Thermodynamic Functions of Micelle Formation

When Y,i N i is very large, say more than 50, the second terms of (5.81) and (5.82) can be neglected compared with the first terms, resulting in 

These equations are equivalent to those for the phase-separation model of micelle formation. 

In the case of an ionic surfactant, the surfactant ions (1) and counterions (2) are regarded as different components. Then we have from (5.79) 

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The thermodynamics of small systems developed by Hill [183] has been applied to non-ionized, non-interacting surfactant systems by Hall and Pethica [184]. In this approach the aggregation number is treated as a thermodynamic variable, thereby enabling variations in the thermodynamic functions of micelle formation with the mean aggregation number n to be examined. The thermodynamic functions of micellization assuming solution ideality are... 

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