BET -type

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... 

Kuge and Yoshikawa (3) related a change in the gas chromatographic peak shape to the beginning of multilayer adsorption on the surface of the solid. For small adsorbate volumes, the peak shape is symmetrical. As the adsorbate volume is increased, a sharp front, diffuse tail, and a defect at the front of the peak top is observed (Figure 11.2). It then acquires a diffuse front and sharp tail. This point corresponds to the B point of the BET Type II adsorption isotherm at which the relative surface area may be calculated. 

Adsorption isotherms at 77 K were simulated for each model material. These data are shown in Figure 2. These isotherms all show standard Type IV behavior characteristic of mesoporous materials. They are described well by BET-type models at low pressures, with capillary rises at high pressures and pore filling at pre.ssures near saturation. The (a) and (b) models have considerably higher maximum adsorption than the (c) and (d) models due to their higher porosity. The (a) and (c) models both have capillary upswings at relative pressures around 0.6, while the (b) and (d) models, which have larger pores, show sharper capillary rises between relative pressures of 0.7 and 0.8. 

The pore pressure is directly responsible for the molecular layering and the pore filling. Having described the pore pressure, we now address the molecular layering process. This process can be described by any appropriate equation. If there is no or weak fluid—fluid interaction, we can use the BET-type equation, while if the fluid-fluid interaction is strong we can use the modified Hill-de Boer equation as suggested by Do and Do [63] to calculate the adsorbed film thickness t. In these equations the affinity constant is a function of pore size and the pressure involved in those equations is the pore pressure. 

The adsorption isotherms for hydrocarbons on wet cellulose approach BET type III (1 0 in form as the relative humidity is increased (9.), and the isosteric heats approach the heat of condensation for all surface coverages of hydrocarbon (11 ). Thus, water lowers the affinity of cellulose for hydrocarbons. This effect is independent of any changes in surface area with relative humidity, and is also observed on regenerated cellulose film (12 ). However, the thermodynamic data indicate that the surface does not behave as expected for pure water, even at very high water contents (ll). In fact, the GC method has also been used to study adsorption of hydrocarbons on liquid water (15, l6). In this case, the interactions are very weak and the adsorption isotherm does not fit the BET theory, so that surface areas cannot be estimated directly (16). 

We have addressed the classical BET equation as well as some of its modified versions. Although these modified equations were claimed to add to the original equation some refmed features, the classical BET equation is still the one that is used by many workers as the primary tool to study surface area. Before closing this section on BET typed equations, it is worthwhile to point out another equation developed by Aranovich, who proposed a form very similar to that of the BET equation. The difference is in the exponent of the term (1 - P/Pq) in the denominator of the two equations. In the BET case, the exponent is one while in the Aranovich case the exponent is one half. 

FIGURE 8.6. Jf- K diagram (a) and corresponding breaklhrou curve b) for adsorption With a favorable-unfavorable (BET) type of isotherm. The broken curve is the hypothetical curve calculated according to equilibrium theory from Eq, (8.11 ). The acbal profile (continuous liiic) consists of a shock front combined with a proporlionate-iiatlem front. The intersection bf these two fronts is at c. ... 

Figure 3.3.42 Typical shapes of adsorption isotherms pA- partial pressure of adsorbate A, p - vapor pressure of liquid A, 0a = coverage relative to monolayer capacity type I Langmuir adsorption, for example, benzene on silica gel, NH3 on charcoal, or H2S on molecular sieve (Figure 3.3.40) type II multilayer BET type of adsorption, for example, water on AI2O3, N2 on silica type III multilayer adsorption, for example, bromine on silica, type IV and V multilayer adsorption and capillary condensation in pores, for example, water on silica or benzene on Fe203 (IV) and water on charcoal (V).

The shape of the front may be related to the adsorption process. For example, Kuge and Yoshikawa (9) relate peak shape to the beginning of multilayer adsorption (Figure 12.2). At injections of very low volume, the peak is symmetric however, injections of larger volumes produces a peak with a sharp front, a diffuse tail, and a defect at the front of the top of the peak. For extremely large injections, the peak has a rather diffuse front and a sharp tail. By using repeated injections, those authors were able to determine the injection volume for which the transition from one behavior to another occurs. This corresponds to point B on a BET type II isotherm, from which the authors were able to calculate the specific surface area. A complete analysis of the front can enable one to determine the adsorption isotherms, and hence specific surface area (10). The description by Kiselev and Yashin (11) is particularly elegant, and we briefly recapitulate it here. 

Braunauer et al. classified the adsorption isotherms typically into five types (Brunauer, 1938 Adamson, 1990), which are shown in Figure 10-1. Type I is the Langmuir type adsorption and corresponds to a monolayer formation. This isotherm shape, with very high adsorption at low relative pressures, is typically observed for microporous solids (pore diameter <2 nm) having relatively small extmial sinfaces (Meixner, 1999). Type II is very common in the case of physical adsorption on non-porous materials, with relatively strong interaction between adsorbent and adsorbate and corresponds to multilayer formation. This type of adsorption isotherm was theoretically developed by Brunauer, Emmett, Telllo, and called the BET type (Brunauer, 1938). Type IB correspond s to the adsorption with rather small interaction between adsorbent and adsorbate and multi-layer formation, but is rarely observed. Types IV and V are observed in the adsorption on porous materials, where capillary condensation phenomena lead to an increase in the adsorbed amount in the... 

The overall isotherms for the loeal BET-type adsorption are represented by Eq. (25). These isotherms may be obtained trom equations generated by Langmuir local behavior [Eq. (15) or (16)] in the following way In the monolayer isotherms Xi ), one replaces the pressure p by the functions H h), and the parameters K andby C = K p and p = Pa/Ps> respectively, and then multiplies the redefined isotherm by the function giQi) [5]. 

The nitrogen adsorption isotherms of the two samples following the VHT are characterized by a multilayer adsorption (BET-type II). Detailed analysis of the low-pressure range of the isotherms (e.g. see Fig. 3a and b) reveals a characteristic shape. In addition to the normal type II behaviour the isotherms show a relative rapid increase in the amoimt of adsorbed gas for a small increase in p/po at approx, p/po 0.14 (marked by arrow in Fig. 3b). This indicates the presence of two types of surface sites. 

Adsorption isotherms. Isothermal microcalorimetry, in conjunction with an RH perfusion device, is a powerful method for mapping surface properties of solids and especially drugs [32]. The principle of the study is to adsorb and desorb water vapour onto and off the surface of a solid in small steps and measure the associated enthalpy change. At low RH values, monolayer water sorption conforms to a BET (Brunauer, Emmett and Teller) model and can therefore be used to determine surface properties. The analysis of the data can be achieved by plotting the water sorption isotherm as a function of RH and fitting to a modified BET type equation [33]. This can provide information about the surface affinity for water and the hydrophilic surface area, parameters... 

Sorption and diffusion of water vapour in polymers have been studied mainly for development of water vapour barriers. Some of these studies date back to 1944 [41]. Many attempts have been made in order to describe the sorption behavior of water vapor onto solid surfaces of the membrane and its pores. As described by Vieth [41], a deviation from Henry s law was observed in 1944, in the sorption of water by hydrated cellulose membranes. It was postulated that two competing phenomena are responsible for this observation dissolution, which obeys Henry s law, and adsorption, which follows the Langmuir isotherm. With other polymer systems the ability of water molecules and/or polar groups in the polymer matrix to interact with each other has given rise to sorption isotherms which may follow Henry s law, Flory-Huggins or BET types [41]. 

An excellent example of work of this type is given by the investigations of Benson and co-workers [127, 128]. They found, for example, a value of = 276 ergs/cm for sodium chloride. Accurate calorimetry is required since there is only a few calories per mole difference between the heats of solution of coarse and finely divided material. The surface area of the latter may be determined by means of the BET gas adsorption method (see Section XVII-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 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. 

As with the BET equation, a number of modihcations of Eqs. XVII-77 or XVn-79 have been proposed, for example Ref. 71. FHH-type equations go to inhnite him thickness (i.e., bulk liquid), as P - F and this cannot be the case if the liquid does not wet the solid, and Adamson [72] proposed... 

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). 

The Type II isotherms obtained experimentally often display a rather long straight portion (BC in Fig. 2.9), a feature not strictly compatible with the properties of the BET equation which, as we have seen, yields a point of... 

The kind of results adduced in the present section justify the conclusion that the quantity n calculated by means of the BET equation from the Type II isotherm corresponds reasonably well to the actual monolayer capacity of the solid. The agreement lies within, say, +20 per cent, or often better, provided the isotherm has a well defined Point B. 

As will be demonstrated in Chapter 4, an isotherm which is reversible and of Type II is quite compatible with the presence of micropores. If such pores are present, the isotherm will be distorted in the low-pressure region, the value of c will be greatly enhanced, and the specific surface derived by the BET procedure will be erroneously high. In particular, a BET specific surface in excess of - 500m g" should be taken as a warning that... 

It follows therefore that the specific surface of a mesoporous solid can be determined by the BET method (or from Point B) in just the same way as that of a non-porous solid. It is interesting, though not really surprising, that monolayer formation occurs by the same mechanism whether the surface is wholly external (Type II isotherm) or is largely located on the walls of mesopores (Type IV isotherm). Since the adsorption field falls off fairly rapidly with distance from the surface, the building up of the monolayer should not be affected by the presence of a neighbouring surface which, as in a mesopore, is situated at a distance large compared with the size of a molecule. 

Striking confirmation of the conclusion that the BET area derived from a Type IV isotherm is indeed equal to the specific surface is afforded by a recent study of a mesoporous silica, Gasil I, undertaken by Havard and Wilson. This material, having been extensively characterized, had already been adopted as a standard adsorbent for surface area determination (cf. Section 2.12). The nitrogen isotherm was of Type IV with a well defined hysteresis loop, which closed at a point below saturation (cf. F, in Fig. 3.1). The BET area calculated from it was 290 5 0 9 m g , in excellent agreement with the value 291 m g obtained from the slope of the initial region of the plot (based on silica TK800 as reference cf. p. 93). 

More often, however, microporosity is associated with an appreciable external surface, or with mesoporosity, or with both. The effect of microporosity on the isotherm will be seen from Fig. 4.11(a) and Fig. 4.12(a). In Fig. 4.11(a) curve (i) refers to a powder made up of nonporous particles and curve (ii) to a solid which is wholly microporous. However, if the particles of the powder are microporous (the total micropore volume being given by the plateau of curve (ii)), the isotherm will assume the form of curve (iii), obtained by summing curves (i) and (ii). Like isotherm (i), the composite isotherm is of Type II, but because of the contribution from the Type 1 isotherm, it has a steep initial portion the relative enhancement of adsorption in the low-pressure region will be reflected in a significantly increased value of the BET c-constant and a shortened linear branch of the BET plot. 

---