Of nitrogen isotherms

Calculation of pore size distribution (Roberts Method"). Worked example from desorption branch of nitrogen isotherm on... 

Specific surface areas of the materials under study were calculated using the BET method [22, 23]. Their pore size distributions were evaluated from adsorption branches of nitrogen isotherms using the BJH method [24] with the corrected form of the Kelvin equation for capillary condensation in cylindrical pores [25, 26]. In addition, adsorption energy distributions (AED) were evaluated from submonolayer parts of nitrogen adsorption isotherms using the algorithm reported in Ref. [27],... 

Figure 6. The pore size distributions of enlarged MCM-41 materials [2-3] calculated from adsorption (dotted lines) and desorption (solid lines) branches of nitrogen isotherms by the NLDFT method.

Figure 7. The pore size distribution of wide-pore material [4] (sample 4 in Table 1) calculated from adsorption and desorption branches of nitrogen isotherm by the NLDFT method.

As explained in Chapter 7, since the multilayer isotherm path is rather insensitive to differences in surface chemistry, for routine mesopore analysis it is possible to make use of a universal form of nitrogen isotherm. However, most activated carbons are highly microporous and the determination of the micropore size distribution remains a more difficult problem. Indeed, as discussed in Chapter 8, even the assessment of the total micropore volume presents conceptual difficulties. We should therefore regard the measurement of a nitrogen adsorption isotherm as only the first stage in the characterization of a microporous carbon. 

Table 10.15. Analysis of nitrogen isotherms on thermally decomposed Mg(OH)2.

Table 12.2. Evolution of the micropore structure of untreated carbon cloth (analysis of nitrogen isotherms of Carrott and Freeman, 1991).

L41 Lawrence, C. D. An Examination of Possible Errors in the Determination of Nitrogen Isotherms on Hydrated Cements (Techn. Rpt 520), 29 pp.. Cement and Concrete Association, Slough, UK (1978). 

Two epoxy-activated related supports, Sepabeads EC-EP3 and EC-EP5 (Figure 11.3), were assayed for the immobilization of A. aculeatus fructosyltransferase. By combination of nitrogen isotherms and mercury porosimetry analyses, the textural properties of both carriers were determined (Table 11.3). As shown, both samples... 

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. 

First, in the case of pores wider than 4 tun, the position of desorption branches of nitrogen isotherms for MCM-41 was found to be dependent not only on the pore size but also on the quality of samples, which was suggested to be caused by presence of constrictions in the porous structure [4]. In contrast, the position of adsorption branches of isotherms for MCM-41 was shown to be dependent essentially only on the pore diameter. 

Already with Jantti s 3PM a timesaving of the stepwise measurement of nitrogen isotherms up to 70 percent was possible 2PM is even faster. For both methods we show that the gain of the shortening of the measurement time is accompanied by a drawback, i.e. the increase of measurement inaccuracy, which is shown to be inversely proportional to the square of the measurement time. In case the molecular adsorption mechanism is not a given factor before the start of the measurement, the application of the time saving measurement will involve extra uncertainties. 

The introduction of a range of user-friendly equipment and software has accompanied the present widespread use of low-temperature nitrogen adsorption. Advances have been made in the development of both routine experimental procedures and on-line processing of the adsorption isotherm data. However, there is now a risk that an unskilled operator may gain the impression that with the aid of a manufacturer s user-friendly software it is relatively easy to evaluate the specific surface area and the pore size distribution of the material under examination. Furthermore, the ready access to sophisticated computational procedures may tend to obscure the limitations of the theoretical models on which they are based. The aims of this paper are to draw attention to these problems and to indicate how further progress can be made in the analysis of nitrogen isotherms on porous carbons. 

The adsorption properties were determined by the measurements of nitrogen isotherms at 77 K on a SATORius balance. 

Micropore volumes of samples under study were determined by the application of the i-method (Table 2). This method is based on the comparison of nitrogen isotherm on solid under investigation with normalized nitrogen isotherm on proper reference non-porous material (silica Davisil, Supelco, USA). The details of this method are given elsewhere [15]. The micropore volume of ZSM-5/3, ZSM-5/7 and ZSM-5/10 samples is smaller than that of the pure ZSM-5 it decreases from 0.163 cm /g for ZSM-5/3 to 0.126 cmVg for ZSM-5/10. This decrease can be attributed to the increasing surface area of mesopores. The Si04 tetrahedra on the mesopore surface do not contribute to the formation of zeolitic channel walls [16]. Thus, as the mesopore surface area increases the micropore volume decreases. 

The Kelvin equation relates the vapor pressure above a meniscus of a liquid to a diameter of a containing pore. This section discusses the use of nitrogen isotherms to descriptions of mesoporosity <20 nm diameter. 

Barrett EP, Joyner LG, Halenda PH. The determination of pore volume and area distributions in porous carbons. I. Computation of nitrogen isotherms. J Am Chem Soc 1951 73 373-380. 

A very important property of nitrogen isotherms measured at 77 K is that these isotherms very rarely have a pure monolayer domain (P g 0), and if this were so, the value of P g from the function l/ Pg) can be determined easily. 

Inspection of the overall shape of a nitrogen isotherm can provide a first useful indication of the nature of the adsorbent porosity and hence of the most appropriate procedure to be adopted for the analysis of the isotherm data. The hypothetical isotherms in Fig. 1 are representative of nitrogen isotherms obtained with a wide variety of adsorbents. The general features of these isotherms are consistent with Types I, II and IV, in the classification already proposed by the International Union of Pure and Applied Chemistry. ... 

The reversible Type Ila isotherm is the normal form of nitrogen isotherm given by a non-porous or macroporous adsorbent and is indicative of unrestricted monolayer-multilayer adsorption. The adsorption branch of a Type Ilb isotherm appears to have the same characteristic Type II shape as a normal monolayer-multilayer isotherm, but the multilayer section of the desorption branch is quite different -giving rise to a form of adsorption hysteresis. Isotherms of this type are generally given by aggregates of platy particles or solids containing slit-shaped mesopores. 

The function ) of the nitrogen isotherm proves that the isotherm does not have a monolayer domain (or a possible monolayer domain cannot be measured in the very low equilibrium relative pressure range). We have evaluated many nitrogen isotherms measured on very different solid adsorbents at 77.3 K. All these isotherms have fiinetions /(pj.) without any monolayer domain. In our opinion the value of />r e 0 of nitrogen isotherms measured at 77.3 K, i.e., the faet that these nitrogen isotherms do not have a monolayer domain (or these domains are limited to very low equilibrium pressure range) is the main reason for the practieal applicability of the BET(N2 ) equation to the calculation of specific surface area. 

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