Hydrophobically associated networks - Physical Gels from Biological and Synthetic Polymers - page 160

The standard free energy of micellization Δ G micelle for a micelle of N agg molecules is

given by

0 0

1

D

G micelle ¼ N agg ðμ

N agg μ

Þ¼

k B T ln K N agg ¼ k B T ln CMC

½ : ð 6 : 6 Þ

The enthalpy of micellization at temperature T and pressure P can be calculated from
the Gibbs - Helmholtz relationship,

P ;

∂ð ln CMC ½ Þ

RT 2

D H micelle ¼ ð 6 : 7 Þ

∂ T

and the entropy of micellization is, as usual,

S micelle ¼ D

H micelle D G micelle

D : ð 6 : 8 Þ

T

When the concentration of amphiphilic molecules is increased above the CMC, further
addition of solute molecules results in the formation of additional aggregates, while the
concentration of single molecules is more or less unchanged, remaining at the CMC value.
Temperature plays an important role in the behaviour of amphiphilic molecules. At
low temperatures, the molecules have a very low solubility and most precipitate as
hydrated crystals, in equilibrium with single molecules in solution. As the temperature
is increased, the amphiphiles become soluble, while maintaining the equilibrium
between micelles and single molecules. At the temperature called the Krafft temperature,
the solubility equals the CMC, as shown in Figure 6.2 . It is assumed that the Krafft
temperature is related to the melting temperature of the crystalline hydrocarbon phase,
the interior of the micelles being a liquid hydrocarbon.
CMCs for some common surfactants are listed in Table 6.1 , determined for each
surfactant above the Krafft temperature. There are several experimental techniques to
determine this, the most usual being measurement of the surface tension at the interface

Solid
+
Solution

Micellar solution

Krafft
point

CMC

Monomer solution

T K (Krafft temperature)
Temperature

Solubility curve for amphiphilic molecules, showing the Krafft temperature.

Figure 6.2