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2011 Autocomplexation of bioligands in aqueous solution One of the most important purposes in molecular technologies is the preparation of supramolecular structures by self-assembling processes. The aromatic molecules self-associate mainly in π−π stacked structures with an aggregate size distribution determined by the association equilibrium constants. A general expression for the equilibrium constants Kn,m which govern the self-association of two aggregates with n and m monomers respectively has been obtained. The model predicts also the concentrations of free monomers, the concentrations of n-mers, and the total concentration of aggregates. 1H NMR experiments have been used to illustrate the applicability of the proposed model in a particular case: π-stacking self-association of ciprofloxacin in solution. The π−π stacking is an important noncovalent interaction between aromatic molecules having a ubiquitous presence and being the main source of the short-range intermolecular attractive force. Even if the self-association (dissociation) processes can be taken as iso-enthalpic in the first approximation, the entropic effects impose a particular dependence of the equilibrium constants on the size of the associating aggregates. Starting with very general statistical thermodynamical hypothesis, we have found the explicit expression of the association constant Kn,m which govern the equilibrium for an association−dissociation process between two aggregates with n and m monomers respectively. For the particular case of stepwise self association processes there are several models which predict quite different relation between Kn and n. Our predictions confirm the results published several years ago. We have found also the explicit expressions which describe the equilibrium size distribution of aggregates which has been used after that to find the mean number of monomers in an aggregate. All information mentioned above can be obtained if one known only two parameters: the total concentration of monomers and the dimerization constant K2. The model can be also extended for the nonideal molecular systems if the nonassociative interactions between aggregates are weak as compared to the associative ones.The developed theoretical approach was tested on the NMR data obtained from ciprofloxacin self-association experiments. Our theoretical predictions are able to fit very accurately the measured data, but we consider that more important than the accuracy of the data fit is the robustness of the proposed model and the well-fundamented approach. The theoretical approach does not use any empirical conjectures relying only on firm statistical thermodynamical arguments.
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