The University of Southampton
Mathematical Sciences

# Improving liquid crystal measurements

Mathematical modelling is often associated with the description of some physical or engineering phenomenon, from the interior of a star to the billowing sails of a racing boat. There is, however, a completely different type of modelling that all of us perform every day, albeit unwittingly: measurement. If we want to tile a floor we need to know the area of each tile. This is easy: we measure its width and height, and multiply them together. In doing this we have implicitly formulated in our head a mathematical model: we have represented the tile, with its slightly curved surface and edges, and its round corners, as a perfect geometrical shape, a rectangle with a perfectly flat surface, razor sharp edges and pinpoint corners. It is the area of the rectangle that is the product of width and height. In our mind we model, or approximate, the tile with the rectangle so that we can use its area formula to find out how big the tile is.

The Soft Photonics Group, a cross-disciplinary group formed by experimental physicists and mathematicians, has taken the mathematics of measurements processes quite a step further. We have developed a new instrument to measure the properties of liquid crystals by making use of advanced mathematical models, coupled to powerful computer codes and precise experiments. This instrument is called OMPA, for Optical Multi-Parameter Analyser.

Liquid crystals are ubiquitous, they are at the heart of most displays, and have properties intermediate between fluids, like water, and solids, like a crystal. Their molecules can flow, so that they behave as viscous liquids, but they also like to be parallel to each other, as in a crystal. This latter effect is caused by elastic forces between the molecules that tend to align them. The OMPA can measure both viscosity and elasticity in a fully automated way. Not only this: we can measure these properties at many points across each device (for example, all over your computer screen) so that we can determine how well constructed the device is.

The instrument is powered by a graphical user interface written in Matlab (see Figure 2) that allows the user to perform the experiment at a click of a button, and perform the data analysis live. We have commercialised this instrument and we are in the process of developing a smaller version (the mini-OMPA) suitable for high-school and university teaching labs.

In Southampton research in liquid crystals is carried out by Professor Giampaolo D'Alessandro, Professor of Mathematical Physics.

List of all staff members in
Staff MemberPrimary Position
Giampaolo D'AlessandroProfessor of Mathematical Physics