Diffusivity, adsorption process

Adsorption Kinetics. In zeoHte adsorption processes the adsorbates migrate into the zeoHte crystals. First, transport must occur between crystals contained in a compact or peUet, and second, diffusion must occur within the crystals. Diffusion coefficients are measured by various methods, including the measurement of adsorption rates and the deterniination of jump times as derived from nmr results. Factors affecting kinetics and diffusion include channel geometry and dimensions molecular size, shape, and polarity zeoHte cation distribution and charge temperature adsorbate concentration impurity molecules and crystal-surface defects. 

Adsorbents, and activated carbon in particular, are typically characterized by a highly porous structure. Adsorbents with the highest adsorption capacity for gasoline or fuel vapors have a large pore volume associated with pore diameters on the order of 50 Angstroms or less. When adsorption occurs in these pores, the process is comparable to condensation in which the pores become filled with hquid adsorbate. Fig. 5 depicts the adsorption process, including transfer of adsorbate molecules through the bulk gas phase to the surface of the solid, and diffusion onto internal surfaces of the adsorbent and into the pores. 

FIGURE 2.23 Schematic diagram showing the routes of possible removal of drug from the receptor compartment. Upon diffusion into the compartment, the drug may be removed by passive adsorption en route. This will cause a constant decrease in the steady-state concentration of the drag at the site of the receptor until the adsorption process is saturated. 

Figure 26 shows the redox potential of 40 monolayers of cytochrome P450scc on ITO glass plate in 0.1 KCl containing 10 mM phosphate buffer. It can be seen that when the cholesterol dissolved in X-triton 100 was added 50 pi at a time, the redox peaks were well distinguishable, and the cathodic peak at -90 mV was developed in addition to the anodic peak at 16 mV. When the potential was scanned from 400 to 400 mV, there could have been reaction of cholesterol. It is possible that the electrochemical process donated electrons to the cytochrome P450scc that reacted with the cholesterol. The kinetics of adsorption and the reduction process could have been the ion-diffusion-controlled process. 

Principal differences between catalysis by dissolved electrolytes and by resins are that with resins as catalysts catalysis overlaps with diffusion, adsorption, and desorption processes, while this is not the case with electrolytes (Naumann, 1959). Also, the matrix of the resin with fixed ionic group may have some influence on the course of reaction. 

Fabrication processing of these materials is highly complex, particularly for materials created to have interfaces in morphology or a microstructure [4—5], for example in co-fired multi-layer ceramics. In addition, there is both a scientific and a practical interest in studying the influence of a particular pore microstructure on the motional behavior of fluids imbibed into these materials [6-9]. This is due to the fact that the actual use of functionalized ceramics in industrial and biomedical applications often involves the movement of one or more fluids through the material. Research in this area is therefore bi-directional one must characterize both how the spatial microstructure (e.g., pore size, surface chemistry, surface area, connectivity) of the material evolves during processing, and how this microstructure affects the motional properties (e.g., molecular diffusion, adsorption coefficients, thermodynamic constants) of fluids contained within it. 

In Figures 3 and 4, plots of Ap and t against the square root of adsorption time, T, are displayed, respectively. Before attainment of adsorption equilibrium both plots are linear within experimental error and therefore, adsorption process of NaPSS is governed by diffusion. 

The performance of adsorption processes results in general from the combined effects of thermodynamic and rate factors. It is convenient to consider first thermodynamic factors. These determine the process performance in a limit where the system behaves ideally i.e. without mass transfer and kinetic limitations and with the fluid phase in perfect piston flow. Rate factors determine the efficiency of the real process in relation to the ideal process performance. Rate factors include heat-and mass-transfer limitations, reaction kinetic limitations, and hydro-dynamic dispersion resulting from the velocity distribution across the bed and from mixing and diffusion in the interparticle void space. 

Modelling biouptake processes helps in the understanding of the key factors involved and their interconnection [1]. In this chapter, uptake is considered in a general sense, without distinction between nutrition or toxicity, in which several elementary processes come together, and among which we highlight diffusion, adsorption and internalisation [2-4], We show how the combination of the equations corresponding with a few elementary physical laws leads to a complex behaviour which can be physically relevant. Some reviews on the subject, from different perspectives, are available in the literature [2,5-7]. 

A rigorous treatment of diffusion to or from a flat surface has been given by Lyklema (1991). Van Leeuwen (1991) has pointed out that in analyzing experimental adsorption data, that are always confined to a certain time window, it is tempting to fit the data to the sum of two or three exponential functions with different arguments. Although such fits are often apparently sucessful, the merit of the fit is purely mathematical a mechanistic interpretation in terms of a first order dependence is usually not justified. With porous materials, diffusion into the pores renders the adsorption process very slow often one gains the impression that the process is irreversible (e.g., Fig. 4.18). 

In dilute solutions of surfactants adsorption processes are controlled by transport of the surfactant from the bulk solution towards the surface as a result of the concentration gradient formed in the diffusion layer the inherent rate of adsorption usually is rapid. For non-equilibrium adsorption the apparent (non-equilibrium) isotherm can be constructed for different time periods that are shifted with respect to the true adsorption isotherm in the direction of higher concentration (Cosovic, 1990) (see Fig. 4.10). 

When chemisorption is involved, or when some additional surface chemical reaction occurs, the process is more complicated. The most common combinations of surface mechanisms have been expressed in the Langmuir-Hinshelwood relationships 36). Since the adsorption process results in the net transfer of molecules from the gas to the adsorbed phase, it is accompanied by a bulk flow of fluid which keeps the total pressure constant. The effect is small and usually neglected. As adsorption proceeds, diffusing molecules may be denied access to parts of the internal surface because the pore system becomes blocked at critical points with condensate. Complex as the situation may be in theory,... 

As already discussed, it indicates that for a diffusion controlled process (i.e. one which does not involve adsorption processes) taking place at a planar electrode, the current (which is proportional to... 

The magnitude of Ds is a measure of how fast the molecules diffuse along the particle and therefore sets a time scale for the adsorption process. Two boundary conditions and one initial condition have to be specified in order to obtain a unique solution to Eq. (60). Initially the solid particle is free of adsorbate, which is expressed as ... 

Three kinetic models were applied to adsorption kinetic data in order to investigate the behavior of adsorption process of adsorbates catechol and resorcinol onto ACC. These models are the pseudo-first-order, the pseudo-second-order and the intraparticle diffusion models. Linear form of pseudo-first-order model can be formulated as... 

Although most of the commercial adsorptive separation processes are operated under the selective-equilibrium adsorption mechanism, adsorptive separation may also be based on diffusion rates through a permeable barrier which are designated as rate-selective adsorption processes. In some instances there may be a combination of equilibriums as well as rate selective adsorption. A rate-selective adsorption process yields good separation when the diffusion rates of the feed components through the permeable barrier differ by a wide margin. 

In the absence of transport limitations, the processes of adsorption, surface diffusion, surface reaction, and desorption can be treated via the transition state theory (Baetzold and Somorjai, 1976 Zhdanov et al, 1988). For example, the application of the TST to a single site adsorption process,... 

Evidently the valency relationship is by no means rigid, and in addition the various observations do not agree amongst themselves. It has already been noted that the process of coagulation is the result of a series of independent operations primarily dependent on an adsorptive process due to diffusion the manner in which the... 

A significant feature of physical adsorption 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 sorption kinetics (Ruthven, 1984). Thus, sorption is viewed and termed in this book as a diffusion-controlled process. The same holds for ion exchange. 

In this expression, U(t) is relative rate of uptake and Cx is relative to equilibrium, i.e. the sites available for ion exchange or adsorption for the specified ratio Vim. 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 Ds). 

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