Average Order Parameter Research Articles

Experimental Evidence of Non-Gaussian Fluctuations near a Critical Point

The orientation fluctuations of the director of a liquid crystal are measured, by a sensitive polarization interferometer, close to the Fréedericksz transition, which is a second-order transition driven by an electric field. We show that, near the critical value of the field, the spatially averaged order parameter has a generalized Gumbel distribution instead of a Gaussian one. The latter is recovered away from the critical point. The relevance of slow modes is pointed out. The parameter of the generalized Gumbel distribution is related to the effective number of degrees of freedom.

CoPt alloy grown on the WSe 2(0 0 0 1) van der Waals surface

The structural and magnetic properties of 3-nm-thick CoPt alloys grown on WSe 2(0 0 0 1) at various temperature are investigated. Deposition at room temperature leads to the formation of a chemically disordered fcc CoPt alloy with [1 1 1] orientation. Growth at elevated temperatures induces L1 0 chemical order starting at 470 K accompanied with an increase in grain size and a change in grain morphology. As a consequence of the [1 1 1] growth direction, the CoPt grains can adopt one of the three possible variants of the L1 0 phase with tetragonal c-axis tilted from the normal to the film plane direction at 54°. The average long-range order parameter is found to be 0.35(±0.05) and does not change with the increase in the deposition temperature from 570 to 730 K. This behavior might be related to Se segregation towards the growing facets and surface disorder effects promoted by a high surface-to-volume ratio. Magnetic studies reveal a superparamagnetic behavior for the films grown at 570 and 730 K in agreement with the film morphology and degree of chemical order. The measurements at 10 K reveal the orientation of the easy axis of the magnetization lying basically in the film plane.

Multicritical dynamical phase diagrams of the kinetic Blume–Emery–Griffiths model with repulsive biquadratic coupling in an oscillating field

We study, within a mean-field approach, the stationary states of the kinetic Blume–Emery–Griffiths model with repulsive biquadratic coupling under the presence of a time-varying (sinusoidal) magnetic field. We employ the Glauber-type stochastic dynamics to construct set of dynamic equations of motion. The behavior of the time dependence of the order parameters and the behavior of the average order parameters in a period, which is also called the dynamic order parameters, as functions of the reduced temperature are investigated. The dynamic phase transition points are calculated and phase diagrams are presented in the reduced magnetic field amplitude and reduced temperature plane. The dynamical transition from one regime to the other can be of first- or second order depending on the region in the phase diagram. According to the values of the crystal field interaction or single-ion anisotropy constant and biquadratic exchange constant, we find 20 fundamental types of phase diagrams which exhibit many dynamic critical points, such as tricritical points, zero-temperature critical points, double critical end points, critical end point, triple point and multicritical point. Moreover, besides a disordered and ordered phases, seven coexistence phase regions exist in the system.

Enhanced ordered structure and relaxor behaviour of0.98Pb(Mg1/3Nb2/3)O3–0.02La(Mg2/3Nb1/3)O3 single crystals

High quality Pb(Mg1/3Nb2/3)O3 (PMN) and La-doped PMN (PLMN) single crystals were grown via a top-seededsolution growth method. At a doping level as low as 2 at.% of La, the 1:1 B-sitecation (chemical) order was significantly enhanced as revealed by the presenceof superlattice peaks in the x-ray diffraction pattern and comparatively large(∼100 nm) chemically ordered regions (CORs) in the transmission electron microscopy dark field images.The average chemical order parameter was calculated (from the intensity of superlattice peaks) tobe S≈0.44. Besides, x-ray diffraction revealed the presence of a low-symmetry (presumablyrhombohedral) phase. The effect of La doping on the dielectric relaxation was notsubstantial. Though the magnitude of the dielectric constant peak in PLMN was reducedby half as compared to pure PMN, the peak temperature and diffuseness as well as theshape of the dielectric relaxation spectra remained almost unchanged. The analysis of thetemperature dependence of the characteristic time for the main relaxation process in termsof the Vögel–Fulcher law revealed the freezing of dipole dynamics at temperatureTf = 192 K, which was onlyslightly lower than the Tf = 213 K in PMN. To reconcile the structural and dielectric data we suggest that therhombohedral phase forms inside CORs while the chemically disordered matrix remainscubic and is populated by dynamic polar nanoregions that give rise to the characteristicdielectric response.

Kinetics of the spin-2 Blume-Capel model under a time-dependent oscillating external field

Within a mean-field approach and using the Glauber-type stochastic dynamics, we study the kinetics of the spin-2 Blume-Capel model in the presence of a time-varying (sinusoidal) magnetic field. We investigate the time dependence of the average order parameter and the behavior of the average order parameter in a period, which is also called the dynamic order parameter, as a function of the reduced temperature. The nature (continuous and discontinuous) of the transition is characterized by the dynamic order parameter. The dynamic phase transition points are obtained and the phase diagrams are presented in the reduced magnetic field amplitude and reduced temperature plane. The phase diagrams exhibit one dynamic tricritical point; besides a disordered and an ordered phases, there are three phase coexistence regions that are strongly dependent on the interaction parameter.

Solution structure of Ca2+‐free rat β‐parvalbumin (oncomodulin)

Relative to other parvalbumin isoforms, the mammalian beta-parvalbumin (oncomodulin) displays attenuated divalent ion affinity. High-resolution structural data for the Ca(2+)-bound protein have provided little insight into the physical basis for this behavior, prompting an examination of the unliganded state. This article describes the solution structure and peptide backbone dynamics of Ca(2+)-free rat beta-parvalbumin (beta-PV). Ca(2+) removal evidently provokes significant structural alterations. Interaction between the D helix and the AB domain in the Ca(2+)-bound protein is greatly diminished in the apo-form, permitting the D helix to straighten. There is also a significant reorganization of the hydrophobic core and a concomitant remodeling of the interface between the AB and CD-EF domains. These modifications perturb the orientation of the C and D helices, and the energetic penalty associated with their reversal could contribute to the low-affinity signature of the CD site. By contrast, Ca(2+) removal causes a comparatively minor perturbation of the E and F helices, consistent with the more typical divalent ion affinity observed for the EF site. Ca(2+)-free rat beta-PV retains structural rigidity on the picosecond-nanosecond timescale. At 20 degrees C, the majority of amide vectors show no evidence for motion on timescales above 20 ps, and the average order parameter for the entire molecule is 0.92.

DYNAMIC PHASE TRANSITION IN THE KINETIC BLUME-EMERY-GRIFFITHS MODEL IN AN OSCILLATING EXTERNAL FIELD

The dynamic phase transitions are studied, within a mean-field approach, in the kinetic Blume-Emery-Grifftihs model under the presence of a time varying (sinusoidal) magnetic field by using the Glauber-type stochastic dynamics and the set of the dynamic equations of motion is obtained. The behavior of the time-dependence of the order parameters and the behavior of the average order parameters in a period, which is also called the dynamic order parameters, as a function of the reduced temperature are investigated. The nature (continuous and discontinuous) of transition is characterized by studying the average order parameters in a period. The dynamic phase transition points are obtained and the phase diagrams are presented in the reduced magnetic field amplitude and reduced temperature plane. We have found that the behavior of system strongly depends on the interaction parameters and nine main different phase diagram topologies have been obtained. We also calculate the Liapunov exponents to verify the stability of the solutions and the dynamic phase transition points.

Residual Dipolar Couplings in Short Peptides Reveal Systematic Conformational Preferences of Individual Amino Acids

Residual dipolar couplings (RDCs) observed by NMR in solution under weak alignment conditions can monitor average net orientations and order parameters of individual bonds. By their simple geometrical dependence, RDCs bear particular promise for the quantitative characterization of conformations in partially folded or unfolded proteins. We have systematically investigated the influence of amino acid substitutions X on the conformation of unfolded model peptides EGAAXAASS as monitored by their (1)H(Nu)-(15)N and (1)H(alpha)-(13)C(alpha) RDCs detected at natural abundance of (15)N and (13)C in strained polyacrylamide gels. In total, 14 single amino acid substitutions were investigated. The RDCs show a specific dependence on the substitution X that correlates to steric or hydrophobic interactions with adjacent amino acids. In particular, the RDCs for the glycine and proline substitutions indicate less or more order, respectively, than the other amino acids. The RDCs for aromatic substitutions tryptophane and tyrosine give evidence of a kink in the peptide backbone. This effect is also observable for orientation by Pf1 phages and corroborated by variations in (13)C(alpha) secondary shifts and (3)J(HNH)(alpha) scalar couplings in isotropic samples. RDCs for a substitution with the beta-turn sequence KNGE differ from single amino acid substitutions. Terminal effects and next neighbor effects could be demonstrated by further specific substitutions. The results were compared to statistical models of unfolded peptide conformations derived from PDB coil subsets, which reproduce overall trends for (1)H(Nu)-(15)N RDCs for most substitutions, but deviate more strongly for (1)H(alpha)-(13)C(alpha) RDCs. The outlined approach opens the possibility to obtain a systematic experimental characterization of the influence of individual amino acid/amino acid interactions on orientational preferences in polypeptides.

Molecular self-organization in cylindrical nanocavities

We studied molecular organization in cylindrical nanocavities using liquid crystals. NMR analysis shows high surface-induced ordering way above the bulk critical temperature. The surface-order evolution reveals replacement of the isotropic phase by a paranematic phase and surface-induced disordering in the nematic phase. Due to strong surface potential and nanoconfinement, complete wetting and continuous evolution of the surface-order parameter are observed through the nematic-paranematic transition. As we show, the counter-intuitive absence of complete phase transition at the interface while an abrupt phase transition was measured in the averaged order parameter is in good agreement with established theories.

Pattern Evolution Induced by Periodic Temperature Modulation in a Binary Polymeric Mixture

AbstractSummary: The process of periodic phase separation is numerically studied based on Cahn‐Hilliard‐Cook theory for a binary polymer blend. The model system is quenched blow and above the critical point alternatively. And hierarchic morphologies consisting of large and small domains are observed. As the periodic phase separation proceeds, small domains are created and destroyed periodically, whereas large domains keep growing. Within the first half of each period, the behavior of small domains is similar to the two‐step phase separation. And the quench to one‐phase region during the second half period not only decreases the peak intensity of structure function for large domains, but also eliminates the high‐wave number peak corresponding to small domains. The average order parameter under oscillatory quenches exhibits a periodic behavior. The minimum of average order parameter in each period approaches to its equilibrium value monotonously and the maximum value increase in the early time regime and decrease in the late time regime. The magnitude of oscillation has considerable effects on the evolution of hierarchic structures. Small magnitude of oscillation hinders the formation of hierarchic morphologies. Moreover, large magnitude of oscillation slows down the coarsening of large domains in the early stage of periodic phase separation and accelerates the growth of large domains in the late time regime. In addition, no scaling invariance could be observed for the net growth of large domains.Snapshot picture of periodic phase separation with \bar \chi, Δχ, and τp.magnified imageSnapshot picture of periodic phase separation with \bar \chi, Δχ, and τp.

Segmental mobility in short-chain grafted-PDMS by homo- and heteronuclear residual dipolar couplings

Different homo- ( 1H– 1H) and heteronuclear ( 1H– 13C) multiple quantum solid-state NMR experiments were applied to a series of short poly (dimethylsiloxane) (PDMS) chains grafted onto hydrophilic silica. The existence and clear separation of a strongly dipolar coupled region which is attributed to the silica–PDMS interface and a weakly dipolar coupled region attributed to the mobile chain portions outside the interface is evident in all experiments. In a sample series with different average chain lengths the residual dipolar couplings and with that the average order parameters are constant for the interface part and correlate for the mobile part linearly with the average chain length. Temperature dependent studies using 1H double quantum experiments indicate the different stages of immobilization of the polymer chains. Solid-state NMR techniques therefore can give detailed information about the microscopic structure of this material and especially the effect of chain anchoring. It is also demonstrated that sample rotation influences the mobility of the mobile component and therefore the analysis of such materials should always be done under static conditions.

Structure and Lipid Interaction of N-Palmitoylsphingomyelin in Bilayer Membranes as Revealed by 2H-NMR Spectroscopy

Selectively deuterated N-palmitoyl sphingomyelins were studied by deuterium nuclear magnetic resonance spectroscopy (2H-NMR) to elucidate the backbone conformation as well as the interaction of the sphingolipids with glycerophospholipids. Macroscopic alignment of the lipid bilayers provided good spectral resolution and permitted the convenient control of bilayer hydration. Selective deuteration at the acyl chain carbons C2 and C3 revealed that the N-acyl chain performs a bend, similar to the sn-2 chain of the phosphatidylcholines. Profiles of C-D bond order parameters were derived from the segmental quadrupolar splittings for sphingomyelin alone and for sphingomyelin-phosphatidycholine mixtures. In the liquid-crystalline state, the N-acyl chain of sphingomyelin alone revealed significantly more configurational order than the chains of homologous disaturated or monounsaturated phosphatidylcholines. The average chain order parameters and the relative width of the order parameter distribution were correlated over a range of bilayer compositions. The temperature dependence of the 2H-NMR spectra revealed phase separation in bilayers composed of sphingomyelin and monounsaturated phosphatidylcholine, in broad agreement with existing phase diagrams.

Density functional theory of liquid crystals and surface anchoring

This paper applies the density functional theory to confined liquid crystals comprising ellipsoidal shaped particles interacting through the hard Gaussian overlap (HGO) potential. The restricted orientation model proposed by Rickayzen [Mol. Phys. 95, 393 (1998)] is extended to study the surface anchoring. The excess free energy is calculated as a functional expansion of density around a reference homogeneous fluid. The pair direct correlation function (DCF) of a homogeneous HGO fluid is approximated, based on the Percus-Yevick DCF for hard spheres; the anisotropy is introduced by means of the closest approach parameter. The average number density and orientational order parameter profiles of a HGO fluid confined in between planar walls are obtained using a hard needle-wall potential to represent the particle-wall interactions. For short and long needle lengths, the homeotropic and planar anchoring are observed, respectively. For the bulk isotropic phase the calculated density and order parameter profiles are in agreement with the Monte Carlo simulation of Barmes and Cleaver [Phys. Rev. E 69, 61705 (2004)]. However, for the bulk nematic phase the theory gives the correct density profile between the walls. The correct order parameters are obtained close to the walls whereas for the region in the middle of the walls, the agreement is less satisfactory.

Microscopic phase-field simulation for nucleation incubation time of Ni75AlxV25−x alloy

With the microscopic phase-field dynamic model, the effects of temperature and concentration on the nucleation incubation time of Ni75AlxV25−x alloy were studied and the relation between the incubation time and precipitation mechanism was investigated by using the atomic occupation probability picture and average order parameter curve. The simulation results demonstrate that there exists the incubation time for different precipitation mechanisms, such as non-classical nucleation, the mixed style of non-classical nucleation and spinodal decomposition, and spinodal ordering; and the incubation time shortens in turn for the three kinds of mechanisms. With the increase of Al content of Ni75AlxV25−x alloy, the incubation time of L12 phases shortens continuously and that of D022 phases is prolonged. The effects of temperature on the incubation time of L12 and D022 phases are accordant, i.e. the incubation time is greatly prolonged with the temperature rising.

Negative creep of metallic glasses as an externally-catalyzed dissipative structure within Ginzburg–Landau kinetics

Negative creep concerns annealing temperatures of metallic glasses approaching ambient where normal densification is negligible but negative dimensional change is dramatically catalyzed by a LeChatelier-like load perturbation and initially accelerated against the load by temperature and load increase. This obtains on the isotherm up to the load point and time increment where normal creep in the opposite direction begins to counter the anomalous effects. The proposed dissipative structure is based upon strain as a global average order parameter satisfying the postulated time-dependent Ginzburg–Landau (TDGL) equation and applied to Cu 60Zr 40 at 473 K. This serves as the Euler–Lagrange equation corresponding to the experimentally verified Ostwald's Step Rule which subsumes autonomous selection for near reversibility and minimum dissipation or equivalent high free energy configurations en route to equilibrium thus sustaining the G–L postulate. This quench-induced self-organizing phenomenon can be conceived as a continuous stroke potential energy-increasing heat engine driven by the quenched-in thermal energy.

Segmental order in end-linked polymer networks: A Monte Carlo study

Segmental order in end-linked monomodal and bimodal polymer networks is investigated by means of bond-fluctuation Monte Carlo simulations. The tensor order parameter, which is a central observable in NMR experiments, is not uniquely related to simple vectorial order. The relaxation of NMR-detected tensorial interactions towards their finite long-time limit is best described by a power law and occurs over much longer time scales than the relaxation of vectorial order. The well-known prediction for the segmental order of Gaussian chains as a simple function of the segment number between constraints is not straightforwardly obeyed, neither in dry nor in swollen networks. Excluded-volume interactions tend to significantly reduce the tensorial order, as is clearly observed in single-chain simulations. A distribution extends along the chain, where order is increased in a region of 30-40 bonds around the cross-links in networks. The dominating contribution to the order parameter distribution arises from the frozen-in distribution of end-to-end separations. We find strong deviations from the Gamma distribution, which has so far been implicitly used in most NMR works, as it is a straightforward consequence of a Gaussian distribution of end separations. Specifically, we find narrower distributions, as small values of the tensor order parameter are strongly suppressed, most probably as a result of trapped entanglements. The markedly subaffine behavior of the average order parameter and the changes in its distribution on swelling are assigned to orientation processes of strands which compensate for the non-affine local deformation. Our central observations and interpretations are well supported by our previous experimental and theoretical work.

Characterization of the flow of anisotropic colloidal particles using energy-dispersive X-ray diffraction

The technique of energy-dispersive X-ray diffraction to study the orientation of microscopic crystalline particles dispersed in a liquid has been described recently. This complements previous neutron diffraction studies by permitting measurements at higher spatial resolution. Work with synchrotron radiation and high-energy X-rays has allowed studies on liquid dispersions flowing in pipes with a thickness of about 1 cm and a spatial resolution of 100 μm. Kaolinite is often found as a dispersion of monocrystalline, microscopic plates. The crystallographic layer structure is commensurate with the particle shape: the 00 l direction is normal to the plane of the plates. Measurements of diffraction of the flowing liquid dispersion in a pipe oriented in various directions to the incident beam can be used to deduce the average orientation and order parameters of the particles. The competing effects of alignment with walls and in flow fields were observed. Further work has measured the orientation near a bend in a pipe.

Changes in Calmodulin Main-Chain Dynamics upon Ligand Binding Revealed by Cross-Correlated NMR Relaxation Measurements

The fast dynamics of protein backbones are often investigated by nuclear magnetic relaxation experiments that report on the degree of spatial restriction of the amide bond vector. By comparing calmodulin in the peptide-bound and peptide-free states with these classical methods, we observe little difference in the dynamics of the polypeptide main chain (average order parameter decrease of 0.01 unit upon binding). However, when using NMR methods that monitor the mobility of the CO-Calpha bond vector, we reveal a significant reduction of dynamics of the protein main chain (average order parameter decrease of 0.048 units). Previous investigations have suggested that the side-chain dynamics is reduced by an average of 0.07 order parameter units upon ligand binding (Lee, A. L.; Kinnear, S. A.; Wand, A. J. Nat. Struct. Biol. 2000, 7, 72-77). The current findings suggest that the change of the CO-Calpha bond vector dynamics is intermediate between the changes in NH and side-chain dynamics and report a previously undetected loss of main-chain entropy. Weak site-to-site correlations between the different motional indicators are also observed.

Tight-binding calculations of NMR transitions in random and partially orderedGaInP2

A tight-binding method is used to obtain the average local order parameter for random and partially ordered ${\mathrm{GaInP}}_{2}$ from the electric field gradients (EFG's) at $\mathrm{Ga}$ sites. The EFG's are obtained from $^{71}\mathrm{Ga}$ nuclear magnetic resonance (NMR). The calculations employed a 17-atom cluster consisting of a central $\mathrm{Ga}$, 4 nearest-neighbor $\mathrm{P}$, and 12 second-nearest-neighbor $\mathrm{Ga}$ or $\mathrm{In}$ atoms. In partially ordered ${\mathrm{GaInP}}_{2}$ there are 8192 such clusters. Distortions from perfect tetrahedral symmetry are obtained using a force balance method with an undistorted bond length of $2.45\phantom{\rule{0.3em}{0ex}}\mathrm{\AA{}}$ (average lattice approximation). Comparisons with the NMR data are obtained for a sample grown by liquid phase epitaxy (LPE), which approximates a random sample, and for a sample grown by organometallic vapor phase epitaxy (OMVPE), which is partially ordered. The random assumption provides good agreement with experiment for the LPE sample, and a least-squares fit to the data for the OMVPE sample yields a local order parameter of $0.4\ifmmode\pm\else\textpm\fi{}0.1$.

Chain order in filled SBR elastomers: a proton multiple-quantum NMR study

A series of cross-linked styrene-butadiene rubbers (SBR) filled with different amounts of carbon black and silica are investigated by proton multiple-quantum nuclear magnetic resonance (NMR). The method yields reliable information on residual dipolar couplings and their distribution, which in turn are related to local chain order and the effective cross-link density in these systems. Fundamental differences between the response of a linear precursor, which undergoes reptational motion, and vulcanized SBR are discussed. For the latter, it is found that the average chain order parameter as well as its distribution does not change significantly with the amount and the type of filler. This is in surprising contrast to recent results from Hahn-echo relaxometry applied to the same samples, which indicated a significant filler effect on the cross-link density.