Thermodynamics of micellization
In colloidal chemistry, the critical micelle concentration (CMC) of a surfactant is one of the parameters in the Gibbs free energy of micellization.
The concentration at which the monomeric surfactants self-assemble into thermodynamically stable aggregates is the CMC.
The interaction between the hydrophilic heads and the hydrophobic tails play a part, as well as the concentration of salt within the solution and surfactants.
[1] Hydrophobic coagulation occurs when a positively charged solution is added with a sodium alkyl sulfate.
Hydrophobic coagulation occurs when a negatively charged solution contains a cationic surfactant.
Because the blocks are covalently bonded to each other, they cannot demix macroscopically as water and oil.
The driving mechanism for micellization is the transfer of hydrocarbon chains from water into the oil-like interior.
Compared to the increase of entropy of the surrounding water molecules, this hydrophobic interaction is relatively small.
Depending on the type of head-group and surface, the attraction will have a short-range contribution for both non-ionic and ionic surfactants.
[2] Aggregation is opposed due to the repulsion of the polar head groups as they come closer to each other.
Hydration repulsion occurs because head groups have to be dehydrated as they come closer to each other.
Two methods to extract the Gibbs free energy based on the value of CMC and
exist; Phillips method[3] based on the law of mass action and the pseudo-phase separation model.
Phillips[3] defined the CMC as the point corresponding to the maximum change in gradient in an ideal property-concentration (
According to Phillips method the Gibbs free energy change of micellization is therefore given by:
That is, for micelles behaving in accordance with the law of mass-action, the pseudo-phase phase separation model is only an approximation and will only become asymptotically equal to the mass-action model as the micelle becomes a true macroscopic phase i.e. for
In this case a chemical equilibrium process can be assumed between the charged micelles
, that is in the limit when then the micelles becomes a true macroscopic phase, the Gibbs free energy is usually approximated by:
In the dressed micelle model, the total Gibbs energy is broken down into several components accounting for the hydrophobic tail, the electrostatic repulsion of the head groups, and the interfacial energy on the surface of the micelle.
[5] where the components of the total Gibbs micellization energy are hydrophobic, electrostatic, and interfacial.
[6] As temperature is raised above the cloud point this causes the distinct surfactant phase to form densely packed micelle groups known as aggregates.
[6] The phase separation is a reversible separation controlled by enthalpy (promotes aggregation/separation) above the cloud point, and entropy (promotes miscibility of micelles in water) below the cloud point.
Below the CMC there is not a high enough density of surfactant to spontaneously precipitate into a distinct phase.
CMC is determined by establishing inflection points for pre-determined surface tension of surfactants in solution.
[8] Below this temperature no level of solubility will be sufficient to precipitate aggregates due to minimal movement of particles in solution.
Because the Tk is fundamentally based on the Caq, which is controlled by surfactant and salt concentration, different combinations of the respective parameters can be altered.
[8] Although, the Caq will maintain the same value despite changes in concentration of surfactant and salt, therefore, thermodynamically speaking the Krafft temperature will remain constant.
≤ 1/3 appear to have a cone-like shape which will pack together to form spherical micelles when in an aqueous environment (top in figure).
≤ 1/2 appear to have a wedge-like shape and will aggregate together in an aqueous environment to form cylindrical micelles (bottom in figure).
> 1/2 appear to have a cylindrical shape and pack together to form a bilayer in an aqueous environment (middle in figure).
