Page 32 - Introduction to Colloid and Surface Chemistry

Kinetic properties 23

Factional ratios

The frictional coefficient of an asymmetric particle depends on its
orientation. At low velocities such particles are in a state of random
orientation through accidental disturbances, and the resistance of the
liquid to their motion can be expressed in terms of a frictionai
coefficient averaged over all possible orientations. For particles of
equal volume the frictional coefficient increases with increasing
asymmetry. This is because, although the resistance of the liquid is
reduced when the asymmetric particle is end-on to the direction of
flow, it is increased to a greater extent with side-on orientations, so
that on average there is an increase in resistance. The frictional
coefficient is also increased by particle solvation.
A particle containing a given volume of dry material will have its
smallest possible frictional coefficient, / 0, in a particular liquid when
it is in the form of an unsolvated sphere. The frictional ratio, f/f Q (i.e.
the ratio of the actual frictional coefficient to the frictional coefficient
of the equivalent unsolvated sphere) is, therefore, a measure of a
combination of asymmetry and solvation.
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With application to dissolved proteins in mind, Oncley has
computed frictional ratios for ellipsoids of revolution of varying
degrees of asymmetry and hydration. The resulting contour diagram
(Figure 2.1) shows the combinations of axial ratio and hydration
which are compatible with given frictional ratios. The separate
contributions of asymmetry and hydration cannot be determined
unless other relevant information is available.

Brownian motion and translational diffusion

Brownian motion

A fundamental consequence of the kinetic theory is that, in the
absence of external forces, all suspended particles, regardless of their
size, have the same average translational kinetic energy. The average
3
translational kinetic energy for any particle is MT, or VikT along a
l l
given axis - i.e. /2m(dxldtf = /ikT, etc.; in other words, the average
particle velocity increases with decreasing particle mass.