Phase diagram of hard colloidal platelets: a theoretical account

Abstract

We construct the complete liquid crystal phase diagram of hard plate-like cylinders for variable aspect ratio using Onsager's second virial theory and employing the Parsons–Lee decoupling approximation to account for higher-body interactions in the isotropic and nematic fluid phases. The stability of the solid (columnar) state at high packing fraction is included by invoking a simple equation of state based on a Lennard–Jones–Devonshire cell model which has proven to be quantitatively reliable over a large range of packing fractions. By employing an asymptotic analysis based on the Gaussian approximation we are able to show that the nematic–columnar transition is universal and independent of particle shape. The predicted phase diagram is in qualitative agreement with simulation results.

Keywords:

• colloidal platelets
• liquid crystals
• phase transitions
• Onsager theory

Acknowledgements

We are grateful to George Jackson and Jeroen van Duijneveldt for fruitful discussions. HHW acknowledges the Ramsay Memorial Fellowship Trust for financial support.