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

Abstract

The colligative property freezing point depression is evaluated as a means for estimating the extent of aggregation for solutions of poly(ethylene oxide) alcohol (CE) nonionic surfactant in cyclohexane. Combined with additional measurements of self-diffusion coefficients, it is shown that both unaggregated CE as well as reverse micelles are significantly present for the entire range of measured CE concentration (0.048-2.35 mol kg). A change in speciation near 0.2 mol kg is indicated by the results from both freezing point depression and self-diffusion coefficient measurements. It is shown that average reverse micelle radii and aggregation numbers obtained from the ratio of solvent and CE 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 CE 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 CE.

Breakdown of the Stokes–Einstein Equation for Solutions of Water in Oil Reverse Micelles

“…The results from this study confirm the prior findings on the binary system C 10 E 6 in cyclohexane (no water added) that the Stokes−Einstein equation fails to provide reasonable aggregate radii for this reverse micelle-forming system. 17 This finding was attributed to a change in mass-transport process from the movement of the small reverse micelles at low surfactant concentration to individual C 10 E 6 molecules jumping from reverse micelle to reverse micelle at high surfactant concentration. Additional insights can be derived from the observation in this study that the cyclohexane self-diffusion coefficient is independent from the amount of present water.…”

“…The latter are plotted in Figure 6 The aggregation numbers for 0% added water reproduce the values reported in our previous study. 17 Vasilescu et al reported for the reverse micellar system of 15% C 12 E 4 in cyclohexane at 8 °C an average aggregation number of 45 when 1% by mass water was added and 67 when 2% by mass water was added. 14 The concentration of 15% C 10 E 6 in cyclohexane was chosen for this study to facilitate comparison with these results.…”

“…As explained in the introduction, a key motivation for this study on C 10 E 6 reverse micelles in cyclohexane as a function of water load was to inspect the validity of (a) the Stokes−Einstein equation and (b) the ratio of cyclohexane and surfactant self-diffusion coefficients, D C 6 H 12 /D C 10 E 6 , to obtain average reverse micelle radii. Thus, the same evaluations to obtain radii in these two ways were carried out here as described previously 17 using eqs 1, 4, and 5, where here too a value of 2.90 Å was taken for r C 6 H 12 . The expression in eq 4 has been derived by Chen and Chen 60 from the microfriction theory by Gierer and Wirtz.…”

“…16 In this regard, a recent study of reverse micelles of C 10 E 6 in cyclohexane used combined measurements of NMR selfdiffusion, viscosity, and melting point depression to characterize the speciation and average reverse micelle size as a function of C 10 E 6 concentration. 17 Unreasonably small radii and thus aggregation numbers were obtained when using the Stokes− Einstein equation with worsening trend as the surfactant concentration was increased. However, reasonable radii and aggregation numbers were obtained when using a simple calculation based on the ratio of C 10 E 6 and cyclohexane selfdiffusion coefficients.…”

Pulsed field gradient NMR diffusion measurement in nanoporous materials

“…[49,50], and Baniani et al this issue). These nuclei offer, with the increase of their electron shell, the additional advantage of facilitating high-resolution measurement, with the option to selectively determine the diffusivity of each individual component in mixtures [38,[50][51][52]] to which we shall refer in more detail in Sects. 4.6 and 4.7.…”