How does temperature affect the critical micelle concentration (CMC) of the common ionic surface active agent (surfactant) sodium dodecyl sulfate measured by using the change in the rate of conductivity as concentration is increased?

In Grade 6, I was introduced to the subject food technology. In one lesson, my teacher was advising us on how to wash our dishes. He said we should use warm water, as warm as we could handle, to wash the dishes. This confused me. At home, we always just used room temperature water. Although I didn’t think about this often, I recently came across surfactants in the manufacturing of ice cream. After a bit of research, I was utterly confused. Clarity came when I found out the purpose of surfactants: to reduce the surface tension of something, thus making ice cream more creamy by reducing the surface tension between oil and water, allowing the oil to be emulsified.

 

Surfactants perform the same function in soaps. By definition, detergents are surfactants. They work by reducing the surface tension between water molecules and oil molecules in clothes, crockery, and even skin. This allows the object to be cleaned. This investigation aims to explore the effectiveness of detergents at different temperatures.

Surfactant is a general term for compounds with a hydrophilic ‘head’ and a hydrophobic ‘tail’.

Surfactants are used in detergents to disrupt hydrogen bonds between water molecules thereby reducing the surface tension of the water. Surfactants are used in soaps at low concentrations (<2%), this is due to the critical micelle concentration (CMC), a unique value for different types of surfactants at different temperatures. The CMC is the concentration at which the surfactant begins to form micelles. Micelles are supramolecular chemical structures formed from surfactant molecules dispersed in liquids. Micelles interfere with surfactant processes like cleaning and reducing surface tension. The formation of micelles is driven by the decrease in Gibbs Free Energy in the system due to the reformation of hydrogen bonds between water molecules surrounding the surfactant molecule.

 

Hydrogen bonding is exothermic. By Le Chatelier’s principle, at higher temperatures, hydrogen bonding will not be promoted entropically or energetically. This allows the surfactant to better disrupt the formation of hydrogen bonds. Furthermore, the formation of micelles above the temperature corresponding to the minimum CMC is also exothermic, thus is also not promoted at higher temperatures. This allows for a higher concentration of surfactants to be present before the formation of micelles. Below the temperature corresponding to the minimum CMC, micelle formation is endothermic, thus, as temperature increases to the minimum CMC, CMC decreases as a lower concentration of ions are required to make the formation of micelles entropically favourable.

 

Although there are multiple ways to measure critical micelle concentration, the main ones are as follows: measuring surface tension using a tensiometer, or measuring conductivity using an ammeter. This investigation uses conductivity due to the accuracy of the available equipment and its availability. Since sodium dodecyl sulphate is an anionic molecule, as it’s concentration increases, the conductivity of the solution increases. However, as micelles start to form, conductivity continues to increase but at a lower rate due to a slower rate of increase of free ions. Thus a graph of concentration versus conductivity would yield two distinct gradients. The intersection of these lines determines the point at which micelles begin to form, thus the critical micelle concentration.

 

It must be noted that increasing temperature increases the conductivity of ionic solutions. However, since data will be collected using the x value of the intersection of two lines, the current (y value) does not affect the result. Furthermore, since all solutions at the same temperature will be equally affected by this effect, it will not have any effects on the results.

Preliminary tests were done to adapt the method. The results of the preliminary results were -

The CMC was determined by graphing concentration versus current. This yielded two clear gradients, the x coordinate of the intersection yielded the CMC at the given temperature. For 25°C, the CMC was 0.00845 moldm-3 , for 65°C, the CMC was 0.01140 moldm-3 . Although this is an extremely small range, 0.00295 moldm-3 , theory suggests that a graph of temperature versus CMC is non-linear: as temperature increases, CMC initially decreases then increases.

 

The results of the preliminary tests dictated the range of concentrations to use. The results showed that the likely maximum CMC would not exceed 0.0200 moldm-3 and would not be lower than 0.00845 moldm-3 . This determined the range of concentrations used in the experiment: 0.00200 moldm-3 to 0.0160 moldm-3 . This ensured that there would be significant data points before and after the CMC.

• The following solutions were prepared - 0.002, 0.004, 0.006, 0.008, 0.010, 0.012, 0.014 and 0.016 moldm -3 of sodium dodecyl sulphate.
• Apparatus was set up as shown in Figure 2
• A measuring cylinder was used to measure 10cm3 of 0.002 moldm-3 , this was poured into a boiling tube
• The boiling tube was placed into a water bath set at 25°C
• A thermometer was placed inside the boiling tube.
• When the thermometer read 25°C, the power pack was turned on and the solution was poured into the electrolytic cell.
• The reading on the multimeter was recorded after 3 seconds.
• Steps 3 - 7 were repeated using concentrations of 0.004, 0.006, 0.008, 0.010, 0.012, 0.014 and 0.016 moldm-3
• Steps 3-8 were repeated at water bath temperatures of 35°C, 45°C, 55°C, 65°C and 75°C.

Justifying uncertainties - 0.2 °C was used as the uncertainty in the table above due to the time delay when taking the boiling tube out of the water and pouring the solution into the electrolytic cell.

 

Qualitative observations: Limited observations were made during the heating of the solutions (no effervescence, colour change, or gases released). After pouring the solutions into the electrolytic cell, there was a spike in current, the current continued to change rapidly in the first second after pouring the solution in. The current then settled and began decreasing at a rate of about 10μA per second. On occasion, the reading changed at the 3-second mark, in this case, the reading before the change was recorded.

 

Anomalies (highlighted in red): At lower temperatures, there are few anomalies, however, as temperature increases, the number of anomalies increases. This is likely due to steady-state

 

conduction. Steady-state conduction says that the rate of heat transfer is proportional to the temperature difference between two substances. Thus a greater temperature would have a greater rate of heat transfer. In trials above 32.1°C, this causes the temperature to decrease more rapidly than trials below 32.1°C. While this may not cause issues with the experiment (as all trials are allowed to cool for 3 seconds and the calculation of CMC does not rely on the measured temperature), it may exaggerate human error. For example, at low temperatures, there may only be a small temperature change between the second and third seconds after taking the solution out of a water bath, but at high temperatures, this temperature change is much higher. Theory suggests that as temperature increases, conductivity increases, thus subtle differences in temperature may cause differences in conductivity across trials, creating more anomalous results at higher temperatures.

Consider temperature = 22.1 ± 0.2 °C

The graph above shows the x value of the intersection of the two lines to be 0.0101 moldm-3 . Since the CMC is defined as the concentration at which micelles start to form and it has previously been determined that the point of change in gradient gives the CMC, due to the rate of increase of conductivity decreasing.

 

Finding CMC_Avg

 

\(CMC_{Avg}=\frac{CMC_1+CMC_2+CMC_3}{3}\)

 

Consider temperature = 22.1 ± 0.2 °C

 

\(CMC_{Avg }=\frac{0.0101+0.0106}{3}\)

 

CMC _Avg  = 0.0104

 

CMC _Avg Uncertainty

 

\(CMC_{Avg} Unc=\frac{CMC_{Max}-CMC_{Min}}{2}\)

 

Consider Temperature = 22.1 ± 0.2 °C

 

\(CMC_{Avg} Unc = \frac{0.0106-0.0101}{2}\)

 

\(CMC_{Avg}Unc=0.0003\)

 

Figure 3 plots critical micelle concentration versus temperature. As the temperature of the solution increases, CMC decreases between T = 22.1°C and T = 32.1 °C. Between T = 42.3°C and T = 71.0°C, CMC increases somewhat linearly. Theory predicted a graph of CMC versus T to decreases between 0°C and 25°C, then increase at an increasing rate after 25°C. Experimentally, the initial data point, (0.0100, 22.1), does not fit the predicted trend. However, from T = 32.1°C and above, there is a positive trend with an increasing gradient, this fits the predicted trend.

 

This may be due to the enthalpy change of micelle formation. In surfactant solutions, surfactant ions arrange themselves on t he surface of the water, this is exothermic as the hydrophilic tail forms a hydrogen bond with water molecules. As the concentration of surfactants increases, the energy released in the formation of micelles becomes greater than the energy released in the formation of hydrogen bonds at the interface because there are more surfactant molecules, this works in line with the fact that there is less space at the air-water interface for the surfactants to bond to. Micelle formation is also entropically favourable at low temperatures as the micelle can move within the solution whereas surfactant molecules are stuck at the surface. However, as temperature increases, micelle formation becomes less energetically favourable as individual particles have more kinetic energy, and thus can move around more. As the concentration of surfactants increases, micelles can form with more molecules, increasing the energy released from its formation. Eventually, the energy released will be great enough to increase the kinetic energy of the water molecules around it enough to be entropically favourable to form a micelle.

 

The CMC of SDS at 25°C was experimentally determined to be 0.0104 ± 0.0003 moldm-3 , the theoretical value is 0.00800 moldm-3 , giving a percent discrepancy of 30%. The systematic error was found to be 23%. This is a relatively large systematic error, suggesting the investigation was relatively inaccurate. The average random percentage error was found to be 4.93% (sum of percentage errors in temperature and CMC). This is relatively high considering the precision of the equipment used (thermometer 0.05°C, multimeter 0.1 μA) suggesting the investigation could be made more precise (see evaluation).

The natural next steps to this experiment would be to investigate other factors affecting the CMC of SDS. This could include pH, the length of the surfactant molecule, and the concentration of other ions in the solution. The same method for determining the CMC could be applied except instead of changing temperature, pH would change using a series of pH buffer solutions.

Mohajeri, Ehsan, and Gholamreza D. Noudeh. "Effect of Temperature on the Critical Micelle Concentration and Micellization Thermodynamic of Nonionic Surfactants: Polyoxyethylene Sorbitan Fatty Acid Esters." E-Journal of Chemistry, vol. 9, no. 4, 2012, pp. 2268-2274.

 

Research Gate, www.researchgate.net/figure/The-chemical-structure-of-Sodium-dodecyl-sulfate-SDS_fig5_3 12498761. Accessed 9 May 2022.

 

Sakhawat, S. S., and Ejaz-ur Rehman. "Effect of Temperature and Aprotic Solvents on the CMC of Sodium Dodecyl Sulphate." Interactions of Water in Ionic and Nonionic Hydrates, 1987.

 

Zieliński, Ryszard, et al. "Effect of temperature on micelle formation in aqueous solutions of alkyltrimethylammonium bromides." Journal of Colloid and Interface Science, vol. 129, no. 1, 1989, pp. 175-184.