Adsoiption kinetics

Polymer Adsorption. A review of the theory and measurement of polymer adsorption points out succinctly the distinquishing features of the behavior of macromolecules at solid - liquid interfaces (118). Polymer adsoiption and desorption kinetics are more complex than those of small molecules, mainly because of the lower diffusion rates of polymer chains in solution and the "rearrangement" of adsorbed chains on a solid surface, characterized by slowly formed, multi-point attachments. The latter point is one which is of special interest in protein adsoiption from aqueous solutions. In the case of proteins, initial adsoiption kinetics may be quite rapid. However, the slow rearrangement step may be much more important in terms of the function of the adsorbed layer in natural processes, such as thrombogenesis or biocorrosion / biofouling caused by cell adhesion. 

Bartal, A., Sparks, D. L., Pesek, J. D., and Feigenbaum, S. (1990). Analyses of adsoiption-kinetics using a stirred-flow chamber, 1 Tlieory and critical tests. Soil Sci. Soc. Am. J. 54, 1273-1278. 

A quantitative description of adsoiption kinetics processes is so far usually based on the model derived in 1946 by Ward and Tordai [3], The various models developed on this basis use mainly different boundary and initial conditions [2], as it becomes clear from the schematic in Fig. 4.1. The diffusion-controlled adsorption model of Ward and Tordai assumes that the step of transfer from the subsurface to the interface is fast compared to the transport from the bulk to the subsurface. It is based on the following general equation,... 

Thermally stimulated exoemission of silicon turned out to be no material property but to depend on the existence of a silicon oxide surface layer [41. Exoemission of ZnO was shown to depend on the adsoiption kinetics of oxygene at the surface [51. Emission phenomena which result from external factors like adsorbate layers may be classified by the term extiInMic exoemission, while other surface and subsurface emission effects that are due to factors inherent to the material should accordingly be called intrinsic exoemission 163. 

The analysis of adsoiption and ion-exchange kinetics is presented in detail in Section 4.2.1, and is based on the diffusion processes and equations rather than on some kind of... 

Furthermore, in its original form (Levenspiel, 1972), the assumption of constant and uniform bulk concentration of A in the fluid phase was made. This is similar to the infinite solution volume concept used in the analysis of adsoiption and ion-exchange kinetics. In the following, the more general solutions are presented, i.e. for changing fluid concentration (finite solution volume). 

Bruemmer, G. W., Gerth, J., and Tiller, K. G. (1988). Reaction kinetics of tlie adsoiption and desorption of nickel, zinc and cadmium by goethite, I Adsorption and diffusion of metals. J. Soil Sci. 39, 37-52. 

Hayes, K. F. (1987). Equilibrium, spectroscopic, and kinetic studies of ion adsorption at the oxide/aqueous interface. Ph.D. dissertation, Stanford University, Stanford, CA. Hayes, K. E., and Leckie, J. O. (1987). Modeling ionic strength effects on cation adsoiption... 

Molecules whose kinetic diameter is about SA or smaller are able to pass through the windows of the X and Y zeolites and be adsorbed within the internal surface. Water (18) and benzene (19-21), for example, can be added as "spectator" guest molecules which do not participate in a reaction sequence in a direct chemical manner, but may strongly influence the course of reaction of another adsorbed reactant by controlling factors such as the site of substrate adsoiption or by influencing the diffusional or rotational motion of the reactants. The number and position of these guest molecules within a supercage may also be varied. 

Table 3 Kinetic parameteis of fiee, immobilized lipase B fiom Candida antarctica obtained by adsoiption and Novoz5fme 435.

A significant feature of physical adsoiption is that the rate of the phenomenon is generally too high and consequently, the overall rate is controlled by mass (or heat transfer) resistance, rather than by the intrinsic soiption kinetics (Ruthven, 1984). Thus, soiption is viewed and termed in this book as a diffusion-controlled process. The same holds for ion exchange. 

In this section, the basic theoiy required for the analysis and inteipretation of adsoiption and ion-exchange kinetics in batch systems is presented. For this analysis, we consider the transient adsoiption of a single solute from a dilute solution in a constant volume, well-mixed batch system, or equivalently, adsoiption of a puie gas. Moreover, uniform spherical particles and isothermal conditions are assumed. Finally, diffusion coefficients ai e considered to be constant. Heat transfer has not been taken into account in the following analysis, since adsoiption and ion exchange aie not chemical reactions and occur principally with little evolution or uptake of heat. Fuitheimore, in environmental applications,... 

In this expression, U(t) is relative rate of uptake and C is relative to equilibrium, i.e. the sites available for ion exchange or adsoiption for the specified ratio V/m. Thus, the absolute rate is a coupled result of kinetics and equilibrium. Note that in a solid diffusion-controlled process, U(t) is relative to the ease of movement of the incoming species in the solid phase (through D ). 

Uie adsoiption isotheim at 20 °C was found to obey the Langinuu equation witli K= 69.2 L/inmol and = 0.709 inmol/g. For the kinetics experiments, CrF solutions of 3.21-niM... 

With increasing 0[ a decrease of the time necessary to achieve the equilibrium state is observed, and the final value of All increases also significantly. This phenomenon is caused by the decrease of the equilibrium adsoiption value for the soluble surfactant in presence of an insoluble monolayer. There are more recent attempts to describe the penetration kinetics, for example the diffusion model for dissolved homologues and ideal monolayers as developed by Sundaram et al. [113]. 

Table 5.6 reports the values of the regression parameters, their standard deviations and the individual 95% confidence intervals. The values of the kinetic and adsoiption constants can be obtained from the fitting of equations (5-23) to (5-25) to the experimental data, with the intrinsic kinetic constants being reported in the last column of this table. 

As a prelude to the development of kinetic rate expressions for heterogeneous chemical reactions, if A reacts with B, for example, then the next step in the mechanism is ha + Ba, forming an activated complex on the snrface. Each reversible step in the seqnence above is characterized by a forward rate constant adsoiption for adsoiption, with units of mol/area time atm, and a backward rate constant A ,desoiption for desorption, with units of mol/area time. The ratio of these rate constants adsorption/ h, desoiption defines the adsorption/desorption equi-... 

Kinetics of Molybdenum Adsoiption. Zhang and Sparks 41) examined molybdate adsorption on goethite using pressure jump relaxation experiments. Molybdate adsorption was proposed to occur via two steps, an initial outer-sphere complex and subsequent replacement of a water molecule by formation of an inner-sphere complex of Mo04, based on optimized fits using the triple layer model. Forward rate constants were on the order of 4x10 L mol s and 40 s for the first and second reaction steps. 

It is shown how the new approadi to adsoiption/desoiption kinetics based on the Statistical Rale Theory can be successfully applied to describe the kinetics of dissociative gas cbemisorplion on solids. 

Positive values of AH show the endothermic nature of adsorption. Similar results have been reported for the adsorption of methylene blue by clay [19].The native values of AG indicate the spontaneous nature of adsoiption for methylene blue at 35, 40, 50 and 60 C. The positive values of AS suggest the increased randomness at die solid /solution interface during the adsorption of (fye on coir pith cartion. Equilibrium data at different temperatures for the adsorption of dye on coir pith carbon do not follow the first order kinetic model but follows the second order kinetic model. The second order rate constants were in the range 0.357-0.879g/mgfoiin. 

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