Viscosity peaks at the cholesteric-isotropic phase transitions

In this work, the effective viscosity of the cholesteryl myristate and cholesteryl nonanoate liquid crystals is studied as a function of temperature at the region of their cholesteric-to-isotropic phase transition, where blue phases are found. Using a change of scale it is shown that the viscosity peaks that characterize these phase transitions are shape invariant, which suggests that large-scale fluctuations on the two-point correlation function give an important contribution to the observed viscosity. The consequences of this fact are investigated and, from the experimental data, the critical exponents associated with the diverging two-point correlation function are calculated. The results found for both compounds are essentially the same, being also in good agreement with the known values of the corresponding critical exponents of nematic-isotropic phase transition.

Figure 1

MBBA viscosity as a function of the reduced temperature. The solid line represents the effective viscosity measured on a nonoriented sample. The dots represent the measurements for the viscosity of the orientated sample [4]. According to these data at the phase transition the viscosity jumps from the isotropic viscosity, at the isotropic phase, and assumes the value of the ${\eta }_2$ Miesowicz’s coefficient, at the nematic phase.

Figure 2

(Color online) The non-Newtonian viscosity behavior of the myristrate and nonanoate samples when submitted to different shear rates. At both samples the temperature ranges stepwisely from the isotropic to the cholesteric phase and the peak corresponds to the isotropic-cholesteric phase transition. These experimental data reveal the high non-Newtonian character of these viscosity peaks, indicating that as the shear ratio increases the viscosity peaks diminish.

Figure 3

(Color online) Results obtained with the rescaling of the experimental data of the myristate and nonanoate peaks at the cholesteric-isotropic phase transition. The original data points, which have been put on detailed in Fig. 2, have been rescaled in such a way that the distance between the distance curves, defined in Eq. (1), become the shortest. The results obtained indicate that, save a multiplicative number, all these curves have the same singular behavior. This is a strong signal that these peaks have an important contribution coming from the unbounded fluctuations that characterize the critical behavior of the $N^{*}\text{−}I$ phase transitions.

Figure 4

(Color online) Critical exponents $\nu$ obtained with the use of the application of Eq. (7) at the data shown at Fig. 3. As the shape of the peaks are scale invariant we have used $\overline{\eta }=1$. Both graphs coherently indicate a critical exponent at the region of $v=0.25$. This result is in good agreement with the known values of this critical exponent for the $N^{*}\text{−}I$ phase transition.