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.

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.

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.

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.

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.

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.

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 vanishing as 1/. The inclusion of elasticity allows relative motion of domains on the surface in response to the random interfacial forces.

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.

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.

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 that must be overcome to bring charged spheres into contact is relatively insensitive to elasticity unless spheres are hundreds of times softer than silica. is also insensitive to roughness and interfacial energy.

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 ε≥6.

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.

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.

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).

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 10-10 carbons in length. We find the yield stress σ saturates for long chains at 6.3 GPa, agreeing well with experiments.

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.

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.

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.

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 obtained for thermal welding of homopolymer slabs. These two processes differ from each other in their interfacial structure since damage leads to increased polydispersity and more short chains.

Capillary adhesion at the nanometer scale.

Molecular dynamics simulations are used to study the capillary adhesion from a nonvolatile liquid meniscus between a spherical tip and a flat substrate. The atomic structure of the tip, the tip radius, the contact angles of the liquid on the two surfaces, and the volume of the liquid bridge are varied. The capillary force between the tip and substrate is calculated as a function of their separation h.

Contact between rough surfaces and a criterion for macroscopic adhesion.

At the molecular scale, there are strong attractive interactions between surfaces, yet few macroscopic surfaces are sticky. Extensive simulations of contact by adhesive surfaces with roughness on nanometer to micrometer scales are used to determine how roughness reduces the area where atoms contact and thus weakens adhesion. The material properties, adhesive strength, and roughness parameters are varied by orders of magnitude.

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 10(3)-10(6) particles.

Structure and Strength at Immiscible Polymer Interfaces.

Thermal welding of polymer-polymer interfaces is important for integrating polymeric elements into devices. When two different polymers are joined, the strength of the weld depends critically on the degree of immiscibility. We perform large-scale molecular dynamics simulations of the structure-strength relation at immiscible polymer interfaces.