The Effect of Pore Size

Up to this point, attention has been focused on calculating diffusion coefficients in straight, round pores. The final challenge is to use this background to calculate DA.p(r) in Eqn. (9-16). Recall that DA.p(r) is the diffusion coefficient of A in an assembly of straight, round pores that has the same distribution of pore sizes as the catalyst. To perform this calculation, something must be known about the pore-size distribution y(r). 

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Fig. 26. The effect of pore size distribution spread (standard deviation) on the predicted tensile failure [jrobability distribution for grade H-451 graphite.

Generally, optimizing the selectivity by choosing a gel medium of suitable pore size and pore size distribution is the single most important parameter. Examples of the effect of pore size on the separation of a protein mixture are given in Fig. 2.15. The gain in selectivity may then be traded for speed and/ or sample load. However, if the selectivity is limited, other parameters such as eluent velocity, column length, and sample load need to be optimized to yield the separation required. 

This paper will be limited to a discussion of our packed column studies in which we have addressed attention to questions regarding, (a) the role of ionic strength and surfactant effects on both HDC and porous packed column behavior, (b) the effects of pore size and pore size distribution on resolution, and (c) the effects of the light scattering characteristics of polystyrene on signal resolution and particle size distribution determination. 

Tanaka, N., Kimata, K., Mikawa, Y., Hosoya, K., Araki, T., Ohtsu, Y., Shiojima, Y., Tsuboi, R., Tsuchiya, H. (1990). Performance of wide-pore silica- and polymer-based packing materials in polypeptide separation the effect of pore size and alkyl chain length. J. Chromatogr. 535, 13-31. 

The effect of pore size on CEC separation was also studied in detail [70-75]. Figure 9 shows the van Deemter plots for a series of 7-pm ODS particles with pore size ranging from 10 to 400 nm. The best efficiency achieved with the large pore packing led to a conclusion that intraparticle flow contributes to the mass transfer in a way similar to that of perfusion chromatography and considerably improves column efficiency. The effect of pore size is also involved in the CEC separations of synthetic polymers in size-exclusion mode [76]. 

An example of the effect of pore size on the separation of a set of native proteins is shown in Figure 8.4. The 4%T, 2.67%C gel shown on the left is essentially nonsieving. Proteins in the artificial sample migrate in the gel more or less on the basis of their free mobility. The 8%T, 2.67%C gel on the right sieves the proteins shown and demonstrates the combined effects of charge and size on protein separation. The relative positions of some proteins are shifted in the sieving gel as compared to the nonsieving one. 

The effect of pore size on the retentive capacity of various octadecyl silica bonded phases is illustrated in Fig. 10. Exclusion effects become appreciable when bulky octadecyl groups (see Table V) are attached to the pore wall in 6 nm pore diameter silica (Si-60). As a result, the stationary... 

It is the purpose of the present paper to study the effect of pore size on the adsorption of xenon on mesoporous MCM-41 molecular sieves. In particular, much attention will be focused on the temperature variation of l2,Xe NMR chemical shifts at low Xe loading to realize the characteristics of the Xe-wall interactions. 

Wheeler<26) considered the problem of chemical selectivity in porous catalysts. Although he employed a cylindrical pore model and restricted his conclusions to the effect of pore size on selectivity, the following discussion will be based on the simple geometrical model of the catalyst pellet introduced earlier (see Fig. 3.2 and Section 3.3.1). 

Fig. 57. Model computation of the effect of pore size on catalyst stability using first-order kinetics and configurational diffusion for a 12.5- A-diameter metal-bearing molecule (Rajago-palan and Luss, 1979).

Hardin, A. H., Ternan, M., and Packwood, R. H., The Effects of Pore Size in MoOrCoO-A1203 Hydroprocessing Catalysts," CANMET Report 81-4E, Energy, Mines and Resources, Canada, 1981 see also ACS Prepr. Div. Petrol. Chem. 23, 1450 (1978). 

Consistent with our previous findings using systems consisting of butyl methacrylate, ethylene dimethacrylate, and 2-acrylamido-2-methyl-l-propanesulfonic acid [54,64,72], the column efficiency of quinidine-functionalized monolithic capillaries again clearly depends on the pore size. Fig. 6.30 illustrates that this holds for chiral monoliths prepared by either thermal or UV initiation [60], As previously found for the reversed phase separations of alkylbenzenes, the effect of pore size on the separation of enantiomers is also rather complex and subtleties of these effects remain to be explored in more detail. 

This chapter discusses the fundamental principles for designing nanoporous adsorbents and recent progress in new sorbent materials. For sorbent design, detail discussion is given on both fundamental interaction forces and the effects of pore size and geometry on adsorption. A summary discussion is made on recent progress on the following types of materials as sorbents activated carbon, activated alumina, silica gel, MCM-41, zeolites, n -complexation sorbents, carbon nano tubes, heteropoly compounds, and pillared clays. 2001 Academic Press. 

Instead, they proposed a time on stream theory to model the catalyst deactivation. However, in an earlier work by Voorhies (2), a linear correlation between conversion and coke on catalyst for fixed-bed catalytic cracking was derived. Rudershausen and Watson (3) also observed the similar behavior. Coke on catalyst can reduce the activity by covering the active sites and blocking the pores. The effects of pore size on catalyst performance during hydrotreating coal oils in trickle-bed reactors have been studied experimentally by Ahmed and Crynes (4) and by Sooter (5). The pore size effects in other studies are also reported 7, 8). Prasher et al. (9) observed that the effective diffusivities of oils in aged catalysts were severely reduced by coke deposition. 

Figure 10 The effect of pore size on the H-u curves of fluorene in reversed-phase CEC. Columns packed with 10- xm reversed-phase particles with a nominal pore size of , 50 nm . 100 nm A, 400 nm.

Wide pore catalysts have been found to be more active in FT synthesis than narrow pore ones both at 1 and 20 bar (Table 4). Figure 4 shows that the effect of pore sizes on FT reaction rate was also significant at higher reactant pressure. 

Up to now, numerous studies have been conducted on their synthesis [9,10], treatment [5,13] and physical properties [4], However only limited number of studies has been carried out on die adsorption of gas in CNTs, including experimental works [8,11] and molecular simulations [3,7,14-lS]. Adsorption behavior depends strongly on the microporous structure of the particular adsorbent. In this work the effect of pore size on the adsorption behavior is of interest. The adsorption equilibria of methane, ethane and their mixture into SWNTs were studied by using a Grand Canonical Monte Carlo (GCMC) method. We reported equilibrium isotherms of methane and ethane, and the selectivity from their equimolar mixture. 

Equations (44) and (46) take into account the overlapping of the neck and void radius distribution. However, these equations have been derived employing the assumptions similar to those used in the mean-field approximation in statistical physics. In particular, Eqs. (44) and (46) ignore the effect of pore-size correlations on mercury intrusion. The latter effect has been recently studied in detail by Tsakiroglou and Payatakes (4J) employing the Monte Carlo method. Simulations were made on a square lattice... 

The importance of diffusional limitations on catalyst deactivation has been recognized for more than four decades (ref.1-2). Voluminous studies have been reported on the deactivation of resid hydrodesulfurization (RHDS) catalysts (ref. 3-4). However, most of the experiments were carried out over the catalysts which have a broad pore size distribution This would cause the difficulty in determining the effect of pore size on the deactivation. 

Fig. 21.3 The effect of pore size and confinement in the asymmetric hydrogenation of methyl benzoylformate to methyl mandelate after 120 min of reaction...

The vapor phase studies also showed that the size of the pores has an important effect on the regioselectivity of the reaction. Fig. 2 illustrates the effect of pore size on product selectivity. The highest selectivity for para-nitrotoluene was observed over H-ZSM5 followed by Mordenite, L, and MCM. The kinetic diameters of the o-, m-, and p- isomers are 6.7, 6.7, and 5.25 A respectively. Experimental results shown in Fig. 2 verify that catalysts with channel diameters of less than 7 A preferentially form the para isomer. Based on these geometric arguments alone, the small amount of ortho isomer observed with the H-ZSM5 catalyst could be generated on acid sites located on the outer surface (2). 

The modelling of gas permeation has been applied by several authors in the qualitative characterisation of porous structures of ceramic membranes [132-138]. Concerning the difficult case of gas transport analysis in microporous membranes, we have to notice the extensive works of A.B. Shelekhin et al. on glass membranes [139,14] as well as those more recent of R.S.A. de Lange et al. on sol-gel derived molecular sieve membranes [137,138]. The influence of errors in measured variables on the reliability of membrane structural parameters have been discussed in [136]. The accuracy of experimental data and the mutual relation between the resistance to gas flow of the separation layer and of the support are the limitations for the application of the permeation method. The interpretation of flux data must be further considered in heterogeneous media due to the effects of pore size distribution and pore connectivity. This can be conveniently done in terms of structure factors [5]. Furthermore the adsorption of gas is often considered as negligible in simple kinetic theories. Application of flow methods should always be critically examined with this in mind. 

The effect of pore size on the kinetics of sorption of large molecules on carbon has been studied. Rapid breakthrough and low-concentration factors of organic compounds have been attributed to slow sorption kinetics (Yous-sefi and Faust, 1980). McCreary and Snoeyink (1980) report that sorptive capacity decreased with increasing-molecular-weight fractions, and that humic acid was slower to attain equilibrium than the smaller fulvic acid. Slow sorption kinetics particularly hamper column-concentration methods, and the choice of proper flow rate is important. 

Figure 7.25. Comparative chromatograms illustrating the effect of pore size on protein separation. Two larger proteins (peaks 5 and 6) show substantial peak broadening due to entangled diffusion within the smaller pores of the second column. Reprinted with permission from reference 35.

In-Vivo Percutaneous Implant Experiment. The principle of percutaneous attachment has extensive application in many biomedical areas, including the attachment of dental and orthopedic prostheses directly to skeletal structures, external attachment for cardiac pacer leads, neuromuscular electrodes, energy transmission to artificial heart and for hemodialysis. Several attempts to solve the problem of fixation and stabilization of percutaneous implants(19) have been made. Failures were also attributed to the inability of the soft tissue interface to form an anatomic seal and a barrier to bacteria. In the current studies, the effect of pore size on soft tissue ingrowth and attachment to porous polyurethane (PU) surface and the effect of the flange to stem ratio and biomechanical compliance on the fixation and stabilization of the percutaneous devices have been investigated.(20)... 

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