Model porous adsorbents

Figure 12. Modeling and measurement of oxygen surface diffusion on Pt. (a) Model I adsorbed oxygen remains in equilibrium with the gas along the gas-exposed Pt surface but must diffuse along the Pt/YSZ interface to reach an active site for reduction. Model II adsorbed oxygen is reduced at the TPB but must diffuse there from the gas-exposed Pt surface, which becomes depleted of oxygen near the TPB due to a finite rate of adsorption, (b) Cotrell plot of current at a porous Pt electrode at 600 °C and = 10 atm vs time. The linear dependence of current with at short times implies semi-infinite diffusion, which is shown by the authors to be consistent only with Model II. (Reprinted with permission from ref 63. Copyright 1990 Electrochemical Society, Inc.)...

The accurate prediction of the elution profiles for polypeptide(s) or protein(s) from columns packed with nonporous and porous adsorbents represents a much more significant challenge. In the case of the use of nonporous sorbents in packed beds, an analytical solution can again be obtained. For porous adsorbents in packed beds, a sectional adsorption model (SAM), based on the (hypothetical) ability to treat the bed as a series of tanks-in-series has found wide application. 

With a number of fairly simple systems, excellent agreement has been obtained between the corresponding DFT-predicted and MC-generated isotherms, 2-D phase transitions and adsorption energies. These are encouraging results, but it must be kept in mind that the computational procedures are not entirely independent. As we have seen, they are dependent on the same model parameters of adsorbent structure and potential functions. At present, there are only a few porous adsorbents which have the... 

Fig. 4. Fluid-fluid radial distribution functions (right) and paitial structure factors (left) for low and high adsorption in the (a) model porous glass. The low-adsoiption data eoire-spond to 2.82 nimol/g adsorbed density (monolayer regime), and the high-adsorption data to 11.51 mmol/g adsorbed density, in the pore-filling regime. The o.scillations at low r in the g r) data and large k in the S k) data are due to local liquid stmcture, while the long-wavelength fluctuations (large r, small k) arc caused by the porous material.

Numerous models have been developed to describe pure and multicomponent gas adsorption on porous adsorbents. The analytical models are, however, most useful for process design. A few analytical models for Type I adsorption systems, which are thermodynamically consistent, are given below ... 

Several examples follow of recent efforts to describe explicitly porous adsorbent materials using disordered structure models. 

Fig. 18. PSDsfor model porous silica glasses [25]. A, B, C, and D are sample glasses prepared by quench MD the samples differ in mean pore size and porosity. The solid curves are exact geometric PSD results for the model adsorbents the dashed lines are the PSDs predicted from BJH pore size analysis of simulated nitrogen isotherms for the model porous glasses.

In terms of the simple model of adsorbed water (8), environmental state B (bulk-like water) is first removed from the pore during dehydration leaving behind the two bound states Ai and 2 (or the combined state A). The combined state A is assumed to occupy two layers of water and is independent of porous glass pore diameter. See Table II in Reference (. ... 

Figure 5. Fragmented cluster model of adsorbed water showing hydrogen-bonded proton clusters in a porous glass pore...

Based on these results, a hydration model - The Fragmented Cluster Model for adsorbed water in porous glass (and possibly cellulose acetate) membranes is proposed. It predicts a priori, that for glass pore sizes above 32 to 52 A, bulk water structure can be established. Observations from the literature indicate that above this pore size range significant desalting is not expected. 

Several assumptions are made to mathematically model the immobilized adsorbent. The small adsorbent particles are assumed to be distributed uniformly inside the hydrogel bead. The external mass transfer resistance due to the boundary layer is assumed to be negligible if the bulk solution is well stirred. This assumption is supported by the experimental observations of Tanaka et al. who studied diffusion of several substrates from well stirred batch solutions into Ca-alginate gel beads (4), However, the boundary conditions can be easily modified to incorporate external diffusion effects if needed. Furthermore product diffusion in both the hydrogel and the porous adsorbent is considered to follow Fickian laws and its diffusivity in each region is assumed to be constant. 

However, the two-sink model as well as other existing adsorption (sink) models do not seem to be able to describe the strong asymmetry between the adsorption/desorption of VOCs on/from indoor surface materials (the desorption process is much slower than the adsorption process). Diffusion combined with internal adsorption is assumed to be capable of explaining the observed asymmetry. Diffusion mechanisms have been considered to play a role in interactions of VOCs with indoor sinks. Dunn and Chen (1993) proposed and tested three unified, diffusion-limited mathematical models to account for such interactions. The phrase unified relates to the ability of the model to predict both the ad/absorption and desorption phases. This is a very important aspect of modeling test chamber kinetics because in actual applications of chamber studies to indoor air quality (lAQ), we will never be able to predict when we will be in an accumulation or decay phase, so that the same model must apply to both. Development of such models is underway by different research groups. An excellent reference, in which the theoretical bases of most of the recently developed sorption models are reviewed, is the paper by Axley and Lorenzetti (1993). The authors proposed four generic families of models formulated as mass transport modules that can be combined with existing lAQ models. These models include processes such as equilibrium adsorption, boundary layer diffusion, porous adsorbent diffusion transport, and conveetion-diffusion transport. In their paper, the authors present applications of these models and propose criteria for selection of models that are based on the boundary layer/conduction heat transfer problem. 

A large number of simple and sophisticated models have been presented to obtain a realistic estimation of PSD of porous adsorbents. Relatively simple but restricted apphcable methods such as Barret, Joyner, and Halenda (BJH), Dollimore and Heal (DH), Mikhail et al., (MP), Horvath and Kawazoe (HK), Jaroniec and Choma (JC), Wojsz and Rozwadowski (WR), Kruk-Jaroniec-Sayari (KJS), and Nguyen and Do (ND) were presented from 1951 to 1999 by various researchers for the prediction of PSD from the adsorption isotherms [133-139]. 

Kanematsu, M., T. M. Young, K. Eukushi, P. G. Green, and J. L. Darby. 2010. Extended triple layer modeling of arsenate and phosphate adsorption on a goethite-based granular porous adsorbent. Environmental Science Technology AA, no. 9 3388-3394. doi 10.1021/es903658h. 

In bidisperse porous adsorbents such as zeolite pellets there are two diffusion mechanisms the macropore diffusion with time constant Rp /Dp and the micropore diffusion with time constant rc /Dc. Bidisperse porous models for ZLC desorption curves have been recently developed by Brandani [28] and Silva and Rodrigues [29]. In bidisperse porous adsorbents, it is important to carry out experiments in pellets with different sizes but with the same crystal size (different Rp, same rc) or pellets with the same size but with different crystals (same Rp, different rc). If macropore diffusion is controlling, time constants for diffusion should depend directly on pellet size and should be insensitive to crystal size changes. If micropore diffusion controls the reverse is true. The influence of temperature is also important when macropore diffusion is dominant the apparent time constant of diffusion defined by Rp2(H-K)/Dp is temperature dependent in the same order of K (directly related to the heat of adsorption) which is determined independently from the isotherm. The type of purge gas is... 

Some simplified approximations have been proposed for describing the rate of adsorption onto a porous adsorbent particle. However, these assumptions produce models that may have drawbacks in terms of flexibility and accuracy. 

There are a number of models which do not ttssume the existence of equilibrium between the liquid and the solid phases. However, they do not incorporate the effect of axial dispersion. In such models of nonequilibrium nondispersive operation of the column, the mass-transfer rate between the liquid and the surface of the adsorbent (primarily in the pores) is not infinitely ftist rather it is finite. Further diffusion in the porous adsorbent particle is quite important One of the earlier models of this type is by Rosen (1952, 1954). 

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