Adsorption on a Single-Site Polymer with Conformational Changes Induced by the Binding Process
One of our main assumptions in the derivation of the Langmuir model [and implicitly made by Langmuir himself (1918)] is that the binding process does not affect the distribution of states of the adsorbent molecules. Removal of this assumption has a profound effect on the form of the BI of systems with more than a single site.
KeywordsMole Fraction Langmuir Isotherm Adsorbent Molecule Langmuir Model Conformational State
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- *.Wyman and Gill (1990) express an apparently different view, referring to single-site systems as cooperative. We shall see in Section 3.5 and in Section 4.6 that this is not a genuine cooperativity, and we shall refer to it as spurious cooperativity.Google Scholar
- †.We suppress the free-energy character of these two states in order to highlight the emergence of new free energies whenever we average either over conformational states (e.g., Section 3.3) or over solvent configurations (see Chapter 9).Google Scholar
- *.More details on this topic can be found in Chapter 3 of Ben-Nairn (1992).Google Scholar
- †.A minimum of two ligands must cooperate to observe a cooperative system. A different view is expressed in Wyman and Gill (1990). These authors correctly point out that in a single binding site there can be no cooperativity (page 51). However, three pages later they refer to a mixture of single-site molecules as being negative cooperative. No less confusing is the usage of two different definitions of “macroscopic” and “microscopic” cooperativities [Bradsley and Waight (1978), Whitehead (1980), Briggs 1984), DiCera (1996)]. These authors rely on the shape of the BI to define cooperativity. As we shall see in this and in the next chapter, definitions of cooperativity based on the shape of the BI could be quite misleading.Google Scholar
- ‡.The GPF of this system depends also on the volume V, but we suppress this dependence in our notation.Google Scholar
- †.more detailed discussion of this point can be found in Chapter 2 of Ben-Nairn (1992).Google Scholar
- ‡.Examples are the heat capacity, the compressibility, etc. For more details, see Chapter 7 in Ben-Nairn (1992).Google Scholar
- *.One may wonder how a system with two conformers, having the same energies, can differ so widely in their binding energies. This is possible. Consider a binding molecule with an asymmetric (or chiral) center. In that case the two enantiomers, one being a mirror image of the other, have exactly the same energy. If the ligand is a single enantiomer of an asymmetric molecule, then it is possible that it will bind with very different binding energies to the two enantiomers of the adsorbent molecule.Google Scholar