Diffusivity in adsorption

There are two types of stmctures one provides an internal pore system comprising interconnected cage-like voids the second provides a system of uniform channels which, in some instances, are one-dimensional and in others intersect with similar channels to produce two- or three-dimensional channel systems. The preferred type has two- or three-dimensional channel systems to provide rapid intracrystalline diffusion in adsorption and catalytic apphcations. 

Figure 3. Coefficients of internal diffusion in adsorption of n-decane from n-decane-toluene solution by type A magnesium zeolites and calcium zeolites at a zeolite uptake of qt in grams n-decane/grams zeolite = 0.120...

R. Krishna, A unified approach to the modeling of intraparticle diffusion in adsorption processes, Gas Sep. Purif. 7(2) 9l (1993). 

We have discussed in the last two chapters about the various transport mechanisms (diffusive and viscous flows) within a porous particle (Chapter 7) and the systematic approach of Stefan-Maxwell in solving multicomponent problems (Chapter 8). The role of diffusion in adsorption processes is important in the sense that in almost every adsorption process diffusion is the rate limiting step owing to the fact that the intrinsic adsorption rate is usually much faster than the diffusion rate. This rate controlling step has been recognized by McBain almost a century ago (McBain, 1919). This has prompted much research in adsorption to study the diffusion process and how this diffusional resistance can be minimized as the smaller is the time scale of adsorption the better is the performance of a process. 

Do, D.D., and Rice, R.G., A simple method of determining pore and surface diffusivities in adsorption studies, Chem. Eng. Commun., 107, 151-162 (1991). 

Satterfield, C. N., Mass Transfer in Heterogeneous Catalysis, MIT Press, Cambridge, MA, (1970), p. 157. For a more detailed discussion of diffusion in porous media, see Krishna, R., A unified approach to the modeling of intraparticle diffusion in adsorption processes. Gas Separat. Purificat. 7 (2), 91-104 (1993). 

Ordinary diffusion involves molecular mixing caused by the random motion of molecules. It is much more pronounced in gases and Hquids than in soHds. The effects of diffusion in fluids are also greatly affected by convection or turbulence. These phenomena are involved in mass-transfer processes, and therefore in separation processes (see Mass transfer Separation systems synthesis). In chemical engineering, the term diffusional unit operations normally refers to the separation processes in which mass is transferred from one phase to another, often across a fluid interface, and in which diffusion is considered to be the rate-controlling mechanism. Thus, the standard unit operations such as distillation (qv), drying (qv), and the sorption processes, as well as the less conventional separation processes, are usually classified under this heading (see Absorption Adsorption Adsorption, gas separation Adsorption, liquid separation). 

Diffusion in porous solids is usually the most important factor con-troUing mass transfer in adsorption, ion exchange, drying, heterogeneous catalysis, leaching, and many other applications. Some of the... 

The quantity d s is often used in adsorption, erushing, and light diffusion applieations. 

To specify these transition probabilities we make the further assumption that the residence time of a particle in a given adsorption site is much longer than the time of an individual transition to or from that state, either in exchange with the gas phase in adsorption and desorption or for hopping across the surface in diffusion. In such situtations there will be only one individual transition at any instant of time and the transition probabilities can be summed, one at a time, over all possible processes (adsorption, desorption, diffusion) and over all adsorption sites on the surface. To implement this we first write... 

Henry Eyring s research has been original and frequently unorthodox. He woj one of the first chemists to apply quantum mechanics in chemistry. He unleashed a revolution in the treatment of reaction rates by use of detailed thermodynamic reasoning. Having formulated the idea of the activated complex, Eyring proceeded to find a myriad of fruitful applications—to viscous flow of liquids, to diffusion in liquids, to conductance, to adsorption, to catalysis. 

In addition to effects on the concentration of anions, the redox potential can affect the oxidation state and solubility of the metal ion directly. The most important examples of this are the dissolution of iron and manganese under reducing conditions. The oxidized forms of these elements (Fe(III) and Mn(IV)) form very insoluble oxides and hydroxides, while the reduced forms (Fe(II) and Mn(II)) are orders of magnitude more soluble (in the absence of S( — II)). The oxidation or reduction of the metals, which can occur fairly rapidly at oxic-anoxic interfaces, has an important "domino" effect on the distribution of many other metals in the system due to the importance of iron and manganese oxides in adsorption reactions. In an interesting example of this, it has been suggested that arsenate accumulates in the upper, oxidized layers of some sediments by diffusion of As(III), Fe(II), and Mn(II) from the deeper, reduced zones. In the aerobic zone, the cations are oxidized by oxygen, and precipitate. The solids can then oxidize, as As(III) to As(V), which is subsequently immobilized by sorption onto other Fe or Mn oxyhydroxide particles (Takamatsu et al, 1985). 

There is a whole spectrum of heterogeneous catalysts, but the most common types consist of an inorganic or polymeric support, which may be inert or have acid or basic functionality, together with a bound metal, often Pd, Pt, Ni or Co. Even if the support is inert its structure is of vital importance to the efficiency of the catal ic reaction. Since the reactants are in a different phase to the catalyst both diffusion and adsorption influence the overall rate, these factors to some extent depending on the nature and structure of the support. 

Petersen LW, Rolston DE, Moldrup P, et al. 1994. Volatile organic vapor diffusion and adsorption in soils. J Environ Qual 23 799-805. 

Dynamics of Crystal Growth hi the preceding section we illustrated the use of a lattice Monte Carlo method related to the study of equilibrium properties. The KMC and DMC method discussed above was applied to the study of dynamic electrochemical nucleation and growth phenomena, where two types of processes were considered adsorption of an adatom on the surface and its diffusion in different environments. 

The artificial lipid bilayer is often prepared via the vesicle-fusion method [8]. In the vesicle fusion process, immersing a solid substrate in a vesicle dispersion solution induces adsorption and rupture of the vesicles on the substrate, which yields a planar and continuous lipid bilayer structure (Figure 13.1) [9]. The Langmuir-Blodgett transfer process is also a useful method [10]. These artificial lipid bilayers can support various biomolecules [11-16]. However, we have to take care because some transmembrane proteins incorporated in these artificial lipid bilayers interact directly with the substrate surface due to a lack of sufficient space between the bilayer and the substrate. This alters the native properties of the proteins and prohibits free diffusion in the lipid bilayer [17[. To avoid this undesirable situation, polymer-supported bilayers [7, 18, 19] or tethered bilayers [20, 21] are used. 

Assuming a linear adsorption isotherm Millard and Hedges (1996) give a form of Pick s Second Law as the equation for diffusion in an infinite plane slab ... 

In the case of porous electrodes, diffusion in the pores can retard the rate of adsorption, in particular at low methanol concentrations. This could be the reason why at a concentration of 10-2 M mainly COH is formed independently of 6 [14]. 

Porosity correction is constant in both time and space. Chemicals move between the three soil phases much more rapidly than they diffuse in the air phase. This means that they appear to be in equilibrium. Adsorption is reversible. 

Table I shows the results of calculating a soil diffusion coefficient and soil diffusion half-lives for the pesticides. The 10% moisture level specified means that the soil is relatively dry and that 40% of the soil volume is air available for diffusion. Complete calculations were not made for methoxychlor, lindane, and malathion because, based on Goring s criteria for the Henry s law constant, they are not volatile enough to diffuse significantly in the gas phase. This lack of volatility is reflected in their low values of X. These materials would move upward in the soil only if carried "by water that was moving upward to replace the water lost through evapotranspiration at the surface. Mirex has a very high Henry s law constant. On the basis of Goring s criteria, Mirex should diffuse in the soil air but, because of its strong adsorption, it has a very large a and consequently a very small soil air diffusion coefficient. The behavior of Mirex shows that Goring s criteria must be applied carefully.

Barrer (19) has developed another widely used nonsteady-state technique for measuring effective diffusivities in porous catalysts. In this approach, an apparatus configuration similar to the steady-state apparatus is used. One side of the pellet is first evacuated and then the increase in the downstream pressure is recorded as a function of time, the upstream pressure being held constant. The pressure drop across the pellet during the experiment is also held relatively constant. There is a time lag before a steady-state flux develops, and effective diffusion coefficients can be determined from either the transient or steady-state data. For the transient analysis, one must allow for accumulation or depletion of material by adsorption if this occurs. 

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