Micropores dimensions

In (8) and (9), I is the intensity scattered by one electron, and Sr are the specific surfaces, or surface areas per unit mass of coal, of the macropores and transition pores, respectively the constant C. is proportional to the weak but constant scattering from the micropores b is a constant characterizing the micropore dimensions M and A are respectively the mass of the sample and its cross-section area perpendicular to the incident beam T is the x-ray transmission and a is a constant inversely proportional to the average dimensions of the transition pores. The factor 1/T is included in (9) to take account of the absorption of x-ray in the samples, since (3) was developed under the assumption that the samples were non-absorbing. The transmission T can be expressed—... 

A nomenclature was adopted internationally by IUPAC. Thus, micropore dimensions are smaller than 2 nm, mesopores fall between 2-50 nm, and macropores are above 50 nm. 

Some particles, however, may have a bimodal distribution for their internal pores. Besides the mode corresponding to the mesopores (t5qjical dimensions between ca 6 and 30 nm), the second mode corresponds either to micropores (dimensions below ca 2 nm) that have properties that are rarely acceptable or to macro- or through-pores (dimensions above 500 nm) that are intermediate in size between the mesopores of an adsorbent and the extraparticle pores of a packed column. 

Protonation of hexene consists of two energy terms adsorption of hexene in the micropore and subsequent protonation. Only the first term depends significantly on micropore dimensions. The overall effect of course is a difference in protonation energy of gas phase olefine for different zeolites. With respect to the protonated state the true activation energy for... 

To satisfy this condition, the Gaussian distribution should be multiplied by the factor 2/[l + erf B/fTg, i2 )] [121] consequently, the isothemi Eq. (54) should be also multiplied by this factor. This factor is negligible for 5/2.3because the erf function is close to unity. Another disadvantage of the truncated Gaussian distribution (i.e., Eq. (53) a 0) is its nonzero value for 5 = 0, which is physically unrealistic 5 = 0 implies that the micropore dimension x = 0 and then the distribution function should be equal to zero [122]. Stoeckli et al. [123-125] and Dubinin [115, 126] showed tliat Eq. (54) gives a good representation of many adsorption isotherms on active carbons. 

In other words, the medium-specific contribution is not easily measured or quantified for probe molecules in interaction with solid surfaces. Moreover, in the case of microporous solids, the short-distance interactions known as "confinement effects" are even more difficult to evaluate. In all comparisons of experimental data one should be aware that the reactivity of probe base molecules is largely influenced by the size of adsorbates and micropore dimensions. As a result, the acidity scales based on the free energy of proton transfer to a specific base are expected to depend on the choice of reference base. This fact has been confirmed experimentally, as calorimetric heats of adsorption of various bases on, e.g., zeolites, depend on the base chosen. For example, a ZH zeolite may be a stronger acid... 

In radical chain oxidation reactions, the relative rates of the termination steps differentiate oxidation steps and, hence, affect the selectivity. The termination of tertiary peroxides is much faster than that of primary peroxides. The constraints of the zeolite micropore dimensions limit the geometry of the bimolecular encounter of alkane and oxy radical. 

Figure 4.37 illustrates the sensitivity dependence of the molecular product distribution on zeolite micropore dimensions for the cracking of n-Cie. The product ratio of branched dimethylbutane (DMB) versus n-Ce is taken as a measure of the selectivity. A maximum in selectivity towards the bulky branched molecule is found for the intermediate pore-size zeolite AFI. This result is curious since one would have expected the wide-pore zeolite Fau to lead to the maximum yield for the more bulky molecule. The differences from expectation appear to be related again to the adsorption properties of hydrocarbons. 

For this determination, the molecular probe must not penetrate into the zeolite micropores (and so not in the mesoporous cavities). Therefore, we must choose a bulky probe molecule whose size is larger than the zeolite micropore dimensions. In these conditions, the concentrations of the probe molecule in the micropores and in the internal mesopores equal zero, so the equation (4) becomes ... 

Zeolites form a special class of oxides, which are catalytically active owing to the presence of acid sites. Zeolites are crystalline alumina-silicates with micropores defined by the crystallographic structure of the solid (Figure 3.8). Micropore dimensions may vary and can be of the order of the size of an organic molecule. 

Adsorbents such as some silica gels and types of carbons and zeolites have pores of the order of molecular dimensions, that is, from several up to 10-15 A in diameter. Adsorption in such pores is not readily treated as a capillary condensation phenomenon—in fact, there is typically no hysteresis loop. What happens physically is that as multilayer adsorption develops, the pore becomes filled by a meeting of the adsorbed films from opposing walls. Pores showing this type of adsorption behavior have come to be called micropores—a conventional definition is that micropore diameters are of width not exceeding 20 A (larger pores are called mesopores), see Ref. 221a. 

These calculations lend theoretical support to the view arrived at earlier on phenomenological grounds, that adsorption in pores of molecular dimensions is sufficiently different from that in coarser pores to justify their assignment to a separate category as micropores. The calculations further indicate that the upper limit of size at which a pore begins to function as a micropore depends on the diameter a of the adsorbate molecule for slit-like pores this limit will lie at a width around I-So, but for pores which approximate to the cylindrical model it lies at a pore diameter around 2 5(t. The exact value of the limit will of course depend on the actual shape of the pore, and may well be raised by cooperative effects. 

These procedures proposed by Dubinin and by Stoeckli arc, as yet, in the pioneer stage. Before they can be regarded as established as a means of evaluating pore size distribution, a wide-ranging study is needed, involving model micropore systems contained in a variety of chemical substances. The relationship between the structural constant B and the actual dimensions of the micropores, together with their distribution, would have to be demonstrated. The micropore volume would need to be evaluated independently from the known structure of the solid, or by the nonane pre-adsorption method, or with the aid of a range of molecular probes. 

If a Type I isotherm exhibits a nearly constant adsorption at high relative pressure, the micropore volume is given by the amount adsorbed (converted to a liquid volume) in the plateau region, since the mesopore volume and the external surface are both relatively small. In the more usual case where the Type I isotherm has a finite slope at high relative pressures, both the external area and the micropore volume can be evaluated by the a,-method provided that a standard isotherm on a suitable non-porous reference solid is available. Alternatively, the nonane pre-adsorption method may be used in appropriate cases to separate the processes of micropore filling and surface coverage. At present, however, there is no reliable procedure for the computation of micropore size distribution from a single isotherm but if the size extends down to micropores of molecular dimensions, adsorptive molecules of selected size can be employed as molecular probes. 

The stmcture of activated carbon is best described as a twisted network of defective carbon layer planes, cross-linked by aHphatic bridging groups (6). X-ray diffraction patterns of activated carbon reveal that it is nongraphitic, remaining amorphous because the randomly cross-linked network inhibits reordering of the stmcture even when heated to 3000°C (7). This property of activated carbon contributes to its most unique feature, namely, the highly developed and accessible internal pore stmcture. The surface area, dimensions, and distribution of the pores depend on the precursor and on the conditions of carbonization and activation. Pore sizes are classified (8) by the International Union of Pure and AppHed Chemistry (lUPAC) as micropores (pore width <2 nm), mesopores (pore width 2—50 nm), and macropores (pore width >50 nm) (see Adsorption). 

The electrolyte used is 1 molar LiPF dissolved in a mixture of 30% ethyl carbonate (EC) and 70% diethyl carbonate (DEC) by volume. This electrolyte IS easy to use because it will self-wet the separator and eleetrodes at atmospheric pressure. The electrolyte is kept under an argon atmosphere in the glove-box. The moleeules of electrolyte solvents, like EC and DEC, have in-plane dimensions of about (4 A x 5 A) to (6 A x 7 A). These molecules are normally larger than the openings of the micropores formed in the region 3 carbons (Fig. 2) as described in section 5. 

Carbons may have closed and open pores with a large variety of dimensions from a few Angstroms to several microns. In terms of structure, the pores in active carbons are divided into three basic classes [66, 69] macropores, transitional pores, and micropores. Pores are formed during the production of carbon (pyrolysis of its precursors), or can be formed by other means such as oxidation by 02, air, C02, or H20 [66]. According to Dubinin s... 

Because the pore dimensions in narrow pore zeolites such as ZSM-22 are of molecular order, hydrocarbon conversion on such zeolites is affected by the geometry of the pores and the hydrocarbons. Acid sites can be situated at different locations in the zeolite framework, each with their specific shape-selective effects. On ZSM-22 bridge, pore mouth and micropore acid sites occur (see Fig. 2). The shape-selective effects observed on ZSM-22 are mainly caused by conversion at the pore mouth sites. These effects are accounted for in the hydrocracking kinetics in the physisorption, protonation and transition state formation [12]. 

Supports such as silica, alumina and carbon usually contain pores that offer a high internal surface area. The pore system of a support is usually rather irregular in shape and contains macropores, due to the spaces between individual crystallites, with diameters of the order of 100 nm, and micropores with characteristic dimensions of 5-10 nm. A good support offers... 

Molecular sieves (zeolites) are artificially prepared aluminosilicates of alXali metals. The most common types for gas chromatography are molecular sieve 5A, a calcium aluminosilicate with an effective pore diameter of 0.5 nm, and molecular sieve 13X, a sodium aluminosilicate with an effective pore diameter of 1 nm. The molecular sieves have a tunnel-liXe pore structure with the pore size being dependent on the geometrical structure of the zeolite and the size of the cation. The pores are essentially microporous as the cross-sectional diameter of the channels is of similar dimensions to those of small molecules. This also contrilsutes to the enormous surface area of these materials. Two features primarily govern retention on molecular sieves. The size of the analyte idiich determines whether it can enter the porous... 

These microporous crystalline materials possess a framework consisting of AIO4 and SiC>4 tetrahedra linked to each other by the oxygen atoms at the comer points of each tetrahedron. The tetrahedral connections lead to the formation of a three-dimensional structure having pores, channels, and cavities of uniform size and dimensions that are similar to those of small molecules. Depending on the arrangement of the tetrahedral connections, which is influenced by the method used for their preparation, several predictable structures may be obtained. The most commonly used zeolites for synthetic transformations include large-pore zeolites, such as zeolites X, Y, Beta, or mordenite, medium-pore zeolites, such as ZSM-5, and small-pore zeolites such as zeolite A (Table I). The latter, whose pore diameters are between 0.3... 

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