Surface concentration, using Gibbs

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. 

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. 

Adsorbent nonpermeability is an important condition, since it essentially states that all processes occurs in the liquid phase. Since adsorption is related to the adsorbent surface, it is possible to consider the analyte distribution between the whole liquid phase and the surface. Using surface concentrations and the Gibbs concept of excess adsorption [20], it is possible to describe the adsorption from binary mixtures without the definition of adsorbed phase volume. 

For many purposes it is conducive to start analyses with thermodynamic considerations. In this way, it is often possible to find laws of general validity and to determine the boundaries between which models can be developed. For the study of (relaxed) double layers the Gibbs adsorption equation is the starting point. Although the interfacial tension of a solid-liquid interface cannot be measured, this equation remains useful because it helps to distinguish measurable and Inoperable variables, and because it can be used to correlate surface concentrations of different species (Including the surface ions), some of which may not be analytically accessible. 

Three characteristics can be used to define the simple Gibbs monolayers that are now under discussion, viz. the surface tension y (or surface pressure x), the surface concentration r and the bulk mole fraction x or concentration c.. Between these... 

III.B. Calculation of Surface Concentrations and Area Per Molecule at the Interface by Use of the Gibbs Equation... 

For surface-active solutes the surface excess concentration, p can be considered to be equal to the actual surface concentration without significant error. The concentration of surfactant at the interface may therefore be calculated from surface or interfacial tension data by use of the appropriate Gibbs equation. Thus, for dilute solutions of a nonionic surfactant, or for a 1 1 ionic surfactant in the presence of a... 

There are two principal problems with penetration experiments the adsorption characteristics of the protein have to be understood, and the amount of protein that adsorbs to the interface when lipid is present has to be determined. Previously, most researchers used the change in film pressure (Atr) as a measure of the amount of protein that interacted with the lipid monolayer. However, this approach implicitly assumes that the adsorption of protein can be described by Gibbs adsorption equation, but as pointed out by Colacicco (6), this is invalid for proteins which adsorb irreversibly. Because the surface concentration of protein is unknown, radiolabeled proteins have been used (8, 9, 10). This work has been concerned exclusively with highly water-soluble proteins whose prime mode of interaction with monolayers (and bilayers) is electrostatic. In these cases a simple description of the packing in the mixed lipid-protein films was impossible (6). 

Number of moles of adsorbed gas (surface excess) using the Gibbs method. Surface concentration, n /a, using the Gibbs method. 

The adsorption of the anionic surfactant sodium dodecyl sulphate (SDS), probably the most frequently studied surfactant and often used as model substance at the air/water and at the decane /interface is given in Fig. 1.5. The surface and interfacial tension have been plotted as a function of SDS concentration in the aqueous phase. From the slope of the tangents to the curves in Fig. 1.5 the interfacial excess concentration (adsorption density) F at different interfacial tensions can be calculated directly using Gibbs fundamental adsorption isotherm (see section 2.4.1),... 

Surface tensions can also be used to predict the behavior of multicomponent solid systems. Unlike single-component systems, the surface tension is no longer equal to the surface free energy G, but is related to the different component concentrations at the surface by the Gibbs equation ... 

Clearly, the Gibbs dividing surface is used in Eq. (53), where Eq = 0. The adsorption isotherm [Eq. (52)] involves another definition of the dividing surface (Lucassen-Reynders surface with Tq 9 0), which inevitably introduces some deficiency when a solution of Eqs (52) and (53) is simultaneous used. For a fixed concentration of inorganic... 

To illustrate the dependence of the mobility function d>y on the concentration of surfactant in the continuous phase, in Fig. 12 we present theoretical curves, calculated in Ref 138 for the nonionic surfactant Triton X-100, for the ionic surfactant SDS ( + 0.1 M NaCl) and for the protein bovine serum albumin (BSA). The parameter values, used to calculated the curves in Fig. 12, are listed in Table 4 and K are parameters of the Langmuir adsorption isotherm used to describe the dependence of surfactant adsorption, surface tension, and Gibbs elasticity on the surfactant concentration (see Tables 1 and 2). As before, we have used the approximation Dj Dj (surface diffusivity equal to the bulk dif-fusivity). The surfactant concentration in Fig. 12 is scaled with the reference concentration cq, which is also given in Table 4 for Triton X-100 and SDS + 0.1 M NaCl, cq is chosen to coincide with the cmc. The driving force, F, was taken to be the buoyancy force for dodecane drops in water. The surface force is identified with the van der Waals attraction the Hamaker function Ajj(A) was calculated by means of Eq. (86) (see below). The mean drop radius in Fig. 12 is a = 20 /pm. As seen in the figure, for such small drops 4>y = 1 for Triton X-100 and BSA, i.e., the drop sur-... 

We see that many isotherm equations (linear, Volmer, Hill-deBoer, Harkins-Jura) can be derived from the generic Gibbs equation (2.3-13). Other equations of state relating the spreading pressure to the surface concentration can also be used, and thence isotherm equations can be obtained. The following table (Table 2.3-1) lists some of the fundamental isotherm equations from a number of equations of state (Ross and Olivier, 1964 Adamson, 1984). 

Theoretically, one can determine the adsorption at the SI interface from the change in 0° with surfactant concentration. Using the Gibbs equation, it is possible to determine the adsorption of surfactant at the 1-2 interface (from dcTuld In c). It is found experimentally that for most hydrocarbon surfactants on nonpolar surfaces, the adsorption at SI is the same as that at the 1-2 interface, or that Fsi F. ... 

First, for all reduced surfactants dissolved in solution at concentrations near their critical micelle concentrations (CMC), oxidation leads to an increase in the surface tension of the solution (Fig. 1). In the case of surfactants I and n, oxidation returns the surface tension of the solution to a value that is similar to the surfactant-free solution of electrolyte (approx. 72 mN/m). The excess surface concentration of surfactant, estimated using the Gibbs adsorption equation, decreases in the case of surfactant II from 10x10 to < 0.1 X10 mol/m upon oxidation. Clearly, oxidation drives the desorption of surfactant from the surface of the solution. The increase in surface tension of... 

The interface in extraction systems is usually studied by measuring the interfacial tension, viscosity and potential. To study the adsorption kinetics, one usually plots the isotherms of the interfacial tension and uses the Gibbs adsorption equation to calculate the surface concentration of the extractant [15-22]. In practice, the concentration of the extractant is selected so as to saturate the monolayer at the interface. In such systems a rise in extractant concentration does not affect the extraction rate if the limiting stage is the surface reaction or a reaction in the adjoining layers [17-20,23]. 

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