A parking lot model for adsorption of polydispersed surfactants

A phenomenological parking lot model for the adsorption of non-ionic polydispersed surfactants on hydrophilic surfaces is derived by equating the rates of adsorption and desorption of each homolog present in the surfactant mixture. The former is proportional to the product of solution concentration and number of empty parking lots available. The empty parking lots, in turn, are a function of solid concentration and surface area, amount and distribution of components adsorbed at the interphase and the size-dependent parking area of the molecules. A coverage factor accounts for the fraction of surfactant molecules in the adsorbed phase which are parked on the surface and it is proportional to the average number of particles attached to the adsorbed phase. A crowding factor, which also depends on the solid concentration, determines the fraction of bare surface that is accessible to the incoming molecules for adsorption. The overall adsorption is obtained by summing over the adsorption of individual components. The model equations are simplified by introducing appropriate mean parking areas and made implementable by invoking simple power law type empirical expressions for the unknown terms. The resulting model describes the overall adsorption isotherm, distribution of adsorbed components, multiple particle attachment and the parking area as a function of chain length. It is generally in good agreement with published data for adsorption of polydispersed ethyleneoxide surfactants on silica.