Surface excess properties

T, may become positive or negative, depending on the particular interface in question. Other surface excess properties, such as the surface internal energy and surface entropy, are defined similarly ... 

It follows that the surface excess properties are macroscopic parameters only. 

What is a Gibbs surface What are the definition and meaning of surface excess properties ... 

In treating interfacial (if) regions, we will follow the method of Gibbs and replace the nonuniform interfacial region by a two-dimensional Gibbs surface phase with uniform properties. Properties of this phase are called surface excess properties and their calculation is illustrated for the surface excess concentration of component i in Fig. 8. Here, the actual interfacial region, the region where properties vary, extends from zj to z2 and is replaced by the surface phase located at position z0, with the uniform bulk a and (1 phases extended up to this position. 

The superscript a is used to denote a surface excess property relative to the Gibbs surface. 

The first calculation of a surface excess property was the determination by Cape and Woodcock of the surface stress, or interfacial tension T. It was calculated by integrating the stress profile through the interface, and was found to have the value... 

The most extensive simulation of surface excess properties, and the first study to determine a directly, was that of Broughton and Gilmer, who looked at the fee (100), (110), and (111) surfaces of a Lennard-Jones crystal-melt system. They determined the surface free energy by calculating the reversible work necessary to cleave the solid and liquid phases and to join the two systems to form a liquid-solid interface. They found the results... 

Careful computer simulation results clearly have an important role to play in the evaluation of surface excess properties. They present major computational challenges, however, because of the difficulty of reaching equilibrium and the sensitivity of surface excess properties (which are obtained as small differences of large numbers) to small uncertainties in the calculated system properties. 

Gibbs Surface A geometrical surface chosen parallel to the interface and used to define surface excess properties such as the extent of adsorption. The surface excess amount of adsorption is the excess amount of a component actually present in a system over that present in a reference system of the same volume as the real system, and in which the bulk concentrations in the two phases remain uniform up to the Gibbs dividing surface. The terms surface excess concentration or surface excess have now replaced the earlier term superficial density. 

It is clear from Equations 1.1 and 1.2 that surface excess quantities do take into account the variation of composition and propalies across an interfacial region of finite thickness. As we shall see shortly, they can be used to define interfacial tension. Moreover, since all surface excess properties are assigned to the reference surface S, the area and curvature of S can be identified as the corresponding properties of the interface and used, for example, to describe interfacial deformation. 

Surface heterogeneity may merely be a reflection of different types of chemisorption and chemisorption sites, as in the examples of Figs. XVIII-9 and XVIII-10. The presence of various crystal planes, as in powders, leads to heterogeneous adsorption behavior the effect may vary with particle size, as in the case of O2 on Pd [107]. Heterogeneity may be deliberate many catalysts consist of combinations of active surfaces, such as bimetallic alloys. In this last case, the surface properties may be intermediate between those of the pure metals (but one component may be in surface excess as with any solution) or they may be distinctly different. In this last case, one speaks of various effects ensemble, dilution, ligand, and kinetic (see Ref. 108 for details). 

The excess energy associated with an interface is formally defined in terms of a surface energy. This may be expressed in terms either of Gibbs, G, or Helmholtz, A, free energies. In order to circumvent difficulties associated with the unavoidably arbitrary position of the surface plane, the surface energy is defined as the surface excess [7,8], i.e the excess (per unit area) of the property concerned consequent upon the presence of the surface. Thus Gibbs surface free energy is defined by... 

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. 

Girault and Schiffrin [4] proposed an alternative model, which questioned the concept of the ion-free inner layer at the ITIES. They suggested that the interfacial region is not molecularly sharp, but consist of a mixed solvent region with a continuous change in the solvent properties [Fig. 1(b)]. Interfacial solvent mixing should lead to the mixed solvation of ions at the ITIES, which influences the surface excess of water [4]. Existence of the mixed solvent layer has been supported by theoretical calculations for the lattice-gas model of the liquid-liquid interface [23], which suggest that the thickness of this layer depends on the miscibility of the two solvents [23]. However, for solvents of experimental interest, the interfacial thickness approaches the sum of solvent radii, which is comparable with the inner-layer thickness in the MVN model. 

It has been reported that the sonochemical reduction of Au(III) reduction in an aqueous solution is strongly affected by the types and concentration of organic additives. Nagata et al. reported that organic additives with an appropriate hydro-phobic property enhance the rate of Au(III) reduction. For example, alcohols, ketones, surfactants and water-soluble polymers act as accelerators for the reduction of Au(III) under ultrasonic irradiation [24]. Grieser and coworkers [25] also reported the effects of alcohol additives on the reduction of Au(III). They suggested that the rate of the sonochemical reduction of Au(III) is related to the Gibbs surface excess concentration of the alcohol additives. 

This is where the trouble begins Generally speaking, the kind of profile sketched in Figure 7.13 will be different for each property considered. Therefore we may choose x0 to accomplish the compensation discussed herein for one property, but this same line will divide the profiles of other properties differently. The difference between the overestimated property and the underestimated one accounts for the surface excess of this property. 

From the point of view of thermodynamics —which is oblivious to details at the molecular level-the dividing boundary may be placed at any value of x in the range r. The actual placement of a 0 is governed by consideration of which properties of the system are most amenable to thermodynamic evaluation. More accurately, that property that is least convenient to handle mathematically may be eliminated by choosing x0 so that the difficult quantity has a surface excess of zero. 

For example, if the property in Figure 7.13 was G and the dividing surface was placed so that the two shaded regions would be equal, then there would be no surface excess G The last term in Equation (30) would be zero. The Gibbs free energy is convenient to work with, however, so such a choice for x0 would not be particularly helpful. Until now we have not had any reason to identify the surface of physical phases with any specific mathematical surface. We had not, that is, until Equation (44) was reached. Now things are somewhat different. 

It should be evident from the foregoing discussion that the property defined to have zero surface excess may be chosen at will, the choice being governed by the experimental or mathematical features of the problem at hand. Choosing the surface excess number of moles of one component to be zero clearly simplifies Equation (44). The same simplification could have been accomplished by defining the mathematical surface so that Y2 would be zero, a choice that would obviously deemphasize the solute. If the total number of moles N, the total volume V, or the total weight W had been the property chosen to show a zero surface excess, then in each case both T, and Y2 (which would be identified as TN, rK, or T for these three conventions) would have nonzero values. Last, note that the surface excess is an algebraic... 

Alteration of this epoxy structure is the result of the fact that the epoxy molecules are both reacting and diffusing at the same time. This process forms a concentration gradient with a high epoxy monomer concentration at the surface which gradually reduces to the bulk concentration away from the surface. The properties of an epoxy with an excess of resin can be quite different from the stoichiometric amount. Figure 2, for example, illustrated the alteration of cured epoxy mechanical properties with epoxy/amine ratio. Excess epoxy or less than the stoichiometric amount of amine produces a brittle material if the mixture is cured in the same manner as the stoichiometric amount (Fig. 2). The stoichiometric sample has the lowest modulus while excess amine produces increased brittleness. The potential for variation in local properties within the epoxy due to the presence of a 200 nm or less layer must be considered. 

The charge density, Volta potential, etc., are calculated for the diffuse double layer formed by adsorption of a strong 1 1 electrolyte from aqueous solution onto solid particles. The experimental isotherm can be resolved into individual isotherms without the common monolayer assumption. That for the electrolyte permits relating Guggenheim-Adam surface excess, double layer properties, and equilibrium concentrations. The ratio u0/T2N declines from two at zero potential toward unity with rising potential. Unity is closely reached near kT/e = 10 for spheres of 1000 A. radius but is still about 1.3 for plates. In dispersions of Sterling FTG in aqueous sodium ff-naphthalene sulfonate a maximum potential of kT/e = 7 (170 mv.) is reached at 4 X 10 3M electrolyte. The results are useful in interpretation of the stability of the dispersions. 

The electronic structure of a solid metal or semiconductor is described by the band theory that considers the possible energy states of delocalized electrons in the crystal lattice. An apparent difficulty for the application of band theory to solid state catalysis is that the theory describes the situation in an infinitely extended lattice whereas the catalytic process is located on an external crystal surface where the lattice ends. In attempting to develop a correlation between catalytic surface processes and the bulk electronic properties of catalysts as described by the band theory, the approach taken in the following pages will be to assume a correlation between bulk and surface electronic properties. For example, it is assumed that lack of electrons in the bulk results in empty orbitals in the surface conversely, excess electrons in the bulk should result in occupied orbitals in the surface (7). This principle gains strong support from the consistency of the description thus achieved. In the following, the principle will be applied to supported catalysts. 

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