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 model is proposed which includes breakable two- and three-body particle interactions to calibrate elastic moduli and mode I and mode 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 nontrivial 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-square 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 and depends on elastic properties of the solid.

From Molecular to Multiasperity Contacts: How Roughness Bridges the Friction Scale Gap.

The tangential force required to observe slip across a whole frictional interface can increase over time under a constant load, due to any combination of creep, chemical, or structural changes of the interface. In macroscopic rate-and-state models, these frictional aging processes are lumped into an ad hoc state variable. Here we explain, for a frictional system exclusively undergoing structural aging, how the macroscopic friction response emerges from the interplay between the surface roughness and the molecular motion within adsorbed monolayers. The existence of contact junctions and their friction dynamics are studied through coupled experimental and computational approaches. The former provides detailed measurements of how the friction force decays, after the stiction peak, to a steady-state value over a few nanometers of sliding distance, while the latter demonstrates how this memory distance is related to the evolution of the number of cross-surface attractive physical links, within contact junctions, between the molecules adsorbed on the rough surfaces. We also show that roughness is a sufficient condition for the appearance of structural aging. Using a unified model for friction between rough adsorbed monolayers, we show how contact junctions are a key component in structural aging and how the infrajunction molecular motion can control the macroscopic response.

Critical Scaling of Solid Fragmentation at Quasistatic and Finite Strain Rates.

Using two-dimensional simulations of sheared, brittle solids, we characterize the resulting fragmentation and explore its underlying critical nature. Under quasistatic loading, a power-law distribution of fragment masses emerges after fracture which grows with increasing strain. With increasing strain rate, the maximum size of a grain decreases and a shallower distribution is produced. We propose a scaling theory for distributions based on a fractal scaling of the largest mass with system size in the quasistatic limit or with a correlation length that diverges as a power of rate in the finite-rate limit. Critical exponents are measured using finite-size scaling techniques.

Green's function method for dynamic contact calculations.

Resolving atomic scale details while capturing long-range elastic deformation is the principal difficulty when solving contact mechanics problems with computer simulations. Fully atomistic simulations must consider large blocks of atoms to support long-wavelength deformation modes, meaning that most atoms are far removed from the region of interest. Building on earlier methods that used elastic surface Green's functions to compute static substrate deformation, we present a numerically efficient dynamic Green's function technique to treat realistic, time-evolving, elastic solids. Our method solves substrate dynamics in reciprocal space and utilizes precomputed Green's functions that exactly reproduce elastic interactions without retaining the atomic degrees of freedom in the bulk. We invoke physical insights to determine the necessary number of explicit substrate layers required to capture the attenuation of subsurface waves as a function of surface wave vector. We observe that truncating substrate dynamics at depths that fall as a power of wave vector allows us to accurately model wave propagation without implementing arbitrary damping. The framework we have developed substantially accelerates molecular dynamics simulations of large elastic substrates. We apply the method to single asperity contact, impact, and sliding friction problems and present our preliminary findings.

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/ß, the Herschel-Bulkley exponent. Finite-size scaling collapses of the stress are used to measure ß 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

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 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.

Sliding Friction of Amorphous Asperities on Crystalline Substrates: Scaling with Contact Radius and Substrate Thickness.

Disorder in the contact between an amorphous slider and a crystalline substrate leads to a cancellation of lateral forces. Atomically flat, rigid surfaces exhibit structural superlubricity, with the frictional stress in circular contacts of radius a vanishing as 1/a. The inclusion of elasticity allows relative motion of domains on the surface in response to the random interfacial forces. The competition between disorder and elastic deformation is predicted to limit structural superlubricity and produce a constant frictional stress for a larger than a characteristic domain size λ that depends on the ratio of the shear modulus G to the magnitude of interfacial shear stresses τ0. Extensive simulations of a flat, amorphous punch sliding on a crystalline substrate with different system sizes and G/τ0 are used to test scaling predictions and determine unknown prefactors that are needed for quantitative analysis. For bulk systems, we find an exponential decrease of the large a frictional stress and 1/λ with increasing G/τ0. For thin free-standing films, the stress and 1/λ are inversely proportional to G/τ0. These results may help explain the size-dependent friction of nanoparticles and plate-like materials used as solid lubricants.

Molecular models for creep in oriented polyethylene fibers.

Highly oriented and crystalline polyetheylene (PE) fibers have a large failure stress under rapid tensile loading but exhibit significant creep at much smaller stresses that limits applications. A possible mechanism is slip of chains due to stress-enhanced, thermally activated nucleation of dislocations at chain ends in crystalline regions. Molecular dynamics simulations are used to parameterize a Frenkel-Kontorova model that provides analytic expressions for the limiting stress and activation energy for dislocation nucleation as a function of stress. Results from four commonly used hydrocarbon potentials are compared to show that the qualitative behavior is robust and estimate quantitative uncertainties. In all cases, the results can be described by an Eyring model with values of the zero-stress activation energy Ea 0≈1.5 eV and activation volume V* ≈ 45 Å3 that are consistent with the experimental results for increasingly crystalline materials. The limiting yield stress is ∼8 GPa. These results suggest that activated dislocation nucleation at chain ends is an important mechanism for creep in highly oriented PE fibers.

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 ℓ_{⊥} scaling as the width along the interface ℓ_{∥} to a power χ=0.85±0.01. The total interface roughness is consistent with self-affine scaling with a roughness exponent ζ≈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.

Effect of Roughness and Elasticity on Interactions between Charged Colloidal Spheres.

The effects of realistic roughness and elasticity on the interactions between charged silica spheres are studied as a function of surface potential, screening length, interfacial energy, and roughness. The repulsive force Frep that must be overcome to bring charged spheres into contact is relatively insensitive to elasticity unless spheres are hundreds of times softer than silica. Frep is also insensitive to roughness and interfacial energy. In contrast, roughness has a large effect on the binding energy of spheres and the force Fsep to separate them. Both are lowered by 1 to 2 orders of magnitude by the measured surface roughness of less than 1 nm on 1 µm silica spheres. The reason is that interactions between rigid spheres are dominated by the highest surface peaks rather than the entire spherical surface. Elasticity can increase the pull-off force of rough spheres by a factor of 2 or more because additional surface area can be brought into contact. The implications of these results for shear-thickening transitions are discussed.

Relating Chain Conformations to Extensional Stress in Entangled Polymer Melts.

Nonlinear extensional flows are common in polymer processing, but they 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 뵳6. 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.

Probing large viscosities in glass-formers with nonequilibrium simulations.

For decades, scientists have debated whether supercooled liquids stop flowing below a glass transition temperature [Formula: see text] or whether motion continues to slow gradually down to zero temperature. Answering this question is challenging because human time scales set a limit on the largest measurable viscosity, and available data are equally well fit to models with opposite conclusions. Here, we use short simulations to determine the nonequilibrium shear response of a typical glass-former, squalane. Fits of the data to an Eyring model allow us to extrapolate predictions for the equilibrium Newtonian viscosity [Formula: see text] over a range of pressures and temperatures that change [Formula: see text] by 25 orders of magnitude. The results agree with the unusually large set of equilibrium and nonequilibrium experiments on squalane and extend them to higher [Formula: see text] Studies at different pressures and temperatures are inconsistent with a diverging viscosity at finite temperature. At all pressures, the predicted viscosity becomes Arrhenius with a single temperature-independent activation barrier at low temperatures and high viscosities ([Formula: see text] Pa[Formula: see text]s). Possible experimental tests of our results are outlined.

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 >10Ne, where Ne is the entanglement length.

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, Fcap, and the meniscus shape of the bridge are computed as the separation between the solid surfaces, h, is varied. Macroscopic theory predicts the meniscus shape and the contribution of liquid/vapor interfacial tension to Fcap quite accurately for separations as small as two or three molecular diameters (1-2 nm). However, the total capillary force differs in sign and magnitude from macroscopic theory for h ≲ 5 nm (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.

Slip boundary conditions over curved surfaces.

Molecular dynamics simulations are used to investigate the influence of surface curvature on the slip boundary condition for a simple fluid. The slip length is measured for flows in planar and cylindrical geometries with a range of wall-fluid interactions. As wall curvature increases, the slip length decreases dramatically for closely packed surfaces and increases for sparse ones. The magnitude of the changes depends on the crystallographic orientation and differs for flow along and perpendicular to the direction of curvature. These different patterns of behavior are related to the curvature-induced variation in the ratio of the spacing between fluid atoms to the spacing between minima in the potential from the solid surface. The results are consistent with a microscopic theory for the viscous friction between fluid and wall that expresses the slip length in terms of the lateral response of the fluid to the wall potential and the characteristic decay time of this response.

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 102-104 carbons in length. We find the yield stress σy 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 ≈ 25 Å and determine the high and low strain rate limits of σy. Our results suggest characterizing the 1D dislocations of polymer crystals as an efficient method for numerically predicting the ultimate tensile strength of aligned fibers.

Opportunities in theoretical and computational polymeric materials and soft matter.

Soft materials are abundant in nature and ubiquitous in living systems. Elucidating their multi-faceted properties and underlying mechanisms is not only theoretically challenging and important in its own right, but also serves as the foundation for new materials and applications that will have wide-ranging impact on technology and the national economy. Recent initiatives in computation and data-driven materials discovery, such as the Materials Genome Initiative and the National Science Foundation Designing Materials to Revolutionize and Engineer our Future (NSF-DMREF) program, recognize and highlight the many future opportunities in the field. Building upon similar past efforts, a workshop was held at the University of California, Santa Barbara in October 2013 to specifically identify the central challenges and opportunities in theoretical and computational studies of polymeric as well as non-polymeric soft materials. This article presents a summary of the main findings of the workshop.

AIREBO-M: a reactive model for hydrocarbons at extreme pressures.

The Adaptive Intermolecular Reactive Empirical Bond Order potential (AIREBO) for hydrocarbons has been widely used to study dynamic bonding processes under ambient conditions. However, its intermolecular interactions are modeled by a Lennard-Jones (LJ) potential whose unphysically divergent power-law repulsion causes AIREBO to fail when applied to systems at high pressure. We present a modified potential, AIREBO-M, where we have replaced the singular Lennard-Jones potential with a Morse potential. We optimize the new functional form to improve intermolecular steric repulsions, while preserving the ambient thermodynamics of the original potentials as much as possible. The potential is fit to experimental measurements of the layer spacing of graphite up to 14 GPa and first principles calculations of steric interactions between small alkanes. To validate AIREBO-M's accuracy and transferability, we apply it to a graphite bilayer and orthorhombic polyethylene. AIREBO-M gives bilayer compression consistent with quantum calculations, and it accurately reproduces the quasistatic and shock compression of orthorhombic polyethlyene up to at least 40 GPa.