Accessible pore volume

In the model described in this work every effort has been made to ensure that it embodies physically meaningful parameters. It is inevitcible, however, that some simplistic idealizations of the physical processes involved in GPC must be made in order to arrive at a system of equations which lends itself to mathematical solution. The parameters considered are, the axial dispersion, interstitial volume fraction, flow rate, gel particle size, column length, intra-particle diffusivity, accessible pore volume fraction and mass transfer between the bulk solution eind the gel particles. 

Here Cp is the accessible pore volume fraction of the gel which is a fijnction of the pore size distribution as well as the size of a polymer molecule. The value of p is given by Equation 3 ... 

This curve was ised to calculate Cp from Equation 12 (which in turn required the calculations of e which will be described in the next section). It is important to note that the accessible pore volume varies for different solutes. If KggQ and i (M) were explicitly available then Equation 3 could be used to obtain Cp. 

The total pore volume is the total internal volume per unit mass of catalyst. Some of this pore volume may be completely enclosed and thus not available to the reaction molecules. Moreover, the accessible pore volume changes with the size of the diffusing molecules. 

The total accessible pore volume may be measured by the amount of adsorbate at the saturation pressure of the adsorptive, calculated as liquid volume, provided the adsorption on the external surface can be neglected or can be evaluated. The accessible pore volume may be different for molecules of different sizes. A method which is not subject to the effect of the external surface is the determination of the dead space by means of a non-sorbable gas (normally helium) in conjunction with the determination of the bulk volume of the adsorbent by means of a non-wetting liquid or by geometrical measurements. 

The porosity of a solid is most easily determined by the imbibition method. A sample of solid is dried, weighed while dry, then saturated with a wetting liquid (such as water or heptane), under vacuum. The accessible pore volume is calculated by a material balance ... 

The recent descriptions of the ALPO-n, SAPO-n and MeAPO-n families of microporous materials illustrate that hydrothermal syntheses can afford a wide and diverse range of four-coordinate framework structures based on nearregular tetrahedra [1,2]. As building blocks, octahedra and tetrahedra can also be combined, in various proportions, into a variety of structure types [3,4]. Reflecting the conditions used for conventional synthesis [3,4], most of these structures are condensed, with little accessible pore volume. There are, however, examples of both synthetic [5-7] and natural materials [8-11] that have microporous crystalline structures. Further, the formation chemistry of silicates and aluminosilicates [12,13] illustrates that the more open structures are generally produced under relatively mild conditions. Open octahedral-tetrahedral structures with large pore systems might therefore also be accessible under appropriate low temperature hydrothermal conditions. 

For the present purpose we define the porosity, e, as the ratio of the total accessible pore volume Vf to the apparent volume of the adsorbent. Thus,... 

Type I is concave and V approaches a limiting value. This type is characteristic for microporous solids ) with negligible external surface areas (e.g. activated carbons, molecular sieve zeolites and certain porous oxides). Although mathematically type 1 isotherms are very well described by the Langmuir isotherm equation, calling them "Langmuir isotherms" is not recommended because the limited uptake is governed by the accessible pore volume rather than by the Internal surface area. 

Commercially available coal based activated carbons Filtrasorb-400, Norit ROW 0.8 and Norit ROX 0.8 were chosen as the adsorbents. The adsorbates used for determination of the pore network connectivity of the carbons were ethyl propionate, ethyl butyrate, ethyl isovalerate, isobutyl acetate, benzaldehyde, hexyl acetate, methyl salicylate and 2-ethyl hexyl acetate. For the evaluation of the pore network connectivity, we used the fitted maximum capacity obtained fi om isotherm fitting to calculate the accessible pore volume [7]. 

Figure 2. Correlation between accessible pore volume and fitted molecular size, estimated based on bimodal gamma function fitting, (a) Filtrsorb-400, (b) Norit ROW 0.8, and (c) Norit ROX 0.8.

This last value indicates the more dramatic effect of functionalization in blocking the previously accessible pore volume compared to the effect on the surface area. Clearly the STPI groups block the mouths of pores and this affects also the connectivity of the system. 

Experimentally, there are some difficulties in using methane or carbon dioxide as a probe at ambient temperatures. One is the need to adsorb at high pressures (in reference 6 pressures of up to 40 atmospheres were used). A second problem is that the correction needed to convert from siu ce excess to absolute adsorption, implying an assumption about the accessible pore volume, cannot be ignored, and may become dominant at h pressure. 

This integration can be performed on the curves in Fig. 12.4. The advantage of the method is that it gives a good assessment of the accessible pore volume by... 

Dubinin model was taken by the authors as evidence that hydrogen displays a fluid behaviour when adsorbed in NaA and an estimate of accessible pore volume led them to infer that all three molecules could enter the smaller P-cages. 

Figure 10. Intrinsic permeability of the compacted clay obtained from saturated water flow and from unsaturated gas flow tests. In gas flow tests, the accessible void ratio indicates the ratio between gas accessible pore volume and particle volume (e( l-S,)).

It has been reported (Stone et al, 1969) that a cellulase molecule has a diameter of 30 A. When the substrate pore volume accessible to the enzyme is zero, the reaction rate is also zero, but, for any additional increase in the accessible pore volume, there is a corresponding increase in reaction rate. Fig. 1 shows that molecules of sizes smaller than 30 A produce positive intercepts on the l axis (accessible pore volume, ml/g, against initial rates, % dissolved per hour) because more water is... 

The accessibility of the pore volume is just one side of the medal even with the lower accessible pore volume the Fractogei tentacle ion exchangers show a very high protein-binding capacity due to the fact that the tentacle network is very well able to bind charged molecules even if it excludes the noncharged marker molecules. 

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