Comparison Of Order Parameters Research Articles

Investigating the quasi-liquid layer on ice surfaces: a comparison of order parameters.

Ice surfaces are characterized by pre-melted quasi-liquid layers (QLLs), which mediate both crystal growth processes and interactions with external agents. Understanding QLLs at the molecular level is necessary to unravel the mechanisms of ice crystal formation. Computational studies of the QLLs heavily rely on the accuracy of the methods employed for identifying the local molecular environment and arrangements, discriminating between solid-like and liquid-like water molecules. Here we compare the results obtained using different order parameters to characterize the QLLs on hexagonal ice (Ih) and cubic ice (Ic) model surfaces investigated with molecular dynamics (MD) simulations in a range of temperatures. For the classification task, in addition to the traditional Steinhardt order parameters in different flavours, we select an entropy fingerprint and a deep learning neural network approach (DeepIce), which are conceptually different methodologies. We find that all the analysis methods give qualitatively similar trends for the behaviours of the QLLs on ice surfaces with temperature, with some subtle differences in the classification sensitivity limited to the solid-liquid interface. The thickness of QLLs on the ice surface increases gradually as the temperature increases. The trends of the QLL size and of the values of the order parameters as a function of temperature for the different facets may be linked to surface growth rates which, in turn, affect crystal morphologies at lower vapour pressure. The choice of the order parameter can be therefore informed by computational convenience except in cases where a very accurate determination of the liquid-solid interface is important.

Elucidation of the de Vries behavior in terms of the orientational order parameter, apparent tilt angle, and field-induced tilt angle for smectic liquid crystals by polarized infrared spectroscopy.

We report experimental results of the orientational order parameter, the apparent tilt angle, and the field-induced tilt angle for three chiral smectic liquid crystalline materials investigated using infrared (IR) polarized spectroscopy. The common feature in these materials is use of the core 5-methyl-2- pyrimidine benzoate as the central part of the mesogen. This core is terminated by siloxane or carbosilane chains on one of the ends and by the chiral alkoxy chains on the opposite. These compounds exhibit low concomitant layer shrinkage at the smectic A^{*} (SmA^{*}) to smectic C^{*} (SmC^{*}) transition temperature and within the SmC^{*} phase itself. The maximum layer shrinkage in SmC^{*} is observed as ∼1.5%. We calculate the apparent orientational order parameter, S_{app} in the laboratory reference frame from the observed IR absorbance for homeotropic aligned samples, and the true order parameter, S, is calculated using the measured tilt angle and is also interpolated from Iso-SmA^{*} transition temperature closer to SmC^{*} phase. The apparent tilt angle in the SmA^{*} phase calculated from a comparison of order parameters S and S_{app} is found to be significantly large. A low magnitude of S_{app} found for homeotropic aligned samples in the SmA^{*} phase indicates that the order parameter plays a vital role in determining the de Vries characteristics, especially of exhibiting larger apparent tilt angles. Furthermore there is a significant increase in the true order parameter at temperatures close to SmA^{*} to SmC^{*} transition temperature in all three compounds. The planar-aligned samples are used to study the dependence of induced tilt angle on the applied electric field. The generalized Langevin-Debye model given by Shen etal. reasonably fits the experimental data on the field-induced tilt angle. The results show that the dipole moment of the tilt correlated domain in SmA^{*} diverges as temperature is lowered to the SmA^{*}-SmC^{*} transition temperature. The generalized Langevin-Debye model is also found to be extremely effective in confirming some of the conclusions of the de Vries behavior.

The Additive Approximation for Heat Transfer and for Stability Calculations in a Multi-Filamentary Superconductor—Part B

A hypothesis shall be confirmed: Non-convergence of a series of numerical solutions, to simulate transient temperature under increasing losses in a superconductor, might tightly be correlated with the superconducting to normal conducting phase transition. Consider as an analogue a standard, mathematical power series expansion: While the exact limit cannot be captured within the series, there is no doubt about its existence. A series of numerical solutions in stability analysis is considered a parallel to the mathematical series convergence problem: Likewise, there is no doubt that a limit of the numerical solution series exists (the phase transition) but it cannot be reached within the series. The concept is applied to multi-filamentary BSCCO 2223 and coated, thin film YBaCuO 123 superconductors and to NbTi superconductor filaments. Support is provided by a microscopic stability model and from comparison of order parameters. Simulation of current transport near phase transitions may become severely in error if length of load steps is in conflict with time needed for its completion.

Class A β-lactamase backbone dynamics - At the crossroads of molecular dynamics and NMR spectroscopy

Protein dynamics reveal crucial information about structure-function relationships. We complement the information obtained through NMR spectroscopy relaxation experiments and model-free analysis for class A beta-lactamases TEM-1 and PSE-4 with results from bioinformatics techniques, chiefly molecular dynamics (MD). Molecular dynamics allows the simulation of a protein's dynamics. The timescales probed using this technique differ from those accessible by NMR spectroscopy, giving a more complete picture of the backbone dynamics. Moreover, comparison of order parameters where the timescales of motions are accessible to both methods serves to validate our in silico approach. Also, MD hints at the atomic details associated with a residue's particular motions. NMR spectroscopy data were re-analyzed under the light of this complementary information, yielding refined model selection and dynamics parameters. Our results suggest that highly structured backbone is a common characteristic of class A beta-lactamases. Nanosecond timescale motions taking place in the omega loop bordering the active site are observed with both techniques.

15NH Backbone Dynamics of Protein GB1: Comparison of Order Parameters and Correlation Times Derived Using Various “Model-Free” Approaches

A new approach that allows visualization of the distribution of motional correlation times is presented and is used to analyze 1 5 N NMR relaxation data [T 1 , T 2 , and { 1 H}- 1 5 N NOE], acquired at 500. 600, and 800 MHz, on the uniformly 1 5 N-enriched, 56 residue B1 domain from immunoglubulin protein G (GB I ). Nanosecond time scale internal motions are found for all NHs of residues in protein GB1, a finding which is consistent with the concept of hierarchical internal motions in proteins first forwarded by Frauenfelder. Order parameters and overall tumbling correlation times derived using this approach are not influenced by the number of internal motional modes. Comparatively, use of the Lipari-Szabo, Clore et al., or Lemaster model-free methods yields underestimated order parameters and overestimated overall tumbling correlation times due to the presence of nanosecond time scale internal motions. This new approach provides a straightforward way to derive more accurate order parameters and correlation times for overall tumbling and internal motions.

Hard ellipsoid rod-plate mixtures: Onsager theory and computer simulations

The liquid crystal phase transitions for a classical fluid mixture of hard ellipsoids with aspect ratios 10 : 1 and 1 : 10, and equal volume, have been studied at two compositions using Onsager theories and by computer simulation. The original Onsager from of the Helmholtz free energy contains the second virial coefficient, but the effect of higher virial coefficients may be taken into account indirectly by resummation theories such as the y-expansion theory of Barboy and Gelbart or by renormalised two-particle theories such as that due to Parsons. A comparison of order parameters and equation of state data calculated by computer simulation and by Onsager, y-expansion-Onsager and Parsons theories shows good qualitative agreement. The resummation of higher virial coefficients is seen to offer improved quantitative agreement with simulation at the level of the second virial coefficient. The predicted phase diagram at this level of approximation is symmetric about the equal mixture of prolate and oblate ellipsoids as a result of the prolate-oblate symmetry of the excluded volume. The direct inclusion of higher virial coefficients has not been attempted but it is anticipated that this would give an asymmetric phase diagram.

The isotropic to nematic liquid crystal transition for hard ellipsoids: An Onsager-like theory and computer simulations

The phase transition from an isotropic to a nematic phase for a classical fluid of hard ellipsoids has been studied using a version of a theory originally due to Onsager and by computer simulation. In the proposed form of the Onsager theory for the Helmholtz free energy, both the second and the third virial coefficients are treated exactly, but the fourth and higher virials are resummed in a manner consistent with the Carnahan-Starling equation of state for hard spheres. This same approach is applied to the calculation of the direct correlation function. A comparison of order parameters, transition densities and pressures calculated by simulation and by the resummed Onsager theory, suggests the following. (i) For 10 : 1 prolate hard ellipsoids, resumming the fourth and higher virial coefficients (rather than simply neglecting them) degrades the agreement by overestimating the importance of the higher virials. (ii) For 5 : 1 prolate and 1 : 5 oblate hard ellipsoids, the resummation yields a considerable improvement over an Onsager theory based on the second and third virials alone. (iii) Although it seems straightforward to predict the liquid crystal transition densities with some accuracy by means of these theories, accurate calculations of the direct and pair correlation functions for hard spheres using our resummation ideas still poses a challenge. Only at packing fractions less than 0·25 does the present theory portray accurately the radial distribution function for hard spheres.

Orientational Ordering of Dyes in the Glassy State of Liquid-Crystalline Side Group Polymers

Abstract Liquid-crystalline side group copolymers containing dyes can be macroscopic-ally oriented and the orientation can be locked-in below the glass transition temperature. The order parameters of anthraquinone dyes and a trisazo dye in nematic and smectic glasses were determined by optical absorption measurements. The dyes have higher degrees of order in the smectic glass than in the nematic glass. A comparison of order parameters of covalently bonded dyes with order parameters of monomeric dyes dissolved in the corresponding homopolymers demonstrates the influence of covalently anchoring the dye to the polymer.