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.