Cooperativity and the Extended Site Binding Model

8 Hamacek, J., Borkovec, M. and Piguet, C., Simple thermodynamics for nnravelling sophisticated self-assemhly processes , Dalton Trans. 2006, 1473-1490. 

In the previous section we came across the concept of effective molarity, EM, an empirical parameter that is used extensively (e.g. in polymer chemistry) to assess the relative efficiency of intra versus inter-molecular complexation processes EM = open (Equation 10.3 and Eigure 10.15). 

If we express EM in terms of free energies we obtain Equation 10.13 and we can recognise that -RTln( M) is an empirical correction factor when an intermolecnlar process is replaced by an intramolecular one. If we substitute into Equation 10.13 the separate enthalpy and entropy terms and recognise that in a strain free ring we get Equation 10.14. 

It is convenient to replace EM with the identical but theoretical parameter effective concentration (c 0- Substituting this nomenclature change into Equation 10.14 we get Equation 10.15 and hence we can derive Equation 10.16 from the original definition of EM (Equation 10.3). 

The same approach can be applied not only to the bulk equilibrium constants (K) but also to the microscopic connection processes (given the symbol k). Recall that the macroscopic equilibrium constant is simply the sum of all the microscopic equilibrium constants. Eor example, if an acid (H2A) has two non-equivalent ionisable protons there are two distinct but equivalent ways to remove a proton to produce H A and hence there are two microscopic equilibrium constants (ki and kf) for this deprotonation process. Thus the macroscopic acid dissociation constant, = ki+k2. Don t get confused between microscopic equilibrium constants and rate constants, both of which have the symbol k. So, in terms of 

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