Scalar Order Parameter Research Articles

Simulation of the Optical Transmittance of IPS LC-Cell on Temperature Variation

In this paper we calculated optical transmittance of the In-Plane Switching (IPS) liquid crystal (LC) cell with respect to temperature. By considering temperature energy term in the Gibb's free energy, we could achieve the temperature parameters that need to calculate the temperature dependence on the electro-optic characteristics. The calculated temperature parameters permit us to calculate scalar order parameter S with respect to temperature, so that finally we could calculate the optical transmittance of the IPS LC cell as a function of temperature.

Coupled order-parameter system on a scale-free network

The system of two scalar order parameters on a complex scale-free network is analyzed in the spirit of Landau theory. To add a microscopic background to the phenomenological approach, we also study a particular spin Hamiltonian that leads to coupled scalar order behavior using the mean-field approximation. Our results show that the system is characterized by either of two types of ordering: either one of the two order parameters is zero or both are nonzero but have the same value. While the critical exponents do not differ from those of a model with a single order parameter on a scale-free network, there are notable differences for the amplitude ratios and the susceptibilities. Another peculiarity of the model is that the transverse susceptibility is divergent at all T<Tc, when O(n) symmetry is present. This behavior is related to the appearance of Goldstone modes.

Scalar Order in PrFe4P12 Studied by Thermal Expansion and Magnetostriction

We present the results of high-resolution measurements of the thermal expansion and magnetostriction of the cubic filled skutterudite compound PrFe 4 P 12 . The temperature dependence of the thermal expansion Δ L ( T )/ L for the three main symmetry directions are nearly identical below T A , in accordance with a recently proposed scalar order parameter for the A-phase. In the field-angle dependence of the transverse thermal expansion Δ L (θ)/ L along the [001] direction (θ is the angle between the [100] direction and the orientation of a magnetic field within the (001) plane), we find clear twofold oscillation. On the basis of mean-field analyses, we show that the observed twofold oscillation can be interpreted as the the crystal field effect for the cubic T h symmetry. Our results suggest that the crystal field scheme consists of a Γ 1 ground state and a Γ 4 (1) first-excited state, in both the non-ordered and A-phases.

Twist grain boundaries in cubic surfactant phases

Twist grain boundaries in bicontinuous cubic surfactant phases are studied by employing a Ginzburg-Landau model of ternary amphiphilic systems. Calculations are performed on a discrete real-space lattice with periodic boundary conditions for the lamellar L(alpha), gyroid G, diamond D, and the Schwarz P phases for various twist angles. An isosurface analysis of the scalar order parameter reveals the structure of the surfactant monolayer at the interfaces between the oil-rich and water-rich regions. The curvature distributions show that the grain boundaries are minimal surfaces. The interfacial free energy per unit area is determined as a function of the twist angle for the G, D, P, and lamellar phases using two complementary approaches: the Ginzburg-Landau free-energy functional and a geometrical approach based on the curvature energy of a monolayer. For the L(alpha), G, and D phases the interfacial free energy per unit area is very small, has the same order of magnitude, and exhibits a nonmonotonic dependence on the twist angle. The P phase is found to be unstable with respect to the nucleation of grain boundaries.

Effect of magnetic fields on out-of-plane orientations of nematic liquid crystalline polymers under simple shear flow

The effect of magnetic fields on out-of-plane orientations of liquid crystalline polymers (LCPs) under simple shear flows is numerically analyzed using the Doi–Hess equation. The evolution equation for the probability distribution function of the LCP molecules is directly solved without any approximation closure. The initial director is parallel to the vorticity direction. Two cases of the magnetic fields are considered (1) the magnetic field parallel to the flow direction, and (2) the magnetic field parallel to the velocity gradient direction. For both cases a log-rolling orientation state is detected at low shear rates. However, the director is quickly aligned along the direction of magnetic fields because of the deformation of molecules. The field affects on the scalar order parameter rather than the major orientation direction for the magnetic field parallel to the flow direction. On the other hand regarding the magnetic field along the vorticity gradient direction, the effect of the magnetic field is more remarkable on the major orientation in comparison with the effect on the scalar order parameter. Also it is be found that the order parameter is increased obviously with increasing the magnetic fields. It is an efficient way to improve the performance of LCP materials.

Effect of Aerosil Gels on de Gennes Nematic−Smectic Coupling

There is a well-known de Gennes coupling between the scalar nematic order parameter S and the smectic density-wave amplitude /Psi/, which causes the nematic-smectic-A phase transition to cross over from second order to first order via a tricritical point. This sort of crossover is observed for numerous liquid crystals (LCs) with small to moderate nematic ranges. Recent studies of LC+aerosil systems, where the aerosil particles form a soft thixotropic gel, have shown that such aerosil gels can greatly reduce or completely suppress this coupling. The underlying LC critical exponents once de Gennes coupling is absent are discussed and compared with theory.

Orientable and Non-Orientable Line Field Models for Uniaxial Nematic Liquid Crystals

Uniaxial nematic liquid crystals are often modeled using the Oseen-Frank theory, in which the mean orientation of the rod-like molecules is described through a unit vector field n. This theory has the apparent drawback that it does not respect the head-to-tail symmetry in which n should be equivalent to − n; that is, instead of n taking values in the unit sphere S 2, it should take values in the sphere with opposite points identified, i.e., in the real projective plane RP 2. The Landau-de Gennes theory respects this symmetry by working with the tensor Q = s (n ⊗ n − 1/3 Id). In the case of a non-zero constant scalar order parameter s the Landau-de Gennes theory is equivalent to that of Oseen-Frank when the director field is orientable. We report on a general study of when the director fields can be oriented, described in terms of the topology of the domain filled by the liquid crystal, the boundary data and the rate of blow-up of possible singularities. We also analyze the circumstances in which the non-orientable configurations are energetically favoured over the orientable ones.

Experimental Test of Curvature-Driven Dynamics in the Phase Ordering of a Two Dimensional Liquid Crystal

We study electric field driven deracemization in an achiral liquid crystal through the formation and coarsening of chiral domains. It is proposed that deracemization in this system is a curvature-driven process. We test this prediction using the recently obtained exact result for the distribution of hull-enclosed areas in two-dimensional coarsening with nonconserved scalar order parameter dynamics [J. J. Arenzon et al., Phys. Rev. Lett. 98, 145701 (2007)]. The experimental data are in very good agreement with the theory. We thus demonstrate that deracemization in such bent-core liquid crystals belongs to the Allen-Cahn universality class, and that the exact formula, which gives us the statistics of domain sizes during coarsening, can also be used as a strict test for this dynamic universality class.

Persistence of zero modes in a gauged Dirac model for bilayer graphene

A recently constructed model for low-lying excitations in bilayer graphene exhibits midgap, zero-energy modes in its Dirac-type spectrum when a scalar order parameter takes a vortex profile. We show that these modes persist when the dynamics is extended by a gauge field interaction, which also renders finite the vortex energy. The effect of the gauge field on the zero-energy wave function is to shift the phase of the (damped) oscillatory component of the wave function in the absence of the gauge field.

Implementation of Q-Tensor Model in Three-Dimensional Finite Element Method Simulator

In this paper, we report the first successful implementation, to the best of our knowledge of a Q-tensor model in a full three-dimensional (3-D) finite element method (FEM) simulator. Our FEM simulation code is based on the Landau–de Gennes Q-tensor model as well as the models of Dickmann and Nakagawa. The Oseen–Frank free-energy representation was formulated into a 3-D FEM code wherein tensor-order parameters as well as scalar-order parameters were employed for handling the defects and topological transitions such as splay-to-bend transition for the optically compensated bend (OCB) mode. The accuracy of our FEM simulator was verified using our simulation results with Mori's simulation data for the OCB mode. Splay-to-bend transition voltage was calculated to be 4 V according to the Q-tensor-model-based simulation while the conventional vector-model-based FEM solver showed 8 V. Our comparative study revealed that the vector model overestimates splay-to-bend voltage for the OCB mode.

Radiation effects in concentrated alloys and compounds: equilibrium and kinetics of driven systems

What organization of condensed matter does resist irradiation, as a function of irradiation conditions? How to characterize the latter? We survey the advances in the field during the past three decades, when irradiation effects reduce to nuclear collisions. While in simple cases (structure defined by a scalar order parameter) one may define a stochastic potential, which yields the stationary states of the compounds under irradiation and their respective stability, in more general cases, we are left with brute force atomistic simulations to explore materials' behaviour as a function of irradiation conditions. Special attention is given to the kinetics of concentration fields under irradiation, a question with several practical implications. We conclude that irradiation conditions are best defined by three parameters: the cascade features (number of displacements and replacements, length of replacement sequences, …), the frequency of cascade occurrence, and the cumulated dose. We suggest cascade features be named ‘(elementary) dose’ and the cascade occurrence frequency ‘dose rate’. To cite this article: G. Martin, P. Bellon, C. R. Physique 9 (2008).

Phenomenological Theory of a Scalar Electronic Order: Application to Skutterudite PrFe4P12

By phenomenological Landau analysis, it is shown that a scalar order parameter with the point-group symmetry $\Gamma_{1g}$ explains most properties associated with the phase transition in PrFe$_4$P$_{12}$ at 6.5 K. The scalar-order model reproduces magnetic and elastic properties in PrFe$_4$P$_{12}$ consistently such as (i) the anomaly of the magnetic susceptibility and elastic constant at the transition temperature, (ii) anisotropy of the magnetic susceptibility in the presence of uniaxial pressure, and (iii) the anomaly in the elastic constant in magnetic field. An Ehrenfest relation is derived which relates the anomaly of the magnetic susceptibility to that of the elastic constant at the transition.

Magnetic properties of two-phase superconductors

We have recently proposed a theoretical model for superconductors endowed with two distinct superconducting phases, described by two scalar order parameters which condensate at different critical temperatures. On analyzing the magnetic behavior of such systems, we have found some observable differences with respect to the case of ordinary Ginzburg–Landau superconductors. In particular, at low temperature the London penetration length is strongly reduced and the Ginzburg–Landau parameter κ becomes a function of temperature. By contrast, in the temperature region between the two-phase transitions κ is constant and the system is a type-I or a type-II superconductor depending on the ratio between the critical temperatures.

Dynamical replica analysis of processes on finitely connected random graphs: I. Vertex covering

We study the stochastic dynamics of Ising spin models with random bonds, interacting on finitely connected Poissonian random graphs. We use the dynamical replica method to derive closed dynamical equations for the joint spin–field probability distribution, and solve these within the replica-symmetry ansatz. Although the theory is developed in a general setting, with a view to future applications in various other fields, in this paper we apply it mainly to the dynamics of the Glauber algorithm (extended with cooling schedules) when running on the so-called vertex cover optimization problem. Our theoretical predictions are tested against both Monte Carlo simulations and known results from equilibrium studies. In contrast to previous dynamical analyses based on deriving closed equations for only a small number of scalar order parameters, the agreement between theory and experiment in the present study is nearly perfect.

Effect of magnetic field on molecular orientation of nematic liquid crystalline polymers under simple shear flow

The effect of magnetic fields on molecular configuration of liquid crystalline polymers (LCPs) under shear flows is numerically analyzed using the Doi theory. The evolution equation for the probability density function of the liquid crystalline polymer (LCP) molecules is directly solved without any closure approximations. Two cases of the magnetic fields are considered: (1) the magnetic field parallel to the flow direction, and (2) the magnetic field parallel to the velocity gradient direction. For both cases, the magnetic fields strongly affect the transition among flow-orientation modes, such as tumbling, wagging, and aligning modes. When the magnetic field is imposed on the LCP shear flow, a new aligning flow-orientation mode emerges at low shear rate, which is macroscopically the same, but microscopically quite different from the ordinary aligning mode. For the magnetic field parallel to the flow direction, the field affects the scalar order parameter rather than the major orientation direction. On the other hand, for the magnetic field parallel to the velocity gradient direction, the effect of the field on the major orientation direction is more remarkable than the effect on the scalar order parameter.

Master crossover functions for one-component fluids

By introducing three well-defined dimensionless numbers, we establish the link between the scale dilatation method able to estimate master (i.e., unique) singular behaviors of the one-component fluid subclass and the universal crossover functions recently estimated [Garrabos and Bervillier, Phys. Rev. E 74, 021113 (2006)] from the bounded results of the massive renormalization scheme applied to the Phi(d)(4)(n) model of scalar order parameter (n=1) and three dimensions (d=3), representative of the Ising-like universality class. The master (i.e., rescaled) crossover functions are then able to fit the singular behaviors of any one-component fluid without adjustable parameter, using only one critical energy scale factor, one critical length scale factor, and two dimensionless asymptotic scale factors, which characterize the fluid critical interaction cell at its liquid-gas critical point. An additional adjustable parameter accounts for quantum effects in light fluids at the critical temperature. The effective extension of the thermal field range along the critical isochore where the master crossover functions seems to be valid corresponds to a correlation length greater than three times the effective range of the microscopic short-range molecular interaction.

Metallomesogens as Biaxial Dopants in a Calamitic Nematic Liquid Crystal

The electric field induced nematic order reconstruction is a way to achieve controlled transitions between uniaxial nematic textures with different topologies, hence allowing intrinsic textural bistability. The order reconstruction connects perpendicular nematic director orientations by exchanging two eigenvalues of the nematic order tensor Q , implying intermediate transient biaxial order. This phenomenon avoids the full nematic melting; in fact the nematic scalar order parameter does not vanish. The Biaxial Order Reconstruction in a calamitic Nematic (BORN) is mainly governed by the biaxial coherence length ξ b . Therefore, by varying ξ b , one can favour or inhibit the transient biaxial order. Recently, it has been demonstrated that ξ b can be controlled by suitable dopants and in this work we study the BORN transition threshold for liquid crystal mixtures made of the commercial nematic liquid crystal E7 and three different metallomesogens with board-like shape.

Chromonic nematic phase and scalar order parameter of indanthrone derivative with ionic additives

We investigate influence of different ionic additives on the phase behaviour and scalar order parameter of lyotropic chromonic nematic liquid crystals formed by the molecules representing derivatives of indanthrone. KI, (NH4)2SO4 and NaCl salts increase biphasic nematic region on the temperature-concentration phase diagram, whereas the scalar orientational order parameter is hardly sensitive to their presence. We suggest that these changes are attributed to increase in the aggregate length and polydispersity of the latter, while the interaction between aggregates remains unaffected. The Na2SO4 salt lowers anomalously the measured value of the scalar order parameter to 0.42, for which the nematic phase should not exist. We address this anomaly to modification of the shape of chromonic aggregates due to growing of side chains within the rod-like aggregates. The NH4Cl salt does not affect the phase diagram and the scalar order parameter of Blue 250 chromonematic. PACS: 78.20.Ci, 87.15.Mi, 78.20.Fm, 42.79.Kr, 61.30.Gd. UDC: 535.34

Orientable and non‐orientable director fields for liquid crystals

AbstractUniaxial nematic liquid crystals are often modelled using the Oseen‐Frank theory, in which the mean orientation of the rodlike molecules is described through a unit vector field n. This theory has the apparent drawback that it does not respect the head‐to‐tail symmetry in which n should be equivalent to −n; that is, instead of n taking values in the unit sphere 𝕊2, it should take values in the sphere with opposite points identified, i.e. in the real projective plane ℝP2. The Landau‐de Gennes theory respects this symmetry by working with the tensor Q = s (n ⊗ n − ⅓Id). In the case of a non‐zero constant scalar order parameter s the Landau‐de Gennes theory is equivalent to that of Oseen‐Frank when the director field is orientable.We report on a general study of when the director fields can be oriented, described in terms of the topology of the domain filled by the liquid crystal, the boundary data and the Sobolev space to which Q belongs. We also analyze the circumstances in which the non‐orientable configurations are energetically favoured over the orientable ones. (© 2008 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Derivation of Frank-Ericksen elastic coefficients for polydomain nematics from mean-field molecular theory for anisotropic particles

The complete free energy density, including all eight Frank-Ericksen elastic coefficients and all anisotropic Ericksen-Leslie viscosities of nematic and discotic polydomain nematic liquid crystals are derived from the kinetic model of a spatially inhomogeneous system of uniaxial liquid crystal molecules with given shape. The authors take into account the known anisotropy of the translational diffusion tensor and its dependence on shape, rotational diffusion, and a macroscopic flow field for elongated particles (including disks). In this manuscript they release all of the previously made assumptions about closure relationships or the interrelationship between Frank elastic coefficients (such as a simple quadratic closure, or the one-constant approximation) in order to derive results which not only generalize or improve earlier results, but also apply to more general cases, and for arbitrary forms of the mean-field potential in terms of the scalar order parameter (or temperature). The kinetic model is shown to confirm all proposed inequalities between Frank-Ericksen-Leslie coefficients, i.e., satisfies the main result of the macroscopic approaches. They resolve quantitatively the effect of molecular shape, order parameters, and mean-field strength and form of the mean-field potential on all results, compare with experimental findings, theoretical predictions, and discuss some implications for various special cases of the general result derived in this work.