Relative 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... 

In general, the choice of the position of the Gibbs dividing surface is arbitrary. It is possible to define quantities which are invariant with respect to the choice of its location. If Fj or Fj, are the relative adsorption and F and Ff the Gibbs surface excess concentrations of components i and 1, respectively, then the relative adsorption of component i with respect to component 1 is defined by... 

In Figure 2.2 equilibrium adsorption data for carbon dioxide (CO2) on zeolite Na 13X (Linde, UOP) are presented for temperatures 298 K and 303 K. The mol numbers of the Gibbs surface excess amounts per unit mass of sorbent are depicted as function of the sorptive gas pressure and temperature. Relative uncertainties of measurements are about ( ttiGE/ GE)-2%- The subcritical isotherms are in the range of pressure measured of Type I - lUPAC classification [2.20]. 

Thermodynamics of the ITIES was developed by several authors [2-6] on the basis of the interfacial phase model of Gibbs or Guggenheim. General treatments were outlined by Kakiuchi and Senda [5] and by Girault and Schiffrin [6]. At a constant temperature T and pressure p the change in the surface tension y can be related to the relative surface excess concentrations Tf " of the species i with respect to both solvents [6],... 

If we compress a surfactant film on water we observe that the surface tension decreases and the surface pressure increases. What is the reason for this decrease in surface tension We can explain it by use of the Gibbs adsorption isotherm (Eq. (3.52)). On compression, the surface excess increases and hence the surface tension has to decrease. This, however, is relatively abstract. A more illustrative explanation is that the surface tension decreases because the highly polar water surface (high surface tension) is more and more converted into a nonpolar hydrocarbon surface (low surface tension). 

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. 

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

In general the values of rA and rB depend on the position chosen for the Gibbs dividing surface. However, two quantities, TB(A) and rB(n) (and correspondingly wBa(A) and nB°(n)), may be defined in a way that is invariant to this choice (see [l.e]). TB(A) is called the relative surface excess concentration of B with respect to A, or more simply the relative adsorption of B it is the value of rB when the surface is chosen to make rA = 0. rB(n) is called the reduced surface excess concentration of B, or more simply the reduced adsorption of B it is the value of rB when the surface is chosen to make the total excess r = rt = 0. 

Excess Properties Defined Relative to a Gibbs Surface... 

When the thermodynamics of surfaces are discussed in terms of excess quantities relative to a Gibbs surface, there is only one way of defining the excess enthalpy, that is, these quantities depend on (y, /4,) but not on (p, V) because... 

The Universal Quasi-chemical Theory or UNIQUAC method of Abrams and Prausnitz divides the excess Gibbs free energy into two parts. The dominant entropic contribution is described by a combinatorial part ( ). Intermolecular forces responsible for the enthalpy of mixing are described by a residual part ( ). The sizes and shapes of the molecule determine the combinatorial part, which is thus dependent on the compositions and requires only pure component data. Since the residual part depends on the intermolecular forces, two adjustable binary parameters are used to better describe the intermolecular forces. As the UNIQUAC equations are about as simple for multi-component solutions as for binary solutions, the UNIQUAC equations for multicomponent solutions are given below. Species are identified by subscript i, subscript j is a dummy index. Here, is a relative molecular surface area and r, is a relative molecular volume. Both of these quantities are pure-species parameters. 

The second quantity obtained from the Gibbs-Duhem equation is the relative surface excess which is the difference of the amount of a substance in the interphase and the relative amount of solvent (s) expressed by the ratio of the mole fractions r, and x. ... 

Pol5mer solutions are binary systems (we assume the polymer is monodis-perse in relative molecular mass) and the variation of surface tension with composition is governed by the Gibbs equation in the same manner as it is for molecules of low relative molecular mass. In principle the hypothetical dividing surface is placed so that each phase either side is uniform up to the surface. In practice, because liquid surfaces are diffuse (due to evaporation processes and capillary waves), the dividing surface is usually placed so that the surface excess of solvent is zero. Figure 8.21 illustrates this and also defines the surface excess of solute. 

The excesses of the system can be represented by three-parameter quantities. For the existence of the equation of definition, the value of the factors can be chosen arbitrarily. The choice = 0 is permitted. When the values of the factors (v = l v = l / = 0) are chosen, the excess adsorption of a multicomponent system is equal to the adsorption capacity of the surface layer, i.e. to the real amount in the layer (Guggenheim excess if the factors are previously given, the relative Gibbs excess or the Findenegg excess, etc., can also be defined). In an inverse procedure the value of belonging to a given excess can be obtained. Thus, relationships of quantities that are inaccessible in the traditional set of tools can be derived. 

We present a discussion of the uncertainty contributions to the amount of fluid in the continuous phase or the density of the same from the SU in sample and dosing volumes and associated pressure data, and the manifold and adsorption system temperature. Each of the coefficients in the EoS also has its inherent uncertainty, which also needs to be considered. We use nitrogen adsorption data (relative to helium dead-space measurements) for a microporous activated carbon cloth (ACC) to demonstrate uncertainty in the various EoS evaluation and its propagation to the combined standard uncertainty in the (Gibbs) specific surface excess amount,, equivalent to the traditionally known amount adsorbed (in low pressure measurement), shown in Eq. (2)... 

---