Dynamic critical behavior in nematic liquid crystals above the nematic-isotropic transition

Using the temperature and frequency dependences of proton relaxation rates in $p$-methoxybenzylidene $p-n$ butylaniline (MBBA), measured in the temperature range of 316.2-350 K and the frequency range of 4-20 MHz, we confirm the necessity of considering critical fluctuations (CF) in two parts—"local" and "nonlocal" as envisaged in a recent theoretical study—characterized by their corresponding correlation times ${\tau }_{\mathrm{CFL}}$ and ${\tau }_{\mathrm{CFN}}$. Both ${\tau }_{\mathrm{CFL}}$ and ${\tau }_{\mathrm{CFN}}$ have also been determined at different temperatures. In such determinations, use has been made of the critical index for ${\tau }_{\mathrm{CFL}}$, the same as observed in light scattering experiments, and our ${\tau }_{\mathrm{CFL}}$ is in reasonable agreement with these results. Like ${\tau }_{\mathrm{CFL}}$, ${\tau }_{\mathrm{CFN}}$ also shows critical behavior but with a slightly higher index. The magnitude of ${\tau }_{\mathrm{CFN}}$ is also appreciably larger than ${\tau }_{\mathrm{CFL}}$ at the same temperature. These observed differences between ${\tau }_{\mathrm{CFL}}$ and ${\tau }_{\mathrm{CFN}}$, and the behavior of nuclear relaxation rate ${\left(T_1\right)}_{\mathrm{CFL}}^{-1\mathrm{}}$ at $T^{*}$ predicted by the Landau-de Gennes theory suggest strongly a close similarity between the nematic-isotropic (NI) transition and the Bose-Einstein condensation; $T^{*}$ is the apparent critical temperature if the IN transition were continuous.