Pore accessibility

The volume of the solid phase Vp is usually measured by a pycnometric technique, which measures the excluded volume of a pycnometric fluid, whose molecules cannot penetrate the solid phase of PS. A simple example of a pycnometric fluid is helium [55], The pycnometric fluid fill in all void space (pores) accessible to it, and presumably do not adsorb on the surface of PS. In the case of microporous PSs, measurement of the volume accessible for guests with various sizes allows the determination of a distribution of micropores volume vs. the characteristic size of guest molecules. This approach lays the basis of the method of molecular probes. The essence of this method is in the following we have a series of probe molecules with different mean sizes (dl>d2>d3>---). The pycnometric measurements of the excluded volume will give a series The difference A V=Vpi-Vpi(i>j) corresponds to the volume of micropores with pycnometric sizes of d in a range dt[Pg.283]

For reasons of simplicity, the Thiele modulus will be defined and calculated for a catalyst plate with pore access at both ends of the plate and not at the bottom or top. Note that for most cases in real-life applications the assumptions have to be modified using polar coordinates for the calculations. The Thiele modulus q> is therefore defined as the product of the length of the catalyst pore, /, and the square root of the quotient of the constant of the speed of the reaction, k. divided by the effective diffusion coefficient DeS ... 

Not all frameworks built from tetrahedra as described above are considered to be zeolites. Dense phases are not considered to be zeolites, only those phases with some porosity. Generally, materials with pores accessible by windows defined by six T-atoms or less (six-rings) are not considered to be zeolites. In fact, the boundary between zeolites and dense phases is somewhat nebulous. lUPAC defines [1] zeolites as a subset of microporous or mesoporous materials containing voids arranged in an ordered manner and with a free volume larger than a 0.25 nm diameter sphere. The Structure Commission of the International Zeolite Association uses the criterion of framework density (T-atoms per lOOOA ) with the maximum framework density for zeolites ranging from 19 to 21. 

Figure 1. A semi-quantitative assessment of structural pore accessibility for several clino samples to a range of molecular kinetic diameters.

Therefore, the molecules are eluted in the inverse order of their molecular size, as indicated in Figures 12.3 and 12.4, and the differences in the elution times of different proteins are related to the fraction of pores accessible to the solutes. Equations can be obtained that relate the fraction of pores of different dimensions, the gel structure, and the molecular size of solutes with so-called distribution coefficients. 

Sakatani, Y., D. Grosso, L. Nicole, C. Boissiere, G. Soler-Illia and C. Sanchez (2006). Optimised photocatalytic activity of grid-like mesoporous TiOj films Effect of crystallinity, pore size distribution, and pore accessibility. Journal of Materials Chemistry, 16(1), 77-82. 

Pores accessible to water molecules are not necessarily accessible to chemical agents. Chemical modification is required to impart many desired properties to cotton fabric. These include color, permanent press, flame resistance, soil release, and antimicrobial properties to name a few. Thus, a knowledge of cotton s accessibility under water-swollen conditions to dyes and other chemical agents of various sizes is required for better control of the various chemical treatments applied to cotton textiles. 

The static measurement is based on the addition of a water-swollen cellulose to a solution of the molecular probe. Water in pores accessible to the solute dilutes the solution. In the chromatographic techniques, either glass or standard liquid chromatography columns were packed with cellulose in various forms. The elution volumes of the molecular probes used were determined. Data is generally plotted as internal volume accessible to individual solutes against their molecular sizes. This is illustrated in Figure 5.43. 

Zeolitic materials have been widely used in the last decades in the chemical and petrochemical industries. This increasing interest on these materials is based in their unique properties a uniform intra-crystalline microporosity that provides aceess to a large and well-defined surface, the molecular sieve effect, and the electrostatic field centered at zeolite cations. Furthermore, some properties of zeolites can be tailored by changing the nature of the compensating cation located in the inner part of the cavities by means of their ion-exchange capability. In this way, the pore accessibility of some zeolites used in gas separation processes, as well as the adsorbent-adsorbate interactions, can be tailored by the introduction of cations with different size and chemical nature. Similarly, different cations can be used to introduce new chemical properties (acid-base, redox, etc.), which are needed for a given application in catalytic processes. 

Coke deposition progressively closing the entrance of micropores centered on Dj, in such a way that Di, representing the diameter of open pores, remains constant. The decrease of pore volume is then induced by the diminution of the number of pores accessible to adsorbate. 

The comparison of pore volume distribution for chars only indicates that they are very different. The char of oiled refinery sludge was enriched in mesopores, the char of communal sewage sediment was enriched mainly in ultramicropores, and the char of scrapped cellulose was enriched in micropores, whereas hard coal char was found to be enriched in micro- and mesopores. Generally, the assumption was apparently confirmed that chars of carbon deposits create the pores accessible for benzene molecules with dimension above 0.4 nm. 

Planar faults are common in zeolites and related crystalline microporous solids. These can influence the sorptive characteristics in any one of several ways (i) they can have little influence on the overall accessibility or capacity, but alter the pore architecture, accessibility or difiusional constraints (ii) they can reduce the limiting dimensions of pore windows while leaving the tot pore volume unaffected (iii) they can block channels. Pores or pore access can also be blocked by detrital material such as alumina extracted from the framework, coke or sintered metal catalyst particles, immobile organic molecules or non-framework cations in blocking positions. 

P50(V2) is the pressure for which half of the interparticular void volume (V2) is filled. Using the Washburn equation one can calculate the corresponding pore access diameter, noted as dp50(V2), also defined as median interparticular void diameter. 

These intraparticular pore access diameters are therefore large enough to allow for Krypton molecules to enter SDDP particles and cover their entire surface, both internal and external... 

The nanoball of the type M0132 shows such molecule-response activity. It can be compared to a nanosponge with a multitude of open pores accessible for a specific substrate, for example, guanidinium cation guests in the case of M0132 ... 

A prerequisite for Eq. 2.43 is the equality of the maximum loadability qsat of all solutes. In case of different loadabilities (qsatA qsMj) for the different solutes Eq. 2.43 no longer accords with the Gibbs-Duhem equation and is thus thermodynamically inconsistent (Broughton, 1948), (Kemball et al. 1948). This is, for example, the case if solutes with substantially different molecular masses are separated on sorbents where the pore accessibility is hindered for large molecules. 

Carrier mediation Mass transfer Surfactant-based separations Pore accessibility... 

The specific surface areas of the Pt/carrier catalysts were determined by volumetric Nj adsorption at 77 K, and the specific Pt surface areas were derived from volumetric CO chemisorption measurements at 298 K (as described in Ref [8]). The results are shown in Table 1. The values of the pore access diameters are obtained from Ref [9]. 

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