Debye-Huckel Theory Research Articles

Electro-Motive Forces Generated in Concentration Cells of LiCl-Glycerol Solutions

Mean ionic activity coefficients of LiCl in Glycerol have been calculated in the concentration range 0.5-500mol.m-3, using the concentration cell technique. Up to the limit of the Debye-Huckel theory (C ≤ 1 mol·m-3), the experimental values lie below the limiting line, showing that the measured Electro-Motive-Force might have been false by using our previous cell design. An alternative method based on Fuoss Paired Ion Model has been used to deduce the theoretical data, and consequently, the values of the EMF'S. By comparing these data to those obtained experimentally with KCI and NaCl, we find that they are consistent with the results in aqueous solutions.

The Definition and Unit of Ionic Strength

The term ionic strength is defined differently in different textbooks and monographs. Some define it in terms of mol kg-1, while others define it in terms of the non-SI unit mol L-1. The conversion to the SI unit mol m3 creates a problem in computing mean ionic activity coefficients. A dimensionless ionic strength unit has also appeared. These various definitions make the concept of ionic strength very confusing to students, especially in the use of this quantity to calculate mean activity coefficients through the Debye-Huckel theory. To resolve this confusion, a recommendation is given to define ionic strength as a dimensionless quantity.

Long-range intermolecular interaction between broken DNA fragments.

We analyzed the long-range intermolecular interaction between fragments of broken DNA. We considered two constituents of long-range intermolecular interaction. The first is a net electrostatic Coulomb interaction between charges, involved in a structure of opposite nucleotides, which we evaluate using Debye-Huckel theory. The second one is the Van der Waals interaction between the nucleotides. The general Lifshitz theory of Van der Waals forces was used to evaluate this interaction. Numerical calculations showed that a repulsive force between broken DNA fragments can arise in specific cases. This repulsion can prevent DNA from repairing itself after a double-strand break. The height of the barrier decreases with an increase of the ionic strength of the intracellular milieu, or with a reduction of its viscosity.

Description of electrolyte effects on the kinetics of reactions between ions in solution, using the mean spherical approximation

The effect of an inert salt on the kinetics of solution reactions between ions is examined in the framework of the mean spherical approximation (MSA) theory. The latter is applied to describe activation- and diffusion-controlled reactions in moderately concentrated electrolyte solutions. The results are compared with those obtained using the Debye–Huckel theory, in particular beyond the limit of applicability of this model. It is shown that both theories may be applied to represent salt effects with nearly equal accuracy.

Self-Consistent Calculation of Activity Coefficients and the Diffusion Layer Capacitance in Asymmetric Electrolytes

It is shown that substituting activities of individual ions for their concentrations in the equation for the ionic strength of solution substantially extends application of the first approximation of the Debye–Huckel theory for electrolytes of different valence. The obtained relationship predicts a changeover from the “square root” law in the charge region where the average distance between ions lis smaller than the ionic-atmosphere thickness 1/κ, to the “cube root” law, at l> 1/κ. The increasing deviation from experimental data upon going from LaCl3solutions to La2(SO4)3is attributed to the formation of ionic pairs LaSO4+.

Computer simulation of the thermodynamic properties of high-temperature chemically-reacting plasmas

The Reaction Ensemble Monte Carlo (REMC) computer simulation method [W. R. Smith and B. Tříska, J. Chem. Phys. 100, 3019 (1994)] is employed to predict the thermodynamic behavior of chemically reacting plasmas using a molecular-level model based on the underlying atomic and ionic interactions. Unlike previous plasma simulation studies, which were restricted to fairly simple systems of fixed composition, the REMC approach is able to take into account the effects of the ionization reactions. In the context of the specified molecular model, the computer simulation approach gives an essentially exact description of the system thermodynamics. We develop and apply the REMC method for the test case of a helium plasma. We calculate plasma compositions, molar enthalpies, molar volumes, molar heat capacities, and coefficients of cubic expansion over a range of temperatures up to 100 000 K and pressures up to 400 MPa. We elucidate the contributions of the Coulombic forces, ionization-potential lowering, and short-ranged interactions to the thermodynamic properties. We compare the results with those obtained using macroscopic-level thermodynamic approximations, including the ideal-gas (IG) and the Debye–Hückel (DH) approaches. For the helium plasma, the short-ranged forces are found to be relatively unimportant, but we expect these to be important for molecular systems. The DH theory is always more accurate than the IG approximation. The DH theory yields compositions that slightly underpredict the overall degree of ionization. For the molar heat capacity and the coefficient of cubic expansion, the DH theory is accurate at lower pressures, but at 400 MPa yields results that are up to 40% in error for the molar heat capacity.

Phase behavior of three-component ionic fluids

We study the phase behavior of solutions consisting of positive and negative ions of valence z to which a third ionic species of valence Z>z is added. Using a discretized Debye-Hueckel theory, we analyze the phase behavior of such systems for different values of the ratio Z/z. We find, for Z/z>1.934, a three-phase coexistence region and, for Z/z>2, a closed (reentrant) coexistence loop at high temperatures. We characterize the behavior of these ternary ionic mixtures as function of charge asymmetry and temperature, and show the complete phase diagrams for the experimentally relevant cases of Z/z=2 and Z/z=3, corresponding to addition of divalent and trivalent ions to monovalent ionic fluids, respectively.

The liquid-vapour interface of the restricted primitive model (RPM) of ionic fluids

The liquid-vapour interface of the restricted primitive model (RPM) of ionic fluids is investigated within a square-gradient theory. We compute density profiles and interfacial tensions for different temperatures using Debye-Hückel (DH) theory and its recent extension for ion-pair formation and interactions between the dipolar ion pairs and free ions developed by Fisher and Levin. This Fisher-Levin (FL) theory is known to give an accurate description of the coexistence curve of the RPM. To account for the inhomogeneities in the interfacial region, the local free-energy density is expanded in terms of the density gradient. For small gradients, e.g. reasonably close to the critical point, such an expansion can be truncated after the square-gradient term. The coefficient of the latter is calculated from the direct correlation function using an approximate (quadratic) hypernetted-chain (AHNC) relation and, alternatively, from an extended van der Waals approach in conjunction with different approximations to the local density. The results from the AHNC relation and various local density approximations in the thermodynamic framework of DH theory and FL theory, respectively, are compared, and it is asserted that the AHNC relation in conjunction with FL theory predicts reliably the interfacial properties of the RPM even within this simple square-gradient theory. In contrast to the situation for simple fluids, the local density approximation must be chosen carefully for ionic fluids since properties such as the interfacial thickness and the surface tension may vary by a factor of three or four depending on the applied local density approximation.

Correlation lengths in electrolytes : Exact results and sensible approximations

Reliably understanding the phase behavior of basic models for ionic systems is still an important task for theory and one that has experimental relevance, particularly for the critical neighborhood of liquid electrolytes [1, 2]. To that end, exact calculations [3-5] of the charge and density correlations lengths (including the Lebowitz length) for hard-sphere electrolytes of general valences, z σ , and diameters, a στ , have been undertaken using Meeron's diagrammatic analysis [J. Chem. Phys. 28 (1958) 630-643] and the hyper-netted chain graphical resummation. A variety of universal types of divergent behavior and leading nonuniversal corrections are found when the overall ionic density approaches zero. The approximate generalized Debye-Huckel theories [6-8], which yield charge and density correlation functions for the restricted primitive model (σ, τ = ±, a στ = a), may be tested and prove exact as regards the universal behavior at low densities. The critical region, however, still poses profound problems (see, e.g., [9]).

Charge effect on relative distance distribution of Fremy’s radical ions in frozen glassy solution studied by PELDOR

The method of pulsed electron double resonance (PELDOR) was used to study the kinetics of phase relaxation due to dipole-dipole spin coupling of Fremy’s radical ions and neutral nitroxyl radicals TEMPON in glassy solutions frozen to 77 K. It is shown that as compared with neutral radicals, in the case of Fremy’s radical ions, the phase relaxation kinetics deviates from the exponential one. The observed low relaxation rate of Fremy’s radical ions corresponds to electrostatic repulsion for the charged radical ions. It is shown that the relative space distribution of radical ions on the basis of the Debye-Huckel theory gives a satisfactory description of the dipole-dipole spin phase relaxation for charged radicals.

Theoretical Evaluation of Diffusion Coefficient of Chloride Ion in Mortar from Mobility

Many researchers have been trying to evaluate the diffusion coefficient of chloride ion in concrete by using qualitative and quantitative electromigration tests. Up to now, however, there has been no sufficient method to closely determine the diffusion coefficient of chloride ion through electromigration tests. This paper investigates the diffusion coefficient of chloride ion in mortar by mobility through an electromigration test. The concept of Einstein's equation, which can relate the diffusion coefficient of the chloride ion and the mobility in an ideal solution with very low concentration, is adapted. Then, for compensating the influence of the concentrations, the Debye-Huckel theory is used. For considering the effect of other existing ions, namely, OH-, Na+, and K+, the electrical neutrality is taken into account. Therefore, using Einstein's equation, the Debye-Huckel theory, and electrical neutrality, the diffusion coefficient of chloride ion can be calculated theoretically from the mobility. The correctness of the calculation is checked by a series of tests.

Effect of electrolytes on the electrochemical behaviour of 11-(ferrocenylcarbonyloxy)undecanethiol SAMs on gold disk electrodes

The interfacial electrochemistry of mixed monolayers formed by self-assembly from a dilute dodecanethiol-11–(ferrocenylcarbonyloxy)undecanethiol (FcSH) ethanolic solution at pre-treated Au electrodes is reported. The effect of different electrolytes on the interaction among electrochemical products, the interfacial capacitance and the heterogeneous electron transfer rate constant (k0), using fast cyclic voltammetry and chronoamperometry, are examined. The anions have a strong influence on the kinetic and thermodynamic parameters of the interfacial redox reaction through the formation of ion pairs with the oxidized ferrocenium. The ion-pairing capability of various anions with immobilized ferrocenium is compared through evaluation of an effective formation constant. The electrolyte cation is shown to affect the thermodynamics of the ferrocene–ferrocenium electrochemical reaction, with cations of lower mobility shifting the apparent formal potential to more positive potentials, which is explained for the first time with the electric force by means of Debye–Huckel theory. A linear relationship between the apparent formal potential of the ferrocene redox couple in self-assembled monolayers and cation mobility and concentration was observed.

Polyampholyte solutions between charged surfaces: Debye–Huckel theory

We calculate the interaction between two identically charged surfaces immersed in a polyampholyte solution in the framework of the linear response approximation. In the case of the randomly charged polyampholyte with equal fractions of positively f+ and negatively f− charged groups the interaction between charged surfaces is similar to that in electrolyte solutions. The screening of the surface potential in the linear response approximation is due to the charge redistribution on the length scales of the polymer coils without the excess of the polymers. In the solution of asymmetric polyampholytes (f+≠f−) the charge density fluctuations result in additional attractive interactions linearly proportional to the charge asymmetry.

Modulation of Bacillus pasteurii cytochrome c 553 reduction potential by structural and solution parameters

Direct cyclic voltammetry and 1H NMR spectroscopy have been combined to investigate the electrochemical and spectroscopic properties of cytochrome c 553 isolated from the alkaliphilic soil bacterium Bacillus pasteurii. A quasi-reversible diffusion-controlled redox process is exhibited by cytochrome c 553 at a pyrolitic graphite edge microelectrode. The temperature dependence of the reduction potential, measured using a non-isothermal electrochemical cell, revealed a discontinuity at 308 K. The thermodynamic parameters determined in the low-temperature range (275–308 K;ΔS°′=–162.7±1.2 J mol–1 K–1, ΔH°′=–53.0±0.5 kJ mol–1, ΔG°′=–4.5±0.1 kJ mol–1, E°′=+47.0±0.6 mV) indicate the presence of large enthalpic and entropic effects, leading, respectively, to stabilization and destabilization of the reduced form of cytochrome c 553. Both effects are more accentuated in the high-temperature range (308–323 K;ΔS°′=–294.1±8.4 J mol–1 K–1, ΔH°′=–93.4±3.1 kJ mol–1, ΔG°′=–5.8±0.6 kJ mol–1, E°′=+60.3±5.8 mV), with the net result being a slight increase of the standard reduction potential. These thermodynamic parameters are interpreted using the compensation theory of hydration of biopolymers as indicating the extrusion, upon reduction, of water molecules from the hydration sphere of the cytochrome. The low-T and high-T conformers differ by the number of water molecules in the solvation sphere: in the high-T conformer, the number of water molecules extruded upon reduction increases, as compared to the low-T conformer. The ionic strength dependence of the reduction potential at 298 K, treated within the frame of extended Debye-Huckel theory, yields values of E °′ (I=0) =–25.4±1.4 mV, z red=–11.3, and z ox=–10.3. The pH dependence of the reduction potential at 298 K shows a plateau in the pH range 7–10 and an increase at more acidic pH, allowing the calculation of pK O=5.5 and pK R=5.7, together with the estimate of the reduction potentials of completely protonated (+71 mV) and deprotonated (+58 mV) forms of cytochrome c 553. 1H NMR spectra of the oxidized paramagnetic cytochrome c 553 indicate the presence of a His-Met axial coordination of the low-spin (S=1/2) heme iron, which is maintained in the temperature interval 288–340 K at pH 7 and in the pH range 4.8–10.0 at 298 K. The temperature dependence of the hyperfine-shifted signals shows both Curie-type and anti-Curie-type behavior, with marked deviations from linearity, interpreted as indicating the presence of a fast equilibrium between the low-T and high-T conformers, having slightly different heme electronic structures resulting from the T-induced conformational change. Increasing the NaCl concentration in the range 0–0.2 M causes a slight change of the 1H NMR chemical shifts of the hyperfine-shifted signals, with no influence on their linewidth. The calculated lower limit value of the apparent affinity constant for specific ion binding is estimated as 5.2±1.1 M–1. The pH dependence of the isotropically shifted 1H NMR signals of the oxidized cytochrome displays at least one ionization step with pK O=5.7. The thermodynamic and spectroscopic data indicate a large solvent-derived entropic effect as the main cause for the observed low reduction potential of B. pasteurii cytochrome c 553.

Macroscopic theory for equilibrium properties of ionic-dipolar mixtures and application to an ionic model fluid

An electrostatic theory for the equilibrium properties of a mixture of equisized ions and dipoles is developed by solving the Debye–Hückel differential equation for the cases of a charge and a dipole, respectively, in a dielectric continuum that contains free charges. This theory yields expressions for the potentials of mean force of ion-ion, ion-dipole, and dipole-dipole interactions. Furthermore, it leads to a formula for the dielectric constant that modifies Onsager’s result by accounting not only for the dipoles, but also for the free ions, and resembles the expression obtained by Adelman and Chen. The theory is applied to calculate thermodynamic properties of the model system of equisized charged hard spheres in a dielectric continuum (restricted primitive model), approximating dipolar ion pairs as spheres. We thus augment the work of Fisher and Levin, who added a shielded dipole-ion interaction term to the traditional Debye–Hückel theory, for a shielded dipole-dipole interaction and a density-dependent dielectric constant. The approximate evaluation of this theory yields a narrowing of the coexistence curve compared to the Fisher–Levin theory along with a considerable decrease of the critical density; however, it does not lead to the dramatic increase of the critical temperature that was observed by Guillot and Guissani who modified the Fisher–Levin theory by including unscreened dipole-dipole interactions adopting the original Onsager theory.

Iron(III) Thiocyanate Revisited: A Physical Chemistry Equilibrium Lab Incorporating Ionic Strength Effects

A physical chemistry laboratory exercise is presented in which the thermodynamic equilibrium constant for Fe3+ + SCN- Fe(SCN)2+ in 0.5 M acid is calculated from the experimentally observed equilibrium constant and activity coefficients generated by the Davies extension of the Debye-Huckel theory.

Counterion condensation on ionic oligomers

The Ramanathan-Woodbury formulas representing the charge density critical for the onset of counterion condensation on finite-length polymers are derived by three alternate methods, an extension of Debye-Huckel theory, a theory of end effects, and by density functional theory. For charged oligomers with length of the same order as the Debye length, the threshold for condensation is the same as for polymers of length much greater than the Debye lenght. However, the threshold depends both on length and salt concentration if the oligomer is shorter than the Debye length, in such a way as to recede to infinity as the ratio of oligomer length to Debye length tends to zero (i.e., condensation vanishes in this limit). The extended Debye-Huckel theory additionally provides a new result for the partition function of the condensed layer, showing that the free energy of the condensed counterions is different on an oligomer and a polymer, even when the fractional extent of condensation is the same. The end effect theory discloses a hitherto unnoticed connection between the number of counterions condensed at the ends of a long polymer and the number condensed on a short oligomer.

Treating Electrostatic Shielding at the Surface of Silica as Discrete Siloxide·Cation Interactions

This work examines the influence of ions in solution on electroosmosis inside a fused silica capillary using capillary electrophoresis; it thereby examines “shielding” at charged interfaces. Theories are reviewed that model ionic solutions as continuous dielectrics: the nonlinear form of the Poisson−Boltzmann equation gives rise to the simplified, more commonly used Debye−Huckel (DH) equation. Capillary electrophoresis (CE) is used to measure the rate of electroosmotic flow as a function of the concentration of different monovalent and divalent cations in aqueous solution. These data are used to test three specific predictions of DH theory: this theory does not describe these data adequately. The central reason behind the inadequacy of DH theory here is its inability to account for details at the level of individual ions other than by mean-field electrostatics: that is, chemical characteristics of ionsfor example, polarizability, hydrated size, energy of hydration, ability to coordinate other ions by c...

Attractive Interaction between Similarly Charged Colloidal Particles

The pair interactions between the charged colloidal particles dispersed in a solvent are studied theoretically by the integral equation method. The pair potential of the mean forces, accounting for the effective pair interaction between colloidal particles, is calculated from the solution of the Ornstein–Zernike equation with the mean spherical approximation (MSA). An attractive interaction was found between two similarly charged colloidal particles in contrast with the purely repulsive force predicted by the Debye–Huckel theory. Such an attractive interaction provides physical insight for the “condensed” phenomena in charged colloidal dispersions, that is, the coexistence of a “condensed” phase and an “expanded” phase (voids). At the higher concentration and charge on colloidal particles, the effective pair interaction becomes oscillatory.

H 2 O activity in concentrated NaCl solutions at high pressures and temperatures measured by the brucite-periclase equilibrium

H2O activities in concentrated NaCl solutions were measured in the ranges 600°–900° C and 2–15 kbar and at NaCl concentrations up to halite saturation by depression of the brucite (Mg(OH)2) – periclase (MgO) dehydration equilibrium. Experiments were made in internally heated Ar pressure apparatus at 2 and 4.2 kbar and in 1.91-cm-diameter piston-cylinder apparatus with NaCl pressure medium at 4.2, 7, 10 and 15 kbar. Fluid compositions in equilibrium with brucite and periclase were reversed to closures of less than 2 mol% by measuring weight changes after drying of punctured Pt capsules. Brucite-periclase equilibrium in the binary system was redetermined using coarsely crystalline synthetic brucite and periclase to inhibit back-reaction in quenching. These data lead to a linear expression for the standard Gibbs free energy of the brucite dehydration reaction in the experimental temperature range: ΔG° (±120J)=73418–134.95T(K). Using this function as a baseline, the experimental dehydration points in the system MgO−H2O−NaCl lead to a simple systematic relationship of high-temperature H2O activity in NaCl solution. At low pressure and low fluid densities near 2 kbar the H2O activity is closely approximated by its mole fraction. At pressures of 10 kbar and greater, with fluid densities approaching those of condensed H2O, the H2O activity becomes nearly equal to the square of its mole fraction. Isobaric halite saturation points terminating the univariant brucite-periclase curves were determined at each experimental pressure. The five temperature-composition points in the system NaCl−H2O are in close agreement with the halite saturation curves (liquidus curves) given by existing data from differential thermal analysis to 6 kbar. Solubility of MgO in the vapor phase near halite saturation is much less than one mole percent and could not have influenced our determinations. Activity concentration relations in the experimental P-T range may be retrieved for the binary system H2O-NaCl from our brucite-periclase data and from halite liquidus data with minor extrapolation. At two kbar, solutions closely approach an ideal gas mixture, whereas at 10 kbar and above the solutions closely approximate an ideal fused salt mixture, where the activities of H2O and NaCl correspond to an ideal activity formulation. This profound pressure-induced change of state may be characterized by the activity (a) – concentration (X) expression: a H 2O=X H 2O/(1+αX NaCl), and a NaCl=(1+α)(1+α)[X NaCl/(1+αX NaCl)](1+α). The parameter α is determined by regression of the brucite-periclase H2O activity data: α=exp[A–B/ϱH 2O ]-CP/T, where A=4.226, B=2.9605, C=164.984, and P is in kbar, T is in Kelvins, and ϱH 2O is the density of H2O at given P and T in g/cm3. These formulas reproduce both the H2O activity data and the NaCl activity data with a standard deviation of ±0.010. The thermodynamic behavior of concentrated NaCl solutions at high temperature and pressure is thus much simpler than portrayed by extended Debye-Huckel theory. The low H2O activity at high pressures in concentrated supercritical NaCl solutions (or hydrosaline melts) indicates that such solutions should be feasible as chemically active fluids capable of coexisting with solid rocks and silicate liquids (and a CO2-rich vapor) in many processes of deep crustal and upper mantle metamorphism and metasomatism.