Effect of silica aerosils on the nematic to isotropic transition: A theoretical treatment

The effect of silica aerosils on a first-order nematic-isotropic (NI) transition temperature shift ΔTNI(ρₛ) and on the enthalpy jump ΔH(ρₛ) is phenomenologically described in the framework of the Landau--de Gennes theory. It is shown that the aerosil network dispersed in the liquid crystal phase creates an additional curvature perturbation, resulting in linear and nonlinear slopes both in the transition temperature shift ΔTNI(ρₛ)=-TNI(0)αρₛ and in the enthalpy jump ${Δ}H({{ρ}}ₛ)=1/4{Δ}H(0)(1+√{1{-}{κ}{{ρ}}ₛ}{)}²(1{-}{α}{{ρ}}ₛ),$ where ${{ρ}}ₛ$ is the aerosil density, and both ${α}$ and ${κ}$ are constants of the theory. In the low ${{ρ}}ₛ(<~0.2{g/cm}³)$ regime, both the calculated and the measured values of ${Δ}H({{ρ}}ₛ)$ for polar liquid crystals, such as $4$-$n$-octyl-${4}^{{'}}$-cyanobiphenyl (8CB) and $4$-$n$-heptyl-${4}^{{'}}$-cyanobiphenyl (7CB) show a good agreement between theory and experiment. The comparisons between the calculated and measured values of ${Δ}{T}NI({{ρ}}ₛ),$ in the low-${{ρ}}ₛ$ regime, show a better agreement in the 7CB+aerosil than in the 8CB+aerosil systems.