Interfacial potential function

With respect to nonionized organic solutes in aqueous solutions, the interfacial interaction force constants were expressed as constants that define the interfacial potential function as follows ... 

The theoretical treatments of Section III-2B have been used to calculate interfacial tensions of solutions using suitable interaction potential functions. Thus Gubbins and co-workers [88] report a molecular dynamics calculation of the surface tension of a solution of A and B molecules obeying Eq. III-46 with o,bb/ o,aa = 0.4 and... 

One fascinating feature of the physical chemistry of surfaces is the direct influence of intermolecular forces on interfacial phenomena. The calculation of surface tension in section III-2B, for example, is based on the Lennard-Jones potential function illustrated in Fig. III-6. The wide use of this model potential is based in physical analysis of intermolecular forces that we summarize in this chapter. In this chapter, we briefly discuss the fundamental electromagnetic forces. The electrostatic forces between charged species are covered in Chapter V. 

The non situ experiment pioneered by Sass uses a preparation of an electrode in an ultrahigh vacuum through cryogenic coadsorption of known quantities of electrolyte species (i.e., solvent, ions, and neutral molecules) on a metal surface. " Such experiments serve as a simulation, or better, as a synthetic model of electrodes. The use of surface spectroscopic techniques makes it possible to determine the coverage and structure of a synthesized electrolyte. The interfacial potential (i.e., the electrode work function) is measured using the voltaic cell technique. Of course, there are reasonable objections to the UHV technique, such as too little water, too low a temperature, too small interfacial potentials, and lack of control of ionic activities. ... 

An electric current flowing through an ITIFS splits into nonfaradaic (charging or capacity) and faradic current contributions. The latter contribution comprises the effects of both the transport of reactants to or from the interface, and the interfacial charge transfer, the rate of which is a function of the interfacial potential difference. By applying a transient electrochemical technique, these two effects can be resolved... 

The presence of an electrical potential drop, i.e., interfacial potential, across the boundary between two dissimilar phases, as well as at their surfaces exposed to a neutral gas phase, is the most characteristic feature of every interface and surface electrified due to the ion separation and dipole orientation. This charge separation is usually described as the formation of the ionic and dipolar double layers. The main interfacial potential is the Galvani potential (termed also by Trasatti the operative potential), which is the difference of inner potentials (p and of both phases. It is a function only of the chemical... 

The ITIES with an adsorbed monolayer of surfactant has been studied as a model system of the interface between microphases in a bicontinuous microemulsion [39]. This latter system has important applications in electrochemical synthesis and catalysis [88-92]. Quantitative measurements of the kinetics of electrochemical processes in microemulsions are difficult to perform directly, due to uncertainties in the area over which the organic and aqueous reactants contact. The SECM feedback mode allowed the rate of catalytic reduction of tra 5-l,2-dibromocyclohexane in benzonitrile by the Co(I) form of vitamin B12, generated electrochemically in an aqueous phase to be measured as a function of interfacial potential drop and adsorbed surfactants [39]. It was found that the reaction at the ITIES could not be interpreted as a simple second-order process. In the absence of surfactant at the ITIES the overall rate of the interfacial reaction was virtually independent of the potential drop across the interface and a similar rate constant was obtained when a cationic surfactant (didodecyldimethylammonium bromide) was adsorbed at the ITIES. In contrast a threefold decrease in the rate constant was observed when an anionic surfactant (dihexadecyl phosphate) was used. 

FIG. 9 Differential capacity C of the interface between 0.1 M LiCl in water and 0.02 M tetrabu-tylammonium tetraphenylborate ( ) or tetrapentylammonium tetrakis[3,5-bis(trifluoromethyl)phe-nyl]borate ( ) in o-nitrophenyl octyl ether as a function of the interfacial potential difference (From Ref 73.)... 

The dependence of the interfacial tension at the W/NB interface on the interfacial potential difference [29,30] was investigated by using an aqueous solution dropping electrode [26,31]. In this investigation, the aqueous solution was forced upward dropwise in NB and the drop time of W was measured as a function of potential difference applied at the W/ NB interface. When W contained 1 MMgS04 and NB contained 4 x 10 " M Cs" TPhB ... 

When the electrolytes on either side of a liquid junction are different, the mathematical analysis of the interfacial potential becomes complex. In nearly all these cases the potential is a function of the geometrical characteristics of the boundary itself. In one general case, however, i.e., for the junction between two uni-univalent electrolytes at the same concentration and having a common ion (e.g., the pair KC1, NaCl), the liquid junction potential is independent of the structure of the boundary and is provided by following equation ... 

When polar or polarizable species are adsorbed on a metal, the work function changes. This is partly due to gs(dip) but is also due to the change in xM and other effects.2 As for the interfacial potential in the electrochemical cell, the contributions of adsorbate and metal cannot be separated. Usually, the latter gets ignored. It is precisely this term that interests us here. 

It follows from Eqn. 4—13 that the electron level o u/av) in the electrode is a function of the chemical potential p.(M) of electrons in the electrode, the interfacial potential (the inner potential difference) between the electrode and the electrolyte solution, and the surface potential Xs/v of the electrolyte solution. It appears that the electron level cx (ii/a/v) in the electrode depends on the interfacial potential of the electrode and the chemical potential of electron in the electrode but does not depend upon the chemical potential of electron in the electrolyte solution. Equation 4-13 is valid when no electrostatic potential gradient exists in the electrolyte solution. In the presence of a potential gradient, an additional electrostatic energy has to be included in Eqn. 4-13. 

Since u,(M) and xsat are characteristic of specific combinations of electrodes and electrolyte solutions, they are constant. For an electrode S3 tem, thereby, the electrode potential is a function of the interfacial potential A u/s only. The electrode potential, E, defined in Eqn. 4—14 corresponds to what is called the absolute electrode potential. The reference zero level of the absolute electrode potential is set at the outer potential of the electrolyte solution in which the electrode is immersed. 

Fig. 10.6 Cdi for the Au/Na-) -Al203 interface as a function of the interfacial potential. Electrode area is 1.7 cm. ...

For interfacial systems, potential functions should ideally be transferrable from the gas-phase to the condensed phase. Aqueous-mineral interfaces are not in the gas phase (although they may be close, see (7)), but both the water molecules and the atoms/ions in the substrate are in contact with an environment that is very different from their bulk environment. The easiest different environment to test, especially when comparing with electronic structure calculations, is a vacuum, so there is likely to be a great deal of information available on either the surface of the solid or the gas-phase polynuclear ion or the gas-phase aquo complex (i.e., Fe(H20)63+, C03(H20)62-). The gas-phase transfer-ability requirements on potential functions are challenging, but it is difficult to imagine constructing effective potential functions for such systems without using gas-phase systems in the construction process. This means that any water molecules used on these complexes must also transfer from the gas phase to the condensed phase. A fundamental aspect of this transferability is polarization. 

The Electron Work Function, Another Interfacial Potential... 

In order to find the explicit potential dependency, Cq and Cr should be substituted by the appropriate relations expressing their potential dependency. Such relations have been derived and discussed in Sect. 7.3.2. where the interfacial potential was presumed to be a step function or to have a time-independent value. Regarding Sects. 7.3.2.(a)—(d), it can be concluded that one can choose either an approximate, but explicit, solution for Cq and Cr or a rigorous, but numerical, solution. 

The counter electrode in the two-electrode system serves two functions. First, it completes the circuit, allowing charge to flow through the cell, second, it is assumed to maintain a constant interfacial potential difference regardless of the current. These two functions are mutually exclusive only under very restricted circumstances. Both needs are better served by two separate electrodes ... 

The interfacial properties of an amphiphilic block copolymer have also attracted much attention for potential functions as polymer compatibilizers, adhesives, colloid stabilizers, and so on. However, only a few studies have dealt with the monolayers o well - defined amphiphilic block copolymers formed at the air - water interface. Ikada et al. [124] have studied monolayers of poly(vinyl alcohol)- polystyrene graft and block copolymers at the air - water interface. Bringuier et al. [125] have studied a block copolymer of poly (methyl methacrylate) and poly (vinyl-4-pyridinium bromide) in order to demonstrate the charge effect on the surface monolayer- forming properties. Niwa et al. [126] and Yoshikawa et al. [127] have reported that the poly (styrene-co-oxyethylene) diblock copolymer forms a monolayer at the air - water... 

The second and third terms on the right hands side of Eq. 9.8 remain constant for a given electrode-electrolyte system, and hence the electrode potential is a linear function of the interfacial potential A MIS of the electrode. This definition of the electrode potential holds valid for all electronic and ionic electrodes, whether the electrode reaction is in equilibrium or non-equilibrium. The potential defined by Eq. 9.8 is called the absolute electrode potential. 

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