Monolayer capacity

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... 

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. 

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. 

In Fig. 2.4, the location of the point of inflection thus calculated is plotted for different values of c. Clearly, the value of n/n at the point of inflection may deviate considerably from unity. At the one value of c = 9 the value of n/n is actually equal to unity and the point of inflection then coincides with the point corresponding to the monolayer capacity but for values of c... 

The ease of locating Point B depends on the shape of the knee of the isotherm.If the knee is sharp, corresponding to a high value of c. Point B can be located with accuracy even if the linear branch of the isotherm is short (see Fig. 2.10, curve (i)). When the knee is rounded, when c is small, Point B becomes difficult to locate, and the estimated value of rig may then differ widely from the BET monolayer capacity n . As will be seen shortly it is doubtful, indeed, how far isotherms in which Point B cannot be identified easily should be used for the estimation of monolayer capacity from either Point B or the BET plot. In practice, this reservation would include all isotherms having a value of c below 20. 

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. 

In practice, the monolayer capacity is of interest, not so much in itself, but as a means of calculating the specific surface with the relation quoted at the beginning of the Chapter, viz... 

When it is desired to evaluate the specific surfaces of a set of closely related samples of solid, however, only one of the samples needs to be calibrated against nitrogen (or argon), provided that all the isotherms of the alternative adsorptive can be shown to have indentical shape. A simple device for testing this identity, by use of the a,-plot, is described in Section 2.13 by means of the a,-plot it is also possible to proceed directly to calculation of the specific surface without having to assign a value to or to evaluate the BET monolayer capacity, of the alternative adsorptive. 

Evaluation of the monolayer capacity from a stepped isotherm raises... 

The f-curve and its associated t-plot were originally devised as a means of allowing for the thickness of the adsorbed layer on the walls of the pores when calculating pore size distribution from the (Type IV) isotherm (Chapter 3). For the purpose of testing for conformity to the standard isotherm, however, a knowledge of the numerical thickness is irrelevant since the object is merely to compare the shape of the isotherm under test with that of the standard isotherm, it is not necessary to involve the number of molecular layers n/fi or even the monolayer capacity itself. 

The BET method for calculation of specific surface A involves two steps evaluation of the monolayer capacity n from the isotherm, and conversion of n into A by means of the molecular area a . 

According to the classical Langmuir model, n is actually equal to the monolayer capacity, and can be converted into the specific surface A of the solid by the standard relation A = n a L (cf. Equation (2.1)). A number of lines of argument would suggest, however, that this interpretation is invalid, and that the value of A arrived at does not represent a true specific surface. 

T = temperature of outgassing of the nonane-charged sample, n. = monolayer capacity calculated from the BET plot. 

When the values of the BET monolayer capacity calculated from Type III isotherms are compared with independent estimates (e.g. from nitrogen adsorption) considerable discrepancies are frequently found. A number of typical examples are collected in Table 5.1. Comparison of the value of the monolayer capacity predicted by the BET equation with the corresponding value determined independently (columns (iv) and (v)) show that occasionally, as in line 6, the two agree reasonably well, but that in the majority... 

Comparison of monolayer capacity n (X) calculated with BET equation from the Type... 

One must conclude therefore that the BET procedure for evaluation of monolayer capacity is not applicable to a Type III (nor by implication, to a Type V) isotherm. 

Even so, it is of interest to calculate the BET monolayer capacity from the composite isotherm of Fig. 5.12(b). Though the isotherm did not conform very closely to the BET equation, the isosteric net heat of adsorption was... 

As will be seen shortly, an analogous result is obtained with the silica-water system, where the BET monolayer capacity of water calculated from the water isotherm is roughly equal to the hydroxyl content of the silica surface. 

The relationship between the BET monolayer capacity of physically adsorbed water and the hydroxyl content of the surface of silica has been examined by Naono and his co-workers in a systematic study, following the earlier work by Morimoto. Samples of the starting material—a silica gel—were heated for 4 hours in vacuum at a succession of temperatures ranging from 25 to 1000°C, and the surface concentration of hydroxyl groups of each sample was obtained from the further loss on ignition at 1100°C combined with the BET-nitrogen area. Two complete water isotherms were determined at 20°C on each sample, and to ensure complete... 

In Table 5.3, is compared with the total hydroxyl concentration (Ni, + N ) of the corresponding fully hydroxylated, sample. The results clearly demonstrate that the physical adsorption is determined by the total hydroxyl content of the surface, showing the adsorption to be localized. It is useful to note that the BET monolayer capacity n JH2O) (= N ) of the water calculated from the water isotherm by the BET procedure corresponds to approximately 1 molecule of water per hydroxyl group, and so provides a convenient means of estimating the hydroxyl concentration on the surface. Since the adsorption is localized, n.(H20) does not, of course, denote a close-packed layer of water molecules. Indeed, the area occupied per molecule of water is determined by the structure of the silica, and is uJH2O) 20A ... 

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