Enthalpy-Entropy Compensation Rule and the Compensation Temperature Observed in Micelle Formation of Different Surfactants in Water. What is the so-called Compensation Temperature?

Abstract

The correlation between the enthalpy (ΔH 0m) and the entropy (ΔS 0m) on micelle formation of more than 20 species of surfastants (including nonionic, anionic and cationic species) or their mixtures reported in the past was examined by the plots of ΔH 0m vs ΔS 0m. For each surfactant system a linear relation having almost the same slope (1/307 K-1), allowing for a small margin of error (±2.3%), was shown, but a different intercept (σ), dependent on the surfactant species, i. e., ΔS 0m=(1/307) ΔH 0m+σ, where 1/307 (K-1) means that the so called compensation temperature (Tc) is 307 K. Strictly speaking, Tc ranges from 299 to 315 K, depending on the species involved. The intercept corresponds to the entropy change at a specific temperature giving ΔH 0m=0 at which the driving force of micelle formation comes only from the entropy term; this temperature is characteristic to the surfactant species. On the other hand, the compensation temperature was extensively discussed and it was concluded that there is found no specially significant meaning other than a mean temperature studied for each surfactant system. However, it was also pointed out that if the Gibbs energy changes (ΔG) for a set of systems have a good linearity with ΔH or ΔS at a fixed temperature, the observed compensation temperature can be attributed to the ratio of enthalpy change difference to entropy change difference (ΔΔH/ΔΔS) which is required to be a constant. For different mixed systems of given nonionic surfactants, abnormally low values in Tc (163 K-180 K) were observed when the compensation relation at each temperature studied was examined as a function of mixing ratio. This was ascribed to the upward convex curve in the CMC-temperature relation.