Determination of the aggregation number for micelles by isothermal titration calorimetry

Abstract

Isothermal titration calorimetry (ITC) has previously been applied to estimate the aggregation number (n), Gibbs free energy (ΔG), enthalpy (ΔH) and entropy (ΔS) of micellization. However, some difficulties of micelle characterization by ITC still remain; most micelles have aggregation numbers which are too high to be measured by ITC and even when n is sufficiently low, dilution enthalpies can obscure determination. Furthermore, as the parameters are highly correlated, their estimates have been questioned. The traditional approach also involves regression with an implicit model function for n > 4 and its mathematical implementation is therefore not straight-forward. It seems as if all of these difficulties can be traced back to the aggregation number. In this work a new principle of data quantification is derived which is easy to apply, interpret and will provide statistical reliable estimates of the aggregation number even for high values of n. With the aggregation number at hand, the remaining parameters are readily obtained. The proposed method can be used to estimate the heat of dilution and is therefore robust towards this ubiquitous error in ITC. Furthermore, the method offers insight into optimal design of titration protocols for micelle characterization. By applying the new method, the aggregation number of sodium dodecyl sulphate and glycochenodeoxycholate was determined at concentrations around their critical micelle concentration (CMC).