Type IV Isotherm

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. 

Type IV isotherm but the argument as to surface area is still valid (cf. Chapter 3). 

If the adsorbent contains mesopores, capillary condensation will occur in each pore when the relative pressure reaches a value which is related to the radius of the pore by the Kelvin equation, and a Type IV isotherm will... 

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. 

A characteristic feature of a Type IV isotherm is its hysteresis loop. The exact shape of the loop varies from one adsorption system to another, but, as indicated in Fig. 3.1, the amount adsorbed is always greater at any given relative pressure along the desorption branch FJD than along the adsorption branch DEF. The loop is reproducible provided that the desorption run is started from a point beyond F which marks the upper limit of the loop. 

Type IV isotherms are often found with inorganic oxide xerogels and other porous solids. With certain qualifications, which will be discussed in this chapter, it is possible to analyse Type IV isotherms (notably those of nitrogen at 77 K) so as to obtain a reasonable estimate of the specific surface and an approximate assessment of the pore size distribution. 

Fig. 3.1 A Type IV isotherm. The corresponding Type II isotherm follows the course ABCN (cf. dashed line).

This widespread conformity to the Gurvitsch rule constitutes powerful support for the capillary condensation hypothesis in relation to Type IV isotherms. It is perhaps hardly necessary to stress that in order to test data for conformity to the rule it is essential that the stage which corresponds to the complete filling of the pores shall be clearly identifiable—as in the... 

A number of attempts have been made to demonstrate the connection between mesoporosity and the Type IV isotherm by comparing the isotherm of a vapour on a nonporous powder before and after it has been formed into a compact. The process of compaction produces pores in the form of interstices between the particles of the original powder such pores will tend to have dimensions of the same order as those of the constituent particles, and it can be arranged that these shall fall within the mesopore range of size. 

Examples are provided by the work of Carman and Raal with CF2CI2 on silica powder, of Zwietering" with nitrogen on silica spherules and of Kiselev" with hexane on carbon black and more recently of Gregg and Langford with nitrogen on alumina spherules compacted at a series of pressures. In all cases, a well defined Type II isotherm obtained with the loose powder became an equally well defined Type IV isotherm with the compact moreover both branches of the hysteresis loop were situated (drove the isotherm for the uncompacted powder, but the pre-hysteresis region was scarcely affected (cf. Fig. 3.4). The results of all these and similar... 

Closer examination reveals that the swing upwards in the Type IV isotherm not infrequently commences before the loop inception, showing that enhanced adsorption, not accompanied by hysteresis, can occur. The implications of this important fact are explored in Section 3.7. 

In calculations of pore size from the Type IV isotherm by use of the Kelvin equation, the region of the isotherm involved is the hysteresis loop, since it is here that capillary condensation is occurring. Consequently there are two values of relative pressure for a given uptake, and the question presents itself as to what is the significance of each of the two values of r which would result from insertion of the two different values of relative pressure into Equation (3.20). Any answer to this question calls for a discussion of the origin of hysteresis, and this must be based on actual models of pore shape, since a purely thermodynamic approach cannot account for two positions of apparent equilibrium. 

These models, though necessarily idealized, are sufficiently close to the actual systems found in practice to enable useful conclusions to be drawn from a given Type IV isotherm as to the pore structure of a solid adsorbent. To facilitate the discussion, it is convenient to simplify the Kelvin equation by putting yVJRT = K, and on occasion to use the exponential form ... 

It was noted earlier (p. 115) that the upward swing in the Type IV isotherm characteristic of capillary condensation not infrequently commences in the region prior to the lower closure point of the hysteresis loop. This feature can be detected by means of an a,-plot or a comparison plot (p. 100). Thus Fig. 3.25(a) shows the nitrogen isotherm and Fig. 3.25(h) the a,-plot for a particular silica gel the isotherm is clearly of Type IV and the closure point is situated around 0 4p° the a,-plot shows an upward swing commencing at a = 0-73, corresponding to relative pressures of 013 and therefore well below the closure point. 

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. 

Evaluation of specific surface from the Type IV isotherm... 

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). 

Equation (3.73) is the basis of the method proposed by Kiselev for the evaluation of surface area from the Type IV isotherm. If perfect gas behaviour is assumed it becomes... 

Fig. 3.28 The Kiselev method for calculation of specific surface from the Type IV isotherm of a compact of alumina powder prepared at 64 ton in". (a) Plot of log, (p7p) against n (showing the upper (n,) and lower (n,) limits of the hysteresis loop) for (i) the desorption branch, and (ii) the adsorption branch of the loop. Values of. 4(des) and /4(ads) are obtained from the area under curves (i) or (ii) respectively, between the limits II, and n,. (6) The relevant part of the isotherm.

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