Intraparticle pores

Measurements of particle porosity are a valuable supplement to studies of specific surface area, and such data are particularly useful in the evaluation of materials used in direct compression processes. For example, both micromeritic properties were measured for several different types of cellulosic-type excipients [53]. Surface areas by the B.E.T. method were used to evaluate all types of pore structures, while the method of mercury intrusion porosimetry used could not detect pores smaller than 10 nm. The data permitted a ready differentiation between the intraparticle pore structure of microcrystalline and agglomerated cellulose powders. 

For reasons explained in Section 19.5.3, large-scale LC employs larger particles (10-70 xm) than analytical HPLC. This increases the Cmu term by deepening the intraparticle pores containing stagnant mobile phase to be penetrated by the solute. (See note to Table 19.1). Pellicular packings, in which each particle contains only a superficially porous layer with an inner solid core, have been used, though the present trend is towards totally porous particles of 15-25 p,m. 

Following the intrusion branch with increasing pressure (Fig. 1.16A), the steep initial rise at low pressures is caused by the filling of interparticle spaces. The breakthrough pressure, i.e. the pressure when the voids between the particles are filled, follows in principle the theory of Mayer and Stowe [94], and is inversely proportional to the particle size [95]. The demarcation between interparticle spaces and actual intraparticle pores may be unclear for microparticles, but in the case of polymer beads from suspension polymerization having particle sizes between 50-500 pm, usually no interference occurs. The second rise of the intrusion branch is caused by pores inside the particles. Shown in Fig. 1.16A is a porous material of rather narrow pore size distribution. 

Wakao and Smith [20] originally developed the random pore model to account for the behaviour of bidisperse systems which contain both micro- and macro-pores. Many industrial catalysts, for example, when prepared in pellet form, contain not only the smaller intraparticle pores, but also larger pores consisting of the voids between compressed particles. Transport within the pellet is assumed to occur through void regions... 

The lumped kinetic model can be obtained with further simplifications from the lumped pore model. We now ignore the presence of the intraparticle pores in which the mobile phase is stagnant. Thus, p = 0 and the external porosity becomes identical to the total bed porosity e. The mobile phase velocity in this model is the linear mobile phase velocity rather than the interstitial velocity u = L/Iq. There is now a single mass balance equation that is written in the same form as Equation 10.8. 

The experimental method employed in mercury porosimetry, discussed more extensively in Chapter 20, involves the evacuation of all gas from the volume containing the sample. Mercury is then transferred into the sample container while under vacuum. Finally, pressure is applied to force mercury into the interparticle voids and intraparticle pores. A means of monitoring both the applied pressure and the intruded volume are integral parts of all mercury porosimeters. 

Recently various kinds of porous materials have been developed and their properties and structures have been gathering great concerns in science. There are two types of pores of intraparticle pores and interparticle ones[l]. The intraparticle pores are in the primary particle itself, while the interparticle pores originate from the interparticle void spaces. Zeolites are the most representative porous solids whose pores come from the structurally intrinsic intraparticle pores. The pore geometry can be evaluated by their crystallographic data. The carbon nanotube of which pore wall is composed of graphitic sheets is also the... 

Figure 1.13 illustrates flow through a bed packed with porous particles and ui and U2 are the EOF velocities through the small intraparticle pores and the larger interstitial channels, respectively. For pressure driven flow, assuming that the path length and the pressure drops are the same for the two cases the flow velocity varies as square of... 

Therefore, it is conceivable that the micropore and macropore are interparticle pores, while the mesopore presumably is the intra-particle pore. During the course of calcination, the connection of interparticle was destroyed and this finally resulted in the vanishing of macropore. Because the mesopore was the intraparticle pores, it had relative fine thermal stability though the pore size was enlarged in the calcination. The reasons may be attributed to the steric dispersant effect of non-ionic surfactant PEG [12]. In the synthesis course, PEG gave steric hindrance to the assembling of mesophase and improved the pore structure. 

In many processes of interest to the hydrocarbon processing industry the size and shape of the catalyst has been chosen as a compromise between catalyst effectiveness and pressure drop. Hence, with effectiveness factors for the main reaction somewhat below 1, intraparticle pore diffusion is generally a factor to be reckoned with. Its effect is not easily quantified since the processing of a practical feedstock involves the conversion of a large variety of molecules with widely different reaction rates and therefore the translation of catalyst performance data obtained with crushed particles to that of the actual catalyst may be difficult and of questionable validity. 

The catalytic conversion is therefore dependent upon mass transfer from the gas flowing through the stagnant gas surrounding the catalyst particles and through the intraparticle pores to the catalytic surface. 

When the length-over-diameter ratio of the catalyst beads is not much larger than 0.5 (and the particles are not very tightly packed on the strings), the LC model is obviously expected to underestimate the reactant conversion in the BSR if the performance is limited by intraparticle pore diffusion. 

The intraparticle (pore) diffusion coefficient defined in Section 6.2.2.4 may estimated by the Mackie-Meares correlation (Mackie and Meares, 1955) ... 

Although this solution was derived for plug flow (Da = 0), it can be generalized by using an apparent mass transfer coefficient to account for axial dispersion, a coefficient that is related to axial dispersion, the external film mass transfer coefficient and intraparticle pore diffusion through the following equation [16] ... 

Based on their origin Intraparticle pores Interpartide pores Intrinsic Intraparticle pores Extrinsic intraparticle pores Rigid interparticle pores Flexible interpartide pores... 

Based on their origin, the pores can be classified into two classes, Intraparticle and interparticle pores. The intraparticle pores are further classified into two, intrinsic and extrinsic intraparticle pores. The fonner class owes its origin to the crystal stmcture, of which... 

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