Fig. 3.11 Capillary condensation in cylindrical pores, (a) Cylinder closed at one end, B. The meniscus is hemispherical during both capillary condensation and capillary evaporation, (h) and (c) Cylinder open at both ends. The meniscus is cylindrical during capillary condensation and hemispherical during capillary evaporation. Dotted lines denote the |

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 [Pg.95]

At the point where capillary condensation commences in the finest mesopores, the walls of the whole mesopore system are already coated with an adsorbed film of area A, say. The quantity A comprises the area of the core walls and is less than the specific surface A (unless the pores happen to be parallel-sided slits). When capillary condensation takes place within a pore, the film-gas interface in that pore is destroyed, and when the pore system is completely filled with capillary condensate (e.g. at F in Fig. 3.1) the whole of the film-gas interface will have disappeared. It should therefore be possible to determine the area by suitable treatment of the adsorption data for the region of the isotherm where capillary condensation is occurring. [Pg.169]

We consider first a cylinder closed at one end, B (Fig. 3.11(a)). Capillary condensation commences at that end to form a hemispherical meniscus r, and are equal to one another and therefore to r , which in turn is equal to r, the radius of the core (cf. Equation (3.7) and Fig. 3.7). Thus capillary condensation, to fill the whole pore, takes place at the relative pressure [Pg.126]

The volume i>r,) of the multilayer film on the walls of all pores which have already given up their capillary condensate is [Pg.139]

As already indicated in Section 3.1, the study of mesoporous solids is closely bound up with the concept of capillary condensation and its quantitative expression in the Kelvin equation. This equation is, indeed, the basis of virtually all the various procedures for the calculation of pore size [Pg.116]

Consider stage i in the desorption process where the thickness of the adsorbed film is and the pores of radius r, have just lost their capillary condensate. The volume of multilayer lining the pores of any radius r, where r > ri, will then be (since the pores are cylindrical) [Pg.139]

Fig. 3.15 (a) A pore in the form of an interstice between close-packed and equal-sized spherical particles. The adsorbed him which precedes capillary condensation is indicated, (b) Adsorption isotherm (idealized). [Pg.130]

Note that /4 = 0 when capillary condensation is complete.) Integration by measurement of the area under the curve of ln(p°/p) against n between the stated limits therefore gives the value of A, which is the area of the walls of the cores, not of the pores (cf. Fig. 3.28). [Pg.171]

From the Kelvin equation it follows that the vapour pressure p over a concave meniscus must be less than the saturation vapour pressure p°. Consequently capillary condensation of a vapour to a liquid should occur within a pore at some pressure p determined by the value of r for the pore, and less than the saturation vapour pressure—always provided that the meniscus is concave (i.e. angle of contact <90°). [Pg.121]

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. [Pg.126]

Exanqiles of this pore blocking effect on the desorpdon branch of the isottom Imve been well docummited in the porosimetry literature. Several years ago Kraemer [11] pointed out that in an ink botde-type pore, capillary condensation on the adsorption branch would be dominated by the radius of [Pg.218]

A difficulty in using the method is that of identifying the ptoint F, where capillary condensation commences. This is usually taken as the lower closure point of the loop but as was pointed out in Section 3.5, capillary condensation can occur without hysteresis if the pores are of an appropriate shape—such as wedge-like—before the irreversible condensation responsible for the hysteresis loop sets in. The uncertainty arising from this cause is considerable, since the curve of ln(p°/p) is very steep in this region (cf. Fig. 3.28). [Pg.171]

At adsorption temperatures below the critical temperature of the component to be adsorbed, the adsorbent pores may fill up with liquid adsorpt. This phenomenon is known as capillary condensation and enhances the adsorption capacity of the adsorbent. Assuming cylindrical pores, capillary condensation can be quantitatively described with the aid of the Kelvin equation, the degree of pore filling being inversely proportional to the pore radius. [Pg.1510]

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 [Pg.113]

As Everett points out, however, the analogy of a pore as a narrownecked bottle is over-specialized, and in practice a series of interconnected pore spaces rather than discrete bottles is more likely. The progress of capillary condensation and evaporation in pores of this kind (cf. Fig. 3.13) has been discussed by de Boer, and more recently by Everett. [Pg.129]

The model proposed by Zsigmondy—which in broad terms is still accepted to-day—assumed that along the initial part of the isotherm (ABC of Fig. 3.1), adsorption is restricted to a thin layer on the walls, until at D (the inception of the hysteresis loop) capillary condensation commences in the finest pores. As the pressure is progressively increased, wider and wider pores are filled until at the saturation pressure the entire system is full of condensate. [Pg.113]

As a general rule, adsorbates above their critical temperatures do not give multilayer type isotherms. In such a situation, a porous absorbent behaves like any other, unless the pores are of molecular size, and at this point the distinction between adsorption and absorption dims. Below the critical temperature, multilayer formation is possible and capillary condensation can occur. These two aspects of the behavior of porous solids are discussed briefly in this section. Some lUPAC (International Union of Pure and Applied Chemistry) recommendations for the characterization of porous solids are given in Ref. 178. [Pg.662]

The process of adsorption takes place when the concentration of the adsorptive is greater than the equiUbrium value vahd for the given temperature however, desorption requires a fluid concentration of the adsorptive which is smaller than the equilibrium concentratiom An adsorption isotherm favorable for adsorption is unfavorable for desorption and vice versa. Condensation of gases or vapors and solidification or crystalhzation will start when the relative supersaturation becomes > 1. In the case of adsorbents with capillary or very narrow pores, capillary condensation is observed for relative saturations

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