Concentration Polarization at the Langmuir Monolayer Deposition:  Theoretical Considerations

Abstract

A mathematical model describing the concentration polarization in the three-phase contact region during the Langmuir-Blodgett deposition process is developed. It is shown that the stationary deposition is only possible when, in additional to convective fluxes, electrodiffusion ionic fluxes and corresponding concentration gradients are developed in the system. At a sufficiently low withdrawal speed, the occurring diffusion and migration ionic fluxes restore the steady-state ionic balance. As well, electric charge is accumulated in close vicinity to the three-phase contact line to produce a stationary electric field. The concentration polarization affects the parameters of the deposition process (dynamic contact angle, work of adhesion, maximum deposition rate) as well as morphology, composition, and structure of the deposited monolayer. When the withdrawal speed exceeds a critical value, the transport of counterions becomes insufficient to compensate interfacial charge in close vicinity to the three-phase contact line. Consequently, the electrostatic repulsion between the monolayers becomes sufficiently strong to disrupt the deposition process. The latter can result in meniscus instability. The proposed mechanism correlates with some experimental observations.

Ion redistribution and meniscus stability at Langmuir monolayer deposition

“…The deposition process is similar also to a diffusion-limited electrochemical reaction where the counterions bdischargeQ (adsorb) at the oppositely charged belectrodeQ (monolayer). Accordingly, the formation of ion concentration profiles near three-phase contact line can be expected during monolayer deposition [28][29][30], typically for membrane and electrode systems.…”

“…Then, from Eqs. (16) and (21) the total balance of the ith ion in each film cross-section is given by [29,30] B Bt…”

“…Therefore, the electrochemical potentials of the potential-determining counterions decrease near the contact line and the electro-diffusional fluxes of these ions (Eq. (24)) have to be induced to provide continuity for their total fluxes [29,30]. The coions and counterions of an indifferent electrolyte are not removed with the transferred monolayers.…”

“…However, their convective fluxes are not zero because they are non-uniformly distributed within the overlapping diffuse layers. As a consequence, the electrochemical potentials of these ions also change and the electro-diffusional fluxes are induced to provide their total fluxes of zero [29,30]. The coions are located mainly in the central part of the film, therefore, they are removed by convection from the region of the contact line and their electro-diffusional fluxes are directed toward the contact line.…”

“…Our recent investigations of the Langmuir wetting process have demonstrated that the concentration polarization (local change of concentrations and potential at dynamic conditions) develops within the liquid film near the three-phase contact line, especially in the case of small contact angles [27][28][29][30]. At some specific experimental conditions (pH and bivalent ions concentration in solution) this effect can lead to meniscus instability and to a stripelike composition of the deposited fatty acid monolayer [31].…”