Adsorption diffusion stage

As mentioned above, the kinetics of adsorption is called barrier limited when the stage of surfactant transfer from the subsurface to the surface is much slower than the diffusion stage because of the existence of some kinetic barrier. This barrier can be due to steric hindrance, electrostatic repulsion, or conformational changes accompanying the adsorption of the molecules. As the diffusion is the fast stage, the surfactant concentration in the solution should be uniform and equal to that at equilibrium c(x, t) = = const. In such... 

To diminish methanol crossover, PEMs have been researched for decreasing three stages of methanol crossover (adsorption, diffusion, and desorption). Rigidity and lower swelling of hydrocarbon-based polymers can induce minimization of adsorption and diffusion of methanol. Hydrocarbon-based PEM is needed for optimization in mobility and stiffness of ionic groups. Control of ionic and non-ionic phases also can be developed for satisfactory ionic conductivity and methanol crossover at the same time. A smaller number of ionic groups reduce methanol adsorption to PEM. Distribution of ionic sites in PEM affects the morphology... 

In the potential region where nonequilibrium fluctuations are kept stable, subsequent pitting dissolution of the metal is kept to a minimum. In this case, the passive metal apparently can be treated as an ideally polarized electrode. Then, the passive film is thought to repeat more or less stochastically, rupturing and repairing all over the surface. So it can be assumed that the passive film itself (at least at the initial stage of dissolution) behaves just like an adsorption film dynamically formed by adsorbants. This assumption allows us to employ the usual double-layer theory including a diffuse layer and a Helmholtz layer. 

Relaxation studies have shown that the attachment of an ion to a surface is very fast, but the establishment of equilibrium in wel1-dispersed suspensions of colloidal particles is much slower. Adsorption of cations by hydrous oxides may approach equilibrium within a matter of minutes in some systems (39-40). However, cation and anion sorption processes often exhibit a rapid initial stage of adsorption that is followed by a much slower rate of uptake (24,41-43). Several studies of short-term isotopic exchange of phosphate ions between aqueous solutions and oxide surfaces have demonstrated that the kinetics of phosphate desorption are very slow (43-45). Numerous hypotheses have been suggested for this slow attainment of equilibrium including 1) the formation of binuclear complexes on the surface (44) 2) dynamic particle-particle interactions in which an adsorbing ion enhances contact adhesion between particles (43,45-46) 3) diffusion of ions into adsorbents (47) and 4) surface precipitation (48-50). 

The adsorption of organics from the liquid to a solid phase is generally assumed to occur in three stages [50]. The brst is the movement of the contaminant (adsorbate or solute) through a blm surface surrounding the solid phase (adsorbant). The second is the diffusion of the adsorbate within the pores of the activated carbon. The bnal stage is the sorption of the material onto the surface of the sorbing medium. The overall rate of adsorption is controlled by the rate of diffusion of the solute molecules within the capillary pores of the carbon particles [27]. 

Adsorption of phosphate is initially rapid and is followed by a slow stage (hours to days) that is more pronounced for less crystalline samples of Fe oxides (Barrow et ak, 1981 Torrent et ak, 1990 Nilsson et ak, 1992). The slow stage has been attributed to diffusion into micropores or grooves (Torrent, 1991 Strauss et ak, 1997) and into aggregates of particles (Anderson et ak, 1985 Willet et ak, 1988). Evidence for slow dif-... 

Proteins have a low diffusivity D 2 to 6 x 10 7 cm2/s. Therefore, the initial stages of adsorption are generally diffusion limited and the amount adsorbed is proportional to t1/2. If the adsorption rate, dn/dt is ... 

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