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Pair correlation functions and a free energy functional for the nematic phase
Pankaj Mishra1, Swarn Lata Singh, Jokhan Ram
1Department of Physics, Banaras Hindu University, Varanasi-221 005, India.
The Journal of Chemical Physics
|August 4, 2007
Summary
This study calculates pair correlation functions for spherical particles in a nematic phase using mean spherical approximation (MSA) and Percus-Yevick (PY) theories. Both theories predict a long-range tail in the pair correlation function, essential for describing nematic phase properties.
Area of Science:
- Statistical Mechanics
- Soft Matter Physics
- Liquid Crystals
Background:
- Understanding the behavior of particles with long-range anisotropic interactions is crucial in liquid crystal physics.
- Pair correlation functions are fundamental for characterizing the structure and properties of condensed phases.
- Previous analytical work provides a basis for comparison in integral equation theories.
Purpose of the Study:
- To calculate pair correlation functions for a model of spherical particles with long-range anisotropic interactions.
- To investigate the applicability of mean spherical approximation (MSA) and Percus-Yevick (PY) integral equation theories.
- To study the properties of the nematic phase using free energy functionals and locate the isotropic-nematic transition.
Main Methods:
- Calculation of pair correlation functions using MSA and PY integral equation theories.
- Comparison of MSA results with existing analytical solutions.
- Development and application of free energy functionals incorporating direct pair correlation functions.
- Determination of the isotropic-nematic transition via grand thermodynamic potential.
Main Results:
- Both MSA and PY theories successfully predict a nematic phase with desired pair correlation function features.
- A long-range tail in the harmonic coefficient of the total pair correlation function was observed, consistent with theoretical expectations for director transverse fluctuations.
- A simplified free energy functional using the principal order parameter showed good agreement with the original functional.
Conclusions:
- MSA and PY theories are effective tools for studying the pair correlation functions in nematic phases of anisotropic systems.
- The observed long-range tail in the pair correlation function confirms theoretical predictions for director transverse fluctuations.
- Simplified free energy functionals can accurately represent nematic phase properties, aiding further theoretical investigations.
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