From microscopic theory to macroscopic theory symmetries and order parameters of rigid molecules

Density functional theory is used to describe the phase behaviors of rigid molecules. The construc- tion of the kernel function is discussed. Excluded-volume potential is calculated for two types of molecules with C2v symmetry. Molecular symmetries lead to the symmetries of the kernel function and t...

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Bibliographic Details
Published inScience China. Mathematics Vol. 57; no. 3; pp. 443 - 468
Main Authors Xu, Jie, Zhang, PingWen
Format Journal Article
LanguageEnglish
Published Heidelberg Science China Press 01.03.2014
Subjects
Applications of Mathematics
Approximation
Density
Functions (mathematics)
Kernel functions
Mathematical analysis
Mathematics
Mathematics and Statistics
Order parameters
Polynomials
Symmetry
分子对称性
刚性
命令参数
宏观
密度泛函理论
序参量
微观理论
核函数
bent-core molecules
excluded volume
symmetry
76A15
order parameter
liquid crystals
82D30
Online AccessGet full text
ISSN1674-7283
1869-1862
DOI10.1007/s11425-013-4761-3

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Summary:Density functional theory is used to describe the phase behaviors of rigid molecules. The construc- tion of the kernel function is discussed. Excluded-volume potential is calculated for two types of molecules with C2v symmetry. Molecular symmetries lead to the symmetries of the kernel function and the density function, enabling a reduction of configuration space. By approximating the kernel function with a polynomial, the system can be fully characterized by some moments corresponding to the form of the kernel function. The symmetries of the kernel function determine the form of the polynomial, while the coefficients are determined by the tem- perature and molecular parameters. The analysis of the impact of coefficients helps us to choose independent variables in the moments as order parameters. Combining the analysis and some simulation results, we propose a minimal set of order parameters for bent-core molecules.
Bibliography:Density functional theory is used to describe the phase behaviors of rigid molecules. The construc- tion of the kernel function is discussed. Excluded-volume potential is calculated for two types of molecules with C2v symmetry. Molecular symmetries lead to the symmetries of the kernel function and the density function, enabling a reduction of configuration space. By approximating the kernel function with a polynomial, the system can be fully characterized by some moments corresponding to the form of the kernel function. The symmetries of the kernel function determine the form of the polynomial, while the coefficients are determined by the tem- perature and molecular parameters. The analysis of the impact of coefficients helps us to choose independent variables in the moments as order parameters. Combining the analysis and some simulation results, we propose a minimal set of order parameters for bent-core molecules.
liquid crystals, symmetry, order parameter, bent-core molecules, excluded volume
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ISSN:1674-7283
1869-1862
DOI:10.1007/s11425-013-4761-3