Backgrounds of fitting procedure

For any thermodynamic model of the adsorbed layer implemented in this package, the equation of state can be expressed in a dimensionless form  

Here H is the surface pressure, F is the adsorption, c is the concentration, b is the adsorption equilibrium constant, co is the area per molecule in the surface layer, and F and G are some functions dependent on F, co and other model parameters denoted here as a, 02,. .. a . For the simplest models considered, namely Langmuir and Frumkin models, co is the model parameter, while for more advanced models this is a property which is defined via model equations. It is essential that in each case F enters the equations via the surface coverage coefficient, 8 = Fco. Also, for each model there exists a parameter, say co, which has the dimension of the area per molecule, and, being introduced into Eq. (7.1), enables one to reduce this equation to a dimensionless form 

In most cases the dependence shown here as Eq. (7.5) is defined in an implicit form, i.e., involves a set of (transcendental) equations which should be solved numerically to represent Eq. (7.5). 

Eliminating the 9 and co between Eqs. (7.3) and (7.5) - this is possible due to special forms of the equations - one obtains the dependence 

Here the subscripts ex and cal refer to the experimental and calculated (for the same n,) surfactant concentrations, respectively. As the values of Ac, = c i-c,., jj are small as compared to, one can transform the minimisation condition, Eq. (7.8), into a dimensionless form  

---