Surfactants (Soaps and Detergents) and Physicochemical Properties - Surface and Colloid Chemistry: Principles and Applications - page 51

Effect of alkyl chain length: It has been found that CMC decreases with increas-
ing alkyl chain length.
The following relation has been found for Na-alkyl sulfate detergents:

ln(CMC) = k 1 − k 2 (C alkyl ) (3.7)

where k 1 and k 2 are constants, and C alkyl is the number of carbon atoms in the
alkyl chain.
CMC will change if the additive has an effect on the monomer-micelle equi-
librium, and also if the additive changes detergent solubility. The CMC of all ionic
surfactants will decrease if coions are added. However, nonionic surfactants show
very little change in CMC on the addition of salts, which is to be expected from
theoretical considerations. The change of CMC with NaCl for SDS is as follows
(Figure 3.10):

nacl (mol/l) cmc (mol/l) g/l nagg

0 0.008 2.3 80

0.01 0.005 1.5 90

0.03 0.003 0.09 100

0.05 0.0023 0.08 104

0.1 0.0015 0.05 110

0.2 0.001 0.02 120

0.4 0.0006 0.015 125

The radius of the spherical micelle is reported to be 20 Å, which increases to 23 Å
for the nonspherical micelle.

3

SDS - 25 C

0.1

0 5

NaCl (Mol/Liter)

FIGure 3.10 Variation of CMC with added NaCl for micelles.