M. Salve

Differential capacity curves at adsorption of organic ions: Model approach II

Abstract Theoretical analysis of the double-layer model has been carried out in the presence of the specific adsorption of organic cations accompanied by considerable increase of the inner-layer dimensions. The formulae for calculation of the differential capacity curves of an electrode have been derived. A flat minimum at high negative charges, caused by the diffuse structure of the double layer, has been predicted on the capacity curves. The presence of such minima has been verified experimentally on the mercury and bismuth electrodes. By computer calculation it has been shown that, although. relatively good agreement of the theoretically calculated capacity curves with the experimental curves could he obtained, a physically unrealistic interaction parameter of the specifically adsorbed ions had to be used. As demonstrated, this result is a result of the double-layer model assuming linear dependence of the inner-layer integral capacity of the surface coverage and its independence from the electrode charge.

Adsorption isotherm of ions on electrodes for solutions with constant ionic strength

Summary In the present work the equation of the isotherm for describing the specific adsorption of ions on electrodes from the system of mixed electrolytes with constant ionic strength was derived. In the derivation the buffering effect of the diffuse part of the electrical double layer, which changes by varying the ratio between the surface-active and inactive components in the system, was taken into consideration. The experimental verification of the derived isotherm was carried out on a solid bismuth electrode by studying the specific adsorption of Cs+ from the aqueous and methanolic solutions of the mixed electrolytes LiCl and CsCl at the different values of the constant ionic strength (0.01, 0.03, 0.1, etc.). The adsorption of Cs+ was studied by the differential capacity measurement method. It was found on the basis of the data obtained that the derived isotherm can successfully be applied for the quantitative characterization of the specific adsorption of Cs+ on bismuth only if the assumptions made in the derivation of the isotherm are valid (the absence of specific adsorption of anions in the case of recharge of the electrode by the cations). In full agreement with the equation of the isotherm the graphical plots of { log u2061 ( e 1 / m c 2 ) + ( 1 − f ) [ log u2061 c + 1 2 m log u2061 m + 1 2 ( 1 − m ) log u2061 ( 1 − m ) ] } against e1 give at the constant charge one common line for different ionic strengths of the systems. The parameters of these plots give the constant of the adsorption equilibrium β and the second virial coefficient B. The constant β is, within the limits of experimental error, independent of the ionic strength of the solution, both for water and methanol, and depends linearly on the charge of the electrode. The specific adsorption of Cs+ is stronger from methanol than from the aqueous solutions.

Comparison of the ionic adsorption theories for the electrode/solution interface by computer simulation

Abstract A computer simulation method for the analysis of the ionic adsorption in mixed electrolyte systems with constant ionic strength has been elaborated. It has been shown that the effects due to counter ion coadsorption in the inner layer and to the competitive adsorption of the reference ions, can distort significantly the specific adsorption values obtained by the sensitive calculation methods excluding numerical differentiation. Peculiarities of contemporary double-layer models (the Grahame-Parsons, Alekseev-Popov-Kolotyrkin and Vorotyntsev theories) have been revealed by analysis of a number of different model systems with known true specific adsorption values assuming an independence of the inner-layer capacity on specific adsorption. Criteria for the identity and applicability limits of the models considered have been established.

Comparison of isotherms for specific adsorption of ions from constant ionic strength solutions

Summary It has been shown that the specific adsorption of caesium ions from the constant ionic strength system can be described at the bismuth-aqueous solution interface by the virial isotherm, including the concentration of surface-active ions at the outer Helmholtz plane as a concentration variable; at the same time the specific adsorption of counter-ions must be excluded. Comparison of the main characteristics of adsorption isotherms applicable to description of specific adsorption of cations at the bismuth electrode has been made. An estimate of the accuracy of calculation of the charge of specifically adsorbed ions has been made by means of the potential shift due to adsorption of surface-active ions at constant electrode charge.

Comparison of experiments with calculations using double-layer models: Specific adsorption of Cs+ on bismuth

Abstract General equations for the two-dimensional pressure, the change of the electrode surface charge and for the change of the electrode differential capacity due to specific adsorption of ions have been developed at a constant electrode potential. On the basis of the equations derived, the optimal values of the virial isotherm parameters describing the adsorption of Cs + cations at the Bi/H 2 O phase boundary at various constant potential E and also the adsorption parameters of the Vorotyntsev model have been calculated. It has been established that the experimental data for the systems studied agree with the Grahame-Parsons or with the Vorotyntsev model only in the first approximation; by a more detailed comparison of the divergences from these models the limits of applicability of both double-layer models have been established.

Specific adsorption of ions and charge distribution in an electrical double layer

Abstract The present paper is devoted to the analysis of the model of an electrical double layer on the electrode surface recharged by specifically adsorbed ions. The theoretical analysis is based on the experimental adsorption data obtained mainly on the solid bismuth electrode in aqueous and ethanolic solutions, and also on the mercury drop electrode in N-methyl-formamide solutions of binary or mixed surface-active electrolytes. It has been shown that the entrance of the counter-ions into the inner part of the double layer is a common phenomenon on electrode surfaces recharged by specifically adsorbed ions. An analysis of the calculation methods of the charge of the counter-ions in the inner layer has been carried out and a new calculation method of this quantity has been elaborated. Some general regularities of the entrance of the counter-ions into the inner layer have been established and the models of the charge distribution in the electrical double layer are analysed in the conditions of the specific adsorption of ions on electrodes.

On the theory of ionic adsorption from binary electrolyte solutions at electrodes

Abstract The Grahame-Parsons, Alekseev-Popov-Kolotyrkin and Vorotyntsev models of ionic adsorption in 1:1 binary electrolyte solutions are compared with a computer experiment assuming independence of the inner-layer capacity on the specific adsorption of ions. It is demonstrated that the Grahame-Parsons and Alekseev-Popov-Kolotyrkin models are formally equivalent for the solutions analysed and that their adsorption parameters can be recalculated by the subsequent equations. For infinitely dilute solutions at a given electrode charge, all three models require determination of a limiting value of specific adsorption, X lim For the choice of an adequate adsorption isotherm and double-layer model, the specific adsorption of anions in binary solutions of KCl, KBr and KI on Hg and Bi electrodes was studied. The theoretical analysis showed that the most informative systems were the KBr solutions at the Bi/H 2 O interface, where the transition from undercharged to overcharged surface conditions occurred in the middle of the logarithmic concentration scale. For these systems, the best coincidence was obtained by use of the modified virial isotherm considering the discreteness effect, due to the specifically adsorbed ions, both in the inner and the outer Helmholtz plane.

Model of inner part of electrical double layer on a recharged electrode surface

Abstract The specific adsorption of various anions has been studied on the bismuth electrode in the aqueous and ethanolic solutions of mixed electrolytes with constant ionic strength by measuring the potential dependence of differential capacity of bismuth. The charge due to specifically adsorbed anions was calculated by the Hurwitz-Dutkiewicz-Parsons method. Assuming the entrance of cations into the inner part of the double layer on the bismuth electrode, recharged by the specifically adsorbed anions, the charge due to the cations in the inner layer, the corrected values of the outer Helmholtz plane potential and of the potential drop across the inner layer have been calculated. A simple model of the inner layer in presence of ionic associates is developed. The main parameters characterizing the specific adsorption of ions and the structure of the inner layer have been calculated. A procedure has been developed for the calculation of the charge due to the cations in the inner layer by the dependence on the electrode potential on the charge of specifically adsorbed anions.

Criteria of choice of absorption parameters in the grahame—parsons model: Cesium adsorption on bismuth

Abstract General equations for the two-dimensional pressure, the potential shift and for the change of the differential capacity due to the specific adsorption of ions at a constant electrode charge, are derived. On the basis of the equations derived, a new calculation method for the adsorption parameters in the Grahame—Parsons model is elaborated. With the example of the Cs+ adsorption data for the interface Bi/H2O, the sensitivity of the various verification criteria of the adsorption parameters are compared and the advantages of the new calculation method are demonstrated.

Charge dependence of adsorption energy of ions at electrodes

Abstract Analysis of the energetic and geometric characteristics of the inner part of the electrical double layer has been carried out in the presence of the specific adsorption of ions accompanied by change in the dimensions and dielectric properties of the inner layer. On the basis of the formulae for the electrochemical potential of the adsorbed ion on the electrode surface and for the components of the inner layer capacity, the equations of the Frumkin isotherm and of its parameters have been derived. It has been shown that, in general, the Frumkin isotherm is non-linear at the given electrode charge and the charge dependence of the adsorption equilibrium constant has a parabolic form. The results of the corresponding theoretical calculations have been compared with the experimental data obtained by the study of the specific adsorption of tetra-alkylammonium cations on a bismuth electrode in ethanolic and aqueous solutions. Good agreement of the experimental results with those calculated theoretically confirm the validity of the equations derived.