The surfactants bind monomers together at the air-water interface to reduce the surface tension when they're mixed into water. When the system's surfactant monomers are saturated, they spontaneously join together to form micelles. The smallest concentration at which the molecules of surfactants attach to form micelles is the Critical Micelle Concentration (CMC). This is when one or more of the solution system's parameters (osmotic pressure, interfacial tension, refractive index, conductivity, viscosity) changes.
CMC is one of the major functional markers of surfactants. These parameters can be: their hydrophilic-lipophilic ratio and the number of hydrophilic/hydrophobic groups; molecular weight; purity, among others. So CMC measurement is a crucial part of quality control for surfactant-based pharmaceutical excipients, particularly complex composition excipients. These are some guidelines for CMC measurement.
The conductivity method to calculate the CMC depends on the fact that the conductivity of an ionic surfactant solution changes significantly once the CMC is attained. In particular, when the concentration of the surfactant solution is lower than the CMC, the surfactant molecules are monomers and fully ionized, so conductivity and concentration are linearly related. But when the concentration reaches the CMC, the surfactant molecules create micelles. Micelles don't add much conductivity and therefore the conductivity increases exponentially. This gives rise to an inflection point on the conductivity-concentration curve, and the concentration that lies at that inflexion point is called the CMC.
Fig. 1. Specific conductance of CTAB against different concentrations of CTAB
It should be noted that the conductivity method is primarily suitable for ionic surfactants. For non-ionic surfactants or systems with low surface activity, this method may lack sufficient sensitivity. Other parameters are also considered during the experiment, including temperature, solvent and inorganic salts as these affect conductivity and therefore the calculated CMC value.
The Surface Tension method is a popular one to measure the CMC. The first principle is to measure the difference between the solution surface tension and the amount of surfactant. Once the molecules of surfactant adsorb onto the solution surface and are saturated, the surface tension is much lower. As the concentration increases further, the change in surface tension becomes gradual. The concentration at this point is identified as the CMC.
Specific Steps:
1. Prepare the Solution
Make multiple batches of surfactant solutions of different concentrations. It is usually the solvent deionized water and the volume and concentration range should cover the predicted CMC value.
2. Measure Surface Tension
Determine the surface tension of each solution with a surface tensiometer (Platinum plate or Platinum ring). Multiple measurements for each concentration are recommended to ensure accuracy.
3. Plot the γ-logC Curve
Plot the measured surface tension values (γ) against the logarithmic concentrations (log C) to create a γ-logC curve. On this curve, a distinct inflection point will appear when surfactant molecules begin to form micelles. The concentration corresponding to this point is the CMC.
Fig. 2. Surface Tension Measurement CMC
4. Determine the CMC
Extend the straight-line portions on both sides of the curve and find their intersection point, or directly observe the lowest point on the curve to determine the CMC value. If the inflection point on the curve is not obvious, linear fitting methods can be used for further confirmation.
5. Data Analysis
Record and analyze the experimental data to ensure accuracy and repeatability of the results. There are also other validation techniques (such as conductivity technique or fluorescence technique) to confirm the results.
Note that the surface tension method is applicable to ionic and non-ionic surfactants, and its sensitivity is not influenced by the presence of inorganic salts or impurities in the solution. But this approach involves high instrument accuracy and exact monitoring of temperature and solution purity during the experiment.
The surface tension method is a simple, intuitive, and widely applied approach for determining the CMC. From the γ-logC curve and the inflection point of the curve, it's possible to measure a surfactant's CMC.
Fluorescence to determine the Critical Micelle Concentration (CMC) is a popular and sensitive method that takes advantage of a variation in the fluorescence properties of a probe under various microenvironments to establish the CMC value. This is a simple, sensitive and affordable method, especially useful for measuring the CMC in systems.
This is the fundamental tenet of the fluorescence method: the fluorescence intensities of a probe (pyrene, for example) in polar and non-polar conditions. When the surfactant level is lower than the CMC, the probe is mainly bound to water molecules, and fluorescence becomes dim. When it is higher than the CMC, the probe penetrates into the hydrophobic structure of the surfactant molecules, and the fluorescence intensity jumps up dramatically. The CMC value can be calculated by detecting the intensity shift of fluorescence.
When the probe is pyrene, for instance, the CMC can be calculated by determining the fluorescence intensity ratio of pyrene in different concentrations. Upon passing through the hydrophobic core, pyrene has a huge fluorescence intensity ratio, and so it inflections. The concentration corresponding to this inflection point is the CMC. Additionally, non-linear fitting of the curve can provide a more precise determination of the CMC value.
Fig. 3. CMC measurement by fluorescence employing pyrene as the probe molecule
The fluorescence method can also be coupled with other methods like conductivity and surface tension method for validation. The Fluorescence CMC value has been confirmed by research as being roughly identical to those calculated with conductivity and surface tension techniques. But the fluorescence is probably more sensitive and reliable in some circumstances.
Note that probe selection also makes a big difference to the results. Different probes may exhibit varying sensitivity and applicability to specific surfactants or systems. For example, BCDO and pyrene have demonstrated good consistency when determining the CMC of CTAB, while other probes may require further validation of their suitability.
This fluorescence technique is a very good choice for CMC measurement, especially in high sensitivity and precision research areas. But in practice a suitable probe should be chosen for the given system, and the outcome must be confirmed using alternative methods to make sure of reliability.
It is a popular way to calculate the CMC, based on the change in the turbidity of the solution. When the surfactant solution reaches its CMC, the solution becomes very insoluble with hydrocarbons or insoluble dyes and it suddenly turns opaque. The intensity here is a representation of the CMC.
In use, a small quantity of a hydrocarbon probe compound (eg, pyrene or its derivatives) is added at a certain concentration to a surfactant solution. This solution is slowly decondensed and the fluctuations in turbidity recorded. When a significant change in turbidity is observed, the surfactant concentration at this moment is identified as the CMC.
It should be noted that while the amount of hydrocarbon probe used is small and generally has a minimal effect on the CMC, it may still exert some influence.
Fig. 4. Turbidity of different concentrations of the solution to determine the CMC
The turbidity method offers advantages such as simplicity of operation and low equipment requirements, making it suitable for various types of surfactants. However, this method also has certain limitations, such as potential influences from the type and amount of hydrocarbon probe used. Therefore, adjustments and optimizations may be necessary based on specific situations in practical applications.
The turbidity approach is a great one to measure the CMC because it can correctly determine the CMC by monitoring the turbidity changes of the solution. Yet the probe material should be selected and used in sufficient quantity to minimize its impact on the results.
Calculation of the CMC is important to the interpretation of surfactant behaviour. There are different approaches depending on the type of surfactant and application. For reproducible and repeatable CMC values, it's essential to have optimal experimental conditions and data analysis.
References
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