Horvath Kawazoe method

This equation describes the additional amount of gas adsorbed into the pores due to capillary action. In this case, V is the molar volume of the gas, y its surface tension, R the gas constant, T absolute temperature and r the Kelvin radius. The distribution in the sizes of micropores may be detenninated using the Horvath-Kawazoe method [19]. If the sample has both micropores and mesopores, then the J-plot calculation may be used [20]. The J-plot is obtained by plotting the volume adsorbed against the statistical thickness of adsorbate. This thickness is derived from the surface area of a non-porous sample, and the volume of the liquified gas. 

Thus, either type I or type IV isotherms are obtained in sorption experiments on microporous or mesoporous materials. Of course, a material may contain both types of pores. In this case, a convolution of a type I and type IV isotherm is observed. From the amount of gas that is adsorbed in the micropores of a material, the micropore volume is directly accessible (e.g., from t plot of as plot [1]). The low-pressure part of the isotherm also contains information on the pore size distribution of a given material. Several methods have been proposed for this purpose (e.g., Horvath-Kawazoe method) but most of them give only rough estimates of the real pore sizes. Recently, nonlocal density functional theory (NLDFT) was employed to calculate model isotherms for specific materials with defined pore geometries. From such model isotherms, the calculation of more realistic pore size distributions seems to be feasible provided that appropriate model isotherms are available. The mesopore volume of a mesoporous material is also rather easy accessible. Barrett, Joyner, and Halenda (BJH) developed a method based on the Kelvin equation which allows the calculation of the mesopore size distribution and respective pore volume. Unfortunately, the BJH algorithm underestimates pore diameters, especially at... 

Deficiencies of the Horvath-Kawazoe method and other similar procedures... 

Figure 4.6 shows the PSDs obtained from the high-resolution N2 adsorption isotherms at 77 K (Figure 4.5) by applying the Horvath-Kawazoe method (Figure 4.6a), Dubinin-Astakhov method...

Two kinetic (CMS-Kl, CMS-K2) and one equilibrium (CMS-R) carbon molecular sieves, used originally for separation of gaseous mixtures, were investigated. The adsorption Nj isotherms at 77 K, in static conditions where obtained. In the case of the two first sieves the adsorption was so low that the calculation of parameters characterizing the texture was impossible. The volume of nitrogen adsorbed on the sieve CMS-R is remarkable From obtained results parameters characterizing micropore structure according to Dubinin -Radushkevich equation and Horvath - Kawazoe method were determined. 

From obtained isotherm were determined parameters characterizing micropore structure according to Dubinin - Radushkevich equation [6] and Horvath - Kawazoe method [7] which are presented below ... 

Fig. 3. MPSDs calculated from the Horvath-Kawazoe method.

Figure I Relation between filling pressure and pore width predicted by the modified Kelvin equation (MK), the Horvath-Kawazoe method (HK), density Junctional theory (DFT), and molecidar simulation (points) for nitrogen adsorption in carbon slits at 77 K [8].

The methods differ in the theoretical treatment which is used. A majority of them are based on the Generalised Adsorption Isotherm (GAI) also called the Integral Adsorption Equation (lAE). The more recent approaches use the Monte Carlo simulations or the density functional theory to calculate the local adsorption isotherm. The analytical form of the pore size distribution function (PSD) is not a priori assumed It is determined using the regularization method [1,2,3]. Older methods use the Dubinin-Radushkevich or the Dubinin-Astakhov models as kernel with a gaussian or a gamma-type function for the pore size distribution In some cases, the generalised adsorption equation can be solved analytically and the parameters of the PSD appear directly in the isotherm equation [4,5,6], Other methods which do not rely on the GAI concept are sometimes used the MP and the Horvath-Kawazoe methods are the most well known [7,8]. 

A MODIFIED HORVATH-KAWAZOE METHOD FOR MICROPORE SIZE ANALYSIS... 

A modified Horvath-Kawazoe method for micropore size analysis... 

Hgure It.l Pore-filling pressure dependence on the pore width for nitrogen adsorption in carbon slit pore at 77.35 K. (Solid line) NLDFT. (Dashed line) Horvath-Kawazoe method. (Dash-dot line) Kelvin equation. 

Lastoskie, C.M. (2000). A modified Horvath—Kawazoe method for micropore size analysis. In Studies in Surface Science and Catalysis, Elsevier, Amsterdam, Vol. 128 (K. Unger et al., eds). pp. 475—84. 

The pore size and specific surface area are the most relevant properties for the porous materials. The porosity was measured by the gas adsorption isotherm by using Horvath-Kawazoe method. The relative pressure is expressed by pipo. 

The Horvath-Kawazoe method can also be appUed to adsorption of carbon dioxide at 273 K. This gives information about smaller micropores than does nitrogen adsorption. A partial micropoie distribution for PM-1 from CO2 adsorption is compared with the result from N2 adsorption in Figure 2.3. Extension of the distribution to higher pore widths requires higher pressures than were possible on the instrument used to obtain these data. The apparent distribution from CO2 adsorption may be affected by the presence of specific adsorption sites. Nevertheless, the data support the idea that the material is essentially microporous. 

Valladares, D., and Zgrablich, G., A test of the Horvath-Kawazoe method by Monte-Carlo simulation, Adsorpt. Sci. Technol., 15(1). 15-24(1997). 

Figure 3.8. Differential pore volume of the activated carbon (AC) NORIT Rl EXTRA in the micropore region, calculated from the AI given in Fig. 3.7B by the Horvath-Kawazoe-method [3.29].

Table 2 Physical Properties for Pore Size Distnbution Calculation by Horvath-Kawazoe Method(I983)...

Fig. 2. 18. Effective pore size distributions of carbon molecular sieves calculated by Horvath-Kawazoe method.

Kowalczyk P, Ustinov EA, Terzyk AP, Gauden PA, Kaneko K, Rychlicki G. Description of benzene adsorption in slit-like pores. Theoretical foundations of the improved Horvath-Kawazoe method. Carbon 2004 42(4) 851-864. 

Dubinin-Stoeckli, DS). These methods are based on Dubinin s theory of the volxmie filling of micropores (TVFM), the density functional theory (DFT) and the Horvath-Kawazoe method. However, CO2 provides a complement to N2 adsorption for the assessment of the narrow microporosity [19]. A frequently observed disagreement between the PSD obtained finm adsorption isotherms of different gases is mostly attributed to molecular sieving and networking effects [20], and to specific adsorbate-carbon interactions [9, 21]. Although these factors are important, possible inconsistencies in the PSD may also be caused by the choice of parameters for intermolecular interactions [9]. 

In previous studies [22, 23] the structural characterization of a series of carbonaceous materials obtained from pyrolysis and subsequent activation of PET waste was conducted by means of N2 and CO2 adsorption isotherms. The gas adsorption data were interpreted by the BET, Dubinin-Asthakov, t-plot and Horvath-Kawazoe methods. For the t-plot method, the standard data given by Selles-Perez [24] for a nonporous active carbon treated at 2073 K, was used. Significant discrepancies between the results from the t-plot method and those obtained from the DR and/or DA methods, applied to both N2 and CO2 adsorption isotherms, were found. 

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