Long-range Structural Correlations Research Articles

Anion-polarisation-directed short-range-order in antiperovskite Li2FeSO.

Short-range ordering in cation-disordered cathodes can have a significant effect on their electrochemical properties. Here, we characterise the cation short-range order in the antiperovskite cathode material Li2FeSO, using density functional theory, Monte Carlo simulations, and synchrotron X-ray pair-distribution-function data. We predict partial short-range cation-ordering, characterised by favourable OLi4Fe2 oxygen coordination with a preference for polar cis-OLi4Fe2 over non-polar trans-OLi4Fe2 configurations. This preference for polar cation configurations produces long-range disorder, in agreement with experimental data. The predicted short-range-order preference contrasts with that for a simple point-charge model, which instead predicts preferential trans-OLi4Fe2 oxygen coordination and corresponding long-range crystallographic order. The absence of long-range order in Li2FeSO can therefore be attributed to the relative stability of cis-OLi4Fe2 and other non-OLi4Fe2 oxygen-coordination motifs. We show that this effect is associated with the polarisation of oxide and sulfide anions in polar coordination environments, which stabilises these polar short-range cation orderings. We propose that similar anion-polarisation-directed short-range-ordering may be present in other heterocationic materials that contain cations with different formal charges. Our analysis illustrates the limitations of using simple point-charge models to predict the structure of cation-disordered materials, where other factors, such as anion polarisation, may play a critical role in directing both short- and long-range structural correlations.

Fragile 3D Order in V_{1-x}Mo_{x}O_{2}.

The metal-to-insulator transition in rutile VO_{2} has proven uniquely difficult to characterize because of the complex interplay between electron correlations and atomic structure. Here, we report the discovery of the sudden collapse of three-dimensional order in the low-temperature phase of V_{1-x}Mo_{x}O_{2} at x=0.17 and the emergence of a novel frustrated two-dimensional order at x=0.19, with only a slight change in electronic properties. Single crystal diffuse x-ray scattering reveals that this transition from the 3D M1 phase to a 2D variant of the M2 phase results in long-range structural correlations along symmetry-equivalent (11L) planes of the tetragonal rutile structure, yet extremely short-range correlations transverse to these planes. These findings suggest that this two dimensionality results from a novel form of geometric frustration that is essentially structural in origin.

A hierarchy of coupling free energies underlie the thermodynamic and functional architecture of protein structures.

Protein sequences and structures evolve by satisfying varied physical and biochemical constraints. This multi-level selection is enabled not just by the patterning of amino acids on the sequence, but also via coupling between residues in the native structure. Here, we employ an energetically detailed statistical mechanical model with millions of microstates to extract such long-range structural correlations, i.e. thermodynamic coupling free energies, from a diverse family of protein structures. We find that despite the intricate and anisotropic distribution of coupling patterns, the majority of residues (>70%) are only marginally coupled contributing to functional motions and catalysis. Physical origins of ‘sectors’, determinants of native ensemble heterogeneity in extant, ancient and designed proteins, and the basis for allostery emerge naturally from coupling free energies. The statistical framework highlights how evolutionary selection and optimization occur at the level of global interaction network for a given protein fold impacting folding, function, and allosteric outputs.

Relaxation dynamics in supercooled oligomer liquids: From shear-stress fluctuations to shear modulus and structural correlations

Static and dynamical properties of a model glass-forming oligomer liquid are analyzed using molecular dynamics simulations. The temperature and system size effects are assessed for the affine shear modulus μA, the quasistatic shear modulus μsf (obtained using the stress-fluctuation relation), and the shear relaxation modulus G(t). It is found that while both μA and μsf are nearly independent of the system size, their variances show significant system size dependence, in particular, below the glass transition temperature Tg. It is also shown that the standard deviation of the shear modulus, δμsf(T), exhibits a pronounced peak at T ≈ Tg whose position is nearly independent of the system volume V. Moreover, the whole function δμsf(T) is nearly the same for different system sizes above the glass transition. We propose a theory which quantitatively predicts δμsf(T) at T ≳ Tg and explains both its independence of V and its peak near Tg. It is also established that below Tg the variance of the affine modulus follows the standard power law, δμA2∝1/V, while δμsf shows anomalously a slow decrease with V as δμsf2∝1/Vα with α < 1. On this basis, it is argued that the studied glass-forming systems must show long-range structural correlations in the amorphous state.

Examining the Limits of Predictability of Human Mobility.

We challenge the upper bound of human-mobility predictability that is widely used to corroborate the accuracy of mobility prediction models. We observe that extensions of recurrent-neural network architectures achieve significantly higher prediction accuracy, surpassing this upper bound. Given this discrepancy, the central objective of our work is to show that the methodology behind the estimation of the predictability upper bound is erroneous and identify the reasons behind this discrepancy. In order to explain this anomaly, we shed light on several underlying assumptions that have contributed to this bias. In particular, we highlight the consequences of the assumed Markovian nature of human-mobility on deriving this upper bound on maximum mobility predictability. By using several statistical tests on three real-world mobility datasets, we show that human mobility exhibits scale-invariant long-distance dependencies, contrasting with the initial Markovian assumption. We show that this assumption of exponential decay of information in mobility trajectories, coupled with the inadequate usage of encoding techniques results in entropy inflation, consequently lowering the upper bound on predictability. We highlight that the current upper bound computation methodology based on Fano’s inequality tends to overlook the presence of long-range structural correlations inherent to mobility behaviors and we demonstrate its significance using an alternate encoding scheme. We further show the manifestation of not accounting for these dependencies by probing the mutual information decay in mobility trajectories. We expose the systematic bias that culminates into an inaccurate upper bound and further explain as to why the recurrent-neural architectures, designed to handle long-range structural correlations, surpass this upper limit on human mobility predictability.

New insights into the multiferroic properties of Mn3TeO6

Mn3TeO6 has a trigonal corundum related structure (space group ), and orders in an incommensurate antiferromagnetic (AFM) structure at TN 24 K. A weak ferroelectric order below T * ~ 21 K has recently been reported. In order to investigate possible structural changes below TN leading to the observed dipole order, we have performed a detailed study of the crystal and magnetic structures of Mn3TeO6 using neutron powder diffraction (NPD) in the temperature range of 5–40 K. Complementary low-temperature second harmonic generation (SHG) measurements were performed in order to confirm the reported dipole order at T *. No change in the rhombohedral symmetry associated with a possible displacive phase transition at T * was observed in the long-range structural correlations, and it appears that Mn3TeO6 keeps the same incommensurately modulated magnetic spin structure with the propagation vector k = (0; 0; 0.43) in the whole temperature range from 5 to 24 K.

Microstructures, interactions and dynamics properties studies of aqueous guanidinium triflate ionic liquid from molecular dynamics simulations

In order to understand the phase equilibrium behavior of aqueous ionic liquids (ILs) guanidinium triflate [gua][OTf] solution (binary solvent) at 7 different molar fractions of water ranged from 0.1 to 0.7 at 440.15K classical molecular dynamic simulations were performed. The simulations measured changes in different properties such as density, structural, bonding properties (radial distribution function, water clustering and hydrogen bonding) and dynamic property (diffusion coefficient). The analysis of radial distribution and spatial distribution functions revealed a significant long-range structural correlation between IL and water. Water molecules intercalated in the coordination shell of both ions, thus weakening their electrostatic interaction. It was observed that, water molecules started to connect with each other and formed a large hydrogen bond network throughout the system with the increasing water molar fraction. Thus, improved both translational and rotational motions of [gua]+ and [OTf]− ions significantly. As the results, [OTf]− ions diffused faster than [gua]+ ions and improved both translational and rotation motions of the ions mentioned significantly. The application of aqueous [gua][OTf] at high temperature has a promising potential particularly in the carbon dioxide removal area for natural gas industry.

Structural Properties and Aggregation Behavior of 1-Hexyl-3-methylimidazolium Iodide in Aqueous Solutions.

The structural properties of 1-hexyl-3-methylimidazolium iodide ([C6mim]I)/water mixtures with molar ratios ranging from 1:1 to 1:200 have been investigated using molecular dynamics (MD) simulations with extended X-ray absorption fine structure (EXAFS) experimental data. The presence of a complex network of interactions among cations, anions, and water molecules has been highlighted from the MD simulations, even if water molecules have been found to interact preferentially with the I(-) anion. The EXAFS results show that, also for the 1:1 [C6mim]I/water mixture, the water molecules are placed next to the I(-) anion, and the I(-) hydration shell becomes more and more crowded with increasing water content. Tight ion pairs have been detected in the [C6mim]I/water mixtures with molar ratios from 1:1 to 1:12, while no ionic pairs were found in the most diluted solutions. The aggregation behavior has been determined from MD simulations with the aid of S(q) functions. For the most concentrated IL/water mixtures with molar ratios between 1:1 and 1:12 the existence of long-range structural correlations has been evidenced, even if the apolar chains are not completely segregated as expected for micelle-like structures. Conversely, for the 1:200 mixture, that is above the experimental critical aggregation concentration value, the alkyl chains are completely separated from each other.

Long-range structural correlations in amorphous ternary In-based oxides

Systematic investigations of ternary In-based amorphous oxides, In–X–O with X = Sn, Zn, Ga, Cd, Ge, Sc, Y, or La, are performed using ab-initio molecular-dynamics liquid-quench simulations. The results reveal that the local M–O structure remains nearly intact upon crystalline to amorphous transition and exhibit weak dependence on the composition. In marked contrast, the structural characteristics of the metal–metal shell, namely, the M–M distances and M–O–M angles that determine how MO polyhedra are connected into a network, are affected by the presence of X. Complex interplay between several factors such as the cation ionic size, metal–oxygen bond strength, as well as the natural preference for edge, corner, or face-sharing between the MO polyhedra, leads to a correlated behavior in the long-range structure. These findings highlight the mechanisms of the amorphous structure formation as well as the specifics of the carrier transport in these oxides.

Revealing mesoscopic structural universality with diffusion

Measuring molecular diffusion is widely used for characterizing materials and living organisms noninvasively. This characterization relies on relations between macroscopic diffusion metrics and structure at the mesoscopic scale commensurate with the diffusion length. Establishing such relations remains a fundamental challenge, hindering progress in materials science, porous media, and biomedical imaging. Here we show that the dynamical exponent in the time dependence of the diffusion coefficient distinguishes between the universality classes of the mesoscopic structural complexity. Our approach enables the interpretation of diffusion measurements by objectively selecting and modeling the most relevant structural features. As an example, the specific values of the dynamical exponent allow us to identify the relevant mesoscopic structure affecting MRI-measured water diffusion in muscles and in brain, and to elucidate the structural changes behind the decrease of diffusion coefficient in ischemic stroke.

A neutron total scattering study of local coordination inKTiOPO4 from roomtemperature to 900 °C

Neutron total (Bragg plus diffuse) scattering data have been analysed bymeans of bond valence constrained reverse Monte Carlo modelling, usingRMCProfile software, in order to simultaneously probe the natures of theshort- and long-range structural correlations in potassium titanyl phosphate,KTiOPO4 (KTP). The diffraction data were collected at room temperature, 300, 500, 700 and900 °C, and the resulting partial radial distribution functions,gjk(r), were thoroughly investigated in order to obtain information about the structural aspects thatcause reduced second harmonic generation (SHG) with increasing temperature in KTP. The –TiO6–PO4– lattice shows very little rigid unit motion up to900 °C andthe PO4 tetrahedra were likewise unchanged. However, subtle changes regarding oxygen disordering around theTiO6 octahedra, i.e. the number of short titanyl bonds, andK + cation displacementalong the c axis are carefully mapped out. The latter has a direct detrimental effect on the SHGresponse, whilst the anisotropic Ti–O bond distribution seems to be a prerequisite for theSHG effect.

Random walks with barriers

Restrictions to molecular motion by barriers (membranes) are ubiquitous in porous media, composite materials and biological tissues. A major challenge is to characterize the microstructure of a material or an organism nondestructively using a bulk transport measurement. Here we demonstrate how the long-range structural correlations introduced by permeable membranes give rise to distinct features of transport. We consider Brownian motion restricted by randomly placed and oriented membranes (d − 1 dimensional planes in d dimensions) and focus on the disorder-averaged diffusion propagator using a scattering approach. The renormalization group solution reveals a scaling behavior of the diffusion coefficient for large times, with a characteristically slow inverse square root time dependence for any d. Its origin lies in the strong structural fluctuations introduced by the spatially extended random restrictions, representing a novel universality class of the structural disorder. Our results agree well with Monte Carlo simulations in two dimensions. They can be used to identify permeable barriers as restrictions to transport, and to quantify their permeability and surface area.

Structure and Dynamics of N,N-Diethyl-N-methylammonium Triflate Ionic Liquid, Neat and with Water, from Molecular Dynamics Simulations

We investigated by means of molecular dynamics simulations the properties (structure, thermodynamics, ion transport, and dynamics) of the protic ionic liquid N,N-diethyl-N-methylammonium triflate (dema:Tfl) and of selected aqueous mixtures of dema:Tfl. This ionic liquid, a good candidate for a water-free proton exchange membrane, is shown to exhibit high ion mobility and conductivity. The radial distribution functions reveal a significant long-range structural correlation. The ammonium cations [dema](+) are found to diffuse slightly faster than the triflate anions [Tfl](-), and both types of ions exhibit enhanced mobility at higher temperatures, leading to higher ionic conductivity. Analysis of the dynamics of ion pairing clearly points to the existence of long-lived contact ion pairs. We also examined the effects of water through characterization of properties of dema:Tfl-water mixtures. Water molecules replace counterions in the coordination shell of both ions, thus weakening their association. As water concentration increases, water molecules start to connect with each other and then form a large network that percolates through the system. Water influences ion dynamics in the mixtures. As the concentration of water increases, both translational and rotational motions of [dema](+) and [Tfl](-) are significantly enhanced. As a result, higher vehicular ionic conductivity is observed with increased hydration level.

ANALYSIS AND SIMULATION OF LONG-RANGE CORRELATIONS IN CURVED SPACE

Numerical simulation and analysis of long-range correlations in curved space are studied. The study is motivated by the problem of constructing accurate models of large-scale porous media which usually contain long-range correlations in their various properties (such as their permeability, porosity, and elastic moduli) within and between their strata that are typically curved layers. The problem is, however, relevant to many other important models and phenomena in which extended correlations in curved space play a prominent role. Examples include the nonlinear σ-model in a curved space, models for describing the long-range structural correlations of amorphous semiconductors that consist of polytopes (tilings of positively-curved three-dimensional space), long-range correlations in the extrapolar total zone, and models in which the Universe is created by bubble nucleations and contain long-range correlations in the fluctuations in the curved spacetime. The study is also relevant to the important industrial problem of designing highly curved objects, such as cars and ships, which use composite materials that contain extended correlations in their property values. We study such correlations along two- and three-dimensional curves, as well as curved surfaces. We show that such correlations are well-defined only on developable surfaces, i.e. those that can be flattened to form planar surfaces without any stretching or distortion, and preserve the distance between two points on such surfaces after the stretching. If a given curved surface is not developable, but can be approximated as piecewise developable, one may still define and analyze extended correlations on it. Representative examples are presented and analyzed.

Computational Studies of Structures and Dynamics of 1,3-Dimethylimidazolim Salt Liquids and their Interfaces Using Polarizable Potential Models

The structures, thermodynamics, and dynamical properties of bulk and air/liquid interfaces of three ionic liquids, 1,3-dimethylimidazolium [dmim](+) with Cl(-), Br(-), and I(-) were studied using molecular dynamics techniques and polarizable potential models. In bulk melts, the radial distribution functions reveal a significant long-range structural correlation in these ionic liquids. The single-ion dynamics are studied via mean-square-displacements, velocity and orientational correlation functions. We observe that anion size plays an important role in the dynamics of ionic liquids, with larger anions inducing faster cation and anion motion. The computed density profiles of the ionic liquid/vapor interface exhibit oscillatory behavior, indicative of surface layering at the interface. The computed surface tensions indicate small differences between these ionic liquids and decrease with the increasing anion size. The magnitudes of the computed potential drops of these ionic liquids are found to be small and negative and increase with the decreasing anion size. These results could imply that the cation dipoles on average orient more in the interfacial plane than perpendicular to it. Our results showed that anion type plays a major role in determining IL interfacial behavior.

An investigation of the effects of the structure of gel materials on their adsorptive properties using a simple lattice–gas model

We have used a simple lattice–gas model solved in the mean-field approximation to study the effects of material structure on adsorption and desorption isotherms in simple models of silica aerogels and xerogels. We have varied independently the gel particle radius, the density, the surface wettability and the degree of long-range structural correlation in the gel, and in each case obtained adsorption and desorption data at a series of temperatures. These data are discussed in the context of standard adsorption theories and classifications. Kelvin-like behaviour is observed over the entire range of models studied, for both randomly generated gel structures and diffusion-limited aggregates. The shape of the hysteresis loops in these systems appears to vary smoothly with gel structure and is principally determined by the gel density and gel particle size. We have also measured the structure factor at each pressure along each isotherm, for which we discuss data in developing a microscopic understanding of adsorption in these systems. The relative merits of small-angle scattering data and geometrically defined pore size distributions for understanding adsorptive behaviour are discussed. For the material models considered here, a geometric measure of pore size distribution appears to be the best predictor of adsorptive behaviour.

1H NMR study of the effect of heme insertion on the folding of apomyoglobin

NMR signals arising from His EF5 and His GH1 N ϵH protons of sperm whale myoglobin and apomyoglobin have been assigned, and the protein folding has been studied through the analysis of these signals. His EF5 and His GH1 N ϵH protons participate in the internal hydrogen bonds at the B–GH and EF–H interfaces, respectively, and their signals are remarkably sensitive to local structural alterations at these sites. The shifts of these signals in alkaline pH condition were only slightly affected by the removal of heme, indicating that the overall protein folding is essentially retained in apoprotein. The line width of His EF5 proton signal, however, increased largely in the spectra of apomyoglobin and this result suggests a conformational lability of the EF–H interface in the absence of heme. Furthermore, the His EF5 proton signal was found to be influenced by not only the orientation of heme relative to the protein, but also by the type of hemin used to reconstitute apomyoglobin. These results clearly demonstrate the presence of a long-range structural correlation between the heme active site and the EF–H interface.

A detailed structural characterization of quartz on heating through the α–β phase transition

AbstractTotal neutron scattering measurements, analysed using a modification of the reverse Monte Carlo modelling method to account for long-range crystallographic order, have been used to describe the temperature-dependent behaviour of the structure of quartz. Two key observations are reported. First, the symmetry change associated with the displacive α–β phase transition is observed in both the long-range and short-range structural correlations. Secondly, some aspects of the structure, such as the Si–O bond length and the thermally-induced dynamic disorder, the latter of which sets in significantly below the transition, are relatively insensitive to the phase transition. These results are used to show that the α-domain model of the β-phase disorder is inappropriate and that the classical soft-mode picture of the phase transition is too simplistic. Instead, it is argued that the structural behaviour is best described in terms of its ability to respond to low-frequency, high-amplitude vibrational modes. This view is supported by additional single-crystal diffuse neutron scattering measurements.

The Zeno (Z=1) Behavior of Water: A Molecular Simulation Study

The regularity of fluid properties observed at the Zeno or Z=PV/RT=1 point has been proposed as a means of testing and improving volumetric equations of state. Previous research has shown that molecular interactions can be qualitatively and quantitatively related to the linear Z=1 contour of Tr vs ρr for pure fluids from the Boyle temperature to the triple point. In this study, we expand the molecular simulation analysis of previous work to gain a detailed microscopic understanding of the properties of Zeno-point systems. Our calculations show that popular semiempirical water models, such as SPC and SPC/E water, are able to replicate closely experimentally determined water properties in the Zeno-point region. Detailed molecular dynamics simulations of Z=1.00 and adjacent Z=0.75 and Z=1.25 states reveal common features over a wide range of temperatures and densities, from 77 to 1097°C and 1.01 to 0.029 g·cm−3. Radial distribution functions of high-temperature, high-density Zeno-point fluids display remarkable long-range structural correlation well above the critical temperature and pressure, and examination of hydrogen bonding within each system shows that large water–water hydrogen-bonded clusters persist at high temperatures and supercritical densities. These results are compared to the existing extended corresponding-states approaches for pure fluid properties.

Statistical properties of phonon transmission in one-dimensional disordered system with long-range correlation

We report statistical properties of the distribution of phonon transmission coefficient (PTC) and phonon amplitude in one-dimensional disordered systems with inverse-power-law structural correlations by numerical calculation. The distribution of PTC over an ensemble on impurity configuration is expected to have some different properties from that of standard disordered systems because of its long-range structural correlation. It is shown that the distribution of the Lyapunov exponent of PTC has a slow convergence different from that of standard disordered systems obeying a normal central-limit theorem. It is also observed that the anomalous distribution of PTC over ensemble has a non-universal form, different from the standard disordered one.