I'm doing research that requires me to convert surface tension to surfactant concentration in order to know how big the surfactant concentration is after some treatment is applied to a material until its surface tension is reduced?
According to the classical treatment, along the so-called Gibbs adsorption isotherm, i.e. below the critical micelle concentration (cmc), but not for extremely dilute solutions, there is a logarithmic relationship:
d(gamma)/d(log c) = Cst.
Cst depends on the molecular structure (surface area at the interface) of the surfactant.Above the cmc, the surface tension is almost constant. Thus, you have to apply the previous answers.
Christoph is right. In reality you are trying to solve the inverse problem as diferent molecular weight, structure, functional group will affect the surface tension.
You need to measure the Surface tension of known concentrations of "Your" surfactant in order to answer the question. However you may have problems near the miscelle critical concentration where the relationship between concentration and tension changes behaviour. If this is the case you can dilute the sample to bring it to a lower range.
According to the classical treatment, along the so-called Gibbs adsorption isotherm, i.e. below the critical micelle concentration (cmc), but not for extremely dilute solutions, there is a logarithmic relationship:
d(gamma)/d(log c) = Cst.
Cst depends on the molecular structure (surface area at the interface) of the surfactant.Above the cmc, the surface tension is almost constant. Thus, you have to apply the previous answers.
The question is ambiguous: Are you interested in the surfactant concentration "at the surface" or "in the bulk" of the solution? The first and second answers deal with the bulk concentration, while the third one refers to the surface concentration.
I do not think so. The three previous answers were consistent and dealt with bulk surfactant concentration. When gamma is plotted vs. log c, c means the total surfactant concentration. All along the linear part of the curve (gamma lowering), the surface concentration of the surfactant is almost constant.
OK, Jean. What I meant is that the plot of gamma vs. log c is usually employed to estimate the maximum surface concentration. Of course, it can be used in the reverse sense. However, it remains true that the question posed by Mutiara is ambiguous.
Sure, Stephen Johnson is right. Anyway, I am afraid this method will suffer from lack of accuracy.
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