Role of Equation of State on Studying Surfactant Adsorption Kinetics

Abstract

The adsorption kinetics of a surfactant is used to apply the equilibrium surface tension data γ(C) for the determination of the adsorption isotherm and then to apply the dynamic surface tension γ(t) on determining the controlling mechanism, the diffusivity, and/or the sorption rate constants. A concept for surfactants lacking low surface pressure data has been proposed (Hsu et al. Langmuir 1997, 13, 6204; 1999, 15, 1952): using only a limited range of equilibrium surface tension data to determine the adsorption isotherm can cause a mistake on determining the adsorption mechanism and diffusion coefficient. In this work, the above concept is extended: even though an isotherm describes the γ(C) data well, it may describe the dynamic surface tension data incorrectly. An incorrect controlling mechanism and/or a diffusion coefficient with a significant error may result if only the γ(C) data are applied on determining the adsorption isotherm and model parameters. A second set of equilibrium data, equation of state γ(Γ), is useful and necessary for studying the adsorption kinetics. A theoretical simulation and two examples (for surfactants with either cooperative or anticooperative adsorption) are presented in this article to illustrate this concept.

Modeling of adsorption dynamics at air–liquid interfaces using statistical rate theory (SRT)

“…The geometry of the pendant drop is approximated as a sphere. The diffusion is assumed to be spherically symmetrical and is described by Fick's second law [14][15][16][17],…”

“…Although the rate constants can be calculated from the theory in principle, we estimated these rate constants using reported experimental data and related rate constants of the same system. Table 1 lists the physically realizable range of values for each of the parameters involved in the governing equations [2,[11][12][13][14][15][16][17]19,22,[25][26][27]. For example, the range of the bulk concentrations is considered from a very dilute concentration to the critical micelle concentration of common surfactants.…”

“…The lower and upper limits of the maximum surface concentration (Γ ∞ ), the diffusion coefficient (D), the Langmuir constant (b), and the adsorption rate constant, (K a ) are taken from the literature [2,[11][12][13][14][15][16][17]19,22,[25][26][27]. The lower limit of the bulk concentration (C 0 ) is estimated from the minimum surface concentration needed to induce a change in surface tension and the upper limit is the critical micelle concentration (CMC) of the commonly used surfactants (e.g., short-chain alcohols and bolaform).…”

“…Numerical solutions to the mixed diffusion and transfer model have been reported in the literature, where a diffusion equation and a Langmuir-type kinetic equation were used [2,11,[14][15][16][17]25,33,34]. In all cases, experimental surface tension data were fitted to the model by adjusting fitting parameters.…”

“…The adsorption kinetics is mixed diffusion and transfer controlled when steps (i) and (ii) are equally important. Currently, most of the theoretical models have been developed using the following two mechanisms: diffusion controlled [9][10][11][12] and mixed diffusion and transfer controlled [13][14][15][16][17]. Rearrangements at the surface may consist of reorientation, conformational changes, complex formation, chemical reactions, phase transitions, or formation of three-dimensional structures resembling liquid crystals.…”