Calculations of the Macroscopic Linear and Nonlinear Optical Properties of Nematic Liquid Crystals
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1.0 INTRODUCTION There is a growing interest in using liquid crystals for power limiting applications due to their large electronic nonlinearities. For many of these applications, the liquid crystals are contained within a small region, with a characteristic length scale ranging from nanometers to microns. For continued development of these devices, it is essential to develop methods to quantitatively calculate the linear and nonlinear optical properties. However, the methods employed to calculate molecular optical properties can not bridge the multiple size scales needed for predictions at the mesoscopic or macroscopic level. To illustrate this disparity, consider a small nematic droplet 0.1 tm in diameter. This droplet holds approximately 1.25 million 5CB molecules, containing 48 million atoms and 120 million valence electrons. Even with the rapid increase in computational complexity with size, direct calculations on systems of this extent remain far outside the realm of current abilities, which extend from tens to hundreds of atoms.
307 Mat. Res. Soc. Symp. Proc. Vol. 597 ©2000 Materials Research Society
The goal of this paper is to present further developments in methods to calculate the macroscopic NLO properties of a model liquid crystalline system. The molecular structure of 5CB (4-n-pentyl-4'-cyanobiphenyl) consists of a central biphenyl core with attached cyano and alkyl groups (Figure 1). The structure of biphenyl, and its derivatives, has been the subject of much recent interest. Previous experimental and theoretical work has determined the gas-phase torsion angle between the phenyl rings (ý, in Figure 1) in biphenyl to be in the range of 40-45' [1] with the energy barriers relative to the coplanar and perpendicular cases to be on the order of 1.5kcal/mol. Recent theoretical work on 5CB has shown similar results [2] for the gas-phase torsion angle. The nonlinear optical properties of 5CB have also been previously shown [3] to be sensitive to the torsion angle. We have previously shown the hyperpolarizabilities can exhibit large variation due to Because of the large computational expense associated with geometrical fluctuations. calculations of NLO properties, we have developed a model to relate structural changes to the resulting changes in the NLO properties. This model is first applied to a simple donor-acceptor substituted polyene, and is then applied to 5CB. Examination of the geometrical parameters, and their importance, guides selection of a subset of geometrical parameters responsible for the majority of the hyperpolarizability variation. We also discuss how this model furthers the development of means to quantitatively calculate the optical properties of nematic liquid crystals.
Figure 1 - Schematic structure of 5-cyanobiphenyl (5-CB). Marked on the figure are the final variables used in the fitting of the hyperpolarizability. 2.0 THEORETICAL METHODS Dynamical properties of the gas-phase donor-acceptor substituted polyene and 5CB in a periodic box (32 molecules) were determined using the clas
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