Thermodynamic Contribution of Water in Cryptophane Host-Guest Binding Reaction

Abstract

A detailed examination of binding thermodynamics is undertaken for the interaction between rubidium ion and a water-soluble cryptophane molecule using isothermal titration calorimetry. The equilibrium-binding quotient for this host-guest pair decreases with increasing product formation. When analyzed with a thermodynamic framework that considers water explicitly in the governing equation, the shift in equilibrium is ascribed to an unfavorable change in the free energy of solvation upon formation of the inclusion complex. A van't Hoff analysis of the binding data, as well as an observation of aggregation between inclusion complexes, suggests that charge-charge interactions between rubidium ion and the phenolate groups of the cryptophane host provide the driving force for association in water that overcomes a large and unfavorable change in solvent enthalpy.

Figure 1.

The binding of rubidium ion to host 1 (left) is accompanied by the displacement of water molecules from the central cavity and the hydration shell of rubidium, indicated as (H₂O)_n. Aqueous solubility of host 1 is dependent on the phenolate anions, as achieved in basic solutions.

Figure 2.

Linear binding relationship in accord with eq 15. Slope and y-intercept represent ΔG° and ΔG^H2O, as reported in Table 2. The lower red line was calculated from the average value of K_a obtained for all concentrations and trials at T = 323 K (K_a = 2.86 ± 0.30). Error bars reflect the uncertainty in K_a.

Figure 3.

A van’t Hoff plot of the free energies derived from eq 15 at each temperature. The enthalpy and entropy values correspond to the slope and y-intercept of each line, respectively. Arrows point toward the corresponding axis.