We report results of the splay ($K_{11}$) and bend ($K_{33}$) elastic constants and the effective flexoelectric coefficient of three bent-core liquid crystals belonging to a homologous series of 4-cyanoresorcinol bisbenzoates with varying chain lengths. Based on the results of x-ray scattering studies, one of the three compounds with a shorter chain length (C4) has few, if any, clusters present in its nematic phase and behaves quite normally, whereas the others two with longer chain lengths (C6 and C7) show the presence of cybotactic nematic phase with smectic C type clusters. These grow in size with a reduction in temperature. $K_{33}$ is found to be the least for C7, whereas it is weakly dependent on temperature. $K_{33}$ is somewhat higher for C4 and C6 and is almost independent of temperature. $K_{11}$ for C6 and C7 is higher by 20$\%$ to 50$\%$ than C4 depending on the temperature. $K_{11}$ increases linearly with a reduction in temperature for the three compounds. For C6 $K_{11}>K_{33}$ by a factor up to ∼2 depending on the temperature, for C4 it is greater by a factor up to 1.3, and for C7 it is greater by a factor of ∼2.5. These results suggest that the clusters do not have any effect on $K_{11}$. The magnitude of the effective flexoelectric coefficient $e=\left(\right|e_1-e_3\left|\right)$ is measured by creating a uniform lying helix (ULH) configuration in a planar cell. By doping the bent-core system with a small wt$\%$ of a chiral dopant, the ULH is obtained by cooling planar cells to the cholesteric phase under weak electric field. The effective flexoelectric coefficient is greater for the bent-core systems than for calamatics but it is much lower than would otherwise have been expected for such systems. $|e_1-e_3|$ for C4 > C6 ≈ C7 is greater by 20$\%$ to 25$\%$ than C6 and C7 at the same reduced temperature. These differences in the effective flexoelectric coefficient can easily arise from a difference in the chain lengths among the members of the series but if the presence of clusters were to have an influence on $|e_1-e_3|$, then these would reduce it, contrary to the expectations for the bent-core systems.

• Received 5 June 2013

DOI:https://doi.org/10.1103/PhysRevE.88.032503