Thermodynamics of Bile Salt Micelle Formation

In order to make a rough approximation of the thermodynamic constants associated with bile salt micellization, the mass action approach from which Eq. (8) is derived has been employed (44). In water m//i, i.e., the slope of the log CMC-log counterion concentration is zero in the case of NaTC micelles therefore, Eq. (8) reduces the simple form of 

The assumptions implied in this treatment are (a) that the system is mono-disperse, (b) that an abrupt change in the system occurs at the CMC, and (c) that there is a constant concentration of the monomer above the CMC. More refined calculation should take into account the micelle charge, counterion activity, and electrical free energy at the micelle surface (163). With these limitations in mind one can examine the values of JF , and TAS  

TABLE XII. Standard Thermodynamic Functions Expressed in kcal/mole for Micellization of NaTC and NaTDC in Water at Three Temperatures (44) 

The magnitude of the negative AF values obtained indicates that bile salt micellization is always a spontaneous process, i.e., no external work is needed on the system and the detergent ions in the micelle have a lower energy state than in molecular solution. for NaTDC is less than NaTC, and thus NaTDC can be considered (163) to form more stable micelles. As would be expected from its lower CMC, NaTDC forms larger micelles (see Tables IX and X and Section VIII.G.) 

At temperature higher than 50 C, entropy changes for NaTC are negative at the CMC and for NaTDC may be still slightly positive. At these temperatures the driving force for micelle formation would appear to be primarily the heat component or the magnitude of the negative AH and not the entropy factor. 

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