Anisotropic mechanical response of layered disordered fibrous materials

Mechanically bonded fabrics account for a significant portion of nonwoven products, and serve many niche areas of nonwoven manufacturing. Such fabrics are characterized by layers of disordered fibrous webs, but we lack an understanding of how such microstructures determine bulk material response. Here we numerically determine the linear shear response of needle-punched fabrics modeled as cross-linked sheets of two-dimensional (2D) Mikado networks. We systematically vary the intra-sheet fiber density, inter-sheet separation distance, and direction of shear, and quantify the macroscopic shear modulus alongside the degree of affinity and energy partition. For shear parallel to the sheets, the response is dominated by intrasheet fibers and follows known trends for 2D Mikado networks. By contrast, shears perpendicular to the sheets induce a softer response dominated by either intrasheet or intersheet fibers depending on a quadratic relation between sheet separation and fiber density. These basic trends are reproduced and elucidated by a simple scaling argument that we provide. We discuss the implications of our findings in the context of real nonwoven fabrics.

The impact of electrode resistance on the biogalvanic characterisation technique

Measurement of a tissue-specific electrical resistance may offer a discriminatory metric for evaluation of tissue health during cancer surgery. With a move toward minimally-invasive procedures, applicable contact sensing modalities must be scalable, fast and robust. A passive resistance characterisation method utilising a biogalvanic cell as an intrinsic power source has been proposed as a potentially suitable solution. Previous work has evaluated this system with results showing effective discrimination of tissue type and damage (through electroporation). However, aspects of the biogalvanic cell have been found to influence the characterisation performance, and are not currently accounted for within the system model. In particular, the electrode and salt-bridge resistance are not independently determined, leading to over-predictions of tissue resistivity.

This paper describes a more comprehensive model and characterisation scheme, with electrode parameters and salt-bridge resistivity being evaluated independently. In a generalised form, the presented model illustrates how the relative resistive contributions from the electrodes and medium relate to the existing characterisation method efficacy. We also describe experiments with physiologically relevant salt solutions (1.71, 17.1, 154 mM), used for validation and comparison. The presented model shows improved performance over the current biogalvanic measurement technique at the median conductivity. Both the proposed and extant system models become unable to predict conductivity accurately at high conductivity due to the dominance of the electrodes. The characterisation techniques have also been applied to data collected on freshly excised human colon tissue (healthy and cancerous). The findings suggest that the resistance of the cell under the test conditions is electrode dominated, leading to erroneous tissue resistance determination. Measurement optimisation strategies and the surgical applicability of the biogalvanic technique are discussed in light of these findings.

Importance of non-affine viscoelastic response in disordered fibre networks

Disordered fibre networks are ubiquitous in nature and have a wide range of industrial applications as novel biomaterials. Predicting their viscoelastic response is straightforward for affine deformations that are uniform over all length scales, but when affinity fails, as has been observed experimentally, modelling becomes challenging. Here we present a numerical methodology, related to an existing framework for amorphous packings, to predict the steady-state viscoelastic spectra and degree of affinity for disordered fibre networks driven at arbitrary frequencies. Applying this method to a peptide gel model reveals a monotonic increase of the shear modulus as the soft, non-affine normal modes are successively suppressed as the driving frequency increases. In addition to being dominated by fibril bending, these low frequency network modes are also shown to be delocalised. The presented methodology provides insights into the importance of non-affinity in the viscoelastic response of peptide gels, and is easily extendible to all types of fibre networks.

Universality in the morphology and mechanics of coarsening amyloid fibril networks

Peptide hydrogels have important applications as biomaterials and in nanotechnology, but utilization often depends on their mechanical properties for which we currently have no predictive capability. Here we use a peptide model to simulate the formation of percolating amyloid fibril networks and couple these to the elastic network theory to determine their mechanical properties. We find that the time variation of network length scales can be collapsed onto master curves by using a time scaling function that depends on the peptide interaction anisotropy. The same scaling applies to network mechanics, revealing a nonmonotonic dependence of the shear modulus with time. Our structure-function relationship between the peptide building blocks, network morphology, and network mechanical properties can aid in the design of amyloid fibril networks with tailored mechanical properties.

Nonequilibrium structure and dynamics in a microscopic model of thin-film active gels

In the presence of adenosine triphosphate, molecular motors generate active force dipoles that drive suspensions of protein filaments far from thermodynamic equilibrium, leading to exotic dynamics and pattern formation. Microscopic modeling can help to quantify the relationship between individual motors plus filaments to organization and dynamics on molecular and supramolecular length scales. Here, we present results of extensive numerical simulations of active gels where the motors and filaments are confined between two infinite parallel plates. Thermal fluctuations and excluded-volume interactions between filaments are included. A systematic variation of rates for motor motion, attachment, and detachment, including a differential detachment rate from filament ends, reveals a range of nonequilibrium behavior. Strong motor binding produces structured filament aggregates that we refer to as asters, bundles, or layers, whose stability depends on motor speed and differential end detachment. The gross features of the dependence of the observed structures on the motor rate and the filament concentration can be captured by a simple one-filament model. Loosely bound aggregates exhibit superdiffusive mass transport, where filament translocation scales with lag time with nonunique exponents that depend on motor kinetics. An empirical data collapse of filament speed as a function of motor speed and end detachment is found, suggesting a dimensional reduction of the relevant parameter space. We conclude by discussing the perspectives of microscopic modeling in the field of active gels.

Linear surface roughness growth and flow smoothening in a three-dimensional biofilm model

The sessile microbial communities known as biofilms exhibit varying architectures as environmental factors are varied, which for immersed biofilms includes the shear rate of the surrounding flow. Here we modify an established agent-based biofilm model to include affine flow and employ it to analyze the growth of surface roughness of single-species, three-dimensional biofilms. We find linear growth laws for surface geometry in both horizontal and vertical directions and measure the thickness of the active surface layer, which is shown to anticorrelate with roughness. Flow is shown to monotonically reduce surface roughness without affecting the thickness of the active layer. We argue that the rapid roughening is due to nonlocal surface interactions mediated by the nutrient field, which are curtailed when advection competes with diffusion. We further argue the need for simplified models to elucidate the underlying mechanisms coupling flow to growth.

Nonlocal fluctuation correlations in active gels

Many active materials and biological systems are driven far from equilibrium by embedded agents that spontaneously generate forces and distort the surrounding material. Probing and characterizing these athermal fluctuations are essential to understand the properties and behaviors of such systems. Here we present a mathematical procedure to estimate the local action of force-generating agents from the observed fluctuating displacement fields. The active agents are modeled as oriented force dipoles or isotropic compression foci, and the matrix on which they act is assumed to be either a compressible elastic continuum or a coupled network-solvent system. Correlations at a single point and between points separated by an arbitrary distance are obtained, giving a total of three independent fluctuation modes that can be tested with microrheology experiments. Since oriented dipoles and isotropic compression foci give different contributions to these fluctuation modes, ratiometric analysis allows us characterize the force generators. We also predict and experimentally find a high-frequency ballistic regime, arising from individual force-generating events in the form of the slow buildup of stress followed by rapid but finite decay. Finally, we provide a quantitative statistical model to estimate the mean filament tension from these athermal fluctuations, which leads to stiffening of active networks.

Well defined transition to gel-like aggregates of attractive athermal particles

In an attempt to extend the range of model jamming transitions, we simulate systems of athermal particles which attract when slightly overlapping. Following from recent work on purely repulsive systems, dynamics are neglected and relaxation performed via a potential energy minimisation algorithm. Our central finding is of a transition to a low-density tensile solid which is sharp in the limit of infinite system size. The critical density depends on the range of the attractive regime in the pair-potential. Furthermore, solidity is shown to be related to the coordination number of the packing according to the approximate constraint-counting scheme known as Maxwell counting, although more corrections need to be considered than with the repulsive-only case, as explained. We finish by discussing how the numerical difficulties encountered in this work could be overcome in future studies.

Modeling the elastic deformation of polymer crusts formed by sessile droplet evaporation

Evaporating droplets of polymer or colloid solution may produce a glassy crust at the liquid-vapor interface, which subsequently deforms as an elastic shell. For sessile droplets, the known radial outward flow of solvent is expected to generate crusts that are thicker near the pinned contact line than the apex. Here we investigate, by nonlinear quasistatic simulation and scaling analysis, the deformation mode and stability properties of elastic caps with a nonuniform thickness profile. By suitably scaling the mean thickness and the contact angle between crust and substrate, we find that data collapse onto a master curve for both buckling pressure and deformation mode, thus allowing us to predict when the deformed shape is a dimple, Mexican hat, and so on. This master curve is parameterized by a dimensionless measure of the nonuniformity of the shell. We also speculate on how overlapping time scales for gelation and deformation may alter our findings.

Mechanical response of semiflexible networks to localized perturbations

Previous research on semiflexible polymers including cytoskeletal networks in cells has suggested the existence of distinct regimes of elastic response, in which the strain field is either uniform (affine) or nonuniform (nonaffine) under external stress. Associated with these regimes, it has been further suggested that a mesoscopic length scale emerges, which characterizes the scale for the crossover from nonaffine to affine deformations. Here, we extend these studies by probing the response to localized forces and force dipoles. We show that the previously identified nonaffinity length [D. A. Head, Phys. Rev. E 68, 061907 (2003)] controls the mesoscopic response to point forces and the crossover to continuum elastic behavior at large distances.

Mean-field description of jamming in noncohesive frictionless particulate systems

A theory for kinetic arrest in isotropic systems of repulsive, radially interacting particles is presented that predicts exponents for the scaling of various macroscopic quantities near the rigidity transition that are in agreement with simulations, including the nontrivial shear exponent. Both statics and dynamics are treated in a simplified, one-particle level description and coupled via the assumption that kinetic arrest occurs on the boundary between mechanically stable and unstable regions of the static parameter diagram. This suggests that the arrested states observed in simulations are at (or near) an elastic buckling transition. Some additional numerical evidence to confirm the scaling of microscopic quantities is also provided.

Distinct regimes of elastic response and deformation modes of cross-linked cytoskeletal and semiflexible polymer networks

Semiflexible polymers such as filamentous actin (F-actin) play a vital role in the mechanical behavior of cells, yet the basic properties of cross-linked F-actin networks remain poorly understood. To address this issue, we have performed numerical studies of the linear response of homogeneous and isotropic two-dimensional networks subject to an applied strain at zero temperature. The elastic moduli are found to vanish for network densities at a rigidity percolation threshold. For higher densities, two regimes are observed: one in which the deformation is predominately affine and the filaments stretch and compress; and a second in which bending modes dominate. We identify a dimensionless scalar quantity, being a combination of the material length scales, that specifies to which regime a given network belongs. A scaling argument is presented that approximately agrees with this crossover variable. By a direct geometric measure, we also confirm that the degree of affinity under strain correlates with the distinct elastic regimes. We discuss the implications of our findings and suggest possible directions for future investigations.

Nonuniversality of elastic exponents in random bond-bending networks

We numerically investigate the rigidity percolation transition in two-dimensional flexible, random rod networks with freely rotating cross links. Near the transition, networks are dominated by bending modes and the elastic modulii vanish with an exponent f=3.0+/-0.2, in contrast with central force percolation which shares the same geometric exponents. This indicates that universality for geometric quantities does not imply universality for elastic ones. The implications of this result for actin-fiber networks is discussed.

Rheological chaos in a scalar shear-thickening model

We study a simple scalar constitutive equation for a shear-thickening material at zero Reynolds number, in which the shear stress sigma is driven at a constant shear rate gamma; and relaxes by two parallel decay processes: a nonlinear decay at a nonmonotonic rate R(sigma(1)) and a linear decay at rate lambda sigma(2). Here sigma(1,2)(t)= tau(-1)(1,2) integral (t)(0)sigma(t')exp[-(t-t')/tau(1,2)]dt' are two retarded stresses. For suitable parameters, the steady state flow curve is monotonic but unstable; this arises when tau(2)>tau(1) and 0>R'(sigma)>-lambda so that monotonicity is restored only through the strongly retarded term (which might model a slow evolution of the material structure under stress). Within the unstable region we find a period-doubling sequence leading to chaos. Instability, but not chaos, persists even for the case tau(1)-->0. A similar generic mechanism might also arise in shear thinning systems and in some banded flows.

Universal persistence exponents in an extremally driven system

The local persistence R(t), defined as the proportion of the system still in its initial state at time t, is measured for the Bak-Sneppen model. For one and two dimensions, it is found that the decay of R(t) depends on one of two classes of initial configuration. For a subcritical initial state, R(t) equivalent to t(-theta), where the persistence exponent theta can be expressed in terms of a known universal exponent. Hence theta is universal. Conversely, starting from a supercritical state, R(t) decays by the anomalous form 1-R(t) equivalent to t(tau(all)) until a finite time t(0), where tau(all) is also a known exponent. Finally, for the high dimensional model R(t) decays exponentially with a nonuniversal decay constant.

Jamming, hysteresis, and oscillation in scalar models for shear thickening

We investigate shear thickening and jamming within the framework of a family of spatially homogeneous, scalar rheological models. These are based on the "soft glassy rheology" model of Sollich et al. [Phys. Rev. Lett. 78, 2020 (1997)], but with an effective temperature x that is a decreasing function of either the global stress sigma or the local strain l. For appropriate x=x(sigma), it is shown that the flow curves include a region of negative slope, around which the stress exhibits hysteresis under a cyclically varying imposed strain rate (.)gamma.A subclass of these x(sigma) have flow curves that touch the (.)gamma=0 axis for a finite range of stresses; imposing a stress from this range jams the system, in the sense that the strain gamma creeps only logarithmically with time t, gamma(t) approximately ln t. These same systems may produce a finite asymptotic yield stress under an imposed strain, in a manner that depends on the entire stress history of the sample, a phenomenon we refer to as history-dependent jamming. In contrast, when x=x(l) the flow curves are always monotonic, but we show that some x(l) generate an oscillatory strain response for a range of steady imposed stresses. Similar spontaneous oscillations are observed in a simplified model with fewer degrees of freedom. We discuss this result in relation to the temporal instabilities observed in rheological experiments and stick-slip behavior found in other contexts, and comment on the possible relationship with "delay differential equations" that are known to produce oscillations and chaos.

Phenomenological glass model for vibratory granular compaction

A model for weakly excited granular media is derived by combining the free volume argument of Nowak et al. [Phys. Rev. E 57, 1971 (1998)] and the phenomenological model for supercooled liquids of Adam and Gibbs [J. Chem. Phys. 43, 139 (1965)]. This is made possible by relating the granular excitation parameter Gamma, defined as the peak acceleration of the driving pulse scaled by gravity, to a temperaturelike parameter eta(Gamma). The resulting master equation is formally identical to that of Bouchaud's trap model for glasses [J. Phys. I 2, 1705 (1992)]. Analytic and simulation results are shown to compare favorably with a range of known experimental behavior. This includes the logarithmic densification and power spectrum of fluctuations under constant eta, the annealing curve when eta is varied cyclically in time, and memory effects observed for a discontinuous shift in eta. Finally, we discuss the physical interpretation of the model parameters and suggest further experiments for this class of systems.

Yield of free-ions in the radiolysis of formamide, a liquid of very high dielectric constant

Solutions of N2O in liquid formamide (dielectric constant 109) gave a yield of N2 during γ-radiolysis of G(N2) = 3.3 ± 0.3. Competition between N2O and other scavengers, including water, ethanol, acids, AgNO3, and CdI2 strongly resembled the pattern of reactivity characteristic of solvated electrons found in other polar liquids. Furthermore, the yield obtained (3.3) was consistent with the high dielectric constant and predicted for the free-ion yield by Freeman's model assuming a total ionization of 4.7. However, the absence of an absorption band in nanosecond pulse radiolysis experiments suggests that solvated electrons were not present 10−9 s after the passage of the ionizing radiation. It is quite possible that in this system "solvent anions" (or other reactive reducing ions) were formed in yield equal to the "free-ion" yield. This presupposes that formamide anions readily reduce N2O and Ag+, are inactivated by H+ and do not react with water and alcohols.The high dielectric constant apparently leads to large yields of comparatively long-lived (> 10−7 s) reducing ions (free-ion yield of 3.3) accompanied by rather small yields of H atoms and simple molecular decomposition products. In these respects the radiolysis decomposition of formamide resembles that of water.

Erratum: Radiation chemical data in water using nitrous oxide

not available

Radiation chemical data in water using nitrous oxide

By using small doses and very low dose rates, it is shown that in the γ-irradiation of water ~ 8 × 10−5M nitrous oxide completely scavenges eaq− in the absence of other additives and gives a yield G(eaq−) = 2.45 ± 0.1. When used at concentrations of ~ 15 mM, N2O scavenges a second species having a yield G = 0.65 ± 0.1, which can probably be attributed to a hydrated hydrogen atom species resulting from the reaction of eaq– with H3O+ within the spur. Previous studies on the competition between N2O and Haq+ for eaq− have been conducted at concentrations of N2O much too high for simple competition to be valid, which probably accounts for the erratic results obtained. This paper reports on the competition studied at ~ 10−4 M. The results cannot be interpreted either in terms of a simple competition or by one, or both, of the immediate products reacting with either of the additives. The data can only be rationalized by assuming that in acid solution N2O is converted to a species, tentatively suggested to be H2N2O2, which reacts with eaq− 5 times more slowly than does N2Oaq at pH 7.