A Molecular Statistical Calculation of Pretransitional Effects in Nematic Liquid Crystals

Ypma, J. G. Y.; Vertogen, G.; Köster, H.

doi:10.1080/15421407608084346

Cited by 38 publications

(17 citation statements)

References 11 publications

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“…[8, [33][34][35][36] Die grundlegendste Voraussetzung für alle Arten kommerziell bedeutsamer LCDs ist sicherlich ein breiter Temperaturbereich für die nematische Mesophase des Flüssigkristalls. Zu solchen Kenngröûen gehören z.…”

Section: Physikalische Eigenschaften Nematischer Flüssigkristalleunclassified

Nematische Flüssigkristalle für Aktiv-Matrix-Displays: Design und Synthese

Kirsch

Bremer

2000

Angewandte Chemie

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EinführungInnerhalb nur weniger Jahre sind Flüssigkristall-Anzeigegeräte (LCDs) zu einem nahezu unverzichtbaren Teil unseres täglichen Lebens geworden. Weltweit wurden 1999 mehr als zwei Milliarden LCDs hergestellt. [1] Die Hälfte davon waren kleine, einfarbige Anzeigevorrichtungen für Uhren und Videospiele. Ein bis jetzt noch kleinerer, aber rasch wach-sender Anteil an dieser Gesamtmenge sind Farbdisplays mit hohem graphischem Auflösungsvermögen. Das vielleicht bekannteste Gerät dieser Art mit hohem Informationsgehalt ist der Desktop-PC-Monitor (hiervon wurden 1999 ca. 3.6 Millionen hergestellt, die meisten davon waren 15-Zoll-Bildschirme, d. h. 37.5 cm in der Diagonale), der mittlerweile zu einer ernsthaften Konkurrenz für den Monitor mit der schon lange etablierten Kathodenstrahlröhre (CRT) geworden ist. Nachdem man die schwierigsten Hürden auf dem Weg zu gröûeren Bildschirmen überwunden hat, haben die Displayhersteller als nächstes strategisches Ziel den flachen TV-Wandbildschirm anvisiert. Dieses Ziel wird man gewiss innerhalb der ersten Hälfte dieses Jahrzehnts erreicht haben.Die meisten dieser besonders hochwertigen Displays funktionieren auf der Grundlage der Aktiv-Matrix-Technologie, [2,3] bei der jedes Bildelement (¹Pixelª) einzeln über einen auf dem Displayglas integrierten Dünnfilmtransistor (thin film transistor, TFT) angesteuert wird. Die Hauptkomponenten eines LCD sind das mit Indium-Zinn-Oxid (ITO) als transparentem Elektrodenmaterial beschichtete Glas, Polari-

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Section: Physikalische Eigenschaften Nematischer Flüssigkristalleunclassified

Nematische Flüssigkristalle für Aktiv-Matrix-Displays: Design und Synthese

Kirsch

Bremer

2000

Angewandte Chemie

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“…Consider the effect of exciting a single low-q mode in a sample in which parameter is initially S' say. and S" = S'(1 -n, is initially parallel to (n) and in which the order Following its excitation we have s = S'(1 -t ( P ) ) (1 -W'>) (37) and causes n, to deviate from (n) by a mean square angle ($'). Now for many of the modes ($') vanishes, but it does not do so when (h,k,1) are all odd, and in particular it does not do so for the (1,1,1) modes.…”

Section: The Cluster Monte Carlo Methodsmentioning

confidence: 99%

“…Cluster expansion theories applicable to lattice models of nematics have been worked out for m, = 2 [37,38], 3 [39] and 4 [40]. They clearly provide a much more realistic picture than the Maier-Saupe theory for the correlations of orientation between nearest neighbours, and they predict the nematic-isotropic transition temperature with greater accuracy.…”

Section: Cluster Expansion Theoriesmentioning

confidence: 99%

Director fluctuations in nematic liquid crystals

Faber

1991

Liquid Crystals

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The literature of the past two decades suggests that confusion persists concerning the role of director fluctuations in the theory of nematics. Are these fluctuations necessarily small? If so, the fluctuation spectrum must terminate at a wavevector qc which is of the order of 10"m-', yet fluctuation mpdes with wavevectors in excess of lo9 m--' are commonly invoked to explain, for example, the frequency dependence of N M R relaxation rates. If the cut-off wavevector exceeds lo9 m-' and the fluctuations are not small, are their effects included in standard theories of nematic disorder, or should those theories be renormalized in some way to allow for them? Can we turn to experimental data for nematics, or to the results of computer simulations, in order to learn where qc lies? This paper suggests answers to these questions, based upon an elementary definition of the director which can be applied to groups of molecules of any size, not necessarily macroscopic. In the course of the argument some widely accepted ideas about nematics are challenged, in particular: (i) the idea that mean field theories of the Maier-Saupe type provide an adequate description of them; (ii) the idea that, in so far as mean field theories are not exact, their deficiencies may be rectified by the cluster-expansion approach; (iii) the idea that the processes whcreby molecules in a nematic undergo large changes in orientation, and from time to time experience end-to-end inversion, are essentially distinct from director fluctuations, which d o no more than gently rock the cage within which the molecule is constrained.

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“…Application of the constant-coupling approximation to a binary mixture yields expression (7) for the free energy in terms of the variation parameter S. This parameter is linked with the order-parameter +/ through relation (12), which can be written as…”

Section: Appendixmentioning

confidence: 99%

Two particle cluster calculation of the chemical spinodal

Haegen¹,

Luyckx²,

Lekkerkerker³

1981

Physica A: Statistical Mechanics and its Applications

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The spinodal curve for demixing in a binary mixture is calculated in the two-particle cluster approximation. It is found that the difference between the equilibrium composition x,. and the spinodal composition x, is smaller than in the mean-field approximation. The results agree remarkably well with the semi-empirical formula for the metastable region proposed by Cook and Hilliard (Trans. Met. Soc. AIME 233 (1965) 142).

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A Molecular Statistical Calculation of Pretransitional Effects in Nematic Liquid Crystals

Cited by 38 publications

References 11 publications

Nematische Flüssigkristalle für Aktiv-Matrix-Displays: Design und Synthese

Nematische Flüssigkristalle für Aktiv-Matrix-Displays: Design und Synthese

Director fluctuations in nematic liquid crystals

Two particle cluster calculation of the chemical spinodal

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