Classical Density Functional Theory Research Articles

Variability of entropy force and its coupling with electrostatic and steric hindrance interactions

We investigated the effective interaction potential (EIP) between charged surfaces in solvent comprised of dipole dimer molecules added with a certain amount of ionic liquid. Using classical density functional theory, the EIP is calculated and decoupled into entropic and energy terms. Unlike the traditional Asakura–Oosawa (AO) depletion model, the present entropic term can be positive or negative, depending on the entropy change associated with solvent molecule migration from bulk into slit pore. This is determined by pore congestion and disruption of the bulk dipole network. The energy term is determined by the free energy associated with hard-core repulsion and electrostatic interactions between surface charges, ion charges, and polarized charges carried by the dipole dimer molecules. The calculations in this article clearly demonstrate the variability of the entropy term, which contrasts sharply with the traditional AO depletion model, and the corrective effects of electrostatic and spatial hindrance interactions on the total EIP; we revealed several non-monotonic behaviors of the EIP and its entropic and energy terms concerning solvent bulk concentration and solvent molecule dipole moment; additionally, we demonstrated the promoting effect of dipolar solvent on the emergence of like-charge attraction, even in 1:1 electrolyte solutions. The microscopic origin of the aforementioned phenomena was analyzed to be due to the non-monotonic change of dipolar solvent adsorption with dipole moment under conditions of low solution dielectric constant. The present findings offer novel approaches and molecular-level guidance for regulating the EIP. This insight has implications for understanding fundamental processes in various fields, including biomolecule-ligand binding, activation energy barriers, ion tunneling transport, as well as the formation of hierarchical structures, such as mesophases, micro-, and nanostructures, and beyond.

Toward Modeling the Structure of Electrolytes at Charged Mineral Interfaces Using Classical Density Functional Theory.

The organization of water molecules and ions between charged mineral surfaces determines the stability of colloidal suspensions and the strength of phase-separated particulate gels. In this article, we assemble a density functional that measures the free energy due to the interaction of water molecules and ions in electric double layers. The model accounts for the finite size of the particles using fundamental measure theory, hydrogen-bonding between water molecules using Wertheim's statistical association theory, long-range dispersion interactions using Barker and Henderson's high-temperature expansion, electrostatic correlations using a functionalized mean-spherical approximation, and Coulomb forces through the Poisson equation. These contributions are shown to produce highly correlated structures, aptly rendering the layering of counterions and co-ions at highly charged surfaces and permitting the solvation of ions and surfaces to be measured by a combination of short-range associations and long-ranged attractions. The model is tested in a planar geometry near soft, charged surfaces to reproduce the structure of water near graphene and mica. For mica surfaces, explicitly representing the density of the outer oxygen layer of the exposed silica tetrahedra allows water molecules to hydrogen-bond to the solid. When electrostatic interactions are included, water molecules assume a hybrid character, being accounted for implicitly in the dielectric constant but explicitly otherwise. The disjoining pressure between approaching like-charged surfaces is calculated, demonstrating the model's ability to probe pressure oscillations that arise during the expulsion of ions and water layers from the interfacial gap and predict strong interattractive stresses that form at narrow interfacial spacing when the surface charge is overscreened. This interattractive stress arises not due to in-plane correlations under strong electrostatic coupling but due to the out-of-plane structuring of associating ions and water molecules.

Classical Density Functional Theory Consistent with the SAFT-VR Mie Equation of State: Development of Functionals and Application to Confined Fluids

Classical Density Functional Theory Consistent with the SAFT-VR Mie Equation of State: Development of Functionals and Application to Confined Fluids

Predicting Solvation Free Energies from the Minnesota Solvation Database Using Classical Density Functional Theory Based on the PC-SAFT Equation of State.

We critically assess the capabilities of classical density functional theory (DFT) based on the perturbed-chain statistical associating fluid theory (PC-SAFT) equation of state to predict the solvation free energies of small molecules in various hydrocarbon solvents. We compare DFT results with experimental data from the Minnesota solvation database and utilize statistical methods to analyze the accuracy of our approach, as well as its weaknesses. The mean absolute error of the solvation free energies is 3.7 kJ mol-1 for n-alkane solvents, ranging from pentane to hexadecane, with 473 solute-solvent systems. For solvents consisting of cyclic hydrocarbons (cyclohexane, benzene, toluene, and ethylbenzene) with 245 solute-solvent systems, we report a slightly larger mean absolute error of 4.2 kJ mol-1. We identify three possible sources of errors: (i) the neglect of solute-solvent and solvent-solvent Coulomb interactions, which limits the applicability of PC-SAFT DFT to nonpolar and weakly polar molecules; (ii) the solute's Lennard-Jones parameters supplied by the general AMBER force field, which are not parametrized toward solvation free energies; and (iii) the application of the Lorentz-Berthelot combining rules to the dispersive interactions between a segment of the PC-SAFT solvent and a Lennard-Jones interaction site of the solute. The approach is more accurate than standard implementations of phenomenological models in common chemistry software packages, which exhibit mean absolute errors larger than 9.12 kJ mol-1, even though newer phenomenological models achieve a mean absolute error of about 2 kJ mol-1. PC-SAFT DFT is more computationally efficient than state of the art explicit molecular simulations in combination with free energy perturbation methods. It is predictive with respect to solvation free energies, i.e., the input for the model is the (element-specific) molecular force field, the solute configuration from molecular dynamics simulations, and the (substance-specific) PC-SAFT parameters. The PC-SAFT parametrization uses pure-component data and does not require experimental solvation free energies. The PC-SAFT equation of state, without applying a DFT formalism, can also be used to calculate solvation free energies, provided that the PC-SAFT parameters for the solute are available. A large number of substances was recently parametrized by members of our group (Esper, T.; Bauer, G.; Rehner, P.; Gross, J. Ind. Eng. Chem. Res. 2023, 62), which enables a comparison to the DFT approach for 103 substances. Accurate results are obtained from the PC-SAFT equation of state with an MAE below 2.51 kJ mol-1. The DFT approach does not require PC-SAFT parameters for the solute and can be applied to all solutes that can be represented by the molecular force field.

In vitro antifungal activity, cytotoxicity and binding analysis of imidazolium based ionic liquids with fluconazole: DFT and spectroscopic study

Fungal infections represent a significant challenge in various living organisms, including humans, animals, and plants. Fungi are versatile organisms capable of thriving in diverse environments, which contributes to their widespread presence and potential to cause infections. Recently, imidazolium-based ionic liquids emerged as good antimicrobial agent in either monomeric or polymeric form. Therefore, herein, we have reporting the in-vitro antifungal activity, cytotoxicity, and binding analysis of 1-decyl-3-methylimidazolium chloride, [C10Mim][Cl] and 1-hexyl-3-methylimidazolium chloride, [C6Mim][Cl] ionic liquids with fluconazole (Flz). The antifungal activity of ILs and ILs with Flz against candidiasis species (C. albicans) in terms of minimum inhibitory concentration (MIC) was assessed. The antifungal activity results showed that [C10Mim][Cl]-Flz exhibit good antifungal activity then [C10Mim][Cl] and Flz alone. The cytotoxicity of ILs with Flz was checked against human embryonic kidney (HEK293) cell line regarding cell viability and result showed minute cytotoxicity of the combinations at higher concentrations. Further, the binding of ILs with Flz was also studied using various techniques such as UV–visible, fluorescence, Fourier-transform infrared (FTIR) spectroscopy, isothermal titration calorimetry (ITC), and conductivity method. It was found that [C10Mim][Cl] shows more binding affinity then [C6Mim][Cl] with Flz. In-silico molecular docking analysis of Flz-[C10Mim][Cl] complex show a higher binding affinity with CYP51 which in turn enhanced its ability to inhibit the ergosterol biosynthesis as compared to alone [C10Mim][Cl] and Flz. The classical density functional theory (DFT) model was also utilized which further supports the spectroscopic results.

Viscosities of inhomogeneous systems from generalized entropy scaling

This study extends entropy scaling to inhomogeneous fluids by using the classical density functional theory together with a new viscosity reference that takes into account the influence of solid–fluid interactions on the fluid viscosity. The density functional theory uses a Helmholtz energy functional based on the perturbed-chain statistical associating fluid theory; the local residual entropy per particle is determined from the temperature derivative of the Helmholtz energy functional in combination with an appropriate weighted density profile. The weighted density calculation requires a single transferable parameter, which is adjusted to a reference molecular dynamics simulation. In particular, local viscosity values for fluids under nanoconfinement near solid–fluid interfaces are predicted using the same entropy scaling parameters as for homogeneous fluids. We validate the model by comparing viscosity and velocity profiles with results from non-equilibrium molecular dynamics simulations of a Couette flow in a slit pore. Good agreement is found between the entropy scaling model and the non-equilibrium molecular dynamics results for both the viscosity and velocity profiles of the Lennard–Jones truncated and shifted fluid. The proposed model extrapolates well to systems with different temperatures, fluid densities, and shear forces as well as to systems with different wetting behaviors. These results demonstrate that entropy scaling can be generalized to inhomogeneous fluids using an appropriate combination of residual entropy profile and viscosity reference.

Revisiting the wetting behavior of solid surfaces by water-like models within a density functional theory

We perform the analysis of predictions of a classical density functional theory for associating fluids with different association strength concerned with wetting of solid surfaces. The four associating sites water-like models with non-associative square-well attraction parametrized by Clark et al. [Mol. Phys., 2006, 104, 3561] are considered. The fluid-solid potential is assumed to have a 10-4-3 functional form. The growth of water film on the substrate upon changing the chemical potential is described. The wetting and prewetting critical temperatures, as well as the prewetting phase diagram are evaluated for different fluid-solid attraction strength from the analysis of the adsorption isotherms. Moreover, the temperature dependence of the contact angle is obtained from the Young equation. It yields estimates for the wetting temperature as well. Theoretical findings are compared with experimental results and in a few cases with data from computer simulations. The theory is successful and quite accurate in describing the wetting temperature and contact angle changes with temperature for different values of fluid-substrate attraction. Moreover, the method provides an easy tool to study other associating fluids on solids of importance for chemical engineering, in comparison with laboratory experiments and computer simulations.

Modeling the Electric Double Layer at the Liposome Vesicle via Classical Density Functional Theory: Solution of Poisson's Equations for Curved Membranes.

The electric double layer at the liposome vesicle membrane has been investigated by a modified fundamental-measure theory in the framework of the restricted primitive model. An analytical equation has been obtained for the mean electrostatic potential (MEP) by solving Poisson's equation for curved membranes. This study investigates the influence of vesicle size, membrane thickness, surface charges, and electrolyte concentration on the structure, composition, and width of electric double layers (EDLs) on the inner and outer membrane walls. Our findings indicate that a thin and denser layer of ions is formed at the concave wall of the membrane (inner wall) compared to that at the outer membrane. As expected, the width of the diffuse layer decreases with the concentration and surface charge. Also, when the surface charges on both concave and convex walls are the same, the absolute value of MEPs on the inner membrane, concave wall, is greater than that on the convex wall. We have also investigated the diffuse potential, which decreases with concentration, membrane thickness, and cavity size, whereas it increases with surface charges. As we expect, the contact density of counterions at the inner concave wall of the vesicle cavity is always greater than the corresponding value at the convex wall, whereas this trend reverses for co-ions. Also, the contact density of counterions (co-ions) at the inner wall decreases (increases) with cavity size, whereas it increases at the outer wall (decreases). Finally, depletion of co-ions occurs at the membrane walls with enhancement in surface charges.

Kelvin equationfor bridging transitions.

We study bridging transitions between a pair of nonplanar surfaces. We show that the transition can be described using a generalized Kelvin equationby mapping the system to a slit of finite length. The proposed equationis applied to analyze the asymptotic behavior of the growth of the bridging film, which occurs when the confining walls are gradually flattened. This phenomenon is characterized by a power-law divergence with geometry-dependent critical exponents that we determine for a wide class of walls' geometries. In particular, for a linear-wedge model, a covariance law revealing a relation between a geometric and Young's contact angle is presented. These predictions are shown to be fully in line with the numerical results obtained from a microscopic (classical) density functional theory.

Confinement Effects in Droplet Formation on a Solid Particle.

Formation of a droplet around a spherical solid particle in supersaturated vapor is considered. The number and stability of equilibrium solutions in a closed small system are studied in the canonical ensemble in comparison to an open system in the grand canonical ensemble. Depending on the system's parameters, two modes exist in the canonical ensemble: the first one with only one solution and the second one with three solutions; the presence of the third solution is due to confinement. The analysis is conducted first on a macroscopic thermodynamic level of description, and then the results are supported by studies within two versions of classical density functional theory: the square-gradient approximation with the Carnahan-Starling equation of state for hard spheres on a completely wettable particle and the random-phase approximation with the fundamental measure theory on a poorly wettable particle. In the latter case, a solution breaking the spherical symmetry is observed at a small total number of molecules.

Computer-aided molecular refrigerant design for adsorption chillers based on classical density functional theory and PC-SAFT

Adsorption chillers are a promising technology for sustainable cooling. The performance of adsorption chillers is highly influenced by the selection of the refrigerant. Still, systematic selection of refrigerants is challenging because evaluating adsorption properties requires significant experimental or simulation efforts. Thus, refrigerant design options are often limited.Here, we propose a systematic refrigerant design method for adsorption chillers assessing refrigerants based on their process performance. Our method quantifies adsorption isotherms by 1-dimensional classical density functional theory (DFT) based on the PC-SAFT equation of state. The method is used to screen over 1800 refrigerants based on their coefficient of performance (COP). We identify refrigerants with higher COPs than commonly used refrigerants and highlight the advantage of a process-based objective function over material-based heuristic selection criteria. Finally, we advance from screening to computer-aided molecular design of the refrigerant, leveraging the efficiency of the DFT model to explore the molecular design space systematically.

Temperature Evolution of Sorbonorit-4 Methane-Induced Deformation through the Eyes of Classical Density Functional Theory.

Activated carbons are widely used industrial adsorbents due to their attractive sorption properties. Although extensive research on activated carbon has been carried out for several centuries, some aspects of the adsorption-induced deformation of activated carbon remain unclear. The puzzling temperature dependence of the methane-induced deformation of activated carbon is investigated in the present work. Several experimental studies have shown that an increase in temperature leads to a reversal of the sign of adsorption strain at low pressures, i.e., the contraction turns into an expansion. Here we suggest a possible explanation for this effect by applying classical density functional theory to the adsorption isotherms of nitrogen, carbon dioxide, and methane as well as to methane-induced deformation isotherms. Our calculations show that the adsorption stress generated in the smallest pores predominates at higher temperatures and leads to material swelling. Lowering the temperature, on the other hand, leads to a predominance of larger pores and compression of the activated carbon material. We also investigated the possibility of determining the pore size distribution from methane-induced deformation and adsorption data and the predictive capabilities of our theoretical approach.

Development and application of hybrid AIMD/cDFT simulations for atomic-to-mesoscale chemistry.

Many important chemical processes involve reactivity and dynamics in complex solutions. Gaining a fundamental understanding of these reaction mechanisms is a challenging goal that requires advanced computational and experimental approaches. However, important techniques such as molecular simulation have limitations in terms of scales of time, length, and system complexity. Furthermore, among the currently available solvation models, there are very few designed to describe the interaction between the molecular scale and the mesoscale. To help address this challenge, here, we establish a novel hybrid approach that couples first-principles plane-wave density functional theory with classical density functional theory (cDFT). In this approach, a region of interest described by abinitio molecular dynamics (AIMD) interacts with the surrounding medium described using cDFT to arrive at a self-consistent ground state. cDFT is a robust but efficient mesoscopic approach to accurate thermodynamics of bulk electrolyte solutions over a wide concentration range (up to 2M concentrations). Benchmarking against commonly used continuum models of solvation, such as SMD, as well as experiments, demonstrates that our hybrid AIMD-cDFT method is able to produce reasonable solvation energies for a variety of molecules and ions. With this model, we also examined the solvent effects on a prototype SN2 reaction of the nucleophilic attack of a chloride ion on methyl chloride in the solution. The resulting reaction pathway profile and the solution phase barrier agree well with experiment, showing that our AIMD/cDFT hybrid approach can provide insight into the specific role of the solvent on the reaction coordinate.

Binding potential and wetting behavior of binary liquid mixtures on surfaces.

We present a theory for the interfacial wetting phase behavior of binary liquid mixtures on rigid solid substrates, applicable to both miscible and immiscible mixtures. In particular, we calculate the binding potential as a function of the adsorptions, i.e., the excess amounts of each of the two liquids at the substrate. The binding potential fully describes the corresponding interfacial thermodynamics. Our approach is based on classical density functional theory. Binary liquid mixtures can exhibit complex bulk phase behavior, including both liquid-liquid and vapor-liquid phase separation, depending on the nature of the interactions among all the particles of the two different liquids, the temperature, and the chemical potentials. Here we show that the interplay between the bulk phase behavior of the mixture and the properties of the interactions with the substrate gives rise to a wide variety of interfacial phase behaviors, including mixing and demixing situations. We find situations where the final state is a coexistence of up to three different phases. We determine how the liquid density profiles close to the substrate change as the interaction parameters are varied and how these determine the form of the binding potential, which in certain cases can be a multivalued function of the adsorptions. We also present profiles for sessile droplets of both miscible and immiscible binary liquids.

Unveiling the Role of Electrostatic Forces on Attraction between Opposing Polyelectrolyte Brushes.

Electrostatic interaction and molecular excluded-volume effects are responsible for a plethora of nonintuitive phenomena in soft-matter systems, including local charge inversion and attraction between similar charges. In the current work, we study the surface forces and swelling behavior of opposing polyelectrolyte brushes using a classical density functional theory that accounts for electrostatic and excluded-volume correlations. We observe that the detachment pressure between similarly charged brushes is sensitive to salt concentration in both the osmotic and salted regimes and can be negative in the presence of multivalent counterions. A comparison of the theoretical results with the mean-field predictions unravels the role of correlation effects in determining the surface forces and brush structure. For systems containing multivalent counterions, the detachment pressure attains negative values at an intermediate brush-brush separation, and the attractive region in the pressure vs distance plot is magnified in terms of both the depth and width of attraction with increasing counterion valency. However, the interbrush attraction vanishes when the size-induced correlations are switched off. We also investigated the role of counterion size and polymer chain length on the detachment pressure. It is found that smaller counterions are more effective in neutralizing the polymer charge than bigger counterions, leading to a reduced interbrush repulsion and, in some cases, attraction between like-charged brushes at intermediate distances. Meanwhile, varying the chain length of the grafted polymers only shifts the location of the attraction basin, with little influence on the interaction strength. The theoretical predictions show qualitative agreement with experimental observations and offer valuable insights into the interaction between similarly charged polymer brushes in the presence of multivalent ions.

Machine Learning of a Density Functional for Anisotropic Patchy Particles.

Anisotropic patchy particles have become an archetypical statistical model system for associating fluids. Here, we formulate an approach to the Kern-Frenkel model via the classical density functional theory to describe the positionally and orientationally resolved equilibrium density distributions in flat wall geometries. The density functional is split into a reference part for the orientationally averaged density and an orientational part in mean-field approximation. To bring the orientational part into a kernel form suitable for machine learning (ML) techniques, an expansion into orientational invariants and the proper incorporation of single-particle symmetries are formulated. The mean-field kernel is constructed via ML on the basis of hard wall simulation data. The results are compared to the well-known random-phase approximation, which strongly underestimates the orientational correlations close to the wall. Successes and shortcomings of the mean-field treatment of the orientational part are highlighted and perspectives are given for attaining a full-density functional via ML.

Investigating the properties of the water−vapor and water−graphite interfaces by PC-SAFT based density functional theory: A comparative study of different association functionals and PC-SAFT water parameter sets

In this work, we apply the perturbed-chain statistical associating fluid theory (PC-SAFT) based classical density functional theory to investigate the thermodynamics and structures of the water−vapor and water−graphite interfaces. For the water−vapor interface, we examine the surface tension as well as structural characteristics such as density profiles and hydrogen bonding distributions along the interface. For the water−graphite interface, we investigate these same structural features at a contact angle of 90° at 300 K. Specifically, we focus on comparing the results obtained from the three association functionals and six PC-SAFT water parameter sets from literature with experimental data and molecular simulation results. We find that the three association functionals exhibit qualitatively similar behavior in the calculation of surface tension, and it is more influenced by the parameter set rather than the association functional. The optimal functional or parameter set for the calculation of density profile of the vapor − liquid interface remains inconclusive, whereas preferable parameter sets and functionals have been identified for the water−graphite interface. Furthermore, the three functionals demonstrate a remarkably similar and qualitatively accurate depiction of the hydrogen bonding structures at both interfaces when compared with molecular simulation results. The level of quantitative accuracy, however, relies on whether the parameter set accurately reproduces the average number of hydrogen bonds of bulk water as observed in this particular set of molecular simulation results. The results of the present work offer valuable guidance for further investigation into the adsorption and wetting behavior of water on graphite-like surface, as well as the properties of water confined at the nanoscale.

Prediction of Drug-like Compounds Solubility in Supercritical Carbon Dioxide: A Comparative Study between Classical Density Functional Theory and Machine Learning Approaches

Prediction of Drug-like Compounds Solubility in Supercritical Carbon Dioxide: A Comparative Study between Classical Density Functional Theory and Machine Learning Approaches

On the Na+ transport and electrochemical stability window in NaTFSI:NMA deep eutectic solvent

Deep eutectic solvents (DES), such as the ▪:▪ (sodium bistrifluoromethane sulfonyl imide - N-methyl acetamide) system, have been considered as promising electrolytes for sodium-ion (▪) batteries. However, our current atomistic understanding of those systems is still in a state of evolution and remains incomplete. In this context, we combined classical force field molecular dynamics (MD) simulations and periodic density functional theory (DFT) calculations to enhance our atomistic understanding on the ▪ transport mechanisms, DES structure organization, hydrogen-bond network formation, and electrochemical stability windows (ESWs). Firstly, we obtained a substantial improvement in the description of the DES transport and structural properties using self-consistent MD/DFT calculations to assign effective charges on all atoms, while the remaining OPLS parameters were kept constant. From our analyses, an increasing in the ▪ mole fraction leads to different chemical environments, reflecting an electrolyte with larger aggregates, low conductivity, and high viscosity. The liquid structure seems to remain unchanged as a function of temperature. However, higher temperatures reduce the lifetime of ionic pairs and increase the mobility of ▪ ions. The disruption of the hydrogen-bonds formed between the ▪ species increases with the ▪ concentration. In addition, our periodic DFT calculations reveals the substitution of atomic sites from ▪ to ▪ during the reduction process. Furthermore, the ESW results provided evidence supporting the safeguarding of the solvent from degradation at higher salt concentrations.

Enhancing the Performance and Stability of Li-Ion Batteries with Fluorinated Electrolytes: Insights from MD Simulation and Experimental Analysis

The significance of using fluorinated electrolytes, particularly fluorinated ethylene carbonate (FEC) and difluoro ethylene carbonate (DFEC), in the electrolyte system of 1.2 M LiPF6 in dimethyl carbonate (DMC)/fluorinated solvent (FEC/DFEC), was explored using classical molecular dynamic (MD) simulation and density functional theory (DFT) calculation in this work. Various parameters, such as radial distribution function (RDF), integral over RDF, transference number, coordination number, and solvation energy, were analyzed. The study demonstrated that DFEC enhances the reduction in binding energy of the solvation sheath compared to FEC. Additionally, the electrochemical performance of a practical full-cell 18650 of LiNi0.88Co0.10Al0.02O4 (NCA) cathode and graphite anode batteries was examined, confirming that 1.2 M LiPF6 in DMC/FEC/DFEC (4:0.5:0.5 %v) demonstrated the highest capacity retention after 1,000 cycles, surpassing 1.2M LiPF6 in DMC/fluorinated (4:1 %v, FEC and DFEC, respectively) and the previous electrolyte 1.2 M LiPF6 in EC/EMC/DEC/FEC (1:1:1:1.3 %V). Spectroscopy techniques, including DEMS, NMR, and GC-MS, were utilized to investigate the electrolyte decomposition, revealing CO2 and H2 as the main gas products during decomposition. NMR results identified some species, such as HF, H2O, acetal, formaldehyde, and unknown products, while GC-MS confirmed that all the solvents in the electrolyte take part in the decomposition process. This study highlights the potential of fluorinated electrolytes in battery systems and provides insight into their decomposition mechanism, contributing to the development of more efficient and stable battery systems.