We report results of theoretical and experimental studies of the adsorption of surfactants at the solution-air interface from two aqueous binary nonionic surfactant mixtures: (1) n-dodecyl hexa(ethylene oxide)-n-dodecyl octa(ethylene oxide) (C-12E6-C-12E8), and (2) n-dodecyl hexa(ethylene oxide)-n-decyl tetra(ethylene oxide) (C-12E6-C-10E4). The theory assumes that the surfactant molecules adsorbed at the interface form a mixed monolayer, which is modeled as a binary mixture of hard disks interacting through attractive van der Waals forces. The hard-disk areas are calculated using a Monte Carlo approach which incorporates the conformational characteristics of the chainlike poly(ethylene oxide) surfactant head groups in the context of the rotational isomeric state model. The attractive van der Waals interactions between the surfactant hydrocarbon tails are treated as a perturbation to the hard-disk repulsions, truncated at second order in surface density. The corresponding second-order (virial) coefficients are calculated using detailed molecular information about the two surfactant species present in the monolayer. In so doing, the molecular nature of the mixed monolayer is accounted for explicitly. The behavior of the surfactant molecules in the bulk solution, including the formation of mixed micelles beyond the critical micelle concentration (cmc), is modeled using a recently developed molecular-thermodynamic theory of mixed surfactant solutions. The theoretically predicted surface tension versus bulk surfactant concentration curves at various bulk surfactant compositions are found to be in very good agreement with the experimentally measured ones. The variation of the monolayer composition with total bulk surfactant concentration and composition is also predicted and is found to exhibit an abrupt change at the mixture cmc. This predicted variation of the monolayer composition is rationalized in terms of changes in the distribution of the two surfactant species between the bulk solution and the monolayer due to the onset of mixed micelle formation at the CMC.
