Relation Between Molecular and Macroscopic Properties of Nematic Liquid Crystals
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257 Mat. Res. Soc. Symp. Proc. Vol. 559 © 1999 Materials Research Society
solid, have commonly been used to reduce the computational intensity of the problem. While ab initio methods can be more accurate, interaction potentials and force field techniques are more in line with the computational methodology available. However, the continual effort to reduce the computational intensity for the macroscopic model tends to erode the ability to make accurate predictions at the molecular level. Torsion
Figure 1 - Schematic structure of 5-cyanobiphenyl (5CB) with phenyl-phenyl torsion angle
(0).
Figure 2 - Illustration of eight 5-CB molecules in a periodic box used for nematic phase simulations. In this paper, we have performed electronic structure calculations, isolated species molecule dynamics and periodic representations of 5CB in a nematic phase simulation to investigate the transition of properties from molecular to a larger size scale regime. Both structural and energetic concerns are investigated to determine relevant variables for representative size and time scales.
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COMPUTATIONAL METHODS For the static property investigation, we have used the AM1 Hamiltonian [9] as implemented in MOPAC93 [10], to both calculate the optimized geometries and the hyperpolarizabilities. The AM1 Hamiltonian has been shown to provide accurate descriptions of the hyperpolarizabilities in aromatic molecules [11 ]. All bond lengths and angles were optimized by force relaxation methods [12], with the exception of the phenyl-phenyl twist angle (0) when mapping the torsional space of 5CB. The minimum energy conformation occurs for a twist angle between the phenyl groups of 40.140 in good agreement with the experimental values. Components of the frequency-dependent first and second hyperpolarizabilities were determined by the time dependent HF method implemented by Kurtz [13]. We report the orientationally averaged hyperpolarizabilities in esu units. Dynamical properties of the 5CB molecule and the nematic phase model were determined using the classical molecular dynamics (MD) method in the Tinker program system [14] using the MM3 force field [15] in the NVT ensemble. Initial conformations and periodic boundary dimensions were determined using the Hyperchem program [16]. Coordinate snapshots from the MD trajectory were used as input into electronic structure computations for the dynamic values. RESULTS AND DISCUSSION In order to develop a better picture of materials properties, we needed to develop a time-averaged picture of the structural properties of 5CB as well as large assemblages of 5CB molecules. In Figure 3 below, we show the relative heats of formation for 5CB as a function of the phenyl-phenyl torsion angle for the MM3 force field, MM3 + pi corrections, and a MM3 calibrated against 6-31G* ab initio data [17]. Notably, the energetic minimum for the torsional angle between the phenyl rings is located at 44.2', similar to the minimum found for biphenyl. This minima lies at neither at the maximum (00) or minimum (900) for line
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