Eine einfache molekular-statistische Theorie der nematischen kristallinflüssigen Phase. Teil l<sup>1</sup>.

Maier, W.; Saupe, A.

doi:10.1515/zna-1959-1005

Cited by 1,628 publications

(508 citation statements)

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“…For three-component spins, an analogous Hamiltonianthe RP 2 model -had been introduced by Maier and Saupe [79] and by Lebwohl and Lasher [80] to investigate the isotropic-nematic transition in liquid crystals. An extensive study of the RP 2 model, as well as a detailed investigation of the role of vortices in this transition, has been performed by Lammert et al [81,82].…”

Section: B the Heisenberg Casementioning

confidence: 99%

Nonperturbative renormalization-group approach to frustrated magnets

2004

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This article is devoted to the study of the critical properties of classical XY and Heisenberg frustrated magnets in three dimensions. We first analyze the experimental and numerical situations. We show that the unusual behaviors encountered in these systems, typically nonuniversal scaling, are hardly compatible with the hypothesis of a second order phase transition. Moreover, the fact that the scaling laws are significantly violated and that the anomalous dimension is negative in many cases provides strong indications that the transitions in frustrated magnets are most probably of very weak first order. We then review the various perturbative and early nonperturbative approaches used to investigate these systems. We argue that none of them provides a completely satisfactory description of the three-dimensional critical behavior. We then recall the principles of the nonperturbative approach -the effective average action method -that we have used to investigate the physics of frustrated magnets. First, we recall the treatment of the unfrustrated -O(N ) -case with this method. This allows to introduce its technical aspects. Then, we show how this method unables to clarify most of the problems encountered in the previous theoretical descriptions of frustrated magnets. Firstly, we get an explanation of the long-standing mismatch between different perturbative approaches which consists in a nonperturbative mechanism of annihilation of fixed points between two and three dimensions. Secondly, we get a coherent picture of the physics of frustrated magnets in qualitative and (semi-) quantitative agreement with the numerical and experimental results. The central feature that emerges from our approach is the existence of scaling behaviors without fixed or pseudo-fixed point and that relies on a slowing-down of the renormalization group flow in a whole region in the coupling constants space. This phenomenon allows to explain the occurence of generic weak first order behaviors and to understand the absence of universality in the critical behavior of frustrated magnets.

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Section: B the Heisenberg Casementioning

confidence: 99%

Nonperturbative renormalization-group approach to frustrated magnets

2004

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“…Each of these potentials has the conventional Maier-Saupe form. 45,46 As an aside and in order to make a crude comparison with our model-free approach, we report a RIS fit (column 6) of the two-parameter modified chord model to our experimental results, again using the ethane G β values in 1132 and 5CB as a function of temperature to scale the energy parameters. A simultaneous fit to all our 22 spectra obtained with the modified a Order parameters are for spectra at 298.5 K and (except for 5CB in column 2) are reported for spectra in 1132.…”

Section: Fig 5 D I J (N-pentane)/d Ethane Ratios Versus T Each Ramentioning

confidence: 99%

A model-free temperature-dependent conformational study of n-pentane in nematic liquid crystals

Burnell

Weber

Dong

et al. 2015

The Journal of Chemical Physics

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The proton NMR spectra of n-pentane orientationally ordered in two nematic liquid-crystal solvents are studied over a wide temperature range and analysed using covariance matrix adaptation evolutionary strategy. Since alkanes possess small electrostatic moments, their anisotropic intermolecular interactions are dominated by short-range size-and-shape effects. As we assumed for n-butane, the anisotropic energy parameters of each n-pentane conformer are taken to be proportional to those of ethane and propane, independent of temperature. The observed temperature dependence of the n-pentane dipolar couplings allows a model-free separation between conformer degrees of order and conformer probabilities, which cannot be achieved at a single temperature. In this way for n-pentane 13 anisotropic energy parameters (two for trans trans, tt, five for trans gauche, tg, and three for each of gauche + gauche + , pp, and gauche + gauche − , pm), the isotropic trans-gauche energy difference E tg and its temperature coefficient E ′ tg are obtained. The value obtained for the extra energy associated with the proximity of the two methyl groups in the gauche + gauche − conformers (the pentane effect) is sensitive to minute details of other assumptions and is thus fixed in the calculations. Conformer populations are affected by the environment. In particular, anisotropic interactions increase the trans probability in the ordered phase. C 2015 AIP Publishing LLC. [http://dx

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“…Although the potential parameters obtained herein for the nematic phase of 8OCB, γ and Γ , have magnitudes similar to those for other LC compounds [6,7,34], the value extracted from scaling of the dynamics, γ * = 4.4, is significantly larger than the thermodynamic potential parameter, Γ = 3.15 ( Figure 3). In the context of Maier-Saupe theory of the nematic state [35] (2)); γ * corresponds to the reduced relaxation times (Equation (6)). …”

Section: Discussionmentioning

confidence: 99%

Volumetric study ofn-octyloxy-cyanobiphenyl (8OCB)

et al. 2013

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Volumetric measurements were carried out on n-octyloxy-cyanobiphenyl (8OCB) over temperatures from ambient to 150• C at pressures up to 200 MPa, encompassing the liquid, nematic and smectic liquid crystalline, and crystal states. From the step changes in volume at the transitions, the phase boundaries and the associated activation enthalpies and energies were determined. The results are consistent with prior studies that were limited to a narrower range of thermodynamic conditions. The thermodynamic potential parameter, Γ , found for the isotropic-nematic transition, =3.15, is significantly smaller than the scaling exponent γ (=4.4) that superposes the longitudinal relaxation times in the nematic state. From this non-equivalence, we conclude that the order parameter must vary with pressure along the clearing line. By comparing the phase behaviour of the nematic state for isochoric and isobaric conditions, the relative contribution of volume was determined to be less that the effect of thermal energy on the thermodynamic stability.

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Eine einfache molekular-statistische Theorie der nematischen kristallinflüssigen Phase. Teil l¹.

Cited by 1,628 publications

References 0 publications

Nonperturbative renormalization-group approach to frustrated magnets

Nonperturbative renormalization-group approach to frustrated magnets

A model-free temperature-dependent conformational study of n-pentane in nematic liquid crystals

Volumetric study ofn-octyloxy-cyanobiphenyl (8OCB)

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Eine einfache molekular-statistische Theorie der nematischen kristallinflüssigen Phase. Teil l1.

Cited by 1,628 publications

References 0 publications

Nonperturbative renormalization-group approach to frustrated magnets

Nonperturbative renormalization-group approach to frustrated magnets

A model-free temperature-dependent conformational study of n-pentane in nematic liquid crystals

Volumetric study ofn-octyloxy-cyanobiphenyl (8OCB)

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Product

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Eine einfache molekular-statistische Theorie der nematischen kristallinflüssigen Phase. Teil l¹.