Non-singular disclinations of strength S = + 1 in nematics

It is shown that the energy of a screw disclination of strength + 1 1 (2 π rotation of the director around the line) is reduced if the molecules are allowed to relax out of the plane perpendicular to the line. This solution has no singularity on the axis, r = 0. The calculation is done in the case of the anisotropic elasticity 2 for the pure splay-bend and twist-bend cases. It satisfies de Gennes' 3 molecular field. The line energy of the solution does not depend upon the size R of the specimen. When R becomes smaller than a critical value of the order of several molecular lengths, the Frank solution with an isotropic (or nematic) core is preferable.