drawbacks and can significantly underestimate molecular flux in nanopores. In this work, we use the dual control volume-grand canonical molecular dynamics simulations to investigate methane flow in carbon nanopores at low and high pressure conditions. Our simulations reveal that methane flow in a slit pore width of 1-4 nm can be more than one order of magnitude greater than that from Knudsen diffusion at low pressure and the Hagen-Poiseuille equation at high pressure. Knudsen diffusion and Hagen-Poiseuille equations do not account for surface adsorption and mobility of the adsorbed molecules, and inhomogeneous fluid density distributions. Mobility of molecules in the adsorbed layers significantly increases molecular flux. Molecular velocity profiles in nanopores deviate significantly from the Navier-Stokes hydrodynamic predictions. Our molecular simulation results are in agreement with the enhanced flow measurements in carbon nanotubes.

Application of Density Functional Theory to Study the Double Layer of an Electrolyte with an Explicit Dimer Model for the Solvent.

Most theoretical studies of an electrical double layer, which is formed by an electrolyte in contact with a charged electrode, employ a primitive model in which the solvent is represented by a dielectric continuum. This implicit-solvent model is convenient because computations are comparatively simple. However, it suppresses oscillations in the density profiles of ionic species that result from the discreteness of the solvent molecules. Furthermore, the implicit-solvent model yields poor results for the capacitance. In comparison with experiment at fixed electrode charge density, it predicts a too small electrode potential, and the resultant capacitance is too large. This latter discrepancy can be compensated in part by postulating the existence of an often fictitious inner layer whose properties are parametrized to agree best with experiment. The use of an implicit solvent model and an inner layer helps in correlating experimental results but rests on a faulty microscopic picture. Unfortunately, explicit consideration of solvent molecules poses both theoretical and numerical difficulties and, as a result, studies using an explicit solvent model have been few and far between. In this study, we consider a simple nonprimitive or explicit solvent model in which each solvent molecule is represented by a dimer composed of touching positive and negative hard spheres, with a resulting dipole moment that is equal to that of a water molecule, and the ions are represented by charged hard spheres. The density profiles and charge-potential relationship of this model are examined using the classical density functional theory. We find that the introduction of an explicit solvent increases the electrode potential, at fixed electrode charge, without the need to postulate a parametrized inner layer. Because of the solvent polarity, the ion profiles become strong oscillatory and show local charge inversion near a highly charged electrode surface at all ion concentrations.

A perturbative density functional theory for square-well fluids

We report a perturbative density functional theory for quantitative description of the structural and thermodynamic properties of square-well fluids in the bulk or at inhomogeneous conditions. The free-energy functional combines a modified fundamental measure theory to account for the short-range repulsion and a quadratic density expansion for the long-range attraction. The long-correlation effects are taken into account by using analytical expressions of the direct correlation functions of bulk fluids recently obtained from the first-order mean-spherical approximation. The density functional theory has been calibrated by extensive comparison with simulation data from this work and from the literature. The theory yields good agreement with simulation results for the radial distribution function of bulk systems and for the density profiles of square-well fluids near the surfaces of spherical cavities or in slit pores over a broad range of the parameter space and thermodynamic conditions.

Density functional theory for encapsidated polyelectrolytes: a comparison with Monte Carlo simulation.

Genome packaging inside viral capsids is strongly influenced by the molecular size and the backbone structure of RNA∕DNA chains and their electrostatic affinity with the capsid proteins. Coarse-grained models are able to capture the generic features of non-specific interactions and provide a useful testing ground for theoretical developments. In this work, we use the classical density functional theory (DFT) within the framework of an extended primitive model for electrolyte solutions to investigate the self-organization of flexible and semi-flexible linear polyelectrolytes in spherical capsids that are permeable to small ions but not polymer segments. We compare the DFT predictions with Monte Carlo (MC) simulation for the density distributions of polymer segments and small ions at different backbone flexibilities and several solution conditions. In general, the agreement between DFT and MC is near quantitative except when the simulation results are noticeably influenced by the boundary effects. The numerical efficiency of the DFT calculations makes it promising as a useful tool for quantification of the structural and thermodynamic properties of viral nucleocapsids in vivo and at conditions pertinent to experiments.