Page 45 - Introduction to Colloid and Surface Chemistry

36 Kinetic properties

and, since
2
dx _MD(l-vp)<*> x
dt RT
then
2
dc _ o) M (1 - vp)jcdjc
c RT

Integrating,

(2J9)

where Ci and c 2 are the sedimentation equilibrium concentrations at
fr° m the ax 's of rotation. Ideal behaviour has
distances x t and * 2
been assumed.
When a state of sedimentation-diffusion equilibrium has been
reached, the molecular or particle mass can, therefore, be evaluated
without a knowledge of the diffusion coefficient (and, hence,
independently of shape and solvation) by determining relative
concentrations at various distances from the axis of rotation.
Molecules as small as sugars have been studied by this technique.
Polydispersity introduces complications and is reflected by a drift
of M with x. Conversely, consistency of M with x is an indication of
sample homogeneity with respect to M.
The disadvantage of the sedimentation equilibrium technique is
that the establishment of equilibrium may take as long as several
days, which not only is inconvenient generally, but also accentuates
the importance of avoiding convectional disturbances.
From a theoretical analysis of the intermediate stages during which
the solute is being redistributed, Archibald 136 has developed a
technique which involves measurements at intervals during the early
stages of the sedimentation equilibrium experiment and so does not
entail a long wait for equilibrium to be established. The ratio sID can
be calculated from the expression

2
dc/dx' a> s (2-20)
=
ex D