Dependence Of Order Parameter Research Articles

Investigation of the viscoelastic properties of 4-propoxy-biphenyl-4-carbonitrile

ABSTRACTWe report on the temperature-dependent measurements of dielectric permittivity, birefringence, elastic constants and rotational viscosity for 4-propoxy-biphenyl-4-carbonitrile in the nematic region. The temperature dependence of the three elastic constants was determined from studies of the Freédericksz transition. The thermal dependence of elastic constants shows features similar to the literature (bend > splay > twist). Elastic constants are proportional to the square of the order parameter. Temperature-dependent dielectric characterisation was carried out at a frequency of 10 kHz. The compound shows positive dielectric anisotropy in the nematic phase. The rotational viscosity is found to be relatively low. Temperature dependence of order parameter is estimated using Haller’s method. The figure of merit was also calculated as a function of temperature.

Phase relations in superconductor–normal metal–superconductor tunnel junctions

The phase difference $\phi$, between the superconducting terminals in superconductor-normal metal-superconductor tunnel junctions (SINIS), incorporates the phase differences $\chi_{1,2}$ across thin interfaces of constituent $SIN$ junctions and the phase incursion $\varphi$ between the side faces of the central electrode of length $L$. It is demonstrated here that $\chi_{1,2}$ pass through over their proximity-reduced domain twice, there and back, while $\phi$ changes over the single period. Two corresponding solutions, that describe the double-valued order-parameter dependence on $\chi_{1,2}$, jointly form the single-valued dependence on $\phi$, operating in two adjoining regions of $\phi$. The phase incursion $\varphi$ plays a crucial role in creating such a behavior. The current-phase relation $j(\phi,L)$ is composed of the two solutions and, at a fixed small $L$, is characterized by the phase-dependent effective transmission coefficient.

Graphical representations of the Maier–Saupe mean field theory in nematic liquid crystals

ABSTRACTWe have developed the graphical representation to analyse the Maier–Saupe (MS) mean field theory in nematic molecular system. Based on the molecular field theory, the transcendental equations for the Helmholtz free energy and the orientational order parameter are derived and graphically represented for several physical parameters, from which the critical values of temperatures and order parameters are uniquely determined. The empirical formulae based on a four-parameter power law for temperature dependence of order parameter are presented and compared with the MS theory, of which a modified Haller equation of the form yields the best result in a large portion of nematic range within ~0.5% deviation from the mean field theory. We also present the comparison of the MS theory with the Landau–de Gennes theory for universal ratios of the characteristic order parameters.

Optical and dielectric parameters of a laterally difluorinated phenylbicyclohexane liquid crystalline compound

The temperature variation of the refractive indices in the nematic range of a laterally difluorinated phenylbicyclohexane liquid crystalline compound was determined using the thin prism technique. Birefringence and effective geometry parameter of this LC compound was calculated from the measured refractive indices. Using a four-parameter model, the temperature variation of the refractive indices and birefringence was theoretically fitted. The compound is found to have low value of birefringence and high value of effective geometry parameter. Using refractive index data, three different methods were used in this work to obtain temperature dependence of order parameter, namely Vuks’ method, Haller approximation method, and method based on effective geometry parameter. All of them show the same trend. The temperature variation of dielectric permittivities of the compound was done at frequency 1 kHz by an LCR meter. The temperature variation of dielectric anisotropy of the compound was calculated from the experimentally measured values of dielectric permittivities. The compound shows moderate negative dielectric anisotropy.

Investigation of Phase Transitions in Nematic Liquid Crystals by Fractional Calculation

In this study, we investigate nematic-isotropic phase transitions in liquid crystals using fractionally generalized form of the Maier-Saupe Theory (MST). MST is one of the mean-field theories commonly used in the nematic liquid crystals which proved to be extremely useful in explaining nematic-isotropic phase transitions. Fractionally obtained results compared with those of the experimental data for p-azoxyanisole (PAA) in the literature. In this context, the dependence of fourth rank order parameters on second rank order parameters is handled by being a measure of fractality of space. It is observed that the variation of second-rank and fourth rank order parameters versus temperature are in accordance with some values of fractal dimensions. As a result, we can conclude that there is a close relationship between temperature and fractional derivative order parameters.

Microscopic Theory of Directional-Order-Related Magnetocrystalline Anisotropy Energy of L10-Type Alloys

We have theoretically investigated the chemical order parameter (S) dependence of magnetocrystalline anisotropy energy (MAE) of L10-type alloys by means of the second-order perturbation in terms of...

SU(3) Polyakov Linear-Sigma Model: Magnetic Properties of QCD Matter in Thermal and Dense Medium

The linear-sigma model, in which information about confining gluons is included through the Polyakov-loop potential (PLSM), is considered in order to perform a systematic study for various magnetic properties of QCD matter under extreme conditions of high temperatures and densities and finite magnetic field strengths. The introduction of magnetic field to the PLSM Lagrangian requires suitable utilization of Landau quantization, modification in the dispersion relations, and momentum-space dimension-reduction. We observed that increasing the magnetic field leads to filling-up lower Landau levels first and decreasing the number of occupied levels. We conclude that the population of Landau levels is most sensitive to the magnetic field and to the quark charges. The influences of finite magnetic field on the temperature dependence of chiral and deconfinement order-parameter(s) are studied. We present estimations for the magnetization, the magnetic susceptibility, the permeability and the catalysis properties of QCD matter as functions of temperature. The dependences of the resulting freezeout parameters, temperatures and baryon chemical potentials on the corresponding magnetic field strengths have been analyzed, as well. These calculations are compared with recent lattice QCD simulations, whenever available. We conclude that the QCD matter seems to have paramagnetic property at temperatures greater than the critical one. There is an evidence for weak diamagnetic property at low temperatures. Last but not least, we observe that the magnetic catalysis is inverse, namely the critical temperatures decrease with increasing the magnetic field.

Optical and X-ray studies of a four component cyano liquid crystal mixture: Comparison of properties with that of a similar mixture

Optical and X-ray studies have been conducted on a four component liquid crystal mixture (code name 2013) with cyano–end groups in all the four components and a lateral substitution of fluorine atom in one of them. The variations in the optical birefringence with temperature, have been investigated and the thermal dependence of polarisability anisotropy and orientational order parameter have been evaluated. X-ray studies have been conducted to determine the effective molecular characteristics such as apparent molecular length and inter molecular distance and their variations with temperature. From nature of molecular alignment as envisaged from X-ray photographs the order parameter variation with temperature has been determined and compared with macroscopic order parameter variation as determined from birefringence studies. The results have been compared with these obtained for another structurally similar four-component liquid crystal mixture (code name 2014) with isothiocyanato end group in place of cyano.

Engineering frequency-dependent superfluidity in Bose-Fermi mixtures

Unconventional superconductivity or superfluidity are among the most exciting and fascinating quantum states in condensed matter physics. Usually these states are characterized by non-trivial spatial symmetry of the pairing order parameter, such as in $^{3}He$ and high-$T_{c}$ cuprates. Besides spatial dependence the order parameter could have unconventional frequency dependence, which is also allowed by Fermi-Dirac statistics. For instance, odd-frequency pairing is an exciting paradigm when discussing exotic superfluidity or superconductivity and is yet to be realized in the experiments. In this paper we propose a symmetry-based method of controlling frequency dependence of the pairing order parameter via manipulating the inversion symmetry of the system. First, a toy model is introduced to illustrate that frequency dependence of the order parameter can be adjusted by controlling the inversion symmetry of the system. Second, taking advantage of the recent rapid developments of shaken optical lattices in ultracold gases, we propose a Bose-Fermi mixture to realize such frequency dependent superfluids. The key idea is introducing the frequency-dependent attraction between Fermions mediated by Bogoliubov phonons with asymmetric dispersion. Our proposal should pave an alternative way for exploring frequency-dependent superconductors or superfluids with cold atoms.

Density-Functional Tight-Binding Molecular Dynamics Simulations of Excess Proton Diffusion in Ice Ih, Ice Ic, Ice III, and Melted Ice VI Phases.

The structural, dynamical, and energetic properties of the excess proton in ice were studied using density-functional tight-binding molecular dynamics simulations. The ice systems investigated herein consisted of low-density hexagonal and cubic crystalline variants (ice Ih and Ic) and high-density structures (ice III and melted ice VI). Analysis of the temperature dependence of radial distribution function and bond order parameters served to characterize the distribution and configuration of hundreds of water molecules in a unit cell. We confirmed that ice Ih and Ic possess higher hexagonal symmetries than ice III and melted ice VI. The estimated Grotthuss shuttling diffusion coefficients in ice were larger than that of liquid water, indicating a slower proton diffusion process in high-density structures than in low-density systems. The energy barriers calculated on the basis of the Arrhenius plot of diffusion coefficients were in reasonable agreement with experimental measurement for ice Ih. Furthermore, the energy barriers for high-density structures were several times larger than those of low-density systems. The simulation results were likely related to the suppression of proton transfer in disordered water configurations, in particular, ice with low hexagonal symmetry.

Spin-polarized local density of states around vortex in helical p-wave superconductors

Based on the quasi-classical Eilenberger theory, we investigate the magnetic field dependence of order-parameters and spin-polarized local density of states (LDOS) in the vortex lattice state of helical p-wave superconductors. The spin-polarized LDOS is induced by the vorticity coupling to the chirality of up-spin pair or down-spin pair, even when Knight shift does not change. We clarify the instability of the helical p-wave state at high field, and that the spin-polarized LDOS shows the unique behaviors of the helical p-wave state.

Consistent regularization and renormalization in models with inhomogeneous phases

In many models in condensed matter and high-energy physics, one finds inhomogeneous phases at high density and low temperature. These phases are characterized by a spatially dependent condensate or order parameter. A proper calculation requires that one takes the vacuum fluctuations of the model into account. These fluctuations are ultraviolet divergent and must be regularized. We discuss different ways of consistently regularizing and renormalizing quantum fluctuations, focusing on momentum cutoff, symmetric energy cutoff, and dimensional regularization. We apply these techniques calculating the vacuum energy in the Nambu-Jona-Lasinio model in $1+1$ dimensions in the large-${N}_{c}$ limit and in the $3+1$ dimensional quark-meson model in the mean-field approximation both for a one-dimensional chiral-density wave.

Microcanonical Monte Carlo Simulation of 2D 4-State Potts Model

Monte Carlo simulation of two dimensional 4 state Potts model has been carried out in microcanonical ensemble. The simulations were done on a 30 × 30 system with periodic boundary conditions. The temperature dependence of energy and order parameter has been calculated. The transition in 4-state Potts model is concluded to be first-order in nature. The transition temperature and latent heat of the first-order transition have been found to be 0.92 and 0.18, respectively.

Large reduction in the magnitude and thermal variation of Frank elastic constants in a gold nanorod/nematic composite

We report measurements of splay and bend Frank elastic constants in a composite comprising a nematic liquid crystal doped with a small concentration of sterically stabilized gold nanorods. The composite exhibits not only a large reduction in the magnitude of the threshold voltage for switching (Vth, 20%), as well as of the splay (K11, 40%) and bend (K33, 40%) elastic constants, but also presents an unprecedented feature: a substantial diminution in the temperature dependence of these parameters, almost to the point of becoming thermally invariant. This observation is significant because the electro-optic switching of liquid-crystal devices is largely controlled by the K11 and K33 elastic constants. Electrical conductivity measurements also show interesting behavior upon the inclusion of nanorods. Whereas the intrinsic Arrhenius behavior governing the temperature dependence is enhanced, the frequency dependence shows qualitative features of Jonscher’s universal model, albeit with a higher exponent. Further, photoisomerization of an azobenzene guest component provides an additional influence on the elastic constants. The results are discussed in terms of (a) the effect of the order parameter dependence seen from the viewpoint of an extended mean-field model, and (b) local order. The advantage of incorporating nanorods with photofunctionality is also pointed out.

Travelling waves in arrays of delay-coupled phase oscillators.

We consider the effects of several forms of delays on the existence and stability of travelling waves in non-locally coupled networks of Kuramoto-type phase oscillators and theta neurons. By passing to the continuum limit and using the Ott/Antonsen ansatz, we derive evolution equations for a spatially dependent order parameter. For phase oscillator networks, the travelling waves take the form of uniformly twisted waves, and these can often be characterised analytically. For networks of theta neurons, the waves are studied numerically.

Unusual temperature dependence of elastic constants of an ambient-temperature discotic nematic liquid crystal.

We report the first experimental studies on the temperature dependence of viscoelastic properties of a room temperature discotic nematic liquid crystal. The splay elastic constant is greater than the bend elastic constant and both show unusual temperature and order parameter dependence. The rotational viscosity is remarkably larger than conventional calamitic liquid crystals. We provide a simple physical explanation based on the columnar short-range order to account for the the unusual temperature dependence of the elastic constants.

Ordering Behavior and Linear Dichroism of Pure and Doped Liquid Crystals

In the present paper, C7 liquid crystals' refractive indices have been measured throughout the nematic and isotropic phase, in order to determine the order parameter by using Vuks method and characterization of anisotropic behaviors. The temperature dependence of refractive indices, birefringence and order parameters in the anisotropic phase, has been investigated for this liquid crystal. Furthermore, the dichroic ratios of doped C7 by linear azo dye, obtained on the basis of polarized absorption measurements. Then, the orientational ordering of the doped liquid crystal is analyzed by determining the order parameters, in different dye concentrations. The ordering behavior of a doped liquid crystal mixture is studied. It is found that even in very low compositional percentage of the dyes, the obtained order parameters are strongly affected by increasing the dye concentration.

Thermodynamically consistent phase field approach to dislocation evolution at small and large strains

A thermodynamically consistent, large strain phase field approach to dislocation nucleation and evolution at the nanoscale is developed. Each dislocation is defined by an order parameter, which determines the magnitude of the Burgers vector for the given slip planes and directions. The kinematics is based on the multiplicative decomposition of the deformation gradient into elastic and plastic contributions. The relationship between the rates of the plastic deformation gradient and the order parameters is consistent with phenomenological crystal plasticity. Thermodynamic and stability conditions for homogeneous states are formulated and satisfied by the proper choice of the Helmholtz free energy and the order parameter dependence on the Burgers vector. They allow us to reproduce desired lattice instability conditions and a stress-order parameter curve, as well as to obtain a stress-independent equilibrium Burgers vector and to avoid artificial dissipation during elastic deformation. The Ginzburg–Landau equations are obtained as the linear kinetic relations between the rate of change of the order parameters and the conjugate thermodynamic driving forces. A crystalline energy coefficient for dislocations is defined as a periodic step-wise function of the coordinate along the normal to the slip plane, which provides an energy barrier normal to the slip plane and determines the desired, mesh-independent height of the dislocation bands for any slip system orientation. Gradient energy contains an additional term, which excludes the localization of a dislocation within a height smaller than the prescribed height, but it does not produce artificial interface energy. An additional energy term is introduced that penalizes the interaction of different dislocations at the same point. Non-periodic boundary conditions for dislocations are introduced which include the change of the surface energy due to the exit of dislocations from the crystal. Obtained kinematics, thermodynamics, and kinetics of dislocations at large strains are simplified for small strains and rotations, as well.

A structural study of a two-dimensional electrolyte by Monte Carlo simulations.

Properties of superconducting and superfluid thin films, modeled as a two-dimensional classic Coulomb fluid, are connected to the molecular structure of the system. Monte Carlo simulations to explore structural properties and ordering in the classical two-dimensional Coulomb fluid were performed. The density dependence of translational order parameters at various temperatures and cluster distribution below and above the Kosterlitz-Thouless line were studied, and the percolation temperature threshold was determined. Results show that one could detect the insulator-conductor transition by observing the translational order parameters, average cluster number, or mean cluster size besides dielectric constant and dipole moment of the system.

Microscopic Model and Analytic Derivation of Area Per Molecule for DPPC-Cholesterol Bilayers

An area per molecule dependence on components concentration for DPPC-Cholesterol bilayers is calculated analytically using a microscopic model in a biologically relevant concentration range. DPPC lipid is modeled as flexible string with finite bending rigidity [1,2]. Cholesterol molecule is modeled as rigid rod of finite thickness [3]. Surface tension at hydrophobic interface is linear combination of “partial tensions” of bilayer components. The model's three important parameters are: surface tension at hydrophobic interface for pure DPPC membrane, bending rigidity of DPPC lipid, extrapolated surface tension at hydrophobic interface for cholesterol membrane. These parameters are chosen by nearly perfect fitting agreement of our theoretical curve with molecular dynamics simulations data [4] for these two-component bilayers. The molecular chains order parameter dependence on coordinate for 40% cholesterol - 60% DPPC membrane, measurable in NMR experiments, is calculated analytically and compared with molecular dynamics simulation data [5]. The order parameter calculation allows for DPPC tilt angle. The model parameters found by fitting the MD data are used further to calculate lateral pressure distribution and coefficient of thermal area expansion. The microscopic model allows one to study other thermodynamic coefficients and diffusion phenomena in multi-component bilayers. 1.Mukhin S.I., S. Baoukina, Analytical derivation of thermodynamic characteristics of lipid bilayer from a flexible string model. Phys. Rev. E. 71: 061918 (2005). 2.Mukhin S.I., B.B. Kheyfets, Analytical approach to thermodynamics of bolalipid membranes. Phys. Rev. E. 82: 051901 (2010). 3.Mukhin S.I., B.B. Kheyfets, Pore formation phase diagrams for lipid membranes. JETP Lett. 99: 358-362 (2014). 4. Edholm O., J.F. Nagle. Areas of Molecules in Membranes Consisting of Mixtures. Biophys. J. 89: 1827-1832 (2005). 5. Hofsass C., Lindahl E., and Edholm O. Molecular Dynamics Simulations of Phospholipid Bilayers with Cholesterol. Biophys. J. 84: 2192-2206 (2003).