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Relation of system dimensionality and order parameters.

Bruce H Robinson1, Lewis E Johnson, Bruce E Eichinger

  • 1Department of Chemistry, University of Washington , Seattle, Washington 98195-1700, United States.

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|January 31, 2015
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Summary

Fractional dimensionality offers a novel way to analyze molecular ordering. This method effectively relates centrosymmetric and acentric order parameters in complex materials like liquid crystals.

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Area of Science:

  • Materials Science
  • Statistical Mechanics
  • Physical Chemistry

Background:

  • Orientational order parameters quantify molecular orientation distributions (e.g., dipole moment, optical axis) in materials like liquid crystals.
  • Centrosymmetric moments describe typical ordering, but external fields induce acentric moments, complicating analysis in complex systems.

Purpose of the Study:

  • To develop a method for characterizing the relationship between centrosymmetric and acentric orientational order parameters.
  • To introduce the concept of noninteger dimensionality for analyzing molecular ordering processes.

Main Methods:

  • Utilized the concept of noninteger dimensionality, originally proposed by Stillinger.
  • Applied dimensional constraints, equivalent to restricting rotational degrees of freedom.
  • Performed simulations on independent dipoles with restoring potentials and Monte Carlo simulations of dipolar spheroids.

Main Results:

  • Demonstrated that fractional dimensionality provides a useful framework to relate different types of orientational order parameters.
  • Showcased the equivalence of applying dimensional constraints to removing rotational freedom or restricting volume.
  • Validated the approach through simulations of both simple and complex molecular systems.

Conclusions:

  • Fractional dimensionality is a powerful tool for understanding and quantifying molecular ordering in materials.
  • This approach offers new insights into the complex interplay between different orientational moments.
  • The method has broad applicability for analyzing ordering phenomena in diverse materials.