Gibbs surface concentration

By introducing the surface area A the Gibbs surface concentration or surface excess concentration F is given by... 

Alternatively, may be regarded as the Gibbs surface concentration of i when the Gibbs surface is chosen so that Fi is zero, i.e. the Gibbs surface is chosen so that the reference system contains the same amount of component as the real system, hence f h 0. 

Gibbs Surface Concentration The Gibbs surface excess adsorption amount divided by the area of the interface. 

Reduced Adsorption The relative Gibbs surface concentration of a component with respect to the total Gibbs surface concentration of all components. See also reference 4 for the defining equations. 

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

Gibbs equation of surface concentration This equation relates the surface tension (y) of a solution and the amount (T) of the solute adsorbed at unit area of the surface. For a single non-ionic solute in dilute solution the equation approximates to... 

The stabihty of a single foam film can be explained by the Gibbs elasticity E which results from the reduction ia equiUbrium surface concentration of adsorbed surfactant molecules when the film is extended (15). This produces an iacrease ia equiUbrium surface tension that acts as a restoring force. The Gibbs elasticity is given by equation 1 where O is surface tension and is surface area of the film. 

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... 

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 surface concentrations T depend on the thickness of the interfacial region, and we would like to express them through quantities which are independent of it. This can be done for those species which occur both at the interface and in the solution. Usually one of the components of the solution, the solvent, has a much higher concentration then the others. We denote it by the index 0 , and introduce surface excesses with respect to the solvent in the following way In the bulk of the solution the Gibbs-Duhem equation (at constant T and p) is simply E Ni dfri = 0, or ... 

These excess quantities are independent of the thickness chosen for the interface as long as it incorporates the region where the concentrations are different from those in the bulk that is, it does not matter if one chooses too thick a region (see Problem 1). We cannot refer the surface concentrations of the metal particles M, Mz+, and e to the solution. Nevertheless we will drop the asterisk in their surface concentrations to simplify the writing we will eliminate these quantities later. We can now rewrite the Gibbs adsorption equation in the form ... 

Gibbs adsorption equation phys chem A formula for a system involving a solvent and a solute, according to which there Is an excess surface concentration of solute if the solute decreases the surface tension, and a deficient surface concentration of solute if the solute increases the surface tension. gibz ad sorp shan i.kwa-zhon Gibbs adsorption isotherm physchem An equation for the surface pressure of surface [< ... 

Other experiments performed by Bergeron [34] on air foams stabilized with ionic surfactants reveal that the so-called Gibbs or dilatational elasticity e may play an important role in the coalescence process. The Gibbs elasticity measures the variation of surface tension yi t associated to the variation of the surfactant surface concentration F ... 

The Gibbs adsorption equation is a relation about the solvent and a solute (or many solutes). The solute is present either as excess (if there is an excess surface concentration) if the solute decreases the y, or as a deficient solute concentration (if the surface tension is increased by the addition of the solute). 

The second concept that has to be considered is that of absolute adsorption or adsorption of an individual component. This can be considered as the true adsorption isotherm for a given component that refers to the actual quantity of that component present in the adsorbed phase as opposed to its relative excess relative to the bulk liquid. It is a surface concentration. From a practical point of view, the main interest lies in resolving the composite isotherm into individual isotherms. To do this, the introduction of the concept of a Gibbs dividing surface is necessary. Figure 10.6 shows the concept of the surface phase model. 

These conditions are realisable experimentally with solutions of the higher fatty acids and alcohols with water. The cr, curve falls rapidly at first and subsequently approaches almost asymptotically a limiting value. With the aid of the Gibbs equation we may readily determine the form of the T, W curve, where T is the surface The surface concentration may be assumed equal to V if we... 

He suggested that in all cases for both soluble and insoluble substances and for pure liquids the Gibbs film might be regarded as but one molecule thick and consist of pure solute molecules for substances which lower the surface tension of the solvent. If F be the surface concentration in grm. mols per sq. cm., on the hypothesis... 

The inorganic salts raise the surface tension of water and in accordance with the thermod3mamic considerations implied in the Gibbs equation, the surface concentration of solutions must be less than the bulk concentration. 

It thus appears that the surface concentration calculated with the aid of Gibbs equation is equal on the one hand to minus the surface charge found by Lippmann s equation from the slope of the electro-capillary curve and on the other hand to minus the number of grm. equivalents of mercurous ions taken up by an expanding mercury surface or thrown off a contracting one in the course of the N emst ionic transfer. 

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. 

The maximum surface concentration of benzoic acid obtained by extrapolation of the experimental data is rmax = 5.1 X 1014 molecules cm-2. Determine the parameters P and A in the Frumkin equation of adsorption. Calculate the Gibbs energy of adsorption. Compare the results with the Langmuir isotherm. (Sobkowski)... 

Adsorption onto Particles. The Gibbs Adsorption law relates how adsorption onto surfaces affects interfacial tension, dy = - RTfd In c. where y = intcrfacial or surface tension, in N/m (I N/m = 1000 dyn/cm) R = gas constant T = absolute temperature T = interfacial or surface concentration, m mol/unil area (i.c.. adsorption) and i = dimensionless concentration (d In r- = t/r/r, thus units cancel). 

On the other hand, equilibrium at the polarized interface is described by the Gibbs-Lippmann equation (5.9). Here, the equilibrium potential eq, surface concentration Xj Fj of all adsorbing species, their bulk electrochemical potential fa, and the resulting interfacial charge Qi are linked rather less explicitly to surface tension y. 

These insoluble monomolecular films, or monolayers, represent an extreme case in adsorption at liquid surfaces, as all the molecules in question are concentrated in one molecular layer at the interface. In this respect they lend themselves to direct study. In contrast to monolayers which are formed by adsorption from solution, the surface concentrations of insoluble films are known directly from the amount of material spread and the area of the surface, recourse to the Gibbs equation being unnecessary. 

Quantitative determinations of the thicknesses of a multiple - layered sample (for example, two polymer layers in intimate contact) by ATR spectroscopy has been shown to be possible. The attenuation effect on the evanescent wave by the layer in contact with the IRE surface must be taken into account (112). Extension of this idea of a step-type concentration profile for an adsorbed surfactant layer on an IRE surface was made (113). and equations relating the Gibbs surface excess to the absorbance in the infrared spectrum of a sufficiently thin adsorbed surfactant layer were developed. The addition of a thin layer of a viscous hydrocarbon liquid to the IRE surface was investigated as a model of a liquid-liquid interface (114) for studies of metal extraction ( Ni+2, Cu+2) by a hydrophobic chelating agent. The extraction of the metals from an aqueous buffer into the hydrocarbon layer was monitored kinetically by the appearance of bands unique to the complex formed. 

The subscript G specifies elasticity determined from isothermal equilibrium measurements, such as for the spreading pressure-area method, which is a thermodynamic property and is termed the Gibbs surface elasticity, EG. EG occurs in very thin films where the number of molecules is so low that the surfactant cannot restore the equilibrium surface concentration after deformation. 

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 surface excess concentration (T), which is the surface concentration of surfactant, can be determined by the representative Gibbs adsorption equation. The T can be obtained from the slope of a plot shown in Figure 2.1 (y versus log[C] at constant temperature). 

The values of nBa and rB depend on the convention used to define the position of the Gibbs surface. They are given by the excess amount of B or surface concentration of B over values that would apply if each of the two bulk phases were homogeneous right up to the Gibbs surface. See [l.e], and also additional recommendations on p.64. 

On a liquid-gas interface, the partial pressure of the adsorbed gas is substituted in Equation 1.59. On the solid-gas and solid-liquid interfaces, only the excess surface concentration can be measured directly, and not the surface tension. The Gibbs adsorption isotherm is suitable for the calculation of the change of surface tension. 

The capillary-rise method is used to study the change in surface tension as a function of concentration for aqueous solutions of />butanol and sodium chloride. The data are interpreted in terms of the surface concentration using the Gibbs isotherm. 

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