Random matrix theory identifies preorganized regions of liquid crystals

Liquid crystals are made of ellipsoidal molecules that shift between a disordered and an ordered liquid state depending on the temperature, density or concentration of the system. Spectroscopy of these materials show that immediately before disordered liquid crystals become ordered, the materials have regions where the molecules order locally. Now a team of researchers has shown that a mathematical theory called random matrix theory can be used to reveal preordered regions in liquid crystals.

To theoretically describe the preordered portions of liquid crystals, the team simulated a liquid crystal containing a hundred to a few thousand molecules. As reported in The Journal of Chemical Physics, they applied random matrix theory to explain the material’s behavior. This probability-based theory, which draws statistical insight from matrix properties, is widely used to describe a variety of systems such as the behavior of atomic nuclei, as well as for chaos theory applications.

The approach worked well to describe the liquid crystals in their fully ordered or fully disordered states, but failed to describe the molecules’ behavior in the preordered regions. That failure served as a quantitative signature to identify preordered domains in a liquid crystal transitioning to order.

Understanding molecular behavior in the preordered regions of a liquid crystal could provide insights into how molecules in a supercooled liquid cooperate and organize as the material becomes a glass. The ordering of liquid crystals can occur in a highly fluid state which makes liquid crystals the ideal proving ground for this type of analysis.

Source: “Measuring order in disordered systems and disorder in ordered systems: Random matrix theory for isotropic and nematic liquid crystals and its perspective on pseudo-nematic domains,” by Yan Zhao and Richard M. Stratt, The Journal of Chemical Physics (2018). The article can be accessed at https://doi.org/10.1063/1.5024678 .