Gibbs surface, excess properties defined

Excess Properties Defined Relative to a Gibbs Surface... 

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. 

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... 

To define a surface excess concentration rigorously, we must decide whether or not to recognize the finite thickness of surfaces. In view of the difficulty of defining surface thickness, Gibbs defined the surface (for thermodynamic purposes) as a mathematical plane or dividing surface of zero thickness near the physical surface, and surface properties as the net positive or negative excess in the vicinity of the surface over the magnitude of the same property in the bulk (Adamson, 1990). 

A curious example is that of the distribution of benzene in water benzene will initially spread on water, then as the water becomes saturated with benzene, it will round up into lenses. Virtually all of the thermodynamics of a system will be affected by the presence of the surface. A system containing a surface may be considered as being made up of three parts two bulk phases and the interface separating them. Any extensive thermodynamic property will be apportioned among these parts. For example, in a two-phase multicomponent system, the extra amount of an i component that can be accom-mondated in the system due to the presence of the interface ( ) may be expressed as Qi Qii where is the total number of molecules of i in the whole system, Vj and Vjj are the volumes of phases I and II, respectively, and Q and Qn are the concentrations of i in phases I and II, respectively. The surface (excess) concentration of i is defined as Fj = A, where A is the surface area. At equilibrium, the chemical potential of any component is the same in each bulk phase and at the surface. The Gibbs adsorption equation, which is one of the most widely used expression in surface and colloid science is shown in Eq. (2) ... 

In defining surface thermodynamic functions, the difficulty over the absence of a unique surface plane is circumvented by defining these functions in terms of surface excess— total minus bulk value of the property concerned [46,47]. Thus the Gibbs surface free energy is defined as... 

In this chapter, the fundamental concepts of colloid science have been introduced. The definition of colloidal particles, those with sizes (in all directions) ranging from 1 nm to 10 pm, has been presented, and their relevance in soil science is stated. The importance of surface properties was remarked, introducing several definitions. The specific surface area is the area per unit mass the surface tension (or surface free energy) is defined as the Gibbs free energy per unit area. The surface excess of a given species is the amount (in moles per unit area) which is accumulated... 

In order to use these equations it is necessary to devise a model which enables the surface excess concentration of species i in the interphase to be defined. The interphase itself is defined by enclosing it in two arbitrary planes positioned in such a way that the bulk phases extend homogeneously up to these planes. Any changes in the thermodynamic properties must occur between these planes (Fig. 5.3). If the thickness of the phase is known, then the concentration of species i can be mathematically expressed this is the Guggenheim model. An alternative approach due to Gibbs introduces a third arbitrary plane called the dividing surface which acts as a reference surface. The concentration of species i can then be expressed in terms of an excess or deficiency of component i at the reference surface with respect to its concentration in the bulk phase. 

Fig. 6.1 A hypothetical profile of the density or of some extensive property (e.g., number of moles, internal energy, free energy, enthalpy, Gibbs energy, entropy) in the heterogeneous system as a function of the distance x perpendicular to the planar interface, (a) Real system values of and are determined at such a distance from the interfacial region that the two phases have their bulk properties, (b) Gibbs model of the interface value of the interfacial excess is given by a sum of areas 1 and 11 [1, 6] (c) Surface phase model of the interface interfacial property is defined such that areas 1, II and III compensate for one another [6, 8]...

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