# Analytical Ultracentrifugation: Diffusion broadening

In earlier times, Analytical Ultracentrifugation was readily applied for the determination of
diffusion coefficients. Since then, dynamic light scattering has dominated. Today, Analytical
Ultracentrifugation plays a minor part, but it can contribute valuable services in special cases.

Such cases may be

- when polydispersities, corrected for diffusion, are to be determined,
- when diffusion constants of particle are to be determined in motion,
- when particles are too small to be characterised via dynamic light scattering,
- when multimodal mixtures are to be examined,
- ...

In the centrifugal field, a particle is not only subject to sedimentation, but also to directed and non-directed diffusion. Undirected
diffusion (Brownian motion) is less pronounced than directed diffusion along the concentration decrease at the sedimentation boundary. This
phenomenon causes the sedimentation boundary to broaden with increasing time and creating a too-broad s-distribution.

In the progress of sedimentation, diffusion is more and more overcome by sedimentation, as diffusion follows a [root]t dependency, where
sedimentation is dependent on time. On a scale of sedimentation coefficient distributions, this reflects in an apparent sharpening of the
distribution with time.

The Figure 1 illustrates this. The apparent distribution is broad in the beginning and eventually gets sharper. This shows that sedimentation
becomes dominant with increasing time.

Table 1 gives an example for the dimensions of diffusion broadening for a model system. It shows the Gaussian half width of a sedimentation
boundary in dependence on the angular velocity and the time t required to displace the boundary by one centimeter. It can be clearly seen that
the boundary broadens considerably with time.

Even though diffusion might not be the main subject of investigation, it might be neccessary to consider this effect. Basically, there are
two options:

- Diffusion can be suppressed
*experimentally*, applying high angular velocities and keeping experimental times short, - Diffusion can be eliminated by evaluation, but this may require assumptions.

If the particles are so small that diffusion cannot be eliminated in the experiment, theories will apply that

- eliminate diffusion from sedimentation coefficient distribution,
- determine the diffusion coefficient from the experimental data for further handling.

There are *classical* and *modern approaches*approaches for both options that we have extensively researched. We have developed
an approach for separating the contributions of polydispersity and diffusion to boundary spreading. From this, as well the "real"
polydispersity as the diffusion coefficient are obtained.

Further theoretical background can be found on our scientific website under
www.kolloidanalytik.de (in German).