Higher-order director fluctuations

Abstract

Standard theories of the influence of a fluctuating director on spin relaxation in nematic liquid crystals are based on the notion that the mean-square angular displacement 〈θ²〉 of the director is small, such that terms of this and higher orders are negligible. One consequence of this ‘small-angle’ approximation is that director fluctuations contribute only to the spectral density J₁(ω₀) and not to J₂(2ω₀) or to J₀(0). In this paper the theory of director motion is extended to include terms of order 〈θ²〉. Second-order contributions are found for J₂(2ω₀) and J₀(0). No additional contributions to J₁(ω₀) occur, but it is shown that the order parameter which appears in formulae for all three spectral densities is that for molecular ordering relative to director-fixed axes rather than laboratory–fixed axes. By assuming Gaussian statistics for the fluctuating director, it is shown that the correlation function relevant for J₂(2ω₀) and J₀(0) is just the square of that used to calculate J₁(ω₀). Fourier-transformation of this new correlation function leads to an explicit formula for director fluctuation contributions to J₂(2ω₀) which is found to agree semiquantitatively with experimental data.