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Journal ArticleDOI

Phase transitions in liquid crystals

01 Feb 2000-Physics Reports (North-Holland)-Vol. 324, Iss: 2, pp 107-269
TL;DR: A comprehensive overview of phase transition studies can be found in this article, where the authors identify the essential key concepts and points of difficulty associated with the study of phase transitions and discuss the most widely used experimental techniques for measuring these transition properties.
About: This article is published in Physics Reports.The article was published on 2000-02-01. It has received 308 citations till now. The article focuses on the topics: Phase transition & Liquid crystal.
Citations
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Journal ArticleDOI
TL;DR: By using the united-atom force field developed herein, it is shown that the experimental isotropic-nematic transition temperatures are reproduced within 4 K, allowing a molecular-level interpretation of the odd-even effect along the series.
Abstract: We have studied the important n-cyano biphenyl series of mesogens, n=4-8 using modelling and molecular dynamics simulations. We have been able to obtain spontaneously ordered nematics upon cooling isotropic samples of 250 molecules. We show that, using the united atom force field developed here, the experimental isotropic–nematic transition temperatures are reproduced within 4 K, allowing a molecular level interpretation of the odd–even effect along the series. Other properties, like densities, orientational order parameters and NMR residual dipolar couplings are also well reproduced, demonstrating the feasibility of predictive in silico modelling of nematics from the molecular structure.

167 citations

Journal ArticleDOI
TL;DR: In this paper, the selfassembly of a series of monodisperse rod−coil block copolymers is studied in the weak segregation limit, and the order to microphase disorder transition (ODT) and nematic isotropic (NI) transition are experimentally investigated.
Abstract: The self-assembly of a series of monodisperse rod−coil block copolymers is studied in the weak segregation limit. This unusual weakly segregated system consists of polyisoprene (PI) coil blocks and poly(alkoxyphenylene vinylene) (PPV) rod blocks solubilized with alkoxy side groups. The order to microphase disorder transition (ODT) and nematic isotropic (NI) transition are experimentally investigated to produce a rod−coil block copolymer phase diagram in a system that follows polymeric scaling relationships. Small-angle X-ray scattering (SAXS), transmission electron microscopy (TEM), polarized optical microscopy, depolarized light scattering, and wide-angle X-ray scattering (WAXS) are used to map the phase diagram. As the symmetric diblock copolymer is heated, a series of transitions from lamellar to nematic to isotropic phases are observed. The NI transition temperature decreases with increasing coil fraction, and at high coil fractions only an isotropic phase is observable. The phase behavior is in quali...

161 citations

Journal ArticleDOI
TL;DR: In this paper, the effects of halide substituents on mechanochromic luminescence quenching were investigated for a series of difluoroboron β-diketonate (BF2bdk) compounds.
Abstract: Many difluoroboron β-diketonate (BF2bdk) compounds display mechanochromic luminescence (ML) and substituents can influence their optical properties. For example, the difluoroboron iododibenzoylmethane derivative, BF2dbm(I)OC12H25, exhibits mechanochromic luminescence quenching (MLQ). When annealed films of this dye are smeared under air, the perturbed region becomes dim under UV light. In this study, effects of differing halide substituents on ML were investigated. A series of dyes of the form BF2dbm(X)OC12H25, where X = H, F, Cl, Br, and I, were synthesized. The luminescence properties of these dyes were studied in CH2Cl2 solution, as films on weighing paper, spin-cast films on glass substrates, and as bulk powders. All of the dyes exhibit ML and MLQ. Solid-state emissions from these dyes are also sensitive to annealing temperature. The F, Cl, and Br dyes required higher annealing temperatures than the H and I analogues to achieve ordered emissive states. Spin-cast films of the dyes on glass were studied using atomic force microscopy (AFM) and X-ray diffraction (XRD), revealing a change from an amorphous material in the as-spun state to an ordered, crystalline material after annealing, with the F and Cl dyes showing a propensity to form large lamellar crystallites. Powders were also investigated using XRD and showed changes in diffraction patterns corresponding to thermal annealing and grinding. Finally, halogen substituents greatly diminished the ability of the dye films to recover their ordered emissive states after smearing under ambient conditions. These dyes could be useful for applications in which a more permanent inscription is desirable.

117 citations

Journal ArticleDOI
TL;DR: In this paper, the Flory−Huggins interaction is measured for a model rod-coil block copolymer system, poly(alkoxyphenylenevinylene-b-isoprene), by fitting the interfacial segregation of block copolerant to a homopolymer interface and by using the random phase approximation (RPA) for block co-olymers.
Abstract: The Flory−Huggins interaction is measured for a model rod−coil block copolymer system, poly(alkoxyphenylenevinylene-b-isoprene), by fitting the interfacial segregation of block copolymer to a homopolymer interface and by using the random phase approximation (RPA) for block copolymers The measured interfacial segregation of a block copolymer to the interface between homopolymers, fit with a self-consistent field theory (SCFT) simulation using χ as a variable parameter, gives a functional form χ = 348/T − 0091 When RPA is applied to neutron scattering curves for the rod−coil system above the order−disorder transition, the theoretical structure factors are inconsistent with observed scattering curves due to complex aggregated structures formed in the nematic and isotropic states Using the Flory−Huggins parameter and a previously measured value of the Maier−Saupe parameter, the PPV-b-PI phase diagram may be converted from system-specific variables to dimensionless parameters Under the assumptions that t

101 citations

Journal ArticleDOI
TL;DR: In this article, the qualitative character of entropy has been investigated and several examples from statistical mechanics (including liquid crystal reentrant phases, two different lattice gas models, and the game of poker) demonstrate facets of this difficult question and point toward an answer.
Abstract: What is the qualitative character of entropy? Several examples from statistical mechanics (including liquid crystal reentrant phases, two different lattice gas models, and the game of poker) demonstrate facets of this difficult question and point toward an answer. The common answer of “entropy as disorder” is regarded here as inadequate. An alternative but equally problematic analogy is “entropy as freedom.” Neither simile is perfect, but if both are used cautiously and not too literally, then the combination provides considerable insight.

98 citations

References
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Journal ArticleDOI
TL;DR: In this paper, the Hartree and Hartree-Fock equations are applied to a uniform electron gas, where the exchange and correlation portions of the chemical potential of the gas are used as additional effective potentials.
Abstract: From a theory of Hohenberg and Kohn, approximation methods for treating an inhomogeneous system of interacting electrons are developed. These methods are exact for systems of slowly varying or high density. For the ground state, they lead to self-consistent equations analogous to the Hartree and Hartree-Fock equations, respectively. In these equations the exchange and correlation portions of the chemical potential of a uniform electron gas appear as additional effective potentials. (The exchange portion of our effective potential differs from that due to Slater by a factor of $\frac{2}{3}$.) Electronic systems at finite temperatures and in magnetic fields are also treated by similar methods. An appendix deals with a further correction for systems with short-wavelength density oscillations.

47,477 citations

Journal ArticleDOI
TL;DR: In this article, the ground state of an interacting electron gas in an external potential was investigated and it was proved that there exists a universal functional of the density, called F[n(mathrm{r})], independent of the potential of the electron gas.
Abstract: This paper deals with the ground state of an interacting electron gas in an external potential $v(\mathrm{r})$. It is proved that there exists a universal functional of the density, $F[n(\mathrm{r})]$, independent of $v(\mathrm{r})$, such that the expression $E\ensuremath{\equiv}\ensuremath{\int}v(\mathrm{r})n(\mathrm{r})d\mathrm{r}+F[n(\mathrm{r})]$ has as its minimum value the correct ground-state energy associated with $v(\mathrm{r})$. The functional $F[n(\mathrm{r})]$ is then discussed for two situations: (1) $n(\mathrm{r})={n}_{0}+\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{n}(\mathrm{r})$, $\frac{\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{n}}{{n}_{0}}\ensuremath{\ll}1$, and (2) $n(\mathrm{r})=\ensuremath{\phi}(\frac{\mathrm{r}}{{r}_{0}})$ with $\ensuremath{\phi}$ arbitrary and ${r}_{0}\ensuremath{\rightarrow}\ensuremath{\infty}$. In both cases $F$ can be expressed entirely in terms of the correlation energy and linear and higher order electronic polarizabilities of a uniform electron gas. This approach also sheds some light on generalized Thomas-Fermi methods and their limitations. Some new extensions of these methods are presented.

38,160 citations

17 Jun 1964

28,969 citations

Book
01 Jan 1989
TL;DR: In this paper, a review of current studies in density functional theory and density matrix functional theory is presented, with special attention to the possible applications within chemistry, including the concept of an atom in a molecule, calculation of electronegativities from the Xα method, pressure, Gibbs-Duhem equation, Maxwell relations and stability conditions.
Abstract: Current studies in density functional theory and density matrix functional theory are reviewed, with special attention to the possible applications within chemistry. Topics discussed include the concept of electronegativity, the concept of an atom in a molecule, calculation of electronegativities from the Xα method, the concept of pressure, Gibbs-Duhem equation, Maxwell relations, stability conditions, and local density functional theory.

14,008 citations

Book
01 Feb 1974
TL;DR: In this paper, the authors define an order parameter statistical theories of the nematic order phenomonological description of the nematic-isotopic mixtures and describe the properties of these mixtures.
Abstract: Part 1 Liquid crystals - main types and properties: introduction - what is a liquid crystal? the building blocks nematics and cholesterics smectics columnar phases more on long-, quasi-long and short-range order remarkable features of liquid crystals. Part 2 Long- and short-range order in nematics: definition of an order parameter statistical theories of the nematic order phenomonological description of the nematic-isotopic mixtures. Part 3 Static distortion in a nematic single crystal: principles of the continuum theory magnetic field effects electric field effects in an insulating nematic fluctuations in the alignment hydrostatics of nematics. Part 4 Defects and textures in nematics: observations disclination lines point disclinations walls under magnetic fields umbilics surface disclinations. Part 5 Dynamical properties of nematics: the equations of "nematodynamics" experiments measuring the Leslie co-efficients convective instabilities under electric fields molecular motions. Part 6 Cholesterics: optical properties of an ideal helix agents influencing the pitch dynamical properties textures and defects in cholesterics. Part 7 Smectics: symmetry of the main smectic phases continuum description of smectics A and C remarks on phase and precritical phenomena.

9,683 citations