Chemical Potential of the Solvent: A Crucial Player for Rationalizing Host-Guest Affinities

Abstract

Access to reliable values of the thermodynamic constants β1,1H,G , which control simple host-guest ([HG]) association, is crucial in medicine, biology, pharmacy, and chemistry, since the optimum concentration of an effector (i.e., a drug) acting on a receptor is set to 1β1,1H,G . Intermolecular association between charged species in polar solvents, for which water is the archetype, largely obeys this principle. Any deviation from ideality, which alters the speciation in solution, is mastered by the Debye-Hückel theory of ionic atmosphere. Much less is known for related association reactions involving neutral species in non-polar (lipophilic) media such as membranes, bilayers, or organic polymers. Taking the intermolecular association between [La(hfa)₃ dig] guest (hfa=hexafluoroacetylacetonate, dig=2-{2-methoxyethoxy}ethane) and tridentate polyaromatic host receptors L1-L3 in dichloromethane as a proof-of-concept, we show that the progress of the association reactions, as measured by the increase in the mole fraction of occupied sites of the receptors, disrupt the chemical potential of the solvent to such an extent that β1,1H,G may seemingly be shifted by two orders of magnitude, thus leading to erroneous dose-response prescriptions. A simple chemical model, which considers a subset of solvent molecules in surface contact with the partners of the association reaction, restores reliable access to true and interpretable thermodynamic constants. The concomitant emergence of a concentration-dependent corrective parameter reestablishes satisfying dose-dependent response under real conditions. This "complement" to the law of mass action offers a simple method for safely taking care of the non-predictable variations of the activity coefficients of the various partners when host-guest reactions are conducted in non-polar media.

Keywords: binding isotherms; host-guest; lanthanides; solvation; thermodynamics.