Magnetic field-induced changes in molecular order in nematic liquid crystals

there are two inherent characteristic lengths, the nematic correlation length \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $\zeta$\end{document} and the magnetic coherence length \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $\xi$\end{document}. As the magnetic field increases the magnetic coherence length decreases and the relative ordering of the three length scales determines the director and scalar order parameter configuration through the cell. We use asymptotic expansions in regions defined by these length scales to analytically determine the molecular configuration in terms of these variables. Specifically, we investigate the boundary layer between the cell substrate and the bulk nematic material when strong anchoring forces the nematic director in a different direction to that of the applied field. We find that at low field strengths the classical picture of liquid crystal/magnetic field interaction occurs, that is, the director orientation is governed by the surface alignment until a transition occurs as the magnetic coherence length becomes comparable to the cell thickness and the director changes orientation so as to align with the magnetic field. At high field strengths, we find that a field-induced reduction of the molecular order occurs in a region close to the cell boundary. We are able to analytically determine the director and scalar order parameter configurations for the majority of field strengths and where analytical solutions are not found a numerical solution is presented. It is hoped that further work will extend this basis of analytical solutions to include a solution for all field strengths and for different cell configurations.