SPLAY-BEND SURFACE ELASTIC-CONSTANT OF NEMATIC LIQUID-CRYSTALS - A SOLUTION OF THE SOMOZA-TARAZONA PARADOX

The Nehring-Saupe [J. Chem. Phys. 54, 337 (1971); 56, 5527 (1972)] ela stic free energy of nematic liquid crystals (NLCs) contains the splay- bend elastic constant K-13, which affects only the elastic surface fre e energy. Several years ago, Somoza and Tarazona [Mol. Phys. 72, 991 ( 1991)]. showed that the value of K-13 depends on the nonlocal to local mapping that is used to define the local elastic free energy. Then th ey concluded that the splay-bend constant is not a well-defined physic al parameter. In the present paper we show that the Somoza-Tarazona re sult comes from an inconsistent treatment of the boundary effects. If all the boundary effects are correctly taken into account in an elasti c approach, the elastic surface free energy contains an effective elas tic constant K-13(eff) that is mapping independent. K-13(eff) is the s um of three different constants: the classical Nehring-Saupe bulk cons tant K-13 and two specific interfacial constants K-1 and K-h. While ea ch surface constant (K-13, K-1, and K-h) depends on the kind of nonloc al to local mapping, the resulting surface constant K-13(eff)=K-13+K-1 +K-h is mapping independent. Using a simple molecular model of the int ermolecular interactions, we obtain explicit expressions of K-13(eff) in terms of the characteristic parameters of the intermolecular energy . In the final part of this paper we discuss the meaning and the physi cal consequences of the elastic surface free energy F-s. We show that F-s is a semimacroscopic; parameter that provides an approximate elast ic description of the interfacial layer. Furthermore, we point out tha t the elastic surface free energy should not be confused with the ther modynamic surface free energy that appears in a consistent continuum t heory of NLCs.