Micellar dissolution and diffusion effects on adsorption dynamics of surfactants

A one-dimensional (1-D) model for the diffusion-controlled dynamic adsorption and surface tension in micellar solutions of nonionic surfactants is developed and tested with experimental data. The micellar dissolution rate for monodisperse micelles is described as being proportional to the micellar concentration and to the concentration difference between the critical micelle concentration (cmc) and the local monomer concentration with a micellar dissolution rate constant k. The Langmuir or Frumkin adsorption isotherms are used in a diffusion-controlled adsorption model with micellar dissolution. The hydrodynamic effects due to interface generation in the experiments are simplified as resulting in a stagnant layer with an adjustable finite length L The model is solved rigorously by the finite-element method with a stretched grid and adaptive time step sizes. From simulations, the micellar dissolution rate is found to be much more important for dynamic adsorption than the micellar diffusion rate. Moreover, the size distribution of micelles is found to be insignificant for dynamic adsorption when a narrow distribution is considered. New equilibrium and dynamic surface-tension data for a planar interface in a Langmuir trough has been obtained for two nonionic surfactants, straight-chain alkyl ethylene oxides, C14E6 and C16E6, at concentrations below and above their cmc's. The pre-cmc data are used to obtain the respective Langmuir isotherm parameters Gamma(m,L) and K-L and the effective diffusion length l approximate to 0.3 mm. With values of Gamma(m,L), K-L, and l determined from pre-cmc data, the post-cmc data are fitted fairly well with the micellar dissolution time constant tau(K) equivalent to l/kC* (C* is the cmc), which is 1.2 ms for C14E6 and 4.5 ms for C16E6.