Fundamental equations Gibbs adsorption isotherm

This is the important Gibbs adsorption isotherm. (Note that for concentrated solutions the activity should be used in this equation.) Experimental measurements of y over a range of concentrations allows us to plot y against Inci and hence obtain Ti, the adsorption density at the surface. The validity of this fundamental equation of adsorption has been proven by comparison with direct adsorption measurements. The method is best applied to liquid/vapour and liquid/liquid interfaces, where surface energies can easily be measured. However, care must be taken to allow equilibrium adsorption of the solute (which may be slow) during measurement. 

The most fundamental equation governing the properties of interphases is the Gibbs adsorption isotherm ... 

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 ... 

In the last chapter, we discussed the description of pure component adsorption equilibrium from the fundamental point of view, for example Langmuir isotherm equation derived from the kinetic approach, and Volmer equation from the Gibbs thermodynamic equation. Practical solids, due to their complex pore and surface structure, rarely conform to the fundamental description, that is very often than not fundamental adsorption isotherm equations such as the classical Langmuir equation do not describe the data well because the basic assumptions made in the Langmuir theory are not readily satisfied. To this end, many semi-empirical approaches have been proposed and the resulting adsorption equations are used with success in describing equilibrium data. This chapter will particularly deal with these approaches. We first present a number of commonly used empirical equations, and will discuss some of these equations in more detail in Chapter 6. 

In Sect. 4 we present several adsorption isotherms which are solutions of the Maxwell relations of the Gibbs fundamental equation of the multicomponent adsorbate [7.15]. These isotherms are thermodynamically consistent generalizations of several of the empirical isotherms presented in Sect. 3 to (energetically) heterogenous sorbent materials with surfaces of fractal dimension. In Sect. 5 some general recommendations for use ofAIs in industrial adsorption processes are given. 

The three isotherms discussed, BET, (H-J based on Gibbs equation) and Polanyi s potential theory involve fundamentally different approaches to the problem. All have been developed for gas-solid systems and none is satisfactory in all cases. Many workers have attempted to improve these and have succeeded for particular systems. Adsorption from gas mixtures may often be represented by a modified form of the single adsorbate equation. The Langmuir equation, for example, has been applied to a mixture of n" components 11). 

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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