Isotherm in Solution with No Conformational Changes

Langmuir Isotherm in Solution with No Conformational Changes 

We generalize the adsorption model of section 2.8. Most of the assumptions of the simple Langmuir model are still retained, except for two the sites are not localized, and they are solvated by the solvent (the solvent may be any mixture of liquids, but for simplicity we assume that it is a one-component liquid, denoted by w). The simplest way to obtain the modified binding isotherm is to use the thermodynamic approach of section 2.9.1 with the appropriate modification introduced into the chemical equilibrium condition in solution, as in section 8.3. 

Let 5o and Si be the empty and occupied polymer in a solution containing ligand A. The adsorption of A on So is viewed as a chemical reaction (section 2.9.1) of the form 

Using the general expression for the chemical potential for each of the three species [see Eq. (8.3.3)], we rewrite (8.4.2) as 

We shall use Qa for the internal PF of a single polymer and reserve Qa for the PF of a single ligand. 

---