In eight quadrants,the positive and negative signs of tensor components describing physical properties of biaxial crystals have been given.The distributions of the physical properties described with different order te...In eight quadrants,the positive and negative signs of tensor components describing physical properties of biaxial crystals have been given.The distributions of the physical properties described with different order tensors and their space symmetries have been discussed.These results show that the distributions of effective physical constants are symmetrical in the eight quadrants for the orthorhombic system,but there are two and four kinds of distributions for monoclinic and triclinic systems respectively.Thence,to avoid ambiguities and difficulties in characterizing and applying properties of biaxial crystals,we suggest that the really positive directions of the coordinate axes should be defined before the measurements of their physical properties and their device applications.展开更多
In this paper,a rotational invariant of interaction energy between two biaxial-shaped molecules is assumed and in the mean field approximation,nine elastic constants for simple distortion patterns in biaxial nematics ...In this paper,a rotational invariant of interaction energy between two biaxial-shaped molecules is assumed and in the mean field approximation,nine elastic constants for simple distortion patterns in biaxial nematics are derived in terms of the thermal average D (l) mn D (l ') m ' n ',where D (l) mn is the Wigner rotation matrix.In the lowest order terms,the elastic constants depend on coefficients Γ,Γ ',λ,order parameters ˉ Q 0=Q 0 D (2) 00 + Q 2 D (2) 02 + D (2) 0 2 and ˉ Q 2=Q 0 D (2) 20 + Q 2 D (2) 22 + D (2) 2 2.Here Γ and Γ ' depend on the function form of molecular interaction energy vj ' j '' j (r 12) and probability function fk ' k '' k (r 12),where r 12 is the distance between two molecules,and λ is proportional to temperature.Q 0 and Q 2 are parameters related to multiple moments of molecules.Comparing these results with those obtained from Landau-de Gennes theory,we have obtained relationships between coefficients,order parameters used in both theories.In the special case of uniaxial nematics,both results are reduced to a degenerate case where K 11=K 33.展开更多
基金Project supported by the National Key Research and Development Program of China(Grant No.2016YFB1102201)the 111 Project 2.0(Grant No.BP2018013)+3 种基金the National Natural Science Foundation of China(Grant Nos.51772170,51572155,and 11504389)the Shandong Provincial Key R&D Program,China(Grant No.2018CXGC0411)the Young Scholars Program(Grant No.2018WLJH67)the Fundamental Research Founds of Shandong University(Grant No.2017JC044)。
文摘In eight quadrants,the positive and negative signs of tensor components describing physical properties of biaxial crystals have been given.The distributions of the physical properties described with different order tensors and their space symmetries have been discussed.These results show that the distributions of effective physical constants are symmetrical in the eight quadrants for the orthorhombic system,but there are two and four kinds of distributions for monoclinic and triclinic systems respectively.Thence,to avoid ambiguities and difficulties in characterizing and applying properties of biaxial crystals,we suggest that the really positive directions of the coordinate axes should be defined before the measurements of their physical properties and their device applications.
基金The project supported by the Natural Science Foundation of Liaoning Province under Grant＇ No. 20041021, the Scientific Research Foundation of the Educational Department of Liaoning Province under Grant No. 2004C006, and National Natural Science Foundation of China under Grant No. 50477049.
基金Project supported by the Natural Science Foundation of the Jiangsu Higher Education Institutions of China(Grant No07JKD140095)
文摘In this paper,a rotational invariant of interaction energy between two biaxial-shaped molecules is assumed and in the mean field approximation,nine elastic constants for simple distortion patterns in biaxial nematics are derived in terms of the thermal average D (l) mn D (l ') m ' n ',where D (l) mn is the Wigner rotation matrix.In the lowest order terms,the elastic constants depend on coefficients Γ,Γ ',λ,order parameters ˉ Q 0=Q 0 D (2) 00 + Q 2 D (2) 02 + D (2) 0 2 and ˉ Q 2=Q 0 D (2) 20 + Q 2 D (2) 22 + D (2) 2 2.Here Γ and Γ ' depend on the function form of molecular interaction energy vj ' j '' j (r 12) and probability function fk ' k '' k (r 12),where r 12 is the distance between two molecules,and λ is proportional to temperature.Q 0 and Q 2 are parameters related to multiple moments of molecules.Comparing these results with those obtained from Landau-de Gennes theory,we have obtained relationships between coefficients,order parameters used in both theories.In the special case of uniaxial nematics,both results are reduced to a degenerate case where K 11=K 33.
