Page 135 - Introduction to Colloid and Surface Chemistry

The solid-gas interface 1 25

concave liquid- vapour interface and, therefore, a lower vapour
pressure in the capillary than it would have over a flat surface. Tlhis
vapour pressure difference is given by the Kelvin equation, written in
the form

(5. 3)

where r is the radius of the capillary, and 0 the contact angle between
the liquid and the capillary wall.
Condensation can, therefore, take place in narrow capillaries at
pressures which are lower than the normal saturation vapour
pressure. Zsigmondy (1911) suggested that this phenomenon might
also apply to porous solids. Capillary rise in the pores of a solid will
usually be so large that the pores will tend to be either completely full
of capillary condensed liquid or completely empty. Ideally, at a
certain pressure below the normal condensation pressure all the
pores of a certain size and below will be filled with liquid and the rest
will be empty. It is probably more realistic to assume that an
adsorbed monomolecular film exists on the pore walls before
capillary condensation takes place. By a corresponding modification
of the pore diameter, an estimate of pore size distribution (which will
only be of statistical significance because of the complex shape of the
pores) can be obtained from the adsorption isotherm.
Capillary condensation is also important in the binding of dust and
powder particles by water. Particles separated by a thin layer of water
are held together very strongly by capillary forces. The inhibition of
evaporation due to the concave shape of the air-water interface
enhances the duration of this particle binding.
The capillary condensation theory provides a satisfactory explana-
tion of the phenomenon of adsorption hysteresis, which is frequently
observed for porous solids. 'Adsorption hysteresis' is a term which is
used when the desorption isotherm curve does not coincide with the
adsorption isotherm curve (Figure 5.8).
A possible explanation of this phenomenon is given in terms of
contact angle hysteresis. The contact angle on adsorption, when
liquid is advancing over a dry surface, is usually greater than the
contact angle during desorption, when liquid is receding from a wet
surface. From the Kelvin equation, it is evident that the pressure
below which liquid vaporises from a particular capillary will, under