Optimizing Particle Packings by Shape Variation

The question at the heart of this proposal is one of the most ancient problems in science and engineering: How densely can a volume be filled with objects of a particular shape? Such particle packings are of utmost importance for all industries involved in granular processing and appear in a broad range of current scientific and engineering fields such as self-assembly of nano-particles, liquid crystals, glassy materials, and bio-materials. In fact, understanding the macroscopic behaviour of matter from the properties of its individual constituents is one of the central problems in materials science. Packings of hard objects are one of the simplest matter states, but, nevertheless, pose considerable theoretical challenges. Finding the densest packing is an outstanding mathematical problem that originated with Kepler's famous conjecture on regular cannonball piles. Much less is known about non-spherical shapes, despite the fact that all shapes in nature deviate from the ideal sphere. Recently, it has been conjectured that the sphere - the shape with the highest symmetry - is in fact the worst packing object among all convex shapes in both disordered and regular arrangements. This implies that packing densities can be optimized by searching in the space of object shapes. A deeper understanding of this optimization problem would lead to immediate benefits in many industrial sectors, especially pharmaceutical and chemical industries, which rely on storage and transport of large amounts of granular material.

Particle packings are in general athermal and thus represent non-equilibrium states of matter. As a consequence, the well established framework of statistical mechanics, which is able to successfully predict the phases and macroscopic properties of many-particle systems at equilibrium, does not apply. Moreover, assemblies of non-spherical particles are characterized by strong orientational correlations, in addition to positional ones, which has thus far prohibited any systematic theoretical investigation. Searches for the optimal packing of non-spherical shapes have focused instead on empirical studies on a case-by-case basis using experiments or computer simulations. These studies suffer from the generic shortcoming that the final packing state is strongly protocol dependent leading to a large variance of obtained packing densities even for the same shape. Novel theoretical tools are therefore needed.

The overall aim of this proposal is to provide a general framework to predict the density of packings from the shape of the particles and to understand the organization principles of these packings. To do this, we will generalize our recently developed approach based on a coarse-grained volume function. This will allow us to address the problem of optimizing packing fractions in industry relevant scenarios and to explore novel states of matter due to anisotropic building blocks. The proposal thus has far-reaching consequences both on the practical problem on how to efficiently store granular material as well as on our fundamental understanding of matter away from equilibrium.

If the research objectives are fully achieved, this proposal will have impact on: (i) The immediate research field; (ii) The wider scientific community; (iii) Industrial applications; (iv) The general public; (v) The UK's competitiveness in the world.

(i) The immediate research field. The outcomes directly benefit researchers working on particle packings and are expected to stimulate further theoretical and experimental work. The milestones of the project, such as identifying generic shape features for isochoric ideality or partially ordered phases, will not only provide a deeper understanding of dense matter states, but also highlight new research lines for investigation. Important questions are, e.g., whether these properties are realized in nature or can be exploited to design new functional materials.

(ii) The wider scientific community. Since the theoretical approach used is based on statistical mechanics, which is applied in a wide variety of scientific fields from evolutionary dynamics to risk management, the outcomes will benefit researchers in all these fields. The project sheds light especially on the applicability of statistical mechanics in non-equilibrium situations, a much broader class of systems than thermal equilibrium ones, to which statistical mechanics is usually limited. New problems might be solved using such a first principle approach. Establishing a connection with stochastic processes will also allow for important cross fertilization between applied probability and materials science.

(iii) Industrial applications. Granular matter is ubiquitous in nature and technology and represents the second most handled substance in industry, after water. The project will contribute to a fundamental understanding of these matter states with direct impact on many industrial sectors. Optimizing packing densities is of great importance for all industries involved in the storage and transport of granular matter, e.g., in the pharmaceutical industry, which is strongly represented in the UK. We have already started dialogue with several companies and will build upon these relationships, leveraging resources from QMUL's Innovation Fund.

(iv) The general public. Packing particles is as much an everyday problem as it is a scientific one. Previously publicized work in this field has used, e.g., packings of candies like M&Ms (oblate ellipsoidal shape) to effectively reach a wider audience. In order to promote outreach activities and engage the general public with the science and mathematics of particle packings the project intends to develop an iPhone app. Such an app is appealing in particular for younger audiences with no affiliation to science and can be effectively used in outreach activities to generate interest in STEM fields, which is key for the UK's sustained leadership in science and technology. A number of outreach events during the course of the project are identified.

(v) The UK's competitiveness in the world. The potential benefits from being able to store more material in a given volume are enormous, with transport and storage of granular material being a billion pound business in the UK alone. The project has therefore real potential to enhance the UK's competitiveness and can directly lead to measurable economic impact. The line of research promoted in this proposal is currently under-represented in the UK, with only a few other groups attempting to understand granular matter from first principles. In contrast, there are several large and well-established groups at US universities (e.g., at Princeton, Yale, New York, Michigan), working on related fundamental problems. Increased funding in this field will thus help to improve the UK's standing in this industrially relevant research area.