Surface excess reference

Surface excesses are usually referred to the unit surface area of the dividing plane S (surface excess densities). 

One important advantage of the polarized interface is that one can determine the relative surface excess of an ionic species whose counterions are reversible to a reference electrode. The adsorption properties of an ionic component, e.g., ionic surfactant, can thus be studied independently, i.e., without being disturbed by the presence of counterionic species, unlike the case of ionic surfactant adsorption at nonpolar oil-water and air-water interfaces [25]. The merits of the polarized interface are not available at nonpolarized liquid-liquid interfaces, because of the dependency of the phase-boundary potential on the solution composition. 

The meaning of the surface excess is illustrated in Fig. 1, in which the solid line represents the actual concentration profile of an adsorbate i, when the bulk concentration of i in the phase a (a = O or W) is c . The hatched area corresponds to be the surface excess of i, T,. This quantity depends on the location of the dividing surface. On the other hand, the experimentally accessible quantity should not depend on the location of the artificially introduced dividing surface. The relative surface excess, which is independent of the location of the dividing surface, is defined by relativizing it with respect to those of certain reference components. In oil water interfaces, the mutual solubility of solvents can be significant. The relative surface excess in Eq. (3) is then related to the surface excesses through... 

It is practically impossible to measure 7 for solid electrodes. However, in some applications one needs only the change in 7 with certain parameters. For example, for the determination of the surface excess of a neutral organic species, one requires the change in the interfacial tension with the activity of the species. This can be measured if there is a reference potential 4>r at which the species is not adsorbed the change in the interfacial tension is then referred to this potential. One proceeds in the following way [2] ... 

It is important to realize that the mathematical dividing surface just discussed is a reference level rather than an actual physical boundary. What is physically represented by this situation may be summarized as follows. Two portions of solution containing an identical number of moles of solvent are compared. One is from the surface region and the other from the bulk solution. The number of moles of solute in the sample from the surface minus the number of moles of solute in the sample from the bulk give the surface excess number of moles of solute according to this convention. This quantity divided by the area of the surface equals Y2. To emphasize that the surface excess of component 1 has been chosen to be zero in this determination, the notation Tj is generally used. 

Throughout most of this chapter we have been concerned with adsorption at mobile surfaces. In these systems the surface excess may be determined directly from the experimentally accessible surface tension. At solid surfaces this experimental advantage is missing. All we can obtain from the Gibbs equation in reference to adsorption at solid surfaces is a thermodynamic explanation for the driving force underlying adsorption. Whatever information we require about the surface excess must be obtained from other sources. 

The election of a reference electrode sensitive to one of the ions of the electrolyte leads to the appearance in Eq. (1.71) of the surface excess of the other. Equation (1.71) is usually named as Lippman s electrocapillary equation. 

Gibbs derived a thermodynamic relationship between the surface or interfacial tension y and the amount of surfactant adsorbed per unit area at the A/L or L/L interface, T (referred to as the surface excess),... 

The surface excess amount, or Gibbs adsorption (see Section 6.2.3), of a component i, that is, /if, is defined as the excess of the quantity of this component actually present in the system, in excess of that present in an ideal reference system of the same volume as the real system, and in which the bulk concentrations in the two phases stay uniform up to the GDS. Nevertheless, the discussion of this topic is difficult on the other hand for the purposes of this book, it is enough to describe the practical methodology, in which the amount of solute adsorbed from the liquid phase is calculated by subtracting the remaining concentration after adsorption from the concentration at the beginning of the adsorption process. 

The conceptual meaning of Eq. 4.1 is that nP is the excess moles of substance i in the reacted mixture, relative to the content of a reference substance j in the mixture and to the composition of the separated aqueous solution, indicated by the molalities nij and mj. In the example of the slurry and supernatant solution, np is the excess moles of i in the slurry, as compared to the content of the reference substance j and to an aqueous solution that has the mixed composition indicated by mj and mj. The right side of Eq. 4.1 can be positive (adsorption), zero (no surface excess), or negative (desorption), depending entirely on the relative behavior of the substances i and j when two phases containing them react. In applications of Eq. 4.1 to the reactions of soils with aqueous solutions, the reference substance j is invariably chosen to be liquid water (j = w) ... 

Equation (3) has the same form as one of Gibbs s fundamental equations for a homogeneous phase, and owing to this formal similarity the term surface phase is often used. It must be remembered, however, that the surface phase is not physically of the same definiteness as an ordinary phase, with a precise location in space neither do the quantities c , if, mf refer to the total amounts of energy, entropy, or material components present in the surface region as it exists physioally they are surface excesses , or the amounts by which the actual system exceeds the idealized system in these quantities. Care must be taken not to confuse the exact mathematical expression, surface phase , with the physical concept of the surface layer or surface film. 

The strict thermodynamic analysis of an interfacial region (also called an -> interphase) [ii] is based on data available from the bulk phases (concentration variables) and the total amount of material involved in the whole system yielding relations expressing the relative surface excess of suitably chosen (charged or not charged) components of the system. In addition, the - Gibbs equation for a polarizable interfacial region contains a factor related to the potential difference between one of the phases (metal) and a suitably chosen - reference electrode immersed in the other phase (solution) and attached to a piece of the same metal that forms one of the phases. 

To overcome this problem, Gibbs (1877) proposed an alternative approach. This makes use of the concept of surface excess to quantify the amount adsorbed. Comparison is made with a reference system, which is divided into two zones (A, of volume K3,0 and B, of volume V8,0) by an imaginary surface - the Gibbs dividing surface (or GDS) - which is placed parallel to the adsorbent surface. The reference system occupies the same volume V as the real system, so that ... 

For the sake of simplicity in some later sections of this book, we adopt the symbol n to denote the specific surface excess amount n°lm. Also, for convenience, this quantity will be often referred to as amount adsorbed. 

Equation (2.34) is often referred to as the Gibbs adsorption equation where the interdependence of r and p is given by the adsorption isotherm. TTie Gibbs adsorption equation is a surface equation of state which indicates that, for any equilibrium pressure and temperature, the spreading pressure II is dependent on the surface excess concentration r. The value of spreading pressure, for any surface excess concentration, may be calculated from the adsorption isotherm drawn with the coordinates n/p and p, by integration between the initial state (n = 0, p = 0) and an equilibrium state represented by one point on the isotherm. 

We now return to the definition of the surface excess chemical potential fta given by Equation (2.19) where the partial differentiation of the surface excess Helmholtz energy, Fa, with respect to the surface excess amount, rf, is carried out so that the variables T and A remain constant. This partial derivative is generally referred to as a differential quantity (Hill, 1949 Everett, 1950). Also, for any surface excess thermodynamic quantity Xa, there is a corresponding differential surface excess quantity xa. (According to the mathematical convention, the upper point is used to indicate that we are taking the derivative.) So we may write ... 

Reference electrodes, 37 Relative surface excess, 236 Relaxation time, 358, 366, 369 Repassivation potential, 514 Resistance overpotential, 107 Reverse-pulse techniques, 397 Reverse-step voltaininetry, 400 Reversibility, 78... 

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