Length Scale Of Heterogeneity Research Articles

From the capillary condensation to the glass transition of a confined molecular liquid: Case of toluene

Confinement of glass-forming liquids in nanoporous materials was previously suggested to provide information on the growing heterogeneity length scale responsible of the glass formation. However extensive studies of various liquids under various confinement conditions conclude that the role of surface is dominant over the finite size effects leading to more complex description of the dynamics under confinement. Here we focus on the fluid wall interactions and their contributions at the approach of the glass transition of a simple molecular liquid, toluene. By changing the pore size and the chemistry of the surface, we propose to learn about the pore filling processes from adsorption experiments at high temperature; we relate them to the T-behavior within the pore of a thermodynamic quantity, the averaged density, and the mobility, via the measurements of the mean square displacements over a large T-range where the glass transition spreads out.

Seismic velocities and composition of the Canadian crust

To investigate variations in crustal structure and composition, we analyze approximately 80,000 teleseismic P wave seismograms recorded at 343 broadband stations distributed about the Canadian landmass. These data are binned by horizontal slowness and simultaneously deconvolved into receiver functions. We apply stacking methods to retrieve estimates of the bulk crustal velocity ratio VP/VS and thickness H from this receiver function dataset under the assumption of locally 1D structure. These crustal parameters are analyzed together with a compilation of velocity and thickness estimates from previous active source experiments and global crustal thickness models to investigate competing models of crustal composition and evolution. Crustal thicknesses vary between ~25km and ~48km with an area-weighted average of 37km for all stations. VP/VS estimates range from 1.65 to 1.95 and display a systematic increasing trend from NW to SE across the Churchill, Superior and Grenville provinces. Analysis of intra-crustal conversions indicates little evidence for a well-defined, widespread Conrad discontinuity, although the lower crust appears to be more transparent to teleseismic converted waves than the upper crust. This observation runs contrary to that of P-reflectivity in many active source studies, and may be reconciled through a dominant scale-length of heterogeneity that is less than ~800m. The VP/VS observations and VP constraints from active source studies are compared with laboratory measurements for common crustal rocktypes and found to be consistent with bulk compositions falling between granite gneiss and diorite. Previously reported systematic variations in crustal thickness and VP/VS with age in a global data set are not supported by our data set.

NMR study of interphase structure in layered polymer morphologies with mobility contrast: disorder and confinement effects vs. dynamic heterogeneities

Nanostructured multiphase polymers with mobility contrast, such as semicrystalline polymers or block copolymers with two separate glass transitions, are usually characterized by the presence of an interphase material with in-between mobility. This interphase is often assumed to form a contiguous layer between the adjacent main phases, possibly exhibiting a mobility gradient. Here, we present evidence from proton low-field NMR experiments based upon the spin diffusion effect that suggests less trivial possible arrangements. A numerical analysis of the NMR data based upon a 2D lattice model demonstrates that a part of the mobile phase must be in rather direct contact with the rigid phase. Tentatively, we assume an island-like distribution of the interphase, or its location within the rigid phase, with sizes on the scale of a few nanometers. We observe qualitatively the same phenomenon in a semicrystalline polymer, poly(e-caprolactone), and in a lamellar poly(styrene)-poly(butadiene) block copolymer, suggesting that the phenomenon has some degree of universality. We hypothesize that the non-trivial location of the interphase results from either a higher than one-dimensional constraint imposed by the surrounding rigid phase and disorder effects arising from local roughness or thickness distributions or from the intrinsic dynamic heterogeneity length scale of material close to the glass transition.

Effects of pore fluid pressure and tectonic stress on diverse seismic activities around the Mt. Ontake volcano, central Japan

To understand the effects of pore fluid pressure and tectonic stress in generating diverse seismicity, we deployed 11 temporary seismic stations around an active volcano, Mt. Ontake, in central Japan during the summers of 2009–2011. We obtained well-constrained focal mechanism solutions from the seismic data recorded at the temporary stations and permanent stations located within 50 km around Mt. Ontake. We estimated the 3-D pore fluid pressure field, taking into consideration spatial changes in the tectonic stress pattern, by applying the method of focal mechanism tomography to the dataset. We found overpressurized fluid reservoirs with a peak of 100–150 MPa at depths between 5 and 12 km in the southeast and east flanks of Mt. Ontake. This region has experienced earthquake swarm activity since 1976. Many seismic events concentrated at the edge of the overpressurized fluid reservoirs, where pore fluid pressure gradients are steep. This indicates that a large amount of fluid flow would trigger seismic events by decreasing fault strength caused by an increase in pore fluid pressures. Many small events (M < 3) occurred on pre-existing faults that are unfavorably oriented or severely mis-oriented relative to the tectonic stress pattern, indicating that these events are driven by overpressurized fluids. However, the macroscopic rupture planes of microseismic clouds and larger events (M ≥ 3) appear to release tectonic stresses produced by steady plate subduction. The critical event magnitude (Mc = 3) at which seismic behavior changes would be characterized by a length scale of pore fluid pressure heterogeneity. This quantity might be an indicator of the maximum event magnitude in the region.

Scaling and unified characterization of flow instabilities in layered heterogeneous porous media

The physics of miscible flow displacements with unfavorable mobility ratios through horizontal layered heterogeneous media is investigated. The flow model is solved numerically, and the effects of various physical parameters such as the injection velocity, diffusion, viscosity, and the heterogeneity length scale and variance are examined. The flow instability is characterized qualitatively through concentration contours as well as quantitatively through the mixing zone length and the breakthrough time. This characterization allowed us to identify four distinct regimes that govern the flow displacement. Furthermore, a scaling of the model resulted in generalized curves of the mixing zone length for any flow scenario in which the first three regimes of diffusion, channeling, and lateral dispersion superpose into a single unifying curve and allowed us to clearly identify the onset of the fourth regime. A critical effective Péclet number w_{c} based on the layers' width is proposed to identify flows where heterogeneity effects are expected to be important and those where the flow can be safely treated as homogeneous. A similar scaling of the breakthrough time was obtained and allowed us to identify two optimal effective Péclet numbers w_{opt} that result in the longest and shortest breakthrough times for any flow displacement.

Short length scale mantle heterogeneity beneath Iceland probed by glacial modulation of melting

Glacial modulation of melting beneath Iceland provides a unique opportunity to better understand both the nature and length scale of mantle heterogeneity. At the end of the last glacial period, ∼13000 yr BP, eruption rates were ∼20–100 times greater than in glacial or late postglacial times and geophysical modeling posits that rapid melting of the large ice sheet covering Iceland caused a transient increase in mantle decompression melting rates. Here we present the first time-series of Sr–Nd–Hf–Pb isotopic data for a full glacial cycle from a spatially confined region of basaltic volcanism in northern Iceland. Basalts and picrites erupted during the early postglacial burst of volcanic activity are systematically offset to more depleted isotopic compositions than those of lavas erupted during glacial or recent (<7 kyr) times. These new isotopic data, coupled with major and trace element data, show that the mantle underneath northern Iceland is heterogeneous on small (<100 km) length scales. The temporal response of the isotopic compositions of the basalts to glacial unloading indicates that the isotopic composition of mantle heterogeneities can be linked to their melting behavior. The present geochemical data can be accounted for by a melting model in which a lithologically heterogeneous mantle source contains an enriched component more fusible than its companion depleted component.

Mapping between finite temperature classical and zero temperature quantum systems: Quantum critical jamming and quantum dynamical heterogeneities

Many electronic systems (e.g., the cuprate superconductors and heavy fermions) exhibit striking features in their dynamical response over a prominent range of experimental parameters. While there are some empirical suggestions of particular increasing length scales that accompany such transitions in some cases, this identification is not universal and in numerous instances no large correlation length is evident. To better understand, as a matter of principle, such behavior in quantum systems, we extend a known mapping (earlier studied in stochastic or supersymmetric quantum mechanics) between finite temperature classical Fokker-Planck systems and related quantum systems at zero temperature to include general nonequilibrium dynamics. Unlike Feynman mappings or stochastic quantization methods in field theories (as well as more recent holographic type dualities), the classical systems that we consider and their quantum duals reside in the same number of space-time dimensions. The upshot of our very broad and rigorous result is that a Wick rotation exactly relates (i) the dynamics in general finite temperature classical dissipative systems to (ii) zero temperature dynamics in the corresponding dual many-body quantum systems. Using this correspondence, we illustrate that, even in the absence of imposed disorder, many continuum quantum fluid systems (and possible lattice counterparts) may exhibit a zero-point ``quantum dynamical heterogeneity'' wherein the dynamics, at a given instant, is spatially nonuniform. While the static length scales accompanying this phenomenon do not seem to exhibit a clear divergence in standard correlation functions, the length scale of the dynamical heterogeneities can increase dramatically. We further study ``quantum jamming'' and illustrate how a hard-core bosonic system can undergo a zero temperature quantum critical metal-to-insulator-type transition with an extremely large effective dynamical exponent $z&gt;4$ that is consistent with length scales that increase far more slowly than the relaxation time as a putative critical transition is approached. Similar results may hold for spin-liquid-type as well as interacting electronic systems. We suggest ways to analyze experimental data in order to adduce such phenomena. Our approach may be used to analyze other quenched quantum systems.

Upscaling of solute transport in heterogeneous media with non-uniform flow and dispersion fields

An analytical and computational model for non-reactive solute transport in periodic heterogeneous media with arbitrary non-uniform flow and dispersion fields within the unit cell of length ε is described. The model lumps the effect of non-uniform flow and dispersion into an effective advection velocity Ve and an effective dispersion coefficient De. It is shown that both Ve and De are scale-dependent (dependent on the length scale of the microscopic heterogeneity, ε), dependent on the Péclet number Pe, and on a dimensionless parameter α that represents the effects of microscopic heterogeneity. The parameter α, confined to the range of [−0.5, 0.5] for the numerical example presented, depends on the flow direction and non-uniform flow and dispersion fields. Effective advection velocity Ve and dispersion coefficient De can be derived for any given flow and dispersion fields, and ε. Homogenized solutions describing the macroscopic variations can be obtained from the effective model. Solutions with sub-unit-cell accuracy can be constructed by homogenized solutions and its spatial derivatives. A numerical implementation of the model compared with direct numerical solutions using a fine grid, demonstrated that the new method was in good agreement with direct solutions, but with significant computational savings.

Multiple length and time scales of dynamic heterogeneities in model glass-forming liquids: A systematic analysis of multi-point and multi-time correlations

We report an extensive and systematic investigation of the multi-point and multi-time correlation functions to reveal the spatio-temporal structures of dynamic heterogeneities in glass-forming liquids. Molecular dynamics simulations are carried out for the supercooled states of various prototype models of glass-forming liquids such as binary Kob-Andersen, Wahnström, soft-sphere, and network-forming liquids. While the first three models act as fragile liquids exhibiting super-Arrhenius temperature dependence in their relaxation times, the last is a strong glass-former exhibiting Arrhenius behavior. First, we quantify the length scale of the dynamic heterogeneities utilizing the four-point correlation function. The growth of the dynamic length scale with decreasing temperature is characterized by various scaling relations that are analogous to the critical phenomena. We also examine how the growth of the length scale depends upon the model employed. Second, the four-point correlation function is extended to a three-time correlation function to characterize the temporal structures of the dynamic heterogeneities based on our previous studies [K. Kim and S. Saito, Phys. Rev. E 79, 060501(R) (2009); and J. Chem. Phys. 133, 044511 (2010)]. We provide comprehensive numerical results obtained from the three-time correlation function for the above models. From these calculations, we examine the time scale of the dynamic heterogeneities and determine the associated lifetime in a consistent and systematic way. Our results indicate that the lifetime of the dynamical heterogeneities becomes much longer than the α-relaxation time determined from a two-point correlation function in fragile liquids. The decoupling between the two time scales is remarkable, particularly in supercooled states, and the time scales differ by more than an order of magnitude in a more fragile liquid. In contrast, the lifetime is shorter than the α-relaxation time in tetrahedral network-forming strong liquid, even at lower temperatures.

Diffusion of transition metals in periclase by experiment and first-principles, with implications for core–mantle equilibration during metal percolation

Diffusion of the divalent transition metals in the deep mantle is important for understanding length scales of mantle heterogeneity, transport across the core–mantle boundary, and the degree of equilibration during core formation. Here we report the results of experiments and theoretical calculations on Ni, Co, Fe and Mn diffusion in periclase, the primary repository of these elements in Earth's lower mantle. The periclase used in the experiments was doped with 550ppm Al3+ to fix the cation vacancy concentration, and the experiments were performed at 2GPa and temperatures between 1673 and 2073K. The variation in diffusion coefficients among the transition metals was found to be less than a factor of three, and to increase in the order Ni<Co∼Mn<Fe. Theoretical results on the diffusion energetics, based on density functional theory with electron correlation effects accounted for using the GGA+U method, correctly predict the relative diffusivities, and yield absolute diffusion coefficients in reasonable agreement with the experimental results. A simple crystal field splitting model does not provide even qualitative guidance for the trends in relative diffusivity, but does show strong correlation with changes in migration energy due to spin transitions. The diffusion coefficients are rapid enough under mantle conditions to allow equilibration during core separation through the solid mantle, if the metal percolates through a grain-scale permeable network with channel spacing of centimeters or less.

Length and Time Scales of Structural Heterogeneities in Deeply Supercooled Propylene Carbonate

Deactivation of excited phenanthrene by molecular oxygen is utilized to probe the structural heterogeneity of supercooled propylene carbonate. The diffusion rate of oxygen molecules in different regions varies over two orders of magnitude. The size of the regions of different oxygen mobility was determined to be 1.5 nm. Values from 0.2 to 30 s have been obtained for the lifetime of these regions over a temperature range from T(g)-1 to T(g)+4 K (T(g)=158 K). The heterogeneity lifetime is in close agreement with the α-relaxation time determined by dielectric spectroscopy. The obtained results argue in favor of the statement that the heterogeneous cooperative dynamics of host molecules (so-called dynamical heterogeneity) is of structural origin.

Length scale of mechanical heterogeneity in a glassy polymer determined by atomic force microscopy

Using dynamic force microscopy, nanoscale mechanical heterogeneity in glassy polymer was characterized. The correlation length of heterogeneous viscoelasticity was measured to be ∼2.1 nm, consistent with the length scale of cooperatively rearranging regions at glass transition and is independent of molecular weight. Apparent energy dissipation with the variation of ∼57%, originating from non-uniform distribution of local viscoelasticity, was revealed. The results provide definite experimental evidences on the nanoscale heterogeneity in glassy polymers and bear important insights in understanding the puzzling glass transition.

Impact of soil moisture heterogeneity length scale and gradients on daytime coupled land‐cloudy boundary layer interactions

AbstractUsing a coupled large‐eddy simulation–land surface model framework, the impact of two‐dimensional soil moisture heterogeneity on the cloudy boundary layer under varied free‐atmosphere stabilities is investigated. Specifically, the impacts of soil moisture heterogeneity length scale and heterogeneity in terms of soil moisture gradients on micrometeorological states, surface fluxes, boundary layer characteristics, and cloud development are examined. The results show that mesoscale circulations due to surface heterogeneity in soil moisture play an important role in transferring water vapour within the boundary layer and in regulating cloud distribution at the entrainment zone, which, in turn, provides feedbacks on boundary layer/surface energy budgets. The initial domain‐averaged soil moisture is identical for all homogenous and heterogeneous cases; however, the soil moisture heterogeneity in gradient and length scale between dry and wet regions has a significant impact on the estimates of near‐surface micrometeorological properties and surface fluxes, which further affect the boundary layer states and characteristics. Both liquid water potential temperature and liquid water mixing ratio increase with an increasing soil moisture gradient, whereas the amount of specific humidity decreases. Heterogeneity length scale and free atmosphere stability also amplify these impacts on the boundary layer structure and cloud formation. In a low atmospheric stability condition that potentially allows for a deeper boundary layer and a higher entrainment rate, cloud base height and cloud thickness significantly increase as the soil moisture gradient and length scale increase. Analysis to differentiate the influences of surface heterogeneity type (i.e. length scale vs gradient) shows that in general soil moisture gradient provides a larger impact than heterogeneity length scale, although the heterogeneity length scale is large enough to initiate circulation features responsible for differences in the coupled system between homogeneous and heterogeneous soil moisture cases. Copyright © 2012 John Wiley &amp; Sons, Ltd.

Multiple spatio-temporal scale modeling of composites subjected to cyclic loading

This manuscript presents a multiscale modeling methodology for failure analysis of composites subjected to cyclic loading conditions. Computational homogenization theory with multiple spatial and temporal scales is employed to devise the proposed methodology. Multiple spatial scales address the disparity between the length scale of material heterogeneities and the overall structure, whereas multiple temporal scales with almost periodic fields address the disparity between the load period and overall life under cyclic loading. The computational complexity of the multiscale modeling approach is reduced by employing a meso-mechanical model based on eigendeformation based homogenization with symmetric coefficients in the space domain, and an adaptive time stepping strategy based on a quadratic multistep method with error control in the time domain. The proposed methodology is employed to simulate the response of graphite fiber-reinforced epoxy composites. Model parameters are calibrated using a suite of experiments conducted on unidirectionally reinforced specimens subjected to monotonic and cyclic loading. The calibrated model is employed to predict damage progression in quasi-isotropic specimens. The capabilities of the model are validated using acoustic emission testing.

Contrast variation in spin-echo small angle neutron scattering

The use of contrast variation in spin-echo small angle neutron scattering (SESANS) experiments is discussed for the case of colloidal structural investigation. On the basis of calculations for several model systems, we find that the contrast variation SESANS technique, in terms of the measured SESANS correlation function G(z), is not sensitive to the structural characteristics of colloidal suspensions consisting of particles with uniform scattering length density profiles. However, its ability to resolve structural heterogeneity, at both intra-colloidal and inter-colloidal length scales, is clearly demonstrated. The prospect of using this new technique to investigate structural information that is difficult to probe in other ways is also explored.

Communication: Crystallite nucleation in supercooled glycerol near the glass transition

Heterogeneity and solid-like structures found near the glass transition provide a key to a better understanding of supercooled liquids and of the glass transition. However, the formation of solid-like structures and its effect on spatial heterogeneity in supercooled liquids is neither well documented nor well understood. In this work, we reveal the crystalline nature of the solid-like structures in supercooled glycerol by means of neutron scattering. The results indicate that inhomogeneous nucleation happens at temperatures near T(g). Nevertheless, the thermal history of the sample is essential for crystallization. This implies such structures in supercooled liquids strongly depend on thermal history. Our work suggests that different thermal histories may lead to different structures and therefore to different length and time scales of heterogeneity near the glass transition.

Dynamical heterogeneity in aging colloidal glasses of Laponite

Glasses behave as solids due to their long relaxation time; however the origin of this slow response remains a puzzle. Growing dynamic length scales due to cooperative motion of particles are believed to be central to the understanding of both the slow dynamics and the emergence of rigidity. Here, we provide experimental evidence of a growing dynamical heterogeneity length scale that increases with increasing waiting time in an aging colloidal glass of Laponite. The signature of heterogeneity in the dynamics follows from dynamic light scattering measurements in which we study both the rotational and translational diffusion of the disk-shaped particles of Laponite in suspension. These measurements are accompanied by simultaneous microrheology and macroscopic rheology experiments. We find that rotational diffusion of particles slows down at a faster rate than their translational motion. Such decoupling of translational and orientational degrees of freedom finds its origin in the dynamic heterogeneity since rotation and translation probe different length scales in the sample. The macroscopic rheology experiments show that the low frequency shear viscosity increases at a much faster rate than both rotational and translational diffusive relaxation times.

Modeling the Effects of Molecular Length Scale Electrode Heterogeneity in Organic Solar Cells

Kinetic Monte Carlo simulations of planar heterojunction (PHJ) organic solar cells (OPVs) constructed with electronically heterogeneous electrodes are presented which correlate the extent and length scale of electrode heterogeneity with their capacity for collecting photogenerated charge carriers. The PHJ OPV is modeled as an ensemble of discrete 1 nm3 molecular sites and 1 nm2 electrode sites for which we individually assign various effective activation energies for charge hopping. Utilizing Marcus theory to describe charge transfer reactions within the energetically disordered lattice, described by a Gaussian distribution of discrete site energies, we demonstrate the sensitivity of solar cell device performance to nanometer length scale heterogeneity at the electrode-active layer contact. Such sensitivity is reflected in the steady-state charge density profiles in the vicinity of the electrode-active material interface, charge collection efficiencies, and rates of recombination at the donor–acceptor (D/...

Comparing dynamic correlation lengths from an approximation to the four-point dynamic susceptibility and from the picosecond vibrational dynamics

Recently an alternative approach to the determination of dynamic correlation lengths ξ for supercooled liquids, based on the properties of the slow (picosecond) vibrational dynamics, was carried out [Hong, Novikov, and Sokolov, Phys. Rev. E 83, 061508 (2011)]. Although these vibrational measurements are typically conducted well below the glass transition temperature, the liquid is frozen at T(g), whereby structural correlations, density variations, etc., manifested at low temperatures as spatial fluctuations of local elastic constants, can be related to a dynamic heterogeneity length scale for the liquid state. We compare ξ from this method to values calculated using an approximation to the four-point dynamic susceptibility. For 26 different materials we find good correlation between the two measures; moreover, the pressure dependences are consistent within the large experimental error. However, ξ from Boson peak measurements above T(g) have a different, and unrealistic, temperature dependence.

Heterogeneity length scale for oxygen diffusion in glassy squalane

The kinetics of phenanthrene phosphorescence quenching by mobile oxygen molecules was used to study characteristics of oxygen diffusion on a nanometer length scale in glassy squalane. The phosphorescence decay was described using a model of glassy matrix with spatially correlated oxygen jump rates. The correlation length was determined to be 2.5 nm. The dispersion of barrier energy for oxygen jumps is 1.8 kJ/mol and the average barrier energy is 32 kJ/mol. The structural heterogeneities are deduced to be fluctuations in structure frozen in from the supercooled liquid.