Combining Freezing Point Depression and Self-Diffusion Data for Characterizing Aggregation

The colligative property freezing point depression is evaluated as a means for estimating the extent of aggregation for solutions of poly(ethylene oxide) alcohol (C10E6) nonionic surfactant in cyclohexane. Combined with additional measurements of self-diffusion coefficients, it is shown that both unaggregated C10E6 as well as reverse micelles are significantly present for the entire range of measured C10E6 concentration (0.048−2.35 mol kg−1). A change in speciation near 0.2 mol kg−1 is indicated by the results from both freezing point depression and selfdiffusion coefficient measurements. It is shown that average reverse micelle radii and aggregation numbers obtained from the ratio of solvent and C10E6 self-diffusion coefficients are consistent with prior reported results. However, unreasonably small radii for the reverse micelles as well as for the cyclohexane were obtained from analysis of the results by the Stokes−Einstein equation using additional measured solution viscosities. The concentration of reverse micelles and unaggregated C10E6 was calculated from the freezing point depression results using the aggregation numbers obtained from ratio of self-diffusion coefficients. These concentrations indicate that the reverse micelles become smaller in average size and increase in number with increasing temperature without an increase in unaggregated C10E6.