Surface, Gibbs

The non-consen>ed variable (.t,0 is a broken symmetry variable, it is the instantaneous position of the Gibbs surface, and it is the translational synnnetry in z direction that is broken by the inlioinogeneity due to the liquid-vapour interface. In a more microscopic statistical mechanical approach 121, it is related to the number density fluctuation 3p(x,z,t) as... 

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... 

The above provides a means of showing how the total excess charge on the solution side of the interface q the excess charge due to cations F+ and the excess charge due to anions F, vary with potential in a solution of fixed concentration of electrolyte. On the basis of this approach to the electrocapillary curves it has been shown that the Gibbs surface excess for cations is due solely to electrostatic forces (long-range coulombic), and this is reflected in the fact that the electrocapillary curves for different cations and... 

Gibbs surface excess (free energy) gram... 

D. K. Chattoray and K. S. Birdi, Adsorption and Gibbs Surface Excess, Plenum Press, New York, 1984, Chaps. 5 and 6. 

FIGURE 10.4 Coordinates of interphase boundaries and Gibbs surface. 

The parameter nf always has positive values, whereas the parameters and Fj can have positive or negative values. Parameter Fj is called the Gibbs adsorption or Gibbs surface excess. 

However, the value of T depends on the position of the Gibbs surface. By common convention, this position is selected so that for one of the components (with the index j = 0), the value of T defined by Eq. (10.21) will become zero. The solvent is chosen in this capacity when one of the phases in contact is a solution. Once the position of the Gibbs surface has been fixed, one can unambiguously determine the Gibbs surface excesses of the other components. The adsorption of a component j is thus defined relative to the component y = 0 (relative Gibbs surface excess... 

More commonly used is another definition of Gibbs surface excesses, according to which r, is equal to the amount of substance j that must be added to the system (with a constant amount of the substance j = 0) so that the composition of the bulk phases will remain unchanged when the interface area is increased by unity. This definition can also be used when chemical reactions take place in the surface layer. In the case discussed here, the two definitions coincide. The set of surface excesses of all components is sometimes called the surface phase (in contrast to the real surface layer or interphase). 

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. 

Experiment 2 Saturate distilled water with a rare gas and compare the intensity of the signal with that from air. The luminosity will be enhanced in the rare gas saturated solutions. For any gas atmosphere, add small amounts of volatile water-soluble solutes (e.g. alkyl series alcohols) and quantify the quenching of sonoluminescence as a function of both bulk quencher concentration and surface excess. Good correlation between the extent of quenching and the Gibbs surface excess should be observed. Explain the changes in sonoluminescence intensity when a rare gas atmosphere is used and the quenching of volatile solutes, in terms of simple thermodynamics. 

The purpose of this chapter is to introduce the effect of surfaces and interfaces on the thermodynamics of materials. While interface is a general term used for solid-solid, solid-liquid, liquid-liquid, solid-gas and liquid-gas boundaries, surface is the term normally used for the two latter types of phase boundary. The thermodynamic theory of interfaces between isotropic phases were first formulated by Gibbs [1], The treatment of such systems is based on the definition of an isotropic surface tension, cr, which is an excess surface stress per unit surface area. The Gibbs surface model for fluid surfaces is presented in Section 6.1 along with the derivation of the equilibrium conditions for curved interfaces, the Laplace equation. 

Gibbs surface model and definition of surface tension... 

This is the definition of the surface tension according to the Gibbs surface model [1], According to this definition, the surface tension is related to an interface, which behaves mechanically as a membrane stretched uniformly and isotropically by a force which is the same at all points and in all directions. The surface tension is given in J m-2. It should be noted that the volumes of both phases involved are defined by the Gibbs dividing surface X that is located at the position which makes the contribution from the curvatures negligible. 

If nia and nlfj denote the total moles of the i-th component in the two phases of the idealized system, then the Gibbs surface excess rni of the i-th component can be defined as... 

Azzaroni etal. [163] have used STM to study electrochemical reactivity of thiourea toward Au(lll). Sequential STM imaging has shown that thiourea adsorbs as striped arrays that evolve to the hexagonal close-packed structure when surface charge density is decreased. The transient hep structure undergoes electrooxidation to formamidine disulfide, which slowly yields adsorbed sulfur. Adsorption of thiourea on the pc-Au electrode from KCIO4 solutions has also been studied [164]. The film pressure and the Gibbs surface... 

The change in a, is caused by the change in bulk solute concentration. This is the Gibbs surface tension equation. Basically, these equations describe the fact that increasing the chemical potential of the adsorbing species reduces the energy required to produce new surface (i.e. y). This, of course, is the principal action of surfactants, which will be discussed in more detail in a later section. 

In Section 6.4.2 we will find that T represents the Gibbs-surface excess, i.e., T=N/A -N°/A, where is the number of molecules that would have been there if there had been no double layer, and N is the actual number of molecules in the interfacial region. However, when the bulk concentration of the spedes is small, i.e., tfi — 0, then the number of adsorbed molecules tends to f, i.e., f — N/A. 

A purely thermodynamic approach to adsorption in the double layer allows one to obtain the Gibbs surface excess for both cations and anions. Describe an approach for breaking up the T into diffuse layer and contact-adsorbed contributions. Be careful in making the assumptions. (Bockris)... 

In describing adsorption on an electrode, it is common to write 0 for the fraction of the surface covered. However, in purely thermodynamic analyses, the symbol r is used for the Gibbs surface excess. Describe the difference in meaning between these two quantities and the conditions under which they may tend to become nearly equal. (Bockris)... 

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

Free surface energy, interfacial enthalpy and Gibbs surface energy... 

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