Three-dimensional soliton-like distortions in flexoelectric nematic liquid crystals: modelling and linear analysis

Ashley Earls, M. Carme Calderer

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


This article models experimentally observed three-dimensional particle-like waves that develop in nematic liquid crystals, with negative dielectric and conductive anisotropy, when subject to an applied alternating electric field. The liquid crystal is confined in a thin region between two plates, perpendicular to the applied field. The horizontal, uniformly aligned director field is at equilibrium due to the negative anisotropy of the media. However, such a state is unstable to perturbations that manifest themselves as confined, bullet-like, director distortions travelling up and down the sample at a speed of several hundred microns per second. It is experimentally predicted that flexoelectricity plays a key role in generating the soliton-like behaviour. We develop a variational model that accounts for ansiostropic dielectric, conductive, flexolectric, elastic and viscous forces. We perform a stability analysis of the uniformly aligned equilibrium state to determine the threshold wave numbers, size, phase-shift and speed of the soliton-like disturbance. We show that the model predictions are in very good agreement with the experimentally measured values. The work models and analyzes a three-dimensional soliton-like instability reported, for the first time in flexoelectric liquid crystals, pointing towards a potential application as a new type of nanotransport device.

Original languageEnglish (US)
Pages (from-to)742-757
Number of pages16
JournalLiquid Crystals
Issue number5
StatePublished - 2022

Bibliographical note

Funding Information:
The authors gratefully knowledge the support of the National Science Foundation trhough the grant DMS-DMREF 1729589. The authors want to express their gratitude to Professor Oleg Lavrentovich for the many discussions and the sharing of experimental results, and to Professor Dmitry Golovaty for his helpful comments.

Publisher Copyright:
© 2022 Informa UK Limited, trading as Taylor & Francis Group.


  • Negative dielectric and conducting anisotropy
  • flexoelectricity
  • soliton-like wave
  • unstability


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