Optical and electro-optical derivation of the pretransitional behavior of orientational and shear viscosities in the isotropic phase of liquid crystals

The pretransitional equilibrium properties of isotropic liquids in the proximity of the isotropic-nematic phase transition are well known and successfully modeled. Much less is known about the dynamic behavior, and in particular about the pretransitional viscosity. In this work we combine two techniques [dynamic light scattering (DLS) and electric birefringence spectroscopy (EBS)] offering complementary insights into both static and dynamic pretransitional behavior of the homologous $n\mathrm{CB}$ family ($n\text{−}\mathrm{alkyl}$ cyanobiphenyl). EBS explores the single molecule flipping dynamics retarded by a paranematic potential barrier and enables extracting the associated transport coefficient, which is found to be of Arrhenius type in the whole temperature range explored. DLS reflects the collective dynamics of correlated domains and depends on the viscous damping of the orientational order. Such a viscosity displays Arrhenius behavior only sufficiently far from the transition temperature, with deviations growing as a power law of the appropriate reduced temperature with exponents around 0.1.

Figure 1

Schematic Phase diagram of the $n\mathrm{CB}$ family.

Figure 2

Electrically induced birefringence $\mathrm{\Delta }n$ of 6CB measured at different frequencies as a function of the square of the electric field $E_0$. The continuous lines show the proportionality between $\mathrm{\Delta }n$ and $E_0^2$.

Figure 3

DC component of the Kerr constant $K_{\mathrm{dc}}$ of 8CB measured as a function of the frequency $\omega$ of the external electric field at different temperatures. Lines: best fit with the Debye equation (2).

Figure 4

Time dependence of the autocorrelation function $G_{2,VH}$ of the scattered light intensity in $VH$ configuration of 5CB at different temperatures. Lines: best fit with a monoexponential function.

Figure 5

(a) Inverse of the low frequency value of the birefringence $1∕K_0$ and (b) characteristic times ${\tau }_{\mathrm{EB}}$ measured as a function of the temperature for the $n\mathrm{CB}$ family. Lines: best linear fit from which the divergence temperature $T_{\mathrm{EB}}^{*}$ is obtained.

Figure 6

(a) Ratio of the temperature and the intensity of the scattered light (a) $T∕I_{VV}$ and (b) $T∕I_{VH}$ measured as a function of the temperature. The lines represent the best linear fit to the high temperature data.

Figure 7

Arrhenius plot of the viscosity ${\eta }_{\mathrm{EB}}$ extracted from EBS data for the $n\mathrm{CB}$ family studied. Line: linear fit curves.

Figure 8

Characteristic time (a) ${\tau }_{VV}$ and (b) ${\tau }_{VH}$ measured as a function of the temperature for the $n\mathrm{CB}$s studied.

Figure 9

Arrhenius plot of the orientational viscosities ${\nu }_{VV}$ and ${\nu }_{VH}$ as obtained from DLS experiments in both (a) $VV$ and (b) $VH$ configurations. Lines correspond to the high temperature Arrhenius law.

Figure 10

Critical viscosity ${\nu }_{\mathrm{crit}VV,VH}$ as a function of the reduced temperature $\frac{T-T^{*}}{T^{*}}$ extracted from the low temperature DLS data of Fig. 9. (a) Data from $VV$ and (b) data from $VH$ experiments. Lines correspond to a power law with the exponent $z_{\eta }\approx 0.1$.

Figure 11

(a) Normalized dielectric constant ${\epsilon }^{\prime }$ (data from Ref. 31) and normalized Kerr constant $K_{\mathrm{dc}}$ for 8CB at 41.5 C. Dashed line is the best Debye fitting curve to the dielectric spectra. Solid line is the prediction of the droplet model for the Kerr constant. (b) Arrhenius plot of the characteristic frequency of the dielectric relaxation (${\omega }_{\epsilon }$, full symbols) in the isotropic and nematic phases (data from Ref. 31) and of EBS relaxation (${\omega }_{\mathrm{EB}}=1∕{\tau }_{\mathrm{EB}}$, open symbols, data from Fig. 5). Data taken for 8CB.