Debye-Huckel Type Research Articles

Multidomain Chebyshev pseudo-spectral method applied to the Poisson–Boltzmann equation for two parallel plates

We address a boundary-value problem involving a Poisson–Boltzmann equation that models the electrostatic potential of a channel formed by parallel plates with an electrolyte solution confined between the plates. We show the existence and uniqueness of solution to the problem, with special (particular) solutions as bounds, namely, a Debye–Huckel type solution as lower bound and a Gouy–Chapman type solution as upper bound. Our results are based on the maximum principle for elliptic equations and are useful for characterizing the behavior of the solutions. Also, we introduce a numerical scheme based on the Chebyshev pseudo-spectral method to calculate approximate solutions. This method is applied in conjunction with a multidomain procedure that attempts to capture the dramatic exponential increase/decay of the solution near the plates.

Thermodynamic Study on the Protonation and Complexation of the Neuroleptic Drug, Gabapentin with Na+, Ca2+ and Mg2+ at Various Temperatures and Ionic Strengths

The current work investigates the protonation constants of gabapentin (GP), 2-[1-(aminomethyl)cyclohexyl]acetic acid and the stability constants for the binding of GP to Ca2+ and Mg2+ in a wide range of temperature and ionic strength conditions [283.15 ≤ T/K ≤ 318.15 and ionic strengths of NaCl(aq), 0.12 ≤ I/mol·dm−3 ≤ 4.84]. The pH-potentiometric titration method was applied for gathering experimental data and determination of solution equilibrium constants. The ΔpK method was used for the determination of calcium and magnesium stability constants due to the low values which were predicted. A Debye–Huckel type equation, Specific Ion Interaction Theory, Pitzer and van’t Hoff equations were used for the modeling of ionic strength and temperature effects. Two species, ML and MHL, were found according to the best model for Ca2+ and Mg2+. Both protonation processes are exothermic based on the enthalpy values at 298.15 K and infinite dilution. A case study has been performed taking into account the speciation of GP in seawater.

Investigation of the Specific Ion Interactions and Determining Protonation Constant of 3,5-Dihydroxy-2-(3,4,5-trihydroxybenzoyl)oxy-6-[(3,4,5-trihydroxybenzoyl)oxymethyl] oxan-4-yl] 3,4,5-trihydroxybenzoate at Different Ionic Strength

In this research, the protonation constant value of tannic acid was determined at 25 °C and different ionic strengths (0.1 to 0.7 mol/dm3 NaCl) using potentiometric titration technique. The dependence of protonation constant on ionic strength was modeled and discussed by a Debye-Huckel type equation. Then, based on the obtained data from experiments, the minimizing Sum of Squares Error (SSE) was done by Microsoft's Excel solver program and the most suitable model was chosen. After optimization, the protonation constant of tannic acid at different ionic strengths was calculated and curves of log Kcal and log Kexp were compared. Finally, Daniele constants of C and D were measured and the Specific Ion interaction Theory (SIT) was assessed for this weak acid. The obtained results show that the protonation constants of tannic acid decrease with increasing ionic strength.

Thermodynamic Study on the Interaction of Nicotinic Acid with H+, Na+, Ca2+ and Mg2+ at Different Temperatures and Ionic Strengths

Protonation of nicotinic acid has been investigated by means of potentiometric titrations at different temperatures 283.15 ≤ T (K) ≤ 383.15 and ionic strengths of NaCl(aq), 0.12 ≤ I (mol·kg−1) ≤ 4.84 and mixed NaCl with MgCl2 or CaCl2. Stability constants of the CaL+ and MgL+ species were obtained by means of the ΔpK method. Different models (e.g. Debye–Huckel type equation, Specific Ion Interaction Theory, Pitzer and van’t Hoff) were applied to account for the ionic strength and temperature dependences, in order to obtain data in a standard state and parameters to calculate stability constants in any point of our experimental domain. Speciation studies were performed simulating the conditions of natural fluids. Literature data were investigated for comparison with the experimental results here obtained.

Solubility, acid-base properties and thermodynamics of interaction between three NTA-phosphonate derivatives and the main cationic components (H+, Na+, Mg2+ and Ca2+) of natural fluids

Abstract Solution thermodynamics of three aminophosphonic acids are studied in this work. In particular, the protonation constants [ log ( K i H /mol kg−1)] of N-phosphonomethyliminodiacetic acid (NTAP), N,N-Bis(phosphonomethyl)glycine (NTAP2) and Nitrilotris(methylenephosphonic acid) (NTAP3) and the solubility of NTAP were determined by potentiometric measurements (ISE-[H+] glass electrode) in three different ionic media, namely NaCl(aq), (CH3)4NCl(aq) and (C2H5)4NI(aq) at different ionic strengths (in the range 0 log K i H on ionic strength and temperature was studied by Debye-Huckel type equation and by Specific ion Interaction Theory (SIT). At infinite dilution, the refined values of the first protonation constants are: log ( K i H /mol kg−1) = 11.4 ± 0.1, 12.4 ± 0.1 and 13.3 ± 0.1 for NTAP, NTAP2 and NTAP3, respectively and the enthalpy changes relative to the first protonation step are: −15.7 ± 0.3, −20.5 ± 0.4 and –33.5 ± 0.2 kJ mol−1 (same order). The basicity trend: NTAP3 > NTAP2 > NTAP is observed in all the ionic media. The differences in the values of the protonation constants obtained in the three ionic media were also interpreted in terms of formation of weak complex and eleven Na+/L species are obtained using the so called ΔpK method. Solubility investigations performed on NTAP allowed us to determine the Setschenow and the activity coefficients of the neutral species. The values of the total and specific solubility in pure water are: log ( S 0 T /mol kg−1) = −1.431 ± 0.003 and log ( S 0 0 /mol kg−1) = −2.293 ± 0.006, respectively. The formation constants of the three ligands with Ca2+ and Mg2+ cations were determined at T = 298.15 K in NaCl(aq) at I = 0.151 mol kg−1, finding the presence of the ML and MHL species. The stability of the Ca2+/L is slightly higher than that of the Mg2+/L ones.

Thermodynamic Study on the Protonation and Na+, Ca2+, Mg2+-Complexation of a Biodegradable Chelant (HEIDA) at Different Ionic Strengths and Temperatures

A potentiometric method has been used for the determination of the protonation constants of N-(2-hydroxyethyl)iminodiacetic acid (HEIDA or L) at various temperatures 283.15 ≤ T/K ≤ 383.15 and different ionic strengths of NaCl(aq), 0.12 ≤ I/mol·kg−1 ≤ 4.84. Ionic strength dependence parameters were calculated using a Debye–Huckel type equation, Specific Ion Interaction Theory and Pitzer equations. Protonation constants at infinite dilution calculated by the SIT model are $$ \log_{10} \left( {{}^{T}K_{1}^{\text{H}} } \right) = 8.998 \pm 0.008 $$ (amino group), $$ \log_{10} \left( {{}^{T}K_{2}^{\text{H}} } \right) = 2.515 \pm 0.009 $$ and $$ \log_{10} \left( {{}^{T}K_{3}^{\text{H}} } \right) = 1.06 \pm 0.002 $$ (carboxylic groups). The formation constants of HEIDA complexes with sodium, calcium and magnesium were determined. In the first case, the formation of a weak complex species, NaL, was found and the stability constant value at infinite dilution is log10KNaL = 0.78 ± 0.23. For Ca2+ and Mg2+, the CaL, CaHL, CaL2 and MgL species were found, respectively. The calculated stability constants for the calcium complexes at T = 298.15 K and I = 0.150 mol·dm−3 are: log10βCaL = 4.92 ± 0.01, log10βCaHL = 11.11 ± 0.02 and $$ \log_{10} \beta_{\text{Ca{L}}_{2}} $$ = 7.84 ± 0.03, while for the magnesium complex (at I = 0.176 mol·dm−3): log10βMgL = 2.928 ± 0.006. Protonation thermodynamic functions have also been calculated and interpreted.

Thermodynamic parameters for the interaction between etidronic acid and inorganic and organic mercury(II)

Abstract Thermodynamic parameters of etidronic acid [(1-Hydroxy-1,1-ethanediyl)bis(phosphonic acid), HEDPA] interaction with Hg2+ and CH3Hg+ were determined in NaCl aqueous solution at different ionic strength values (0.1 ≤ I ≤ 1 mol·L−1) and at T = 298.15 K. For Hg2+ system, ML2−, MLH20, MLH3+ and ML(OH)3− species were obtained. In presence of CH3Hg+, ML3−, MLH2−, MLH2−, MLH30 and the dinuclear M2LH− and M2LH20 species were determined with formation constant values lower respect to the Hg2+ species. As an example, log β = 7.98 and 15.61 were obtained for (CH3Hg)L3− and HgL2− species, respectively (at I ≈ 0.1 mol·L−1 and T = 298.15 K). The dependence of the stability constants on ionic strength, studied through a Debye-Huckel type equation, is also reported. To enrich the thermodynamic study, the enthalpy values of the complex species were obtained by calorimetric titrations at I = 0.1 mol·L−1 in NaCl and T = 298.15 K. Finally, the sequestering ability of HEDPA towards Hg2+ and CH3Hg+ was calculated by means of an empirical parameter, known as pL0.5, under blood (I = 0.1 mol·L−1, pH = 7.4, T = 310.15 K) and sea water (I = 0.7 mol·L−1, pH = 8.1, T = 298.15 K) conditions. pL0.5 represents the total ligand concentration required to sequester the 50% of a metal cation present as traces.

Thermodynamics (Solubility and Protonation Constants) of Risedronic Acid in Different Media and Temperatures (283.15–318.15 K)

Potentiometric measurements were carried out to study the protonation constants of risedronic acid (RA) in NaCl(aq), (CH3)4NCl(aq) and (C2H5)4NI(aq) at different ionic strengths and temperatures (283.15 ≤ T/K ≤ 318.15). In the same conditions, solubility measurements were also performed. Calorimetric measurements were done in NaCl to determine the protonation enthalpy values at I = 0.15 mol·dm−3 and 298.15 K. Generally, the proton binding process was endothermic and the driving force was entropic in nature. The values of the protonation constants determined in NaCl(aq) are lower than those obtained in the two tetraalkylammonium salts. The medium effect was interpreted using different thermodynamic models in terms of variation of the activity coefficients with ionic strength (Debye–Huckel type and SIT), or formation of weak complexes between risedronate (Ris4−) and the ions of the supporting electrolytes. Specific interaction coefficients (e) and the stability of five (CH3)4N+/Ris4− (at different temperatures and ionic strengths) species are reported. The total solubility of risedronic acid is higher in NaCl(aq) than in the other two ionic media and, in all cases, increases with increasing temperature. Setschenow and activity coefficients of the neutral species were also computed in all ionic media.

Acid–Base and Thermodynamic Properties ofd-Gluconic Acid and Its Interaction with Sn2+and Zn2+

In this paper, new potentiometric, calorimetric, and voltammetric measurements are reported to model the behavior of d-gluconic acid in aqueous NaCl(aq) and NaNO3(aq) ionic media at different ionic strengths and temperatures (283.15 ≤ T/K ≤ 318.15) also in the presence of Sn2+ and Zn2+. The protonation constants of d-gluconic acid (Gluc– in its deprotonated form) in NaCl(aq) and NaNO3(aq) are very similar. The dependence on ionic strength of the protonation constant was modeled by means of the extended Debye–Huckel type equation, the Specific ion Interaction Theory (SIT) and a weak interaction model. At infinite dilution and T = 298.15 K, the thermodynamic parameters for the proton binding reaction, determined by direct calorimetric titrations and temperature gradients of protonation constants, are log KH0 = 3.709 ± 0.004, ΔG0 = −21.18 ± 0.01 kJ mol–1, ΔH0 = −4.56 ± 0.04 kJ mol–1, and TΔS0 = 16.6 ± 0.1 kJ mol–1, indicating that the reaction is exothermic and entropic in nature. Potentiometric and voltamme...

Thermodynamic Study on the Protonation and Complexation of GLDA with Ca2+and Mg2+at Different Ionic Strengths and Ionic Media at 298.15 K

The protonation constants (log KiH) of l-glutamic acid N,N-diacetic acid tetrasodium salt (GLDA) were determined at T = 298.15 K and various ionic strengths in NaCl(aq), 0.18 ≤ I ≤ 3.20 mol·kg–1, (CH3)4NCl(aq) 0.17 ≤ I ≤ 4.00 mol·kg–1, and (C2H5)4NI(aq) 0.13 ≤ I ≤ 1.10 mol·kg–1 by using the potentiometric method. The calculation of ionic strength dependence parameters was performed by Debye–Huckel type equation, Specific ion Interaction Theory (SIT). and Pitzer equations (only for NaCl(aq)). These equations make it feasible to calculate and predict the protonation constants of GLDA in the desired range of ionic strength theoretically. The values of pure water protonation constants are log K1H 10.558 ± 0.028, log K2H 5.348 ± 0.011, log K3H 3.088 ± 0.015 and log K4H 1.918 ± 0.009, the first protonation refers to the nitrogen group and the other three to carboxylate groups. The different values of log KiH obtained in NaCl(aq), (CH3)4NCl(aq), and (C2H5)4NI(aq) were interpreted in terms of formation of weak co...

Thermodynamic Data for the Modeling of Lanthanoid(III) Sequestration by Reduced Glutathione in Aqueous Solution

This contribution reports the results of an investigation on the speciation of various lanthanoid(III) cations (Ln3+), namely, La3+, Nd3+, Sm3+, Eu3+, Gd3+, Dy3+, and Yb3+, in the presence of reduced glutathione (or simply glutathione, GSH), in NaCl(aq) at I = 0.15 mol·dm–3 and T = 298.15 K. GSH forms in all cases the same four species, namely, Ln(GSH)H3, Ln(GSH)H2, Ln(GSH)H, and Ln(GSH)OH, whose stability depends on the type of lanthanoid, although it is also possible to consider an average stability for a generic lanthanoid, at least for the protonated species. Measurements at different temperatures and ionic strengths for the La3+/GSH and Gd3+/GSH systems have also been performed, to evaluate their effect on the speciation of both GSH and the Ln3+ cations. The dependence of the determined stability constants on I and T has been modeled by an extended Debye–Huckel type and by the van’t Hoff equations. In this last case, the formation enthalpy changes of La3+/GSH species have also been determined. The st...

Interaction mechanisms between dust grains in the presence of asymmetric ion flow and an external magnetic field in complex plasma

We have reported a theoretical study on the interaction mechanism between dust particles in the presence of asymmetric ion flow and an external magnetic field in complex plasma. The recent experimental and numerical results on the particle-wake interaction ensures the dominance of the wake effect in the subsonic regime of plasma flow using the cold ion approximation. The recent developments in dusty plasma research and its growing interest towards more realistic magnetized dusty plasma scenarios also demand serious attention to study the wake effect both in the sub and supersonic regimes in the presence of a magnetic field. It is a challenging task to develop a correct, quantitative theory of wake potential for different regimes of magnetic field and ion flow velocity. Analytic expressions for the wake potential have been reported in this paper for both subsonic and supersonic regimes in the presence of an external magnetic field along with Debye-Huckel type potentials. The results show that the wake potential plays a dominant role in the subsonic regime and its strength increases with an increase in magnetic field. The behaviour of the wake potential is found to have an interesting effect on the Coulomb crystallization of dust grains and is studied with the help of molecular dynamic (MD) simulation.

Some Thermodynamic Properties of Aqueous 2-Mercaptopyridine-N-Oxide (Pyrithione) Solutions

The thermodynamic properties of 2-mercaptopyridine-N-oxide (pyrithione, PT) were studied potentiometrically in NaCl aqueous solutions at different ionic strengths and temperatures. A set of protonation constants is provided, together with distribution (water/2-methyl-1-propanol) and solubility data. The total and the specific solubility (solubility of neutral species) values of pyrithione were determined and, for example, are 0.0561 and 0.0518 mol·dm−3 at cNaCl = 0.244 mol·dm−3 and T = 298.15 K. By fitting the distribution and solubility results against the ionic strength, the Setschenow coefficient and the activity coefficients of the neutral species were determined. In pure water, the specific solubility is log10\( S_{m 0}^{0} = \, {-} 1. 20 \, \pm \, 0.0 4 \). To determine the activity coefficient of the charged species and the protonation constant at infinite dilution, the data were analyzed by different models, namely the Debye–Huckel type equation, the SIT (Specific ion Interaction Theory) and the Pitzer approach. The interaction coefficient of the deprotonated pyrithione species was determined [e(Na+, PT−) = −0.105 ± 0.002]. The protonation enthalpy was also determined, is slightly positive, and the protonation process is entropic in nature. At infinite dilution and T = 298.15 K, log10KH0 = 4.620 ± 0.002, ΔG0 = –26.4 ± 0.1 kJ·mol−1, ΔH0 = 2.1 ± 0.5 kJ·mol−1 and TΔS0 = 28.5 ± 0.5 kJ·mol−1. The electrochemical behavior of pyrithione was studied in NaCl solutions at T = 298.15 K. It was found that voltammetry can be used to study the binding ability of pyrithione towards metal cations. The results of this work are in agreement with literature findings and improve the knowledge of the chemistry of pyrithione in aqueous solutions.

Speciation and Stability of Dioxovanadium(V) Complexes with Diethylenetriaminepentaacetic Acid at Different Ionic Strengths

UV spectroscopic measurements have been used to determine the binding ability of diethylenetriaminepentaacetic acid (DTPA) ligand towards the $$ {\text{VO}}_2^+ $$ ion at different ionic strengths of sodium chloride (0.11–0.95 mol·dm−3) and at T = 298 K. Dissociation constants of DTPA have been gathered from the literature. Calculations allowed us to identify the formation of three species VO2H3L, VO2H2L− and VO2HL2− in the pH range of about 1.00–2.50. All of these complexes were characterized in terms of their stability constants on the basis of two different thermodynamic models (extended Debye–Huckel type and specific ion interaction theory) for the investigation of the ionic strength dependence of the stability and dissociation constants. Comparison with literature data is also reported.

Lowest lying doubly-excited P-and D-state resonances of Ps− in weakly coupled plasmas

The lowest-lying 1, 3Po and 1De resonances of positronium negative ion, Ps−, in weakly coupled plasmas have been investigated employing the close-coupling approximation. Three different basis sets have been employed in the present study. The plasma screening condition obtained from the Debye-Huckel type potential is used to represent the interaction between the charged particles. The resonance energies and the corresponding widths of one 1Po, two 3Po, and one 1De resonant states associated with the n = 2 threshold of the positronium atom for various Debye lengths ranging from infinity to small values are reported. The 1Po resonance as well as the higher lying 3Po resonant state transforms to a shape resonance for denser plasma conditions. The 1De resonant state also changes to a shape-type resonance for very dense plasmas.

Complexation of Dioxovanadium(V) with D-(-)-Quinic Acid at Different Ionic Strengths Using Different Models Based on the Debye-Hückel Theory

The complex formation reaction between the dioxovanadium(V) cation \(\mathrm{VO}_{2}^{+}\) and D-(-)-quinic acid {(1R,3R,4S,5R)-(-)-1,3,4,5-tetrahydroxycyclohexane-1-carboxylic acid} has been studied in aqueous solutions. The UV data and the values of the derived conditional stability constants are presented and discussed in the light of one stoichiometric model for the reaction at T=298 K and different ionic strengths (0.10 to 1.00) mol⋅dm−3 of sodium chloride. Speciation diagrams and dissociation constants were obtained on the basis of UV spectroscopic measurements and potentiometric titrations, respectively. Our results show that one complex species, VO2L, exists in solution in the pH range of about 1.00 to 3.00. The parabolic, Specific Ion Interaction Theory (SIT), and extended Debye-Huckel type (EDH) models successfully describe the ionic strength dependence of the stability constants. A comparison with literature data is also reported.

Investigation on the Complexation of Molybdenum(VI) with d-(−)-Quinic Acid at Different Ionic Strengths

Potentiometric and UV spectroscopic measurements have been carried out to determine the stability constants for the complexation of the MoO42– ion with d-(−)-quinic acid {(1R,3R,4S,5R)-(−)-1,3,4,5-tetrahydroxycyclohexane-1-carboxylic acid} in sodium chloride aqueous solutions for ionic strengths between (0.10 to 1.00) mol·L–1 of sodium chloride at T = 298 K. The Job method of continuous variations was applied for the determination of the metal-to-ligand ratio which was 1:1 at pH = 6.50. Extended Debye–Huckel type (EDH), specific ion interaction theory (SIT), and parabolic equations were investigated to derive the necessary ionic strength dependence parameters, and the results were justified.

Complex Formation of the Cerium(IV) Ion with Glycyl-Glycine at Different Ionic Strengths

The protonation equilibria of glycyl-glycine and its complex formation with the cerium(IV) ion in aqueous solution were studied over a wide pH range (2 to 12) using a combination of potentiometric and spectrophotometric methods at constant temperature (25 °C) and different ionic strengths [(0.02, 0.05, 0.10, 0.15, 0.30, 0.50, 0.70, and 1.00) mol·dm–3 sodium perchlorate]. Least-squares regression calculations are consistent with the formation of the CeL3+ and CeHL4+ species for the studied system, where L– represents the deprotonated peptide. The species concentrations were plotted at different pH values and were discussed. The dependence of the protonation of the ligand and the stability constant of the complex species on ionic strength is described by a Debye–Huckel type equation, and finally the results have been compared with the values reported previously and interpreted.

Thermodynamic Protonation Parameters of some Sulfur-Containing Anions in NaClaq and (CH3)4NClaq at t=25 °C

Protonation constants of one thiocarboxylate (thioacetate) and four sulfur-containing carboxylates (2-methylthioacetate, thiolactate, thiomalate, 3-mercaptopropionate) were determined by potentiometric measurements in a wide ionic strength range [0≤I≤5 mol⋅L−1 in NaCl and 0 ≤I≤3 mol⋅L−1 in (CH3)4NCl] at t=25 °C. For two of these ligands (2-methylthioacetate and thiolactate), the protonation enthalpies were also determined by calorimetric measurements in NaCl ionic medium [0 ≤I≤5 mol⋅L−1] at t=25 °C. Individual UV spectra of the protonated and unprotonated 3-mercaptopropionate species, together with values of the protonation constants, were obtained by spectrophotometric titrations. Results were analyzed in terms of their dependence on the ionic medium by using different thermodynamic models [Debye-Huckel type, SIT (Specific ion Interaction Theory) and Pitzer’s equations]. Differences among protonation constants obtained in different media were also interpreted in terms of weak complex formation.

Comparison of the application of Debye-Huckel and specific ion interaction theories for the complexation of tungsten(VI) with ethylenediaminediacetic acid

Equilibrium of the reaction of tungsten(VI) with ethylenediaminediacetic acid (EDDA) has been investigated in aqueous solution of pH 7.5 and 25°C. All measurements have been carried out at different ionic strengths ranging from (0.1 to 1.0) mol dm−3 (NaClO4). According to our results the metal to ligand ratio is 1: 1. Stability constants and stoichiometry of the complex have been determined from a combination of potentiometric and UV spectroscopic measurements. In this semi-empirical model, two parameters have been introduced in a Debye-Huckel type equation based on the Gauss—Newton nonlinear least-squares method and minimizing the sum of the squares of the errors. Comparison of the ionic strength effect on these complex formation reactions has been made using a Debye-Huckel type equation and Bronsted—Guggenheim—Scatchard specific ion interaction theory (SIT).