Axial Order Parameter Research Articles

Multiferroic order parameters in rhombic antiferromagnets RCrO3

Currently, active research is aimed at perovskite—based oxides, including rare earth orthochromites, which exhibit magnetoelectric properties owed to intrinsic magnetic interactions in external electric and magnetic fields. Due to a variety of structural instabilities and couplings in these materials, understanding the underlying magnetoelectric mechanisms is a challenge. In this paper, we explore magnetoelectric properties of the rare earth orthochromites in the framework of symmetry analysis. Our calculations show the presence in RCrO3 of electric dipole moments localized in the vicinity of Cr3+ ions. The electric dipole moments, appearing due to the displacements of oxygen ions from their highly symmetric positions in the parent perovskite phase, are arranged in an antiferroelectric mode. We have demonstrated the presence of electric dipole moments in the unit cell of RCrO3, localized in the vicinity of Cr3+ ions. The inversion symmetry breaks due to the displacements of oxygen ions from their highly symmetric positions in the parent perovskite phase, the electric dipoles become arranged in an antiferroelectric mode. We have introduced the basic distortive order parameters in consistence with the symmetry of RCrO3: the polar order parameters ( D , Q 2, Q 3, P ) and the axial order parameter Ω b and classified them according to the irreducible representations of the RCrO3 symmetry group (D 2h 16). We have determined the symmetry—allowed couplings between distortive, ferroelectric and magnetic orderings and found possible exchange-coupled magnetic and ferroelectric structures. The presented analysis makes it possible to explain experimentally observed polarization reversal and the concomitant reorientation of spins in a series of RCrO3 compounds and to predict the possible scenarios of phase transitions in RCrO3.

EPR moments for site-directed spin-labelling

The absolute-value first moment and second moment of nitroxide EPR absorption spectra, which can be used for systematic analysis in site-directed spin-labelling, are analysed in terms of the rotational mobility and angular motional amplitude of the spin probe. Spectral simulations with the stochastic Liouville equation are used to give calibrations of second and absolute-value first moments as a function of isotropic rotational correlation time τR and axial order parameter Szz, over the entire range of sensitivity to these parameters. Both moments are additive for multicomponent spectra, e.g., for multiple conformations. The absolute-value first moment has the advantage over the central line width in that it does not overemphasize fast motional components, and over the second moment in that it is less sensitive to noise in the outer wings of the spectrum and to baseline cutoff.

Three Entropic Classes of Side Chain in a Globular Protein

The relationship between the NMR methyl group axial order parameter and the side chain conformational entropy is investigated in inhibitor-bound and apo human HIV protease using molecular dynamics simulation. Three distinct entropic classes of methyl-bearing side chains, determined by the topological distance of the methyl group from the protein backbone (i.e., the number of χ-bonds between the Cα and the carbon of the CH3 group), are revealed by atomistic trajectory analyses performed in the local frame of reference of individual methyl probes. The results demonstrate that topologically equivalent methyl groups experience similar nonbonded microenvironments regardless of the type of residues to which they are attached. Similarly, methyl groups that belong to the same side chain but that are not topologically equivalent exhibit different thermodynamic and dynamic properties. The two-parameter classification (based upon entropy and methyl axial order parameter) of side chains described here permits improved estimates of the conformational entropies of proteins from NMR motional parameters.

The dynamical response of hen egg white lysozyme to the binding of a carbohydrate ligand

It has become clear that the binding of small and large ligands to proteins can invoke significant changes in side chain and main chain motion in the fast picosecond to nanosecond timescale. Recently, the use of a "dynamical proxy" has indicated that changes in these motions often reflect significant changes in conformational entropy. These entropic contributions are sometimes of the same order as the total entropy of binding. Thus, it is important to understand the connections amongst motion between the manifold of states accessible to the native state of proteins, the corresponding entropy, and how this impacts the overall energetics of protein function. The interaction of proteins with carbohydrate ligands is central to a range of biological functions. Here, we examine a classic carbohydrate interaction with an enzyme: the binding of wild-type hen egg white lysozyme (HEWL) to the natural, competitive inhibitor chitotriose. Using NMR relaxation experiments, backbone amide and side chain methyl axial order parameters were obtained across apo and chitotriose-bound HEWL. Upon binding, changes in the apparent amplitude of picosecond to nanosecond main chain and side chain motions are seen across the protein. Indeed, binding of chitotriose renders a large contiguous fraction of HEWL effectively completely rigid. Changes in methyl flexibility are most pronounced closest to the binding site, but average to only a small overall change in the dynamics across the protein. The corresponding change in conformational entropy is unfavorable and estimated to be a significant fraction of the total binding entropy.

Symmetry of Nematic Phase and Oblique Axial Order

Nematic order is usually described by a uniaxial order parameter, or occasionally by a biaxial order parameter together with the uniaxial one, in a typical configuration. In a general case of a system exposed to two different types of external fields, e.g., an electric field and a magnetic field, an additional order parameter, here called an oblique axial order parameter, is shown to be necessary, in addition to the above order parameters, to describe transition phenomena of the system correctly. The symmetry of the phase with the triplet of the order parameters is discussed. Effect of the oblique axial order are demonstrated practically in two phenomena: (i) qualitative change of the phase transition when the oblique axial order is neglected; (ii) disappearance of phase transition between ordered phases with different ordering axes when an oblique axial field conjugate to the oblique axial order parameter exists.

Nonextensive mean-field theory for ferroelectric nematic liquid crystal phases

Ferroelectric ordering in a nematic liquid crystal system is described using nonextensive thermostatistics. We use a mean-field potential, including effective potentials for both axial and polar interactions. By using a self-consistent numerical analysis, a complete q-dependent phase diagram is obtained as a function of the axial and polar interaction potential strengths. The phase transition behaviours and the generalized angular orientational distribution function of the molecules were investigated by studying the dependence of the polar and the axial order parameters on the reduced temperature for various values of the entropic index. This study can provide basic information to further detailed theoretical studies of molecular interactions.

Ferroelectric phase transitions in systems of axially symmetric dipolar particles in elongational flow

Effects of steady elongational flow on orientational phase transitions in systems of uniaxial, elongated particles with dipole moments are considered. The Onsager model is used with mean-field dipole–dipole and excluded-volume quadrupole interactions, combined with quadrupole effects introduced by elongational flow. Self-consistent, equilibrium orientation distribution of dipole particles, equilibrium thermodynamic properties and phase transitions are controlled by three dimensionless parameters related to dipole–dipole interactions, excluded-volume effects and intensity of the flow field. Dipole and axial order parameters, phase equilibria, and phase instability points are discussed in the space of dipole and quadrupole interaction parameters. Apolar-to-polar phase transitions, as well as transitions between individual apolar phases are affected significantly by coupling between excluded-volume effects and elongational flow. Three ranges of flow intensity inducing different phase behaviour are discussed. In a the weak flow range, a single polar phase and two different apolar phases are predicted. Phase diagram shows a triple point and three equilibrium lines for different pairs of phases. In the medium flow range, the triple point disappears and phase diagram reduces to two phases, apolar and polar, with a single line of coexistence. The first-order apolar-to-polar phase transition appears at relatively low values of the quadrupole interaction parameter, while at higher values of the parameter, second-order transition takes place. The first-order ferroelectric transition, as well as the coexistence of apolar and polar phases, disappear at a critical flow intensity separating the range of medium and strong flow. Within the strong flow range, the ferroelectric transition is second-order in the entire range of quadrupole interactions. Dipole–dipole interactions, critical for the ferroelectric transition, are significantly reduced by flow potential, especially at stronger excluded-volume interactions. A critical flow intensity has been found at which ferroelectric transition is stabilised solely by the elongational flow. Above the critical flow intensity, the system exhibits single-phase behaviour with stable polar order. No elongational flow is capable to induce ferroelectric phase transition in systems with dipole interaction parameter lower than unity.

Generalized mean-field potential description for ferroelectric ordering in nematic liquid crystals.

Ferroelectric ordering in a nematic liquid crystal system is described using a generalized mean-field potential including effective potentials for both axial and polar interactions. From a self-consistent numerical analysis, a complete phase diagram is obtained as a function of the axial and polar interaction potential strengths. The obtained phase diagram exhibits not only the usual isotropic-nematic phase transition but also nematic-ferroelectric nematic and direct isotropic-ferroelectric nematic phase transitions with a tricritical point among the phases. The phase transition behaviors and the angular orientational distribution function of the molecules were investigated by studying the dependence of the polar and the axial order parameters on the reduced temperature. Moreover, the other polar order parameters responsible for second-harmonic generation (SHG) were also investigated in the generalized mean-field potential description. As a concrete example, we performed a quantitative analysis of the SHG signal reported previously in a lyotropic poly L-glutamate system, detailing the relationship between the angular distribution function and the order parameters based on our potential model. This clarifies the nature of the ferroelectric phase responsible for SHG in nematics.