Influence of adhesion and friction on the geometry of packings of spherical particles

Friction and Adhesion Govern Yielding of Disordered Nanoparticle Packings: A Multiscale Adhesive Discrete Element Method Study

Recent studies have demonstrated that amorphous materials, from granular packings to atomic glasses, share multiple striking similarities, including a universal onset strain level for yield. This is despite vast differences in length scales and in the constituent particles' interactions. However, the nature of localized particle rearrangements is not well understood, and how local interactions affect overall performance remains unknown. Here, we introduce a multiscale adhesive discrete element method to simulate recent novel experiments of disordered nanoparticle packings indented and imaged with single nanoparticle resolution. The simulations exhibit multiple behaviors matching the experiments. By directly monitoring spatial rearrangements and interparticle bonding/debonding under the packing's surface, we uncover the mechanisms of the yielding and hardening phenomena observed in experiments. Interparticle friction and adhesion synergistically toughen the packings and retard plastic deformation. Moreover, plasticity can result from bond switching without particle rearrangements. These results furnish insights for understanding yielding in amorphous materials generally.

X-ray nanotomography of dry colloidal packings

Random packings are crucial in understanding arrangement and geometry of particles. Random packings of dry small particles may be subject to adhesion or friction, as expected theoretically and numerically. We explore experimentally random packings of dry colloids with X-ray nanotomography that directly provides three-dimensional structural and geometric information of dry colloidal packings. We find that dry colloidal packings, as characterized by contact number and packing density, are quite consistent with adhesive loose packings that significantly deviate from random loose packings for hard spheres. This study may offer direct evidence for adhesive loose packings comprising dry small particles, as proven by X-ray nanotomography.

Unified size-density and size-topology relations in random packings of dry adhesive polydisperse spheres

We study the size-density and size-topology relations in random packings of dry adhesive polydisperse microspheres with Gaussian and lognormal size distributions through a geometric tessellation. We find that the dependence of the neighbor number on the centric particle size is always quasilinear, regardless of the size distribution, size span, or interparticle adhesion. The average local packing fraction as a function of normalized particle size for different size variances is well regressed on the same profile, which increases to larger values as the relative strength of adhesion decreases. The variations of the local coordination number with the particle size converge onto a single curve for all adhesive particles, but gradually transfer to another branch for nonadhesive particles. Such adhesion-induced size-density and size-topology relations are interpreted theoretically with a modified geometrical "granocentric" model, where the model parameters are dependent on a single dimensionless adhesion number. Our findings, together with the modified theory, provide a more unified perspective on the substantial geometry of amorphous polydisperse systems, especially those with fairly loose structures.

Equation of state for random sphere packings with arbitrary adhesion and friction

We systematically generate a large set of random micro-particle packings over a wide range of adhesion and friction by means of adhesive contact dynamics simulation. The ensemble of generated packings covers a range of volume fractions ϕ from 0.135 ± 0.007 to 0.639 ± 0.004, and of coordination numbers Z from 2.11 ± 0.03 to 6.40 ± 0.06. We determine ϕ and Z at four limits (random close packing, random loose packing, adhesive close packing, and adhesive loose packing), and find a universal equation of state ϕ(Z) to describe packings with arbitrary adhesion and friction. From a mechanical equilibrium analysis, we determine the critical friction coefficient μ_f,c: when the friction coefficient μ_f is below μ_f,c, particles' rearrangements are dominated by sliding, otherwise they are dominated by rolling. Because of this reason, both ϕ(μ_f) and Z(μ_f) change sharply across μ_f,c. Finally, we generalize the Maxwell counting argument to micro-particle packings, and show that the loosest packing, i.e., adhesive loose packing, satisfies the isostatic condition at Z = 2.

Adhesive loose packings of small dry particles

We explore adhesive loose packings of small dry spherical particles of micrometer size using 3D discrete-element simulations with adhesive contact mechanics and statistical ensemble theory. A dimensionless adhesion parameter (Ad) successfully combines the effects of particle velocities, sizes and the work of adhesion, identifying a universal regime of adhesive packings for Ad > 1. The structural properties of the packings in this regime are well described by an ensemble approach based on a coarse-grained volume function that includes the correlation between bulk and contact spheres. Our theoretical and numerical results predict: (i) an equation of state for adhesive loose packings that appear as a continuation from the frictionless random close packing (RCP) point in the jamming phase diagram and (ii) the existence of an asymptotic adhesive loose packing point at a coordination number Z = 2 and a packing fraction ϕ = 1/2(3). Our results highlight that adhesion leads to a universal packing regime at packing fractions much smaller than the random loose packing (RLP), which can be described within a statistical mechanical framework. We present a general phase diagram of jammed matter comprising frictionless, frictional, adhesive as well as non-spherical particles, providing a classification of packings in terms of their continuation from the spherical frictionless RCP.