CHARGE EFFECTS IN THE TRANSIENT ADSORPTION OF IONIC SURFACTANTS AT FLUID INTERFACES

A rigorous model is presented for diffusive transport of ionic surfact ants to an adsorbing interface. The proposed model considers both the diffusion and migration of surfactant, counterions, and background ele ctrolyte in the electric field that develops as the charged surfactant adsorbs at an interface. The transient electrical double-layer struct ure arising from specific adsorption of the surfactant is calculated b y solving the coupled Nernst-Planck and Poisson equations in the bulk phase using a Frumkin constitutive relation for the interfacial bounda ry condition. The resulting transient double-layer model is valid over all time scales and for interfacial potentials and background electro lyte concentrations of any magnitude. Therefore, the proposed model is more general than previously derived ''quasiequilibrium'' models of i onic surfactant transport to the interface that require instantaneous equilibrium potentials in the double layer.(1-4) We compare results fr om the proposed ionic surfactant transport model to results from the s tandard Ward-Tordai model for nonionic surfactants adsorbing at a flui d/fluid interface. For low concentrations of strongly adsorbing surfac tant, in the absence of background electrolyte, electrostatic effects decrease the equilibrium adsorption of surfactant by an order of magni tude. Correspondingly, the time required for equilibration of the inte rface is decreased. When the transient adsorption is scaled to elimina te differences due solely to different equilibrium adsorption, we disc over that the rate of diffusion-limited transport of an ionic surfacta nt is decreased by an order of magnitude compared to that of an equiva lent nonionic surfactant. Addition of nonadsorbing background electrol yte, increasing surfactant concentration, or weaker adsorption of surf actants decreases the electrostatic effects. A simple quasiequilibrium model that assumes a double layer in instantaneous equilibrium with a n electroneutral bulk solution is also developed. Comparison of this q uasiequilibrium model to the full transient model shows that, for a ty pical surfactant (e.g., sodium dodecyl sulfate) adsorbing at the water /air interface, differences between the full transient model and quasi equilibrium model occur only at times inaccessible to current dynamic surface tension techniques.