Pore width distribution

The models of Matranga, Myers and Glandt [22] and Tan and Gubbins [23] for supercritical methane adsorption on carbon using a slit shaped pore have shown the importance of pore width on adsorbate density. An estimate of the pore width distribution has been recognized as a valuable tool in evaluating adsorbents. Several methods have been reported for obtaining pore size distributions, (PSDs), some of which are discussed below. 

Isotherms for argon at 87 K adsorbed on typical activated carbons are shown in Figs 7.8 and 7.9, along with the reconstructed isotherm resulting from the pore width distributions shown. 

While the fit to the data is satisfactory in both cases, inspection of the pore width distributions obtained for these and many other activated carbon samples reveals a disturbing similarity they aU show deep minima at regular multiples of the probe molecule diameter, particularly near 1 nm (3xXq) [21, 23]. This can be traced to packing effects inherent in the kernel function models that seem to be missing in the real data. Figure 7.10 shows how the pore fluid density as calculated by DFT varies with pore width, with density maxima near the pore width distribution minima. 

G activated carbon (points) with the fit given by the nonlocal density functional theory (NLDFT) models (line), (b) The pore width distribution for the carbon. 

By assuming that the wall thickness is distributed randomly, following a Poisson distribution, and that the average wall thickness is correlated with pore width, Bhatia is able to solve Eqn (7.13) by the usual means without introducing new parameters. The results yield both a pore width distribution and a wall thickness distribution. Compared with the simple model, this method yields pore width distributions that are shifted toward smaller widths, as expected. However, the distributions are similarly multimodal, showing periodic minima notably near 1 nm pore width. 

The first reports using this method are quite encouraging. The pore width distributions obtained are significantly less complex than given by the simple model, without the anomalous periodicity, and the fit to the data is notably superior. 

The pH stability of silicas is restricted to the range of approximately pH 1-8. Silicas with pore widths up to 400 nm (and a particle size of 10 Xm) are produced for use in size-exclusion chromatography. These stationary phases must have a well defined pore width and pore-width distribution and no adsorptive properties. 

Figure 9.16 (a) N2 adsorption-desorption isotherms at 77 K, and the pore width distribution of CGC caiculated from (b) desorption branch and (c) adsorption branch. Copyright the Royai Society of Chemistry, reproduced with permission from Ref. 102. 

Here n is the number of graphene layers in the pore wall, Ais the interlayer spacing and Ps is the number of carbon atoms per unit area in a single sheet. Following Steele [6] we use the values A = 0.335 nm and ps = 0.3817 atoms.A for carbon. Considering the adsorption of an LJ fluid in a carbon having slit pore width distribution and random pore wall thickness characterized by the probability distribution/>( ), we obtain the overall isotherm... 

It would be difficult to over-estimate the extent to which the BET method has contributed to the development of those branches of physical chemistry such as heterogeneous catalysis, adsorption or particle size estimation, which involve finely divided or porous solids in all of these fields the BET surface area is a household phrase. But it is perhaps the very breadth of its scope which has led to a somewhat uncritical application of the method as a kind of infallible yardstick, and to a lack of appreciation of the nature of its basic assumptions or of the circumstances under which it may, or may not, be expected to yield a reliable result. This is particularly true of those solids which contain very fine pores and give rise to Langmuir-type isotherms, for the BET procedure may then give quite erroneous values for the surface area. If the pores are rather larger—tens to hundreds of Angstroms in width—the pore size distribution may be calculated from the adsorption isotherm of a vapour with the aid of the Kelvin equation, and within recent years a number of detailed procedures for carrying out the calculation have been put forward but all too often the limitations on the validity of the results, and the difficulty of interpretation in terms of the actual solid, tend to be insufficiently stressed or even entirely overlooked. And in the time-honoured method for the estimation of surface area from measurements of adsorption from solution, the complications introduced by... 

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 selectivity of a gel, defined by the incremental increase in distribution coefficient for an incremental decrease in solute size, is related to the width of the pore size distribution of the gel. A narrow pore size distribution will typically have a separation range of one decade in solute size, which corresponds to roughly three decades in protein molecular mass (Hagel, 1988). However, the largest selectivity obtainable is the one where the solute of interest is either totally excluded (which is achieved when the solute size is of the same order as the pore size) or totally included (as for a very small solute) and the impurities differ more than a decade in size from the target solute. In this case, a gel of suitable pore size may be found and the separation carried out as a desalting step. This is very favorable from an operational point of view (see later). 

Most size exclusion chromatography (SEC) practitioners select their columns primarily to cover the molar mass area of interest and to ensure compatibility with the mobile phase(s) applied. A further parameter to judge is the column efficiency expressed, e.g., by the theoretical plate count or related values, which are measured by appropriate low molar mass probes. It follows the apparent linearity of the calibration dependence and the attainable selectivity of separation the latter parameter is in turn connected with the width of the molar mass range covered by the column and depends on both the pore size distribution and the pore volume of the packing material. Other important column parameters are the column production repeatability, availability, and price. Unfortunately, the interactive properties of SEC columns are often overlooked. 

Effectiveness of selective adsorption of phenanthrene in Triton X-100 solution depends on surface area, pore size distribution, and surface chemical properties of adsorbents. Since the micellar structure is not rigid, the monomer enters the pores and is adsorbed on the internal surfaces. The size of a monomer of Triton X-100 (27 A) is larger than phenanthrene (11.8 A) [4]. Therefore, only phenanthrene enters micropores with width between 11.8 A and 27 A. Table 1 shows that the area only for phenanthrene adsorption is the highest for 20 40 mesh. From XPS results, the carbon content on the surfaces was increased with decreasing particle size. Thus, 20 40 mesh activated carbon is more beneficial for selective adsorption of phenanthrene compared to Triton X-100. 

In a preliminary screening, the alkylation of 2-methylnaphthalene was studied using a variety of acid zeolites with different pore widths. In principal agreement with the earlier work of Fraenkel et al. [22-25] it was found that the best selectivities for the slim alkylation products, i. e., 2,3-, 2,6- and 2,7-dimethylnaphthalene, are obtained on HZSM-5 and HZSM-11. On these catalysts it was observed that the alkylation is always accompanied by the undesired isomerization into 1-methylnaphthalene. Moreover, a peculiar deactivation behavior was encountered With time on stream, the yield of 1-methylnaphthalene always dropped while the yield of alkylation products remained practically constant or even slightly increased. An example for the conversion and yield curves is given in Fig. 4. The distribution of the dimethylnaphthalene isomers is shown for the same experiment in Fig. 5. Bearing in mind that in equilibrium one would expect roughly 12 mole-% of each of the slim isomers, the... 

Sbet - BET specific surface area V, - single-point total pore volume w - pore width at the maximum of the pore size distribution calculated using the BJH method with the corrected form of the Kelvin equation [34]. 

Nitrogen adsorption isotherms for the OMMs studied were recorded at 77K using a Micromeritics ASAP 2010 adsorption analyzer. All samples prior to adsorption analysis were degassed at 120°C for 2h under vacuum. The BET specific surface area was calculated from the adsorption data in the range of the relative pressure from 0.04 to 0.2 according to the BET method.46 The total pore volume was estimated from the amount adsorbed taken at the relative pressure about 0.99.47 The pore width was estimated at the pore size distribution maximum obtained by the KJS method.48... 

Makrolon has a mean free pore-volume of 0.1 nm3 and the width at half-height of the corresponding distribution is 0.04 nm3 [22], The polymer layer reacts to the exposition of the analyte molecules by swelling and by changes of the refractive index. Due to the pore-volume distribution (see Fig. 1), the interaction kinetic depends on the molecule size [23], The analytes used in this work are methanol with a size smaller, ethanol with a size almost equal to and 1-propanol with a size bigger than the mean free pore-volume. 

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