Surface area adsorption isotherms

The phenomenon of adsorption was introduced in sec. 1.1.2. There one can find definitions of elementary notions, including those of adsorbent, adsorbate, adsorptive, desorption, specific surface area, adsorption isotherm (equation) and two-dimensional equation of state. Adsorbed amounts can eonveniently be expressed as moles adsorbed (n ), moles adsorbed per unit area or surface concentration (F = n /A) or, if the adsorption in a monolayer r(max) is known, as... 

All equipment designed to measure surface area, adsorption-desorption isotherms or pore volume by adsorption actually determines the quantity of gas condensed on a solid surface at some equilibrium vapor pressure. The surface area or pore volumes and pore sizes are then calculated by means of an appropriate theory used to treat the adsorption and/or desorption data. Depending on the apparatus employed, the adsorbed quantity is measured as volume or weight. The accuracy of an adsorption apparatus is, therefore, dependent upon its ability to correctly measure either of these quantities. 

Determination of Surface Areas (10). At temperatures well below Tg, retention of probe molecules is primarily through adsorption at the polymer surface. The adsorption isotherm can be determined by the elution technique, where the probe is injected onto the colunn, and the shape of the isotherm is found from a single, asjometrical peak (10). Using this method, it can be shown that for each gas-phase concentration c of a solute (mol/m3) there is a corresponding retention volume V(c), m3, according to... 

In surface chemistry, adsorption isotherms describe the equiUhrium situation. However, just as in the consideration of the gas-phase chemistry in the interstellar medium, it is the kinetics of surface processes which are more relevant. Two mechanisms for surface-catalysed reactions can be distinguished and are illustrated by the cartoons in Fig. 1.6. In the Eley-Rideal mechanism, it is assumed that reaction occurs when a species (say, A) from the gas-phase impacts on a species (say, B) that is adsorbed on the surface. At significant surface coverage, the rate of reaction will be proportional to the product of the fraction of the surface covered in B (6b) and the pressure (p ) of the species A, which will be proportional to the rate of collisions of A with unit area of the solid surface. An alternative picture is encapsulated in the Langmuir-Hinshelwood mechanism. Here it is assumed that reaction occurs in encounters between species both of which are adsorbed on the surface. Then the rate of reaction will be proportional to the product of the fractions of the surface covered by A and by B that is proportional to 0a b-... 

There are complexities. The wetting of carbon blacks is very dependent on the degree of surface oxidation Healey et al. [19] found that q mm in water varied with the fraction of hydrophilic sites as determined by water adsorption isotherms. In the case of oxides such as Ti02 and Si02, can vary considerably with pretreatment and with the specific surface area [17, 20, 21]. Morimoto and co-workers report a considerable variation in q mm of ZnO with the degree of heat treatment (see Ref. 22). 

Fig. X-1. Adsorption isotherms for n-octane, n-propanol, and n-butanol on a powdered quartz of specific surface area 0.033 m /g at 30°C. (From Ref. 23.)...

For adsorption on Spheron 6 from benzene-cyclohexane solutions, the plot of N N2/noAN2 versus N2 (cyclohexane being component 2) has a slope of 2.3 and an intercept of 0.4. (a) Calculate K. (b) Taking the area per molecule to be 40 A, calculate the specific surface area of the spheron 6. (c) Plot the isotherm of composition change. Note Assume that is in millimoles per gram. 

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... 

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... 

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... 

An interesting example of a large specific surface which is wholly external in nature is provided by a dispersed aerosol composed of fine particles free of cracks and fissures. As soon as the aerosol settles out, of course, its particles come into contact with one another and form aggregates but if the particles are spherical, more particularly if the material is hard, the particle-to-particle contacts will be very small in area the interparticulate junctions will then be so weak that many of them will become broken apart during mechanical handling, or be prized open by the film of adsorbate during an adsorption experiment. In favourable cases the flocculated specimen may have so open a structure that it behaves, as far as its adsorptive properties are concerned, as a completely non-porous material. Solids of this kind are of importance because of their relevance to standard adsorption isotherms (cf. Section 2.12) which play a fundamental role in procedures for the evaluation of specific surface area and pore size distribution by adsorption methods. 

A Type II isotherm indicates that the solid is non-porous, whilst the Type IV isotherm is characteristic of a mesoporous solid. From both types of isotherm it is possible, provided certain complications are absent, to calculate the specific surface of the solid, as is explained in Chapter 2. Indeed, the method most widely used at the present time for the determination of the surface area of finely divided solids is based on the adsorption of nitrogen at its boiling point. From the Type IV isotherm the pore size distribution may also be evaluated, using procedures outlined in Chapter 3. 

The physical adsorption of gases by non-porous solids, in the vast majority of cases, gives rise to a Type II isotherm. From the Type II isotherm of a given gas on a particular solid it is possible in principle to derive a value of the monolayer capacity of the solid, which in turn can be used to calculate the specific surface of the solid. The monolayer capacity is defined as the amount of adsorbate which can be accommodated in a completely filled, single molecular layer—a monolayer—on the surface of unit mass (1 g) of the solid. It is related to the specific surface area A, the surface area of 1 g of the solid, by the simple equation... 

Following the pioneer work of Beebe in 1945, the adsorption of krypton at 77 K has come into widespread use for the determination of relatively small surface areas because its saturation vapour pressure is rather low (p° 2Torr). Consequently the dead space correction for unadsorbed gas is small enough to permit the measurement of quite small adsorption with reasonable precision. Estimates of specific surface as low as 10 cm g" have been reported. Unfortunately, however, there are some complications in the interpretation of the adsorption isotherm. 

As explained in Section 2.13, the use of iz,-plots makes it possible to avoid the involvement of either n or when an alternative adsorptive is being used for evaluating the surface areas of a set of related solids. It is then no longer necessary to exclude the use of isotherms having a low value of c, consequently the method is applicable even if the isotherm of the alternative adsorptive is of Type III (cf. Chapter 5). Calibration of one sample by nitrogen or argon adsorption is still required. 

Fig. 3.Z3 Adsorption isotherm of n-butane at 273 K on a sample of artificial graphite ball-milled for 192 b. The shoulder F appeared at a relative pressure which was the same for all six samples in the first milling run, all six in the second milling run, and also for two of the milled samples which had been compacted. The milling time varied between 0 and 1024 h, and the BET-nilrogen areas of the surfaces between 9 and 610 m g ...

The evaluation of pore size distribution by application of the Kelvin equation to Type IV isotherms has hitherto been almost entirely restricted to nitrogen as adsorptive. This is largely a reflection of the widespread use of nitrogen for surface area determination, which has meant that both the pore size distribution and the specific surface can be derived from the same isotherm. 

Fig. 5.12 (a) Water adsorption isotherms at 20°C on Graphon activated to 24-9 % burn-off, where its active surface was covered to varying extents by oxygen complex. (b) The results of (a) plotted as amount adsorbed per of active surface area (left-hand scale) and also as number of molecules of water per atom of chemisorbed oxygen (right-hand scale). (After Walker.)... 

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