Modified Langmuir—Hinselwood kinetics for dynamic adsorption of surfactants at the air/water interface

The Langmuir—Hinselwood (L-H) equation is the simplest kinetic equation which is consistent with Langmuir's equilibrium isotherm. This kinetic equation cannot describe well the dynamic surface tension data for octanol, sodium dodecyl sulfate (SDS), and other surfactants. A new kinetic equation for the rate of adsorption from the subsurface (dl/dt = k^a_Lc(θ,t)(1−θ) exp(−Bθ)−k^d_L Γ exp(−Bθ). where θ is the fractional surface coverage Γ/Γ_m, c(θ,t) is the subsurface concentration, and k^a_L, k^d_L, and B are constants) includes modification of the kinetics but not of the equilibrium isotherm. The new equation describes better the capture efficiency of the interfacial monolayer for additional surfactant, and can describe activation barriers for adsorption and desorption, or cooperative adsorption caused by primarily attractive interactions between the monolayer and the dissolved surfactant. This equation was used in a new model of mixed kinetics for one-dimensional diffusion/adsorption/desorption. For octanol and heptanol, the initial adsorption rate is controlled by intrinsic adsorption/desorption kinetics (slow adsorption/desorption). With increasing surface coverage, dynamic adsorption gets closer to the diffusion-controlled limit (fast adsorption/desorption relative to diffusion). This indicates attractive and cooperative interactions of alcohol molecules in the monolayer. For sodium di-2-ethylhexylsulfosuccinate (DESS or AOT) and SDS, adsorption is much slower than predicted by diffusion-controlled models. The modified L-H equation in a mixed-kinetics model can fit the data well. The capture efficiency factor, k^a_L exp(−bθ), increases with increasing SDS concentration c_SDS or NaCl concentration c_s, indicating that adsorption is strongly affected by electrostatic barriers. For c_s = 0 and c_SDS = 1.7 to 5.9 mM (for θ_c<0.4), the estimated surface electrical potential is in the range 150–230 mV, and is consistent with classical double-layer theory. For θ_c > 0.4 and a high salt concentration, the parameter B may involve substantial steric or other interactions.