Horvath-Kawazoe method nitrogen adsorption

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. 

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].

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. 

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. 

Specific surface areas and micropore volumes were obtained from nitrogen adsorption - desorption isotherms at -196°C using Micromeritics ASAP 2010. Prior to the measurements all powdered samples were degassed at 175 °C under vacuum 10 6 Torr for 6 hours. The total surface area was calculated using BET equation. The method of Horvath and Kawazoe was used to determine the pore size diameters of the product. 

Fig. 16. Comparison of PSDs obtained using the Dubinin-Stoeckli (DS), Horvath-Kawazoe (HK), and density functional theory (DFT) methods to interpret an isotherm generated from molecular simulation of nitrogen adsorption in a model carbon that has a Gaussian distribution of slit pore widths [120]. Results are shown for mean pore widths of 8.9 A (left) and 16.9 A (right).

The Horvath and Kawazoe (HK) method [39] was developed to determine the PSD of active carbons from nitrogen adsorption isotherm. All pores are assumed to have slit shape. This method rests on the assumption that the adsorption state of a pore is either empty or completely fiUed. The demarcation pressure between these two states is called the pore-filling pressure, and it is a function of pore width. The equilibrium of a pore exposed to a bulk phase of constant chemical potential is obtained from the minimization of the following grand thermodynamic potential ... 

One of the simplest quantitative models was proposed by Horvath and Kawazoe (ref. 12) developed for adsorption in active carbons. It is employed in these studies to compare different zeolites, but, recognizing the differences between active carbons and zeolites, it is only a qualitative measure of pore dimensions. This method (denoted "H-K ) is based on statistical thermodynamics of the adsorbed gas molecules on surfaces. They use a 10-6 Lennard-Jones potential model to relate the free energy of a sorbed gas molecule to the distance between the gas molecule and solid surface. The smallest pore size is constrained by the diameter of the sorbent molecule (e.g., for nitrogen 3.65 A). Sensitivity increases with decreasing pore size. The comparison between the pore size predicted by the Kelvin and H-K theories is shown below in figure 1. 

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