Multiple equilibria of objects with several equivalent binding, docking, coupling, or adsorption sites for neutral or charged species play an important role in all fields of chemistry, including systems with interface dominated structures and functions. The influence of entropy in multiple equilibria can be dominant. We have analyzed them by studying the particle distribution for the conditions that the binding enthalpy of the species is the same for all sites and independent of those that are already bonded. This delivers information on the evolution of the entropy as the reaction proceeds. The validity of the results is independent of the nature and the strength of the binding. The results are relevant for analyzing and interpreting experimental data: e.g. acid-base, ligand exchange or ion exchange reactions, adsorption of species on a surface and insertion of charged or neutral guests into the cavities of microporous and mesoporous hosts. They are also important for understanding observations and planning the synthesis of new host-guest composites. The quantitative link between the description of multiple equilibria and Langmuir’s isotherm was found to provide new insight.[1]
We now investigate systems with two different types of sites, for the conditions that the binding enthalpy of the species is the same for each type of sites and independent of those that are already bonded, by analyzing them using the particle distribution theory as described in ref. [1], for each type of sites separately. Procedure and results are exemplified for an Xm{AB}Xn system with m=0,1,2,3 and n=0,1,2. A numerical analysis of experimental data for system with 5 different types of sites has been carried out previously and has allowed to correct earlier reports on the reaction entropy of silver zeolite A.[2] We now improve the physical insight by using a theoretical description.
[1] G. Calzaferri, PhysChemChemPhys, 19, 2017, 10611-10621.
[2] M. Meyer, C. Leiggener, G. Calzaferri, ChemPhysChem, 6, 2005, 1071-1080.
Prof Calzaferri's analysis is moreover presented in a very didactic fashion.
The presence of multiple equilibria implies that many species are concomitantly present in the system.
A simple expression to obtain the concentration of each species is proposed based only on two parameters.
Beside elegant, I think that this expression would be very useful to experimentalists. It allows to approximately predict the partitioning of multiple species on chemically different sites. This parameter is of key relevance not only in catalysis but also for the production of advanced materials based on inclusion composites.
