arXiv subjects

Mark O. Robbins

Publications and source records attributed to Mark O. Robbins.

At least 19 recordsLinked to original sources

arXiv2023

Universal behavior in fragmenting brittle, isotropic solids across material properties

A bonded particle model is used to explore how variations in the material properties of brittle, isotropic solids affect critical behavior in fragmentation. To control material properties, a new model is proposed which includes breakable two- and three-body particle interactions to calibrate elastic moduli and mode I and II fracture toughnesses. In the quasistatic limit, fragmentation leads to a power-law distribution of grain sizes which is truncated at a maximum grain mass that grows as a non-trivial power of system size. In the high-rate limit, truncation occurs at a mass that decreases as a power of increasing rate. A scaling description is used to characterize this behavior by collapsing the mean squared grain mass across rates and system sizes. Consistent scaling persists across all material properties studied although there are differences in the evolution of grain size distributions with strain as the initial number of grains at fracture and their subsequent rate of production depend on Poisson's ratio. This evolving granular structure is found to induce a unique rheology where the ratio of the shear stress to pressure, an internal friction coefficient, decays approximately as the logarithm of increasing strain rate. The stress ratio also decreases at all rates with increasing strain as fragmentation progresses.

cond-mat.soft↗

arXiv2022

From molecular to multi-asperity contacts: how roughness bridges the friction scale gap

While friction stems from the fundamental interactions between atoms at a contact interface, its best descriptions at the macroscopic scale remain phenomenological. The so called "rate-and-state" models, which specify the friction response in terms of the relative sliding velocity and the "age" of the contact interface, fail to uncover the nano-scale mechanisms governing the macro-scale response, while models of friction at the atomic scale often overlook how roughness can alter the friction behavior. Here we bridge this gap between nano and macro descriptions of friction by correlating the physical origin of macroscopic friction to the existence, due to nanometric roughness, of contact junctions between adsorbed monolayers. Their dynamics, as we show, emerges from molecular motion. Through coupled experimental and atomic simulations, we highlight that transient friction overshoots its steady-state value after the system is allowed to rest, with the friction force decaying to a steady-state value over a distance of a few nanometers, much smaller than the junction size, even with a root-mean-square roughness of 0.6 nm. We demonstrate how this transient decay is intrinsically related to the evolution of the number of cross-surface attractive physical links between adsorbed molecules on rough surfaces. We also show that roughness is a sufficient condition for the appearance of frictional aging. In systems that show structural aging, this paints contact junctions as a key component in the observation of the transient friction overshoot, and shows how infrajunction molecular motion can control the macroscopic response.

cond-mat.soft↗

arXiv2022

Probing the nonequilibrium dynamics of stress, orientation and entanglements in polymer melts with orthogonal interrupted shear simulations

Both entangled and unentangled polymer melts exhibit stress overshoots when subject to shearing flow. The size of the overshoot depends on the applied shear rate and is related to relaxation mechanisms such as reptation, chain stretch and convective constraint release. Previous experimental work shows that melts subjected to interrupted shear flows exhibit a smaller overshoot when sheared after partial relaxation. This has been shown to be consistent with predictions by constitutive models. Here, we report molecular dynamics simulations of interrupted shear of polymer melts where the shear flow after the relaxation stage is orthogonal to the original applied flow. We observe that, for a given relaxation time, the size of the stress overshoot under orthogonal interrupted shear is larger than observed during parallel interrupted shear, which is not captured by constitutive models. Differences in maxima are also observed for overshoots in the first normal stress and chain end-to-end distance. We also show that measurements of the average number of entanglements per chain and average orientation at different scales along the chain are affected by the change in shear direction, leading to non-monotonic relaxation of the off-diagonal components of orientation and an appearance of a 'double peak' in the average number of entanglements during the transient. We propose that such complex behavior of entanglements is responsible for the increase in the overshoots of stress components, and that models of the dynamics of entanglements might be improved upon by considering a tensorial measurement of entanglements that can be coupled to orientation.

cond-mat.soft↗

arXiv2021

Criticality in sheared, disordered solids. I. Rate effects in stress and diffusion

Rate-effects in sheared disordered solids are studied using molecular dynamics simulations of binary Lennard-Jones glasses in two and three dimensions. In the quasistatic (QS) regime, systems exhibit critical behavior: the magnitudes of avalanches are power-law distributed with a maximum cutoff that diverges with increasing system size $L$. With increasing rate, systems move away from the critical yielding point and the average flow stress rises as a power of the strain rate with exponent $1/β$, the Herschel-Bulkley exponent. Finite-size scaling collapses of the stress are used to measure $β$ as well as the exponent $ν$ which characterizes the divergence of the correlation length. The stress and kinetic energy per particle experience fluctuations with strain that scale as $L^{-d/2}$. As the largest avalanche in a system scales as $L^α$, this implies $α< d/2$. The diffusion rate of particles diverges as a power of decreasing rate before saturating in the QS regime. A scaling theory for the diffusion is derived using the QS avalanche rate distribution and generalized to the finite strain rate regime. This theory is used to collapse curves for different system sizes and confirm $β/ν$.

cond-mat.soft↗

arXiv2021

Criticality in sheared, disordered solids. II. Correlations in avalanche dynamics

Disordered solids respond to quasistatic shear with intermittent avalanches of plastic activity, an example of the crackling noise observed in many nonequilibrium critical systems. The temporal power spectrum of activity within disordered solids consists of three distinct domains: a novel power-law rise with frequency at low frequencies indicating anticorrelation, white-noise at intermediate frequencies, and a power-law decay at high frequencies. As the strain rate increases, the white-noise regime shrinks and ultimately disappears as the finite strain rate restricts the maximum size of an avalanche. A new strain-rate- and system-size-dependent scaling theory is derived for power spectra in both the quasistatic and finite-strain-rate regimes. This theory is validated using data from overdamped two- and three-dimensional molecular dynamics simulations. We identify important exponents in the yielding transition including the dynamic exponent $z$ which relates the size of an avalanche to its duration, the fractal dimension of avalanches, and the exponent characterizing the divergence in correlations with strain rate. Results are related to temporal correlations within a single avalanche and between multiple avalanches.

cond-mat.soft↗

arXiv2020

Effect of flow-induced molecular alignment on welding and strength of polymer interfaces

Structures formed by fused filament fabrication are often substantially weaker than those made with conventional techniques, and fail at the welds between successive layers. One factor that may influence strength is flow-induced alignment of deposited material. Recent work suggests that alignment reduces the entanglement density and thus should accelerate welding by diffusion. Here, coarse-grained molecular simulations are used to test the effect of molecular alignment on diffusion and weld strength. While standard measures show a decrease of the entanglement density with alignment, there is no change in the rate of diffusion normal to the interface or the rate of formation of entanglements across the interface. The time for chain reorientation also remains equal to the equilibrium disentanglement time $τ_d$. Despite this, simulations of mechanical tests show that welds formed from aligned states are weaker until several $τ_d$. This is not because the weld itself is weaker, but because aligned material near the weld is weaker than unaligned material. The maximum shear strength and tensile fracture energy of welded systems are the same as bulk systems with the same alignment.

cond-mat.soft↗

arXiv2019

Anisotropic Avalanches and Critical Depinning of Three-Dimensional Magnetic Domain Walls

Simulations with more than $10^{12}$ spins are used to study the motion of a domain wall driven through a three-dimensional random-field Ising magnet (RFIM) by an external field $H$. The interface advances in a series of avalanches whose size diverges at a critical external field $H_c$. Finite-size scaling is applied to determine critical exponents and test scaling relations. Growth is intrinsically anisotropic with the height of an avalanche normal to the interface $\ell_\perp$ scaling as the width along the interface $\ell_\|$ to a power $χ=0.85 \pm 0.01$. The total interface roughness is consistent with self-affine scaling with a roughness exponent $ζ\approx χ$ that is much larger than values found previously for the RFIM and related models that explicitly break orientational symmetry by requiring the interface to be single-valued. Because the RFIM maintains orientational symmetry, the interface develops overhangs that may surround unfavorable regions to create uninvaded bubbles. Overhangs complicate measures of the roughness exponent but decrease in importance with increasing system size.

cond-mat.soft↗

arXiv2019

Rheological properties of liquids under conditions of elastohydrodynamic lubrication

There is an ongoing debate concerning the best rheological model for liquid flows in elastohydrodynamic lubrication (EHL). Due to the small contact area and high relative velocities of bounding solids, the lubricant experiences pressures in excess of 500 MPa and strain rates that are typically $10^5 -10^7$ $\textrm{s}^{-1}$. The high pressures lead to a dramatic rise in Newtonian viscosity $η_{N}$ and the high rates lead to large shear stresses and pronounced shear-thinning. This paper presents detailed simulations of a model EHL fluid, squalane, using nonequilibrium molecular dynamics methods to extract the scaling of its viscosity with shear rate ($10^5 - 10^{10}$ $\textrm{s}^{-1}$) over a wide range of pressure $P$ (0.1 MPa to 1.2 GPa), and temperature $T$ ($150 - 373$ K). Simulation results are consistent with a broad range of equilibrium and nonequilibrium experiments. At high $T$ and low $P$, where $η_{N}$ is low, the response can be fit to a power-law, as in the common Carreau model. Shear-thinning becomes steeper as $η_{N}$ increases, and for $η_{N}\gtrsim 1$ Pa-s, shear-thinning is consistent with the thermally activated flow assumed by another common model, Eyring theory. Simulations for a bi-disperse Lennard-Jones (LJ) system show that the transition from Carreau to Eyring is generic. For both squalane and the LJ system, the viscosity decreases by only about a decade in the Carreau regime, but may fall by many orders of magnitude in the Eyring regime. Shear thinning is often assumed to reflect changing molecular alignment, but the alignment of squalane molecules saturates after the viscosity has dropped by only about a factor of three. In contrast, thermal activation describes shear thinning by six or more decades in viscosity. Changes in the diagonal elements of the stress tensor with rate and shear stress are also studied.

cond-mat.soft↗

arXiv2019

O'Connor, Alvarez, and Robbins Reply to Xu et al. (arXiv:1808.05390)

The preceding Comment by Xu et al. (Phys. Rev. Lett. 122, 059803 (2019); arXiv:1808.05390) erroneously applies the entropic stress expression in our Letter (T.C. O'Connor et al., Phys. Rev. Lett. 121, 047801 (2018); arXiv:1806.09509) to transient stress. In addition, the authors only apply this expression at extreme extension rates where we clearly showed deviations from the entropic stress expression for steady-state extensional flow. Hence the surprisingly minor discrepancies noted in the Comment between observed and "predicted" stress are entirely expected and have no bearing on the discussion or conclusions in our Letter.

cond-mat.soft↗

arXiv2019

Determination of pressure-viscosity relation of 2,2,4-trimethylhexane by all-atom molecular dynamics simulations

The Newtonian viscosity of 2,2,4-trimethylhexane at 293K is determined at pressures from 0.1MPa to 1000MPa. Non-equilibrium molecular dynamics simulations are performed using AIREBO-M, an all-atom potential for hydrocarbons especially parameterized for high pressures. The steady-state shear stress and viscosity are determined from simple shear simulations at rates between $10^7$ and $5\cdot 10^9\ \textrm{s}^{-1}$. At low pressures, simulation rates are low enough to reach the Newtonian regime. At high pressures, results are extrapolated to the Newtonian limit by fitting rate-dependent viscosities to Eyring theory. The resulting pressure dependent viscosity is typical of small molecules and fits to a common model are discussed.

cond-mat.soft↗

arXiv2018

Relating Chain Conformations to Extensional Stress In Entangled Polymer Melts

Nonlinear extensional flows are common in polymer processing but remain challenging theoretically because dramatic stretching of chains deforms the entanglement network far from equilibrium. Here, we present coarse-grained simulations of extensional flows in entangled polymer melts for Rouse-Weissenberg numbers $Wi_R=0.06$-$52$ and Hencky strains $ε\geq6$. Simulations reproduce experimental trends in extensional viscosity with time, rate and molecular weight. Studies of molecular structure reveal an elongation and thinning of the confining tube with increasing $Wi_R$. The rising stress is quantitatively consistent with the decreasing entropy of chains at the equilibrium entanglement length. Molecular weight dependent trends in viscosity are related to a crossover from the Newtonian limit to a high rate limit that scales differently with chain length.

cond-mat.soft↗

arXiv2016

Crazing of Nanocomposites with Polymer-Tethered Nanoparticles

The crazing behavior of polymer nanocomposites formed by blending polymer grafted nanoparticles with an entangled polymer melt is studied by molecular dynamics simulations. We focus on the three key differences in the crazing behavior of a composite relative to the pure homopolymer matrix, namely, a lower yield stress, a smaller extension ratio and a grafted chain length dependent failure stress. The yield behavior is found to be mostly controlled by the local nanoparticle-grafted polymer interfacial energy, with the grafted polymer-polymer matrix interfacial structure being of little to no relevance. Increasing the attraction between nanoparticle core and the grafted polymer inhibits void nucleation and leads to a higher yield stress. In the craze growth regime, the presence of grafted chain sections of 100 monomers alters the mechanical response of composite samples, giving rise to smaller extension ratios and higher drawing stresses than for the homopolymer matrix. The dominant failure mechanism of composite samples depends strongly on the length of the grafted chains, with disentanglement being the dominant mechanism for short chains, while bond breaking is the failure mode for chain lengths greater than 10Ne, where Ne is the entanglement length.

cond-mat.soft↗

arXiv2016

Nanocapillary adhesion between parallel plates

Molecular dynamics simulations are used to study capillary adhesion from a nanometer scale liquid bridge between two parallel flat solid surfaces. The capillary force and the meniscus shape of the bridge are computed as the separation between the solid surfaces is varied. Macroscopic theory predicts the meniscus shape and the contribution of liquid/vapor interfacial tension to the capillary force quite accurately for separations as small as 2 or 3 molecular diameters (1-2nm). However the total capillary force differs in sign and magnitude from macroscopic theory for separations less than about 5nm (8-10 diameters) because of molecular layering that is not included in macroscopic theory. For these small separations, the pressure tensor in the fluid becomes anisotropic. The components in the plane of the surface vary smoothly and are consistent with theory based on the macroscopic surface tension. Capillary adhesion is affected by only the perpendicular component, which has strong oscillations as the molecular layering changes.

cond-mat.soft↗

arXiv2016

Contact area of rough spheres: Large scale simulations and simple scaling laws

We use molecular simulations to study the nonadhesive and adhesive atomic-scale contact of rough spheres with radii ranging from nanometers to micrometers over more than ten orders of magnitude in applied normal load. At the lowest loads, the interfacial mechanics is governed by the contact mechanics of the first asperity that touches. The dependence of contact area on normal force becomes linear at intermediate loads and crosses over to Hertzian at the largest loads. By combining theories for the limiting cases of nominally flat rough surfaces and smooth spheres, we provide parameter-free analytical expressions for contact area over the whole range of loads. Our results establish a range of validity for common approximations that neglect curvature or roughness in modeling objects on scales from atomic force microscope tips to ball bearings.

cond-mat.soft↗

arXiv2015

Chain Ends and the Ultimate Strength of Polyethylene Fibers

We use large scale molecular dynamics (MD) simulations to determine the tensile yield mechanism of orthorhombic polyethylene (PE) crystals with finite chains spanning $10^2-10^4$ carbons in length. We find the yield stress $σ_y$ saturates for long chains at 6.3 GPa, agreeing well with experiments. We show chains do not break but always yield by slip, after nucleation of 1D dislocations at chain ends. Dislocations are accurately described by a Frenkel-Kontorova model parametrized by the mechanical properties of an ideal crystal. We compute a dislocation core size $ξ\approx25$Å and determine the high and low strain rate limits of $σ_y$. Our results suggest characterizing the 1D dislocations of polymer crystals as an efficient method for numerically predicting the ultimate tensile strength of aligned fibers.

cond-mat.soft↗

arXiv2015

The effect of inertia on sheared disordered solids: Critical scaling of avalanches in two and three dimensions

Molecular dynamics simulations with varying damping are used to examine the effects of inertia and spatial dimension on sheared disordered solids in the athermal, quasistatic limit. In all cases the distribution of avalanche sizes follows a power law over at least three orders of magnitude in dissipated energy or stress drop. Scaling exponents are determined using finite-size scaling for systems with thousands to millions of particles. Three distinct universality classes are identified corresponding to overdamped and underdamped limits, as well as a crossover damping that separates the two regimes. For each universality class, the exponent describing the avalanche distributions is the same in two and three dimensions. The spatial extent of plastic damage is proportional to the energy dissipated in an avalanche. Both rise much more rapidly with system size in the underdamped limit where inertia is important. Inertia also lowers the mean energy of configurations sampled by the system and leads to an excess of large events like that seen in earthquake distributions for individual faults. The distribution of stress values during shear narrows to zero with increasing system size and may provide useful information about the size of elemental events in experimental systems. For overdamped and crossover systems the stress variation scales inversely with the square root of the system size. For underdamped systems the variation is determined by the size of the largest events.

cond-mat.soft↗

arXiv2014

Tensile Fracture of Welded Polymer Interfaces: Miscibility, Entanglements and Crazing

Large-scale molecular simulations are performed to investigate tensile failure of polymer interfaces as a function of welding time $t$. Changes in the tensile stress, mode of failure and interfacial fracture energy $G_I$ are correlated to changes in the interfacial entanglements as determined from Primitive Path Analysis. Bulk polymers fail through craze formation, followed by craze breakdown through chain scission. At small $t$ welded interfaces are not strong enough to support craze formation and fail at small strains through chain pullout at the interface. Once chains have formed an average of about one entanglement across the interface, a stable craze is formed throughout the sample. The failure stress of the craze rises with welding time and the mode of craze breakdown changes from chain pullout to chain scission as the interface approaches bulk strength. The interfacial fracture energy $G_I$ is calculated by coupling the simulation results to a continuum fracture mechanics model. As in experiment, $G_I$ increases as $t^{1/2}$ before saturating at the average bulk fracture energy $G_b$. As in previous simulations of shear strength, saturation coincides with the recovery of the bulk entanglement density. Before saturation, $G_I$ is proportional to the areal density of interfacial entanglements. Immiscibiltiy limits interdiffusion and thus suppresses entanglements at the interface. Even small degrees of immisciblity reduce interfacial entanglements enough that failure occurs by chain pullout and $G_I \ll G_b$.

cond-mat.soft↗

arXiv2014

Healing of polymer interfaces: Interfacial dynamics, entanglements, and strength

Self-healing of polymer films often takes place as the molecules diffuse across a damaged region, above their melting temperature. Using molecular dynamics simulations we probe the healing of polymer films and compare the results with those for thermal welding of homopolymer slabs. The two processes differ in their interfacial structure since damage leads to increased polydispersity and more short chains. A polymer sample was cut into two separate films that were then held together in the melt state. The recovery of the damaged film was followed as time elapsed and polymer molecules diffused across the interface. The mass uptake and formation of entanglements, as obtained from primitive path analysis, are extracted and correlated with the interfacial strength obtained from shear simulations. We find that the interdiffusion is significantly faster in the damaged film compared to welding because of the presence of short chains. Though interfacial entanglements increase more rapidly for the damaged films, a large fraction of them are near chain ends. As a result, the interfacial strength of the healing film increases more slowly than for welding. For both healing and welding, the interfacial strength saturates as the bulk entanglement density is recovered across the interface. However, the saturation strength of the damaged film is below the bulk strength for the polymer sample. At saturation, cut chains remain near the healing interface. They are less entangled and thus mechanically weaken the interface. When the interfacial strength saturates, the number of interfacial entanglements scales with the corresponding bulk entanglement density. Chain stiffness increases the density of entanglements, which increases the interfacial strength. Our results show that a few entanglements across the interface are sufficient to resist interfacial chain pullout and enhance the mechanical strength.

cond-mat.soft↗