Question

Compounds like sodium stearate, called "surfactants" in general, can form structures known as micelles in water, once the solution concentration reaches the value known as the critical micelle concentration (cmc). Micelles contain dozens to hundreds of molecules. The cmc depends on the substance, the solvent, and the temperature. At and above the \(\mathrm{cmc}\), the properties of the solution vary drastically. (a) The turbidity (the amount of light scattering) of solutions increases dramatically at the \(\mathrm{cmc}\). Suggest an explanation. (b) The ionic conductivity of the solution dramatically changes at the \(\mathrm{cmc}\). Suggest an explanation. (c) Chemists have developed fluorescent dyes that glow brightly only when the dye molecules are in a hydrophobic environment. Predict how the intensity of such fluorescence would relate to the concentration of sodium stearate as the sodium stearate concentration approaches and then increases past the \(\mathrm{cmc}\).

Short answer

(a) At the cmc, micelles form, causing an increase in turbidity due to the larger size of micelles which scatter more light. (b) The ionic conductivity changes at the cmc because sodium ions become "trapped" inside the micelles, reducing their contribution to the ionic conductivity. (c) As the sodium stearate concentration approaches and surpasses the cmc, the fluorescence intensity increases due to the increasing availability of hydrophobic environments inside the micelles for the dye to fluoresce.

Step-by-step solution

Part (a): Turbidity Increase Explanation

When the concentration of sodium stearate reaches the critical micelle concentration (cmc), micelles start to form. Micelles are aggregates of amphiphilic surfactant molecules (like sodium stearate), with hydrophobic tails facing inward and hydrophilic heads facing outward towards the water. The formation of micelles can cause a significant increase in turbidity (light scattering) because the aggregated micelles are larger than individual sodium stearate molecules, and therefore scatter more light.

Part (b): Ionic Conductivity Change Explanation

The ionic conductivity of a solution is related to the number of free ions that can move and carry an electrical charge. Below the cmc, sodium stearate is dissolved as individual ions (sodium and stearate), which can readily move and contribute to higher ionic conductivity. However, at and above the cmc, a notable portion of the sodium stearate forms micelles. In the micelles, the sodium ions are "trapped" as they are associated with the stearate ions, which reduces their contribution to the ionic conductivity. That's why the ionic conductivity dramatically changes at the cmc.

Part (c): Fluorescence Intensity Prediction

In the presence of sodium stearate, a fluorescent dye will glow brightly only when it is in a hydrophobic environment. Since the interior of micelles is formed by the hydrophobic tails of sodium stearate molecules, it provides a hydrophobic environment for the dye to fluoresce. As the sodium stearate concentration approaches the cmc, the number of micelles starts to increase, providing more hydrophobic environments for the dye to fluoresce in. So, the intensity of fluorescence will increase. Once the concentration surpasses the cmc, micelles are more abundant, and the fluorescence intensity will be higher. However, as the overall micelle concentration increases past the cmc, the increase in intensity may not be as rapid as it was below the cmc since more micelles are already present to accommodate dye molecules.

Key concepts

Surfactants

Surfactants are compounds that have a unique structure, allowing them to lower the surface tension between different substances, such as water and oil. They contain two distinct parts:
- A hydrophilic (water-attracting) head
- A hydrophobic (water-repelling) tail
Due to this structure, surfactants are known as amphiphilic molecules. They can align themselves at the interface of water and oil, making them effective in cleaning products like soaps and detergents. Surfactants can also significantly change the behavior of solutions, especially at higher concentrations when micelles are formed. This process happens at a specific concentration known as the critical micelle concentration (cmc).
At the cmc, surfactants aggregate to form micelles, which can encapsulate oil molecules and enhance cleaning power. The cmc is crucial as it marks a threshold where the properties of the solution change, influencing aspects like turbidity, ionic conductivity, and fluorescence with the addition of certain dyes.

Micelles

Micelles are clusters of surfactant molecules that spontaneously form in a solution when the concentration of surfactants reaches the critical micelle concentration (cmc). Each micelle consists of a core of hydrophobic tails shielded by hydrophilic heads facing the surrounding water.
This configuration forms a spherical shape, allowing the micelles to act like tiny containers for oily substances. As the concentration of surfactants exceeds the cmc, more micelles form, providing more hydrophobic environments. The size of a micelle is significantly larger than individual surfactant molecules, which results in changes to solution properties such as turbidity and ionic conductivity. Additionally, micelles provide unique environments useful in various applications, including encapsulating drugs for delivery in the medical field.

Turbidity

Turbidity is a measure of how clear a liquid is based on the scattering of light. When light shines through a liquid, particles in the liquid scatter the light, causing the liquid to appear cloudy. This cloudiness, or turbidity, increases dramatically at the cmc when micelles begin to form.
Micelles are relatively large compared to individual surfactant molecules, and their presence can cause significant scattering of light. Therefore, at the cmc, the sharp increase in the number of micelles results in more light scattering, and the solution becomes noticeably turbid. This is one of the key indicators that micelle formation has begun in a surfactant solution, making it useful for determining the cmc in experimental settings.

Ionic Conductivity

Ionic conductivity refers to a solution's ability to conduct electricity, which is dependent on the movement of ions within the solution. At concentrations below the cmc, individual ions, such as sodium ions from sodium stearate, are free to move around, contributing significantly to ionic conductivity.
However, at and beyond the cmc, many ions become part of micelles, where they are less mobile. In micelles, the positively charged sodium ions are associated with the negatively charged stearate ions, effectively trapping them within the micelle's structure. This reduces the number of free ions available to conduct electricity, resulting in a notable change in the solution's ionic conductivity. The reduction in ionic mobility is a hallmark of reaching or exceeding the cmc in surfactant solutions.

Fluorescence

Fluorescence is the emission of light by a substance that has absorbed light or other electromagnetic radiation. Certain fluorescent dyes can indicate changes in their environment, such as moving into a hydrophobic space like the interior of a micelle. As micelles provide a hydrophobic core, they create the perfect environment for these dyes to shine brightly.
As the concentration of surfactants like sodium stearate approaches the cmc, micelles start to form, providing increasing sites for the dye to fluoresce. This makes the solution's fluorescence intensity rise as more micelles form. Once the concentration surpasses the cmc, the rate of increase in fluorescence intensity may slow, as there are already plenty of micelles present. This change in fluorescence is a valuable tool in identifying the occurrence and concentration of micelles in solution.