Gibbs adsorption relation

These surface active agents have weaker intermoiecular attractive forces than the solvent, and therefore tend to concentrate in the surface at the expense of the water molecules. The accumulation of adsorbed surface active agent is related to the change in surface tension according to the Gibbs adsorption equation... 

The value of 9 can be estimated on purely theoretical grounds from estimates of the adsorption of surfactant which, in turn, can be estimated from the Gibbs adsorption equation relating adsorption to surface-tension lowering. 

Adsorption onto Particles. The Gibbs Adsorption Law relates how adsorption (qv) onto surfaces affects interfacial tension,... 

The appreciation of the importance of adsorption phenomena at liquid interfaces is probably as old as human history, since it is easily recognized in many facets of everyday life. It is not surprising that liquid interfaces have been a favorite subject of scientific interest since as early as the eighteenth century [3,4], From an experimental point of view, one obvious virtue of the liquid interfaces for studying adsorption phenomena is that we can use surface tension or interfacial tension for thermodynamic analysis of the surface properties. The interfacial tension is related to the adsorbed amount of surface active substances through the Gibbs adsorption equation. 

The Gibbs equation relates the extent of adsorption at an interface (reversible equilibrium) to the change in interfacial tension qualitatively, Eq. (4.3) predicts that a substance which reduces the surface (interfacial) tension [(Sy/8 In aj) < 0] will be adsorbed at the surface (interface). Electrolytes have the tendency to increase (slightly) y, but most organic molecules, especially surface active substances (long chain fatty acids, detergents, surfactants) decrease the surface tension (Fig. 4.1). Amphi-pathic molecules (which contain hydrophobic and hydrophilic groups) become oriented at the interface. 

Equation 17.23 has the form of an adsorption isotherm since it relates the amount adsorbed to the corresponding pressure. This is known as the Gibbs Adsorption Isotherm. For it to be useful, an expression is required for T. Assuming an analogy between adsorbed and liquid films, Harkins and Jura(15) have proposed that ... 

The Gibbs adsorption theory (Birdi, 1989,1999, 2002, 2008 Defay et al., 1966 Chattoraj and Birdi, 1984) considers the surface of liquids to be monolayer. The surface tension of water decreases appreciably on the addition of very small quantities of soaps and detergents. The Gibbs adsorption theory relates the change in surface tension to the change in soap concentration. The experiments that analyze the spread monolayers are also based on one molecular layer. The latter data indeed conclusively verifies the Gibbs assumption (as described later). Detergents (soaps, etc.) and other similar kind of molecules are found to exhibit self-assembly characteristics. The subject related to self-assembly monolayer (SAM) structures will be treated extensively (Birdi, 1999). However, no procedure exists that can provide information by direct measurement. The composition of the surface of a solution with two components or more would require additional comments. 

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). 

Ionic surfactants are electrolytes dissociated in water, forming an electrical double layer consisting of counterions and co-ions at the interface. The Gouy-Chapman theory is used to model the double layer. In conjunction with the Gibbs adsorption equation and the equations of state, the theory allows the surfactant adsorption and the related interfacial properties to be determined [9,10] (The Gibbs adsorption model is certainly simpler than the Butler-Lucassen-Reynders model for this case.). 

This is the Gibbs adsorption equation that relates y to the number of moles and the chemical potentials of the components in the interface. 

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). 

While the derivation of these quantities seems at first a bit of a mathematical card trick without a real application, interfacial scientists do utilize these equations on a day-to-day basis. The Gibbs adsorption equation that relates interfacial tension to the interfacial coverage is a perfect example of a thermodynamic relationship that can be obtained from... 

The choice of the ideal interface in the Gibbs adsorption isotherm (3.52) for a two-component system is, in a certain view, arbitrary. It is, however, convenient. There are two reasons First, on the right side there are physically measurable quantities (a, 7, T), which are related in a simple way to the interfacial excess. Any other choice of the interface would lead to a more complicated expression. Second, the choice of the interface is intuitively evident, at least for ci > C2. One should, however, keep in mind that different spatial distributions of the solute can lead to the same T. Figure 3.6 shows two examples of the same interfacial excess concentration In the first case the distribution of molecules 2 stretches out beyond the interface, but the concentration is nowhere increased. In the second case, the concentration of the molecules 2 is actually increased. 

For solutions the Gibbs dividing plane is conveniently positioned so that the surface excess of the solvent is zero. Then the Gibbs adsorption isotherm (Eq. 3.52) relates the surface tension to the amount of solute adsorbed at the interface ... 

By using the Gibbs adsorption theorem and the relation between the three-dimensional pressure p and the film pressure de Boer and Hill derived from Eq. 36 and equation for a two-dimensional adsorption with two separate types of interactions4 ... 

The interfacial tension y and the bending stress C are not independent quantities, being related via the generalized Gibbs adsorption equation derived by Buff (refs. 18,16). It has the f ortn ... 

The image force formalism was intended primarily to relate, via the Gibbs adsorption equation, the increase of the surface tension of water to the negative adsorption of the electrolyte ions. Its effect on the double layer interactions was examined by Jonsson and Wennerstrom [4]. 

The increase of the surface tension of water by the addition of an electrolyte was traditionally related (via Gibbs adsorption equation) to the negative adsorption of ions on the interface. However, some electrolytes decrease the interfacial tension [29], hence should be positively adsorbed. Therefore, if the van der Waals interactions would repel all the ions from the interface, some additional interactions have to be included to explain the positive adsorption. 

Gibbs s analytical proof of the adsorption formula is, mutatis mutandis, analogous to the analytical deduction of the Gibbs-Duhem relation both depend on the integration of the formula for the increment in energy, followed by differentiation and comparison of the result with the original formula. 

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... 

The relation between film stability, spreading coefficient on a substrate and surface pressure can be found using the method proposed by Frumkin [20] and Derjaguin [538]. A diagram is drawn of the dependence film tension versus area of a mole of the substance in the film (Ao = I/O, T being the number of moles of the substance in a unit area. At small substance concentrations (pressures) in the gas phase, its adsorption is close to Gibbs adsorption. 

Gibbs-Duhem relations, the Gibbs adsorption equation and the Phase Rule... 

Standard Gibbs energies of adsorption are often encountered. When A j G is accurately known as a function of temperature, standard enthalpies and entropies of adsorption can also be obtained, using the appropriate Gibbs Helmholtz relations (sec. 1.2.15). 

The Gibbs--Duhem Relation as a Basic Expression for Gas Adsorption... 

In this equation and F are real excesses in the interface. At issue now is whether these are identical to the analytically determined ones, using some depletion technique. The problem is that in such methods one measures the decrease of the solute concentration by adsorption, but how can one do that in practice when the system contains more solute them solvent We discussed this issue in detail in secs. II.2.1 and 4. Let us briefly elaborate this for consfaint temperature. In [4.2.1] d/Xj and d/x are coupled by the Gibbs-Duhem relation (l-x)d/Xj -i-xd/x =0, so we can eliminate either one of the chemieal potentials, obtaining these alternatives... 

Of these, (1) and (ii) have been encountered over and again. Adsorption isotherms were discussed in some detail in chapters 1.3 and II. 1 and 2. Appendix 1 of Volume II gives a survey of the most relevant isotherm equations. The corresponding 2D equations of state are repeated and extended in table 3.3 in sec. 3.4e. Now we consider set (lii). For each Isotherm is fully determined by and Tj(Cj), but as we also have the Gibbs equation, relating to changes in x and there is redundancy x(Cj) can be obtained in more than one way. 

Adsorption of surfactants (molecules that contain a hydrophobic moiety). Interfacial tension and adsorption are intimately related through the Gibbs adsorption law its content—expressed in a simple way—is that substances that reduce surface tension become adsorbed at interfaces. 

The Gibbs equation relates the extent of adsorption at an interface (reversible equilibrium) to the change in interfacial tension equation 19 predicts that a... 

An increase in surface concentration of active substance T occurs in the following relation with surface tension y (the Gibbs adsorption isotherm) ... 

The equations (28.28), (28.29) and (28.30) are forms of the Gibbs adsorption equation, first derived by J. Willard Gibbs (1878) it relates the surface excess of the solute to the variation of the surface tension of the solution with the concentration (or activity). If an increase in the concentration of the solute causes the surface tension of the solution to decrease, i.e., (dy/dc)T9 is negative, F2 will be positive, by equation (28.30), so that there is an actual excess of solute in the surface in other words, adsorption of the solute occurs under these conditions. If (dy/dc)T is positive, F2 is negative and there is a deficiency of the solute in the surface this phenomenon is referred to as negative adsorption. 

Gas-solid equilibria have been studied for over 200 years, since Fontana showed that activated charcoal adsorbs gases and vapors at room temperature [1]. A considerable amoxmt of theoretical and experimental literature is available. The Gibbs isotherm [2] and the multilayer adsorption theory of Brunauer, Emmett and Teller [3], provide serious theoretical guidelines and support in understanding the results of experimental studies. Although, gas-sohd isotherms are difficult to predict quantitatively [4], this branch of adsorption thermod3mamics is much easier than liquid-solid adsorption because of the relative simplicity of the gas-sohd interface as compared to the liquid-solid interface. The Gibbs equation relates the amoimt of a compoimd adsorbed per unit surface area of a hquid-gas or a hquid-hquid interface and the surface or interfacial tensions [2]. This relationship provides a useful theoretical framework. 

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