Isotropic-nematic interface of hard spherocylinders: Beyond the square-gradient approximation

We numerically evaluate the inhomogeneous grand-potential functional for a planar interface separating coexisting isotropic and nematic phases of long, hard spherocylinders. This approach avoids the use of a second-order gradient expansion that could bias the theory's predictions about the orientation of the interface relative to the bulk nematic phase. As in Onsager's pioneering treatment of the bulk phases, we truncate the expansion of the nonideal free energy at second order in the density. For aspect ratios L/D (the length of the spherocylinders divided by their width) greater than about 10, the theory predicts that the nematic director should lie perpendicular to the interfacial normal in accord with a previous, square-gradient calculation. As the aspect ratio decreases, the interface broadens as does the range of the correlations between spherocylinders. For L/D10, we observe a nontrivial tilt of the director compared to the interfacial normal. We compare our findings to recent experimental and theoretical calculations of isotropic-nematic interfacial properties and briefly discuss the effects that the second-order truncation of the free energy may have on our results.