The critical behavior of the pitch divergence of cholesteric liquid crystals in the vicinity to smectic-$A^{\ast }$ $\left(\text{Sm}{A}^{\ast }\right)$ and smectic-$C^{\ast }$ $\left(\text{Sm}{C}^{\ast }\right)$ phases is studied experimentally and compared with conflicting theoretical interpretations. Members of two homologous series were studied with varying polymorphism from ${\text{N}}^{\ast }\text{-Sm}{C}^{\ast }$ to ${\text{N}}^{\ast }\text{-Sm}{A}^{\ast }$. A modified functionality of the temperature dependence of the pitch is introduced to determine the critical exponent, and it is shown that the latter is independent of sample geometry. In contrast to several earlier investigations aiming to determine the critical exponent, which were inconclusive, the results of our critical exponents for the pitch divergence provide evidence for the model by Chen and Lubensky which predicts a critical exponent of $\nu =1/2$ for the ${\text{N}}^{\ast }\text{-Sm}{A}^{\ast }$ and $\nu =1$ for the ${\text{N}}^{\ast }\text{-Sm}{C}^{\ast }$ transition. This specifically implies that fluctuations cannot be neglected in the consideration of the nature of the phase transition.

• Received 12 September 2009

DOI:https://doi.org/10.1103/PhysRevE.82.011705