Research On Disordered Jammed Packings Of Monodisperse And Polydisperse Non--spherical Particles

A packing system is defined as a collection of non-overlapping convex objects in low dimensional space.In nature,there exist different packing systems across a broad range of length scales,including three dimensional(3D)hard sphere systems for liquids,self-assembled nanoparticle structures,cellular tissues,and granular media.Researchers focus on the col-lective behaviors from individual constituent particles towards the overall packing.Two key measurements for the static packing structure are the packing fraction defined by the ratio of the total particle volume over the volume of packing space,and the coordination number defined by the average number of contacts per particle.Disordered jammed packing(or ran-dom close packing),which is mainly defined for the macroscopic non-equilibrium frictionless granular materials,corresponds to randomly generated,mechanically stable state with lowest packing fraction.The disordered jammed packing fraction of 3D monodisperse frictionless spheres φJ≈0.64 is validated by extensive experiments and simulations.In recent decades,researchers initiated studies on disordered jammed packings for non-spherical particles.Yet,comprehensive discussions are lacking.Moreover,few is known about packings with coupled particle size and shape polydispersity(generalized polydisperse packings).In this article,we numerically investigate both monodisperse and polydisperse disordered jammed packings for frictionless non-spherical particles.Various non-spherical particle mod-els including spherocylinders,ellipsoids,superellipsoids and spheropolyhedra are considered.This article systematically study the dependencies of φJ and coordination number z on the par-ticle shape for the monodisperse packings.As particle asphericity A increases(deviating from sphere),φJ first increases from～0.64 and then decreases.A considerable part of non-spherical packings are hypostatic with z<z iso,whose mechanical stability is validated by the analysis of dynamical matrix.Monodisperse disordered j ammed packings are found to be the key to understand polydis-perse systems.The linear superposition state for poly disperse-shaped packings can be regarded as the simple mixture of monodisperse disordered j ammed packings corresponding to different shape components.The factor αC is used to calibrate the particle size ratio for such critical state,and its prior estimation is proposed.αC naturally leads to the definition of equivalent packing diameter for non-spherical particles De.Two distribution parameters of De in a poly disperse system are utilized to predict the packing fraction increment beyond the linear superposition state.This point extends the observation that size dispersity always facilitates the packing in polydisperse spherical packings.The set Voronoi tessellation method is implemented to study the local structures for poly-disperse packings.The relative particle surface area defined by De determines its normalized(local)free volume vf.To a large extent,the relation between vf and A is universal,and the semi-empirical prediction on vf(A)is proposed.These analyses about local structures help to reproducing a packing in the bottom-up approach,especially for φJ.Both φJ and αC are the intrinsic properties for a certain particle shape and they can be calibrated priorly.Based on this,the results in this article indicate that both the local pack-ing structures and the overall packing fraction are predictable for a generalized polydisperse packing.This finding contributes to the rationale design of colloidal and granular materials.