Bend and splay elastic constants at a reentrant isotropic–calamitic-nematic phase transition

By measuring the ratio between the major and minor axes of closed elliptical loops created by a magnetic field, the ratio between the bend $\left(K_{33}\right)$ and splay $\left(K_{11}\right)$ elastic constants of a lyotropic mixture of potassium laurate, decanol, and water in the calamitic nematic phase is measured as a function of temperature. Since these systems present two nematic-isotropic phase transitions—the usual one, at high temperatures, and a reentrant one, at low temperatures—such measurements are used to compare the behavior of these elastic constants at the neighborhoods of these two distinct regions, which have in common the vanishing of the order parameter. The experimental data have revealed the existence of two elastic constant branches, characterizing a distinct low- and high-temperature behavior. To explain such asymmetry we support that, because of the lyotropic nature of the compound, the micellar variation, which is mainly responsible for the reentrant phase, plays a distinct role at these two phase transitions.

Figure 1

(Color online) Closed elliptical loops observed at the polarizing microscope along the ${\vec{e}}_z$ axis between crossed polarizers, magnification $\times 50$, in the presence of magnetic field $H=8kG$ applied along the ${\vec{e}}_y$ axis, after $\sim 20\mathrm{h}$. The calamitic nematic phase is $45\mathrm{deg}$ from the ${\vec{e}}_x$ axis.

Figure 2

Ratio between the bend and slay elastic constants $K_{33}∕K_{11}$ as function of the temperature. $I_{\mathit{RE}}$, $N_C$, and $I$ are isotropic reentrant, calamitic nematic, and isotropic phases, respectively.

Figure 3

Optical birefringence $(\Delta n\times {10}^{-3})$ vs temperature obtained as described in Refs. 9, 14. Because the birefringence is a measure of the orientational anisotropy of the nematic sample, it must be proportional to the orientational order parameter [1]. Consequently, save for a multiplicative global parameter, these data are proportional to the order parameter [18].

Figure 4

(Color online) Parametric curve representing $K_{33}∕K_{11}$ vs optical birefringence. It reveals that the elastic constants are not univocally determined by the orientational order parameter showing, unambiguously, that another parameter must be introduced to fully describe the phenomenology of the lyotropic materials. Furthermore, it also confirms that the reentrant isotropic-calamitic nematic phase transition and the classical calamitic nematic-isotropic phase transition each have a different nature [9].