Topological defects and the short-distance behavior of the structure factor in nematic liquid crystals

TL;DR

This paper theoretically analyzes how topological defects influence the high-wave-vector scattering behavior in nematic liquid crystals, providing quantitative predictions for the Porod tail contributions and their experimental observability.

Contribution

It calculates defect-related Porod amplitudes and exponents in nematics and estimates the experimental range where defect contributions dominate scattering signals.

Findings

Defects cause power-law tails in the structure factor at large k.

The Porod tail extends over one to three decades in k for realistic defect densities.

Experimental data on phase ordering are consistent with the theoretical predictions.

Abstract

The scattering of light at large wave-vector magnitudes k in nematic systems containing topological defects is investigated theoretically. At large k the structure factor S(k) is dominated by power-law contributions originating from singular order-parameter variations associated with topological defects and from transverse thermal fluctuations of the nematic director. These defects (nematic disclinations and hedgehogs) lead to contributions of the form rho A k^{-xi} (``the Porod tail''), where rho is the number density of a given type of defect, A is a dimensionless Porod amplitude, and xi is an integer-valued Porod exponent. The Porod amplitudes and exponents are calculated for all types of topologically stable defects occurring in uniaxial and biaxial nematics in two or three spatial dimensions. The range of wave-vectors in which the contributions to the scattering intensity due to defects dominate the contribution due to thermal fluctuations is estimated, and it is concluded that for experimentally accessible defect densities the range of observability of the Porod tail extends over one to three decades in scattering wave-vector magnitude k. Available experimental results on phase ordering in uniaxial nematics are analyzed, and applications of our results are suggested for light-scattering studies of other nematic systems containing numerous defects.