Linear analysis of pattern formation in nematics in oblique magnetic fields

Abstract

The dynamics of nematic director ® eld reorientation in non-Fre  edericksz geometries, after a magnetic ® eld H is applied at an oblique angle relatively to the initial homogeneous director n0 (H not normal to n0 ), is studied considering a magnetic reorientation driven by hydrodynamic instabilities (with back¯ow). This study is carried out for bounded samples between two parallel plates with planar boundary conditions and with rigid anchoring. Linear stability and wave vector selection analysis predict that, when the angle of the magnetic to the initial director ® eld is increased, for a given magnetic ® eld intensity, two transitions from a homogeneous to a transient distorted director ® eld reorientation can occur: a transition at a ® rst critical angle to an aperiodic distorted director ® eld and a transition at a second critical angle to a periodic distorted director ® eld. It is shown that the periodic mode is cut oV at a higher reduced ® eld when the magnetic ® eld acts away from the normal direction.

NMR spectra simulation of the magnetic reorientation of a lyotropic nematic polymer cell in the Freedericksz and a non-Freedericksz twist geometry

“…At early times after the application of the magnetic field the fastest growing distortion mode may be calculated from the linear theory [10]. Under that condition, ρ q in (8), can be taken as the corresponding reduced bend wavevector [9]:…”

“…For α < α c , where α c is the critical angle for the selection of the periodic mode [9], equation (11) gives ρ 2 q < 0 and this should be replaced by ρ q = 0 in equation (8). When ρ q = 0 equation ( 8) reduces to a homogeneous reorientation equation.…”

“…We establish the non-linear equations, in the frame of the Ericksen-Leslie continuum theory [8], that describe the magnetic reorientation of the director field in the case of a bounded sample between two parallel plates with planar boundary conditions and rigid anchoring. For in-plane oblique magnetic fields making an angle α with respect to the initially aligned, unperturbed director, there is a critical angle α c for the development of periodic distortions in the director field [9]. In this work we focus on the case α < α c (non-Freedericksz geometry), corresponding to a non-periodic director reorientation with only a twist distortion, and in the case α = π/2 (Freedericksz geometry), corresponding to a periodic director reorientation with a twist-bend distortion [10,11].…”