Page 44 - Introduction to Colloid and Surface Chemistry

Kinetic properties 35

where x\ and x 2 are the distances of the boundary from the axis of
rotation at times t\ and t 2. Therefore,

(2.18)

It is evident from the above expressions that the appropriate diffusion
coefficient must also be measured in order that molecular or particle
masses may be determined from sedimentation velocity data. In this
respect, a separate experiment is required, since the diffusion
coefficient cannot be determined accurately in situ, because there is a
certain self-sharpening of the peak due to the sedimentation
coefficient increasing with decreasing concentration.
Care must be taken to ensure that the system under investigation
remains uncoagulated. This applies to any technique for determining
molecular or particle masses. s, D and v are corrected to a standard
temperature, usually 20°C, and should be extrapolated to zero
concentration.
With polydispersed systems either a broadening of the boundary
(in addition to that caused by diffusion) or the formation of distinct
peaks representing the various fractions is observed. Sedimentation
does not provide an unequivocal method for establishing the
homogeneity of a colloidal system. For example, a mixture of serum
albumin and haemoglobin is homogeneous with respect to sedimenta-
tion velocity but the two proteins are easily distinguished from each
other by electrophoresis.
Knowledge of M and v enables D 0 and, hence, the ratio D^/D (the
f fictional ratio) to be calculated.

Sedimentation equilibrium

Consider the flow of molecules or particles across an area A in a
colloidal solution where the concentration is c and the concentration
gradient is dc/dx . The rate of flow is cA (dx/dt) due to sedimentation,
and, from Pick's first law, -DA (dc/djc) due to diffusion. When
sedimentation equilibrium is attained, the net flow is zero, so that

dx dc
c— = D —
d? dx