# Three-Site Systems: Nonadditivity and Long-Range Correlations

Chapter

## Abstract

In this chapter we discuss three-site systems. We extend the three models treated in Chapter 4: direct correlation, indirect correlation mediated through the adsorbent molecule, and indirect correlation mediated by a chain of communicating subunits. Here, we discuss separately two possible structures of the system, a linear and a triangle arrangement of the sites (Fig. 5.1). Two fundamentally new features are discussed in considerable detail: the nonadditivity of the triplet correlation and the possibility of long-range correlations.

## Keywords

Binding Constant Adsorbent Molecule Pair Correlation Binding System Binding Isotherm
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## References

- *.Note that we always assume that the ligand is very small relative to the adsorbent molecule. Otherwise, even when the binding energy is the same for each site, the PFs for singly occupied molecules could differ, e.g., the rotational PF of a molecule having a ligand bound to the center or to the edge will be different. See also Section 5.10 and Appendix B.Google Scholar
- †.This is sometimes referred to as a perturbation effect. In this book we shall not use this term. In general, we shall include in the binding free energy the interactions of the ligand at site; with the
*entire*molecule. See also Section 2.2 and Appendix I.Google Scholar - *.This is sometimes referred to as the “identical-symmetrical” case. Symmetry in itself is not enough to distinguish between a weak and strict sense. (Both linear and triangle, and similarly square and tetrahedral, models are symmetric.) Perhaps the requirement of the arrangement with highest symmetry better characterizes the identity in the strict sense.Google Scholar
- †.Note, however, that
*k*_{1}depends on the interaction of the proton with the other two charges on the two carboxylate groups. Hence, it is different from*k*_{1}of benzoic acid; see Section 5.9. Similarly,*k*_{11}depends on the interaction with the third carboxylate group—hence it differs from*k*_{11}for 1,3-dibenzoic acid.Google Scholar - *.For details of the calculations, see Ben-Nairn (1997,1998). †See Ben-Nairn (1998) as well as Appendix I.Google Scholar

## Copyright information

© Springer Science+Business Media New York 2001