Dollimore-Heal method

BJH and Dollimore-Heal methods are based on the assumption that the statistical thickness of the adsorbed layer is independent of the surface curvature and assume that the meniscus between vapor and condensed phase is hemispherical. This kind of meniscus is met in the case of a cylindrical pore during desorption. The hypothesis of constant thickness, independently of surface curvature, is justified for large mesopores, but generally leads to underestimation of pore size [7]. 

They so called BJH (Barret-Joyer-Halenda) and DH (Dollimore-Heal) methods have been widely used for such calculations. However, in other articles, only a simple Fortran program for the DH method is shown. (This program can be easily used for the analysis of the mesopore size distribution). The thickness correction is done by the Dollimore-Heal equation. One can calculate the mesopore size distribution for cylindrical or slit-shaped mesopores with this program. Therefore, the adsorption branch provides more reliable results. However, the adsorption branch gives a wide distribution compared to the desorption branch due to gradual uptake. Theoretical studies on these points are still done [133]. 

The values of the mesopore volumes and radii and the value of the fiactal dimension, are convergent, as for the size order, with the corresponding values obtained during studies of the structure AI2O3 [64], Values of pore volume near 2 nm have the highest intensity in this curve. The concentration of mesopores decreases with increase of their radius. The observed shape of the pore-size distribution curve is typical for most industrial mesoporous adsorbents. For example, this shape is similar to that found from low-temperature nitrogen adsorption isotherms on various activated carbons by using the Dollimore-Heal method [63]. 

On dry gels, standard characterization techniques for porous media are used, several of which have been described in Volume 2 of this series helium pycnometry for pore volume determination (Section 6.3.1.2) as well as nitrogen adsorption at 77 K for surface area (Section 6.3.2.2, BET method), for microporosity (Section 6.3.3.2, Dubinin-Radushkevich method), for pore size distribution (Section 6.3.3.3, BJFl method), and for total pore volume (Section 6.3.3.4). When characterizing gels by nitrogen adsorption, other methods are also used for data interpretation, for example, the t-plot method for microporosity (Lippens and de Boer, 1965) and the Dollimore-Heal method (Dollimore and Heal, 1964) or Broekhoff-de Boer theory for mesoporosity (Lecloux, 1981). 

BJH, Dollimore-Heal and BdB methods were compared for assessment of mesoporosity. Owing to the pore shape of the material used, the first two methods lead to an underestimation of pore size, and hence to an overestimation of total mesoporous surface. The last method is more general, and when the appropriate shape factor is used, a reliable estimation of the mesoporous texture is obtained. The S sdB estimator is almost a perfectly linear function of y, and vanishes in the X(IOO) sample. The external surface area, Xext, computed from the t-plot leads to an overestimation of the true mesoporous surface. 

The pore size distributions are calculated using the micropore (MP) method [26] and the Dollimore-Heal (DH) method [27] based on the adsorption isotherm data. Prior to calculating the micropore distribution by the MP method, it is necessary to convert the adsorption isotherms into plots [25], The amount adsorbed at... 

However, the overlapping below P/Pq = 0.4 were not perfectly as observed in ZSM-5. These N2 adsorption isotherms were analyzed with Dollimore-Heal (DH) method to determine the mesopore size distributions, which are shown in Fig.2. The micropore size distributions of the mesopore-added zeolites coincided with those of the reference zeolites. The mesopore size distributions are considerably uniform and their peaks are in the range of 10 to 12 nm. In particular, mesopore-added ZSM-5 gives the very sharp distribution. These mesopore-added zeolites are hopeful adsorbents and catalysts. 

To facilitate application of the method, Dollimore and Heal gave a standard table of the relevant parameters, based on regular intervals of P extending from 100 A down to 7 A (-values were calculated with Halsey s equation (p. 89). Table 3.2B retains the essential features of their original table, but P no longer extends below 17 A (cf. p. 160) and the /-values are now based on an experimentally determined standard isotherm.(p. 93). 

Calculation of pore size distribution (Method of Dollimore and Heal )... 

Many different mathematical procedures based on the Kelvin equation have been proposed for the calculation of the meso-PSD from nitrogen adsorption isotherms. The most popular method was proposed by Barrett et al. [49] (known as BJH method), but others like Cranston and Inkley [50], Dollimore and Heal [51], and Robert [52] methods are also currently used. 

Dollimore D and Heal GR. Improved method for calculation of pore size distribution from adsorption data. J. Appl. Chem. USSR, 1964 14(3) 109. 

Dollimore and Heal [65] applied method 2 to determine the thickness of the film on the outside of the particles. Ramakrishna and Rao [66] criticize this approach and prefer method 3. In a later discussion [67] they stated that their criticism was because equation (6.92) was being used outside its range of validity (i.e. at > 0.8) and in this region equation (6.89) must be used. Pierce [68], in the same discussion, suggested the use of equation (6.87). 

A large number of simple and sophisticated models have been presented to obtain a realistic estimation of PSD of porous adsorbents. Relatively simple but restricted apphcable methods such as Barret, Joyner, and Halenda (BJH), Dollimore and Heal (DH), Mikhail et al., (MP), Horvath and Kawazoe (HK), Jaroniec and Choma (JC), Wojsz and Rozwadowski (WR), Kruk-Jaroniec-Sayari (KJS), and Nguyen and Do (ND) were presented from 1951 to 1999 by various researchers for the prediction of PSD from the adsorption isotherms [133-139]. 

Dollimore and Heal [53] examined the effect upon the distribution, of changing the method for calculating r, on 36 desorption isotherms and preferred an equation of the same form as equation (3.25) with y = 0.355 nm. 

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