Correlation length and chirality of the fluctuations in the isotropic phase of nematic and cholesteric liquid crystals

Light-scattering measurements of the correlation length in the isotropic phase of a nematic liquid crystal reveal a temperature dependence following Landau–de Gennes theory for the isotropic phase with a bare correlation length smaller than has been measured in other liquid crystals. Similar measurements in a cholesteric liquid crystal demonstrate that the correlation length in the isotropic phase is larger than typically found in nematics and that the chirality of the fluctuations in the isotropic phase is slightly higher than the chirality of the cholesteric phase. Landau–de Gennes theory of the cholesteric phase describes the chirality in the cholesteric phase well but predicts that the chirality in the isotropic phase is temperature independent, which is not consistent with the data. There is a discontinuity in the chirality at the cholesteric-isotropic transition of about 15%, which is less than the predictions of Landau–de Gennes theory but more than the typical specific volume discontinuity at transitions to the isotropic phase. Except for a mismatch in the discontinuities at the transition, the chirality data resemble the temperature behavior of variables just below a critical point, in spite of the fact that this system is far from a critical point.

Figure 1

Geometry for calculating the contribution from double scattering. The scattering angle is $\theta$, the first scattering event occurs at point $X$, and the second scattering event occurs somewhere along line $CD$. The probability of double scattering is proportional to the angle $\alpha +\beta$. This angle is then averaged for all points along line $AB$ a distance $x$ from the center.

Figure 2

Scattering intensity as a function of scattering angle for 5CB. The inset shows the contributions from single and double scattering resulting from the fitting procedure described in the text that results in a correlation length of $5.00\pm 0.23\mathrm{nm}$.

Figure 3

Correlation length vs. temperature in the isotropic phase of 5CB. The bare correlation length resulting from the fit to Eq. (8) is $0.40\pm 0.03\mathrm{nm}$.

Figure 4

Scattering intensity normalized to the scattering at high temperature (see text) as a function of scattering wave vector for CE6/CE6R. The line shows the fit to Eq. (13), which results in a determination of the chirality of $q_0=-30.7\pm 0.4\mu {\mathrm{m}}^{-1}$.

Figure 5

Chirality (a) and correlation length (b) for the isotropic phase of CE6/CE6R.

Figure 6

Wavelength dependence of measured absorption due to selective reflection at one temperature in the cholesteric phase of CE6/CE6R. The small oscillations are due to multiple reflections in the sample chamber, and the noise at the highest wavelengths is due to the decreasing sensitivity of the detector.

Figure 7

Chirality as a function of temperature in both the cholesteric and isotropic phases of CE6/CE6R as a function of reduced temperature, $(T-T_{\mathrm{c}})∕T_{\mathrm{c}}$ (closed circles). Data on the specific volume of 4OAB from [19] has been graphed for comparison (open circles). The three solid lines are fits of the modified Landau–de Gennes theory (different $q_0$ vs $S$ dependences) to the data as described in the text. The dashed curve is a fit of a general critical point theory to the data as also described in the text.