Adsorption diffusion

Whitaker, S, Transient Diffusion, Adsorption and Reaction in Porous Catalysts The Reaction Controlled, Quasi-Steady Catalytic Surface, Chemical Engineering Science 41, 3015, 1986. 

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. 

Figure 4. Modeled U-series date profiles across a 10 ky bone according to the D-A model under constant conditions. The dates are calculated using the closed system assumption. The parameter D/R is the diffusion-adsorption parameter and is related to the water content of the soil, the state of preservation of the bone and aspects of the geochemistry of the burial environment. After Pike et al. (2002). [Used by permission of Elsevier Science, from Pike et al. (2002), Geochim Cosmochim Acta, Vol. 66, Fig. 2, p. 4275.]...

The application of the Diffusion-Adsorption model to dating bone (by AP) was funded by a NERC grant to Robert Hedges at the Research Laboratory for Archaeology, University of Oxford. The U-series date profiles shown here were measured at the NERC U-series dating facility at Open University, and the laser ablation U-series profile was measured at the Research School for Earth Sciences, Australian National University, Canberra in collaboration with Steve Eggins and Rainer Griin. 

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. 

Soled catalyzed roocUono. These involve simultaneous diffusion, adsorption and surface reaction. See Chapter <5. 

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]. 

Millard, A. R. and Hedges, R. E. M. (1996). A diffusion-adsorption model of uranium uptake by archaeological bone. Geochimica et Cosmochimica Acta 60 2139-2152. 

The alkaline earth ions have fairly diffuse adsorption edges which cover a wide pH range, e.g. 7-11.5 for (Ali and Dzombak, 1996) and 7-11 for Sr on... 

On the basis of these results and predictions, a diffusion-adsorption model has been proposed to explain the results of water-to-droplet MT of FeCp-PrOH [53,97]. Assumptions of the model are as follows. Mass transfer of FeCp-X across the droplet/water interface competes with adsorption on the droplet interface. As illustrated in Figure 20, electrolysis of an FeCp-X/NB droplet renders distribution of the molecule to the water phase as FeCp-X+ at t = 0. At = , although FeCp-X transfers to the droplet interface with a diffusion-limited rate in water, redistribution of the molecule to the droplet interior competes with adsorption on the droplet/water interface. When the droplet surface is occupied by adsorbed FeCp-X to some extent at t = t", distribution of the compound to the droplet interior is assumed to be controlled by the fraction of the interfacial area adsorbed by FeCp-X (r/rx), where V is the amount of FeCp-X adsorbed on the droplet/water interface. 

Figure 20. Schematic illustration of a diffusion-adsorption model.

Abstract We formulate the balance principles for an immiscible mixture of continua with micro structure in the broadest sense for include, e.g., phenomena of diffusion, adsorption and chemical reactions. After we consider the flow of a fluid/adsorbate mixture through big pores of an elastic solid skeleton and propose suitable constitutive equations to study the coupling of adsorption and diffusion under isothermal conditions. 

A.W.G. Pike, R.E.M. Hedges, P. Van Calsteren, U-series dating of bone using the diffusion-adsorption model, Geochem. Cosmochem. Acta 66 (2002) 4273-4286. 

Figure 1.8 Computer-generated illustration of the accommodation (diffusion / adsorption) of molecules of titanocene dichloride inside a pore (30 A diameter) of siliceous MCM-41. For simplicity, none of the pendant Si-OH (silanol) groups, that make it possible to graft organometallic moieties inside the mesoporous host, are shown. Reproduced from Maschmeyer et a/.[93) by permission of Macmillan Publishers Ltd...

If we analyze all the steps taking part in the process, the final result will be very complicated. The diffusion, adsorption, and desorption processes are fast enough in comparison with the chemical reaction. Therefore, the adsorption process is in equilibrium during the catalytic reaction, since it is a fast process, and as a result, we can use an adsorption isotherm, for example, the Langmuir isotherm to calculate the amount of reactant in the surface. 

The author of this book has been permanently active during his career in the held of materials science, studying diffusion, adsorption, ion exchange, cationic conduction, catalysis and permeation in metals, zeolites, silica, and perovskites. From his experience, the author considers that during the last years, a new held in materials science, that he calls the physical chemistry of materials, which emphasizes the study of materials for chemical, sustainable energy, and pollution abatement applications, has been developed. With regard to this development, the aim of this book is to teach the methods of syntheses and characterization of adsorbents, ion exchangers, cationic conductors, catalysts, and permeable porous and dense materials and their properties and applications. 

As a first step toward overcoming the above problems, a hybrid diffusion-adsorption model for the terrace linked with a KMC model near the steps was developed (Schulze, 2004 Schulze et al., 2003). This domain decomposition stems from a natural separation of scales. The continuum terrace model between steps is... 

Note that in this specific model, desorption is neglected, and sites get regenerated upon adsorption, so the classic Langmuir blocking of sites is uncommon for MBE modeling. Furthermore, the diffusion-adsorption model for the terrace is only approximate since interactions between molecules are not accounted for. As a result, this hybrid model cannot handle nucleation between terraces, and applies only to small supersaturations or high temperatures [note that for high temperatures, one needs to include desorption in Eq. (2)] where the adatom concentration on terraces is relatively low. 

The rationale of using hybrid simulation here is that a classic diffusion-adsorption type of model, Eq. (2), can efficiently handle large distances between steps by a finite difference coarse discretization in space. As often happens in hybrid simulations, an explicit, forward discretization in time was employed. On the other hand, KMC can properly handle thermal fluctuations at the steps, i.e., provide suitable boundary conditions to the continuum model. Initial simulations were done in (1 + 1) dimensions [a pseudo-2D KMC and a ID version of Eq. (2)] and subsequently extended to (2 + 1) dimensions [a pseudo-3D KMC and a 2D version of Eq. (2)] (Schulze, 2004 Schulze et al., 2003). Again, the term pseudo is used as above to imply the SOS approximation. Speedup up to a factor of 5 was reported in comparison with KMC (Schulze, 2004), which while important, is not as dramatic, at least for the conditions studied. As pointed out by Schulze, one would expect improved speedup, as the separation between steps increases while the KMC region remains relatively fixed in size. At the same time, implementation is definitely complex because it involves swapping a microscopic KMC cell with continuum model cells as the steps move on the surface of a growing film. 

After the spatially 2D or 3D model of the porous catalyst support and the distribution of catalyst are generated, the multicomponent diffusion, adsorption, and chemical reaction within this porous structure can be modeled. 

Among the chemical reactions of interest catalyzed by zeolites, those involving alkanes are specially important from the technological point of view. Thus, some alkane molecules were selected and a systematic study was conducted, on the various steps of the process (diffusion, adsorption and chemical reaction), in order to develop adequate methodologies to investigate such catalytic reactions. Linear alkanes, from methane to n-butane, as well as isobutane and neopentane, chosen as prototypes for branched alkanes, were considered in the diffusion and adsorption studies. Since the chemical step requires the use of the more time demanding quantum-mechanical techniques, only methane, ethane, propane and isobutane were considered. 

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