The formation of micellar aggregates causes significant changes in a number of physical and chemical properties of the system, such as surface tension, conductivity, fluorescence, pH, etc. (Figure 1). The rate of change of these properties with respect to the surfactant concentration show different trends above and below the CMC. This fact is exploited to follow the formation of micelles and to determine the CMC. Therefore, the determination of CMC essentially turns out to be the determination of the position of the breaking point in the concentration dependence of the selected physical or chemical property of the surfactant solution. Many techniques are available for the determination of the CMCs based on the measurements of surface tension, spectrophotometric, kinetics, conductivity, osmotic pressure, etc. as a function of surfactant concentrations.

Ionic surfactant molecules at low concentrations act like normal electrolytes in aqueous solution but show different behaviour at or above the CMC. Sodium dodecyl sulphate (SDS), cetyltrimethylammonium bromide (CTAB), etc. dissociate in aqueous solutions into pairs of cation and anion where one of the ions is surface active and the other ion with opposite charge is called the counter ion. Thus, an aqueous ionic surfactant solution is like a normal electrolyte solution below the CMC. However, above the CMC when micellar aggregates form, a fraction of the counter ions bind to the aggregates and hence the mobility of such aggregates differs from that of their free monomeric ions. Therefore, electrochemical measurements like the electrical conductance (and specific conductance or conductivity) of ionic surfactant solutions with varying concentrations provide a simple method for the determination of CMCs in the cases of ionic surfactants. The specific conductance (κ) of the solution reflects the charge, mobility as well as the concentrations of all ions present in the solution.

κ=F Σ |z_i|. u_i. C_i = Σλ_i C_i

where F is the Faraday constant (96,485 Coulomb/mol), λ_i =F.z_i.u_i is the molar conductivity, z_i is the charge, u_i is the mobility, and C_i is the molar concentration of ion, i. The specific conductance (κ) is calculated from the product of measured conductance (G) and the electrode cell constant (the ratio L/A, where L is the length of the separation between the electrodes and A is the common area of the electrodes).

κ = G x (L/A)

The value of the cell constant is determined by measuring the conductance of a standard solution of known specific conductance (conductivity). For example, the conductivity of a standard solution of 0.01 mol/L potassium chloride (KCl) is 0.0014088 mho.cm^-1 at 25°C.

If we assume that micelles do not exist below the CMC, then the addition of SDS causes an increase in charge carriers, Na⁺(aq) and CH₃(CH₂)₁₁OSO₃^-(aq). Hence the conductivity (specific conductance), κ, of the surfactant solution below the CMC can be written as the sum of the conductivities of the ions produced by the dissociation of surfactant molecule. If one assumes that the aqueous surfactant solutions obey Kohlrausch's law, then the specific conductance, κ, of surfactant solutions can be written as:

κ = (λ_S + λ_DS) [SDS] = m₁ [SDS] (1)

where λ_S is the ionic conductivity of sodium ion (Na+), λ_DS the ionic conductivity of dodecyl sulphate anion (CH₃(CH₂)₁₁OSO₃^-), [SDS] is the total SDS concentration, and m₁ is the slope of the plot of κ (specific conductance) vs. [SDS] below the CMC. Equation 1 shows the linear relationship between the conductivity and surfactant concentration below the CMC.

The conductivity of surfactant solutions at concentrations above the CMC is different from that below the CMC. Above the CMC, micellar aggregates form. Any further increase in surfactant concentration results in an increase in micelle concentration while the monomer concentration remains approximately constant at the CMC level. Thus, above the CMC, the monomers of concentration CMC as well as the micelles contribute to the conductivity. The dissociation of the molecules involved in forming the micelles is different from that of the monomer molecules. All the counter ions of the long chain ions involved in forming the micelles are not free for participation in electrical conductance due to their inclusion to the head group charge within the micelle. If α is the degree of micellar ionization (in other words, the fraction of surfactant molecules in the micellar aggregate that do not have bound counter ions), then the concentration of such micellar counter ions, S (Na+, in the case of the SDS surfactant) that participate in conductance is given by

[S] = α ([SDS] - CMC),

Thus, one gets three different contributions to the conductivity of the solution above the CMC: (1) conductivity contributions from the ions of free monomers (of concentration = CMC), (2) conductivity from the charged micelles, and (3) the conductivity from the fraction of unbound micellar counter ions.

The conductivity above the CMC is given by:

κ = (λ_S + λ_DS). CMC + λ_mic [micelles] + λ_S α ([SDS] - CMC) (2)

where [micelles] = ([SDS] - CMC)/N and N is the micelle aggregation number. If one assumes that the micelle conductivity is the same as the conductivity of all monomers with electrical charge in the micellar aggregate, then λ_mic = a N. λ_DS and eq. (2) is rearranged as:

κ = (λ_S + λ_DS)(1 - α). CMC + α (λ_S + λ_DS)[SDS] = κ_o + m₂ [SDS] (3)

where m2 is the slope and κo is the intercept of the linear plot of κ versus [SDS] above the CMC. Comparing eq. (1) and (3) one gets α = m₂/m₁, the ratio of the slopes of the straight lines obtained by plotting κ versus [SDS] above and below the CMC, respectively. The CMC value can be determined graphically as the intersection of the two straight lines defined by eqs. (1) and (3). The CMC can also be obtained from the intercept of the straight line obtained above CMC (eq 3). In this case one requires to divide the intercept (κo) by (λ_S + λ_DS)(1 - α) where (λ_S + λ_DS) = m1 and α = m₂/m₁.

The CMC value can also be determined graphically as the intersection of the two straight lines obtained by plotting molar conductance, λ_m versus √C (Kohlrausch Law, where C is the molar concentration), if the surfactant behaves as a strong electrolyte. Values of the molar conductance are calculated from the specific conductivity (κ) and the molar concentration of solution by using the relation, λ_m = κ /C.

FeCl₃ (aq) + 3H₂O (l) → Fe(OH)₃ (s) + 3HCl (aq) >

If a concentrated FeCl3 solution is added to a large quantity of hot water, colloidal iron oxide particles form giving rise to a cherry-red color to the solution.