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between each colloidal droplet and the dispersion medium, thereby lowering the inter- Section 7.10
facial tension and preventing coagulation. The cleansing action of soaps and other Summary
detergents results in part from their acting as emulsifying agents to keep tiny droplets
of grease suspended in water. Milk is an O/W emulsion of butterfat droplets in water;
the emulsifying agent is the protein casein. Many pharmaceutical preparations and
cosmetics (salves, ointments, cold cream) are emulsions.

Gels
A gel is a semirigid colloidal system of at least two components in which both
components extend continuously throughout the system. An inorganic gel typically
consists of water trapped within a three-dimensional network of tiny crystals of an
inorganic solid. The crystals are held together by van der Waals forces, and the water
is both adsorbed on the crystals and mechanically enclosed by them. Recall the white
gelatinous precipitate of Al(OH) obtained in the qualitative-analysis scheme. In con-
3
trast to a gel, the solid particles in a colloidal suspension are well separated from one
another and move about freely in the liquid.
When an aqueous solution of the protein gelatin is cooled, a polymer gel is
formed. Here, water is trapped within a network formed by the long-chain polymer
molecules. In this network, polymer chains are entangled with one another and are
held together by van der Waals forces, by hydrogen bonds, and perhaps by some
covalent bonds. (Include lots of sugar and some artificial flavor and color with the
gelatin, and you’ve got Jell-O.) The polysaccharide agar forms a polymer gel with
water, which is used as a culture medium for bacteria.
If the liquid phase of a gel is removed by heating and pressurizing the gel above
the critical temperature and pressure of the liquid (supercritical conditions; Sec 8.3)
and allowing the fluid to vent, one obtains an aerogel. An aerogel is a strong, low-
density solid whose volume is only a bit less than that of the original gel. The space
formerly filled by the liquid in a gel contains air in the aerogel, so the aerogel is per-
meated by tiny pores. The most-studied aerogel is silica aerogel, where the solid is
SiO (silica), which is a covalent-network solid (Sec. 23.3) with a three-dimensional
2
array of bonded Si and O atoms. (Silica occurs in nature as sand and is the main in-
gredient in glass.) The original gel can be made by the reaction Si(OC H ) 2H O →
2
2
5 4
SiO (s) 4C H OH carried out in the solvent ethanol and yielding a gel with ethanol
2
2
5
3
as the liquid. Some silica aerogel properties are: density typically 0.1 g/cm but can be
3
as low as 0.003 g/cm ; internal surface area (determined by N adsorption) typically
2
2
800 m /g; internal free volume typically 95% but can be as high as 99.9%; typical ther-
mal conductivity 0.00015 J s 1 cm 1 K 1 (which is extremely low for a solid; see Fig.
15.2); mean pore diameter 20 nm. Aerogels may find uses in catalysis and in thermal
insulation.
The spacecraft Stardust visited the comet Wild 2 in 2004 and returned to Earth in
2006. Dust was collected from the comet by impact with blocks of low-density silica
aerogel, and interstellar dust was collected on the opposite sides of the blocks
(stardust.jpl.nasa.gov). Analysis of the dust produced some surprising results
(Science, Dec. 15, 2006).
7.10 SUMMARY
The phase rule f c p 2 r a gives the number of degrees of freedom f for
an equilibrium system containing c chemical species and p phases and having r inde-
pendent chemical reactions and a additional restrictions on the mole fractions. f is the
number of intensive variables needed to specify the intensive state of the system.
The stable phase of a one-component system at a given T and P is the phase with
the lowest G m at that T and P.
m