Gibbs surface excess density

This relation allows one to calculate the Gibbs surface excess (mQE) from mass and density measurements of the sorptive gas (m, p, p ) and accompanying helium measurements leading to calibration parameters (mHe.PHe). Details of the experimental procedure by volumetric / manometric measurements and several examples will be given in Chap. 2. 

In the Gibbs model of an ideal interface there is one problem where precisely do we position the ideal interface Let us therefore look at a liquid-vapor interface of a pure liquid more closely. The density decreases continuously from the high density of the bulk liquid to the low density of the bulk vapor (see Fig. 3.2). There could even be a density maximum in between since it should in principle be possible to have an increased density at the interface. It is natural to place the ideal interface in the middle of the interfacial region so that T = 0. In this case the two dotted regions, left and right from the ideal interface, are equal in size. If the ideal interface is placed more into the vapor phase the total number of molecules extrapolated from the bulk densities is higher than the real number of molecules, N < caVa + c V13. Therefore the surface excess is negative. Vice versa if the ideal interface is placed more into the liquid phase, the total number of molecules extrapolated from the bulk densities is lower than the real number of molecules, N > caVa + surface excess is positive. 

Gibbs defined the superficial density , now more commonly called the adsorption or surface excess , for a solution, as follows. In Fig. 26, I, let the horizontal dotted lines represent approximately the limits of the transitional region, between the upper phase a and the lower phase p a normal to the surface is moved round so as to enclose a volume of cross-section A perpendicular to the surface. The volume is finally defined by drawing surfaces PaQa and PpQp parallel to the physical surface, in... 

The surface tension depends on the potential (the excess charge on the surface) and the composition (chemical potentials of the species) of the contacting phases. For the relation between y and the potential see - Lipp-mann equation. For the composition dependence see -> Gibbs adsorption equation. Since in these equations y is considered being independent of A, they can be used only for fluids, e.g., liquid liquid such as liquid mercury electrolyte, interfaces. By measuring the surface tension of a mercury drop in contact with an electrolyte solution as a function of potential important quantities, such as surface charge density, surface excess of ions, differential capacitance (subentry of... 

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. 

Superficial Density An older term now replaced by the Gibbs surface concentration, or simply, the surface excess. 

In the case of sulfate adsorption the surface excesses determined from the charge density data were compared with the Gibbs excesses determined from radiochemical measurements using -labeled sulfate solutions. Very good agreement of the data was reported [89]. 

Mote than a century ago, Gibbs (1878) introduced surface excess quantities as a first step toward resolving this problem. The basic idea is to choose a reference surface S somewhere in the interfadal region. This surface is everywhere perpendicular to the local density or concentration gradient. Consider a property such as internal energy in the region between surfaces and of Figure 1.2 whieh are parallel to S but are located in the respective bulk phases. Because the... 

For a two-dimensional surface, as described by the excess densities introduced by Gibbs, in a thermodynamic system the Gibbs equation is ... 

Fig. 9 shows the ellipsometric isotherm A — Ao(triangles) of the cationic surfactant C12-DMP bromide. A pronounced non-monotonic behaviour is shown with an extremum at an intermidiate concentration far below the cmc. Also shown is the number density of amphiphiles adsorbed to the interface (circles) as determined by Surface second harmonic generation (SHG). At these bulk concentrations the measured number density equals the surface excess F. SHG reveals a monotoneous increase in the surface excess in qualitative agreement to a thermodynamic analysis within the Gibb s framework. The data also clearly prove that the ellipsometric quantity need not be proportional to the adsorbed amount for a soluble ionic surfactant. What causes the nonmonotonous behaviour and how can it be understood ... 

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)... 

This is the form of the Gibbs adsorption isotherm that is commonly used. It relates changes in the surface tension y to the charge density and the surface excess... 

They analyzed their results using a thermodynamic approach based on the Gibbs adsorption equation and the main conclusion of their work was that relative surface excesses of the ionic species were well described by the Gouy-Chapman theory. They adopted the MVN model of the ideally polarized interface stating that the compact layer is an ion-free layer consisting of laminated layers of water and nitrobenzene sandwiched between two diffuse layers. The potential difference across this inner layer was estimated to be about 20 mV at the PZC but was found to vary with the surface charge density. 

In Chapter 9 we have shown the thermodynamic relationships among the surface tension, y, (which is the same as the excess surface Gibbs energy), the excess charge density on the metal, qM, the double layer capacitance, Cai, and the surface excess of a particular species, F,- (cf. Eqs. (9.8) to (9.14)). 

When the Gibbs equation is used for an electrode-electrolyte interface, the charged species (electrons, ions) are characterized by their electrochemical potentials, while the interface is regarded as electroneutral that is, the surface density, 2, of excess charges in the metal caused by positive or negative adsorption of electrons ... 

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