  Elastic moduli of liquid crystals, known as Frank constants, are of
quintessential importance for understanding fundamental properties of these
materials and for the design of their applications. Although there are many
methods to measure the Frank constants in the nematic phase, little is known
about the elastic constants of the chiral version of the nematic, the so-called
cholesteric liquid crystal, since the helicoidal structure of the cholesteric
renders these methods inadequate. Here we present a technique to measure the
bend modulus $K_{33}$ of cholesterics that is based on the electrically tunable
reflection of light at an oblique helicoidal $Ch_{OH}$ cholesteric structure.
$K_{33}$ is typically smaller than 0.6 pN, showing a non-monotonous temperature
dependence with a slight increase near the transition to the twist-bend phase.
$K_{33}$ depends strongly on the molecular composition. In particular, chiral
mixtures that contain the flexible dimer 1'',7''-bis(4-cyanobiphenyl-4'-yl)
heptane (CB7CB) and rod-like molecules such as pentylcyanobiphenyl (5CB) show a
$K_{33}$ value that is 5 times smaller than $K_{33}$ of pure CB7CB or of
mixtures of CB7CB with chiral dopants. Furthermore, $K_{33}$ in CB11CB doped
with a chiral agent is noticeably smaller than $K_{33}$ in a similarly doped
CB7CB which is explained by the longer flexible link in CB11CB. The proposed
technique allows a direct in-situ determination of how the molecular
composition, molecular structure and molecular chirality affect the elastic
properties of chiral liquid crystals.
