In this paper,we are concerned with a three-dimensional non-isothermal model for the compressible nematic liquid crystal flows in a periodic domain.Under some smallness and structural assumptions imposed on the time-p...In this paper,we are concerned with a three-dimensional non-isothermal model for the compressible nematic liquid crystal flows in a periodic domain.Under some smallness and structural assumptions imposed on the time-periodic force,we establish the existence of the time-periodic solutions to the system by using a regularized approximation scheme and the topological degree theory.We also prove a uniqueness result via energy estimates.展开更多
In this paper,we establish some regularity conditions on the density and velocity fields to guarantee the energy conservation of the weak solutions for the three-dimensional compressible nematic liquid crystal flow in...In this paper,we establish some regularity conditions on the density and velocity fields to guarantee the energy conservation of the weak solutions for the three-dimensional compressible nematic liquid crystal flow in the periodic domain.展开更多
In this article, we prove the global existence of weak solutions to the non- isothermal nematic liquid crystal system on T2, on the basis of a new approximate system which is different from the classical Ginzburg-Land...In this article, we prove the global existence of weak solutions to the non- isothermal nematic liquid crystal system on T2, on the basis of a new approximate system which is different from the classical Ginzburg-Landau approximation. Local in space energy inequalities are employed to recover the estimates on the second order spatial derivatives of the director fields locally in time, which cannot be derived from the basic energy balance. It is shown that these weak solutions satisfy the temperature equation, and also the total energy equation but away from at most finite many "singular" times, at which the energy concentration occurs and the director field losses its second order derivatives.展开更多
A detailed theoretical analysis of determining the sum of flexoelectric coefficients in nematic liquid crystals using the capacitance method is given. In the strong anchoring parallel aligned nematic (PAN) and hybri...A detailed theoretical analysis of determining the sum of flexoelectric coefficients in nematic liquid crystals using the capacitance method is given. In the strong anchoring parallel aligned nematic (PAN) and hybrid aligned nematic (HAN) cells, the dependences of the capacitance on the sum of flexoelectric coefficients and the applied voltage are obtained by numerical simulations, and the distributions of the director and the electric potential for different applied voltages and flexoelectric coefficients are also given. Based on this theoretical analysis, we propose an experimental design for measuring the capacitance of a liquid crystal cell using the improved precision LCR meter E4980A (Agilent). Through comparing the experimental data with the simulated results, the sum of flexoeletric coefficients can be determined.展开更多
In this paper,we study a nematic liquid crystals system in three-dimensional whole space R3 and obtain the time decay rates of the higher-order spatial derivatives of the solution by the method of spectral analysis an...In this paper,we study a nematic liquid crystals system in three-dimensional whole space R3 and obtain the time decay rates of the higher-order spatial derivatives of the solution by the method of spectral analysis and energy estimates if the initial data belongs to L1(R3) additionally.展开更多
In this paper we derive LPS's criterion for the breakdown of classical solutions to the incompressible nematic liquid crystal flow, a simplified version of Ericksen-Leslie system modeling the hydrodynamic evolution o...In this paper we derive LPS's criterion for the breakdown of classical solutions to the incompressible nematic liquid crystal flow, a simplified version of Ericksen-Leslie system modeling the hydrodynamic evolution of nematic liquid crystals in R^3. We show that if 0 〈 T 〈 +∞ is the maximal time interval for the unique smooth solution u ∈ C^∞([0, T),R^3),then |u|+|△d|∈L^q([0,T],L^p(R^3)),where p and q satisfy the Ladyzhenskaya-Prodi-Serrin's condition:3/p+2/q=1 and p∈(3,+∞].展开更多
Temperature dependence of ratio between dielectric anisotropy and order parameter of fluorinated nematic liquid crystal is investigated by using a semi-empirical molecular orbital package that can accurately calculate...Temperature dependence of ratio between dielectric anisotropy and order parameter of fluorinated nematic liquid crystal is investigated by using a semi-empirical molecular orbital package that can accurately calculate an angle between molecular dipole moment and long axis. We optimize the molecular conformations with three semi-empirical Hamiltonians AM1, PM3 and PM5, and then make a comparison between computational results and experimental measurements. It is shown that the results obtained from AM1 method are in good agreement with the measurements. The present study offers an applicable method to predict the dielectric properties of liquid crystal material.展开更多
The disadvantages of Normally White Twisted Nematic Liquid Crystal Display (NW-TN-LCD) were discussed. The reason that the negative birefringent polyimide thin films were used to compensate NW-TN-LCD to decrease off-a...The disadvantages of Normally White Twisted Nematic Liquid Crystal Display (NW-TN-LCD) were discussed. The reason that the negative birefringent polyimide thin films were used to compensate NW-TN-LCD to decrease off-axis leakage, improve contrast ratios and enlarge viewing angles was explained in this paper. A certain polyimide thin film was taken as an example to show compensation effect on NW-TN-LCD.展开更多
This paper investigates the average dielectric permittivity (^-ε) in the Maier-Meier theory for calculating the dielectric anisotropy (△ε) of nematic liquid crystals.For the reason that ^-ε of nematics has the...This paper investigates the average dielectric permittivity (^-ε) in the Maier-Meier theory for calculating the dielectric anisotropy (△ε) of nematic liquid crystals.For the reason that ^-ε of nematics has the same expression as the dielectric permittivity of the isotropic state,the Onsager equation for isotropic dielectric was used to calculate it.The computed ^-ε shows reasonable agreement with the results of the numerical methods used in the literature.Molecular parameters,such as the polarizability and its anisotropy,the dipole moment and its angle with the molecular long axis,were taken from semi-empirical quantum chemistry (MOCPAC/AM1) modeling.The calculated values of △ε according to the Maier-Meier equation are in good agreement with the experimental results for the investigated compounds having different core structures and polar substituents.展开更多
We develop a microscopic theory of the nematic phase with consideration of the effect of the collective excitation on properties of nematic liquid crystals. The model is based on the Heisenberg's exchange model of th...We develop a microscopic theory of the nematic phase with consideration of the effect of the collective excitation on properties of nematic liquid crystals. The model is based on the Heisenberg's exchange model of the ferromagnetic materials. Since the orientation of the molecular long axis and the angular momentum of the molecule rotating around its long axis have the same direction, operators can be introduced to research the nematic liquid crystals. Using the lattice model and the Holstein-Primakoff transformation, the Hamiltonian of the system can be obtained, which has the same form as that of the ferromagnetic substance. The relation between the order parameter and reduced temperature can be gotten. It is in good agreement with the experimental results in the low temperature region, the accordance is better than that of the molecular field theory and the computer simulation. In high temperature region close to the transition point, by considering the effect of the higher-order terms in the Hamiltonian, theoretical prediction is in better agreement with the experiment. That indicates the many-body effect is important to nematic liquid crystals.展开更多
In this paper, we consider the short time classical solution to a simplified hydro-dynamic flow modeling incompressible, nematic liquid crystal materials in R3. We establisha criterion for possible breakdown of such s...In this paper, we consider the short time classical solution to a simplified hydro-dynamic flow modeling incompressible, nematic liquid crystal materials in R3. We establisha criterion for possible breakdown of such solutions at a finite time. More precisely, if (u, d)is smooth up to time T provided that ∫T 0‖△×u(t, ·)‖BMO(R3) +‖△d(t, ·)‖8L4(R3)dt 〈∞.展开更多
Basea on the new model and concept of mtramolecular orientational order parameter, a molecular field theory was built up for main chain liquid crystalline polymer (MC-LCPs) with flexible spacers. The theory takes acco...Basea on the new model and concept of mtramolecular orientational order parameter, a molecular field theory was built up for main chain liquid crystalline polymer (MC-LCPs) with flexible spacers. The theory takes account of orientational correlation among all mesogens in a polymer chain and the relationship between the intramolecular orientation and spatial orientation of the mesogens. The free energy, temperature and entropy of the nematic-isotropic transition were determined with the theory and compared with experiments in current work. It was found that many unique transition properties of the MC-LCPs comprising flexible spacer are correctly predicted by the theory and the agreement of the theory with the experiments is impressive.展开更多
A new scheme for recording a dynamic phase grating with an asymmetric profile in C60-doped homeotropically aligned nematic liquid crystal(NLC) was presented.An oblique incidence beam was used to record the thin asym...A new scheme for recording a dynamic phase grating with an asymmetric profile in C60-doped homeotropically aligned nematic liquid crystal(NLC) was presented.An oblique incidence beam was used to record the thin asymmetric dynamic phase holographic grating.The diffraction efficiency we achieved is more than 40%,exceeding the theoretical limit for symmetric profile gratings.Both facts can be explained by assuming that a grating with an asymmetric saw-tooth profile is formed in the NLC.Finally,physical mechanism and mathematical model for characterizing the asymmetric phase holographic grating were presented,based on the photo-refractive-like(PR-like) effect.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 nematic...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 (Dmn^(l)) (Dm'n'^(l')), where Dmn^(l) is the Wigner rotation matrix. In the lowest order terms, the elastic constants depend on coefficients Γ,Γ', λ, order parameters Q0 = Q0(D00^(2)) +Q2(D02^(2)+D0-2^(2)) and Q2 = Q0(D20^(2)) + Q2(D22^(2)+D2-2^(2)). Here Γ and Γ' depend on the function form of molecular interaction energy vj′j″j (τ12) and probability function fk′k″k (τ12), where r12 is the distance between two molecules, and λ is proportional to temperature. Q0 and Q2 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 K11=K33.展开更多
Fully atomistic molecular dynamics (MD) simulations at 293, 303 and 313 K have been performed for the four- component liquid crystal mixture, E7, using the software package Material Studio. Order parameters and orie...Fully atomistic molecular dynamics (MD) simulations at 293, 303 and 313 K have been performed for the four- component liquid crystal mixture, E7, using the software package Material Studio. Order parameters and orientational time correlation functions (TCFs) were calculated from MD trajectories. The rotational viscosity coefficients (RVCs) of the mixture were calculated using the Nemtsov-Zakharov and Fialkowski methods based on statistical-mechanical approaches. Temperature dependences of RVC and density were discussed in detail. Reasonable agreement between the simulated and experimental values was found.展开更多
The influences of an external magnetic field on the optical properties of the TEB30A nematic liquid crystal doped with thulium oxides (Gd203, Dy203, Nd203, Y203, and Sm203) are studied. It is shown that a magnetic f...The influences of an external magnetic field on the optical properties of the TEB30A nematic liquid crystal doped with thulium oxides (Gd203, Dy203, Nd203, Y203, and Sm203) are studied. It is shown that a magnetic field applied parallelly to the sample cell surface leads to the rotational orientation of mesogenes. All samples except for the sample doped with Sm203 nanoparticles undergo structural deformations. The behavior of the TEB30A/Sm203 differs from those of the TEB30A liquid crystal doped with other four nanoparticles. The presence of Sm203 nanoparticles in the TEB30A liquid crystal does not cause the structural deformation of the liquid crystal matrix. At the same time, the anchoring type of the liquid crystal molecules on the nanoparticle surface is different. The director n is parallel to the magnetic moment/~ in the TEB30A/Sm203, and inclined to the magnetic moment/~ in the TEB30A/Nd203, and perpendicular to the magnetic moment/~ in each of TEB30A/Gd203, TEB30A/Dy203, and TEB30A/Y203. Besides, the dependence of the structural deformation on the critical magnetic field for the TEB30A is obtained.展开更多
In this paper,we investigate the effects of kinematic transports on the nematic liquid crystal system numerically and theoretically.The model we used is a"1+2"elastic continuum model simplified from the Eric...In this paper,we investigate the effects of kinematic transports on the nematic liquid crystal system numerically and theoretically.The model we used is a"1+2"elastic continuum model simplified from the Ericksen-Leslie system.The numerical experiments are carried out by using a Legendre-Galerkin spectral method which can preserve the energy law in the discrete form.Based on this highly accurate numerical approach we find some interesting and important relationships between the kinematic transports and the characteristics of the flow.We make some analysis to explain these results.Several significant scaling properties are also verified by our simulations.展开更多
Here we investigate the kinematic transports of the defects in the nematic liquid crystal system by numerical experiments.The model is a shear flow case of the viscoelastic continuummodel simplified fromthe Ericksen-L...Here we investigate the kinematic transports of the defects in the nematic liquid crystal system by numerical experiments.The model is a shear flow case of the viscoelastic continuummodel simplified fromthe Ericksen-Leslie system.The numerical experiments are carried out by using a differencemethod.Based on these numerical experiments we find some interesting and important relationships between the kinematic transports and the characteristics of the flow.We present the development and interaction of the defects.These results are partly consistent with the observation from the experiments.Thus this scheme illustrates,to some extent,the kinematic effects of the defects.展开更多
In this paper, we investigate the global existence and long time behavior of strong solutions for compressible nematic liquid crystal flows in threedimensional whole space. The global existence of strong solutions is ...In this paper, we investigate the global existence and long time behavior of strong solutions for compressible nematic liquid crystal flows in threedimensional whole space. The global existence of strong solutions is obtained by the standard energy method under the condition that the initial data are close to the constant equilibrium state in H2-framework. If the initial datas in Ll-norm are finite additionally, the optimal time decay rates of strong solutions are established. With the help of Fourier splitting method, one also establishes optimal time decay rates for the higher order spatial derivatives of director.展开更多
The approaches to obtaining desired intensity or phase modulation by twisted-nematic liquid crystal display (TN-LCD) have been extensively studied based on the knowledge of the LCD's internal structure parameters. ...The approaches to obtaining desired intensity or phase modulation by twisted-nematic liquid crystal display (TN-LCD) have been extensively studied based on the knowledge of the LCD's internal structure parameters. Generally, the TN-LCD placed between two linear polarizers (P) produces coupled intensity and phase modulation. To obtain the commonly used phase-only modulation, quarter wave plates (QWPs) are often used in front of and/or behind the LCD. Here we present a method to optimize the optical modulation properties of the TN-LCD to obtain phase-only modulation in the configuration of P-QWP-LCD-QWP-P each with proper orientation. Our method is based on the macroscopical Jones matrix descriptions for the LCD, the QWPs, and the linear polarizers. Through Jones matrix calculations, the orientations of the polarizers and QWPs can be optimized to satisfy differently desired modulation demands. In contrast to the traditional method, which requires knowledge of the LCD's internal structure parameters, our method simplified the complicated theory analysis and can work in the absence of information on the LCD's internal structure parameters, which are usually not available for the commercial products.展开更多
基金partially supported by the Science and Technology Research Program of Chongqing Municipal Education Commission(KJQN202100523,KJQN202000536)the National Natural Science Foundation of China(12001074)+3 种基金the Natural Science Foundation of Chongqing(cstc2020jcyj-msxmX0606)supported by the National Natural Science Foundation of Chongqing(CSTB2023NSCQ-MSX0278)the Science and Technology Research Program of Chongqing Municipal Education Commission(KJZD-K202100503)the Research Project of Chongqing Education Commission(CXQT21014)。
文摘In this paper,we are concerned with a three-dimensional non-isothermal model for the compressible nematic liquid crystal flows in a periodic domain.Under some smallness and structural assumptions imposed on the time-periodic force,we establish the existence of the time-periodic solutions to the system by using a regularized approximation scheme and the topological degree theory.We also prove a uniqueness result via energy estimates.
基金support by the NSFC(12071391,12231016)the Guangdong Basic and Applied Basic Research Foundation(2022A1515010860)support by the China Postdoctoral Science Foundation(2023M742401)。
文摘In this paper,we establish some regularity conditions on the density and velocity fields to guarantee the energy conservation of the weak solutions for the three-dimensional compressible nematic liquid crystal flow in the periodic domain.
基金Hong Kong RGC Earmarked Research Grants 14305315,CUHK4041/11P and CUHK4048/13PThe Chinese University of Hong Kong,a Croucher Foundation-CAS Joint Grant,and a NSFC/RGC Joint Research Scheme(N-CUHK443/14)
文摘In this article, we prove the global existence of weak solutions to the non- isothermal nematic liquid crystal system on T2, on the basis of a new approximate system which is different from the classical Ginzburg-Landau approximation. Local in space energy inequalities are employed to recover the estimates on the second order spatial derivatives of the director fields locally in time, which cannot be derived from the basic energy balance. It is shown that these weak solutions satisfy the temperature equation, and also the total energy equation but away from at most finite many "singular" times, at which the energy concentration occurs and the director field losses its second order derivatives.
基金supported by the National Natural Science Foundation of China(Grant Nos.11274088,11374087,and 11304074)the Natural Science Foundation of Hebei Province,China(Grant No.A2014202123)+2 种基金the Research Project of Hebei Education Department,China(Grant Nos.Z2012061 and QN2014130)the Science and Technology Plan Project of Hebei Province,China(Grant No.134576260)the Key Subject Construction Project of Hebei Province University,China
文摘A detailed theoretical analysis of determining the sum of flexoelectric coefficients in nematic liquid crystals using the capacitance method is given. In the strong anchoring parallel aligned nematic (PAN) and hybrid aligned nematic (HAN) cells, the dependences of the capacitance on the sum of flexoelectric coefficients and the applied voltage are obtained by numerical simulations, and the distributions of the director and the electric potential for different applied voltages and flexoelectric coefficients are also given. Based on this theoretical analysis, we propose an experimental design for measuring the capacitance of a liquid crystal cell using the improved precision LCR meter E4980A (Agilent). Through comparing the experimental data with the simulated results, the sum of flexoeletric coefficients can be determined.
基金supported by NNSFC(11271381and 11501373)China 973 Program(2011CB808002)+5 种基金the Natural Science Foundation of Guangdong Province(2016A0300310019 and 2016A030307042)Guangdong Provincial culture of seedling of China(2013LYM0081)the Education research platform project of Guangdong Province(2014KQNCX208)the Education Reform Project of Guangdong Province(2015558)the Shaoguan Science and Technology Foundation(20157201)Education Reform Project of Shaoguan University(SYJY20121361 and SYJY20141576)
文摘In this paper,we study a nematic liquid crystals system in three-dimensional whole space R3 and obtain the time decay rates of the higher-order spatial derivatives of the solution by the method of spectral analysis and energy estimates if the initial data belongs to L1(R3) additionally.
基金Supported by National Natural Science Foundation of China (10976026, 11271305, 11301439, 11226174)
文摘In this paper we derive LPS's criterion for the breakdown of classical solutions to the incompressible nematic liquid crystal flow, a simplified version of Ericksen-Leslie system modeling the hydrodynamic evolution of nematic liquid crystals in R^3. We show that if 0 〈 T 〈 +∞ is the maximal time interval for the unique smooth solution u ∈ C^∞([0, T),R^3),then |u|+|△d|∈L^q([0,T],L^p(R^3)),where p and q satisfy the Ladyzhenskaya-Prodi-Serrin's condition:3/p+2/q=1 and p∈(3,+∞].
基金Project supported by the National Natural Science Foundation of China (Grant No 60577050)
文摘Temperature dependence of ratio between dielectric anisotropy and order parameter of fluorinated nematic liquid crystal is investigated by using a semi-empirical molecular orbital package that can accurately calculate an angle between molecular dipole moment and long axis. We optimize the molecular conformations with three semi-empirical Hamiltonians AM1, PM3 and PM5, and then make a comparison between computational results and experimental measurements. It is shown that the results obtained from AM1 method are in good agreement with the measurements. The present study offers an applicable method to predict the dielectric properties of liquid crystal material.
基金Supported by’94 Outstanding Young Scientist Foundation of NSFC
文摘The disadvantages of Normally White Twisted Nematic Liquid Crystal Display (NW-TN-LCD) were discussed. The reason that the negative birefringent polyimide thin films were used to compensate NW-TN-LCD to decrease off-axis leakage, improve contrast ratios and enlarge viewing angles was explained in this paper. A certain polyimide thin film was taken as an example to show compensation effect on NW-TN-LCD.
基金Project supported by the National Natural Science Foundation of China (Grant Nos 60578035 and 60736042)the Science Foundation of Jilin Province of China (Grant Nos 20050520 and 20050321-2)
文摘This paper investigates the average dielectric permittivity (^-ε) in the Maier-Meier theory for calculating the dielectric anisotropy (△ε) of nematic liquid crystals.For the reason that ^-ε of nematics has the same expression as the dielectric permittivity of the isotropic state,the Onsager equation for isotropic dielectric was used to calculate it.The computed ^-ε shows reasonable agreement with the results of the numerical methods used in the literature.Molecular parameters,such as the polarizability and its anisotropy,the dipole moment and its angle with the molecular long axis,were taken from semi-empirical quantum chemistry (MOCPAC/AM1) modeling.The calculated values of △ε according to the Maier-Meier equation are in good agreement with the experimental results for the investigated compounds having different core structures and polar substituents.
基金Project supported by the Hebei Natural Science Foundation, China (Grant No A2004000140) and the Natural Science Foundation of Hebei Educational Committee, China (Grant No 2003107).
文摘We develop a microscopic theory of the nematic phase with consideration of the effect of the collective excitation on properties of nematic liquid crystals. The model is based on the Heisenberg's exchange model of the ferromagnetic materials. Since the orientation of the molecular long axis and the angular momentum of the molecule rotating around its long axis have the same direction, operators can be introduced to research the nematic liquid crystals. Using the lattice model and the Holstein-Primakoff transformation, the Hamiltonian of the system can be obtained, which has the same form as that of the ferromagnetic substance. The relation between the order parameter and reduced temperature can be gotten. It is in good agreement with the experimental results in the low temperature region, the accordance is better than that of the molecular field theory and the computer simulation. In high temperature region close to the transition point, by considering the effect of the higher-order terms in the Hamiltonian, theoretical prediction is in better agreement with the experiment. That indicates the many-body effect is important to nematic liquid crystals.
基金supported by the Natural Science Key Foundation of Universities of Fujian Province(JZ160406)Natural Science Foundation of Fujian Province(2015J01582)
文摘In this paper, we consider the short time classical solution to a simplified hydro-dynamic flow modeling incompressible, nematic liquid crystal materials in R3. We establisha criterion for possible breakdown of such solutions at a finite time. More precisely, if (u, d)is smooth up to time T provided that ∫T 0‖△×u(t, ·)‖BMO(R3) +‖△d(t, ·)‖8L4(R3)dt 〈∞.
文摘Basea on the new model and concept of mtramolecular orientational order parameter, a molecular field theory was built up for main chain liquid crystalline polymer (MC-LCPs) with flexible spacers. The theory takes account of orientational correlation among all mesogens in a polymer chain and the relationship between the intramolecular orientation and spatial orientation of the mesogens. The free energy, temperature and entropy of the nematic-isotropic transition were determined with the theory and compared with experiments in current work. It was found that many unique transition properties of the MC-LCPs comprising flexible spacer are correctly predicted by the theory and the agreement of the theory with the experiments is impressive.
基金Project supported by the Science and Technology Programs of the Educational Committee of Heilongjiang Province,China(Grant No.12541730)the National Natural Science Foundation of China(Grant No.61405057)
文摘A new scheme for recording a dynamic phase grating with an asymmetric profile in C60-doped homeotropically aligned nematic liquid crystal(NLC) was presented.An oblique incidence beam was used to record the thin asymmetric dynamic phase holographic grating.The diffraction efficiency we achieved is more than 40%,exceeding the theoretical limit for symmetric profile gratings.Both facts can be explained by assuming that a grating with an asymmetric saw-tooth profile is formed in the NLC.Finally,physical mechanism and mathematical model for characterizing the asymmetric phase holographic grating were presented,based on the photo-refractive-like(PR-like) effect.
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 (Dmn^(l)) (Dm'n'^(l')), where Dmn^(l) is the Wigner rotation matrix. In the lowest order terms, the elastic constants depend on coefficients Γ,Γ', λ, order parameters Q0 = Q0(D00^(2)) +Q2(D02^(2)+D0-2^(2)) and Q2 = Q0(D20^(2)) + Q2(D22^(2)+D2-2^(2)). Here Γ and Γ' depend on the function form of molecular interaction energy vj′j″j (τ12) and probability function fk′k″k (τ12), where r12 is the distance between two molecules, and λ is proportional to temperature. Q0 and Q2 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 K11=K33.
基金Project supported by the National Natural Science Foundation of China (Grant Nos 60578035 and 60736042)
文摘Fully atomistic molecular dynamics (MD) simulations at 293, 303 and 313 K have been performed for the four- component liquid crystal mixture, E7, using the software package Material Studio. Order parameters and orientational time correlation functions (TCFs) were calculated from MD trajectories. The rotational viscosity coefficients (RVCs) of the mixture were calculated using the Nemtsov-Zakharov and Fialkowski methods based on statistical-mechanical approaches. Temperature dependences of RVC and density were discussed in detail. Reasonable agreement between the simulated and experimental values was found.
基金Project supported by the National Natural Science Foundation of China(Grant No.50862007)the Natural Science Foundation of Inner Mongolia Autonomous Region,China(Grant No.20080404MS0114)the Inner Mongolia Autonomous Region Scientific Research Fund,China(Grant No.NJZY12203)
文摘The influences of an external magnetic field on the optical properties of the TEB30A nematic liquid crystal doped with thulium oxides (Gd203, Dy203, Nd203, Y203, and Sm203) are studied. It is shown that a magnetic field applied parallelly to the sample cell surface leads to the rotational orientation of mesogenes. All samples except for the sample doped with Sm203 nanoparticles undergo structural deformations. The behavior of the TEB30A/Sm203 differs from those of the TEB30A liquid crystal doped with other four nanoparticles. The presence of Sm203 nanoparticles in the TEB30A liquid crystal does not cause the structural deformation of the liquid crystal matrix. At the same time, the anchoring type of the liquid crystal molecules on the nanoparticle surface is different. The director n is parallel to the magnetic moment/~ in the TEB30A/Sm203, and inclined to the magnetic moment/~ in the TEB30A/Nd203, and perpendicular to the magnetic moment/~ in each of TEB30A/Gd203, TEB30A/Dy203, and TEB30A/Y203. Besides, the dependence of the structural deformation on the critical magnetic field for the TEB30A is obtained.
基金supported by NSF of China 10871028.Chun Liu is partially supported by NSF Grantssupported by NSF of China 10871028 and state key basic research project of China 2005CB321704.
文摘In this paper,we investigate the effects of kinematic transports on the nematic liquid crystal system numerically and theoretically.The model we used is a"1+2"elastic continuum model simplified from the Ericksen-Leslie system.The numerical experiments are carried out by using a Legendre-Galerkin spectral method which can preserve the energy law in the discrete form.Based on this highly accurate numerical approach we find some interesting and important relationships between the kinematic transports and the characteristics of the flow.We make some analysis to explain these results.Several significant scaling properties are also verified by our simulations.
基金We are grateful to Prof.Qiang Du of Pennsylvania State University and Dr.Yanzhi Zhang of Missouri University of Science and Technology for many helpful discussions.This work was partially donewhile Hui Zhang was visiting National University of Singapore.HereHui Zhang is very grateful to Prof.Weizhu Bao for his hospitable friend.Hui Zhang is partially supported by NSFC grant No.11471046 and NSFC-RGC No.11261160486 and the Ministry of Education Program for New Century Excellent Talents Project NCET-12-0053.
文摘Here we investigate the kinematic transports of the defects in the nematic liquid crystal system by numerical experiments.The model is a shear flow case of the viscoelastic continuummodel simplified fromthe Ericksen-Leslie system.The numerical experiments are carried out by using a differencemethod.Based on these numerical experiments we find some interesting and important relationships between the kinematic transports and the characteristics of the flow.We present the development and interaction of the defects.These results are partly consistent with the observation from the experiments.Thus this scheme illustrates,to some extent,the kinematic effects of the defects.
文摘In this paper, we investigate the global existence and long time behavior of strong solutions for compressible nematic liquid crystal flows in threedimensional whole space. The global existence of strong solutions is obtained by the standard energy method under the condition that the initial data are close to the constant equilibrium state in H2-framework. If the initial datas in Ll-norm are finite additionally, the optimal time decay rates of strong solutions are established. With the help of Fourier splitting method, one also establishes optimal time decay rates for the higher order spatial derivatives of director.
基金supported by the National Natural Science Foundation of China (Nos. 10874240 and 60678023)the Shanxi Province 13115 Science and Technology Innovative Project (No. 2008ZDKG-68)
文摘The approaches to obtaining desired intensity or phase modulation by twisted-nematic liquid crystal display (TN-LCD) have been extensively studied based on the knowledge of the LCD's internal structure parameters. Generally, the TN-LCD placed between two linear polarizers (P) produces coupled intensity and phase modulation. To obtain the commonly used phase-only modulation, quarter wave plates (QWPs) are often used in front of and/or behind the LCD. Here we present a method to optimize the optical modulation properties of the TN-LCD to obtain phase-only modulation in the configuration of P-QWP-LCD-QWP-P each with proper orientation. Our method is based on the macroscopical Jones matrix descriptions for the LCD, the QWPs, and the linear polarizers. Through Jones matrix calculations, the orientations of the polarizers and QWPs can be optimized to satisfy differently desired modulation demands. In contrast to the traditional method, which requires knowledge of the LCD's internal structure parameters, our method simplified the complicated theory analysis and can work in the absence of information on the LCD's internal structure parameters, which are usually not available for the commercial products.