Critical micelle concentration mixed surfactant values

The surface tension of the aqueous solution of dode-cylaitunonium chloride (DAC) — decylairanonium chloride (DeAC) mixture was measured as a function of the total molality m of surfactants and the mole fraction X of DeAC in the total surfactant in the neighborhood of the critical micelle concentration (CMC). By use of the thermodynamic equations derived previously, the mole fraction in the mixed adsorbed film was evaluated from the y vs. X and m vs. X curves. Further, the mole fraction in the mixed micelle was evaluated from the CMC vs. X curve. By comparing these values at the CMC, it was concluded that the behavior of DAC and DeAC molecules in the mixed micelle is fairly similar to that in the mixed adsorbed film. 

One of the main characteristics of the behavior of surfactants in aqueous systems is their tendency to form larger aggregates (micelles) when a certain concentration is reached (critical micelle concentration, CMC). The CMC is specific for each given tenside at a given temperature, but the values given in the literature should be viewed with caution as it is also known that the size of the surfactant aggregates increases with concentration. When different species of surface-active substances are present in a solution, mixed micelles are formed and the CMC of the blend is different from that of each individual surfactant. 

The determination of nonionic surfactants has been demonstrated using mixed micelle formation. This relies on the principle that, to a great extent, micelle formation is additive, i.e., if two surfactants are present, each will be present in the micelles, and the critical micelle concentration (CMC) is the sum of the concentrations of the two surfactants. A dye is chosen which has an absorbance which changes if surfactant micelles are present in solution. A blank solution is titrated with a surfactant, usually an anionic, to determine the CMC. A solution of the unknown surfactant is then titrated, giving an apparent CMC lower than the blank. The difference in the two values represents the contribution of the unknown surfactant, a contribution which is additive over a useful concentration range (85). 

Monomer/Micelle Equilibrium Mixtures of surfactants, like any surfactant species in an aqueous solution, give rise to monomer or micelle aggregates provided that the concentration reaches a minimum value, called the critical micellar concentration (CMC). The micelles thus formed are mixed, i.e. made up of the different surfactant species in solution. 

Molecular interactions between two surfactants at an interface or in micelles are frequently described through the so-called parameters, which can be obtained from surface (or interfacial) tension or from critical micellar concentration data [13]. Attractive interactions are characterized by negative values of this parameter and, specifically, it has been found that it becomes less negative as the mole fraction of the co-surfactant increases. It has also been previously observed [14] that this tendency, for different mixed surfactant systems, can be explained by the role played by the interactions of the cationic surfactants head groups in the stability of the mixed micelles. Desai and Dixit [15] have found similar variations depending on the mixtures composition of cationic and polyoxyethylenic non-ionic surfactants. 

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