Gibbs adsorption isotherm applications

The quantitative relationship between the degree of adsorption at a solution interface (7), G—L or L—L, and the lowering of the free-surface eneigy can be deduced by using an approximate form of the Gibbs adsorption isotherm (eq. 9), which is applicable to dilute binary solutions where the activity coefficient is unity and the radius of curvature of the surface is not too great ... 

The simplest application of the Gibbs adsorption isotherm is a system of two components, e.g., a solvent 1 and a solute 2. In this case we have... 

S. Ikeda, M. Tsunoda and H. Maeda, Application of Gibbs adsorption isotherm to aqueous solutions of a nonionic cationic surfactant, J. Colloid Interface Sci. 67 (1978) 336-348. 

An excellent application of LEED not requiring detailed understanding of diffracted intensities is the study of diffusion of adsorbed atoms into the substrate bulk. Conversely, segregation at a surface of atoms previously dissolved in the substrate lattice can be observed too. These processes, bulk solution and precipitation at a surface, are ultimately controlled by the Gibbs adsorption isotherm which determines equilibrium concentration at the interface. Atoms from the gas phase can contribute to such surface equilibria also. Distribution of foreign atoms between surface and bulk may be important in catalysis (393). 

The preferential sorption-capillary flow model starts from the consideration of the solid-liquid interface. For example, aqueous sodium chloride solution is in contact with a solid surface. Sodium chloride solution represents the reverse osmosis system where the separation of solute (sodium chloride) flrom solvent (water) occurs. This system also represents one of the most important applications of reverse osmosis, i.e., seawater desalination. A concentration gradient should inevitably appear at the solution-solid interface, as shown in Figure 6.1. The Gibbs adsorption isotherm... 

The dependence of interfacial tension upon applied potential may be derived by application of the Gibbs adsorption isotherm to the system of... 

The isotherm is applicable only to monolayer adsorption. The last point may seem obvious when an isotherm is discussed in the context of adsorption of intermediates in electrode kinetics, but it should be emphasized here that this does not apply to the discussion of surface excess and the Gibbs adsorption isotherm, which were treated in Section 9.1. 

The applicability of eq. (11.22) to a successful description of adsorption from a solution was established by Langmuir himself, when he compared his adsorption isotherm to the Gibbs equation and ended up with the Szyszkowski equation as a result. The transition from localized to non-localized adsorption (which can be viewed as the transition from fixed adsorption sites to moving ones) does not, therefore, change general trends in the adsorption in the cases described. One should also keep in mind that the liquid interface is more uniform in terms of energy than the solid interface, which contains active sites with different interaction potentials.4 The latter is probably the reason why... 

We have addressed the various adsorption isotherm equations derived from the Gibbs fundamental equation. Those equations (Volmer, Fowler-Guggenheim and Hill de Boer) are for monolayer coverage situation. The Gibbs equation, however, can be used to derive equations which are applicable in multilayer adsorption as well. Here we show such application to derive the Harkins-Jura equation for multilayer adsorption. Analogous to monolayer films on liquids, Harkins and Jura (1943) proposed the following equation of state ... 

The approach of IAS of Myers and Prausnitz presented in Sections 5.3 and 5.4 is widely used to calculate the multicomponent adsorption isotherm for systems not deviated too far from ideality. For binary systems, the treatment of LeVan and Vermeulen presented below provides a useful solution for the adsorbed phase compositions when the pure component isotherms follow either Langmuir equation or Freundlich equation. These expressions are in the form of series, which converges rapidly. These arise as a result of the analytical expression of the spreading pressure in terms of the gaseous partial pressures and the application of the Gibbs isotherm equation. 

The multicomponent adsorption isotherm for the component 1 is obtained by the application of the Gibbs equation ... 

An appendix to this paper discusses thermodynamic consistency tests for binary solute adsorption. Provided that the data are within the Henry s law region of the isotherm, it is shown that application of the Gibbs adsorption equation leads, for any closed path, to... 

Application of the extended set of tools allows isotherms of binary systems to be computed, on the basis of Eq. (8) and the Gibbs adsorption equation, without any direct adsorption experiment. 

Alternatively, q x may be obtained from the application of Eq. XVII-107 to adsorption data at two or more temperatures (see Ref. 89). Similarly, q is obtainable from isotherm data by means of Eq. XVII-115, but now only provided that isotherms down to low pressures are available so that Gibbs integrations to obtain v values are possible. 

Gomez etal. [160] have studied specific adsorption of potassium penicillin G (salt K) on Hg electrode from electrocapillary and capacity measurements. The Frumkin isotherm has been found applicable to the quantitative description of the data repulsive interaction parameter equaled —3.5 and standard free Gibbs energy of adsorption at the zero charge was —38.6 kJ mol h depended linearly... 

When a surfactant is injected into the liquid beneath an insoluble monolayer, surfactant molecules may adsorb at the surface, penetrating between the monolayer molecules. However it is difficult to determine the extent of this penetration. In principle, equilibrium penetration is described by the Gibbs equation, but the practical application of this equation is complicated by the need to evaluate the dependence of the activity of monolayer substance on surface pressure. There have been several approaches to this problem. In this paper, previously published surface pressure-area Isotherms for cholesterol monolayers on solutions of hexadecy1-trimethyl-ammonium bromide have been analysed by three different methods and the results compared. For this system there is no significant difference between the adsorption calculated by the equation of Pethica and that from the procedure of Alexander and Barnes, but analysis by the method of Motomura, et al. gives results which differ considerably. These differences indicate that an independent experimental measurement of the adsorption should be capable of discriminating between the Motomura method and the other two. 

The material in this chapter is organized broadly in two segments. The topics on monolayers (e.g., basic definitions, experimental techniques for measurement of surface tension and sur-face-pressure-versus-area isotherms, phase equilibria and morphology of the monolayers, formulation of equation of state, interfacial viscosity, and some standard applications of mono-layers) are presented first in Sections 7.2-7.6. This is followed by the theories and experimental aspects of adsorption (adsorption from solution and Gibbs equation for the relation between... 

In many practical applications, the wetting liquid in question is a solution, e.g. an aqueous solution containing surface-active components. Then, the possibility of adsorption at all interfaces surrounding the three-phase contact-line (tcl) must be considered. According to the Gibbs isotherm for adsorption at the ij interface ... 

We start this book with a chapter (Chapter 2) on the fundamentals of pure component equilibria. Results of this chapter are mainly applicable to ideal solids or surfaces, and rarely applied to real solids. Langmuir equation is the most celebrated equation, and therefore is the cornerstone of all theories of adsorption and is dealt with first. To generalise the fundamental theory for ideal solids, the Gibbs approach is introduced, and from which many fundamental isotherm equations, such as Volmer, Fowler-Guggenheim, Hill-de Boer, Jura-Harkins can be derived. A recent equation introduced by Nitta and co-workers is presented to allow for the multi-site adsorption. We finally close this chapter by presenting the vacancy solution theory of Danner and co-workers. The results of Chapter 2 are used as a basis for the... 

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