Hysteretic Behavior of Capillary Bridges between Flat Plates.

We studied the evolution of capillary bridges between nominally flat plates undergoing multiple cycles of compression and stretching in experiments and simulations. We varied the distance between the plates in small increments to study the full evolution of the bridge shape. Experiments show that contact angle hysteresis determines the shape of the bridge. In sliding drops, hysteresis can be modeled using a contact angle-dependent resistive force F̃R applied at the contact line. We developed a model that accurately captures the evolution of the bridge shape by combining F̃R and constrained energy minimization. Unlike previous work, this allows for both complete and partial contact line pinning. We also explored the effect of using nonparallel plates. The asymmetry in the bridge shape causes the movement of the center of mass of the bridge and can be explained by contact angle hysteresis. We find that even a slight misalignment between the flat plates can have a measurable effect.

Correction: The structural, vibrational, and mechanical properties of jammed packings of deformable particles in three dimensions.

Correction for 'The structural, vibrational, and mechanical properties of jammed packings of deformable particles in three dimensions' by Dong Wang et al., Soft Matter, 2021, 17, 9901-9915, DOI: 10.1039/D1SM01228B.

Hopper flows of deformable particles.

Numerous experimental and computational studies show that continuous hopper flows of granular materials obey the Beverloo equation that relates the volume flow rate Q and the orifice width w: Q ∼ (w/σavg - k)ß, where σavg is the average particle diameter, kσavg is an offset where Q ∼ 0, the power-law scaling exponent ß = d - 1/2, and d is the spatial dimension. Recent studies of hopper flows of deformable particles in different background fluids suggest that the particle stiffness and dissipation mechanism can also strongly affect the power-law scaling exponent ß. We carry out computational studies of hopper flows of deformable particles with both kinetic friction and background fluid dissipation in two and three dimensions. We show that the exponent ß varies continuously with the ratio of the viscous drag to the kinetic friction coefficient, λ = ζ/µ. ß = d - 1/2 in the λ → 0 limit and d - 3/2 in the λ → ∞ limit, with a midpoint λc that depends on the hopper opening angle θw. We also characterize the spatial structure of the flows and associate changes in spatial structure of the hopper flows to changes in the exponent ß. The offset k increases with particle stiffness until k ∼ kmax in the hard-particle limit, where kmax ∼ 3.5 is larger for λ → ∞ compared to that for λ → 0. Finally, we show that the simulations of hopper flows of deformable particles in the λ → ∞ limit recapitulate the experimental results for quasi-2D hopper flows of oil droplets in water.

Using delaunay triangularization to characterize non-affine displacement fields during athermal, quasistatic deformation of amorphous solids.

We investigate the non-affine displacement fields that occur in two-dimensional Lennard-Jones models of metallic glasses subjected to athermal, quasistatic simple shear (AQS). During AQS, the shear stress versus strain displays continuous quasi-elastic segments punctuated by rapid drops in shear stress, which correspond to atomic rearrangement events. We capture all information concerning the atomic motion during the quasi-elastic segments and shear stress drops by performing Delaunay triangularizations and tracking the deformation gradient tensor Fα associated with each triangle α. To understand the spatio-temporal evolution of the displacement fields during shear stress drops, we calculate Fα along minimal energy paths from the mechanically stable configuration immediately before to that after the stress drop. We find that quadrupolar displacement fields form and dissipate both during the quasi-elastic segments and shear stress drops. We then perform local perturbations (rotation, dilation, simple and pure shear) to single triangles and measure the resulting displacement fields. We find that local pure shear deformations of single triangles give rise to mostly quadrupolar displacement fields, and thus pure shear strain is the primary type of local strain that is activated by bulk, athermal quasistatic simple shear. Other local perturbations, e.g. rotations, dilations, and simple shear of single triangles, give rise to vortex-like and dipolar displacement fields that are not frequently activated by bulk AQS. These results provide fundamental insights into the non-affine atomic motion that occurs in driven, glassy materials.

The structural, vibrational, and mechanical properties of jammed packings of deformable particles in three dimensions.

We investigate the structural, vibrational, and mechanical properties of jammed packings of deformable particles with shape degrees of freedom in three dimensions (3D). Each 3D deformable particle is modeled as a surface-triangulated polyhedron, with spherical vertices whose positions are determined by a shape-energy function with terms that constrain the particle surface area, volume, and curvature, and prevent interparticle overlap. We show that jammed packings of deformable particles without bending energy possess low-frequency, quartic vibrational modes, whose number decreases with increasing asphericity and matches the number of missing contacts relative to the isostatic value. In contrast, jammed packings of deformable particles with non-zero bending energy are isostatic in 3D, with no quartic modes. We find that the contributions to the eigenmodes of the dynamical matrix from the shape degrees of freedom are significant over the full range of frequency and shape parameters for particles with zero bending energy. We further show that the ensemble-averaged shear modulus 〈G〉 scales with pressure P as 〈G〉 ∼ Pß, with ß ≈ 0.75 for jammed packings of deformable particles with zero bending energy. In contrast, ß ≈ 0.5 for packings of deformable particles with non-zero bending energy, which matches the value for jammed packings of soft, spherical particles with fixed shape. These studies underscore the importance of incorporating particle deformability and shape change when modeling the properties of jammed soft materials.

Pressure Dependent Shear Response of Jammed Packings of Frictionless Spherical Particles.

The mechanical response of packings of purely repulsive, spherical particles to athermal, quasistatic simple shear near jamming onset is highly nonlinear. Previous studies have shown that, at small pressure p, the ensemble-averaged static shear modulus ⟨G-G_{0}⟩ scales with p^{α}, where α≈1, but above a characteristic pressure p^{**}, ⟨G-G_{0}⟩∼p^{ß}, where ß≈0.5. However, we find that the shear modulus G^{i} for an individual packing typically decreases linearly with p along a geometrical family where the contact network does not change. We resolve this discrepancy by showing that, while the shear modulus does decrease linearly within geometrical families, ⟨G⟩ also depends on a contribution from discontinuous jumps in ⟨G⟩ that occur at the transitions between geometrical families. For p>p^{**}, geometrical-family and rearrangement contributions to ⟨G⟩ are of opposite signs and remain comparable for all system sizes. ⟨G⟩ can be described by a scaling function that smoothly transitions between two power-law exponents α and ß. We also demonstrate the phenomenon of compression unjamming, where a jammed packing unjams via isotropic compression.

Homogeneous Crystallization in Cyclically Sheared Frictionless Grains.

Many experiments over the past half century have shown that, for a range of protocols, granular materials compact under pressure and repeated small disturbances. A recent experiment on cyclically sheared spherical grains showed significant compaction via homogeneous crystallization (Rietz et al., 2018). Here we present numerical simulations of frictionless, purely repulsive spheres undergoing cyclic simple shear via Newtonian dynamics with linear viscous drag at fixed vertical load. We show that for sufficiently small strain amplitudes, cyclic shear gives rise to homogeneous crystallization at a volume fraction ϕ=0.646±0.001. This result indicates that neither friction nor gravity is essential for homogeneous crystallization in driven granular media. Understanding how crystal formation is initiated within a homogeneous disordered state gives key insights into the old open problem of glass formation in fluids.

Contact network changes in ordered and disordered disk packings.

We investigate the mechanical response of packings of purely repulsive, frictionless disks to quasistatic deformations. The deformations include simple shear strain at constant packing fraction and at constant pressure, "polydispersity" strain (in which we change the particle size distribution) at constant packing fraction and at constant pressure, and isotropic compression. For each deformation, we show that there are two classes of changes in the interparticle contact networks: jump changes and point changes. Jump changes occur when a contact network becomes mechanically unstable, particles "rearrange", and the potential energy (when the strain is applied at constant packing fraction) or enthalpy (when the strain is applied at constant pressure) and all derivatives are discontinuous. During point changes, a single contact is either added to or removed from the contact network. For repulsive linear spring interactions, second- and higher-order derivatives of the potential energy/enthalpy are discontinuous at a point change, while for Hertzian interactions, third- and higher-order derivatives of the potential energy/enthalpy are discontinuous. We illustrate the importance of point changes by studying the transition from a hexagonal crystal to a disordered crystal induced by applying polydispersity strain. During this transition, the system only undergoes point changes, with no jump changes. We emphasize that one must understand point changes, as well as jump changes, to predict the mechanical properties of jammed packings.

Jammed packings of 3D superellipsoids with tunable packing fraction, coordination number, and ordering.

We carry out numerical studies of static packings of frictionless superellipsoidal particles in three spatial dimensions. We consider more than 200 different particle shapes by varying the three shape parameters that define superellipsoids. We characterize the structural and mechanical properties of both disordered and ordered packings using two packing-generation protocols. We perform athermal quasi-static compression simulations starting from either random, dilute configurations (Protocol 1) or thermalized, dense configurations (Protocol 2), which allows us to tune the orientational order of the packings. In general, we find that superellipsoid packings are hypostatic, with coordination number zJ < ziso, where ziso = 2df and df = 5 or 6 depending on whether the particles are axi-symmetric or not. Over the full range of orientational order, we find that the number of quartic modes of the dynamical matrix for the packings always matches the number of missing contacts relative to the isostatic value. This result suggests that there are no mechanically redundant contacts for ordered, yet hypostatic packings of superellipsoidal particles. Additionally, we find that the packing fraction at jamming onset for disordered packings of superellipsoidal depends on at least two particle shape parameters, e.g. the asphericity A and reduced aspect ratio ß of the particles.

The role of deformability in determining the structural and mechanical properties of bubbles and emulsions.

We perform computational studies of jammed particle packings in two dimensions undergoing isotropic compression using the well-characterized soft particle (SP) model and deformable particle (DP) model that we developed for bubbles and emulsions. In the SP model, circular particles are allowed to overlap, generating purely repulsive forces. In the DP model, particles minimize their perimeter, while deforming at fixed area to avoid overlap during compression. We compare the structural and mechanical properties of jammed packings generated using the SP and DP models as a function of the packing fraction ρ, instead of the reduced number density φ. We show that near jamming onset the excess contact number Δz = z - zJ and shear modulus G scale as Δρ0.5 in the large system limit for both models, where Δρ = ρ - ρJ and zJ ≈ 4 and ρJ ≈ 0.842 are the values at jamming onset. Δz and G for the SP and DP models begin to differ for ρ ⪆ 0.88. In this regime, Δz ∼ G can be described by a sum of two power-laws in Δρ, i.e. Δz ∼ G ∼ C0Δρ0.5 + C1Δρ1.0 to lowest order. We show that the ratio C1/C0 is much larger for the DP model compared to that for the SP model. We also characterize the void space in jammed packings as a function of ρ. We find that the DP model can describe the formation of Plateau borders as ρ → 1. We further show that the results for z and the shape factor A versus ρ for the DP model agree with recent experimental studies of foams and emulsions.

Intrinsic dissipation mechanisms in metallic glass resonators.

Micro- and nanoresonators have important applications including sensing, navigation, and biochemical detection. Their performance is quantified using the quality factor Q, which gives the ratio of the energy stored to the energy dissipated per cycle. Metallic glasses are a promising material class for micro- and nanoscale resonators since they are amorphous and can be fabricated precisely into complex shapes on these length scales. To understand the intrinsic dissipation mechanisms that ultimately limit large Q-values in metallic glasses, we perform molecular dynamics simulations to model metallic glass resonators subjected to bending vibrations at low temperatures. We calculate the power spectrum of the kinetic energy, redistribution of energy from the fundamental mode of vibration, and Q vs the kinetic energy per atom K of the excitation. In the harmonic and anharmonic response regimes where there are no atomic rearrangements, we find that Q → ∞ over the time periods we consider (since we do not consider coupling to the environment). We identify a characteristic Kr above which atomic rearrangements occur, and there is significant energy leakage from the fundamental mode to higher frequencies, causing finite Q. Thus, Kr is a critical parameter determining resonator performance. We show that Kr decreases as a power-law, Kr ∼ N-k, with increasing system size N, where k ≈ 1.3. We estimate the critical strain ⟨γr⟩∼ 10-8 for micrometer-sized resonators below which atomic rearrangements do not occur in the millikelvin temperature range, and thus, large Q-values can be obtained when they are operated below γr. We also find that Kr for amorphous resonators is comparable to that for resonators with crystalline order.

Jamming of Deformable Polygons.

We introduce the deformable particle (DP) model for cells, foams, emulsions, and other soft particulate materials, which adds to the benefits and eliminates deficiencies of existing models. The DP model combines the ability to model individual soft particles with the shape-energy function of the vertex model, and adds arbitrary particle deformations. We focus on 2D deformable polygons with a shape-energy function that is minimized for area a_{0} and perimeter p_{0} and repulsive interparticle forces. We study the onset of jamming versus particle asphericity, A=p_{0}^{2}/4πa_{0}, and find that the packing fraction grows with A until reaching A^{*}=1.16 of the underlying Voronoi cells at confluence. We find that DP packings above and below A^{*} are solidlike, which helps explain the solid-to-fluid transition at A^{*} in the vertex model as a transition from tension- to compression-dominated regimes.

The glass-forming ability of model metal-metalloid alloys.

Bulk metallic glasses (BMGs) are amorphous alloys with desirable mechanical properties and processing capabilities. To date, the design of new BMGs has largely employed empirical rules and trial-and-error experimental approaches. Ab initio computational methods are currently prohibitively slow to be practically used in searching the vast space of possible atomic combinations for bulk glass formers. Here, we perform molecular dynamics simulations of a coarse-grained, anisotropic potential, which mimics interatomic covalent bonding, to measure the critical cooling rates for metal-metalloid alloys as a function of the atomic size ratio σS/σL and number fraction xS of the metalloid species. We show that the regime in the space of σS/σL and xS where well-mixed, optimal glass formers occur for patchy and LJ particle mixtures, coincides with that for experimentally observed metal-metalloid glass formers. Thus, our simple computational model provides the capability to perform combinatorial searches to identify novel glass-forming alloys.

On the origin of multi-component bulk metallic glasses: Atomic size mismatches and de-mixing.

The likelihood that an undercooled liquid vitrifies or crystallizes depends on the cooling rate R. The critical cooling rate R(c), below which the liquid crystallizes upon cooling, characterizes the glass-forming ability (GFA) of the system. While pure metals are typically poor glass formers with R(c)>10(12)K/s, specific multi-component alloys can form bulk metallic glasses (BMGs) even at cooling rates below R∼1 K/s. Conventional wisdom asserts that metal alloys with three or more components are better glass formers (with smaller R(c)) than binary alloys. However, there is currently no theoretical framework that provides quantitative predictions for R(c) for multi-component alloys. In this manuscript, we perform simulations of ternary hard-sphere systems, which have been shown to be accurate models for the glass-forming ability of BMGs, to understand the roles of geometric frustration and demixing in determining R(c). Specifically, we compress ternary hard sphere mixtures into jammed packings and measure the critical compression rate, below which the system crystallizes, as a function of the diameter ratios σ(B)/σ(A) and σ(C)/σ(A) and number fractions x(A), x(B), and x(C). We find two distinct regimes for the GFA in parameter space for ternary hard spheres. When the diameter ratios are close to 1, such that the largest (A) and smallest (C) species are well-mixed, the GFA of ternary systems is no better than that of the optimal binary glass former. However, when σ(C)/σ(A) ≲ 0.8 is below the demixing threshold for binary systems, adding a third component B with σ(C) < σ(B) < σ(A) increases the GFA of the system by preventing demixing of A and C. Analysis of the available data from experimental studies indicates that most ternary BMGs are below the binary demixing threshold with σ(C)/σ(A) < 0.8.

Beyond packing of hard spheres: The effects of core softness, non-additivity, intermediate-range repulsion, and many-body interactions on the glass-forming ability of bulk metallic glasses.

When a liquid is cooled well below its melting temperature at a rate that exceeds the critical cooling rate Rc, the crystalline state is bypassed and a metastable, amorphous glassy state forms instead. Rc (or the corresponding critical casting thickness dc) characterizes the glass-forming ability (GFA) of each material. While silica is an excellent glass-former with small Rc < 10(-2) K/s, pure metals and most alloys are typically poor glass-formers with large Rc > 10(10) K/s. Only in the past thirty years have bulk metallic glasses (BMGs) been identified with Rc approaching that for silica. Recent simulations have shown that simple, hard-sphere models are able to identify the atomic size ratio and number fraction regime where BMGs exist with critical cooling rates more than 13 orders of magnitude smaller than those for pure metals. However, there are a number of other features of interatomic potentials beyond hard-core interactions. How do these other features affect the glass-forming ability of BMGs? In this manuscript, we perform molecular dynamics simulations to determine how variations in the softness and non-additivity of the repulsive core and form of the interatomic pair potential at intermediate distances affect the GFA of binary alloys. These variations in the interatomic pair potential allow us to introduce geometric frustration and change the crystal phases that compete with glass formation. We also investigate the effect of tuning the strength of the many-body interactions from zero to the full embedded atom model on the GFA for pure metals. We then employ the full embedded atom model for binary BMGs and show that hard-core interactions play the dominant role in setting the GFA of alloys, while other features of the interatomic potential only change the GFA by one to two orders of magnitude. Despite their perturbative effect, understanding the detailed form of the intermetallic potential is important for designing BMGs with cm or greater casting thickness.

Dynamic nuclear spin polarization of liquids and gases in contact with nanostructured diamond.

Optical pumping of spin polarization can produce almost complete spin order but its application is restricted to select atomic gases and condensed matter systems. Here, we theoretically investigate a novel route to nuclear spin hyperpolarization in arbitrary fluids in which target molecules are exposed to polarized paramagnetic centers located near the surface of a host material. We find that adsorbed nuclear spins relax to positive or negative polarization depending on the average paramagnetic center depth and nanoscale surface topology. For the particular case of optically pumped nitrogen-vacancy centers in diamond, we calculate strong nuclear spin polarization at moderate magnetic fields provided the crystal surface is engineered with surface roughness in the few-nanometer range. The equilibrium nuclear spin temperature depends only weakly on the correlation time describing the molecular adsorption dynamics and is robust in the presence of other, unpolarized paramagnetic centers. These features could be exploited to polarize flowing liquids or gases, as we illustrate numerically for the model case of a fluid brought in contact with an optically pumped diamond nanostructure.

Statistics of frictional families.

We develop a theoretical description for mechanically stable frictional packings in terms of the difference between the total number of contacts required for isostatic packings of frictionless disks and the number of contacts in frictional packings, m=Nc0 - Nc. The saddle order m represents the number of unconstrained degrees of freedom that a static packing would possess if friction were removed. Using a novel numerical method that allows us to enumerate disk packings for each m, we show that the probability to obtain a packing with saddle order m at a given static friction coefficient µ, Pm(µ), can be expressed as a power series in µ. Using this form for Pm(µ), we quantitatively describe the dependence of the average contact number on the friction coefficient for static disk packings obtained from direct simulations of the Cundall-Strack model for all µ and N.

Modeling the Effects of Varying the Ti Concentration on the Mechanical Properties of Cu-Ti Alloys.

The mechanical properties of CuTi alloys have been characterized extensively through experimental studies. However, a detailed understanding of why the strength of Cu increases after a small fraction of Ti atoms are added to the alloy is still missing. In this work, we address this question using density functional theory (DFT) and molecular dynamics (MD) simulations with the modified embedded atom method (MEAM) interatomic potentials. First, we performed calculations of the uniaxial tension deformations of small bicrystalline Cu cells using DFT static simulations. We then carried out uniaxial tension deformations on much larger bicrystalline and polycrystalline Cu cells by using MEAM MD simulations. In bicrystalline Cu, the inclusion of Ti increases the grain boundary separation energy and the maximum tensile stress. The DFT calculations demonstrate that the increase in the tensile stress can be attributed to an increase in the local charge density arising from Ti. MEAM simulations in larger bicrystalline systems have shown that increasing the Ti concentration decreases the density of the stacking faults. This observation is enhanced in polycrystalline Cu, where the addition of Ti atoms, even at concentrations as low as 1.5 atomic (at.) %, increases the yield strength and elastic modulus of the material compared to pure Cu. Under uniaxial tensile loading, the addition of small amounts of Ti hinders the formation of partial Shockley dislocations in the grain boundaries of Cu, leading to a reduced level of local deformation. These results shed light on the role of Ti in determining the mechanical properties of polycrystalline Cu and enable the engineering of grain boundaries and the inclusion of Ti to improve degradation resistance.

Connecting polymer collapse and the onset of jamming.

Previous studies have shown that the interiors of proteins are densely packed, reaching packing fractions that are as large as those found for static packings of individual amino-acid-shaped particles. How can the interiors of proteins take on such high packing fractions given that amino acids are connected by peptide bonds and many amino acids are hydrophobic with attractive interactions? We investigate this question by comparing the structural and mechanical properties of collapsed attractive disk-shaped bead-spring polymers to those of three reference systems: static packings of repulsive disks, of attractive disks, and of repulsive disk-shaped bead-spring polymers. We show that the attractive systems quenched to temperatures below the glass transition T≪T_{g} and static packings of both repulsive disks and bead-spring polymers possess similar interior packing fractions. Previous studies have shown that static packings of repulsive disks are isostatic at jamming onset, i.e., the number of interparticle contacts N_{c} matches the number of degrees of freedom, which strongly influences their mechanical properties. We find that repulsive polymer packings are hypostatic at jamming onset (i.e., with fewer contacts than degrees of freedom) but are effectively isostatic when including stabilizing quartic modes, which give rise to quartic scaling of the potential energy with displacements along these modes. While attractive disk and polymer packings are often considered hyperstatic with excess contacts over the isostatic number, we identify a definition for interparticle contacts for which they can also be considered as effectively isostatic. As a result, we show that the mechanical properties (e.g., scaling of the potential energy with excess contact number and low-frequency contribution to the density of vibrational modes) of weakly attractive disk and polymer packings are similar to those of isostatic repulsive disk and polymer packings. Our results demonstrate that static packings generated via attractive collapse or compression of repulsive particles possess similar structural and mechanical properties.

Computational modeling of the physical features that influence breast cancer invasion into adipose tissue.

Breast cancer invasion into adipose tissue strongly influences disease progression and metastasis. The degree of cancer cell invasion into adipose tissue depends on both biochemical signaling and the mechanical properties of cancer cells, adipocytes, and other key components of adipose tissue. We model breast cancer invasion into adipose tissue using discrete element method simulations of active, cohesive spherical particles (cancer cells) invading into confluent packings of deformable polyhedra (adipocytes). We quantify the degree of invasion by calculating the interfacial area At between cancer cells and adipocytes. We determine the long-time value of At vs the activity and strength of the cohesion between cancer cells, as well as the mechanical properties of the adipocytes and extracellular matrix in which adipocytes are embedded. We show that the degree of invasion collapses onto a master curve as a function of the dimensionless energy scale Ec , which grows linearly with the cancer cell velocity persistence time and fluctuations, is inversely proportional to the system pressure, and is offset by the cancer cell cohesive energy. When E c > 1 , cancer cells will invade the adipose tissue, whereas for E c < 1 , cancer cells and adipocytes remain de-mixed. We also show that At decreases when the adipocytes are constrained by the ECM by an amount that depends on the spatial heterogeneity of the adipose tissue.