Selective determination of surface density of bromide ion through XAFS and its application to verification of a criterion of an ideal mixing of surfactant mixture

The mole fraction of chloride ion of dodecyltrimethylammonium bromide (DTAB) and dodecyltrimethylammonium chloride (DTAC) mixture in the adsorbed film XHC was estimated not only by the thermodynamic analysis of the surface tension data but also by analyzing the Br K-edge jump of the XAFS spectrum under the total reflection condition (TRXAFS method). The phase diagrams of adsorption (PDA) at several surface tensions from the two methods were in good agreement. On the basis of the PDA obtained, it was clearly shown that the criterion of an ideal mixing for the DTAB-DTAC system is not given by the linear relation between the total molality of surfactant mixture m and XHC, m = m0B + (m0C - m0B)XHC, but by the one between m2 and XHC, m2 = (m0B)2 + (m0C)2 - (m0B)2]XHC. Furthermore, it was demonstrated that the theoretical approach that provides the latter relation draws a distinction between the criteria for an ionic surfactant mixture without a common ion and that for an ionic surfactant mixture with a common ion.