Elastic Constants of Nematic Liquid Crystals

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Abstract
In this paper the splay k11 and bend k33 elastic constants for the homologous series 4,4′-di (n-alkoxy)azoxybenzene (from methyloxy to hexyloxy) were measured as a function of temperature by studying the deformation of the liquid crystal in a magnetic field. The values of these elastic constants (10-6 to 10-5 dyne) all decrease with increasing temperature. The reduced elastic con­stants C11 and C33 which were derived by Saupe and which take into consideration the effect of temperature on the order parameter and on the mole volume should be independent of temperature if there are no changes in short range order. In the region of the isotropic transition temperature the reduced elastic constants of the homo­logous series show a general increase with increasing alkoxy chain length. This trend can be ex­plained by the increasing molecular length. There is still a strong alternation superimposed upon this trend, however, which can not be due to the alternation of the anisotropic polarizabilities. To first approximation, the elastic constant ratios for the homologous series can be summarized on a single universal curve. The temperature behavior of the elastic constants can be divided into four groups, each having its own characteristic short range order structure. Region IV, which is near the smectic phase transition, is characterized by cybotactic groups which exist in the nematic phase and which have a smectic like structure. C33 as well as C11 show a very strong increase in this region as the smectic C phase is approached. This abnormal temperature behavior can be explained as a pretransitional effect because in the smectic C phase C33 and C11 must be quite large because of the planar structure where the molecules are tilted with respect to the plane. In a smectic A phase where the molecules are perpendicular to the plane a pretransitional effect occurs only in C33 as Cheung and Meyer have shown. In region III C33/C11 ~ 1 and this ratio is temperature independent. This behavior is in agree­ment with our model calculation if the steric units contain only a few' molecules and are approximately spherical and are arranged to form a planar structure. In region II C33/C11 ~ 2 and C11 and C33 are both independent of temperature. The assumptions made for region III are also valid here except that the steric groups in region II are not arranged in a planar configuration. This assumption is in agreement with the model calculation and has been verified through x-ray experiments. In region I, which borders upon the isotropic phase, C11 is nearly independent of temperature whereas C33 becomes smaller with inceasing temperature. The model calculation show's that C33 is more sensitive to structural changes than C11. The abnormal temperature behavior of the mole volume in this region is an indication that changes in the short range order structure are occurring.

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