Defect Dynamics of a Nematic Polymer in a Magnetic Field
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Defect Dynamics of a Nematic Polymer in a Magnetic Field ALEJANDRO D. REY McGill University, Department of Chemical Engineering, Canada H3A2A7
Montreal, Quebec,
ABSTRACT Analysis of the nonlinear dynamical response of a rod-like nematic liquid crystalline polymer, between parallel untreated plates, in a magnetic field is presented. Numerical solutions to the torque balance equations show that when a uniformly aligned polymer is acted by a magnetic field normal to the initial polymer orientation an array of inversion walls develops. Stability analysis shows that the inversion walls are unstable to localized perturbations. The nonlinear resolution of the instability leads to the nucleation of an array of disclination line pairs of strength ±1/2. A perturbation analysis is used to obtain the evolution of the polymer structure towards equilibrium. INTRODUCTION Experimental evidence (1,2) indicates that when a rigid rod-like nematic polymer , uniformly aligned between two thinly spaced parallel plates is acted by a sufficiently strong magnetic field normal to the initial polymer orientation, a transient periodic pattern develops. At short times a dominant wave vector ,that depends on the viscoelastic properties of the material, the plate spacing and the strength of the field, dominates the response. The observed wave length is usually longer that that predicted by the linear theory; the difference between the two increases with increasing field strengths. In this work we use Galerkin Finite Elements to solve the governing Leslie-Ericksen equations (3) to describe the orientation and velocity fields taking into account the anchoring condition of the polymer at the two polymer-plate interfaces. We show that for the selected wave length a periodic texture, consisting of counter-rotating domains, evolves into an array of splay-bend inversion walls. It was found that the anchoring condition of the polymer at the bounding surface does not affect the wave length selection. The inversion walls are metastable, since a lower energy state is available. A possible mechanism of decay to the homogeneous equilibrium state is through nucleation of disclination line pairs of strength ±1/2. We show that the interaction of inversion walls and disclination lines leads to the motion of the lines into the inversion walls. This mechanism leads to the dissolution of walls and to a homogeneous equilibrium texture.
Mat. Res. Soc. Symp. Proc. Vol. 209. 01991 Materials Research Society
300
INVERSION WALLS The phenomenon is best described in Cartesian coordinates. The initial state is one of uniform alignment in the z direction , with a director field n=(O,O, 1). At time t=O a uniform field is imposed in the x- direction. The x-z plane is assumed to be of infinite extent. We assume that the director is in the x-z plane, n=(cos8,O,sinO). The orientation is given by 0 in units of radians. The velocity is given by v=(u,0,0), and appears due to the intimate coupling between orientation and flow, characteristic of ordered liquids. The exact balanc
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