## Transmittograms

### Quick Start

If over time you can measure the % transmission of a particulate formulation along a centrifuge tube, you will see an increase near the top and a decrease towards the bottom. Interpretation of the results was hard until Shalmali Bapat^{1}, working in the lab of Prof Doris Segets University of Duisburg-Essen, developed the Transmittogram technique shown here.

### Transmittograms

When you centrifuge a particulate formulation and measure how the transmission of light varies with height, it starts off at uniformly low transmission (here assumed to be 0% so all runs start off black) and then as the particles move to the bottom the transmission steadily increases.

With a device such as the LUMiSizer where you follow the transmission in real time, you get a series of transmission curves from which software can extract information about the rate(s) of sedimentation of the particles.

Unfortunately, the raw curves are not intuitive to the human eye. By translating those curves in to a transmittogram, we get an intuitive idea of what's going on. We have time along the X-axis and at each time slice we can see the amount of light being transmitted, using a grey scale of 0-255 from the original opacity to fully clear.

The default setup has a formulation with 4 different particle sizes. Each moves to the bottom in a time t given by

`t=(18μlog(h/h_0))/(Δρ.ω^2r^2)`

μ is the viscosity, h_{0} is the height of the tube at the meniscus and h at time t, Δρ is the difference in densities of the particle and liquid, ω is the angular speed and r is the particle radius (note that the inputs are diameters, D).

So what you see, in this idealised case, is a series of triangles ending at the t relevant to that particle size. At any point, the transmission contains the sum of the absorptions of all the particles still at that height, which is assumed to be a function of the weight fraction φ and an intrinsic Absorbancy at the measurement wavelength, assumed to be 1 as a default.

If those words don't make a lot of sense, then just make your own formulations and see what you would see in an ideal experiment. Alter the rpm, viscosity, particle sizes and their ratios.

To see a more complex mix, click the Gaussian option which takes the D1 value as the centre and Width as the Gaussian width. For simplicity, all particle sizes are assumed to be equally absorbtive of the measurement wavelength.

The T-Power is a simple attempt to mimic some of the more sophisticated visualisation tools used in the paper. When this is 1, the transmission scale is linear. If you reduce it, detail hidden in the shadows might appear, if you increase it, the lighter details become darker.

The help from Shalmali Bapat and Doris Segets in creating this app is gratefully acknowledged.

^{1}Shalmi Bapat and Doris Segets, *Sedimentation Dynamics of Colloidal Formulations through Direct Visualization: Implications for Fuel Cell Catalyst Inks*, ACS Appl. Nano Mater. 2020, 3, 7384−7391