Barrett-Joyner-Halenda method Kelvin equation

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. 

The gas adsorption-desorption technique relates to the adsorption of nitrogen (or, less commonly, carbon dioxide, argon, xenon, and krypton), at cryogenic temperatures, via adsorption and capillary condensation from the gas phase, with subsequent desorption occurring after complete pore filling. An adsorption-desorption isotherm is constructed based upon the relationship between the pressure of the adsorbate gas and the volume of gas adsorbed/desorbed. Computational analysis of the isotherms based on the BET (Brunauer-Emmett-Teller) (Brunauer et al. 1938) and/or BJH (Barrett-Joyner-Halenda) (Barrett et al. 1951) methods, underpinned by the classical Kelvin equation, facilitates the calculation of surface area, pore volume, average pore size, and pore size distribution. 

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... 

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... 

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... 

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 ... 

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... 

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