On the determination of micellar aggregation numbers from the concentration dependence of13C NMR chemical shifts

The assumptions underlying the extraction of micellar aggregation numbers by means of applying the mass action law to the concentration dependence of¹³C Nuclear Magnetic Resonance (NMR) shift data are discussed. Such data are presented for sodium dodecylsulfate and it is shown that the extracted aggregation numbers are far too small. It is argued that this is in part due to a failure of the mass action law to describe the micellization process but also due to covariance in the parameters of the mass action law. We also suggest a way to analyse¹³C shifts from surfactant systems that is void of artefacts due to changes in volume magnetic susceptibilities and other unwanted artefacts. Finally, we point out that by combining¹³C shifts with the fraction of micellized surfactant (as measured by for instance self diffusion coefficients) it should be possible to monitor changes in micellar shapes as the conditions are changed.