Synergism in binary mixtures of surfactants: I. Theoretical analysis

Abstract

Nonideal solution theory is used to derive equations for the conditions under which synergism can exist in aqueous binary mixtures of surfactants. For synergism in surface tension reduction efficiency, β, the experimentally obtained molecular interaction parameter at the aqueous solution/air interface, must be negative and ∥ ln ( C 1 0 C 2 0 )∥ must be <∥β M∥, where C 1 0 and C 2 0 are the solution phase molar concentrations of surfactants 1 and 2, respectively, required to produce a given surface tension (reduction). For synergism in mixed micelle formation, β M , the molecular interaction parameter in mixed micelle, must be negative and ∥ ln ( C I M C 2 M )∥ must be <∥ β M ∥, where C 1 M and C 2 M are the respective critical micelle concentrations (CMC) of surfactants 1 and 2. For synergism in surface tension reduction effectiveness, the condition is: f 1, c X c < f 1 M X M , where X M and X c are the mole fractions of surfactant 1 in the total surfactant in the mixed micelle and in the mixed monolayer at the aqueous solution/air interface, respectively, and f 1, c and f 1 M are the activity coefficients in the surface phase at the CMC and in the micelle, respectively.