Characteristic Correlation Length Research Articles

Revisiting the structure–property relationship of metallic glasses: Common spatial correlation revealed as a hidden rule

What determines the glass property remains one of the major unsolved problems in both condensed matter physics and materials science. Despite extensive research attempting to identify possible structural features as property signatures in glasses obeying the conventional philosophy of ``structure determines property'' in matter, the hidden rule about why some proposed structures predict properties effectively but others do not is still poorly understood. Here we revisit some earlier proposed successful ``structural descriptors'' in glasses, e.g., vibrational mean-squared displacement, flexibility volume, participation fraction of low-frequency vibrational modes, and two-body excess entropy, correlating them with the long-time dynamic property of model glass probed via the activation energy for local structural excitation. We find that all four structural descriptors correlate strongly with the activation energy, presenting large Pearson's correlation coefficients. By examining the spatial nature of the activation energy and the structural descriptors, a common rule for the robustness of structure--property relationships in glasses is established, according to which there exists a critical characteristic correlation length. We further demonstrate the concept that complex structures determine the glass property by manipulating the cutoff distance used to define the two-body excess entropy. Only if this structural descriptor is defined involving atoms beyond the first nearest neighbor does it reproduce the feature of common spatial correlation range in glass. The presence of a common spatial correlation length strongly indicates that it is necessary to include the spatial correlation of a complex structure accounting for the dynamic property of metallic glasses.

Large scale random fields generation using localized Karhunen\u2013Lo\xe8ve expansion

In this paper the generation of random fields when the domain is much larger than the characteristic correlation length is made using an adaptation of the Karhunen–Loève expansion (KLE). The KLE requires the computation of the eigen-functions and the eigen-values of the covariance operator for its modal representation. This step can be very expensive if the domain is much larger than the correlation length. To deal with this issue, the domain is split in sub-domains where this modal decomposition can be comfortably computed. The random coefficients of the KLE are conditioned in order to guarantee the continuity of the field and a proper representation of the covariance function on the whole domain. This technique can also be parallelized and applied for non-stationary random fields. Some numerical studies, with different correlation functions and lengths, are presented.

Membrane undulations in a structured fluid: Universal dynamics at intermediate length and time scales.

The dynamics of membrane undulations inside a viscous solvent is governed by distinctive, anomalous, power laws. Inside a viscoelastic continuous medium these universal behaviors are modified by the specific bulk viscoelastic spectrum. Yet, in structured fluids the continuum limit is reached only beyond a characteristic correlation length. We study the crossover to this asymptotic bulk dynamics. The analysis relies on a recent generalization of the hydrodynamic interaction in structured fluids, which shows a slow spatial decay of the interaction toward the bulk limit. For membranes which are weakly coupled to the structured medium we find a wide crossover regime characterized by different, universal, dynamic power laws. We discuss various systems for which this behavior is relevant, and delineate the time regime over which it may be observed.

Structure of Polymerized Ionic Liquids from Neutron Scattering Perspective

Recent enthusiasm in polymerized ionic liquids (polyILs) with enhanced mechanical characteristics of polymers and unique physicochemical properties inherent in ionic liquids is fueled by their ability to selectively transport ions. Experiments suggest the morphology of polyILs has a significant effect on ion transport. Despite significant interest in the morphology of polyILs, investigation by traditional experimental techniques remains elusive. Few X-ray scattering experiments yield structural information, and provide little atomistic details. Neutron scattering has not been done on this important class of materials. In our recent ACS Macro Letters work, we reported a comparison of results from atomistic simulations with X-ray scattering experiments on 3 homologous polyILs that strongly support the capability of simulations to provide fundamental understanding of the structure and morphology. Herein, we extend the analysis of morphology to a complete homologous series of poly(CnVim Tf2N) (2 <= n <= 8) with emphasis on selective neutron scattering. We have demonstrated that neutron scattering with isotopic labeling along with X-ray scattering provides versatile ways to vet the intrinsic structure. The neutron scattering profiles markedly depend on the isotopic substitution pattern and that isotopically labeled neutron and X-ray scattering data do not necessarily lead to the same characteristic correlation length. Such an unintended consequence has a nontrivial implication on exploitation of scattering experiments. Moreover, the experimentally accessible difference scattering spectra based on common factor analysis offer a complementary view to the detailed decomposition of the total structure factor provided in molecular simulation and ESPR modeling. We hope the current work might stimulate experimentalists to explore polyILs using selective neutron scattering.

Effect of surface disorder on the domain structure of PLZT ceramics

ABSTRACTPb1-xLax(Zr0.65Ti0.35)1-x/4O3 (PLZT x/65/35) ceramics were studied by Piezoresponse Force Microscopy in order to understand the origin of domain structure as a function of La content. We show that the domain topology is mainly determined by the composition and grain size. The characteristic correlation length decreases with increasing La content, being sensitive also to the synthesis method. The behavior of the correlation length is linked to the macroscopic properties, showing a strong increase of disorder with La doping. The roughness exponent for the domain wall in PLZT 9/65/35 is close to 2/3 indicating 1D character of domain walls in relaxors.

Opioid Receptors are Organized into Nanodomains in the Plasma Membrane

Opioid receptors (ORs) are essential for mediating some of the normal functions of our respiratory, immune, and neuroendocrine systems. ORs are the subjects of numerous pharmacological studies because they are involved in important physiological processes such as pain regulation; reward and motivation processing; and drug addiction and abuse. While the signaling cascades that are responsible for the receptors’ physiological effects are well understood, little is known about the physical organization of these receptors on cell membranes and the impact of that organization on signaling outcomes. To clarify the lateral organization of ORs at a molecular level, we investigated three ORs variants: kappa opioid receptor (KOP), mu opioid receptor (MOPWT), and a naturally occurring MOP receptor variant (MOPN40D). We transiently transfected COS-7 cells with our functional constructs (OR tagged with photoactivatable GFP) and used quantitative super-resolution microscopy methods to delineate their nanoscale distribution. Spatial auto-correlation curves with two characteristic correlation lengths indicate that ORs exhibit distinct and complex lateral organization: long-distance correlations indicate that opioid receptors are organized into nano-domains; short-distance correlations indicate that receptor organization within these nano-domains is not random. Additionally, we found that domain radius and occupancy increase in the following order: MOPN40D, MOPWT, and KOP. These results were validated by ensemble-averaged Monte Carlo simulations. Finally, using a clustering algorithm and the domain size obtained from analysis, we estimated the number of molecules partitioned in domains versus the number of free molecules in the plasma membrane. KOP had the largest and MOPN40D had the smallest fraction of molecules in domains. These results provide new insight into OR nano-organization and complement our ongoing Fluorescence Correlation Spectroscopy measurements.

Characterization of relaxation processes in interacting vortex matter through a time-dependent correlation length

Vortex lines in type-II superconductors display complicated relaxation processes due to the intricate competition between their mutual repulsive interactions and pinning to attractive point or extended defects. We perform extensive Monte Carlo simulations for an interacting elastic line model with either point-like or columnar pinning centers. From measurements of the space- and time-dependent height-height correlation function for lateral flux line fluctuations, we extract a characteristic correlation length that we use to investigate different non-equilibrium relaxation regimes. The specific time dependence of this correlation length for different disorder configurations displays characteristic features that provide a novel diagnostic tool to distinguish between point-like pinning centers and extended columnar defects.

Effect of Uniaxial Deformation on Structure and Transport in Hydrated Nafion 117: Molecular Dynamics Simulation Study

Abstract The deformation of hydrated Nafion 117 was implemented using full-atomistic molecular dynamics simulation method to elucidate how the mechanical deformation affects the structure and transport of hydrated Nafion membrane. First, Nafion 117 membrane was equilibrated with 20 wt. % water content through an annealing procedure. The simulated characteristic correlation length and the diffusion coefficient of water and hydronium ions were analyzed for comparison with those observed in experiments. Then, the equilibrated Nafion membrane was deformed uniaxially up to 300 % of strain with a constant strain rate. The change in nanophase-segregation of hydrated Nafion during the deformation process was characterized using a directional structure factor as well as the pair correlation function in order to achieve fundamental understanding of the relationship of such structural change as a function of strain with the proton transport. It was found from the pair correlation analysis that the sulfonate distribution and sulfonate-hydronium correlation became stronger through the deformation while the hydronium ion solvation and the internal structure of water phase were not dependent on the deformation. From the directional structure factor profile, it was found that the long range correlation was developed in the perpendicular direction to the extension. The diffusions of water and hydronium ions were enhanced by 30 and 2 %, respectively, after the deformation. From this study, we suggested that it is desirable to investigate the proton transport using simulation methods covering larger dimensions with a long time scale.

Spatial correlations, clustering and percolation-like transitions in homicide crimes

The spatial dynamics of criminal activities has been recently studied through statistical physics methods; however, models and results have been focusing on local scales (city level) and much less is known about these patterns at larger scales, e.g. at a country level. Here we report on a characterization of the spatial dynamics of the homicide crimes along the Brazilian territory using data from all cities in a period of more than thirty years. Our results show that the spatial correlation function in the per capita homicides decays exponentially with the distance between cities and that the characteristic correlation length displays an acute increasing trend in the latest years. We also investigate the formation of spatial clusters of cities via a percolation-like analysis, where clustering of cities and a phase-transition–like behavior describing the size of the largest cluster as a function of a homicide threshold are observed. This transition-like behavior presents evolutive features characterized by an increasing in the homicide threshold (where the transitions occur) and by a decreasing in the transition magnitudes (length of the jumps in the cluster size). We believe that our work sheds new light on the spatial patterns of criminal activities at large scales, which may contribute for better political decisions and resources allocation as well as opens new possibilities for modeling criminal activities by setting up fundamental empirical patterns at large scales.

Variability of interconnected wind plants: correlation length and its dependence on variability time scale

The variability in wind-generated electricity complicates the integration of this electricity into the electrical grid. This challenge steepens as the percentage of renewably-generated electricity on the grid grows, but variability can be reduced by exploiting geographic diversity: correlations between wind farms decrease as the separation between wind farms increases. But how far is far enough to reduce variability? Grid management requires balancing production on various timescales, and so consideration of correlations reflective of those timescales can guide the appropriate spatial scales of geographic diversity grid integration. To answer ‘how far is far enough,’ we investigate the universal behavior of geographic diversity by exploring wind-speed correlations using three extensive datasets spanning continents, durations and time resolution. First, one year of five-minute wind power generation data from 29 wind farms span 1270 km across Southeastern Australia (Australian Energy Market Operator). Second, 45 years of hourly 10 m wind-speeds from 117 stations span 5000 km across Canada (National Climate Data Archive of Environment Canada). Finally, four years of five-minute wind-speeds from 14 meteorological towers span 350 km of the Northwestern US (Bonneville Power Administration). After removing diurnal cycles and seasonal trends from all datasets, we investigate dependence of correlation length on time scale by digitally high-pass filtering the data on 0.25–2000 h timescales and calculating correlations between sites for each high-pass filter cut-off. Correlations fall to zero with increasing station separation distance, but the characteristic correlation length varies with the high-pass filter applied: the higher the cut-off frequency, the smaller the station separation required to achieve de-correlation. Remarkable similarities between these three datasets reveal behavior that, if universal, could be particularly useful for grid management. For high-pass filter time constants shorter than about τ = 38 h, all datasets exhibit a correlation length that falls at least as fast as . Since the inter-site separation needed for statistical independence falls for shorter time scales, higher-rate fluctuations can be effectively smoothed by aggregating wind plants over areas smaller than otherwise estimated.

Molecular Dynamics Simulation Study of a Polysulfone-Based Anion Exchange Membrane in Comparison with the Proton Exchange Membrane

We investigate two types of polysulfone-based membranes (quaternary ammonium-functionalized anion exchange membrane and sulfonated proton exchange membrane) using molecular dynamics simulations to compare their nanophase-segregated structures and transport properties. Although the distribution of ionic groups on the polymer backbone is similar for both types, the quaternary ammonium groups and hydroxide ions in the anion exchange membrane are more solvated by water compared to the sulfonate groups and hydronium ions in the proton exchange membrane. Correspondingly, such better solvation of the ammonium groups and hydroxide ions leads the internal structure to a less matured hydrogen bonding network in the water phase, especially at low water content conditions. Through analysis of the nanophase segregation of the membranes, it is found that the characteristic correlation length has a similar value for both membranes, whereas the concentration contrast between the polymer domain and water phase is more dis...

Origin of α and β relaxations of Nafion.

Our experiments disentangle the low and high frequency dispersions in perfluorosulfonate ionomer solutions and membranes, providing a reasonable model for understanding these relaxations. Dielectric spectroscopy (DS) and small angle x-ray scattering (SAXS) measurements revealed that the dielectric relaxations observed at low (α relaxation) and high (β relaxation) frequencies show typical features of the longitudinal and radial polarization, respectively, of rodlike polymeric aggregates. Such relaxations were attributed to counterion fluctuations in the vicinity of sulfonic acid groups, in resemblance with polyelectrolytes. Characteristic correlation lengths calculated from both DS and SAXS data are in good agreement adding further evidence to the proposed model. Such description provides insights for the understanding of the crossover from polyelectrolytes, dominated by charge repulsion, to ionomers, dominated by dipolar attraction.

Constraints on the multi-lognormal magnetic fields from the observations of the cosmic microwave background and the matter power spectrum

Primordial magnetic fields (PMFs), which were generated in the early Universe before recombination, affect the motion of plasma and then the cosmic microwave background and the matter power spectrum. We consider constraints on PMFs with a characteristic correlation length from the observations of the anisotropies of the cosmic microwave background and the matter power spectrum. The spectrum of PMFs is modeled with multi-lognormal distributions, rather than power-law distribution, and we derive constraints on the strength $|\mathbf{B}_k|$ at each wave number $k$ along with the standard cosmological parameters in the flat Universe and the foreground sources. We obtain upper bounds on the field strengths at $k=10^{-1}, 10^{-2}, 10^{-4}$, and $10^{-5}$ Mpc$^{-1}$ as 4.7 nG, 2.1 nG, 5.3 nG, and 10.9 nG ($2\sigma$ C.L.) respectively, while the field strength at $k=10^{-3} $Mpc$^{-1}$ turns out to have a finite value as $|\mathbf{B}_{k = 10^{-3}}| = 6.2 \pm 1.3 $ nG ($1\sigma$ C.L.). This finite value is attributed to the finite values of BB mode data at $\ell > 300$ obtained from the QUAD experiment. If we do not include the BB mode data, we obtain only the upper bound on $B_{k=10^{-3}}$.

Formation of artificial opals viewed in situ by X-ray grazing insidence diffraction

Formation of artificial opal films by a vertical deposition method was in situ studied using the grazing incidence X-ray diffraction technique. Monodisperse spherical polymethyl methacrylate particles (200 nm in diameter) were deposited on the polished Si substrate from an aqueous suspension. The ordering of particles on a fixed area of the substrate located in turn in the bulk suspension under the meniscus and in the air was continuously monitored by the X-ray scattering upon moving the meniscus down owing to evaporation of the solvent. The triple air-liquid-solid phase boundary, i.e. the top line of the meniscus, is identified as the most probable location of the crystallization process. The analysis of observed Bragg reflections and the particle form-factor indicates that the obtained artificial opal-like structures are composed of the spheres arranged in a close-packed hexagonal layers parallel to the substrate. The characteristic correlation length along the normal to the substrate of 550 ± 100 nm is obtained from the half full width of Bragg peaks.

Covalent bond connectivity, medium range order and physical properties of GexIn8Se92−x glasses

The GexIn8Se92−x glasses (14 ≤ x ≤ 23.5) were extensively characterized by X-ray diffraction (XRD). The chemical composition is determined using energy dispersive spectrometers (EDS). The atomic structure of these glasses is investigated by using (XRD) technique. The first sharp diffraction peak (FSDP) in the structural factor indicates the existence of medium range order (MRO) in these glasses. The position of the FSDP and its full width at half maximum (FWHM), obtained after fitting the XRD of the glasses. The repetitive characteristic distance, R and structural correlation length, L, which characterizing the intermediate structure are deduced. The effect of composition and average coordination number <CN>, on the atomic volume, the density and compactness are studied. The connectivity of the system is discussed in terms of the total number of constraints which also influence the mean bond energy of the system. The intensity of the FSDP, the atomic volume and compactness of the structure, have anomalous change at <CN> = 2.67 indicating, a topological threshold occurs. The occurrence of this dependence leads to the Ge content has a marked effect on the MRO and physical properties parameters.

Nanostructures of Nematic Materials of Laterally Branched Molecules

The synthesis and small-angle X-ray scattering (SAXS) characterization is reported for 20 laterally branched mesogenic molecules, which are derived from the common rod-shaped 2,5-bis([4-(octyloxy)phenyl]carbonyloxy) benzoic acid unit. These compounds have a varying degree of flexibility, in that their lateral branch is formed upon conversion of the acid to either an ester or an amide, and most laterally branched molecules exhibit relatively wide nematic liquid-crystal phases with a direct nematic-to-crystal transition at lower temperatures. SAXS studies reveal the presence of smectic-like nanostructures (clusters) with short-range order in the nematic phase, with characteristic correlation lengths from 3 to over 10 nm. The smectic layers that are contained in these clusters are tilted with respect to the nematic director by angles ranging from 0° (i.e. untilted) to 55°. In some compounds, the intensity of the SAXS peak corresponding to the smectic layer spacing depends strongly on temperature. The main features of the nanostructures can be understood based on the molecular structure; therefore, guiding future synthetic work towards more precisely controlled and technologically useful nanostructures in nematics.

Displacement characteristics of coarse fluvial bed sediment

AbstractPrevious work highlights the need for data collection to identify appropriate models for temporal evolution of tracer dispersal in rivers. Results of 64 gravel‐bed field tracer experiments covering a wide range of flow and sediment supply regimes are compiled here to determine the probabilistic character of gravel transport. We focus on whether particle travel distances and waits are thin‐ or heavy‐tailed. While heavy‐tailed travel distance distributions are observed between successive monitoring events in different hydrological and sediment supply regimes, heavy‐tailedness does not persist through total travel distance over multiple monitoring events, suggesting that individual monitoring events occur before particle travel distance exceeds the characteristic correlation length for the channel (such that particles that start in fast paths remain in fast paths and particles in slow paths remain in slow paths). After a large number of transport events, super‐diffusive spreading was not observed at any of the gravel bed streams. Continuous‐time tracking of x, y, z coordinates of tracers in natural streams is necessary to capture exact step and waiting time distributions.

Powder structure of magnetic nanoparticles with a substituted pyrrole copolymer shells according to small-angle neutron scattering

Powders of magnetic nanoparticles coated by biocompatible block copolymers (substituted pyrroles) are investigated by small-angle neutron scattering. It is found that the structure of the final precipitates depends on the type of stabilizing shell in the initial magnetic fluids. When dodecylbenzene sulfonic acid is used, separate polydisperse particles with a radius of gyration of 3–5 nm and an irregular surface (fractal dimension of 2.24) are observed in the final samples. For systems with lauric acid, additional scattering from a quasicrystalline structure with a characteristic correlation length of about 10 nm can be seen in the experimental spectra. The difference in the organization of the structure of the studied powders is related to a different polymer coating rate on the surface of the magnetic nanoparticles, which depends on the sorption properties of surfactants in the initial magnetic fluids.

In situ Electrochemical Small-Angle Neutron Scattering (eSANS) for Quantitative Structure and Redox Properties of Nanoparticles.

The rapid growth in nanomaterial applications have revealed limitations in available physicochemical characterization methods. An in situ electrochemical small-angle neutron scattering (eSANS) methodology was devised that enables direct measurements of nanomaterial dispersion structure while undergoing reduction-oxidation (redox) reactions at the vitreous carbon electrode. Furthermore, these porous electrodes are amenable to contrast-variant neutron scattering strategies to measure nanoparticle structure and polymer conformation in multicomponent systems. The eSANS method was tested for feasibility by characterizing ZnO nanoparticles in 50 mmol/L NaCl deuterium oxide solution undergoing bulk electrolysis at negative potentials. Irreversible nanoparticle structural changes are observed during the potential cycle. The complete reduction of Zn(2+) to Zn(0) nanoparticles is unlikely, but a peak in the characteristic correlation length occurs during the redox bias with reduced average characteristic size.

Nonlocal viscosity kernel of mixtures

In this Brief Report we investigate the multiscale hydrodynamical response of a liquid as a function of mixture composition. This is done via a series of molecular dynamics simulations in which the wave-vector-dependent viscosity kernel is computed for three mixtures, each with 7-15 different compositions. We observe that the viscosity kernel is dependent on composition for simple atomic mixtures for all the wave vectors studied here; however, for a molecular mixture the kernel is independent of composition for large wave vectors. The deviation from ideal mixing is also studied. Here it is shown that the Lorentz-Berthelot interaction rule follows ideal mixing surprisingly well for a large range of wave vectors, whereas for both the Kob-Andersen and molecular mixtures large deviations are found. Furthermore, for the molecular system the deviation is wave-vector dependent such that there exists a characteristic correlation length scale at which the ideal mixing goes from underestimating to overestimating the viscosity.