Density-functional theory for the structures and thermodynamic properties of highly asymmetric electrolyte and neutral component mixtures

Correlating Ionic Conductivity to Structure and Dynamics of Li-Ion Battery Electrolyte Systems: Raman Spectroscopy, Dielectric Relaxation Measurements, and Streak Camera Solvation Data Analysis

A correlation between ionic conductivity and electrolyte solution structure and dynamics was explored by performing electrolyte concentration- and temperature-dependent measurements of conductivity, viscosity, and dielectric relaxation (DR) in solutions of lithium bis(trifluoromethane)sulfonimide (LiTFSI) in triethylene glycol dimethyl ether (also known as triglyme, G3). In addition, an electrolyte concentration-dependent Raman spectroscopic study and ultrafast dynamic fluorescence Stokes shift measurements of solvation of a dissolved solute by employing a streak camera detection technique were carried out. Measured conductivities (σ) and the average DR times (⟨τDR⟩) were found to be partially decoupled from the solution viscosities (η) and obeyed the relation, σ or ⟨τDR⟩-1 ∝(η/T)-p, with p = 0.6-0.75 for σ and p = 0.2-0.45 for ⟨τDR⟩-1. Raman data indicated the formation of ion pairs and ionic aggregates in these solutions, while the measured glass transition temperature increased with LiTFSI concentration. Conductivities (σ) showed a nonlinear concentration dependence but increased linearly with the solution static dielectric constants (εs). The latter may be explained by considering the temperature effects on complex electrolyte species and the subsequent solution dielectric behavior. Interestingly, an inverse power-law dependence of σ on the measured DR or solvation time scales, σ ∝ (τx)-m, with m = 1.2-1.9, was observed. This dependence may be explained by considering that the same environmental friction regulates both the ion diffusion and the medium polarization relaxation. The control of a slow process (ion translation) by relatively faster medium dynamics (dipolar rotation), although quite fascinating for the present system, warrants further experimental scrutiny for other electrolyte systems relevant to battery applications.

Understanding the K+/Na+-Selectivity-Enabled Osmotic Power Generation: High Selectivity May Not Be Indispensable

By mixing ionic solutions, considerable energy can be harvested from entropy change. Recently, we proposed a concept of potassium-permselectivity enabled osmotic power generation (PoPee-OPG) by mixing equimolar KCl and NaCl solutions via artificial potassium ion channels (APICs, Natl. Sci. Rev. 2023, 10, nwad260). However, a fundamental understanding of the relationship between the K+/Na+ selectivity and optimal performance remains unexplored. Herein, we establish a primitive molecular thermodynamic model to investigate the energy extraction process. We find PoPee-OPG differs from previous charge-selectivity-based techniques, such as the salinity gradient power generation, in two distinct ways. First, the extractable energy density and efficiency positively depend on concentration. More surprisingly, a very high potassium selectivity is not indispensable for satisfactory efficiency and energy density. An optimal K+/Na+ selectivity region of 3 to 10 is found. This somewhat counterintuitive discovery provides a renewed understanding of the emerging PoPee-OPG, and it predicts a broad applicability among existing APICs.

Boosting Salinity Energy Extraction Efficiency in Capacitive Mixing by Polyelectrolyte Surface Coating

The extraction of salinity gradient energy in the capacitive mixing (CapMix) technique can be enhanced by using polyelectrolyte-coated electrodes. The micromechanism of polyelectrolyte (PE) coating enhancing the salinity energy extraction is studied by using a statistical thermodynamic theory. When PE takes same charge sign as the coated electrodes, the extraction efficiency can be boosted owing to the enhanced response of electrical double layer (EDL) to external cell voltage (V0). For the optimal case studied, the extraction efficiency was boosted from 0.25 to 1.25% by PE coatings. Owing to counterion adsorption and the enhanced response of EDL, the extraction energy density presented a local maximum at V0 = 0, which is higher than another local maximum value when V0 ≠ 0. This provides important guidance on the two approaches of CapMix in terms of capacitive Donnan potential (CDP, V0 = 0) and capacitive double-layer expansion (CDLE, V0 ≠ 0). Under the effects of PE coating, the extraction efficiency by CDLE can be improved to about 11% by CDP for the optimal studied case. The synergistic effect of grafting conditions can significantly elevate the energy density and extraction efficiency of the CDP process.

Designing artificial ion channels with strict K+/Na+ selectivity toward next-generation electric-eel-mimetic ionic power generation

A biological potassium channel is >1000 times more permeable to K+ than to Na+ and exhibits a giant permeation rate of ∼108 ions/s. It is a great challenge to construct artificial potassium channels with such high selectivity and ion conduction rate. Herein, we unveil a long-overlooked structural feature that underpins the ultra-high K+/Na+ selectivity. By carrying out massive molecular dynamics simulation for ion transport through carbonyl-oxygen-modified bi-layer graphene nanopores, we find that the twisted carbonyl rings enable strict potassium selectivity with a dynamic K+/Na+ selectivity ratio of 1295 and a K+ conduction rate of 3.5 × 107 ions/s, approaching those of the biological counterparts. Intriguingly, atomic trajectories of K+ permeation events suggest a dual-ion transport mode, i.e. two like-charged potassium ions are successively captured by the nanopores in the graphene bi-layer and are interconnected by sharing one or two interlayer water molecules. The dual-ion behavior allows rapid release of the exiting potassium ion via a soft knock-on mechanism, which has previously been found only in biological ion channels. As a proof-of-concept utilization of this discovery, we propose a novel way for ionic power generation by mixing KCl and NaCl solutions through the bi-layer graphene nanopores, termed potassium-permselectivity enabled osmotic power generation (PoPee-OPG). Theoretically, the biomimetic device achieves a very high power density of >1000 W/m2 with graphene sheets of <1% porosity. This study provides a blueprint for artificial potassium channels and thus paves the way toward next-generation electric-eel-mimetic ionic power generation.

Spiers Memorial Lecture: Towards understanding of iontronic systems: electroosmotic flow of monovalent and divalent electrolyte through charged cylindrical nanopores

In many practical applications, ions are the primary charge carrier and must move through either semipermeable membranes or through pores, which mimic ion channels in biological systems. In analogy to electronic devices, the "iontronic" ones use electric fields to induce the charge motion. However, unlike the electrons that move through a conductor, motion of ions is usually associated with simultaneous solvent flow. A study of electroosmotic flow through narrow pores is an outstanding challenge that lies at the interface of non-equilibrium statistical mechanics and fluid dynamics. In this paper, we will review recent works that use dissipative particle dynamics simulations to tackle this difficult problem. We will also present a classical density functional theory (DFT) based on the hypernetted-chain approximation (HNC), which allows us to calculate the velocity of electroosmotic flows inside nanopores containing 1 : 1 or 2 : 1 electrolyte solution. The theoretical results will be compared with simulations. In simulations, the electrostatic interactions are treated using the recently introduced pseudo-1D Ewald summation method. The zeta potentials calculated from the location of the shear plane of a pure solvent are found to agree reasonably well with the Smoluchowski equation. However, the quantitative structure of the fluid velocity profiles deviates significantly from the predictions of the Smoluchowski equation in the case of charged pores with 2 : 1 electrolyte. For low to moderate surface charge densities, the DFT allows us to accurately calculate the electrostatic potential profiles and the zeta potentials inside the nanopores. For pores with 1 : 1 electrolyte, the agreement between theory and simulation is particularly good for large ions, for which steric effects dominate over the ionic electrostatic correlations. The electroosmotic flow is found to depend very strongly on the ionic radii. In the case of pores containing 2 : 1 electrolyte, we observe a reentrant transition in which the electroosmotic flow first reverses and then returns to normal as the surface change density of the pore is increased.

Revisiting the Charged Shell Model: A Density Functional Theory for Electrolytes

Classical density functional theory (DFT) has proven to be a sophisticated and efficient approach for investigating charge systems. In DFT, the excess free energy functional for inhomogeneous charged hard-sphere fluids consists of hard-core interactions and charge-charge electrostatic interactions. The former component can be precisely described by well-established fundamental measure theory (FMT). The latter component is usually computed using the Poisson equation combined with the mean spherical approximation (MSA). In order to predict accurate density profiles of ions and satisfy some thermodynamics sum rules, Roth and Gillespie [J. Phys.: Condens. Matter 2016, 28, 244006] proposed a DFT combining a functional-based version of MSA and an approximated charged shell model. Here, we rebuild the DFT based on the exact charged shell model, and the analytic expressions for the shell interaction potential and the corresponding thermodynamic quantities are provided. The structural and thermodynamic properties of both bulk and inhomogeneous electrolyte systems are analyzed. Moreover, the software named Atif (an advanced theoretical tool for inhomogeneous fluids) is released to the public via this work.

Surface Charge Density in Electrical Double Layer Capacitors with Nanoscale Cathode-Anode Separation

Using a dynamic density functional theory, we study the charging dynamics, the final equilibrium structure, and the energy storage in an electrical double layer capacitor with nanoscale cathode-anode separation in a slit geometry. We derive a simple expression for the surface charge density that naturally separates the effects of the charge polarization due to the ions from those due to the polarization of the dielectric medium and allows a more intuitive understanding of how the ion distribution within the cell affects the surface charge density. We find that charge neutrality in the half-cell does not hold during the dynamic charging process for any cathode-anode separation, and also does not hold at the final equilibrium state for small separations. Therefore, the charge accumulation in the half-cell in general does not equal the surface charge density. The relationships between the surface charge density and the charge accumulation within the half-cell are systematically investigated by tuning the electrolyte concentration, cathode-anode separation, and applied voltage. For high electrolyte concentrations, we observe charge inversion at which the charge accumulation exceeds the surface charge at special values of the separation. In addition, we find that the energy density has a maximum at intermediate electrolyte concentrations for a high applied voltage.

Ionic Layering and Overcharging in Electrical Double Layers in a Poisson-Boltzmann Model

Electrical double layers (EDLs) play a significant role in a broad range of physical phenomena related to colloidal stability, diffuse-charge dynamics, electrokinetics, and energy storage applications. Recently, it has been suggested that for large ion sizes or multivalent electrolytes, ions can arrange in a layered structure inside the EDLs. However, the widely used Poisson-Boltzmann models for EDLs are unable to capture the details of ion concentration oscillations and the effect of electrolyte valence on such oscillations. Here, by treating a pair of ions as hard spheres below the distance of closest approach and as point charges otherwise, we are able to predict ionic layering without any additional parameters or boundary conditions while still being compatible with the Poisson-Boltzmann framework. Depending on the combination of ion valence, size, and concentration, our model reveals a structured EDL with spatially oscillating ion concentrations. We report the dependence of critical ion concentration, i.e., the ion concentration above which the oscillations are observed, on the counter-ion valence and the ion size. More importantly, our model displays quantitative agreement with the results of computationally intensive models of the EDL. Finally, we analyze the nonequilibrium problem of EDL charging and demonstrate that ionic layering increases the total charge storage capacity and the charging timescale.

Modeling Surface Charge Regulation of Colloidal Particles in Aqueous Solutions

Colloidal particles are mostly charged in an aqueous solution because of the protonation or deprotonation of ionizable groups on the surface. The surface charge density reflects a complex interplay of ion distributions within the electric double layer and the surface reaction equilibrium. In this work, we present a coarse-grained model to describe the charge regulation of various colloidal systems by an explicit consideration of the inhomogeneous ion distributions and surface reactions. With the primitive model for aqueous solutions and equilibrium constants for surface reactions as the inputs, the theoretical model is able to make quantitative predictions of the surface-charge densities and zeta potentials for diverse colloidal particles over a wide range of pH and ionic conditions. By accounting for the ionic size effects and electrostatic correlations, our model is applicable to systems with multivalent ions that exhibit charge inversion and provides a faithful description of the interfacial properties without evoking the empirical Stern capacitance or specific ion adsorptions.

Effects of Kinetic Dielectric Decrement on Ion Diffusion and Capacitance in Electrochemical Systems

Diffusion of ionic components in electrolytes not only eliminates the gradients of ionic concentrations but also alters the local dielectric environment, and the coupling effect between kinetic dielectric decrement and ionic concentration gradient on the diffusion dynamics is not well understood. Herein, taking the charging process in electrical double layer systems as a case study, we conduct a multiscale investigation of ion diffusions in aqueous electrolytes by combining the dynamic density functional theory and an ion-concentration-dependent dielectric constant model. By properly considering the time evolutions of local dielectric constant coupled with ion density, we report an interesting phenomenon on the suppression of surface charge density that is not captured by conventional models. In addition, we show that the usage of aqueous electrolyte with small dielectric decrement coefficients promotes the capacitance, in quantitative agreement with experimental measurements.

A hybrid theoretical method for predicting electrokinetic energy conversion in nanochannels

The traditional methods to predict electrokinetic energy conversion (EKEC) in nanochannels are mostly based on the Navier-Stokes (NS) equation for ionic flow and the Poisson-Boltzmann (PB) equation for charge distributions, which is questionable for ion transport through highly charged nanochannels. In this work, the classical density functional theory (cDFT) is used together with molecular dynamics (MD) simulation and the Navier-Stokes (NS) equation to predict the electrical current and the thermodynamic efficiency of electrokinetic energy conversion in nanochannels. By introducing numerical results for the slip length calculated from MD simulation, a significant increase of the electrokinetic current is predicted in comparison to that obtained from the traditional electrokinetic equations with the non-slip boundary condition, leading to the theoretical predictions of the thermodynamic efficiency for electrokinetic energy conversion in nanochannels in good agreement with recent experiments. The hybrid method predicts that maximum electrokinetic efficiency can be achieved by tuning the channel height and solution conditions including electrolyte concentrations, ion valences, and surface energies. The theoretical results provide new insights into pressure-driven electrical energy generation processes and helpful guidelines for engineering design and optimization of electrokinetic energy conversion.

Electrical Double Layers: Effects of Asymmetry in Electrolyte Valence on Steric Effects, Dielectric Decrement, and Ion-Ion Correlations

We study the effects of asymmetry in electrolyte valence (i.e., non z: z electrolytes) on mean field theory of the electrical double layer. Specifically, we study the effect of valence asymmetry on finite ion-size effects, the dielectric decrement, and ion-ion correlations. For a model configuration of an electrolyte near a charged surface in equilibrium, we present comprehensive analytical and numerical results for the potential distribution, electrode charge density, capacitance, and dimensionless salt uptake. We emphasize that the asymmetry in electrolyte valence significantly influences the diffuse-charge relations, and prior results reported in the literature are readily extended to non z: z electrolytes. We develop scaling relations and invoke physical arguments to examine the importance of asymmetry in electrolyte valence on the aforementioned effects. We conclude by providing implications of our findings on diffuse-charge dynamics and other electrokinetic phenomena.

Density functional theory for charged fluids

An improved density functional theory (DFT) for an inhomogeneous charged system (including electrolyte and/or polyelectrolyte) is proposed based on fundamental measure theory, thermodynamic perturbation theory and mean-spherical approximation. Our DFT combines the existing treatment of hard-sphere contributions using fundamental measure theory (FMT) with a new treatment of the electrostatic correlations for the non-bonded ions and chain connectivity that are approximated by employing a first-order Taylor expansion, with the reference fluid density determined using the technique from Gillespie et al. [D. Gillespie et al., J. Phys.: Condens. Matter, 2002, 14, 12129]. We show that the first-order Taylor expansion for the non-bonded electrostatic correlations yields numerically comparable results to the more involved second-order expansion. Furthermore, we find that the existing treatment of the chain connectivity correlation predicts a spurious layer-by-layer phase at moderately large Bjerrum lengths, which is avoided in our new treatment. These simplifications and improvements should significantly facilitate the implementation and reduce the computational cost.

Structure of electric double layers in capacitive systems and to what extent (classical) density functional theory describes it

Ongoing scientific interest is aimed at the properties and structure of electric double layers (EDLs), which are crucial for capacitive energy storage, water treatment, and energy harvesting technologies like supercapacitors, desalination devices, blue engines, and thermocapacitive heat-to-current converters. A promising tool to describe their physics on a microscopic level is (classical) density functional theory (DFT), which can be applied in order to analyze pair correlations and charge ordering in the primitive model of charged hard spheres. This simple model captures the main properties of ionic liquids and solutions and it predicts many of the phenomena that occur in EDLs. The latter often lead to anomalous response in the differential capacitance of EDLs. This work constructively reviews the powerful theoretical framework of DFT and its recent developments regarding the description of EDLs. It explains to what extent current approaches in DFT describe structural ordering and in-plane transitions in EDLs, which occur when the corresponding electrodes are charged. Further, the review briefly summarizes the history of modeling EDLs, presents applications, and points out limitations and strengths in present theoretical approaches. It concludes that DFT as a sophisticated microscopic theory for ionic systems is expecting a challenging but promising future in both fundamental research and applications in supercapacitive technologies.

Electrical double layer properties of spherical oxide nanoparticles

The accurate characterization of the electrical double layer properties of nanoparticles is of fundamental importance for optimizing their physicochemical properties for specific biotechnological and biomedical applications. In this article, we use classical solvation density functional theory and a surface complexation model to investigate the effects of the pH and the nanoparticle size on the structural and electrostatic properties of an electrolyte solution surrounding a spherical silica oxide nanoparticle. The formulation has been particularly useful for identifying dominant interactions governing the ionic driving force at a variety of pH levels and nanoparticle sizes. As a result of the energetic interplay displayed between electrostatic potential, ion-ion correlation and particle crowding effects on the nanoparticle surface titration, rich, non-trivial ion density profiles and mean electrostatic potential behavior have been found.

On the hydrophilicity of electrodes for capacitive energy extraction

The so-called Capmix technique for energy extraction is based on the cyclic expansion of electrical double layers to harvest dissipative energy arising from the salinity difference between freshwater and seawater. Its optimal performance requires a careful selection of the electrical potentials for the charging and discharging processes, which must be matched with the pore characteristics of the electrode materials. While a number of recent studies have examined the effects of the electrode pore size and geometry on the capacitive energy extraction processes, there is little knowledge on how the surface properties of the electrodes affect the thermodynamic efficiency. In this work, we investigate the Capmix processes using the classical density functional theory for a realistic model of electrolyte solutions. The theoretical predictions allow us to identify optimal operation parameters for capacitive energy extraction with porous electrodes of different surface hydrophobicity. In agreement with recent experiments, we find that the thermodynamic efficiency can be much improved by using most hydrophilic electrodes.

Charge neutrality breakdown in confined aqueous electrolytes: Theory and simulation

We study, using Density Functional theory (DFT) and Monte Carlo simulations, aqueous electrolyte solutions between charged infinite planar surfaces, in contact with a bulk salt reservoir. In agreement with recent experimental observations [Z. Luo et al., Nat. Commun. 6, 6358 (2015)], we find that the confined electrolyte lacks local charge neutrality. We show that a DFT based on a bulk-HNC expansion properly accounts for strong electrostatic correlations and allows us to accurately calculate the ionic density profiles between the charged surfaces, even for electrolytes containing trivalent counterions. The DFT allows us to explore the degree of local charge neutrality violation, as a function of plate separation and bulk electrolyte concentration, and to accurately calculate the interaction force between the charged surfaces.

Entropy prediction for H2 adsorption in metal-organic frameworks

Entropy is an important thermodynamic property and serves as a bridge connecting equilibrium and non-equilibrium systems, which provides a basic understanding of various practical phenomena. In this study, classical density functional theory was introduced to efficiently predict entropy. The theory was applied to a high-throughput prediction of entropy and excess entropy for H2 adsorption in metal-organic frameworks. It seems that the entropy screening and uptake screening are generally equivalent at high temperature. Based on the entropy screening, the best hydrogen storage materials have been identified. The correlations between entropy and thermodynamic properties, such as uptake, isosteric heat and adsorption degree, were examined and are explained. The results imply that among the tested thermodynamic properties, the correlation between entropy and isosteric heat is the strongest.

A Thermodynamic Model for Genome Packaging in Hepatitis B Virus

Understanding the fundamentals of genome packaging in viral capsids is important for finding effective antiviral strategies and for utilizing benign viral particles for gene therapy. While the structure of encapsidated genomic materials has been routinely characterized with experimental techniques such as cryo-electron microscopy and x-ray diffraction, much less is known about the molecular driving forces underlying genome assembly in an intracellular environment and its in vivo interactions with the capsid proteins. Here we study the thermodynamic basis of the pregenomic RNA encapsidation in human Hepatitis B virus in vivo using a coarse-grained molecular model that captures the essential components of nonspecific intermolecular interactions. The thermodynamic model is used to examine how the electrostatic interaction between the packaged RNA and the highly charged C-terminal domains (CTD) of capsid proteins regulate the nucleocapsid formation. The theoretical model predicts optimal RNA content in Hepatitis B virus nucleocapsids with different CTD lengths in good agreement with mutagenesis measurements, confirming the predominant role of electrostatic interactions and molecular excluded-volume effects in genome packaging. We find that the amount of encapsidated RNA is not linearly correlated with the net charge of CTD tails as suggested by earlier theoretical studies. Our thermodynamic analysis of the nucleocapsid structure and stability indicates that ∼10% of the CTD residues are free from complexation with RNA, resulting in partially exposed CTD tails. The thermodynamic model also predicts the free energy of complex formation between macromolecules, which corroborates experimental results for the impact of CTD truncation on the nucleocapsid stability.

Swelling of ionic microgel particles in the presence of excluded-volume interactions: a density functional approach

In this work a new density functional theory framework is developed to predict the salt-concentration dependent swelling state of charged microgels and the local concentration of monovalent ions inside and outside the microgel.

A molecular theory for optimal blue energy extraction by electrical double layer expansion

Tuning the electrode pore size (H) and the charging potential (Ψ₀) may lead to significant increases of the thermodynamic efficiency and the work output for capacitive double layer expansion processes.

Molecular Theory for Electrokinetic Transport in pH-Regulated Nanochannels

Ion transport through nanochannels depends on various external driving forces as well as the structural and hydrodynamic inhomogeneity of the confined fluid inside of the pore. Conventional models of electrokinetic transport neglect the discrete nature of ionic species and electrostatic correlations important at the boundary and often lead to inconsistent predictions of the surface potential and the surface charge density. Here, we demonstrate that the electrokinetic phenomena can be successfully described by the classical density functional theory in conjunction with the Navier-Stokes equation for the fluid flow. The new theoretical procedure predicts ion conductivity in various pH-regulated nanochannels under different driving forces, in excellent agreement with experimental data.

Ionic asymmetry and solvent excluded volume effects on spherical electric double layers: a density functional approach

In this article, we present a classical density functional theory for electrical double layers of spherical macroions that extends the capabilities of conventional approaches by accounting for electrostatic ion correlations, size asymmetry, and excluded volume effects. The approach is based on a recent approximation introduced by Hansen-Goos and Roth for the hard sphere excess free energy of inhomogeneous fluids [J. Chem. Phys. 124, 154506 (2006); Hansen-Goos and Roth, J. Phys.: Condens. Matter 18, 8413 (2006)]. It accounts for the proper and efficient description of the effects of ionic asymmetry and solvent excluded volume, especially at high ion concentrations and size asymmetry ratios including those observed in experimental studies. Additionally, we utilize a leading functional Taylor expansion approximation of the ion density profiles. In addition, we use the mean spherical approximation for multi-component charged hard sphere fluids to account for the electrostatic ion correlation effects. These approximations are implemented in our theoretical formulation into a suitable decomposition of the excess free energy which plays a key role in capturing the complex interplay between charge correlations and excluded volume effects. We perform Monte Carlo simulations in various scenarios to validate the proposed approach, obtaining a good compromise between accuracy and computational cost. We use the proposed computational approach to study the effects of ion size, ion size asymmetry, and solvent excluded volume on the ion profiles, integrated charge, mean electrostatic potential, and ionic coordination number around spherical macroions in various electrolyte mixtures. Our results show that both solvent hard sphere diameter and density play a dominant role in the distribution of ions around spherical macroions, mainly for experimental water molarity and size values where the counterion distribution is characterized by a tight binding to the macroion, similar to that predicted by the Stern model.

Ionic Interactions Are Everywhere

Ionic solutions are dominated by interactions because they must be electrically neutral, but classical theory assumes no interactions. Biological solutions are rather like seawater, concentrated enough so that the diameter of ions also produces important interactions. In my view, the theory of complex fluids is needed to deal with the interacting reality of biological solutions.

Structure of spherical electric double layers containing mixed electrolytes: a systematic study by Monte Carlo simulations and density functional theory

The structure of spherical electric double layers in the presence of mixed electrolytes is studied using Monte Carlo simulation and density functional theory within the restricted primitive model. The macroion is modeled as an impenetrable charged hard sphere carrying a uniform surface charge density, surrounded by the small ions represented as charged hard spheres, and the solvent is taken as a dielectric continuum. The density functional theory uses a partially perturbative scheme, where the hard-sphere contribution to the one-particle correlation function is evaluated using weighted density approximation and the ionic interactions are calculated using a second-order functional Taylor expansion with respect to a bulk electrolyte. The Monte Carlo simulations have been performed in canonical ensemble. The system is studied at varying ionic concentrations, at different concentration ratios of mono- and multivalent counterions of mixed electrolytes, at different diameters of hard spheres, at different macroion radius, and at varying polyion surface charge densities. The theoretical predictions in terms of the density profiles and the mean electrostatic potential profiles are found to be in good agreement with the simulation results. This model study shows clear manipulations of ionic size and charge correlations in dictating a number of interesting phenomena relating to width of the diffuse layer and charge inversion under different parametric conditions.

Molecular solvent model of spherical electric double layers: a systematic study by Monte Carlo simulations and density functional theory

The structure of spherical electric double layers is studied using Monte Carlo simulation and density functional theory by considering solvent as the third component. In this molecular solvent model (MSM), ions and solvent molecules are considered as charged and neutral hard spheres, respectively, having equal diameter. The macroion is considered as an isolated hard sphere having uniform surface charge density surrounded by the electrolyte and the solvent. The theory is partially perturbative as the hard-sphere contribution to the one particle correlation function is evaluated using suitably averaged weighted density, and the ionic part is obtained through a second-order functional Taylor expansion around the bulk electrolyte. The Monte Carlo simulations have been performed in a canonical ensemble. The system is studied at varying concentrations of electrolytes, and the solvent molecules, at different valences of the electrolyte, at different macroion radii, and at varying surface charge densities. The theory is found to be in good agreement with the simulation results over a wide range of parametric conditions. The excluded volume effects due to the molecular nature of the solvent are shown to have much richer features in diffuse layer phenomena like layering and charge inversion.

Electrostatic regulation of genome packaging in human hepatitis B virus

Hepatitis B virus (HBV) is a contagious human pathogen causing liver diseases such as cirrhosis and hepatocellular carcinoma. An essential step during HBV replication is packaging of a pregenomic (pg) RNA within the capsid of core antigens (HBcAgs) that each contains a flexible C-terminal tail rich in arginine residues. Mutagenesis experiments suggest that pgRNA encapsidation hinges on its strong electrostatic interaction with oppositely charged C-terminal tails of the HBcAgs, and that the net charge of the capsid and C-terminal tails determines the genome size and nucleocapsid stability. Here, we elucidate the biophysical basis for electrostatic regulation of pgRNA packaging in HBV by using a coarse-grained molecular model that explicitly accounts for all nonspecific interactions among key components within the nucleocapsid. We find that for mutants with variant C-terminal length, an optimal genome size minimizes an appropriately defined thermodynamic free energy. The thermodynamic driving force of RNA packaging arises from a combination of electrostatic interactions and molecular excluded-volume effects. The theoretical predictions of the RNA length and nucleocapsid internal structure are in good agreement with available experiments for the wild-type HBV and mutants with truncated HBcAg C-termini.

Energetics of divalent selectivity in a calcium channel: the ryanodine receptor case study

A model of the ryanodine receptor (RyR) calcium channel is used to study the energetics of binding selectivity of Ca(2+) versus monovalent cations. RyR is a calcium-selective channel with a DDDD locus in the selectivity filter, similar to the EEEE locus of the L-type calcium channel. While the affinity of RyR for Ca(2+) is in the millimolar range (as opposed to the micromolar range of the L-type channel), the ease of single-channel measurements compared to L-type and its similar selectivity filter make RyR an excellent candidate for studying calcium selectivity. A Poisson-Nernst-Planck/density functional theory model of RyR is used to calculate the energetics of selectivity. Ca(2+) versus monovalent selectivity is driven by the charge/space competition mechanism in which selectivity arises from a balance of electrostatics and the excluded volume of ions in the crowded selectivity filter. While electrostatic terms dominate the selectivity, the much smaller excluded-volume term also plays a substantial role. In the D4899N and D4938N mutations of RyR that are analyzed, substantial changes in specific components of the chemical potential profiles are found far from the mutation site. These changes result in the significant reduction of Ca(2+) selectivity found in both theory and experiments.

Osmotic pressure and packaging structure of caged DNA

We present a theoretical model for aqueous solutions of double-stranded (ds) DNA with explicit consideration of electrostatic interactions, excluded-volume effects, van der Waals attractions, and salt ions. With reasonable parameters estimated from the DNA structure and experimental data for electrolytes, we are able to reproduce the DNA osmotic pressure in the bulk in good agreement with experiment. The predicted DNA osmotic pressure in lambda-bacteriophages is found to coincide with that of the PEG8000 solution that inhibits DNA ejection as reported in recent experiments. Based on the radial distributions of DNA segments and of counterions at different degrees of packaging, we find that in the presence of Mg(2+), DNA forms a multilayer structure near the inner surface of a fully loaded bacteriophage, but at low packing density the DNA segments are depleted from the surface owing to the local condensation of DNA induced by the divalent counterions. By contrast, the multilayer DNA structure is less distinctive in the presence of Na(+) despite the increase of the DNA density at contact, and the depletion near the capsid surface is not found at low packing density.

Density functional theory for planar electric double layers: closing the gap between simple and polyelectrolytes

We report a nonlocal density functional theory (NLDFT) for polyelectrolyte solutions within the primitive model; i.e., the solvent is represented by a continuous dielectric medium, and the small ions and polyions by single and tangentially connected charged hard spheres, respectively. The excess Helmholtz energy functional is derived from a modified fundamental measure theory for hard-sphere repulsion, an extended first-order thermodynamic perturbation theory for chain connectivity, and a quadratic functional Taylor expansion for electrostatic correlations. With the direct and cavity correlation functions of the corresponding monomeric systems as inputs, the NLDFT predicts the segment-level microscopic structures and adsorption isotherms of polyelectrolytes at oppositely charged surfaces in good agreement with molecular simulations. In particular, it faithfully reproduces the layering structures of polyions, charge inversion, and overcharging that cannot be captured by alternative methods including the polyelectrolyte Poisson-Boltzmann equation and an earlier version of DFT. The NLDFT has also been used to investigate the influences of the small ion valence, polyion chain length, and size disparity between polyion segments and counterions on the microscopic structure, mean electrostatic potential, and overcharging in planar electric double layers containing polyelectrolytes.