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Book ChapterDOI

Spatial Correlations in Nematic Liquid Crystals

01 Jan 1984-Vol. 4, pp 653-672
TL;DR: In this article, the spatial correlations between molecules are accounted for in the "orientationally averaged pair correlations" approximation (OAPC) to affect the macroscopic properties of nematic liquid crystals and a cell model calculation in which both the molecular orientational distribution and the spatial distribution about lattice sites are determined self-consistently, by solving coupled Euler-Lagrange equations which minimize the free energy.
Abstract: Liquid crystals are liquids. At such densities, spatial correlations between molecules are expected to play an important role in the determination of their collective and phase transition properties. At short range, these correlations are quite anisotropic as a result of anisotropic intermolecular repulsions. We recall a molecular potential model that takes into account anisotropic forces. We show how spatial correlations are accounted for in the “orientationally averaged pair correlations” approximation (OAPC) to affect the macroscopic properties of nematic liquid crystals. We then perform a cell model calculation in which both the molecular orientational distribution and the spatial distribution about lattice sites are determined self-consistently, by solving coupled Euler-Lagrange equations which minimize the free energy. Numerical work is carried out for a simple potential without anisotropicters. We are able to determine the potential parameters which reproduce earlier OAPC results. Such an exercise illustrates how the cell approximation works and provides us with a theoretical framework for introducing anisotropic forces and pair correlations into later work. It is hoped that the latter would help remove some of the serious discrepancies between molecular theories and esperiment.
Citations
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Proceedings ArticleDOI
24 Jul 2006
TL;DR: In this article, a switchable polarization interference filter was proposed to obtain near diffraction limited performance over the instantaneous field-of-view (IFOV) at the wavelength(s) of interest.
Abstract: The development of sensors that are smaller, lighter weight and require less bandwidth is critical for the success of space-based and airborne imaging systems. One solution to this problem is foveated imaging, wherein a liquid crystal spatial light modulator is used to selectively enhance resolution in a wide field-of-view imaging system. Selective enhancement decreases the bulk and complexity of the optical train, while simultaneously reducing data transmission and processing requirements. This enhancement is done modulo 2/spl pi/, as such it is inherently a monochromatic correction. In this paper, we propose to overcome that limitation by introducing a switchable polarization interference filter, obtaining near diffraction limited performance over the instantaneous field-of-view (IFOV) at the wavelength(s) of interest.

9 citations

References
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Book
01 Jan 1976
TL;DR: In this paper, the authors present a model of the Nematic-Isotropic phase transition and its relation to the elastic continuuum theory of liquid crystals, which is used to describe the properties of liquid crystal structures.
Abstract: 1 Liquid Crystal Mesophases.- 1. Mesophases.- 1.1 Disordered Crystal Mesophases.- 1.2 Ordered Fluid Mesophases.- 2. Types of Liquid Crystals.- 2.1 Thermotropic Liquid Crystals.- 2.2 Lyotropic Liquid Crystals.- 3. Classification According to Molecular Order.- 3.1 Nematic Order.- 3.2 Cholesteric Order.- 3.3 Smectic Order.- 4. Polymorphism in Thermotropic Liquid Crystals.- 5. Molecular Structure of Thermotropic Mesogens.- 6. Properties of Ordered Fluid Mesophases.- 2 Structure-Property Relationships in Thermotropic Organic Liquid Crystals.- 1. Introduction.- 2. Organic Mesophases.- 3. General Structural Features of Mesogens.- 4. Effects of Structure on Mesophase Thermal Stability.- 5. Homologous Series.- 6. Materials for Device Applications.- 7. Summary.- 3 Introduction to the Molecular Theory of Nematic Liquid Crystals.- 1. Introduction.- 2. Symmetry and the Order Parameter.- 3. The Molecular Potential.- 4. The Orientational Distribution function.- 5. Thermodynamics of the Nematic Phase.- 6. Fluctuations at Tc.- 4 Generalized Mean Field Theory of Nematic Liquid Crystals.- 1. Introduction.- 2. The Pair Interaction Potential.- 3. The Mean Field Approximation.- 4. Statistical Thermodynamics.- 5. Nature of the Parameters UL.- 6. The Need for Higher Order Terms in V1.- 5 Hard Rod Model of the Nematic-Isotropic Phase Transition.- 1. Introduction.- 2. Derivation of Onsager Equations.- 3. Solution of Onsager Equations in a Simplified Case.- 6 Nematic Order: The Long Range Orientational Distribution Function.- 1. Introduction.- 2. The Orientational Distribution function.- 3. Macroscopic Definition of Nematic Order.- 4. Relationship Between Microscopic and Macroscopic Order Parameters.- 5. Experimental Measurements.- 5.1 Measurements of ?P2(cos ?)? Based on Macroscopic Anisotropies.- 5.2 Measurements of ?P2(cos ?)? Based on Microscopic Anisotropies.- 6. Experimental Data.- 7 Introduction to the Molecular Theory of Smectic-A Liquid Crystals.- 1. Introduction.- 2. Symmetry, Structure and Order Parameters.- 3. Phase Diagrams.- 4. The Molecular Potential.- 5. Statistical Thermodynamics.- 6. Numerical Results.- 7. Improved Theory.- 8. The Possibility of Second-Order Transitions.- 8 Introduction to the Elastic Continuum Theory of Liquid Crystals.- 1. Introduction.- 2. The Fundamental Equation of the Continuum Theory of Liquid Crystals.- 3. Applications of the Elastic Continuum Theory.- 3.1 Twisted Nematic Cell.- 3.2 Magnetic Coherence Length.- 3.3 Freedericksz Transition.- 3.4 Field-Induced Cholesteric-Nematic Transition.- 4. Concluding Remarks.- 9 Electrohydrodynamic Instabilities in Nematic Liquid Crystals.- 1. Introduction.- 2. Nature of the Instability and the Balance of Forces.- 3. Dielectric Response.- 4. Hydrodynamic Effects.- 5. The Boundary Value Problem in the Conduction Regime.- 6. The Torque Balance Equation.- 7. Numerical Results and Comparison with Experiment.- 8. Range of Applicability.- 10 The Landau-de Gennes Theory of Liquid Crystal Phase Transitions.- 1. Introduction.- 2. Derivation of the Fundamental Equations of the Landau-de Gennes Theory.- 2.1 The Partition function.- 2.2 The Landau Expansion.- 2.3 Generalization of the Landau Expansion to Liquid Crystals.- 3. Thermodynamic Properties of Liquid Crystal Phase Transitions.- 4. Fluctuation Phenomena.- 4.1 Homophase Fluctuations in the Isotropic Phase.- 4.2 Heterophase Fluctuations.- 5. Observation of Fluctuations Using Light Scattering.- 6. Magnetic Birefringence and the Paranematic Susceptibility.- Appendix A.- Appendix B.- 11 Introduction to the Optical Properties of Cholesteric and Chiral Nematic Liquid Crystals.- 1. Introduction.- 2. Maxwell's Equations.- 3. Discussion.- 4. Conclusion.- Appendix A.- Appendix B.- 12 Liquid-Crystal Displays-Packaging and Surface Treatments.- 1. Introduction.- 2. Packaging.- 3. Electrodes.- 4. Surface Orientation.- 5. Influence of Packaging on Surface Orientation.- 6. Summary.- 13 Pressure Effects in Sealed Liquid-Crystal Cells.- 1. Introduction.- 2. Effect of Temperature Change.- 3. Effect of Glass Thickness.- 4. The Case of a Rigid Container.- 14 Liquid-Crystal Displays-Electro-optic Effects and Addressing Techniques.- 1. Introduction.- 2. Electro-optic Phenomena.- 2.1 Field-Induced Birefringence.- 2.2 Twisted Nematic Effect.- 2.3 Guest-Host Effect.- 2.4 Cholesteric-to-Nematic Transition.- 2.5 Dynamic Scattering.- 2.6 Storage Mode.- 2.7 Transient Response.- 3. Display-Related Parameters.- 3.1 Display Life.- 3.2 Temperature Dependence.- 4. Addressing Techniques.- 4.1 Matrix Addressing.- 4.2 Beam Scanning.- 5. Summary.- 15 Liquid-Crystal Optical Waveguides.- 1. Introduction.- 2. Guided Optical Waves.- 3. Phase Matching and Coupling.- 4. Scattering.- 5. Liquid Crystal Waveguides.- 6. Conclusions.- 16 The Electro-optic Transfer Function in Nematic Liquids.- 1. Introduction.- 2. Geometrical Considerations in Optical Measurements.- 3. Field Effects-Negative Dielectric Anisotropy.- 4. Field Effects-Positive Dielectric Anisotropy.- 5. Hydrodynamic Effects-Diffraction by Domains.- 6. Dynamic Scattering.- 7. Photoconductor Control.- 17 Electrochemistry in Nematic Liquid-Crystal Solvents.- 1. Introduction.- 2. Equilibrium Properties of Bulk Solutions.- 3. Electrochemical Reactions.- 18 Lyotropic Liquid Crystals and Biological Membranes: The Crucial Role of Water.- 1. Introduction.- 2. Lyotropic Liquid Crystals.- 2.1 Constituents of Lyotropics.- 2.2 Micelles.- 2.3 Structure of Lyotropics.- 3. Biological Membranes.- 3.1 Constituents of Membranes.- 3.2 Structures of Membranes.- 4. Interaction of Amphiphilic Compounds with Water.- 4.1 Solubility of Hydrocarbons in Water.- 4.2 Solubility of Ionized Species in Water.- 4.3 Aggregation of Amphiphilic Compounds.- 5. Conclusion.

842 citations

Journal ArticleDOI
TL;DR: In this paper, the authors measured the optical Kerr effect and the intensity-dependent ellipse rotation in order to study the pretransitional behavior of field-induced molecular alignment in the isotropic nematic substances.
Abstract: We have measured the optical Kerr effect and the intensity-dependent ellipse rotation in order to study the pretransitional behavior of field-induced molecular alignment in the isotropic nematic substances $p$-methoxy-benzylidene $p\ensuremath{-}n$-butylaniline (MBBA) and $p$-ethoxy-benzylidene-$p$-butylaniline (EBBA). The results agree well with predictions of the Landau---de Gennes model. Both the order-parameter relaxation time and the steady-state field-induced birefringence show critical divergence towards the isotropic \ensuremath{\rightarrow} nematic transition with a ${(T\ensuremath{-}{T}^{*})}^{\ensuremath{-}1}$ temperature dependence. In the case of MBBA, our results are also consistent with the results from light scattering, but the method we use is perhaps more straightforward and accurate. The nonlinear refractive indices and other relevant parameters of the materials are derived from the experiment.

135 citations

Journal ArticleDOI
TL;DR: In this paper, the authors measured the density and determined the coefficient of expansion of MBBA about its isotropic−nematic transition temperature using a Mettler/Paar density meter.
Abstract: We have measured the density and determined the coefficient of expansion of MBBA about its isotropic−nematic transition temperature using a Mettler/Paar density meter. Our results show essential agreement with those of Press and Arrott using a buoyancy method. The small difference (<0.3°C) between the actual transition temperature and the virtual critical temperature differs from that determined by light scattering studies which yield values of about 1°C. Further examination on the nature of the virtual critical temperature is suggested.

38 citations

Journal ArticleDOI
TL;DR: In this article, the experimentally observed strong pretransitional effects in nematogens can be described in terms of a mean field theory if the free energy expansion is not truncated at the quadratic term.
Abstract: We show in this note that the experimentally observed strong pretransitional effects in nematogens can be described in terms of a mean field theory if the free energy expansion is not truncated at the quadratic term. A simple uniform fluctuation model gives rise to light scattering intensity in good agreement with experiment.

20 citations

Journal ArticleDOI
TL;DR: In this paper, the authors reformulated the molecular theory of nematic liquid crystals rigorously on the basis of a general probability distribution function and showed that both the mean field theory (MFT) and the above-stated orientation-averaged pair-correlation theory (OAPC) arise from applying low-order approximations to ${P}_{N}$.
Abstract: In a previous paper (I) we carried out a model calculation for nematic liquid crystals which treats spatial correlations between molecules as for a classical isotropic liquid and orientational correlations in the meanfield approximation. Generalized Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) equations were derived for the density function and an orientationally averaged pair-correlation function. They were solved for a simple pairwise potential chosen to fit certain experimental data on $p$-azoxyanisole (PAA). A free-energy expression was obtained by identifying its Euler-Lagrange equation to the first BBGKY equation. In this paper we reformulated the molecular theory of nematic liquid crystals rigorously on the basis of a general probability distribution function ${P}_{N}(1,\dots{},N)$. It was shown that both the mean-field theory (MFT) and the above-stated orientation-averaged pair-correlation theory (OAPC) arise from applying low-order approximations to ${P}_{N}$. In the case of MFT, ${P}_{N}$ was approximated as a product of single-particle functions. In the case of OAPC, spatial correlations were introduced, but decoupling of spatial and orientational dependences were assumed. It is now clear how higher-order-approximation schemes can be systematically constructed. Furthermore, for each scheme chosen, the present formulation offers a uniquely consistent formula for the free energy. This places our previous work on a firm theoretical foundation. The theory in OAPC approximation was applied to model systems described by a more general pairwise potential than that employed in I. Potential parameters were chosen to mimic PAA and methoxybenzylidene butylaniline. For each substance we calculated the isotropic-nematic coexistence curve, temperature dependence of the order parameter, latent heat, and volume change at transition. The results were compared to experimental data.

8 citations