Experimental determination of the elastic constant k₁₃ of a nematic liquid crystal

Abstract

The elastic constant k₁₃ is the coefficient of a divergence term in the free energy density and involves the second derivative of the director field. Thus its influence is felt only at the surface of the sample. We have analysed the optical path difference of a hybrid aligned nematic liquid crystal PCH7 taken in a cell which has a weak homeotropic alignment on one glass plate and a strong homogeneous alignment on the other. We use the approximation that solutions in the class of Euler-lagrange equations are valid up to the boundaries and extract both k₁₃ and the anchoring energy at the homeotropically aligned surface. In view of the recent argument by Oldano and Barbero that the k₁₃ term by itself may lead to discontinuities in the director configuration near the surfaces our measurements may be taken to yield an 'effective' value which may have contributions from other terms influencing the director configuration at the surface.