NMR studies of binary surfactant mixture thermodynamics: Molecular size model for asymmetric activity coefficients

Pulsed-field-gradient NMR methods are used for determining the partitioning of surfactants between unimeric and micellar forms in mixed surfactant sys tems. The method allows determination of the composition dependence of acti vity coefficients in binary surfactant mixtures. Application of the regular solution approach to NMR data for several mixtures gives beta parameters w hich are dependent on concentration and which differ systematically among t he surfactants within the same binary mixtures. The beta parameter summariz es interactions among different pairs of surfactants and, in principle, sho uld not be composition dependent. The observed behavior is therefore not co nsistent with expectations from the regular solution model. Use of the van Laar expressions, on the other hand, accounts well for the composition depe ndence of the activity coefficients. The van Laar expressions also account for the often-observed composition dependence of regular solution beta para meters determined from CMC measurements. Though similar to the symmetric re gular solution model, the van Laar expressions contain an additional parame ter which reflects differences in the sizes of the mixture components. The results therefore suggest that headgroup size and headgroup packing are imp ortant contributors to nonideal surfactant behavior. Computer algorithms ar e described for extracting the van Laar interaction energy- and size-relate d parameters from NMR-derived results, from mixed critical micelle concentr ations, or from heats of mixing. Data for several binary surfactant mixture s are presented and discussed. The results emphasize that when accurate dat a are available, the single-parameter regular solution model will not alway s fully account for nonideal surfactant mixing.