Relaxation of the nematic deformation when the distorting field is removed

E. K. Lenzi, G. Barbero, PHYSICAL REVIEW E 81, 021703 (2010). PDF | DOI

We investigate the relaxation of the nematic deformation when the distorting field is switched off. We show that the usual analysis based on the diffusionlike equation does not allow a complete description of the phenomenon because it does not permit one to satisfy the initial boundary condition, at t=0, on the first time derivative of the nematic tilt angle. An alternative approach to the problem, taking into account the inertial properties of the nematic molecules, allows one to satisfy the initial boundary conditions on the first-order time derivative of the tilt angle. In this framework the dynamical evolution of the nematic deformation, in the initial time, depends on the inertial properties of the nematic molecules. However, the typical relaxation time is so short that, for all practical effects, the first time derivative of the tilt angle is discontinuous at t=0. A more realistic description involves the switching time of the distorting field. In this framework, the initial boundary condition of the first-order derivative is automatically satisfied. Our analysis shows that the description based on the diffusion equation works well when the switching time is very small with respect to the diffusion time.