Boers Standard-Plots

Sing (see Ref. 207 and earlier papers) developed a modification of the de Boer r-plot idea. The latter rests on the observation of a characteristic isotherm (Section XVII-9), that is, on the conclusion that the adsorption isotherm is independent of the adsorbent in the multilayer region. Sing recognized that there were differences for different adsorbents, and used an appropriate standard isotherm for each system, the standard isotherm being for a nonporous adsorbent of composition similar to that of the porous one being studied. He then defined a quantity = n/nx)s where nx is the amount adsorbed by the nonporous reference material at the selected P/P. The values are used to correct pore radii for multilayer adsorption in much the same manner as with de Boer. Lecloux and Pirard [208] have discussed further the use of standard isotherms. 

An important modification of the de Boer f-plot has been proposed by Sing and his co-workers [20], who introduced the concept of "standard isotherm" for each adsorbent system. The standard isotherm is defined for a non-porous adsorbent with a similar composition to that of the porous one being investigated. He further introduced a quantity, Ug = n/riy) where nx is the amount adsorbed on the non-porous reference material, to be used for the correction of pore radii for multilayer adsorption. 

The characteristic isotherm concept was elaborated by de Boer and coworkers [90]. By accepting a reference from a BET fit to a standard system and assuming a density for the adsorbed film, one may convert n/rim to film thickness t. The characteristic isotherm for a given adsorbate may then be plotted as t versus P/P. For any new system, one reads t from the standard r-curve and n from the new isotherm, for various P/P values. De Boer and co-work-ers t values are given in Table XVII-4. A plot of t versus n should be linear if the experimental isotherm has the same shape as the reference characteristic isotherm, and the slope gives E ... 

Fig. 2.26 Comparison of a number of standard isotherms of nitrogen at 77 K, plotted as n/n against pip . O, Shnll x, Pierce , de Boer el , Cranston and Inkley. ...

A convenient method is provided by the t-plot of Lippens and De Boer.37 It consists of plotting the volume of gas adsorbed vs t, the statistical thickness of the adsorbed film, t is a function of p/p0, as measured in the standard isotherm, according to the Halsey equation or one of its modifications.38,39,40,41... 

This is the equation used by Lippens and de Boer (1963) to plot a /-curve, i.e. the -standard multilayer thickness versus pfp°, for nitrogen adsorption at 77 K. 

The way in which Lippens and de Boer (1965) made use of the universal /-curve is simple. The experimental isotherm is transformed into a /-plot in the following manner the amount adsorbed, n, is replotted against /, the standard multilayer thickness on the reference non-porous material at the corresponding p/p°. Any difference in shape between the experimental isotherm and the standard /-curve is thus revealed as a non-linear region of the /-plot and/or a finite (positive or negative) intercept of the extrapolated /-plot (i.e. at / = 0). By this method a specific surface area, denoted a(t), can be calculated from the slope, s, = nft, of a linear section. From Equations (6.10), (6.11) and (6.15) we then get ... 

The nitrogen isotherm was replotted by Cases et al. (1992) in the usual BET coordinates and as a t plot. The derived BET area of 43.3 m2 g"1 appeared to be not far removed from the value of 45.9 m2 g 1 obtained from the amount adsorbed at Point B. The r-plot was constructed in the manner originally proposed by de Boer et al. (1966), which involved adopting a standard isotherm with the same value of C, which in this case was 485. It was not easy to interpret the /-plot, although three short linear sections were identified. From the initial slope, the total surface area appeared to be c. 50 m2 g-1. Back-extrapolation of a linear region at higher p/p° gave an apparent micropore volume of c. 0.01 cm3 g 1. 

Figure 1.27 anticipates the discussion of porous materials (see sec. 1.6b and fig. 1.32). One procedure for assessing amounts adsorbed in pores is by comparison with a standard curve on a non-porous sample having otherwise identical surface properties. Two variants exist, the t-plot of De Boer et al. and the a-plot... 

The /-plot for nonporous but very finely divided voluminous silica shows deviation from the standard /-curve. This is believed by De Boer et al. to be due to adsorption at points of contact of the very small particles. They developed an adsorption equation taking into account the packing geometry of the particles. 

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). 

Lippens and de Boer devised a simple and convenient way of comparing the shape of one isotherm with that of another. However, their t-method suffers from the disadvantage that it is dependent on the use of the BET method to obtain the standard multilayer thickness (t-curve). An improvement was developed in the form of the -method, which provides a more rigorous approach and allows a more refined analysis of the isotherm shape. The amount of gas adsorbed is plotted against, the reduced... 

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