92168.pdf

Kinetic properties 37

where dc/d*' is the concentration gradient at the meniscus, c' the

concentration at the meniscus and x' the distance of the meniscus

from the axis of rotation.

Charge effects

The treatment of sedimentation and diffusion is a little more
complicated when the particles under consideration are charged. The
smaller counter-ions (see Chapter 7) tend to sediment at a slower rate
and lag behind the sedimenting colloidal particles. A potential is thus
set up which tends to restore the original condition of overall
electrical neutrality by accelerating the motion of the counter-ions
and retarding the motion of the colloidal particles.
The reverse situation applies to diffusion. The smaller counter-ions
tend to diffuse faster than the colloidal particles and drag the particles
along with them and increase their rate of diffusion.
These effects can be overcome by employing swamping electrolyte
concentrations. Any potentials which might develop are then readily
dissipated by a very small displacement of a large number of counter-
ions.

Osmotic pressure

The measurement of a colligative property (i.e. lowering of vapour
pressure, depression of freezing point, elevation of boiling point or
osmotic pressure) is a standard procedure for determining the
relative molecular mass of a dissolved substance. Of these properties,
osmotic pressure is the only one with a practical value in the study of
macromolecules. Consider, for example, a solution of 1 g of
macromolecular material of relative molecular mass 50 000 dissolved
in 100 cm^3 of water. Assuming ideal behaviour, the depression of
freezing point would be 0.0004 K and the osmotic pressure (at 25°C)
would be 500 Nm~^2 (i.e. 5 cm water). This freezing point depression
would be far too small "to be measured with sufficient accuracy by
conventional methods and, even more important, it would be far too
sensitive to small amounts of low relative molecular mass impurity; in
fact, it would be doubled by the presence of just 1 mg of impurity of
relative molecular mass 50. Not only does osmotic pressure provide a
measurable effect, but also the effect of any low relative molecular