If I e.g. would like to find the CMC for a surfactant molecule, I would make a dilution series from a relatively concentrated stock solution, expectedly well above the CMC. I expect to be able to measure particle sizes down to the CMC, however, when i keep diluting, the particle-numbers per volume naturally decreases. So my question is, how do I know that i have found the CMC and not just the limit of detection for the instrument?
I am aware that DLS works best with dilute dispersions so to have minimal particle interactions etc. But can it get too dilute?
Hi Philipp,
It is possible for a solution to be too dilute for DLS.
In a DLS measurement we detect the scattering from several particles as they diffuse, but if the concentration is so low that the number of particles in the detection volume becomes sensitive to particles migrating in and out of the detection volume, then the detected scattering will vary due to the number of particles as well as their diffusive nature.
This can typically be detected by a high correlation function intercept (>1), as the change in average scattering intensity will effect the normalisation of the correlation data.
Dear Philipp Alexander Elvang , above the CMC surfactant molecules were self-organized in spherical micelles. Usually in DLS measurements, surfactant micelles (like polymer chains) were considered as sphere diffusive particles (that's why we measure hydrodynamic radius or hydrodynamic diameter). So, the difference between the scattered intensity of surfactant micelles and single surfactant molecules should be visible. In the other side, I think that in the limit of detection for the instrument, it will not show any scattered intensity instead of the case of the surfactant molecules below CMC.
The problem with dilute solutions is that they become sensitive to dust and stray light. A single dust particle may generate noise signal that will overwhelm your signal. Similarly small scratches on the glassware will generate stray light, that will invalidate the basic assumptions of DLS. You have better chances with SLS than with DLS for your purposes.
below CMC you don't have particles, so you cannot measure particle size. Above CMC, likely you must have a minimum number of particles (counts) in oder to obtain a measurement statistically acceptable
Hi Philip,
It is better to use another type of technique to determine the cmc of a surfactant, namely tensiometry. With this technique, it is possible to determine the cmc by measuring the variation of the surface tension with the surfactant concentration.
Hi Philipp,
yes there is a lower limit, it would depend on size and is sample dependent. Typically when there are below ~100 particles in the scattering volume number fluctuations will begin. Also the scattering intensity should be significantly higher than the solvent/background alone.
If you plot scattering intensity versus concentration you should see two slopes: at low concentration a "flat" slope of monomer/surfactant only and at higher concentration a "steeper" slope of micelles. The critical micelle concentration is where the two intersect. Above the cmc DLS should work, below cmc it should just be a flat (albeit noisy) baseline.
Malvern has an application note at https://www.malvern.com/en/support/resource-center/application-notes/AN101104SurfactantMicelleCharacterization.html for Triton X-100 showing the two slopes
With DLS you are measuring the diffusion coefficient. For a neutral surfactant this D will not depend a great deal on surfactant concentration. You might do better with static light scattering, since d Intensity/dc changes a lot at the CMC.
The hydrodynamic radius R_h is the radius of a sphere having the same D. There is no assumption that the micelles are spheres. The volume within r_h may contain a great deal of solvent. See some of my papers from two decades back, e.g., the study on Triton X-100.
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