Adsorption under barrier control

Adsorption under Diffusion Control Small Initial Perturbation Large Initial Perturbation Generalization for Ionic Surfactants Adsorption under Barrier Control... 

The overall rate of surfactant adsorption is controlled by the slowest stage. If it is stage (1), we deal with diffusion control, whereas if stage (2) is slower, the adsorption occurs under barrier (kinetic) control. The next four subsections are dedicated to processes under diffusion control (which are the most frequently observed), whereas in Section 5.2.2.5 we consider adsorption under barrier control. 

Note that the adsorption isotherms, relating the surface concentration, F, with the subsurface value of the bulk concentration, (see Section 5.2.2.1 above), or the respective kinetic Equation 5.86 for adsorption under barrier control (see Section 5.2.2.5), should also be employed in the computations based on Equations 5.276 to 5.279 in order for a complete set of equations to be obtained. 

Equation 5.88 predicts that the perturbation of surface tension, Ao(f) = o(f) — o,- relaxes exponentially. This is an important difference with the cases of adsorption under diffusion and electrodiffusion control, for which Ao(f) 1/x/f see Equations 5.70, 5.76, and 5.78. Thus, a test whether or not the adsorption occurs under purely barrier control is to plot data for ln[Aa(f)] vs. t and to check if the plot complies with a straight line. 

Equation 5.93 reflects the fact that in the diffusion regime the surface is always assumed to be equilibrated with the subsurface. In particular, if E, = 0, then we must have Cj = 0. In contrast, Equation 5.94 stems from the presence of barrier for time intervals shorter than the characteristic time of transfer, the removal of the surfactant from the interface (Tj = 0) cannot affect the subsurface layer (because of the barrier) and then Cij(O) = c. This purely theoretical consideration implies that the effect of barrier could show up at the short times of adsorption, whereas at the long times the adsorption will occur under diffusion control." The existence of barrier-affected adsorption regime at the short adsorption times could be confirmed or rejected by means of the fastest methods for measurement of dynamic surface tension. 

Due to diphylic character of MR and its ability of self-organization in a solution it can behave similarly to nonionic surfactants. Adsorption of MR was shown to be mixed-diffusion barrier controlled (pH 7.4). MR was also shown to change thermodynamic affinity of lysozyme to the solvent with the resulting the protein being slightly less or more surface active depending on MR concentration. Under used conditions MR and lysozyme can compete in adsorption process at air/water interface [4]. 

Simple metal single crystals prepared under well-controlled conditions are extensively characterized with respect to their geometric and electronic properties [28, 29]. With techniques such as MBS, one can describe details of reaction mechanisms and obtain reaction probabilities and rate constants for elementary reaction steps, activation barriers for surface processes, and adsorption quantities [30-33], Kinetic data from single crystal experiments may be vastly different from that of technical... 

To fully characterize an adsorbate-adsorbent system one should run ZLC experiments at low flowrates to obtain the adsorption isotherm [8]. Having obtained the isotherm, possibly also through other independent measurements, one should use a numerical code to obtain the limiting diffusivity and surface barrier kinetic constant from the simultaneous fit of multiple high flowrate and partial loading experiments. It should be noted that the partial loading experiment, together with experiments at multiple flowrates, can be used also to show that the system is not under equilibrium control. 

As mentioned earlier, below we focus om attention on the kinetics of surfactant adsorption. First, we introduce the basic equations. Next, we consider the two alternative cases of surfactant adsorption under diffusion and barrier control. Special attention is paid to the adsorption of ionic surfactants, whose molecules are involved in long-range electrostatic interactions. Finally, we consider the adsorption from micellar surfactant solutions, which is accompanied by micelle diffusion, assembly, or disintegration. 

The c0—tr curve for the same compound enables us to check the validity of such interpretations by transforming the tt vs. t curve into an adsorption vs. time relationship. For the case under consideration, the r vs. yft curve is given in Figure 10. Here the induction period has completely disappeared, and the linearity of the initial part of the T vs. y/t plot is consistent with a diffusion-controlled mechanism, rather than with the presence of an adsorption barrier. From the Ward-Tordai (12) equation for the initial part of the adsorption ... 

Figure 6 provides a comparison between measured spectra and theoretical spectra calculated under the assumption that the adsorption/desorption process is controlled by either intracrystalline diffusion (Fig. 6a) or external transport resistances such as surface barriers (Fig. 6b). For simplicity in the calculations, the crystallites have been assumed to be of nearly spherical shape with a concentration-independent transport diffusivity Dj or surface permeability a, respectively. Values of the intracrystalline mean lifetime are therefore given by...

Many practical processes (foaming, emulsification, dispersing, wetting, washing, solubilization) are influenced by the rate of adsorption from surfactant solutions. This rate depends on whether the adsorption takes place under diffusion, electro-diffusion, barrier, or convective control. The presence of surfactant micelles, which serve as carriers, and a reservoir of surfactants can strongly accelerate the kinetics of adsorption see Secs. 

---