Weighted Density Approximation Research Articles

Local thermal conductivity of inhomogeneous nano-fluidic films: A density functional theory perspective

Combining the mean field Pozhar–Gubbins (PG) theory and the weighted density approximation, a novel method for local thermal conductivity of inhomogeneous fluids is proposed. The correlation effect that is beyond the mean field treatment is taken into account by the simulation-based empirical correlations. The application of this method to confined argon in slit pore shows that its prediction agrees well with the simulation results, and that it performs better than the original PG theory as well as the local averaged density model (LADM). In its further application to the nano-fluidic films, the influences of fluid parameters and pore parameters on the thermal conductivity are calculated and investigated. It is found that both the local thermal conductivity and the overall thermal conductivity can be significantly modulated by these parameters. Specifically, in the supercritical states, the thermal conductivity of the confined fluid shows positive correlation to the bulk density as well as the temperature. However, when the bulk density is small, the thermal conductivity exhibits a decrease-increase transition as the temperature is increased. This is also the case in which the temperature is low. In fact, the decrease–increase transition in both the small-bulk-density and low-temperature cases arises from the capillary condensation in the pore. Furthermore, smaller pore width and/or stronger adsorption potential can raise the critical temperature for condensation, and then are beneficial to the enhancement of the thermal conductivity. These modulation behaviors of the local thermal conductivity lead immediately to the significant difference of the overall thermal conductivity in different phase regions.

Classical density functional theory for interfacial properties of hydrogen, helium, deuterium, neon, and their mixtures.

We present a classical density functional theory (DFT) for fluid mixtures that is based on a third-order thermodynamic perturbation theory of Feynman-Hibbs-corrected Mie potentials. The DFT is developed to study the interfacial properties of hydrogen, helium, neon, deuterium, and their mixtures, i.e., fluids that are strongly influenced by quantum effects at low temperatures. White Bear fundamental measure theory is used for the hard-sphere contribution of the Helmholtz energy functional, and a weighted density approximation is used for the dispersion contribution. For mixtures, a contribution is included to account for non-additivity in the Lorentz-Berthelot combination rule. Predictions of the radial distribution function from DFT are in excellent agreement with results from molecular simulations, both for pure components and mixtures. Above the normal boiling point and 5% below the critical temperature, the DFT yields surface tensions of neon, hydrogen, and deuterium with average deviations from experiments of 7.5%, 4.4%, and 1.8%, respectively. The surface tensions of hydrogen/deuterium, para-hydrogen/helium, deuterium/helium, and hydrogen/neon mixtures are reproduced with a mean absolute error of 5.4%, 8.1%, 1.3%, and 7.5%, respectively. The surface tensions are predicted with an excellent accuracy at temperatures above 20K. The poor accuracy below 20K is due to the inability of Feynman-Hibbs-corrected Mie potentials to represent the real fluid behavior at these conditions, motivating the development of new intermolecular potentials. This DFT can be leveraged in the future to study confined fluids and assess the performance of porous materials for hydrogen storage and transport.

Dynamic density functional theory for drying colloidal suspensions: Comparison of hard-sphere free-energy functionals.

Dynamic density functional theory (DDFT) is a promising approach for predicting the structural evolution of a drying suspension containing one or more types of colloidal particles. The assumed free-energy functional is a key component of DDFT that dictates the thermodynamics of the model and, in turn, the density flux due to a concentration gradient. In this work, we compare several commonly used free-energy functionals for drying hard-sphere suspensions, including local-density approximations based on the ideal-gas, virial, and Boublík-Mansoori-Carnahan-Starling-Leland (BMCSL) equations of state as well as a weighted-density approximation based on fundamental measure theory (FMT). To determine the accuracy of each functional, we model one- and two-component hard-sphere suspensions in a drying film with varied initial heights and compositions, and we compare the DDFT-predicted volume fraction profiles to particle-based Brownian dynamics (BD) simulations. FMT accurately predicts the structure of the one-component suspensions even at high concentrations and when significant density gradients develop, but the virial and BMCSL equations of state provide reasonable approximations for smaller concentrations at a reduced computational cost. In the two-component suspensions, FMT and BMCSL are similar to each other but modestly overpredict the extent of stratification by size compared to BD simulations. This work provides helpful guidance for selecting thermodynamic models for soft materials in nonequilibrium processes, such as solvent drying, solvent freezing, and sedimentation.

A combined experimental and theoretical study of small and large vacancy clusters in tungsten

Tungsten is considered to be used in the future fusion reactors as plasma-facing material. In such extreme environments, defects are induced in materials that modify their macroscopic properties such as the mechanical ones. It is of paramount importance to be able to determine concentration and size of the vacancy defects, from the mono vacancy to the large cavities, to validate the models developed to predict the evolution of the microstructure of irradiated materials. Positrons are very useful non-destructive probes that can characterize vacancy-type defects in materials. We present a combined experimental and theoretical study on detecting and estimating the sizes of vacancy clusters that are invisible with electron microscopy in tungsten, using positron annihilation spectroscopy. We here model the positron annihilation in the tungsten lattice and in vacancy-type defects using state-of-the-art first principles methodology. The Doppler broadening spectra and positron lifetimes in tungsten are calculated with two-component density functional theory with local density approximation and weighted density approximation. Our calculations are in excellent agreement with our experimental results. We show that the sizes of vacancy clusters in tungsten can be well estimated by combining both positron lifetimes and Doppler broadening spectra. We also determine the limit of validity of the canonical calculation method, which here is shown to fail when the vacancy clusters grow beyond their nucleation stage. This work is a first step needed to better interpret the measured positron annihilation characteristics (Doppler and lifetime) in tungsten and then extract quantitative data on small vacancy defects required to improve the understanding of early-stage vacancy defect evolution in tungsten. The method used in this paper could be used to study other metallic materials.

Self-consistent construction of grand potential functional with hierarchical integral equations and its application to solvation thermodynamics.

The construction of the density functional for grand potential is fundamental in understanding a broad range of interesting physical phenomena, such as phase equilibrium, interfacial thermodynamics, and solvation. However, the knowledge of a general functional accurately describing the many-body correlation of molecules is far from complete. Here, we propose a self-consistent construction of the grand potential functional based on the weighted density approximation (WDA) utilizing hierarchical integral equations. Different from our previous study [T. Yagi and H. Sato, J. Chem. Phys. 154, 124113, (2021)], we apply the WDA to the excess Helmholtz free energy functional rather than the bridge functional. To assess the performance of the present functional, we apply it to the solvation thermodynamics of Lennard-Jones fluids. Compared to the modified Benedict-Webb-Rubin equation of state, the present functional qualitatively predicts the liquid-vapor equilibrium. The solvation free energy obtained from the present functional provides a much better agreement with the Monte Carlo simulation result than the hypernetted chain functionals. It constitutes a general starting point for a systematic improvement in the accuracy of the grand potential functional.

A self-consistent perturbative density functional theory for hard-core fluids: phase diagrams, structural and interfacial properties

The classical Density functional theory (DFT) has become a powerful tool to describe the microscopic structure of fluids as the radial distribution function. One of its particular capabilities is to express the thermodynamic properties of those fluids even under the influence of external potentials, such as fluid-solid interaction. However, good models for the Helmholtz free-energy functionals are necessary to improve the results. In this work, we present a self-consistent thermodynamic perturbation theory for the excess Helmholtz free-energy from the DFT applied to hard-core fluids. The new perturbation theory is solved self-consistently without any closure relation to solving the Ornstein-Zernike equation explicitly. We compare the performance of our self-consistent perturbation theory with the results obtained with the well-known second-order Barker-Henderson perturbation theory for the hard-core Yukawa and square-well fluids. Moreover, we propose two versions of the DFT to describe the perturbative contribution: one based on the weighted density approximation theory and another from a modified mean-field theory. The present results confirm the modified mean-field theory as a better option to calculate the thermodynamic and structural properties of hard-core fluids.

Self-consistent construction of bridge functional based on the weighted density approximation.

A parameter-free bridge functional is presented using a weighted density approximation (WDA). The key point of this scheme is the utilization of Baxter's relation connecting the second-order direct correlation function (DCF) to the higher-order DCF with the density derivative. The free energy density required for the WDA is determined in a self-consistent manner using Baxter's relation and Percus's test particle method. This self-consistent scheme enables us to employ any type of potential model for simple liquids. The new functional is applied to calculate density distribution functions for the inhomogeneous fluids interacting via the hard-sphere, Lennard-Jones, and hard-core Yukawa potentials under an external field from a planar wall and a slit pore.

Flow-Driven Release of Molecules from a Porous Surface Explored Using Dynamical Density Functional Theory

We investigate the release of hard-sphere-like molecules from a porous medium to a continuum fluid using dynamical density functional theory. The hard-sphere interactions are employed on the basis of the weighted density approximation. The model porous medium is assumed as a planar wall and molecules are loaded in the medium at an effective density. An equivalent surface density of molecules is applied to determine the surface flux taking into account both the effective medium density and near-wall density fluctuations in the fluid. In the presence of an external flow field which is parabolic near wall, a diffusion layer similar to the mass transfer boundary layer is developed downstream. We compare the effects of various physical parameters including molecular diffusivity, velocity field, interfacial mass transfer resistance, interfacial normal velocity, and effective medium density. We demonstrate that wall-mediated hard-sphere interactions impact the density distribution of released molecules such that the diffusion layer thickness is increased and the near-wall density fluctuation is observed. Moreover, for transient release with a finite amount of loaded molecules, the maximum concentration of the released molecules at different times is identified as a function of distance from the surface. The information gained in this study would be useful to predict the desorption or release efficiency of molecules from a given porous material subjected to various physically-relevant conditions.

On the study of the vapor-liquid interface of associating fluids with classical density functional theory

Classical density functional theory (DFT) is applied to study the vapor-liquid interface of associating fluids. Our classical DFT implementation uses a Helmholtz free energy functional that reduces to the perturbed-chain statistical associating fluid theory (PC-SAFT) equation of state in the bulk limit. We apply a new association functional, presented in one of our previous works, based on the weighted density approximation to calculate the interfacial tension of associating fluids and compare them with two of the most used association functionals from literature. It is found that classical DFT with the three association functionals and the current molecular parameters of PC-SAFT is not able to predict satisfactorily the interfacial tension of alkanols. Therefore, the experimental interfacial tension of alkanols and some associating fluids is included in the determination of the pure molecular parameters of PC-SAFT. With this approach the determination of interfacial tension of pure associating fluids can be greatly improved with the new parameters, but at the expense of slightly higher deviations in the vapor pressure. The new parameters are tested for the determination of vapor-liquid equilibria (VLE) and the prediction of interfacial tension of binary mixtures containing at least one associating compound. Good agreement is found between experimental data of VLE and interfacial tension of the binary mixtures and the three association functionals. Furthermore, we discuss about the limitations and capabilities of the current classical DFT implementation in the study of the vapor-liquid interface of associating fluids.

Simple Parameter-Free Bridge Functionals for Molecular Density Functional Theory. Application to Hydrophobic Solvation.

Computer simulations have been fundamental in understanding the fine details of hydrophobic solvation and hydrophobic interactions. Alternative approaches based on liquid-state theories have been proposed, but are not yet at the same degree of completeness and accuracy. In this vein, a classical, molecular density functional theory approach to hydrophobic solvation is introduced. The lowest, second-order approximation of the theory, equivalent to the hypernetted chain approximation in integral equations, fails in describing correctly cavitation free-energies. It is corrected here by two simple, angular-independent, so-called bridge functionals; they are parameter-free in the sense that all variables can be fixed unambiguously from the water bulk properties, including pressure, isothermal compressibility, and liquid-gas surface tension. A hard-sphere bridge functional, based on the known functional of a reference hard fluid system, turns out to face strong limitations for water. A simpler weighted density approximation is shown to properly reproduce the solvation free energy of hydrophobes of various sizes, from microscopic ones to the nanoscale, and predicting the solvation free energy of a data set of more than 600 model hydrophobic molecules having a variety of shapes and sizes with an accuracy of a quarter of kBT compared to Monte Carlo simulations values. It constitutes an excellent starting point for a general functional describing accurately both hydrophobic and hydrophilic solvation, and making it possible to study nonidealized hydrophobic interactions.

A new study of associating inhomogeneous fluids with classical density functional theory

ABSTRACT A new density functional for the study of associating inhomogeneous fluids based on Wertheim's first-order thermodynamic perturbation theory is presented and compared to the most currently used associating density functionals. This functional is developed using the weighted density approximation in the range of association of hard spheres. We implement this functional within the framework of classical density functional theory together with modified fundamental measure theory to account for volume exclusion of hard spheres. This approach is tested against molecular simulations from literature of pure associating hard spheres and mixtures of non-associationg and associating hard spheres with different number of bonding sites close to a hard uniform wall. Furthermore, we compare and review our results with the performance of associating functionals from literature, one based on fundamental measure theory and the inhomogeneous version of Wertheim's perturbation theory. Results obtained with classical DFT and the three functionals show excellent agreement with molecular simulations in systems with one hard wall. For the cases of small pores where only one or two layers of fluid are allowed discrepancies between results with classical DFT and molecular simulations were found.

Time-dependent density functional theory for the freezing/melting transition in interfacial systems

We propose a three-dimensional time-dependent density functional theory (TDDFT) to investigate the freezing/melting of Lennard-Jones fluids in interfacial systems including flat interfaces and nano-droplets. The theory is based on a modified fundamental measure theory (MFMT) for the hard-sphere reference system plus mean field theory (MFT) for the attractive contributions plus an additional weighted density approximation (WDA) contribution to enforce that bulk liquid equation of state is that of modified Benedict, Webb and Rubin (MBWR). By using different initial states, our theory generated a series of equilibrium structures including crystals and polyhedral particles. The non-linear effect and the irreversibility of the freezing/melting process were captured. The profiles for free energy and the order parameter indicate that the free energy barrier existing in the freezing/melting process is caused by the break in symmetry. Additionally, the time-dependent properties were also examined, and provided insight into the mechanism of the freezing process.

Nature of the Positron State in CdSe Quantum Dots.

Previous studies have shown that positron-annihilation spectroscopy is a highly sensitive probe of the electronic structure and surface composition of ligand-capped semiconductor quantum dots (QDs) embedded in thin films. The nature of the associated positron state, however, whether the positron is confined inside the QDs or localized at their surfaces, has so far remained unresolved. Our positron-annihilation lifetime spectroscopy studies of CdSe QDs reveal the presence of a strong lifetime component in the narrow range of 358-371ps, indicating abundant trapping and annihilation of positrons at the surfaces of the QDs. Furthermore, our abinitio calculations of the positron wave function and lifetime employing a recent formulation of the weighted density approximation demonstrate the presence of a positron surface state and predict positron lifetimes close to experimental values. Our study thus resolves the long-standing question regarding the nature of the positron state in semiconductor QDs and opens the way to extract quantitative information on surface composition and ligand-surface interactions of colloidal semiconductor QDs through highly sensitive positron-annihilation techniques.

Comparison of Peng-Robinson Equation of State With Capillary Pressure Model With Engineering Density-Functional Theory in Describing the Phase Behavior of Confined Hydrocarbons

Summary The Peng-Robinson equation of state (PR-EOS) (Robinson and Peng 1978) with capillary effect has been used extensively to describe the phase behavior of hydrocarbons under nanoconfinement in shale reservoirs. In nanopores, surface adsorption may be significant, and molecular distribution is heterogeneous. Although the PR-EOS cannot consider these effects, statistical thermodynamic approaches such as density-functional theory (DFT) can explicitly consider the intermolecular and fluid/surface interactions. In this work, we compare the phase behavior of pure hydrocarbons and mixtures in nanopores from the PR-EOS with capillary effect and engineering DFT. We apply the Young-Laplace (YL) equation, assuming zero contact angle to calculate the capillary pressure in the PR-EOS with capillary effect. On the other hand, we extend the PR-EOS to inhomogeneous conditions with weighted-density approximation (WDA) in engineering DFT. For pure components, both approaches predict that the dewpoint temperature increases in hydrocarbon-wet nanopores. Although engineering DFT predicts that the confined dewpoint temperature approaches bulk saturation point when pore size approaches 30 nm, the saturation point obtained from the PR-EOS with capillary effect approaches bulk only when the pore size is as large as 1000 nm. With engineering DFT, the critical points in nanopores deviate from those in bulk, but no change is observed from the PR-EOS with capillary-effect model. The difference on the dewpoint temperature between the PR-EOS with capillary effect and engineering DFT decreases as the system pressure approaches the critical pressure. At low-pressure conditions, the PR-EOS with capillary-effect model becomes unreliable. For binary mixtures, both approaches predict that the lower dewpoint decreases and the upper dewpoint increases. More interestingly, phase transition can still occur when the system temperature is higher than the bulk cricondentherm point. Engineering DFT predicts that the confined lower dewpoint approaches bulk when pore size approaches 20 nm, whereas the dewpoint obtained from the PR-EOS with capillary effect approaches bulk only when the pore size is as large as 100 nm. This work illustrates that assuming homogeneous distributions in nanopores may not be appropriate to predict the phase behavior of hydrocarbons under nanoconfinement.

An improved theoretical procedure for the pore-size analysis of activated carbon by gas adsorption

Abstract Amorphous carbon materials play a vital role in adsorbed natural gas (ANG) storage. One of the key issues in the more prevalent use of ANG is the limited adsorption capacity, which is primarily determined by the porosity and surface characteristics of porous materials. To identify suitable adsorbents, we need a reliable computational tool for pore characterization and, subsequently, quantitative prediction of the adsorption behavior. Within the framework of adsorption integral equation (AIE), the pore-size distribution (PSD) is sensitive to the adopted theoretical models and numerical algorithms through isotherm fitting. In recent years, the classical density functional theory (DFT) has emerged as a common choice to describe adsorption isotherms for AIE kernel construction. However, rarely considered is the accuracy of the mean-field approximation (MFA) commonly used in commercial software. In this work, we calibrate four versions of DFT methods with grand canonical Monte Carlo (GCMC) molecular simulation for the adsorption of CH 4 and CO 2 gas in slit pores at 298 K with the pore width varying from 0.65 to 5.00 nm and pressure from 0.2 to 2.0 MPa. It is found that a weighted-density approximation proposed by Yu (WDA-Yu) is more accurate than MFA and other non-local DFT methods. In combination with the trapezoid discretization of AIE, the WDA-Yu method provides a faithful representation of experimental data, with the accuracy and stability improved by 90.0% and 91.2%, respectively, in comparison with the corresponding results from MFA for fitting CO 2 isotherms. In particular, those distributions in the feature pore width range (FPWR) are proved more representative for the pore-size analysis. The new theoretical procedure for pore characterization has also been tested with the methane adsorption capacity in seven activated carbon samples.

A Diagonally Updated Limited-Memory Quasi-Newton Method for the Weighted Density Approximation

We propose a limited-memory quasi-Newton method using the bad Broyden update and apply it to the nonlinear equations that must be solved to determine the effective Fermi momentum in the weighted density approximation for the exchange energy density functional. This algorithm has advantages for nonlinear systems of equations with diagonally dominant Jacobians, because it is easy to generalize the method to allow for periodic updates of the diagonal of the Jacobian. Systematic tests of the method for atoms show that one can determine the effective Fermi momentum at thousands of points in less than fifteen iterations.

Two-point weighted density approximations for the kinetic energy density functional

We construct a model for the one-electron reduced density matrix that is symmetric and which satisfies the diagonal of the idempotency constraint and then use this model to evaluate the kinetic energy. This strategy for designing density functionals directly addresses the N-representability problem for kinetic energy density functionals. Results for atoms and molecules are encouraging, especially considering the simplicity of the model. However, like all of the other kinetic energy functionals in the literature, quantitative accuracy is not achieved.

Application of the weighted-density approximation to the accurate description of electron-positron correlation effects in materials

We discuss positron-annihilation lifetimes for a set of illustrative bulk materials within the framework of the weighted-density approximation (WDA). The WDA can correctly describe electron-positron correlations in strongly inhomogeneous systems, such as surfaces, where the applicability of (semi-)local approximations is limited. We analyze the WDA in detail and show that the electrons which cannot screen external charges efficiently, such as the core electrons, cannot be treated accurately via the pair correlation of the homogeneous electron gas. We discuss how this problem can be addressed by reducing the screening in the homogeneous electron gas by adding terms depending on the gradient of the electron density. Further improvements are obtained when core electrons are treated within the LDA and the valence electron using the WDA. Finally, we discuss a semiempirical WDA-based approach in which a sum rule is imposed to reproduce the experimental lifetimes.

Spherical electric double layers containing mixed electrolytes: A case study for multivalent counterions

Spherical electric double layers containing mixed electrolytes with multivalent counterions, is studied using density functional theory and Monte Carlo simulation. The macroion and small ions are represented as uniformly charged hard spheres within a continuum solvent. The theory involves an weighted density approximation for the hard-sphere contribution, whereas the electrical part is evaluated through a functional expansion around the uniform fluid. The system includes a number of parameters, viz. ionic concentrations, macroion charge density, and the valence of the counterion. This study points towards the distinctive evidence of size and charge correlations manifested through layering and charge reversal phenomena.

Primitive electrolyte solutions around a charged colloid: density functional approach

ABSTRACTWe have developed the density functional theory, which is based both on the modified fundamental-measure theory for the hard spheres and on the weighted-density approximation for the electrostatic residual contribution, for studying the structure of the size-symmetric and asymmetric electrolyte solutions around a charged hard colloid. The calculation shows that the present theory provides an excellent description of the primitive electrolyte solutions and indicates the suitability of the approximations used in the formalism. The preset theory provides better the structural results than the density functional theories based on the excess free energy functional expansion with respect to the bulk ionic density and the hypernetted-chain equation based on the mean spherical approximation over a wide range of colloid sizes, ion concentrations and valence of a colloid. We have confirmed that the present theory is able to predict the phenomena of charge reversal and overcharging occurring near a colloidal interface, in agreement with previous primitive model Monte Carlo simulations and theoretical studies reported in the literature.