CMC prediction for ionic surfactants in pure water and aqueous salt solutions based solely on tabulated molecular...

The critical micelle concentration (CMC) of various surfactants is difficult to predict accurately, yet often necessary to do in both industry and science. Hence, quantum-chemical software packages for precise calculation of CMC were developed, but they are expensive and time consuming. We show here an easy method for calculating CMC with a reasonable accuracy. Firstly, CMC₀ (intrinsic CMC, absent added salt) was coupled with quantitative structure - property relationship (QSPR) with defined by us parameter "CMC predictor" f₁. It can be easily calculated from a number of tabulated molecular parameters - the adsorption energy of surfactant's head, the adsorption energy of its methylene groups, its number of carbon atoms, the specific adsorption energy of its counter-ions, their valency and bare radius. We applied this method to determine CMC₀ to a test set of 11 ionic surfactants, yielding 7.5% accuracy. Furthermore, we calculated CMC in the presence of added salts using the advanced version of Corrin-Harkins equation, which accounts for both the intrinsic and the added counter-ions. Our salt-saturation multiplier, accounts for both the type and concentration of the added counter-ions. We applied our theory to a test set containing 11 anionic/cationic surfactant+salt systems, achieving 8% accuracy.