Barrett, Joyner, and Halenda BJH method

Based upon the Kelvin equation, the PSD of the meso/macropores has been generally determined by Barrett, Joyner, and Halenda (BJH) method.104 Furthermore, the density functional theory94 which is based upon a molecular-based statistical thermodynamic theory was recently introduced in order to analyze... 

Of the various classical procedures proposed for mesopore size analysis, the Barrett, Joyner and Halenda (BJH) method appears to remain the most popular. The application of the standard BJH method involves the following assumptions ... 

The surface areas of all the samples were measured using the B.E.T. method with nitrogen adsorption at 77 K and a Micromeritics ASAP 2000 for the determination of the pore size distribution for the most interesting ones. Mesopore size distributions were calculated using the Barrett, Joyner and Halenda (BJH) method, assuming a cylindrical pore model (IS). In the analysis of micropore volume and area, the t-plot method is used in conjunction with the Harkins-Jura thickness equation (16). 

A number of models have been developed for the analysis of the adsorption data, including the most common Langmuir [49] and BET (Brunauer, Emmet, and Teller) [50] equations, and others such as t-plot [51], H-K (Horvath-Kawazoe) [52], and BJH (Barrett, Joyner, and Halenda) [53] methods. The BET model is often the method of choice, and is usually used for the measurement of total surface areas. In contrast, t-plots and the BJH method are best employed to calculate total micropore and mesopore volume, respectively [46], A combination of isothermal adsorption measurements can provide a fairly complete picture of the pore size distribution in sohd catalysts. Mary surface area analyzers and software based on this methodology are commercially available nowadays. 

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... 

The BET specific surface area [28] was calculated in the relative pressure range between 0.04 and 0.2. The total pore volume was determined from the amount adsorbed at a relative pressure of 0.99 [28], The primary mesopore volume and external surface area were evaluated using the as-plot method [24, 28, 29] with the reference adsorption isotherm for macroporous silica [29], The pore size distributions were determined using the Kruk-Jaroniec-Sayari (KJS) equation [30] and the calculation procedure proposed by Barrett, Joyner and Halenda (BJH) [31]. 

Pore size distributions were calculated by the ASAP 2000 analysis program using the method by Barrett, Joyner and Halenda (BJH) [12,9] which assumes cylindrical pores. 

The method devised by Barrett, Joyner, and Halenda (BJH) [35] is one of the earhest methods developed to address the pore size distribution of mesoporous sohds. This method assumes that adsorption in mesoporous solid (cylindrical pore is assumed) follows two sequential processes — building up of adsorbed layer on the surface followed by a capillary condensation process. Karnaukhov and Kiselev [45] accounted for the curvature in the first process, but Bonnetain et al. [46] found that this improvement has httle influence on the determination of pore size distribution. The second process is described by either the Cohan equation (for adsorption branch) or the Kelvin equation (for desorption branch). 

The pore size distributions were calculated by using the desorption isotherm, following the method of Barrett, Joyner, and Halenda (BJH) (4). In this procedure the Kelvin equation is used to calculate the radius rp of the capillaries, which are assumed to be cylindrical ... 

Important methods for the determination of the specific surface area and of the pore size distribution are based on the measurement of the gas adsorption isotherm [1,2]. The gas adsorption method and the evaluation according to Brunauer, Emmett and Teller using the two-parameter BET equation has been standardized in several countries for a number of years and an ISO standard just appeared. To establish the pore size distribution the method of Barrett, Joyner and Halenda (BJH) is generally accepted. Other methods for this purpose make use of the flow resistance of air through the compressed sample. The Blaine test and other flow tests used to characterize building materials are standardized world-wide. 

Pore systems of solids may vary substantially both in size and shape. Therefore, it is somewhat difficult to determine the pore width and, more precisely, the pore size distribution of a solid. Most methods for obtaining pore size distributions make the assumption that the pores are nonintersecting cylinders or slit-Uke pores, while often porous solids actually contain networks of interconnected pores. To determine pore size distributions, several methods are available, based on thermodynamics (34), geometrical considerations (35-37), or statistical thermodynamic approaches (34,38,39). For cylindrical pores, one of the most commonly applied methods is the one described in 1951 by Barrett, Joyner, and Halenda (the BJH model Reference 40), adapted from... 

N2 isotherms at 77 K are used for practical reasons (e.g., simultaneous determination of the BET surface area). The use of the Kelvin equation was a popular approach for estimating the pore size distribution. Many procedures were proposed for calculating the pore size distribution from the N2 isotherms over the period between 1945 and 1970 (Rouquerol et al., 1999). The method proposed by Barrett, Joyner, and Halenda (1951), known as the BJH method, continues to be used today. In the BJH method, the desorption branch of the isotherm is used, which is the desorption branch of the usual hysteresis loop of the isotherm for the mesoporous sorbent. The underlying assumptions for this method are... 

Physical properties of calcined catalysts were investigated by N2 adsorption at 77 K with an AUTOSORB-l-C analyzer (Quantachrome Instruments). Before the measurements, the samples were degassed at 523 K for 5 h. Specific surface areas (,S BEX) of the samples were calculated by multiplot BET method. Total pore volume (Vtot) was calculated by the Barrett-Joyner-Halenda (BJH) method from the desorption isotherm. The average pore diameter (Dave) was then calculated by assuming cylindrical pore structure. Nonlocal density functional theory (NL-DFT) analysis was also carried out to evaluate the distribution of micro- and mesopores. 

The surface area was calculated using the BET equation,36 while the total pore volume and the average pore size were calculated from the nitrogen desorption branch applying the Barrett-Joyner-Halenda (BJH) method.37 BET and BJH adsorption measurements were carried out with a Micromeritics Tri-Star system on both the supports and the calcined catalysts. Prior to measurements, the samples were evacuated at 433 K to approximately 50 mTorr for 4 h. 

The nitrogen adsorption-desorption isotherms were obtained at 77K by AutoSorb-1 -C (Quantachrome). Prior to measurement, the samples were outgassed at 300°C for 3 h. The specific surface areas of the samples were determined from the linear portion of the BET plots. Pore size distribution was calculated from the desorption branch of N2 desorption isotherm using the conventional Barrett-Joyner-Halenda (BJH) method, as suggested by Tanev and Vlaev [15], because the desorption branch can provide more information about the degree of blocking than the adsorption branch. 

Figure 1. Plots of differential pore volume against pore diameter calculated from the N2 gas adsorption isotherms obtained from meso/macroporous carbon specimens I (-0-), II (- -), and III (-A-) using Barrett-Joyner-Halenda (BJH) method. Reprinted with permission from G. -J. Lee and S. -I. Pyun, Carbon, 43 (2005) 1804. Copyright 2005, with permission from Elsevier.

However, the characterization of composite isotherms, i.e those indicating the presence of supermicropores and/or mesopores, requires the combined application of more than one method to deduce the PSD extending over the micro- and mesopore range e g. the Barrett-Joyner-Halenda (BJH) method [6] to evaluate the mesopore range and one of the DR-DA-DS, HK, BP (i.e. the method of Mikhail et al. [7]) for the evaluation of microporosity. Micropore volume and surface area estimates are practically obtained by using the empirical a,5-plot method [1]. 

Important trends in N2 isotherm when the PS beads are used as a physical template are shown in Table 1 and Fig. 2. In Table 1, PI is the alumina prepared without any templates, P2 is prepared without ]4iysical template (PS bead), P3 is prepared without chemical template (stearic acid), and P4 is prepared with all templates. For above 10 nm of pore size and spherical pore system, the Barrett-Joyner-Halenda (BJH) method underestimates the characteristics for spherical pores, while the Broekhoff-de Boer-Frenkel-Halsey-Hill (BdB-FHH) model is more accurate than the BJH model at the range 10-100 nm [13]. Therefore, the pore size distribution between 1 and 10 nm and between 10 and 100 nm obtained from the BJH model and BdB-FHH model on the desorption branch of nitrogen isotherm, respectively. N2 isotherm of P2 has typical type IV and hysteresis loop, while that of P3 shows reduced hysteresis loop at P/Po ca. 0.5 and sharp lifting-up hysteresis loop at P/Po > 0.8. This sharp inflection implies a change in the texture, namely, textural macro-porosity [4,14]. It should be noted that P3 shows only macropore due to the PS bead-free from alumina framework. 

Such more realistic models of porous materials can also be used to rigorously test existing characterization methods. The model material is precisely characterized (we know the location of every atom in the material, hence the pore sizes, surface area and so on). By simulating adsorption of simple molecules in the model material and then inverting the isotherm, we can obtain a pore size distribution for any particular theory or method. Such a test for porous glasses is shown in Figure 8, where the exactly known (geometric) PSD is compared to that predicted by the Barrett-Joyner-Halenda (BJH) method, which is based on the modified Kelvin equation. 

For a qualitative determination of the mesopore size distribution, mathematical models have to be used. Of these, the Barrett, Joyner, Halenda (BJH) method [30] is widely used for OMCs [14, 31, 32] and other carbon materials. However, for OMCs this model has some important shortcomings. As already mentioned above, the OMC mesopores might be as narrow as 2 nm. For such mesopores, the BJH method seriously underestimates the pore width [33]. Thus, improved data treatment methods have been proposed [33, 34]. As an example, the mesopore size distributions for an OMC of the CMK-1 type calculated with... 

The solids were analyzed by X-ray diffraction (XRD) using Cu-Ka radiation in the range between 0.5 to 20 °2Q. The data obtained from the nitrogen adsorption/desorption isotherms were used to estimate the specific surface area SBE-d [6], the pore size distribution by the Barrett-Joyner-Halenda (BJH) method [7] and to establish the micropore volume (F icro) by the t-plot analysis [8]. 

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