Fundamental equations monolayers

Another important field of the application of fractal approach to texturology is related to surface roughness. Anvir and Pfeifer [212,213] proposed characterization of surface irregularities by adsorption and established two methods, based on Mandelbrot s fundamental equations of type 9.69. According to the first method of Dt calculation, one uses the relations that interrelate a number of molecules in a complete monolayer during physisorption, nm, or an accessible surface area, A, with a cross-sectional area, w, which correspond to one molecule in a monolayer ... 

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 this review, we focus on the recent advances of SSHG at liquid/liquid interfaces. We first present the theoretical background with the fundamental equations necessary to analyse the data. Then, we discuss the origin of the SH response at liquid/liquid interfaces before presenting a review on experimental results at liquid/liquid interfaces. We first describe the structure of amphiphile monolayers at free interfaces and ITIES, in particular, the interfacial orientation and solvation properties of the monolayers. We then present dynamics studies like isomerization processes, chemical equilibria and finally charge-transfer reactions across liquid/liquid interfaces. 

Fundamental Equations in Colloid and Surface Science 87 Four states of monolayers (films)... 

The two fundamental properties of surfactants are monolayer formation at interfaces and micelle formation in solution for surfactant mixtures, the characteristic phenomena are mixed monolayer formation at interfaces (Chapter 2, Section RIG) and mixed micelle formation in solution (Chapter 3, Section VIII). The molecular interaction parameters for mixed monolayer formation by two different surfactants at an interface can be evaluated using equations 11.1 and 11.2 which are based upon the application of nonideal solution theory to the thermodynamics of the system (Rosen, 1982) ... 

The derivation of Equations (435) and (436) from dilute solutions is only approximate. It is also possible to thermodynamically derive more fundamental types of these equations by using the activity concept, but initially we need to define non-localized, ideal and nonideal monolayers. If all the solute molecules are mobile in a monolayer, this is called a non-localized monolayer. We may consider three types of molecules in non-localized mono-layers ideal point molecules having no mass and volume where no lateral interactions are present between these point molecules non-ideal molecules having their mass and volume but no lateral interactions taking place between them, as above and non-ideal molecules having their mass and volume, and in addition appreciable lateral interactions taking place between them. 

---