Surfactants (Soaps and Detergents) and Physicochemical Properties - Surface and Colloid Chemistry: Principles and Applications - page 65

Slope = 14

Micellar
Phase

CMC
SDS (Mol/Liter)

FIGure 3.18 Solubilization of naphthalene in SDS solutions.

Size analyses of (using light scatter) some spherical micelles of SDS have indeed
shown that the radius of the micelle is almost the same as the length of the SDS mole-
cule. However, if the solute interferes with the outer polar part of the micelle, then the
micelle system may change in such a way that the CMC and other properties change.
This is observed in the case of the addition of dodecanol to SDS solutions. However,
very small additions of solutes show very little effect on CMC. The data in Figure 3.18
show the change in the solubility of naphthalene in SDS aqueous solutions.
Below CMC the amount dissolved remains constant, which corresponds to its sol-
ubility in pure water. The slope of the plot above CMC corresponds to 14 mole SDS:1
mol naphthalene. It is seen that, at the CMC, the solubility of naphthalene abruptly
increases. This is because all micelles can solubilize water-insoluble organic com-
pounds. A more useful analysis can be carried out by considering the thermodynam-
ics of this solubilization process.
At equilibrium, the chemical potential of a solute (naphthalene, etc.) will be given as

μ s s = μ s aq = μ s M (3.43)

where μ s s , μ s aq , and μ s M are the chemical potentials of the solute in the solid state,
aqueous phase, and micellar phase, respectively. It must be noted that, in these
micellar solutions, we will describe the system in terms of the aqueous phase and
the micellar phase. The standard free energy change involved in the solubilization,
ΔG o sol , is given as follows:

ΔG° sol = − R T ln (C s,M /C s,aq ) (3.44)

where C s,aq and C s,M are the concentrations of the solute in the aqueous phase and in
the micellar phase, respectively. The free energy change is the difference between
the energy when the solute is transferred from the solid state to the micelle interior.
It has been found from many systematic studies that ΔG sol is dependent on the chain