The formation of a liquid phase from the vapour at any pressure below saturation cannot occur in the absence of a solid surface which serves to nucleate the process. Within a pore, the adsorbed film acts as a nucleus upon which condensation can take place when the relative pressure reaches the figure given by the Kelvin equation. In the converse process of evaporation, the problem of nucleation does not arise the liquid phase is already present and evaporation can occur spontaneously from the meniscus as soon as the pressure is low enough. It is because the processes of condensation and evaporation do not necessarily take place as exact reverses of each other that hysteresis can arise. [Pg.126]

The working out of these ideas will be illustrated by reference to a number of simple pore models the cylinder, the parallel-sided slit, the wedge-shape and the cavity between spheres in contact. [Pg.126]

The process of evaporation can commence at the hemispherical meniscus at A, and continues at the same relative pressure (p/p°)i. so that there is no hysteresis. [Pg.126]

If the cylinder is open at both ends, the course of events is different, because condensation has to be nucleated by the filin on the walls of the cylinderThe meniscus is now cylindrical in form (cf. Fig. 3.11(b) and (c)) thus r, = r and = oo, so that by Equation (3.7), = 2r. [Pg.127]

as pointed out by Cohan who first suggested this model, condensation and evaporation occur at difi erent relative pressures and there is hysteresis. The value of r calculated by the standard Kelvin equation (3.20) for a given uptake, will be equal to the core radius r,. if the desorption branch of the hysteresis loop is used, but equal to twice the core radius if the adsorption branch is used. The two values of should, of course, be the same in practice this is rarely found to be so. [Pg.127]

The variant of the cylindrical model which has played a prominent part in the development of the subject is the ink-bottle , composed of a cylindrical pore closed one end and with a narrow neck at the other (Fig. 3.12(a)). The course of events is different according as the core radius r of the body is greater or less than twice the core radius r of the neck. Nucleation to give a hemispherical meniscus, can occur at the base B at the relative pressure p/p°)i = exp( —2K/r ) but a meniscus originating in the neck is necessarily cylindrical so that its formation would need the pressure (P/P°)n = exp(-K/r ). If now r /r, 2, (p/p ), is lower than p/p°)n, so that condensation will commence at the base B and will All the whole pore, neck as well as body, at the relative pressure exp( —2K/r ). Evaporation from the full pore will commence from the hemispherical meniscus in the neck at the relative pressure p/p°) = cxp(-2K/r ) and will continue till the core of the body is also empty, since the pressure is already lower than the equilibrium value (p/p°)i) for evaporation from the body. Thus the adsorption branch of the loop leads to values of the core radius of the body, and the desorption branch to values of the core radius of the neck. [Pg.128]

In the converse case where r /r, 2, (p/p ), = exp — K/r ) will be lower than (p/p )ii = exp( —2K/r ,) so that condensation takes place in the neck, but will not be able to extend into the body until the pressure rises to (p/p°)i. Evaporation will occur just as before, and the core will empty completely at the pressure (p/p°)i = exp(-2K/r ), so that hysteresis will be found. [Pg.128]

Both the cone-shaped and the wedge-like pore give rise to simple, hysteresis-free behaviour. The meniscus is nucleated at the apex of the cone (Fig. 3.14(a)) or at the intersection of the two planes of the wedge (Fig. 3.14(b)), giving a spherical meniscus in the first case and a cylindrical one in the second. In both systems the process of evaporation is the exact reverse of that of condensation, and hysteresis is therefore absent. [Pg.129]

Numerous porous solids are made up of spherical particles, each in contact with two or more of its neighbours (cf. Section 1.6). For discussion of capillary condensation and evaporation in solids of this kind, a simplified model consisting of equal-sized spheres in some form of close-packing must be resorted to. In the pore illustrated in Fig. 3.15(a) condensation will be nucleated by the adsorbed film in the crevices between contiguous spheres to give a torus of liquid which, as pressure increases, will extend inwards until adjacent tori coalesce the spherical cavity, of radius r, say, will then suddenly fill up, the relative pressure being exp(-2K/r,). During desorption from a filled cavity, the state of affairs is somewhat similar to that in the ink-bottle model evaporation commences at a hemispherical meniscus in the foramen (window) of the cavity, and the cavity then empties jumpwise at the relative pressure txp(-2K/r ) where rj is the radius of a circle inscribed in the foramen. Since Tj r, hysteresis is present and the isotherm should have the general form illustrated in Fig. 3.15(h). [Pg.130]

Finally, the simplifying assumption that 6 = 0 (p. 125) should always be borne in mind. In principle, the angle of contact during capillary condensation can differ from zero. This is particularly likely when the adsorbed film has a considerable degree of localization (p. 8), for its molecular order will then differ significantly from that of a bulk liquid moreover the molecular order of the film could well be different during adsorption than during desorption, since in the latter situation the film has been part of the liquid condensate. However, in view of the intractable nature of the theoretical problem in its quantitative aspects, the possible divergence of 0 from zero is ignored in calculations of pore size from capillary condensation data. [Pg.131]

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