Adsorption potential classical thermodynamics

The models presented above have also been reviewed in Ref 18. Recently, an expression for the adsorption potential at the free water surface based on a combination of the electrostatic theory of dielectrics and classical thermodynamics has also been proposed." ... 

According to the laws of classical thermodynamics, the amount adsorbed is controlled by the chemical potential of the adsorptive (see Section 2.3). It follows that the two branches of a loop cannot both satisfy the requirement of thermodynamic reversibility. The appearance of reproducible and stable hysteresis therefore implies the existence of certain well-defined metastable states. 

The treatment presented above has shown that classical thermodynamics fed with a minimum of modelistic assumptions can be used for the determination of the explicit dependence of the electrochemical potentials of adsorbed species upon the dipole-dipole interactions among these species. The electrochemical potentials can be further used for the derivation of the adsorption isotherm and more general the equilibrium properties of adsorbed layers at uncharged interfaces. 

The macroscopic description of the adsorption on electrodes is characterised by the development of models based on classical thermodynamics and the electrostatic theory. Within the frames of these theories we can distinguish two approaches. The first approach, originated from Frumkin s work on the parallel condensers (PC) model,attempts to determine the dependence of upon the applied potential E based on the Gibbs adsorption equation. From the relationship = g( ), the surface tension y and the differential capacity C can be obtained as a function of E by simple mathematical transformations and they can be further compared with experimental data. The second approach denoted as STE (simple thermodynamic-electrostatic approach) has been developed in our laboratory, and it is based on the determination of analytical expressions for the chemical potentials of the constituents of the adsorbed layer. If these expressions are known, the equilibrium properties of the adsorbed layer are derived from the equilibrium equations among the chemical potentials. Note that the relationship = g( ), between and , is also needed for this approach to express the equilibrium properties in terms of either or E. Flere, this relationship is determined by means of the Gauss theorem of electrostatics. 

The processes taking place on the surface of the solid are complicated and great in number. We measure a certain common resultant effect as the powder electrode potential. The full mastery of the subject would have to be based on the elaboration of a chemical and physicochemical model of all processes (i.e., giving the chemical equations of reactions in process, indicating the processes of solution, adsorption, desorption, and secondary reactions, etc.) as well as on the classical thermodynamic description, and possibly by thermodynamics of irreversible processes, and chemical and electrochemical kinetics. 

The Potential Theory as originally conceived by Polanyi is well documented in the classic text by Brunauer (1943). Polanyi considered contours of equipotential energy above solid surfaces and ascribed a volume to the space between the ith equipotential surface of energy e and the adsorbent surface. The potential was assumed to be independent of temperature so that = /(0) is essentially an isotherm equation. The adsorption potential is defined as the work of compression of the gas from a pressure p to the saturation pressure ps. For one mole of a perfect gas of volume v in an open thermodynamic system the adsorption potential is therefore... 

Other thermodynamic quantities that can be evaluated equally well by Monte Carlo and by MD simulations include the molar energy of adsorption, which is just the total potential energy of the adsorbed particles divided by their number, for a classical system [7] the surface tension of the adsorbed fUm [3] and the pressure normal to the surface. In principle, the dependence of the normal component of the pressure tensor upon amount adsorbed could be used to construct an adsorption isotherm since this pressure must be independent of distance from the surface in order to maintain mechanical equilibrium [3,7]. Thus, fer from the surface it must be equal to the bulk gas pressure. However, in practice the normal pressure is hard to evaluate with sufficient accuracy to be useful in an isotherm calculation, especially at the temperatures at or below the normal boiling point of the bulk... 

The presence of ionic specific adsorption may be confirmed by examining the dependence of the PZC on electrolyte concentration. From the data presented in fig. 10.6, it is seen that the PZC measured with respect to a constant reference electrode is approximately independent of electrolyte concentration when ionic adsorption is absent. The classic example of such a system is NaF in water at an Hg electrode. However, when anion adsorption occurs the PZC shifts in the negative direction with increase in electrolyte concentration. This is most pronounced for the I anion in the case of the halides. When cations are adsorbed, the PZC shifts in the positive direction. The interpretation of the shift of the PZC with electrolyte concentration can be put on a sound thermodynamic basis when the electrode potential is measured with a reference electrode reversible to one of... 

An alternative analysis of colloidal interaction and stability based on classical solution thermodynamics has been proposed independently by Hall (1972) and Ash etal. (1973) and the practical implications with particular interest in the effects of polymers and surfactants has been discussed by Pethica (1986). In this theory, the forces between particles are governed in a straightforward way by the adsorptions of the components of the system and their dependence of particle separation and chemical potentials (which are defined by the composition) according to the equation... 

Let us consider the simplest surface that shows ion-specific adsorption, namely the water-air interface. In a by now classical series of papers, Jungwirth and co-workers have shown that iodide ions do adsorb at the air-water interface, in strong contrast with the traditional view. Those simulations were performed with polarisable force fields, while the non-polarisable force fields employed at that time did not show adsorption of iodide. It was concluded that the polarisability plays a dominant role in the adsorption mechanism. Let us reconsider that problem using our novel thermodynamically optimised force fields discussed in the earlier section. We show results for the potential of mean force of a single ion at an air-water interface, calculated using umbrella sampling and the WHAM method. ... 

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