Isotropic to Nematic Transition of Aerosil-Disordered Liquid Crystals

We present a high-resolution study of the isotropic to nematic phase transition of a low birefringence liquid-crystal compound incorporating an aerosil gel. Calorimetry, light scattering, and microscopy data coherently combine to allow for an accurate determination of the temperature dependence of the onset of the nematic state. The nematic order develops on cooling through two distinct processes while the nematic correlation length mildly decreases. We understand the doubling of the phase transition as due to a crossover from a random-dilution regime, where the silica gel couples to the scalar part of the nematic order parameter, to a low-$T$ random-field regime, where the coupling induces distortions in the director field.

Figure 1

Excess specific heat $\Delta C_B$ (a) and turbidity $\tau$ [(b) left axis] measured as a function of the temperature shift $\Delta T$ within the two-phase coexistence region for the $\mathrm{L}\mathrm{C}+A$ ${\rho }_S=0.075$ sample. Also shown, the bulk birefringence squared $\Delta n^2$ [(b) right axis]: measured values (solid line) and linear extrapolation (dashed line). Inset: $\tau$ and $\Delta n^2$ over a wide $\Delta T$ range.

Figure 2

Upper left panel: nematic correlation length ${\xi }_N$ raw data (solid dot) and double scattering corrected (open dot) and $\Delta C_B$ (arbitrary scale) for the ${\rho }_S=0.075$ sample measured as a function of $\Delta T$. Panels (a)–(c): optical cross-polarized microscope pictures taken at a $\Delta T$ of $-0.033$ (a), $-0.07$ (b), and $-0.2\mathrm{K}$ (c) indicated by the vertical dotted lines in the upper left panel. The bar corresponds to $10\mu \mathrm{m}$.

Figure 3

Nematic volume fraction ${\varphi }_N$ obtained from the integral of $\Delta C_B(0.075)$ (solid dots) and deduced from optical measurements ${\varphi }_N\propto \tau /(\Delta n^2{\xi }_N)$ (open dots) as a function of $\Delta T$ through the two-phase coexistence region. Inset: $N$ volume fraction ${\varphi }_{N2}$ converted through the low temperature $C_P$ peak, as a function of ${\rho }_S$.

Figure 4

Proposed interpretation. (a) Model (continuous line) and $\Delta C_B$ (full dots) versus $\Delta T$ for the ${\rho }_S=0.075$ sample. (b) Distribution of transition temperatures $\Delta T$ within the two-phase coexistence region (solid line) versus disorder density $({\rho }_S)$ crossing over from random-dilution effects (dashed line) to random-field effects (dotted line). (c) Local density distribution versus disorder density which successfully reconstructs $\Delta C_B$.