Numerical Study of a Disclination Loop in a Nematic Liquid Crystal Droplet

By extending the theory of Mori and Nakanishi [J. Phys. Soc. Jpn. 57 (1988) 1281], we study a disclination loop of strength 1/2 in a spherical droplet of a nematic liquid crystal. The director field is obtained by numerically solving the Euler-Lagrange equation for a given value of loop radius a, and the dependence of the free energy on a is investigated to obtain the equilibrium radius a*. We find that a* increases with droplet radius towards a limiting value, that depends on the choice of disclinaiton core energy. The present results are compared with that in earlier works based on a different theory.