Debye-Huckel Theory Research Articles

Comment on "Binding Debye-Hückel theory for associative electrolyte solutions" [J. Chem. Phys. 159, 154503 (2023)

It is argued that the Binding Debye-Hückel (BiDH) model proposed by Naseri Boroujeni et al. [J. Chem. Phys. 159, 154503 (2023)] might not be appropriate for the description of Monte Carlo simulation data obtained for primitive model electrolytes. The first reason is that the original Debye-Hückel (DH) theory is of low accuracy for describing deviations from ideality in concentrated solutions of strong salts. The DH framework is thus a poor basis for building a model including association. The second reason is that the mean-spherical approximation, without assumption of association, apparently predicts Monte Carlo (MC) data for primitive electrolytes better than BiDH. Thus, the BiDH model seems to be simply a way of compensating for the deficiencies of DH theory by assuming association.

Response to "Comment on 'Binding Debye-Hückel theory for associative electrolyte solutions'" [J. Chem. Phys. 159, 154503 (2023)

This Response addresses critiques raised about the Binding Debye-Hückel (BiDH) theory [Naseri Boroujeni et al., J. Chem. Phys. 159, 154503 (2023)] by Simonin and Bernard [J.-P. Simonin and O. Bernard, J. Chem. Phys. (2024)]. The critiques questioned the foundational framework of the Debye-Hückel (DH) theory, the relevance of ion pairing in primitive model fluids, and the accuracy of the BiDH model compared to mean spherical approximation model. Through a systematic rebuttal, supported by extensive literature review and comparison with Monte Carlo simulation data, this Response addresses these concerns. It demonstrates the efficacy of DH theory in describing real electrolyte solutions, validates the relevance of ion pairing in primitive model fluids, and establishes the BiDH model's accuracy in describing electrolyte properties.

Systematic Incorporation of Ionic Hard-Core Size into the Debye-Hückel Theory via the Cumulant Expansion of the Schwinger-Dyson Equations.

The Debye-Hückel (DH) formalism of bulk electrolytes equivalent to the Gaussian-level closure of the electrostatic Schwinger-Dyson identities without the interionic hard-core (HC) coupling is extended via the cumulant treatment of these equations augmented by HC interactions. By comparing the monovalent ion activity and pressure predictions of our cumulant-corrected DH (CCDH) theory with hypernetted-chain results and Monte Carlo simulations from the literature, we show that this rectification extends the accuracy of the DH formalism from submolar to molar salt concentrations. In the case of internal energies or the general case of divalent electrolytes mainly governed by charge correlations, the improved accuracy of the CCDH theory is limited to submolar ion concentrations. Comparison with experimental data from the literature shows that, via the adjustment of the hydrated ion radii, CCDH formalism can equally reproduce the nonuniform effect of salt increment on the ionic activity coefficients up to molar concentrations. The inequality satisfied by these HC sizes coincides with the cationic branch of the Hofmeister series.

Effects of Non-Thermal Plasma on the Transition from Nano-Crystalline to Amorphous Structure in Water and Subsequent Effects on Viscosity

Recent studies have demonstrated that the physical properties of water treated with non-thermal plasma, or plasma-activated water (PAW), significantly differ from those of distilled water. For example, contrary to expectation, the viscosity of PAW becomes lower than that of distilled water at certain temperatures. This study developed a model to explain these differences by combining the two-state model of ordinary water, which describes water as a combination of nano-crystalline clusters and amorphous, free-floating molecules, using the Debye–Huckel theory for a fluid containing ions. A model for the viscosity of PAW was then developed from the general model. It explains how PAW has a lower viscosity than distilled water as the temperature decreases and why this effect is stronger than the colligative effect for ideal solutions. Finally, the viscosity model is compared to the experimental measurements of PAW treated with gliding arc plasma, showing that the data match the predicted values quite well. The model of PAW developed here can be used to understand other physical properties beyond viscosity, such as the surface tension, contact angle, electric conductivity, heat capacity, isothermal compressibility, and density, potentially facilitating new applications of PAW.

Binding Debye-Hückel theory for associative electrolyte solutions.

This study presents a new equation of state (EOS) for charged hard sphere fluids that incorporates ion-ion association. The EOS is developed using the Debye-Hückel (DH) theory, reference cavity approximation, and Wertheim's theory. Predictive accuracy is evaluated by comparing the model's predictions with Monte Carlo simulations for various charged hard-sphere fluids. The assessment focuses on mean ionic activity coefficient, individual ionic activity coefficient, and osmotic coefficients. The results demonstrate good agreement between the model and simulations, indicating its success for different electrolyte systems. Incorporating ion-ion association improves accuracy compared to the DH theory. The importance of the cavity function and ion-dipole interactions is emphasized in accurately representing structural properties. Overall, the developed EOS shows promising predictive capabilities for charged hard sphere fluids, providing validation and highlighting the significance of ion-ion association in thermodynamic predictions of electrolyte solutions.

Minimum-modified Debye-Hückel theory for size-asymmetric electrolyte solutions with moderate concentrations

A minimum-modified Debye-Hückel (DH) theory for electrolytes with size asymmetry is developed. Compared with the conventional DH theory, the minimum-modified DH theory only introduces an extra surface charge density to capture the electrostatic effect of the size asymmetry of the electrolytes and hence facilitates a boundary element method for electrostatic potential calculation. This theory can distinguish the electrostatic energies and excess chemical potentials of ions with the same sizes but opposite charges, and is applied to a binary primitive electrolyte solution with moderate electrostatic coupling. Compared with the hyper-netted chain theory, the validity of this modified DH theory demonstrates significant improvement over the conventional DH theory.

Application of Debye–Huckel and Bronsted-Bjerrum theory to mass transfer rate in supported liquid membrane; effect of ionic strength on separation factor, an analysis through case studies

ABSTRACT The Debye–Huckel and Bronsted-Bjerrum theory has been applied to supported liquid membrane process to understand the effect of ionic strength on separation factor. The effect of ionic strength due to different salts and their concentration on the separation factor of Cu(II) and Zn(II) by supported liquid membrane using Di-2 ethyl-hexyl phosphoric acid (D2EHPA) as a mobile carrier has been studied. For those studies, different salts, i.e., NaCl, NaNO3, NaClO3, Na2SO4, and CH3COONa, have been used. A mathematical model for the dependency of separation factor of Cu(II) and Zn(II) on ionic strength considering Debye–Huckel theory and Bronsted–Bjerrum theory has been developed. Experiments were carried out using a batch-type permeator of micro-porous polypropylene thin sheet as the solid support for the liquid membrane in the presence of different ionic strength of anions. The calculated separation factor is well agreed with the obtained results within 95% confidence interval.

Activity coefficient of multi-ions and Gibbs free energy calculation during electrochemical nitrate reduction in synthetic and actual wastewater

This study reports the calculation of individual ion's activity coefficient and total minimum Gibbs energy for electrochemical denitrification of nitrate ions in synthetic and actual wastewater. The concentration of nitrate ion continuously decreased during treatment via the electrochemical method. During the treatment, nitrate ions got reduced into nitrite and ammonium ion. The individual ion activity coefficient was examined by applying Pitzer, Lin and Lee modified Debye-Huckel theory which is based on the interaction of ion-ion (long-range, i.e., LR interaction-electrostatic effect) and ion-water (short-range, i.e., SR interaction-solvation effect) in the aqueous solution. The equilibrium composition of these ions was calculated by minimizing the error between total minimum Gibbs energy calculated by using experimental and predicted compositions. The individual ion activity coefficient, which was calculated through this model, was used to measure the total minimum Gibbs energy (Gtotal). Variation of individual ion activity coefficient and Gtotal with initial nitrate ion concentration, applied current density, initial pH, and concentration of NaCl as electrolyte has been studied. It was found that the experimental and calculated composition of nitrate, nitrite, and ammonium ions were in good agreement for electrochemical denitrification of synthetic and actual wastewater.

Electrical Propagation of Condensed and Diffuse Ions Along Actin Filaments.

In this article, we elucidate the roles of divalent ion condensation and highly polarized immobile water molecules on the propagation of ionic calcium waves along actin filaments. We introduced a novel electrical triple layer model and used a non-linear Debye-Huckel theory with a non-linear, dissipative, electrical transmission line model to characterize the physicochemical properties of each monomer in the filament. This characterization is carried out in terms of an electric circuit model containing monomeric flow resistances and ionic capacitances in both the condensed and diffuse layers. We considered resting and excited states of a neuron using representative mono and divalent electrolyte mixtures. Additionally, we used 0.05V and 0.15V voltage inputs to study ionic wavesalong actin filaments in voltage clamp experiments. Our results reveal that the physicochemical properties characterizing the condensed and diffuse layers lead to different electrical conductive mediums depending on the ionic species and the neuron state. This region specific propagation mechanism provides a more realistic avenue of delivery by way of cytoskeleton filaments for larger charged cationic species. A new direct path for transporting divalent ions might be crucial for many electrical processes found in localized neuron elements such as at mitochondria and dendritic spines.

Fast Calculation of Electrostatic Solvation Free Energy in Simple Ionic Fluids Using an Energy-Scaled Debye-Hückel Theory.

Continuum theories are useful to compute the solvation free energy in ionic fluids. Herein, the electrostatic solvation free energy (ESFE) in simple ionic fluids is studied with an energy-scaled Debye-Hückel (ESDH) theory. Given the ESFEs of simple spherical ions as input, the ESDH theory is applicable to molecules with various complex geometries and charge distributions. Specifically, the ESDH theory is applied to molecules in a molten salt system, where the predicted ESFEs are in good agreement with molecular dynamics simulation results. Our study sheds light on accurately predicting the ESFE in ionic fluids with phenomenological continuum theories.

A Systematic Way to Extend the Debye-Hückel Theory beyond Dilute Electrolyte Solutions.

An extended Debye-Hückel theory with fourth order gradient term is developed for electrolyte solutions; namely, the electric potential φ(r) of the bulk electrolyte solution can be described by ∇2φ(r) = κ2φ(r) + LQ2∇4φ(r), where the parameters κ and LQ are chosen to reproduce the first two roots of the dielectric response function of the bulk solution. Three boundary conditions for solving the electric potential problem are proposed based upon the continuity conditions of involving functions at the dielectric boundary, with which a boundary element method for the electric potential of a solute with a general geometrical shape and charge distribution is derived. Solutions for the electric potential of a spherical ion and a diatomic molecule are found and used to calculate their electrostatic solvation energies. The validity of the theory is successfully demonstrated when applied to binary as well as multicomponent primitive models of electrolyte solutions.

Distribution of Electrons and Ions Near an Absorbing Spherical Body in a Nonequilibrium Plasma

The applicability of the collision kinetic model of point sinks, viz., the linearized theory of screening of the electric field produced by a charged dust particle, based on the Vlasov equations for electrons and ions in a nonequilibrium plasma, which are supplemented with collision terms in the Bhatnagar–Gross–Crook form and effective point sinks to dust particle, is analyzed. The criterion for the applicability of the collision kinetic model of point sinks is the smallness of the deviation of the electron and ion number densities near an absorbing spherical body from unperturbed values. The distributions of electron and ion number densities obtained using the collision kinetic model of point sinks and the orbit motion limited approach are compared. It is shown that the latter approach is applicable only in the low-pressure limit, and upon an increase in pressure, the Coulomb asymptotics of the potential, which is proportional to the frequency electron and ion collisions with neutral atoms (molecules), renders the orbit motion limited approach inapplicable for calculating the ion distribution. It is established that the domain of applicability of the collision kinetic model of point sinks is close to the applicability domain of the Debye–Huckel theory.

The Activity Coefficients of High-Charge Electrolytes in Aqueous Dilute Solutions

We examine in detail the activity coefficient of higher-charge electrolytes, which, in dilute solutions, can display negative deviations from the Debye–Huckel limiting law instead of the usual positive deviations typical of lower-charge electrolytes. This fact is of considerable relevance for scientists concerned with extrapolation to infinite dilution of thermodynamic and kinetic quantities. It is shown that this “strange” behavior originates merely from the electrostatic interactions between each ion and all other ions, with no necessity of hypothesizing the presence of chemical association; these negative deviations, indeed, are predicted even at the level of the “primitive model” (ions assumed as charged, unpolarizable, rigid spheres inside an unstructured, isotropic, dielectric fluid). Three different approximations for the behavior of the primitive model of low-charge and high-charge electrolytes are tested, in addition to the Debye–Huckel theory; i.e. IPBE (a numerical accurate integration of the Poisson–Boltzmann equation), the Mayer theory of the electrolytes in the so-called DHLL + B2 approximation, and the Bjerrum theory. In the Supporting Information, the fundamentals of the respective algorithms are reported, and the effects produced by the differences of size between cations and anions, are also examined.

Mulitphase Atmospheric Chemistry in Liquid Water: Impacts and Controllability of Organic Aerosol.

Liquid water is a dominant and critical tropospheric constituent. Over polluted land masses low level cumulus clouds interact with boundary layer aerosol. The planetary boundary layer (PBL) is the lowest atmospheric layer and is directly influenced by Earth's surface. Water-aerosol interactions are critical to processes that govern the fate and transport of trace species in the Earth system and their impacts on air quality, radiative forcing, and regional hydrological cycling. In the PBL, air parcels rise adiabatically from the surface, and anthropogenically influenced hygroscopic aerosols take up water and serve as cloud condensation nuclei (CCN) to form clouds. Water-soluble gases partition to liquid water in wet aerosols and cloud droplets and undergo aqueous-phase photochemistry. Most cloud droplets evaporate, and low volatility material formed during aqueous phase chemistry remains in the condensed phase and adds to aerosol mass. The resulting cloud-processed aerosol has different physicochemical properties compared to the original CCN. Organic species that undergo multiphase chemistry in atmospheric liquid water transform gases to highly concentrated, nonideal ionic aqueous solutions and form secondary organic aerosol (SOA). In recent years, SOA formation modulated by atmospheric waters has received considerable interest.Key uncertainties are related to the chemical nature of hygroscopic aerosols that become CCN and their interaction with organic species. Gas-to-droplet or gas-to-aqueous aerosol partitioning of organic compounds is affected by the intrinsic chemical properties of the organic species in addition to the pre-existing condensed phase. Environmentally relevant conditions for atmospheric aerosol are nonideal. Salt identity and concentration, in addition to aerosol phase state, can dramatically affect organic gas miscibility for many compounds, in particular when ionic strength and salt molality are outside the bounds of limiting laws. For example, Henry's law and Debye-Hückel theory are valid only for dilute aqueous systems uncharacteristic of real atmospheric conditions. Chemical theory is incomplete, and at ambient conditions, this chemistry plays a determining role in total aerosol mass and particle size, controlling factors for air quality and climate-relevant aerosol properties.Accurate predictive skill to understand the impacts of societal choices and policies on air quality and climate requires that models contain correct chemical mechanisms and appropriate feedbacks. Globally, SOA is a dominant contributor to the atmospheric organic aerosol burden, and most mass can be traced back to precursor gas-phase volatile organic compounds (VOCs) emitted from the biosphere. However, organic aerosol concentrations in the Amazon Rainforest, the largest emitter of biogenic VOCs, are generally lower than in U.S. national parks. The Interagency Monitoring of Protected Visual Environments (IMPROVE) air quality network, with sites located predominantly in national parks, provides the longest continuous record of organic aerosol measurements in the U.S. Analysis of IMPROVE data provides a useful chemical climatology of changing air resources in response to environmental rules and shifting economic trends. IMPROVE data provides an excellent test bed for case studies to assess model skill to accurately predict changes in organic aerosol concentrations in the context of a changing climate.

Relationship of the Permittivity with the Activity Coefficients of Water and Ions in Aqueous Solutions of Lithium and Sodium Sulfates

The activity coefficients in aqueous solutions of lithium and sodium sulfates at 298 K were calculated by the generalized Debye–Huckel theory using the experimental values of the static permittivity of the solutions. The effect of the hydration and ion association on the dielectric and thermodynamic properties of the electrolyte solutions was considered.

Formation of Glycinate Complexes of Iron(II) in Solutions of Different Ionic Strengths

Processes of complexation in the Fe(0)–Fe(II)–glycine–Na(H)ClO4–H2O system at a temperature of 298.15 K, an ionic strength of solutions of 0.1–1.0 (NaClO4), СFe(II) = 1 × 10−3, and in the pH range of 0.8–8.0 are studied according to the Clark–Nikolsky oxidation potential. Experimental curves are obtained for the dependences of EMF on concentration, рН, pCFe(II), рСHL. Successive approximation of theoretical and experimental oxidative potential functions is used to calculate the constants of complexation. The dependence of the constant of complexation on the ionic strength of the solution is calculated on the basis of the Debye–Huckel theory. It is found that the formation constants of coordination compounds fall as the ionic strength of a solution rises.

Heat transfer and Helmholtz-Smoluchowski velocity in Bingham fluid flow

A mathematical study is developed for the electro-osmotic flow of a non-Newtonian fluid in a wavy microchannel in which a Bingham viscoplastic fluid model is considered. For electric potential distributions, a Poisson-Boltzmann equation is employed in the presence of an electrical double layer (EDL). The analytical solutions of dimensionless boundary value problems are obtained with the Debye-Huckel theory, the lubrication theory, and the long wavelength approximations. The effects of the Debyelength parameter, the plug flow width, the Helmholtz-Smoluchowski velocity, and the Joule heating on the normalized temperature, the velocity, the pressure gradient, the volumetric flow rate, and the Nusselt number for heat transfer are evaluated in detail using graphs. The analysis provides important findings regarding heat transfer in electroosmotic flows through a wavy microchannel.

Molecular interactions analysis of some aluminium salts in binary aqueous solutions of tetrahydrofuran (THF): Acoustic and Conductometric approach

In the present investigation conductance and speed of sound of aluminium sulphate, aluminium nitrate, and aluminium chloride were experimentally determined in aqueous medium as well in binary aqueous mixtures of THF. Various conductance and acoustic parameters viz; molar conductance, limiting molar conductance, partial molar adiabatic compressibility, coefficient of adiabatic compressibility were also determined using Kohlrausch's Law, Debye-Huckel theory and Masson’s equation at working temperatures and different compositions of THF. Analysis reveals that limiting molar conductivity decreases with increase in composition of THF in water indicating the decrease in the ion-solvent interactions with increase in composition THF in water. Further it was found that with increase in temperature the values increase for all the three salts which support the increase in ion-solvent interactions with increase in temperature. The values of partial molar isentropic compression were found negative and these values further increase with increase in composition of THF indicating that on increase in composition, attractive interactions develop between THF and water which induces dehydration of aluminium salts which make the water molecules of aluminium salts more compressible than that of lower THF concentration resulting in decrease of ion solvent interactions with increase in THF composition in water. On the other hand with increase in temperature, the values of further increase leading to increase in ion-solvent interactions of aluminium salts in water and 5% THF+ water. Walden product and its temperature coefficient i.e. have also been calculated which confirms that aluminium salts act as structure breaker in different compositions of THF in water.

Explicit Ions for Coarse-Grained Simulations of Intrinsically Disordered Proteins via Hydrophobicity/Hydrophilicity Scales

Intrinsically disordered proteins (IDPs) play a role in many different biological functions, such as molecular signaling or formation of membraneless organelles. A common method for studying IDPs is coarse-grained simulations due to large length and timescales that must be probed to simulate phenomena of interest. Many IDPs are highly charged and can have strong interactions with ions in solution. While most coarse-grained simulations rely on screened electrostatics interactions inspired by Debye-Huckel theory to implicitly capture the effect of ions on, implicit ions are ineffective in properly capturing the effects of the variation of ionic strength and Hofmeister effects, as well as the entropic contribution from ion release on binding. In order to better capture these effects, we have developed explicit ions for inclusion in the otherwise implicit solvent, hydrophobicity scale coarse-grained model for implicitly disordered proteins. Explicit ions are modeled by taking advantage of a hydrophilicity scale, which allows for the modification of the attractive part of the non-bonded interaction without modifying the excluded volume. The hydrophilicity parameter of a series of ions is parameterized by matching chain properties of a set of IDPs in a solution of a variety of ions. The hydrophilicity is then related to the free energy of hydration to predict parameters ions not in the parameterization set. The change in upper critical solution temperature as a function of ion type and ionic strength is also investigated, and related to experiment.

Screening length for finite-size ions in concentrated electrolytes.

The classical Debye-Hückel (DH) theory clearly accounts for the origin of screening in electrolyte solutions and works rather well for dilute electrolyte solutions. While the Debye screening length decreases with the ion concentration and is independent of ion size, recent surface-force measurements imply that for concentrated solutions, the screening length exhibits an opposite trend; it increases with ion concentration and depends on the ionic size. The screening length is usually defined by the response of the electrolyte solution to a test charge but can equivalently be derived from the charge-charge correlation function. By going beyond DH theory, we predict the effects of ion size on the charge-charge correlation function. A simple modification of the Coulomb interaction kernel to account for the excluded volume of neighboring ions yields a nonmonotonic dependence of the screening length (correlation length) on the ionic concentration, as well as damped charge oscillations for high concentrations.