Comparison of electrical double layer models postulating the linear or quadratic dependence of the anion adsorption energy on the electrode charge

Equations for calculating the concentration of a singly charged specifically adsorbed anion, the electrode potential, the differential capacitance, and interface tension are derived under the condition that the anion transition from the outer to the inner Helmholtz plane is described by the Frumkin isotherm and the energy of this transition (βG _A) is a quadratic function of the electrode charge q. By the example of the Hg/[H₂O + mc NH₄NO₃ + (1 − m)c NH₄F] system, it is shown that in contrast to the linear ΔG _A vs. q dependence, the quadratic dependence allows the differential capacitance curves to be adequately described throughout the m range. However, this model gives no way of describing the transition from the quadratic δG _A vs. q dependence for small m to the linear dependence observed experimentally in binary solutions with m = 1.     

Description of the Hg/[H<Subscript>2</Subscript>O + <Emphasis Type="Italic">mc</Emphasis> KCl + (1 − <Emphasis Type="Italic">m</Emphasis>)<Emphasis Type="Italic">c</Emphasis> KF] system in terms of the modified model of electrical double layer

Specific adsorption of anion Cl⁻ at the Hg/H₂O interface from mixed solutions mc KCl + (1 − m)c KF is analyzed in terms of a recently put forward modified model of electrical double layer. The calculations showed that the modified model of electrical double layer not only adequately gives the form of experiment curves of differential capacitance but also allows explaining the deviation from linearity of the dependence of the adsorption energy on the electrode charge. Of importance is a decrease in the dense layer capacitance when passing from KF to KCl under the condition of constant surface coverage with the Cl⁻ ions. The results of calculations in terms of the modified model of electrical double layer are compared with those obtained in terms of the Sanz-Gonzalez model.     

Specific adsorption of bromide and iodide ions from N-methyl formamide solutions with constant ionic strength on liquid ga electrode

The differential capacitance curves were measured with an ac bridge in the Ga/[N-MF + 0.1 m M KBr + 0.1 (1 − m) M KClO₄] and Ga/[N-MF + 0.1 m M KI + 0.1 (1 − m) M KClO₄] systems at the following fractions m of surface-active anions: 0, 0.01, 0.02, 0.05, 0.1, 0.2, 0.5, and 1. As compared with other solvents, N-methyl formamide (N-MF) enables one to realize the largest positive charges of Ga electrode, at which it remains ideally polarizable (up to 20 μ/cm²). The data on the specific adsorption of Br⁻ and I⁻ anions in the system can be quantitatively described by the Frumkin’s isotherm; to the first approximation, free energy of halide ion (Hal⁻) adsorption DG_{adsHal ^{- 1}} \Delta G_{adsHal^{ - 1} } is a linear function of electrode charge. It is found that, in contrast to the Hg/N-MF interface, DG_{adsHal ^{- 1}} \Delta G_{adsHal^{ - 1} } at the Ga/N-MF interface varies in the reverse order: Br^t— ∼ I⁻ < Cl⁻. From the measured results, we can conclude that the energy of metal-Hal⁻ interaction increases in series: $\Delta G_{M - Cl^ - } > \Delta G_{M - Br^ - } > \Delta G_{M - I^ - } $\Delta G_{M - Cl^ - } > \Delta G_{M - Br^ - } > \Delta G_{M - I^ - } and the difference (DG_{Ga - Hal1^-} - DG_{Ga - Hal2^-} )(\Delta G_{Ga - Hal_1^ - } - \Delta G_{Ga - Hal_2^ - } ) is larger than the difference between the solvation energies of Hal^- (DG_{S - Hal1^-} - DG_{S - Hal2^-} )Hal^ - (\Delta G_{S - Hal_1^ - } - \Delta G_{S - Hal_2^ - } ).     

Modified model of electrical double layer for mixed solutions of constant ionic strength

A model is suggested, which generalized the Alekseev-Popov-Kolotyrkin model for the case of mixed solutions of constant ionic strength of the type mc KA_*⁻ + (1 − m)c KA, where A_*⁻ is the surface-active anion that lowers the electrical double layer capacitance as compared with that observed in the presence of surface-inactive anion A⁻. Calculations made for a real system mc NaNO₃ + (1 − m)c NaF showed that at 0.2 ≤ m ≤ 1 a transition occurred from quadratic to linear dependence of adsorption energy on the electrode potential (or charge). The conclusions are in agreement with experimental data obtained for the studied system.     

Specific adsorption of chloride ions on liquid Ga electrode from N-methylformamide solutions with constant ionic strength

Differential capacitance curves are measured by mans of an ac-bridge in the system Ga/[N-MF + 0.1m M KCl + 0.1(1 − m) M KClO₄] with the surface-active anion taken in the following molar fractions m: 0, 0.01, 0.02, 0.05, 0.1, 0.2, 0.5, and 1. As compared with the other solvents, N-methylformamide (N-MF) makes it possible to realize the highest positive charges of the Ga electrode at which the electrode remains ideally polarizable (up to 20 μC/cm²). The data on the specific adsorption of Cl⁻ ions in the mentioned system can be described qualitatively by the Frumkin isotherm in which the free energy is considered as a linear function of the electrode charge.     

Micellization of dodecyldimethylethyl- ammonium bromide in aqueous solution

Specific conductivity of aqueous solutions of dodecyldimethylethylammonium bromide has been determined in the temperature range of 15-40°C. The critical micelle concentration (cmc) and ionization degree of the micelles, b, were determined from the data. Thermodynamic functions, such as standard Gibbs free energy, ΔG _m°, enthalpy, ΔG _m°, and entropy, ΔG _m°, of micellization, were estimated by assuming that the system conforms to the mass action model. The change in heat capacity upon micellization, ΔG _m°, was estimated from the temperature dependence of ΔG _m°. An enthalpy-entropy compensation phenomenom for the studied system has been found. This revised version was published online in July 2006 with corrections to the Cover Date.     

Volumetric and Transport Properties of Ternary Mixtures Containing 1-Butanol or 1-Pentanol,Triethylamine and Cyclohexane at 303.15 K: Experimental Data,Correlation and Prediction by the ERAS Model

The excess molar volumes, V _m^E, viscosity deviations, Δη, and excess Gibbs energies of activation, ΔG ^*E, of viscous flow have been investigated from density and viscosity measurements for two ternary mixtures, 1-butanol + triethylamine + cyclohexane and 1-pentanol + triethylamine + cyclohexane, and corresponding binaries at 303.15 K and atmospheric pressure over the entire range of composition. The empirical equations due to Redlich-Kister, Kohler, Rastogi et al., Jacob-Fitzner, Tsao-Smith, Lark et al., Heric-Brewer, and Singh et al. have been employed to correlate V _m^E, Δη and ΔG ^*E of the ternary mixtures with their corresponding binary parameters. The results are discussed in terms of the molecular interactions between the components of the mixture. Further, the Extended Real Associated Solution, ERAS, model has been applied to V _m^E for the present binary and ternary mixtures, and the results are compared with experimental data.     

Studies on CMC and thermodynamic function of anionic surfactants in DMA/long-chain alcohol systems using microcalorimetric method

The critical micelle concentration (CMC) and the thermodynamic function of the anionic surfactant, sodium laurate (SLA) and sodium dodecyl sulfate (SDS) in the N,N-dimethyl acetamide (DMA)/long-chain alcohol systems were studied using titration microcalorimetric method. The power-time curves of SLA and SDS in the presence of a long-chain alcohol (n-heptanol, n-octanol, n-nonanol, n-decanol) in the DMA medium were determined. Then, from the curves, the critical micelle concentration (CMC) and the thermodynamic standard formation functions (ΔH ^ϑ _m, ΔG ^ϑ _m and ΔS ^ϑ _m) were obtained through thermodynamic theories. The relationships between temperature, alcohol’s carbon number, concentration and thermodynamic properties were discussed. For SLA or SDS in a DMA solution, under the same concentration of alcohol, the values of CMC, ΔH ^ϑ _m and ΔS ^ϑ _m increase, while the value of ΔG ^ϑ _m decrease with the increase of temperature. Under the same condition of identical temperature and alcohol concentration, the values of CMC, ΔH ^ϑ _m, ΔG ^ϑ _m and ΔS ^ϑ _m decrease with the increase of the alcohol’s carbon number. In the presence of the same kind of alcohol, the values of CMC and ΔG ^ϑ _m increase, but the values of ΔH ^ϑ _m and ΔS ^ϑ _m decrease with the concentration increases in alcohol series at the same temperature. __________ Translated from Acta Chimica Sinica, 2007, 65(10): 906–912 [译自: 化学学报]     

Study of an Alcohol’s Influence on the CMC and Thermodynamic Functions of Anionic Surfactants in DMA/Long-chain Alcohol Solutions Using a Microcalorimetric Method

The power-time curves for the micelle formation process were determined for two anionic surfactants, sodium laurate (SLA) and sodium dodecyl sulfate (SDS), in mixed alcohol + N,N-dimethylacetamide (DMA) solvent using titration microcalorimetry. From the data of the lowest point and the area of the power-time curves, their critical micelle concentration (CMC) and ΔH _m^o were obtained. The other thermodynamic functions of the micellization process (ΔG _m^o and ΔS _m^o) were also calculated with thermodynamic equations. For both surfactants, the effects of the carbon number (chain length) of the alcohol, the concentration of alcohol, and the temperature on the CMC and thermodynamic functions are discussed. For systems containing identical concentrations of a different alcohol, values of the CMC, ΔH _m^o and ΔS _m^o increased whereas ΔG _m^o decreased with increasing temperature. For systems containing an identical alcohol concentration at the same temperature, values of the CMC, ΔH _m^o,ΔG _m^o and ΔS _m^o decrease with increasing carbon number of alcohol. For systems containing the same alcohol at the same temperature, the CMC and ΔG _m^o values increase whereas ΔH _m^o and ΔS _m^o decrease with increasing alcohol concentration.     

Studies on the CMC and Thermodynamic Functions of a Cationic Surfactant in DMF/Long-Chain Alcohol Systems Using a Microcalorimetric Method

The power-time curves of the micelle formation process were determined at four temperatures for a cationic surfactant [cetyltrimethylammonium bromide (CTAB)] in a non-aqueous solvent [N,N-dimethylformamide (DMF)] by titration microcalorimetry. From the data of the minimum of the titration point and the area of the power-time curves, values of their CMC and ΔH _m ^θ were obtained. Values of ΔG _m ^θ and ΔS _m ^θ were also calculated according to standard thermodynamic relations. For the cationic surfactant CTAB, the relationships involving the carbon numbers of the alcohols, the alcohol’s concentration, and the temperature on the CMC, and also the thermodynamic functions for micellization are discussed. For systems containing an identical concentration of various alcohols, values of the CMC, ΔH _m ^θ and ΔS _m ^θ increased whereas those of ΔG _m ^θ decreased with increasing temperature. For systems containing identical alcohol concentrations at the same constant temperature, values of the CMC, ΔH _m ^θ ,ΔG _m ^θ and ΔS _m ^θ decreased with increasing carbon number of the alcohol. For systems containing the same alcohol at the same temperature, the CMC and ΔG _m ^θ values increased whereas ΔH _m ^θ and ΔS _m ^θ decreased with increasing alcohol concentration.     

Thermodynamics of mixed-ligand complexation of gadolinium ethylenediaminetetraacetate with amino acids in aqueous solution

Mixed-ligand complexation of GdEdta⁻ with glycinate, L-glutamate, DL-aspartate, iminodiacetate, and nitrilotriacetate anions in aqueous solutions at 298.15 K and the ionic strength I = 0.5 (KNO₃) was studied. The thermodynamic parameters (logK, Δ _r G, Δ _r H, Δ _r S) of these reactions were determined from calorimetric and pH-metric data. The most probable way of coordination of the amino acids in the heteroleptic complexes is discussed.     

Search for a model to describe the specific adsorption of anions A? in Ga/[N-Methylformamide + mc KCl + (1 ? m)c KClO4] Systems, where KA is KCl, KBr, or KI

The adsorption parameters for systems Ga/[NMF + 0.1m M KCl + 0.1(1 ? m) M KClO₄], Ga/[NMF + 0.1m M KBr + 0.1(1 ? m) M KClO₄], and Ga/[NMF + 0.1m M KI + 0.1(1 ? m) M KClO₄] are calculated by using the regression analysis of the adsorption potential shift vs. electrode charge dependences for the following molar fractions m of the surface-active anion: 0.05, 0.1, 0.2, 0.5, and 1 within the framework of two models. The models are based on the Frumkin isotherm with the free adsorption energy dependent on the electrode charge, of which one model takes into account the diffuse layer and the other ignores it. It is shown that for electrode charges q ?? 16 ??C/cm², both models provide equal accuracy; however, for higher q, preference should be given to the model that takes into account the contribution of the double layer diffuse part.     

Micellization of cetyltrimethylammonium bromide in the presence of 9-anthryl alkanols

 Surface tension measure-ments in aqueous cetyltrimethyl ammonium bromide were performed in presence of various amounts of 9-(hydroxymethyl)anthracene (AM), 9-[1-(1-hydroxy)ethyl]anthracene (THAE), and 9-[1-(1-hydroxy-2,2,2-trifluoro)ethyl]anthracene (TFAE). Free energies ΔG ^⊖ _m and ΔG ^⊖ _i of micellization and of adsorption to the air–water interface, respectively, were determined as well as the corresponding enthalpies and entropies. ΔG ^o− _m of micellization increased in the presence of AM and THAE, but became more negative when TFAE was added. In contrast to AM and THAE, TFAE addition decreases ΔS ^⊖ _i. For this peculiarity of TFAE, its location and orientation in micellar solution was investigated by means of UV and ¹⁹F-NMR spectroscopy. Received: 26 March 1997 Accepted: 16 May 1997     

Effect of temperature on thermodynamic characteristics of the dissociation of glycylglycine in aqueous solutions of electrolytes

Heats of reaction of glycylglycine with nitric acid and potassium hydroxide solutions are determined by two calorimetric procedures at 288.15, 298.15, 308.15 K and an ionic strength of solution of 0.25, 0.50, and 0.75 in the presence of KNO₃. Standard thermodynamic characteristics (Δ_r H°, Δ_r G°, Δ_r S°, and Δ_p C°) are calculated for the acid-base reactions in aqueous peptide solutions. The effects of the concentration of background electrolyte and temperature on the heats of dissociation of glycylglycine are considered.     

Effect of salt concentrations on the displacement adsorption enthalpies of denatured protein folding at a moderately hydrophobic surface

Lead(II) complexes of reduced glutathione (GSH) of general composition [Pb(L)(X)]·H₂O (where L=GSH; X=Cl, NO₃, CH₃COO, NCS) have been synthesized and characterized by elemental analyses, infrared spectra and electronic spectra. Thermogravimetric (TG) and differential thermal analytical (DTA) studies have been carried out for these complexes. Infrared spectra indicate deprotonation and coordination of cysteinyl sulphur with metal ion. It indicates the presence of water molecule in the complexes that has been supported by TG/DTA. The thermal behaviour of complexes shows that water molecule is removed in first step-followed removal of anions and then decomposition of the ligand molecule in the subsequent steps. Thermal decomposition of all the complexes proceeds via first order kinetics. The thermodynamic activation parameters, such as E*, A, ΔH*, ΔS* and ΔG* have been calculated. The geometry of the metal complexes has been studied with the help of molecular modeling for energy minimization calculation.     

Studies on the electrochemical and thermodynamic behaviour of Hg-HgS electrode in the presence of sulphide ions

Mercury-mercury (II) sulphide electrode has been prepared and its electrochemical and thermodynamic behaviour has been studied in different media. The electrode is found to show Nernstian response to pS (− log [S²⁻]) over the range 5.19–10.38. In the pH range 7.96–11.98, at constant [S²⁻]_v, its response is also Nernstian. The values of thermodynamic functions, viz., ΔG⁰. ΔH⁰, and ΔS⁰ for the electrode reaction: Hg₍₃)+S²⁻ _aμ ⇌HgS_(s)+2e, have been determined. Further, the standard free energy of formation (ΔG _f ⁰ ) and solubility product constant (K _vp ) of HgS in aqueous medium at 25±0.1°C have also been determined.     

Effect of dielectric medium on angiotensin converting enzyme inhibitors binding to Zn<Superscript>2+</Superscript>

The Becke3LYP density functional was used to study structural and thermodynamic parameters of bivalent zinc cation complexes with selected substrates and ACE inhibitors (H₂O/OH⁻, neutral forms of captopril, zofenoprilat, omapatrilat, CH₃CONHCH₃, and N-terminal anions of captopril, zofenoprilat, omapatrilat, enalaprilat, perindoprilat, trandolaprilat, and fosinoprilat). The combination of DFT and the conductor-like polarizable continuum model (CPCM) were employed to compute the Gibbs interaction energies (ΔG) between Zn²⁺ and the selected ACE inhibitors for dielectric media with ɛ = 5 (to simulate the protein environment) and for water media (ɛ = 78.39) for comparison purposes. The results show that ΔG is sensitive to the dielectric constant of the environment and that lower dielectric medium favors the binding of inhibitors to the zinc cation.     

Thermodynamic investigation of effect of salt concentrations on denatured α-Amylase adsorbed onto a moderately hydrophobic surface

The displacement adsorption enthalpies (ΔH) of denatured α-Amylase (by 1.8 mol L⁻¹ GuHCl) adsorbed onto a moderately hydrophobic surface (PEG-600, the end-group of polyethylene glycol) from solutions (x mol L⁻¹ (NH₄)₂SO₄, 0.05 mol L⁻¹ KH₂PO₄, pH 7.0) at 298 K are determined by microcalorimeter. Further, entropies (ΔS), Gibbs free energies (ΔG) and the fractions of ΔH, ΔS, and ΔG for net adsorption of protein and net desorption of water are calculated in combination with adsorption isotherms of α-Amylase based on the stoichiometric displacement theory for adsorption (SDT-A) and its thermodynamics. It is found that the displacement adsorptions of denatured α-Amylase onto PEG-600 surface are exothermic and enthalpy driven processes, and the processes of protein adsorption are accompanied with the hydration by which hydrogen bond form between the adsorbed protein molecules favor formation of β-sheet and β-turn structures. The Fourier transformation infrared spectroscopy (FTIR) analysis shows that the contents of ordered secondary structures of adsorbed α-Amylase increase with surface coverages and salt concentrations increment.     

Metallosurfactants of Chromium(III) Coordination Complexes. Synthesis, Characterization and Determination of CMC Values

A number of mixed ligand chromium(III)–surfactant coordination complexes, of the type cis-[Cr(en)₂(A)X]²⁺ and cis-α-[Cr(trien)(A)X]²⁺ (A = Dodecyl or Cetylamine; X = F⁻, Cl⁻, Br⁻) were synthesized from the corresponding dihalogeno complexes by ligand substitution. These compounds form foam in aqueous solution when shaken. The critical micelle concentration (CMC) values of these surfactant metal complexes in aqueous solution were obtained from conductance measurements. Specific conductivity data (at 303, 308 and 313 K) served for evaluation of the temperature-dependent critical micelle concentration (cmc) and the thermodynamics of micellization (Δ G_m⁰, Δ H_m⁰ and Δ S_m⁰).     

Study of the adsorption of cytochrome c on a gold nanoparticle – modified gold electrode by using cyclic voltammetry, electrochemical impedance spectroscopy and chronopotentiometry

Adsorption of cytochrome c (Cyt c) on a gold nanoparticle – modified gold electrode was studied by using cyclic voltammetry, electrochemical impedance spectroscopy and chronopotentiometry in a phosphate buffer solution. It is shown that the charge transfer resistance is directly proportional to the amount of adsorbed Cyt c. The effects of temperature and time on the course of adsorption were also studied. The trends obtained in ΔG_ADS showed that Cyt c was found to have a smaller affinity for the modified electrode as indicated by their smaller negative ΔG_ADS values.