Hill-Langmuir equation derivation

Appendix 1.2B Step-by-Step Derivation of the Hill-Langmuir Equation... 

Here, KA and KB are the dissociation equilibrium constants for the binding of agonist and antagonist, respectively. This is the Gaddum equation, named after J. H. Gaddum, who was the first to derive it in the context of competitive antagonism. Note that if [B] is set to zero, we have the Hill-Langmuir equation (Section 1.2.1). 

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... 

Physisorption arises from the van der Waals forces, and these forces also condense gas molecules into their liquid state. Thus, in principle, there is no reason to stop upon completion of a monolayer during physisorption. Indeed, the formation of multi-layers, which are basically liquid in nature, is very common in physisorption experiments. Brunauer, Emmett and Teller developed a theory in 1938 to describe physisorption, where the adsorbate thickness exceeds a monolayer, and this isotherm equation is known by the initials of the authors (B.E.T.). The original derivation of the B.E.T. equation is an extension of Langmuir s treatment of monolayer adsorption from kinetic arguments. Later, in 1946, Hill derived this equation from statistical mechanics. In the B.E.T. isotherm, it is assumed that ... 

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