Brunauer

Brunauer and co-workers [129, 130] found values of of 1310, 1180, and 386 ergs/cm for CaO, Ca(OH)2 and tobermorite (a calcium silicate hydrate). Jura and Garland [131] reported a value of 1040 ergs/cm for magnesium oxide. Patterson and coworkers [132] used fractionated sodium chloride particles prepared by a volatilization method to find that the surface contribution to the low-temperature heat capacity varied approximately in proportion to the area determined by gas adsorption. Questions of equilibrium arise in these and adsorption studies on finely divided surfaces as discussed in Section X-3. 

Adsorption isotherms are by no means all of the Langmuir type as to shape, and Brunauer [34] considered that there are five principal forms, as illustrated in Fig. XVII-7. TVpe I is the Langmuir type, roughly characterized by a monotonic approach to a limiting adsorption at presumably corresponds to a complete monolayer. Type II is very common in the case of physical adsorption... 

Fig. XVII-7. Brunauer s five types of adsorption isotherms. (From Ref. 34.)...

A still different approach to multilayer adsorption considers that there is a potential field at the surface of a solid into which adsorbate molecules fall. The adsorbed layer thus resembles the atmosphere of a planet—it is most compressed at the surface of the solid and decreases in density outward. The general idea is quite old, but was first formalized by Polanyi in about 1914—see Brunauer [34]. As illustrated in Fig. XVII-12, one can draw surfaces of equipo-tential that appear as lines in a cross-sectional view of the surface region. The space between each set of equipotential surfaces corresponds to a definite volume, and there will thus be a relationship between potential U and volume 0. 

Brunauer (see Refs. 136-138) defended these defects as deliberate approximations needed to obtain a practical two-constant equation. The assumption of a constant heat of adsorption in the first layer represents a balance between the effects of surface heterogeneity and of lateral interaction, and the assumption of a constant instead of a decreasing heat of adsorption for the succeeding layers balances the overestimate of the entropy of adsorption. These comments do help to explain why the model works as well as it does. However, since these approximations are inherent in the treatment, one can see why the BET model does not lend itself readily to any detailed insight into the real physical nature of multilayers. In summary, the BET equation will undoubtedly maintain its usefulness in surface area determinations, and it does provide some physical information about the nature of the adsorbed film, but only at the level of approximation inherent in the model. Mainly, the c value provides an estimate of the first layer heat of adsorption, averaged over the region of fit. 

Brunauer and co-workers [211, 212] proposed a modelless method for obtaining pore size distributions no specific capillary shape is assumed. Use is made of the general thermodynamic relationship due to Kiselev [213]... 

S. Brunauer, The Adsorption of Gases and Vapors, Vol. 1, Princeton University Press, Princeton, NJ, 1945. 

S. Brunauer, in Surface Area Determination, Proc. Int. Symp., Bristol, 1969, But-terworths, Lxjndon. 

Emmett P H and Brunauer S 1937 The use of low temperature van der Waals adsorption isotherms in determining the surface area of iron synthetic ammonia catalysts J. Am. Chem. See. 59 1553-64... 

Fig. I.l The five types of adsorption isotherm, I to V, in the classification of Brunauer, Deming, Deming and Teller (BDDT), together with Type VI, the stepped isotherm.

To obtain the monolayer capacity from the isotherm, it is necessary to interpret the (Type II) isotherm in quantitative terms. A number of theories have been advanced for this purpose from time to time, none with complete success. The best known of them, and perhaps the most useful in relation to surface area determination, is that of Brunauer, Emmett and Teller. Though based on a model which is admittedly over-simplified and open to criticism on a number of grounds, the theory leads to an expression—the BET equation —which, when applied with discrimination, has proved remarkably successful in evaluating the specific surface from a Type II isotherm. 

Langmuir referred to the possibility that the evaporation-condensation mechanism could also apply to second and higher molecular layers, but the equation he derived for the isotherm was complex and has been little used. By adopting the Langmuir mechanism but introducing a number of simplifying assumptions Brunauer, Emmett and Teller in 1938 were able to arrive at their well known equation for multilayer adsorption, which has enjoyed widespread use ever since. 

Now in principle each layer will have its own values of a, q, and v, and consequently the summation of Equation (2.11) cannot be carried out unless simplifying assumptions are made. Brunauer, Emmett and Teller made three such assumptions (a) that in all layers except the first the heat of adsorption is equal to the molar heat of condensation q, (b) that in all layers except the first the evaporation-condensation conditions are identical, i.e. that... 

From the earliest days, the BET model has been subject to a number of criticisms. The model assumes all the adsorption sites on the surface to be energetically identical, but as was indicated in Section 1.5 (p. 18) homogeneous surfaces of this kind are the exception and energetically heterogeneous surfaces are the rule. Experimental evidence—e.g. in curves of the heat of adsorption as a function of the amount adsorbed (cf. Fig. 2.14)—demonstrates that the degree of heterogeneity can be very considerable. Indeed, Brunauer, Emmett and Teller adduced this nonuniformity as the reason for the failure of their equation to reproduce experimental data in the low-pressure region. 

Plot of pMp° - p) against p/p° (r is expressed in cm (stp)). (1) Unpromoted Fe catalyst (2) AljOj-promoted Fe catalyst (3) AI2O3-KjO-promoted Fe catalyst (4) fused copper catalyst (5) chromium oxide gel (6) silica gel. (Courtesy Brunauer, Emmett and Teller.)... 

A number of attempts have been made to modify the BET equation so as to obtain better agreement with the experimental isotherm data in the multilayer region. One of the most recent is that of Brunauer and his co-workers ... 

In their pioneer work, Brunauer and Emmett adopted the value a (Ar) = 13-8 for the molecular area of argon, by insertion of the liquid density Pi in the standard equation (2.27). The same figure was recommended by McClellan and Harnsberger " as a result of their comprehensive survey of the literature, already referred to. These workers noted that the recorded values of a (based on a (N2) = 16 2 A ) extended over the wide range 10-19 A, and concluded that the area occupied per molecule of argon in the completed monolayer varied from one adsorbent to another. 

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