limited due to the requirement of specialized software and an adequate database of
simulated isotherms (i.e., kernel), which describes the adsorbate-adsorbent interaction and the adsorbent pore geometry. In addition to the methods mentioned above,
there also exist the classical macroscopic (thermodynamic) methods, some of them
using adsorbent-adsorbate interactions such as HK, and other based in classical
thermodynamic using Kelvin equations and its modified forms as BJH, DH, and
VBS, among others; these can be implemented by simply using a spreadsheet.
In the case of zeolites, the micropore size distribution is often obtained with the
HK method for different pore geometries, because it has been demonstrated that for
microporous materials it works correctly, as long as the proper interaction parameters (of both adsorbate and adsorbent) and the adsorbent pore geometries are
considered [48]. These methods are HK for slit pores [33], Saito and Foley
(SF) for cylindrical pores [49], and Cheng and Yang (CY) for spherical pores
[50]. All models also consider the type of adsorbent, adsorptive, and the temperature
of the analysis. To apply all these methods, it is essential to have a high-resolution
adsorption isotherm at low relative pressures from the beginning up to the completion of micropore filling.
For the analysis of the microporous zone of zeolites, it is difficult to find a suitable
microscopic model, whereas there exist macroscopic methods as HK, which works
well. This problem is not present in mesoporous regions, because there are several
available kernels, which provide reliable information. On the other hand, the use of
the macroscopic method, using the Kelvin equation, is more direct because it is only
needed the isotherms data and some other accessible information.
In the following sections, examples for the analysis of the pore size distribution in
the micro and mesoporous zone of some zeolites are given.
3.3.1 Micropore Size Distribution
Figure 12 shows the Ar adsorption isotherms (at 77 or 87 K) for three different
zeolites: two of them with spherical cavities (Zeolite 5A and faujasite (FAU)) and the
third with cylindrical-like channels (ZSM-5). The isotherms presented in the figure
include the stage of micropore filling, and from these data the micropore size
distribution is obtained.
Figures 13 and 14 show the PSD of the zeolites obtained with the HK, CY, and SF
methods and using the interaction parameters of aluminosilicate oxide ion for the
adsorbent [48]. Figure 13 is the PSD for the ZSM-5 zeolite, an aluminosilicate
presenting three-dimensional pore channels of 0.56 Â 0.53 nm of width, assuming a
cylindrical geometry. It can be observed that the PSD obtained with the SF method
predicts a micropore sizes of 0.53 and 0.56 nm, which is in good agreement with the
dimensions and the geometry assumed for the pore channels of this zeolite. In
contrast, HK and CY methods underestimate these values.
Figure 14 shows the PSD and the scheme of the respective structures for Zeolite
5A and FAU (theoretical window sizes of 0.49 and 0.74 nm, and spherical cavities of
1.14 and 1.37 nm, respectively). In this figure it can be seen that with CY method is
48
J. Villarroel-Rocha et al.
simulated isotherms (i.e., kernel), which describes the adsorbate-adsorbent interaction and the adsorbent pore geometry. In addition to the methods mentioned above,
there also exist the classical macroscopic (thermodynamic) methods, some of them
using adsorbent-adsorbate interactions such as HK, and other based in classical
thermodynamic using Kelvin equations and its modified forms as BJH, DH, and
VBS, among others; these can be implemented by simply using a spreadsheet.
In the case of zeolites, the micropore size distribution is often obtained with the
HK method for different pore geometries, because it has been demonstrated that for
microporous materials it works correctly, as long as the proper interaction parameters (of both adsorbate and adsorbent) and the adsorbent pore geometries are
considered [48]. These methods are HK for slit pores [33], Saito and Foley
(SF) for cylindrical pores [49], and Cheng and Yang (CY) for spherical pores
[50]. All models also consider the type of adsorbent, adsorptive, and the temperature
of the analysis. To apply all these methods, it is essential to have a high-resolution
adsorption isotherm at low relative pressures from the beginning up to the completion of micropore filling.
For the analysis of the microporous zone of zeolites, it is difficult to find a suitable
microscopic model, whereas there exist macroscopic methods as HK, which works
well. This problem is not present in mesoporous regions, because there are several
available kernels, which provide reliable information. On the other hand, the use of
the macroscopic method, using the Kelvin equation, is more direct because it is only
needed the isotherms data and some other accessible information.
In the following sections, examples for the analysis of the pore size distribution in
the micro and mesoporous zone of some zeolites are given.
3.3.1 Micropore Size Distribution
Figure 12 shows the Ar adsorption isotherms (at 77 or 87 K) for three different
zeolites: two of them with spherical cavities (Zeolite 5A and faujasite (FAU)) and the
third with cylindrical-like channels (ZSM-5). The isotherms presented in the figure
include the stage of micropore filling, and from these data the micropore size
distribution is obtained.
Figures 13 and 14 show the PSD of the zeolites obtained with the HK, CY, and SF
methods and using the interaction parameters of aluminosilicate oxide ion for the
adsorbent [48]. Figure 13 is the PSD for the ZSM-5 zeolite, an aluminosilicate
presenting three-dimensional pore channels of 0.56 Â 0.53 nm of width, assuming a
cylindrical geometry. It can be observed that the PSD obtained with the SF method
predicts a micropore sizes of 0.53 and 0.56 nm, which is in good agreement with the
dimensions and the geometry assumed for the pore channels of this zeolite. In
contrast, HK and CY methods underestimate these values.
Figure 14 shows the PSD and the scheme of the respective structures for Zeolite
5A and FAU (theoretical window sizes of 0.49 and 0.74 nm, and spherical cavities of
1.14 and 1.37 nm, respectively). In this figure it can be seen that with CY method is
48
J. Villarroel-Rocha et al.