On Dissipation Of Fracatlity
On Dissipation of fracatlity
in Production Batch of Activated Carbon
B. J. Trznadel
Military Institute of Chemistry and Radiometry, 00-910 Warsaw, Poland
Microporous activated carbons are disordered solids derived from a variety of organic precursors by suitable carbonisation and activation processes. The internal surface of activated carbons is very complex from a structural point of view. Moreover, the adsorbent activity is dependent on the magnitude of the internal surface, the pore size distribution and the shape of the pores. The quantitative evaluation of the geometric surface area plays an important role in the characterisation of porous solids. On the other hand surface roughness and irregularities are additional characteristics of such materials. The earliest work in fractal analysis (Pfeifer and Avnir, 1983, Avnir et al., 1983) has shown that the degree of surface roughness or irregularities can be expressed by the fractal dimension D, where 2£D³3; a perfectly smooth surface has a D=2, while a highly rough, disordered surface has a D=3. The importance of this technique is that the roughness of solid surfaces can now be quantified on areasonable basis.
The stochastic character of the activated carbon production process, particularly chemical reactions, influences on dispersion of porous structure parameters in production batch of activated carbon. Similarly it affects the distribution of fractal dimension. But, in acase of porous materials such as activated carbons, IUPAC has recommended that the pore volume can be correctly determined, while the surface area is an ill-defined quantity (Rouquerol et al. 1994). On the other hand there are few methods for evaluation of fractal dimension, but any one has not IUPAC recommendation. Therefore this work has two objectives. The first one is the quantitative evaluation of the dissipation of fractal dimension and dispersion of basic geometric parameters describing the structure of activated carbons. The second objective is comparison between different methods of calculation of fractal dimension and geometric surface area.
Granulated activated carbon obtained from hardcoal by steam activation produced by HPSDD Hajnówka (Poland) was partially ground to make uniform granule shape and dimensions. Next granules of diameter of about 1mm was separated by sieving. Buczek et al. (2000) showed that values of different structural parameters depends on the granule radius. Moreover, the outer parts of granules of different degree of activation exhibit very similar values of porous structure parameters. According to these conclusions the partial grounding was used for greater differentiation of structural parameters. Such prepared granules were fractionated in air stream of constant flow-rate using the apparatus (Fig.1) proposed by Diduszko et al. (2000). However, previously Smišek et al. (1962) proposed classification of carbon samples by using elutriation in air stream of various flow-rates. This stepwise procedure was used by Kadlec and Daneš (1967) to separate into eight fractions of various specific weights. While, the method proposed by Diduszko et al. gives possible to devide activated carbon batch in to several fractions only in one step. It is based on oblique throw, so the distance from the outlet tube is the differentiation factor. Moreover, this method seems to be very useful even in the case of a low level of porosity differentiation in the production batch.
The oblique throw leads to the spot of activated carbon granules with elliptic shape. The minor axis of this ellipse was about 0.7m and major axis was about 1.1m. This spot was divided into 11 equal bars across major axis. Fig.2 depicts dispersion of fractions ((a) as apercent of total mass of analysed batch of activated carbon, (b) as a quantity of granules in each fraction). The samples are designated by the number of bar: A1-A11.
The low temperature (at 77.5K) nitrogen adsorption-desorption isotherms were determined using a Micromeritics Model ASAP2405N adsorption analyser. Obtained isotherms are shown in Fig.3 for whole range of relative adsorption pressure and in Fig.4 as a DR plots (for relative adsorption pressure up to the beginning of hysteresis loop i.e. p/p0 equal to 0.4).
The fractal analysis was performed on the basis a three independent methods. The first was based on FHH theory (Ismail and Pfeifer, 1994). The second one was based on modified BET model proposed by Khalili et al. (2000). The third method is based on thermodynamical analysis of adsorption isotherms (Ehrburger-Dolle, 1999). It was found on the basis of these methods that surface roughness decreases due to increasing level of activation. It means that wider pores affect surface irregularity.
On the other hand analysis of the dispersion of geometric structural parameters (volumetric, superficial and linear) in activated carbon production batch was performed in two ways. The first was based on the theory of volume filling of micropores (the equation of Dubinin-Astakhov (1971) and Dubinin-Izotova (1965) were used). The second was based on statistical thermodynamics and the equation of Horvath-Kawazoe (1983) (HK) was used. Values of the total, micropore and mesopore volumes were taken as a volumetric parameters. The geometric surface areas were determined for micropore and mesopore structures by the use of different methods of calculation and were compared with BET surface. Average micropore sizes, estimated by different methods were chosen as a linear structural parameters. The correction factor (Trznadel, Œwi¹tkowski 1999) describing the amount of nitrogen adsorbed in mesopores in parallel with micropore filling was used in a case of evaluation of the values of structural parameters connected with the micropore structure. While the geometric surface of mesopores was calculated from Kisielev equation (1957).
Additional linear parameter was analysed. It is defined as an average micropore size associated with the power law describing pore size distribution in the range where fractality prevails (Jaroniec et al. 1993). The more precision correlation between this linear parameter and fractal dimension was found by using the thermodynamical limits for fractality range. These limits, according to previous proposal (Trznadel, Œwi¹tkowski 1999), are based on the HK equation: the lower limit is the size of an adsorbate molecule radius and the upper limit is the solution of the HK equation for relative adsorption pressure related to the beginning of hysteresis loop. This correlation is independent on methods used for evaluation of fractal dimension.
The statistical analysis of the dissipation of fractal dimension and the dispersion of all structural parameters was performed. It was found that average micropore size associated with the power law varies in the lowest range. On the other hand the total volume of pores and the mesopore surface area exhibit the widest range of changes.
The fractality factor defined as a distance from a completely smooth surface was used for analysis of influence of fractality on other structural parameters. The correlations between chosen structural parameters and fractality factor were determined.
Discussion on examined methods of evaluation of fractal dimension leads to the conclusion that, in a case of analysis of nitrogen adsorption isotherms, method (Ehrburger-Dolle, 1999) based on free path of adsorbed molecule in the gas phase seems to be the most suitable.
This work was supported by Research Project No0T00A03212 sponsored by Committee of Scientific Research (Poland).
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