Uniaxial Phase Research Articles

Influence of flexibility on the biaxial nematic phase of bent core liquid crystals: A Monte Carlo simulation study

The influence of flexibility on the phase behavior of bent core biaxial nematic liquid crystals is investigated using Monte Carlo simulation. A generic model for rigid V-shaped molecules is extended to include a bending potential, which allows us to investigate the relationship between the flexibility of a bent core molecule and its ability to form a biaxial nematic phase. The simulation results indicate that, as the flexibility is increased, the biaxial nematic phase is typically forced to lower temperatures. In contrast, the stability of the uniaxial nematic phase with respect to the isotropic phase is not significantly affected. The Landau point is split into a line of first order phase transitions between two different uniaxial phases. In some cases, the uniaxial nematic to biaxial nematic transition becomes first order, and a shape change is observed at this transition.

Macroscopic and molecular symmetries of unconventional nematic phases

The effects of the molecular symmetry on macroscopic properties of conventional and unconventional nematic phases are investigated theoretically. These effects concern: (1) the form of the molecular orientation fluctuations, (2) the thermodynamic behavior and the list of stable ordered phases, (3) the effective symmetry of the molecules in the ordered phases. The order-parameter consists of tensors forming the main harmonics of the fluctuation distribution. In conventional models (valid for uniaxial molecules) a single tensor is sufficient while unconventional models (valid for less symmetric molecules) need several tensors with the same rank. We analyze the qualitative differences arising when the number of equivalent tensors varies. We show how to work out complete models in the general case, and to calculate the sequences of stable phases and the corresponding effective molecular symmetries. This yields, for each molecular group and each tensor rank, a complete classification and a deep insight into the structure of thermotropic nematics. This work generalizes the approach we have applied to polar nematics recently observed in polyester compounds and to unconventional uniaxial and biaxial phases of bent-core materials.

Electric-Field-Induced Polar Biaxial Order in a Nontilted Smectic Phase of an Asymmetric Bent-Core Liquid Crystal

A polarization reorientation process has been studied by means of optical second-harmonic generation in an optically uniaxial smectic phase of an asymmetric bent-core liquid crystal. A nontilted polar smectic order with a biaxial order is induced by applying an electric field to the uniaxial nonpolar smectic phase. This phenomenon was well simulated by the two-dimensional Langevin process, i.e., electric-field-induced continuous molecular reorientation against thermal agitation. The simulation suggests that about 200s of molecules form a polar domain and cooperatively respond to the applied field. The existence of the polar domains and their reorientation are consistent to the dielectric measurement; a high dielectric constant of about 60 at the kHz range is markedly suppressed by applying a bias field.

Theory of the intermediate tilted smectic phases and their helical rotation

A molecular-statistical theory for the entire sequence of the chiral tilted smectic phases is derived. Uniaxial and biaxial subphases were found to be stable in different temperature ranges depending on the molecular parameters. The model of a chiral molecule possessing a strong transverse terminal dipole moment and a quadrupole moment located in the molecular core was used. Direct dispersion and electrostatic interactions (modulated by shape) between molecules located in the same or in the neighboring smectic layers are taken into account. An effective long-range interaction arises after the minimization of the free energy with respect to polarization vectors. If the molecular quadrupole moment is small, only uniaxial phases with different periodicities arise. Their periodicity may be tens and hundreds of layers (Sm-C*), or approximately two layers (Sm-C*)(Sm-C*A), or several layers (Sm-C*alpha). In the presence of the nonpolar biaxial ordering (in addition to polarization) there is a cap-shaped border in the phase diagram that separates Sm-C*A, Sm-C*, and Sm-C*alpha. If the molecules are nonchiral, Sm-CA, Sm-C, and the de Vries's phases arise instead of the three phases mentioned above. If the molecular quadrupole moment is large, the left "arm" of the border breaks into two lines, and a sequence of biaxial subphases arises in the area between these two lines. Among these biaxial subphases, the one with periodicity of three smectic layers appears to be the broadest in the temperature range. In addition, the subphases with different periodicities were found to be stable in narrow temperature ranges. The long helical rotation in every biaxial subphase is calculated. It is found to change sign between the three-layer subphase and Sm-C*, and may diverge in the four-layer subphase if it arises. All calculations are done with help of (A)FLC Phase Diagram Plotter software developed by the first author and available at his web-page.

Transverse Rupture Strength of M3:2 High Speed Steel Produced through Conventional Casting and Powder Metallurgy Techniques

The main aim of this work is to study the influence of the heat treatment on the transverse rupture strength of three M3:2 high speed steel obtained by differents techniques. PM Sinter 23 obtained by hot isostatic pressing (HIP) of gas atomized powders, a vacuum sintered high speed steel obtained by uniaxial cold compaction and liquid phase sintering of M3:2 water atomized powders and a conventional (cast to ingot and hot work) VWM3C were submitted to hardening in order to determine the influence of this treatment on the transverse rupture strength. The two PM high speed steels and the conventional one were submitted to heat treatment of hardening with austenitizing temperatures of 1140, 1160, 1180 and 1200 °C and tempering at 540 and 560 °C. The effectiveness of the heat treatment was determined by hardness tests (Rockwell C hardness). The microstructure was evaluated by scanning eletronic microscopy (SEM). At least five samples of these three high speed steels were manufactured, austenitized, quenched and tempered as described above and fractured in three point bending tests in order to evaluate the influence of this treatment on the transverse rupture strength (TRS).

Uniaxial to unidirectional transition of perpendicular interlayer coupling in IrMn∕CoFe∕NiFeO∕CoFe quadrilayers

We studied the interlayer coupling in the quadrilayer consisting of IrMn∕CoFe (bottom layer)/NiFeOx∕CoFe (top layer). An in-plane perpendicular interlayer coupling is observed between CoFe layers at room temperature. An anisotropy transition from uniaxial to unidirectional in a perpendicular direction is observed around Tt=55K. The nano-oxide layer NiFeOx shows no distinguishable ferromagnetic signal in the high-temperature (uniaxial) phase, while a strong signal appeared in the low-temperature (unidirectional) phase. A possible two-component scenario, in which the nano-oxide layer may contain both amorphous short-range antiferromagnetic domains and superparamagneitc clusters, is proposed to explain the phase transition.

Uniaxial ordering and rotator phase of ribbonlike polymers

The phase transition in bended and twisted ribbonlike polymer systems is described in meanfield approximation by use of the lattice model with directed self-correlated walks. This phase transition can be of either first or second order depending on the ratio of the constants in the effective energy of interaction of a polymer with the environment. For the first-order phase transition it is found, in particular, that the phase transition temperature depends on polymer length, decreasing linearly with reciprocal length for lengths exceeding 100 monomer units. On the other hand, the jump of the specific entropy is independent of the polymer length for the molecules containing more than 30 monomers. The obtained results are in full agreement with the existing experimental data.

Theory of uniaxial and biaxial nematic phases in bent-core systems

We present a phenomenological theory of the uniaxial and biaxial nematic phases recently observed in bent-core mesogenic systems. To take into account the molecular anisotropy we introduce two types of symmetry transformation: "external" rotations which turn the molecules with respect to the laboratory axes and "internal" rotations which turn them with respect to the molecular axes. We show then that the description of bent-core nematic phases involves two isomorphic copies of the conventional tensor order parameter instead of one for conventional rod like and disk like molecules. The second tensor stabilizes additional monoclinic and triclinic phases and merges the calamitic and diskotic uniaxial states into a single phase. The uniaxial and biaxial phases can appear, respectively, in six and 21 distinct configurations according to the molecular axis that dominates the ordering process. We predict a number of isostructural transitions between these configurations within a thermodynamic Landau-type approach. Because bent-core molecules have the same microscopic behavior as orthorhombic micelles, the biaxial phase can be stabilized in both systems.

Chain dynamics in a chiral C phase by deuteron spin relaxation study

Molecular reorientations and internal conformational transitions of an aligned chiral liquid crystal (LC) 10B1M7 are studied by means of deuterium spin-lattice relaxation in its smectic A (SmA) and smectic C* (SmC*) phase. The motional model which is applicable to uniaxial phases of many LCs is found to be adequate even when the phase is a tilted SmC* phase. The deuterium NMR spectrum in this phase cannot discern rotations of the molecular director about the pitch axis. The basic assumption is that the phase biaxiality is practically unobservable. However, the relaxation rates can be accounted for by the tilt angle between the molecular director and the layer normal in the SmC* phase. The tumbling motion appears to show a higher activation energy upon entering from the uniaxial SmA into the SmC* phase.

Damages and Microstructural Variation of High-lead and Eutectic SnPb Composite Flip Chip Solder Bumps Induced by Electromigration

The electromigration behavior of the high-lead and eutectic SnPb composite solder bumps was investigated at 150 °C with 5 × 103 A/cm2 current stressing for up to 1711 h. The diameter of the bumps was about 125 μm. The underbump metallization (UBM) on the chip side was sputtered Al/Ni(V)/Cu thin films, and the Cu pad on the board side was plated with electroless Ni/Au. It was observed that damages occurred in the joints in a downward electron flow (from chip side to the substrate side), while those joints having the opposite current polarity showed only minor changes. In the case of downward electron flow, electromigration damages were observed in the UBM and solder bumps. The vanadium in Ni(V) layer was broken under current stressing of 1711 h while it was still intact after current stressing of 1000 h. The electron probe microanalyzer (EPMA) elemental mapping clearly shows that the Al atoms in the trace migrated through the UBM into the solder bump during current stressing. Voids were found in the solder bump near the UBM/solder interface. The Sn-rich phases of the solder bumps showed gradual streaking and reorientation upon current stressing. This resulted in the formation of uniaxial Sn-rich phases in the middle of the solder bump, while the columnar and fibrous Sn-rich phases were formed in the surrounding regions. The formation mechanism of electromigration-induced damage to the UBM structure and solder bump were discussed.

Nanobelt Self-Assembly from an Organic n-Type Semiconductor: Propoxyethyl-PTCDI

Nanobelt structures have been fabricated for an n-type semiconductor molecule, N,N'-di(propoxyethyl)perylene-3,4,9,10-tetracarboxylic diimide (PTCDI). The short alkyloxy side chain not only affords effective pi-pi stacking in polar solvents for self-assembling but also provides sufficient solubility in nonpolar solvents for solution processing. As revealed by both AFM and electron microscopies, the nanobelts have an approximately rectangular cross section, with a typical thickness of about 100 nm and a width in the range of 300-500 nm. The length of the nanobelts ranges from 10 to a few tens of micrometers. The highly organized molecular packing (uniaxial crystalline phase) has been deduced from the measurement of electron diffraction and polarized microscopy imaging. The detected optical axis is consistent with the one-dimensional stacking of the molecules.

Tricritical points in biaxial liquid crystal phases

We further pursue the analysis of a mean-field model recently proposed by Sonnet [Phys. Rev. E 67, 061701 (2003)] to describe nematic biaxial phases. This model, which is based on a simplified version of Straley's pair potential, is characterized by the prediction of a tricritical point along the transition line between uniaxial and biaxial phases. We show that the same model predicts another tricritical point, but along the line of the direct isotropic-to-biaxial transition. Our prediction is quantitative, as it stems from an analytical criterion for tricriticality.

Spin-Reorientation Transitions and Domain Structure in TbFe[sub 11 – ][sub x][sub ]Co[sub x]Ti Single Crystals

The magnetic structure of single-crystal TbFe11−xCoxTi compounds has been studied over a broad temperature range and in strong magnetic fields (up to 14 T). Measurements of magnetization and magnetostriction and a study of the domain structure revealed that spin-reorientation transitions (SRTs) in TbFe11−xCoxTi single crystals depend substantially on the cobalt concentration. It was established that the SRT temperatures and threshold magnetic fields are governed by the interplay between the magnetic anisotropies of the 3d and terbium sublattices. It is shown that, in these compounds, the low-temperature phase with planar anisotropy is separated in temperature from the high-temperature phase with uniaxial anisotropy by an intermediate metastable phase containing domains of the uniaxial or planar phase.

Phase diagram of transitions from an isotropic phase to nematic and smectic (uniaxial, biaxial) phases in liquid crystals with achiral molecules

The phase diagrams of transitions from an isotropic phase to nematic and smectic phases are investigated within a simple phenomenological model of the Landau thermodynamic potential. The conditions of the isomorphic phase transition between two uniaxial smectic phases and the direct transition from the isotropic phase to the uniaxial and biaxial smectic phases are determined. The behavior of the order parameters is described along different thermodynamic paths. The theoretical results are discussed using the example of liquid-crystal phases in compounds with banana-shaped achiral molecules.

Cholesteric Liquid‐Crystalline Side‐on Polysiloxanes: Effects of Biaxiality on the Cholesteric Structure

AbstractSummary: Biaxial side‐on cholesteric copolysiloxanes with laterally attached mesogenic groups were investigated in mixtures with a low molar mass liquid crystal. While mixtures with a low concentration of the polymer exhibit the conventional fingerprint texture, for concentrations above about 60 mol‐% characteristic irregularities appear in the cholesteric structure that are obviously due to phase biaxiality. Besides the absence of pseudo‐isotropic lines, irregular patterns perpendicular to the helix axis emerge and the periodic distance of regions with similar optical properties along the helix axis is strongly disturbed. This suggests that the photonic band gap width of a uniaxial cholesteric phase becomes strongly affected when a phase transformation into a biaxial cholesteric phase occurs.Cholesteric fingerprint texture of a mixture of uniaxial nematic monomer and biaxial cholesteric polymer.magnified imageCholesteric fingerprint texture of a mixture of uniaxial nematic monomer and biaxial cholesteric polymer.

MOLECULAR THEORY ON LIQUID CRYSTALLINE MIXTURES

The nematic-isotropic phase transitions in mixtures of rod-like and disc-like molecules are studied by a mean field theory. We consider both attraction and hard-core repulsion for the model molecules, thermotropic phase transitions are found from the isotropic to one of the two types of uniaxially symmetric nematic phases: optically positive N+ and negative N−. On the other hand, biaxially symmetric nematic phase is shown to be always less stable than the uniaxial phase. We predict that re-entrant phase transition occur for the lyotropic system.

A new approach to the extraction of dynamic information from the analysis of 2H NMR relaxation times in tilted chiral mesophases

A new approach to analyze 2H spin-lattice relaxation times in tilted smectic phases in terms of dynamic parameters for individual molecular and internal motions is reported. Such analysis, commonly applied to uniaxial phases, could not be extended so far to chiral smectic phases for both experimental and theoretical reasons. These problems have been here overcome neglecting the dependence of spectral densities on the azimuthal angle φ, and adopting a global target approach. In this way, the existing diffusional models can be used to determine dynamic parameters in chiral smectic C phases. An application to the ferroelectric mesogen 8BEF5 is reported.

Dielectric shape dispersion and biaxial transitions in nematic liquid crystals

Using two order tensors, we propose a mean-field model to describe the uniaxial and biaxial phases of nematogenic molecules presenting a shape dispersion of their biaxial dielectric susceptibility. We recover the classical isotropic-uniaxial-biaxial sequence of phases. The phase diagram exhibits a tricritical point, a feature that cannot be retraced in the other mean-field models established for molecules without shape dispersion.

Exchange coupling in FePt permanent magnets

FePt (for 40–60 at. % Fe) exhibits an order–disorder transformation. The disordered phase is face centered cubic and magnetically soft while the ordered phase is tetragonal and shows high magnetic anisotropy. Since the changes in volume between the two phases are small, it is easy for the soft and hard phases to coexist in a uniform manner. Thus, we have an ideal system with which to investigate the basic features of exchange coupled magnets. Bulk Fe0.6Pt0.4 exhibits reasonably large permanent magnetic properties with a maximum energy product of ∼15 MG Oe (120 kJ/m3) without the need for special processes to promote grain alignment. The high energy product is partially a result of the high ratio of remanence to the saturation induction which amounts to 0.68 as opposed to the ratio of 0.5 for an assembly of randomly oriented uniaxial magnets. This enhanced remanence is predicted by the exchange-spring magnet model for a mixture of cubic and uniaxial phases. In order to verify that the high remanence of the FePt magnets is indeed caused by this exchange mechanism and not by a fortuitous formation of magnetic texture during sample preparation, we have prepared cubic samples of Fe0.6Pt0.4 and measured the B–H loops along the three principal directions of the cube using a vibrating sample magnetometer. The hysteresis loops are identical in all three directions, indicating the absence of strong texture in this material. After correction of the demagnetizing factor, the ratio of remanence to saturation induction is 0.66–0.68. This is consistent with that in the exchange coupling model. The highest energy product in our study was found for the as-quenched samples. Further annealing, with the intention of promoting the formation of hard magnetic phases, reduced the coercivity and remanence. This suggests that improved results may be achieved by initial suppression of the formation of the hard phases by modification of the quenching process and alloying. An ideal exchange coupled system could be designed based on such a starting material.

Theory and simulation of biaxial nematic and orthogonal smectic phases formed by mixtures of board-like molecules

Variational cluster calculations and Monte Carlo simulations are applied to hard-body board-like models of biaxial molecules forming liquid crystalline phases. The molecular long axes are assumed for simplicity to be fully oriented. Depending on the extent of transverse anisometry in the molecular shape, these systems can exhibit biaxial nematic phases as well as uniaxial and biaxial orthogonal smectic phases. It is shown that the region of thermodynamic stability for the biaxial nematic phase is considerably broadened in binary mixtures of molecules with the same cross section but differing in their long dimension.