Long-range Elasticity Research Articles

Velocity of interfaces with short and long ranged elasticity under sinusoidal creep

Plenty of research on elastic interfaces has been done on systems where the interface is pushed with a constant force. We studied the average velocity of an interface under a sinusoidal driving in the creep region, considering both short-range elastic systems, such as magnetic domain walls during a hysteresis loop, and long-ranged systems such as fractures. We obtained a modified version of the creep velocity with approximate power-law behavior and a material-dependent exponent for short ranged systems and simpler behavior for long-range elasticity. We discuss whether the model can be applied to fatigue fractures or if extra physics is needed.

Asymmetric Roughness of Elastic Interfaces at the Depinning Threshold.

Roughness of driven elastic interfaces in random media is typically understood to be characterized by a single roughness exponent ζ. We show that at the depinning threshold, due to symmetry breaking caused by the direction of the driving force, elastic interfaces with local, long-range, and mean-field elasticity exhibit asymmetric roughness. It is manifested as a skewed distribution of the local interface heights, and can be quantified by using detrended fluctuation analysis to compute a spectrum of local, segment-level scaling exponents. The asymmetry is observed as approximately linear dependence of the local scaling exponents on the difference of the segment height from the mean interface height.

Theory of the Effects of Specific Attractions and Chain Connectivity on the Activated Dynamics and Selective Transport of Penetrants in Polymer Melts

We generalize and apply a microscopic force level statistical mechanical theory of activated spherical penetrant dynamics in glass-forming liquids to study the influence of semiflexible polymer connectivity and penetrant–polymer attractive interactions on the penetrant hopping rate. The detailed manner that attractions of highly variable strength and spatial range modify the penetrant size and polymer melt density (from the rubbery state to slightly beyond the kinetic glass transition) dependences of penetrant activation barriers is established. Of special interest are possible nonadditive consequences of physical bonding and steric caging, the degree of coupling of penetrant hopping and the Kuhn segment scale alpha relaxation process, the relative importance of local caging and long-range matrix collective elasticity as a function of penetrant size, and implications for optimizing transport selectivity. With increasing attraction strength, the repulsive caging-restriction effect on penetrant mobility is predicted to grow, in contrast to the effect of the equilibrium penetrant–matrix solvation shell size, which decreases. The former dynamical effect results in a significant enhancement of the importance of the local cage barrier, while the latter effect results in a decrease of the importance of the nonlocal collective elastic barrier. These two competing effects have a very strong influence on selective penetrant transport for different sized penetrants: selectivity varies nonmonotonically with attraction strength in the deeply supercooled state but decreases monotonically in the rubbery state and at fixed attraction strength, exhibits a nonmonotonic variation with the matrix packing fraction. By comparing results based on modeling the matrix as semiflexible polymer chains with analogous calculations using the same dynamical theory but for a disconnected hard sphere matrix, the effect of chain connectivity is revealed and found to have quantitative, but not qualitative, consequences on penetrant-activated dynamics.

Force Correlations in Disordered Magnets.

We present a proof of principle for the validity of the functional renormalization group, by measuring the force correlations in Barkhausen-noise experiments. Our samples are soft ferromagnets in two distinct universality classes, differing in the range of spin interactions, and the effects of eddy currents. We show that the force correlations have a universal form predicted by the functional renormalization group, distinct for short-range and long-range elasticity, and mostly independent of eddy currents. In all cases correlations grow linearly at small distances, as in mean-field models, but in contrast to the latter are bounded at large distances. As a consequence, avalanches are anti-correlated. We derive bounds for these anticorrelations, which are saturated in the experiments, showing that the multiple domain walls in our samples effectively behave as a single wall.

Clusters in an Epidemic Model with Long-Range Dispersal.

In the presence of long-range dispersal, epidemics spread in spatially disconnected regions known as clusters. Here, we characterize exactly their statistical properties in a solvable model, in both the supercritical (outbreak) and critical regimes. We identify two diverging length scales, corresponding to the bulk and the outskirt of the epidemic. We reveal a nontrivial critical exponent that governs the cluster number and the distribution of their sizes and of the distances between them. We also discuss applications to depinning avalanches with long-range elasticity.

Effect of thresholding on avalanches and their clustering for interfaces with long-range elasticity.

Avalanches are often defined as signals higher than some detection level in bursty systems. The choice of the detection threshold affects the number of avalanches, but it can also affect their temporal correlations. We simulated the depinning of a long-range elastic interface and applied different thresholds including a zero one on the data to see how the sizes and durations of events change and how this affects temporal avalanche clustering. Higher thresholds result in steeper size and duration distributions and cause the avalanches to cluster temporally. Using methods from seismology, the frequency of the events in the clusters was found to decrease as a power-law of time, and the size of an event in a cluster was found to help predict how many events it is followed by. The results bring closer theoretical studies of this class of models to real experiments, but also highlight how different phenomena can be obtained from the same set of data.

Experimental test of a predicted dynamics–structure–thermodynamics connection in molecularly complex glass-forming liquids

Understanding in a unified manner the generic and chemically specific aspects of activated dynamics in diverse glass-forming liquids over 14 or more decades in time is a grand challenge in condensed matter physics, physical chemistry, and materials science and engineering. Large families of conceptually distinct models have postulated a causal connection with qualitatively different "order parameters" including various measures of structure, free volume, thermodynamic properties, short or intermediate time dynamics, and mechanical properties. Construction of a predictive theory that covers both the noncooperative and cooperative activated relaxation regimes remains elusive. Here, we test using solely experimental data a recent microscopic dynamical theory prediction that although activated relaxation is a spatially coupled local-nonlocal event with barriers quantified by local pair structure, it can also be understood based on the dimensionless compressibility via an equilibrium statistical mechanics connection between thermodynamics and structure. This prediction is found to be consistent with observations on diverse fragile molecular liquids under isobaric and isochoric conditions and provides a different conceptual view of the global relaxation map. As a corollary, a theoretical basis is established for the structural relaxation time scale growing exponentially with inverse temperature to a high power, consistent with experiments in the deeply supercooled regime. A criterion for the irrelevance of collective elasticity effects is deduced and shown to be consistent with viscous flow in low-fragility inorganic network-forming melts. Finally, implications for relaxation in the equilibrated deep glass state are briefly considered.

Spatial Clustering of Depinning Avalanches in Presence of Long-Range Interactions.

Disordered elastic interfaces display avalanche dynamics at the depinning transition. For short-range interactions, avalanches correspond to compact reorganizations of the interface well described by the depinning theory. For long-range elasticity, an avalanche is a collection of spatially disconnected clusters. In this Letter we determine the scaling properties of the clusters and relate them to the roughness exponent of the interface. The key observation of our analysis is the identification of a Bienaymé-Galton-Watson process describing the statistics of the number of clusters. Our work has concrete importance for experimental applications where the cluster statistics is a key probe of avalanche dynamics.

Formation of two glass phases in binary Cu-Ag liquid

The glass transition is alternatively described as either a dynamic transition in which there is a dramatic slowing down of the kinetics, or as a thermodynamic phase transition. To examine the physical origin of the glass transition in fragile Cu-Ag liquids, we employed molecular dynamics (MD) simulations on systems in the range of 32,000 to 2,048,000 atoms. Surprisingly, we identified a 1st order freezing transition from liquid (L) to metastable heterogenous solid-like phase, denoted as the G-glass, when a supercooled liquid evolves isothermally below its melting temperature at deep undercooling. In contrast, a more homogenous liquid-like glass, denoted as the l-glass, is achieved when the liquid is quenched continuously to room temperature with a fast cooling rate of ~1011 K/sec. We report a thermodynamic description of the l-G transition and characterize the correlation length of the heterogenous structure in the G-glass. The shear modulus of the G-glass is significantly higher than the l-glass, suggesting that the first order l-G transition is linked fundamentally to long-range elasticity involving elementary configurational excitations in the G-glass.

Thermal fluctuations of dislocations reveal the interplay between their core energy and long-range elasticity

Equilibrium fluctuations of dislocations are central to the plastic response of metals and alloys because they control the attempt frequency of thermally activated events. We analyze here atomic-scale simulations of thermally vibrating dislocations with the help of an analytical model and show that thermal fluctuations intimately involve both long-range elasticity and short-range core effects. In addition, equilibrium fluctuations of edge and screw dislocations in aluminum are used to derive quantitative parameters that characterize their energetics and dynamics and we discuss how large-scale models such as dislocation dynamics can be parametrized based on these results. In particular, we show that the core parameters found here through fluctuations are transferable and can be used to predict dislocation bow-out under an applied stress.

Quantitative Scaling of Magnetic Avalanches.

We provide the first quantitative comparison between Barkhausen noise experiments and recent predictions from the theory of avalanches for pinned interfaces, both in and beyond mean field. We study different classes of soft magnetic materials, including polycrystals and amorphous samples-which are characterized by long-range and short-range elasticity, respectively-both for thick and thin samples, i.e., with and without eddy currents. The temporal avalanche shape at fixed size as well as observables related to the joint distribution of sizes and durations are analyzed in detail. Both long-range and short-range samples with no eddy currents are fitted extremely well by the theoretical predictions. In particular, the short-range samples provide the first reliable test of the theory beyond mean field. The thick samples show systematic deviations from the scaling theory, providing unambiguous signatures for the presence of eddy currents.

Biophysical and biological characterisation of collagen/resilin-like protein composite fibres

Collagen type I, in various physical forms, is widely used in tissue engineering and regenerative medicine. To control the mechanical properties and biodegradability of collagen-based devices, exogenous cross-links are introduced into the 3D supramolecular structure. However, potent cross-linking methods are associated with cytotoxicity, whilst mild cross-linking methods are associated with suboptimal mechanical resilience. Herein, we assessed the influence of resilin, a super-elastic and highly stretchable protein found within structures in arthropods where energy storage and long-range elasticity are needed, on the biophysical and biological properties of mildly cross-linked extruded collagen fibres. The addition of resilin-like protein in the 4-arm poly(ethylene glycol) ether tetrasuccinimidyl glutarate cross-linked collagen fibres resulted in a significant increase of stress and strain at break values and a significant decrease of modulus values. The addition of resilin-like protein did not compromise cell metabolic activity and DNA concentration. All groups are supported parallel to the longitudinal fibre axis cell orientation. Herein we provide evidence that the addition of resilin-like protein in mildly cross-linked collagen fibres improves their biomechanical properties, without jeopardising their biological properties.

The structure and mechanical properties of the proteins of lamprey cartilage.

The cyanogen bromide-resistant proteins of lamprey cartilage are biochemically related to the mammalian elastic protein, elastin. This study investigates their mechanical properties and enquires whether, like elastin, long-range elasticity arises in them from a combination of entropic and hydrophobic mechanisms. Branchial and pericardial proteins resembled elastin mechanically, with elastic moduli of 0.13-0.35 MPa, breaking strains of 50%, and low hysteresis. Annular and piston proteins had higher elastic moduli (0.27-0.75 MPa) and larger hysteresis. Exchanging solvent water for trifluoroethanol increased the elastic moduli, whereas increasing temperature lowered the elastic moduli. Raman microspectrometry showed small differences in side-chain modes consistent with reported biochemical differences. Decomposition of the amide I band indicated that the secondary structures were like those of elastin, preponderantly unordered, which probably confer the conformational flexibility necessary for entropy elasticity. Piston and annular proteins showed the strongest interactions with water, suggesting, together with the mechanical testing data, a greater role of hydrophobic interactions in their mechanics. Two-photon imaging of intrinsic fluorescence and dye injection experiments showed that annular and piston proteins formed closed-cell honeycomb structures, whereas the branchial and pericardial proteins formed open-cell structures, which may account for the differences in mechanical properties.

Relaxation in yield stress systems through elastically interacting activated events.

We study consequences of long-range elasticity in thermally assisted dynamics of yield stress materials. Within a two-dimensional mesoscopic model we calculate the mean-square displacement and the dynamical structure factor for tracer particle trajectories. The ballistic regime at short time scales is associated with a compressed exponential decay in the dynamical structure factor, followed by a subdiffusive crossover prior to the onset of diffusion. We relate this crossover to spatiotemporal correlations and thus go beyond established mean field predictions.

The structure and micromechanics of elastic tissue.

Elastin is a major component of tissues such as lung and blood vessels, and endows them with the long-range elasticity necessary for their physiological functions. Recent research has revealed the complexity of these elastin structures and drawn attention to the existence of extensive networks of fine elastin fibres in tissues such as articular cartilage and the intervertebral disc. Nonlinear microscopy, allowing the visualization of these structures in living tissues, is informing analysis of their mechanical properties. Elastic fibres are complex in composition and structure containing, in addition to elastin, an array of microfibrillar proteins, principally fibrillin. Raman microspectrometry and X-ray scattering have provided new insights into the mechanisms of elasticity of the individual component proteins at the molecular and fibrillar levels, but more remains to be done in understanding their mechanical interactions in composite matrices. Elastic tissue is one of the most stable components of the extracellular matrix, but impaired mechanical function is associated with ageing and diseases such as atherosclerosis and diabetes. Efforts to understand these associations through studying the effects of processes such as calcium and lipid binding and glycation on the mechanical properties of elastin preparations in vitro have produced a confusing picture, and further efforts are required to determine the molecular basis of such effects.

Domain walls in helical magnets: Elasticity and pinning

Recently completely new types of domain walls (DWs) have been discovered in helical magnets, consisting generically of a regular array of pairs of magnetic vortex lines (Li F. et al., Phys. Rev. Lett., 108 (2012) 107203). Only for special orientations DWs are free of vortices. In this paper we calculate their elastic and pinning properties, using the pitch angle θ as a small parameter. In particular we show that vortex-free DWs exhibit long-range elasticity which makes them very stiff and suppresses their pinning by impurities. Their roughening transition temperature is of the order of the Néel temperature. DWs including vortices (either by orientation or due to step formation above their roughening transition) show short-range elasticity and strong pinning by impurities. These results apply both to centrosymmetric as well as to non-centrosymmetric systems. The application to chiral liquid crystals is briefly discussed.

Nanoindentation to quantify the effect of insect dimorphism on the mechanical properties of insect rubberlike cuticle

Abstract

Molecular dynamics simulations of the stable structures of single atomic contacts in gold nanojunctions

Molecular dynamics simulations are performed to investigate the breaking forces and stable atomic contacts in different gold nanojunctions. These forces and structures are obtained through repeated jump-to-contact and jump-out-of-contact trainings with the aid of a simple driving-spring model, which can reasonably represent the long-range elasticity of the gold electrode. For the three stable trained atomic contacts obtained in this work, we find that the breaking force and binding energy of a gold dimer in the 3-1-1-3 contact are 0.87 nN and 0.38 eV, respectively, which are much smaller than those of the 3-1-3 and 3-1-2 contacts. The binding energies of these stable nanojunctions vary from 0.38--0.74 eV, consistent with other experimental measurements.

Long-range linear elasticity and mechanical instability of self-scrolling binormal nanohelices under a uniaxial load

Mechanical properties of self-scrolling binormal nanohelices with a rectangular cross-section are investigated under uniaxial tensile and compressive loads using nanorobotic manipulation and Cosserat curve theory. Stretching experiments demonstrate that small-pitch nanohelices have an exceptionally large linear elasticity region and excellent mechanical stability, which are attributed to their structural flexibility based on an analytical model. In comparison between helices with a circular, square and rectangular cross-section, modeling results indicate that, while the binormal helical structure is stretched with a large strain, the stress on the material remains low. This is of particular significance for such applications as elastic components in micro-/nanoelectromechanical systems (MEMS/NEMS). The mechanical instability of a self-scrolling nanohelix under compressive load is also investigated, and the low critical load for buckling suggests that the self-scrolling nanohelices are more suitable for extension springs in MEMS/NEMS.

Studies on resilin-like gene products in insects

Putative pro-resilins from 12 Drosophila species are compared with each other and with some pro-resilin-related proteins from other insect species, in an attempt to decide which structural features are likely to be important for the characteristic properties of resilins. The putative pro-resilins from the 12 Drosophila species are very similar; their structures are characterized by a chitin-binding R&R Consensus sequence of type RR-2, surrounded by two repeat-containing regions. The repeat-containing regions are assumed to be responsible for the long-range elasticity characteristic for resilin. Pronounced differences are present between the Drosophila pro-resilins and the resilin-like gene products present in other insect species. It is suggested that gene products, which are predicted both to be cuticular proteins and to possess long-range elasticity, should be classified as either putative pro-resilins or pro-resilin-like proteins. Gene products which are predicted to possess long-range elasticity, but do not contain a chitin-binding region, should not be classified as pro-resilin-like proteins until it has been established that they are cuticular proteins.