# Landau-de Gennes model with the inclusion of density change for the nematic-isotropic phase transition

10 Jul 1996-Modern Physics Letters B (World Scientific Publishing Company)-Vol. 10, Iss: 16, pp 777-778

Abstract: The Landau-de Gennes model of the nematic-isotropic phase transition with the inclusion of the density change and a higher order term (sixth-order term) in a simple way is examined. The temperature difference TNI−T* obtained is in good agreement with the experimental one. We also obtained the value of the ratio (Q*–QNI)/QNI. The value of (Q*–QNI)/QNI is not improved over the earlier attempt, but there is a definite improvement in the value of TNI–T* which is obtained as 1.045 K.

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Abstract: Mesogenic materials exhibit a multitude of transitions involving new phases. Studies of these phases are of importance in a wide range of scientific fields and as such have stimulated considerable theoretical and experimental efforts over the decades. This review article presents a comprehensive overview until this date of the developments in this subject. An attempt is made to identify the essential key concepts and points of difficulty associated with the study of phase transitions. The article begins with a brief introduction about the symmetry, structure and types of liquid crystalline phases. This is followed by a discussion of the distribution functions and order parameters which are considered as the basic knowledge essential for the study of ordered phases. A brief discussion of the thermodynamic properties at and in the vicinity of phase transitions, which are required to understand the molecular structure phase stability relationship, is given. The most widely used experimental techniques for measuring these transition properties are critically examined. The remaining parts of the article are concerned with the current status of the theoretical developments and experimental studies in this field. The application of the various theories to the description of isotropic liquid-uniaxial nematic, uniaxial nematic-smectic A, uniaxial nematic-biaxial nematic, smectic A–smectic C phase transitions are reviewed comprehensively. The basic ideas of Landau–de Gennes theory and its applications to study these transitions are discussed. Since the formation of liquid crystals depends on the anisotropy in the intermolecular interactions, questions concerning its role in the mesophase transitions are addressed. The hard particle, Maier-Saupe and van der Waals types of theories are reviewed. The application of density functional theory in studying mesophase transitions is described. A critical assessment of the experimental investigations concerning reentrant phase transitions in liquid crystals is made and the factors which impede its proper understanding are identified. A survey is given of existing computer simulation studies of the isotropic to nematic transition, the nematic to smectic A transition, the smectic A to hexatic S B transition, the smectic A to reentrant nematic transition, and transitions to the discotic phase. The current status of the study of phase transitions involving hexatic smectic, cholesteric, polymeric and ferroelectric liquid crystals is outlined. Finally, a range of unexplored problems and some of the areas which are in greatest need of future attention are identified.

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Abstract: The low value of , where is the nematic-isotropic phase transition temperature and denotes the virtual transition temperature, is a long-standing puzzle in the physics of liquid crystals. The present review presents experimental and theoretical results on this long-standing problem. New experimental and theoretical results for the critical behaviour in the isotropic phase of nematogens are reviewed. We calculate in a unified approach the low value of , at both critical and tricritical points. The possibility of tricritical behaviour at the nematic-isotropic transition is also discussed by means of Landau theory. The various predictions are compared with the available experimental results.

59 citations

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TL;DR: The isotropic-nematic phase transition in liquid crystals is described in the context of the slowing of orientational relaxation associated with divergent growth of the orientational correlation length, and the correlation length of the density fluctuations is diverging with the same temperature dependence as the pseudonematic domain correlation length.

Abstract: The isotropic phase of nematogenic liquid crystals has nanometer length scale domains with pseudonematic ordering. As the isotropic to nematic phase transition temperature (TNI) is approached from above, the orientational correlation length, ξ, of the pseudonematic domains grows as (T - T(*))(-1/2), where T(*) is 0.5-1 K below TNI. The orientational relaxation, which is a collective property of the pseudonematic domains, was measured with optical heterodyne detected-optical Kerr effect (OHD-OKE). The orientational relaxation obeys Landau-de Gennes theory, as has been shown previously. To examine the environmental evolution experienced by molecules in the pseudonematic domains, two-dimensional infrared (2D IR) vibrational echo experiments on the CN stretching mode of the non-perturbative vibrational probes 4-pentyl-4(')-selenocyanobiphenyl (5SeCB) and 4-pentyl-4(')-thiocyanobiphenyl (5SCB) in the nematogen 4-cyano-4(')-pentylbiphenyl (5CB) were performed. The 2D IR experiments measure spectral diffusion, which is caused by structural fluctuations that couple to the CN vibrational frequency. Temperature dependent studies were performed just above TNI, where the correlation length of pseudonematic domains is large and changing rapidly with temperature. These studies were compared to 2D IR experiments on 4-pentylbiphenyl (5B), a non-mesogenic liquid that is very similar in structure to 5CB. The time constants of spectral diffusion in 5CB and 5B are practically identical at temperatures ≥5 K above TNI. As the temperature is lowered, spectral diffusion in 5B slows gradually. However, the time constants for spectral diffusion in 5CB slow dramatically and diverge as T(*) is approached. This divergence has temperature dependence proportional to (T - T(*))(-1/2), precisely the same as seen for the correlation length of pseudonematic domains, but different from the observed orientational relaxation times, which are given by the Landau-de Gennes theory. The data and previous results show that spectral diffusion in 5CB has no contributions from orientational relaxation, and the structural dynamics responsible for the spectral diffusion are likely a result of density fluctuations. The results suggest that the correlation length of the density fluctuations is diverging with the same temperature dependence as the pseudonematic domain correlation length, ξ. The isotropic-nematic phase transition in liquid crystals is described in the context of the slowing of orientational relaxation associated with divergent growth of the orientational correlation length. The results presented here show that there is another divergent dynamical process, likely associated with density fluctuations.

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Abstract: Tricritical behavior at the nematic–isotropic phase transition is discussed by means of Landau–de Gennes phenomenological theory. The temperature difference TNI-T* is obtained near the tricritical point. We also obtained the value of the ratio (Q*-QNI)/QNI, where Q* is the order parameter at the temperature T* of the absolute stability limit of the isotropic phase and QNI is the order parameter at the nematic–isotropic transition temperature TNI. As a definite improvement over the earlier attempts utilizing Landau–de Gennes scheme the present work can reproduce low values of (Q*-QNI)/QNI and that of TNI-T* as demanded by experimental observations. The tricritical exponents are calculated from the scaling theory and compared with observed values. Using the Ginzburg criterion, we also determine the critical region of the nematic–isotropic phase transition.

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Abstract: The trends of temperature dependence of the surface order parameter and of the anchoring strength coefficient are theoretically evaluated in the Landau-de Gennes phenomenological theory for nematic liquid crystals. The cases of planar, homeotropic and tilted alignment at a planar limiting surface are considered. It is shown that the cases with surface order parameter greater than the bulk one or smaller than this can occur in function of the phenomenological coefficients in the surface free energy expression. The anchoring strength coefficient, W, diminishes when temperature approaches the nematic-isotropic point, after passing through a maximum in most of cases. The possibility of a non-zero anchoring strength at temperatures above the transition temperature is revealed. The obtained trends of W(T) describe well a large variety of experimental results from literature.

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