Reply to the comment by G. Barbero and N. V. Madhusudana ‘On a theoretical analysis on the influence of non-uniformity of the order parameter on the surface energy in nematics’ (1990, Liquid Crystals, 7, 299)

Abstract

In their comment to our recent paper [I] Barbero and Madhusudana argue that the mathematical problem is ill-posed and thus the consideration should be revised. The objection is based on the ideas published in a set of papers [2–4], where it has been shown that if the K₁₃term is used in the usual nematic free energy density, the function n(z) may be discontinuous at the surface and in this case we have to include second order elasticity ∼(V ²n)² into our consideration. In principal, we agree with this objection, although it is very difficult to estimate whether the corresponding contribu-tion to n(z) is essential, because no real problem with second order elasticity has been solved up to now. At the same time it is obvious that if we do not take the K_l3 term into account, the solution of the minimizing problem with the traditional nematic free energy remains correct and does not contradict experimental observations.