A (partial) resolution of binding enthalpy discrepancies in ITC studies of Ba²⁺ crown ether complexation: The...

By conducting binding experiments at a range of temperatures T using isothermal titration calorimetry (ITC), one can obtain two estimates of the binding enthalpy - calorimetric (ΔH°_cal) from the experiments at each T, and van't Hoff (ΔH°_vH) from the T dependence of the binding constant K°. From thermodynamics it is clear that these two must be identical, but early efforts to demonstrate this for ITC data indicated significant inconsistency. In an extensive 2004 study of the Ba²⁺ + 18-crown-6 ether complexation used in prior comparisons, Mizoue and Tellinghuisen found modest (10-20%) but statistically significant differences, which were tentatively attributed to problems converting the calorimetric estimates to their standard state values, as implied by the superscript ° in the notation. In the present work the 2004 results are reanalyzed using results obtained since then from temperature, heat, and volume calibration of the instrument and a better determination of the data variance function required for the weighted least-squares fitting of the data. The new results show consistency for temperatures 5-30 °C but persistent statistically significant differences from 35 to 46 °C. Several possible explanations for the remaining discrepancies are examined, with methods that include fitting the K and ΔH_cal data together.