Volmer

Vol. 1

ADSORPTION

149

known, the monolayer surface can be determined. This method is most useful when the solid surface is nearly fiat and energetically homogeneous. The BET method can be used in the interval where the experimental data give a straight linę on the BET plot. Normally nitrogen isotherms are applied at 77 K.

Other methods (<*_s, t-method, etc.) have also been developed for improving the numerical reality of specific surface values. The modified a_s-method is suitable for the analysis of solid-solute adsorption data, where the traditionally used Chemical is iodine. The fractal-theory is a new branch in this field, its application has some technical difficulties at present.

Many porous materials are used in the fields of catalysis and adsorption. IUPAC classifies the pores as macro (>50 nm), meso (2-50 nm), and micro (<2 nm). The total porosity can be easily determined by employing a helium den-sitometer and a mercury porosimeter. The principle of this method is that the helium being a nonadsorbable gas, PV would be a constant at constant temperaturę. Therefore, the t.rue volume of porous sample can be measured by compai-ing the pressure changes, observed in an empty pycnometer and a pycnometer con-taining the porous sample. As mercury cannot, at normal pressure, penetrate into pores smaller than 7.5 //m, the difference between the two measured volumes would be the whole porę volume. Naturally, the porę volume consists of pores of different sizes and shapes.

Mercury can, however, penetrate into the pores at higher pressures. The porę size of a given geometry, which sometimes fundamentally differs from the real physical shape, can be calculated from the pressure-penetrated volume data. The basis of traditional treatment is the Kelvin eąuation. An ordinary mercury porosimeter uses maximal pressures as high as 300 MPa, which makes it possible to determine porę sizes down to 2.5 nm s. The applied pressure is so high that the ąuestion as to whether the porę structure is damaged naturally arises.

When adsorption data are used for the calculation (gas condensation methods), the desorption data are also taken into consideration. At any given pressure related to the porę radius, a porę loses in one step, a certain amount of condensed liąuid adsorbate (Fig. 5). The main idea of this method is the for any cylindrical shape, an eąuilibrium exists across the meniscus of a capillary condensate:

(19)

Po    A 7 >'k

Difficulties in calculation arise when the porę sizes reach 7.5 nm. The Kelvin eąuation is not valid in this region. Another fact is that two parallel processes are taking place: one is the capillary desorption, and the other is the multilayer desorption (22). So the measured desorbed amount consists of two parts, namely, the condensed liąuid that was empted from the pores and that which was lost from the surface. From the measured data, only one independent variable can be calculated; therefore, the other parameters have to be determined from other sources. The geometrical shape of pores have a fundamental influence on the result, and it can be concluded that morę realistic shapes provide better results. For N₂ isotherms the applied eąuations are

(20)

(21)

t = 0.43l5/ln(p₀/p)l^1/3

= 0.953/ln(po/p)