Light-scattering measurement of the nematic correlation length in a liquid crystal with quenched disorder

We have studied a composite system formed by a nematic thermotropic liquid crystal in which small silica particles have been dispersed. The colloids are aggregated and exert a randomizing effect on the nematic structure. The distorted pattern of the optical axis gives rise to a strong optical turbidity τ. We have measured τ as a function of the silica concentration Φ and of the temperature $T$ in both the isotropic and nematic phase. We have found that, at fixed $T,$ τ has a maximum as a function of Φ, and that, upon changing Φ, the whole shape of $\tau \mathrm{}\left(T\right)\mathrm{}$ drastically transforms. We have devised a model to describe the scattering of light from a distorted uniaxial system. The model has been developed both in the Born approximation and in the anomalous diffraction approximation, the two regimes which cover the broad range of experimental conditions. The family of $\tau \mathrm{}\left(T\right)\mathrm{}$ curves experimentally obtained at different Φ’s is remarkably well described by the theoretical model, using as the only fitting parameter the correlation length ζ. We have found that, upon decreasing Φ, the nematic correlation length diverges as a power law of Φ. We compare the exponent of the power law with the prediction of the Imry-Ma theory of phase behavior in disordered systems, and we discuss the connection between ζ and the fractal correlation length of the silica aggregates.