Barrett, Joyner and Halenda

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]. 

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... 

The Barrett, Joyner, and Halenda (2) method of pore size distribution calculation requires data for the volumes of vapor adsorbed at 64 relative pressures, between 0.046 and 0.967. The volume of gas in the system at these pressures may be read from a smooth curve drawn through the equilibration points of the chart record or may be interpolated mathematically from a set of data points. In the procedure used, the pressure-volume points, and other data pertinent to the sample and the experiment, are listed in a form convenient to transcribe by key punch to IBM cards. The arrangement of the data on the punch cards is determined by the particular computer program. In this case, a program of the Barrett, Joyner, and Halenda method of pore size distribution calculation had been written for an IBM 704 data-processing unit. 

At the top of the sheet, the sample file number, weight, and other descriptive material for the experimental run are given. Immediately below these, are listed the cubic centimeters of nitrogen, at standard temperature and pressure, adsorbed per gram of sample at the 64 pressure points used in the Barrett, Joyner, and Halenda calculation method. 

Over the period 1945-1970 many different mathematical procedures were proposed for the derivation of the pore size distribution from nitrogen adsorption isotherms. It is appropriate to refer to these computational methods as classical since they were all based on the application of the Kelvin equation for the estimation of pore size. Amongst the methods which remain in current use were those proposed by Barrett, Joyner and Halenda (1951), apparently still the most popular Cranston and Inkley... 

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 ... 

In designing an adsorption column, the characterization of adsorbents should be done prior to experiments. In particular, one should know not only the specific area but also the pore size distribution of the adsorbent in order to confirm that it would be proper for a given purpose. Nitrogen adsorption and desorption isotherms, BET surface areas, and BJH (Barrett, Joyner and Halenda) pore size distributions of the synthesized sorbents... 

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 ... 

An improved method of deriving pore-size distributions from adsorption isotherms is described which is also believed to provide information on pore shapes. The theory is similar in principle to that of Barrett, Joyner, and Halenda (JS), but the method of calculation is more precise. 

The Kelvin equation has frequently been applied directly to the desorption branch of the isotherm 1) and the results so obtained certainly give a qualitative picture of pore structure. Various refinements have been described in which allowance is made for the thickness of the adsorbed layer which exists at pressures too low for capillary condensed liquid to be present 2, 3). The approaches of Carman (4) and of Barrett, Joyner, and Halenda... 

Fio. 3. Pore-size distribution of a sample of bone char as measured by the application of the method of Barrett, Joyner, and Halenda (SS) to the desorption isotherm for nitrogen at —195° (solid line) compared with values obtained by Joyner, Barrett, and Skold (39) (points) by use of a mercury porosimeter (40, 40a). A wetting angle of 140° was assumed for the mercury on the bone char. 

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... 

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). 

Porosity can be used to describe the pore distribution and pores size associated with an LDH. Pore distribution is related to the method of LDH formation (383) and ions associated with the material, whereas pore size is related more to the method of preparation and interconnection of LDH platelets. The porosity of a material is commonly analyzed by N2 adsorption/desorption and pore size distribution analysis. N2 adsorption/desorption isotherms are a plot of the volume of N2 adsorbed versus relative pressures. Pore size distributions are calculated using the Barrett, Joyner, and Halenda method based on the isotham data (385). 

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... 

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. 

From the adsorption isotherms in Figure 1.13 the mesopore spectra (pore radii r > 1 nm) of the carbons have been calculated applying the method of Barrett, Joyner, and Halenda [1.3, 1.55]. Results are sketched in Figure 1.14. They clearly show that the mesopore volume in the carbon is reduced considerably by the impregnation but regained partly by the pyrolyzation process. 

---