Micelle Formation: Explanation with CMC

Micelle is a cluster of amphiphilic molecules dispersed in a liquid. They form a colloidal suspension when surfactants tend to dissociate in water. They are also known as the associate colloidal systems. The molecule of micelle contains two parts that are head and tail. The head is a hydrophilic part while the tail is a hydrophobic part. For example, in water, the head region makes a contact with solvent (water) while the tail regions are oriented toward the center of the micelle.

micelle formation

Structure of Micelles

A scientist named Hartley proposed that micelles are basically spherical in their structure. He explained there is some charged group attached to the surface of micelles. Another scientist McBrain suggested that lamellar and spherical forms of micelles exist side by side. Later x-ray studies of micelles by Harkin et al verified the sandwich or lamellar model.

Debye and Anacker suggest they are rod-like shaped instead of spherical. In 1956, Hartley’s spherical-shaped model of micelles was accepted which is published by scientist Reich. Finally, the spherical shape of the micelle is the actual structure.

structure and shapes of micelles

Micelles formation by ionic surfactant has a balance between hydrocarbon chain attraction and ionic repulsion. They have a net charge that is less than the degree of aggregation. This indicates micelles have a large number of counterions. These counterions remain associated with micelles. They also form the stern layer at the surface of micelles.

For nonionic surfactants, the hydrocarbon chain attraction is against the hydrophilic groups. However, the structure of micelles can be determined by equilibrium. This equilibrium is established between the repulsive forces of hydrophilic groups and attractive forces of hydrophobic groups.

Theoretical explanation

The theoretical treatment of micelles depends on whether they are considered chemical species or as a separate phase. There are two models, the mass action model, and the phase separation model.

The mass action model considers micelles as chemical species while the phase separation model regards them as a separate phase. To apply the mass action model, micelle aggregation must be uniform in size and shape or the numerical value of each association must be assumed constant. However, according to the phase separation model, surfactant molecule activity or the surface tension of a surfactant solution should remain constant over the critical micelle concentration.

When micelle is considered a phase. There are three phases (micellar phase, surfactant solid phase, intermicellar bulk phase) that exist with the solubility curve above the kraft temperature (Tk) and Gibbs’s phase rule

f = C – P + 2

where,

  • f = degree of freedom
  • C = component
  • P = phase

The below graph illustrated the changes in solubility on the y-axis and CMC of sodium tetradecyl sulfonate with temperature on the x-axis.

theoritical explanation of micelles

There is only one degree of freedom and the number of components is two that are solvent water and surfactant. According to this model, at constant pressure, the solubility cannot be changed with temperature. This is because the solubility can be automatically determined by the pressure.

When the mass action model is applied, the problem of solubility can be solved. In addition to this, there is an increase in solubility by changing temperature. Let’s suppose an association equilibrium between the surfactant monomers (S) and the micelles (Mn) with aggregation number n,

Kn is the micellization constant. It can also be written as,

Ct is the equivalent concentration of surfactant that is used for micelles and it becomes,

The ratio of the equivalent concentration at T(temperature) at Tk(kraft point) is,

Due to the small temperature range, the value of Kn is assumed constant. The heat of dissolution gets from the solubility change with temperature is about 100 kJmol for ionic surfactants. The solubility change with temperature can be explained as,

If the ΔT = 0.2 oC, the above rations become 2.8 and 13.8 for n = 50 and n =100.

Therefore, a small temperature can bring a large increase in solubility. The abrupt change (increase) in solubility above the Tk is not by the increase in solubility of monomeric surfactant but is due to the increase in the number of micelles.

Therefore, the treatment of micelles as to be separate phase is incorrect while the mass action model is correct with phase rule as well as solubility increase.

Related topics

Critical Micelle Concentration (CMC)

The amphiphilic molecules or surfactants have the capacity to aggregate in solutions. The process of aggregation depends on the condition of the system in which amphiphilic molecules are dissolved. There is an abrupt change that occurs in the chemical and physical properties of the aqueous solution of amphiphilic molecules when a specific concentration is exceeded. This led to the formation of oriented colloidal aggregates.

The narrow concentration range in which those changes occur is called critical micelle concentration (CMC). However, those molecules that are aggregated in the form of clusters above the CMC range are called micelles.

Factors affecting the value of the CMC

There are the following factors that affect the value of CMC in an aqueous solution.

  • Structure of surfactant
  • The electrolyte in the solution
  • Organic compounds in the solution
  • Presence of second liquid phase
  • Temperature

Uses of Micelles

  • They are used in electrophoresis (a technique used to separate the DNA, and RNA molecules).
  • Micelles are used as separation media in chromatography techniques.
  • When surfactants are above the CMC value, micelles act as emulsifiers. They allow compounds to dissolve which are insoluble. For example, the cleaning action of detergents on lipophilic material.
  • They are used in animal bodies for the absorption of fat-soluble vitamins and lipids. Bile salts contain micelles of fatty acids. This allows the absorption of lecithin and vitamins such as A, D, E, and K.
  • They can be used for targeted drug delivery.

Concepts Berg

Why does micelle formation occur?

It occurs by the combined interaction of its head and tail with solvents.

How is the micelle of soap formed?

When soap is added to a solvent( water) it starts interacting with water poles. As soaps are sodium and potassium salts of long carboxylic acids, they start dissociating in the solvent. It does not completely ionize and start micelle formation.

How do micelles enter the cell?

The tail of the micelle is hydrophobic in nature. It can interact with lipid-by-layer of membrane and enter the cell.

How does soap work intermolecular forces?

Soap is sodium stearate salt. As all salt of sodium is water-soluble, on adding in the water, it starts dissolving by creating dipole interaction with water molecules.

What is the cleansing action of soap?

Soaps contain long organic anionic chains which interact with organic impurities on cloth and utensils and remove them.

What is the chemical formula of detergent?

Detergents have a chemical formula of sodium dodecylbenzene sulphonate (C18H29NaO3S).

References

  • Micelle’s theoretical and applied aspects by Yoshikiyo Moroi (Department of Chemistry) (Kyushu University)
  • Surfactants and Interfacial Phenomena: fourth edition by Milton J. Rosen and Joy T. Kunjappu

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