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Onsager's missing steps retraced.

Peter Palffy-Muhoray1, Epifanio G Virga2, Xiaoyu Zheng3

  • 1Liquid Crystal Institute, Kent State University, OH, United States of America.

Journal of Physics. Condensed Matter : an Institute of Physics Journal
|October 18, 2017
PubMed
Summary

Onsager

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Area of Science:

  • Colloidal science
  • Soft matter physics
  • Liquid crystal theory

Background:

  • Onsager's theory is a foundational work for understanding phase transitions in anisotropic colloidal systems.
  • The original derivation has limitations regarding its applicability at realistic number densities.

Purpose of the Study:

  • To rigorously re-evaluate the validity of Onsager's theory for lyotropic liquid crystals.
  • To propose a corrected theoretical framework applicable to realistic system densities.

Main Methods:

  • Application of Penrose's tree identity.
  • Development of a modified mean-field approach.
  • Analysis of purely repulsive, hard-core interactions.

Main Results:

  • Onsager's theory is rigorously valid only for extremely low number densities.
  • The proposed theory extends the validity of Onsager's findings to a reasonable range of densities.
  • The corrected theory accurately describes phase transition and coexistence phenomena.

Conclusions:

  • Onsager's seminal work requires modification for practical applications in lyotropic liquid crystals.
  • The new theoretical approach provides a more robust framework for studying colloidal systems.
  • This research offers a refined understanding of phase behavior in anisotropic colloidal systems.

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