BET-isotherm

Figure 5. Pore size distribution of sol-gel glass (described in text) as determined by nitrogen adsorption isotherm (BET).

In designing an adsorption column, the characterization of adsorbents should be done prior to experiments. In particular, one should know not only the specific area but also the pore size distribution of the adsorbent in order to confirm that it would be proper for a given purpose. Nitrogen adsorption and desorption isotherms, BET surface areas, and BJH (Barrett, Joyner and Halenda) pore size distributions of the synthesized sorbents... 

Mesoporous silica, FSM-16, was prepared in the same way as the previous study [11]. The structure was confirmed by XRD pattern and N2 adsorption isotherm. BET surface area was 1025 m g. ... 

Multilayer adsorption and other complications are accounted for in the more elaborate Brunauer-Emmett-Teller isotherm (BET isotherm) [28], which involves the heats of adsorption of the first and subsequent layers and with which not only Type I behavior can be approximated. In its simplest form, for an unlimited number of adsorption layers and partial pressures well below saturation, the BET equation can be written... 

Brunauer-Emmett-Teller Isotherm (BET Isotherm) An adsorption isotherm equation that accounts for the possibility of multilayer adsorption and different enthalpy of adsorption between the first and subsequent layers. Five types of adsorption isotherm are usually distinguished. These are denoted by roman numerals and refer to different characteristic shapes. See Adsorption Isotherm. 

Figure 7.12. The BET-adsorption isotherm (BET AI), Eq. (7.70) showing for C>2 an inflection point and at the sorptive gas saturation pressure p = Ps(T) a singularity n — 00 indicating pore condensation and the appearance of a bulk liquid phase [7.1-7.5],...

Because of their prevalence in physical adsorption studies on high-energy, powdered solids, type II isotherms are of considerable practical importance. Bmnauer, Emmett, and Teller (BET) [39] showed how to extent Langmuir s approach to multilayer adsorption, and their equation has come to be known as the BET equation. The derivation that follows is the traditional one, based on a detailed balancing of forward and reverse rates. 

The BET equation filled an annoying gap in the interpretation of adsorption isotherms, and at the time of its appearance in 1938 it was also hailed as a general method for obtaining surface areas from adsorption data. The equation can be put in the form... 

The very considerable success of the BET equation stimulated various investigators to consider modifications of it that would correct certain approximations and give a better fit to type II isotherms. Thus if it is assumed that multilayer formation is limited to n layers, perhaps because of the opposing walls of a capillary being involved, one... 

Equation XVII-78 turns out to ht type II adsorption isotherms quite well—generally better than does the BET equation. Furthermore, the exact form of the potential function is not very critical if an inverse square dependence is used, the ht tends to be about as good as with the inverse-cube law, and the equation now resembles that for a condensed him in Table XVII-2. Here again, quite similar equations have resulted from deductions based on rather different models. 

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 ... 

The multilayer isotherms illustrated thus far have all been of a continuous appearance—it was such isotherms that the BET, FHH, and other equations treated. About 30 years ago, however, multilayer adsorption on smooth sur-... 

Adsorption isotherms in the micropore region may start off looking like one of the high BET c-value curves of Fig. XVII-10, but will then level off much like a Langmuir isotherm (Fig. XVII-3) as the pores fill and the surface area available for further adsorption greatly diminishes. The BET-type equation for adsorption limited to n layers (Eq. XVII-65) will sometimes fit this type of behavior. Currently, however, more use is made of the Dubinin-Raduschkevich or DR equation. Tliis is Eq. XVII-75, but now put in the form... 

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. 

When c is less than 2 but still positive, the BET equation results in a curve having the general shape of a Type III isotherm (cf. Fig. 2.1, Curve A and Fig. 2.3). 

As is seen from Fig. 2.L, the BET equation yields an isotherm which (so long as c exceeds 2) has a point of inflection this point is close to, but not necessarily coincident with, the point where the amount adsorbed is equal to the BET monolayer capacity. 

Fig. 2.4 The BET equation. Plot ofX, calculated for different values of c, against Y,. X, is the value of n/ii at the point of inflection in the isotherm F, is the relative pressure at the point of inflection. Each point on the curve is marked with the corresponding value of c in brackets.

Fig. 2.6 Adsorption of gases on silver foil. (a) BET plots h) adsorption isotherms. (Solid symbols are desorption points.) (Courtesy Davis, Dc Witt...

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 ... 

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