True Order Parameter Research Articles

Elucidation of the de Vries behavior in terms of the orientational order parameter, apparent tilt angle, and field-induced tilt angle for smectic liquid crystals by polarized infrared spectroscopy.

We report experimental results of the orientational order parameter, the apparent tilt angle, and the field-induced tilt angle for three chiral smectic liquid crystalline materials investigated using infrared (IR) polarized spectroscopy. The common feature in these materials is use of the core 5-methyl-2- pyrimidine benzoate as the central part of the mesogen. This core is terminated by siloxane or carbosilane chains on one of the ends and by the chiral alkoxy chains on the opposite. These compounds exhibit low concomitant layer shrinkage at the smectic A^{*} (SmA^{*}) to smectic C^{*} (SmC^{*}) transition temperature and within the SmC^{*} phase itself. The maximum layer shrinkage in SmC^{*} is observed as ∼1.5%. We calculate the apparent orientational order parameter, S_{app} in the laboratory reference frame from the observed IR absorbance for homeotropic aligned samples, and the true order parameter, S, is calculated using the measured tilt angle and is also interpolated from Iso-SmA^{*} transition temperature closer to SmC^{*} phase. The apparent tilt angle in the SmA^{*} phase calculated from a comparison of order parameters S and S_{app} is found to be significantly large. A low magnitude of S_{app} found for homeotropic aligned samples in the SmA^{*} phase indicates that the order parameter plays a vital role in determining the de Vries characteristics, especially of exhibiting larger apparent tilt angles. Furthermore there is a significant increase in the true order parameter at temperatures close to SmA^{*} to SmC^{*} transition temperature in all three compounds. The planar-aligned samples are used to study the dependence of induced tilt angle on the applied electric field. The generalized Langevin-Debye model given by Shen etal. reasonably fits the experimental data on the field-induced tilt angle. The results show that the dipole moment of the tilt correlated domain in SmA^{*} diverges as temperature is lowered to the SmA^{*}-SmC^{*} transition temperature. The generalized Langevin-Debye model is also found to be extremely effective in confirming some of the conclusions of the de Vries behavior.

Regarding the measurement of microviscosity in lipid bilayers by EPR

Simulations of electron paramagnetic resonance spectra of stearic acid spin labels in lipid bilayers are used to illustrate the fact that the apparent order parameter Sapp calculated from the spectral shape does not coincide with the true order parameter S in the case of slow motions. While S reflects a static property as the degree of order of the lipid chains, Sapp depends on both order and dynamics. Thus, calibration procedures intended to obtain bilayer microviscosity values from Sapp in the slow motion regime are not reliable. However, Sapp is a useful tool to describe trends in membrane fluidity.

Spherical Model on a Cayley Tree: Large Deviations

We study the spherical model of a ferromagnet on a Cayley tree and show that in the case of empty boundary conditions a ferromagnetic phase transition takes place at the critical temperature \(T_\mathrm{c} =\frac{6\sqrt{2}}{5}J\), where J is the interaction strength. For any temperature the equilibrium magnetization, \(m_n\), tends to zero in the thermodynamic limit, and the true order parameter is the renormalized magnetization \(r_n=n^{3/2}m_n\), where n is the number of generations in the Cayley tree. Below \(T_\mathrm{c}\), the equilibrium values of the order parameter are given by \(\pm \rho ^*\), where $$\begin{aligned} \rho ^*=\frac{2\pi }{(\sqrt{2}-1)^2}\sqrt{1-\frac{T}{T_\mathrm{c}}}. \end{aligned}$$ One more notable temperature in the model is the penetration temperature $$\begin{aligned} T_\mathrm{p}=\frac{J}{W_\mathrm{Cayley}(3/2)}\left( 1-\frac{1}{\sqrt{2}}\left( \frac{h}{2J}\right) ^2\right) . \end{aligned}$$ Below \(T_\mathrm{p}\) the influence of homogeneous boundary field of magnitude h penetrates throughout the tree. The main new technical result of the paper is a complete set of orthonormal eigenvectors for the discrete Laplace operator on a Cayley tree.

Phenomenological theory of uniaxial relaxor ferroelectrics

A phenomenological thermodynamic theory of uniaxial relaxor strontium barium niobate is developed using the Landau–Devonshire approach with two order parameters. The fourth-order thermodynamic potential allowed to explain the shape of the polarization hysteresis loops experimentally observed at different temperatures. We show that the broad maximum of the dielectric permittivity is not related to the phase transition and arise due to the coupling between polarization and true order parameter which has antiferroelectric nature. We found that the phase transition temperature is much higher than the maximum of the dielectric permittivity and very likely corresponds to so-called Burn’s temperature. True order parameter has no simple relation with polar modes.

Probing the A1 to L1 transformation in FeCuPt using the first order reversal curve method

The A1-L10 phase transformation has been investigated in (001) FeCuPt thin films prepared by atomic-scale multilayer sputtering and rapid thermal annealing (RTA). Traditional x-ray diffraction is not always applicable in generating a true order parameter, due to non-ideal crystallinity of the A1 phase. Using the first-order reversal curve (FORC) method, the A1 and L10 phases are deconvoluted into two distinct features in the FORC distribution, whose relative intensities change with the RTA temperature. The L10 ordering takes place via a nucleation-and-growth mode. A magnetization-based phase fraction is extracted, providing a quantitative measure of the L10 phase homogeneity.

Experimental demonstration, using polarized Raman and infrared spectroscopy, that both conventional and de Vries smectic-Aphases may exist in smectic liquid crystals with a first-orderA−C*transition

Two models exist for the orientational distribution of the long molecular axes in smectic-A liquid crystals: the conventional unimodal distribution and the "cone-shaped" de Vries distribution. The de Vries hypothesis provides a plausible picture of how, at a molecular level, a first-order Sm-A to Sm-C* transition may occur, especially if there is little or no concomitant shrinkage of the layer spacing. This work investigates two materials with such transitions: C7 and TSiKN65. The azimuthal distribution of in-layer directors is probed using IR and polarized Raman spectroscopy, which allows us to obtain orientational order parameters. In C7, we observe a discontinuous change in the order parameter, the magnitude of which is small compared with the corresponding change in the in-layer director tilt angle Theta . Assuming that the smectic-A liquid crystal is of the de Vries type, we calculate the Theta required to reproduce the apparent order parameter <P2>app, obtained from IR, by using the true order parameter <P2>, obtained from polarized Raman scattering. The results indicate that, for C7, the tilt angle so calculated is much smaller than that in the Sm-C* angle and hence de Vries behavior may not be the appropriate explanation in this case. Conversely, we find that TSiKN65 shows a different behavior to C7, which can be explained in terms of the de Vries concept. Thus, we conclude that either type of distribution may exist in Sm-A phases which undergo a first-order transition to the Sm-C* phase. We also discuss the changes in the smectic layer spacing and the orientational order parameters across the Sm-A-Sm-C* phase transition, together with changes in birefringence with applied electric field.

Ferroelectric Liquid Crystals

Abstract The idea either to reveal or to construct a liquid ferroelectric was never abandoned by researchers since the discovery of ferroelectricity in solid crystals at the beginning of this century. In principle, nature does not forbid the existence of ferroelectric liquids. For instance, a centro-symmetric liquid can change its point symmetry from the K h , to C∝v , group with the formation of a uniform ferroelectric phase. A liquid without the inversion center can have a phase transition K → C∝, into the inhomogeneous, helical structure. In both these hypothetical cases the spontaneous polarization, P s , would play the role of the true order parameter. However, such liquid ferroelectric phases (proper ferroelectrics) have not been discovered as yet.