Stress Testing Theories of the Glass and Jamming Transitions Using Hyperellipsoids

NONTECHNICAL SUMMARY

This award supports theoretical and computational research and education in the fields of solidification processes, statistical mechanics, and computer simulations. How does a given liquid decide whether to crystallize or to form a disordered solid like window glass when it is cooled? This question remains unanswered, and is a principal focus of current materials research.

Glass-formation is closely related to the jamming transition, the solidification of a granular material, like sand or coffee beans, that occurs when it is compressed. Although great advances in theories of the glass-jamming transition have been made over the past decade, most of these theories assume particles are spherical. This is a potentially serious limitation because very few real-world glassy and granular materials are composed of spherical molecules or grains.

This project aims to advance our knowledge of the glass-jamming transition by conducting a coherent research program that focuses upon its dependence on particle asphericity. The research will systematically relate differences in the structure of glassy and jammed systems composed of model ellipsoidal particles to differences in particle shape and sample preparation protocol.

The relatively low computational cost of the ellipsoidal-particle model will be exploited to explore relevant parameter spaces far more broadly than is feasible for chemically-detailed models. Key questions to be addressed are: (1) Does the importance of particle anisotropy decrease as spatial dimension increases? and (2) To what extent do the peculiar features of ellipsoids’ jamming transitions influence their glass transitions?

The planned studies are designed with the aim to contribute maximally to the long-term goal of obtaining a level of physical understanding sufficient to develop predictive design principles for granular and glassy materials with tailorable structural, mechanical, and acoustic properties.

This award will fund the training of one PhD student and one undergraduate student in granular and glass physics, statistical mechanics, and computer simulations. The PI will also develop and disseminate “EllJam”, an iPhone/iPad app that illustrates the solidification physics of 2D ellipsoids. Playing with parameters such as the particle aspect ratio and compression rate will allow the user to discover and distinguish parameter values leading to crystalline solids from those which lead to disordered solids, and hence to develop some basic intuition for which factors control the outcome of solidification. This app is intended to capture the interest of K-12 students and young researchers.

TECHNICAL SUMMARY

This award supports theoretical and computational research and education in the fields of solidification processes, specifically, the glass-jamming transition, statistical mechanics, and computer simulations. While the importance of particle anisotropy in controlling macroscopic properties of glassy and jammed systems has long been recognized, it is only within the past decade that the development of cheap high-output 3D printers has allowed production of grains with a wide variety of precisely specified shapes.

Advances in synthesis techniques have allowed comparable shape control for colloids as well as preparation of orientationally-ordered small-molecule glasses. Over this time, computers have become powerful enough to simulate large systems of aspherical particles over long timescales. Although great advances in theories of the glass-jamming transition have been made over the past decade, most of these theories assume particles are spherical and hence cannot capture the effects of particle anisotropy.

This is a potentially serious limitation because very few real-world glassy and granular materials are composed of spherically symmetric molecules or grains.

The PI will carry out studies that will systematically relate differences in the structure of glassy and jammed systems composed of ellipsoidal particles to differences in particle shape via a coherent program of coarse-grained simulations and analytic modeling. The PI will also “stress-test” recently developed high-dimensional theories of the glass-jamming transition by determining whether they remain at least qualitatively accurate for systems composed of aspherical particles.

Specifically, the research team will first develop a parallel molecular dynamics code for simulating hyperellipsoids. Then it will conduct simulations and analytic work aimed at determining how coupled dimension and particle-aspect-ratio-dependent effects influence both jamming and the thermal glass transition. Key amongst the questions to be answered by these studies are: (1) Does particle anisotropy become less important as spatial dimension increases and the tendency of particles to locally order decreases — and if it does, how rapidly? and (2) To what extent do the peculiar features of jamming transitions in ellipsoids, more precisely jamming densities that become singular as the aspect ratio of a particle approaches unity, influence their thermal glass transitions?

Answering these questions will contribute to the soft matter theory community’s long-term goal of obtaining a level of physical understanding sufficient to develop predictive design principles for granular and glassy materials with tailorable structural, mechanical, and acoustic properties.

This award will fund the training of one PhD student and one undergraduate student in granular and glass physics, statistical mechanics, and computer simulations. The PI will also develop and publicize “EllJam”, an iPhone/iPad app that illustrates’ 2D ellipsoids’ jamming physics. The user will be able to choose the system size, the particle aspect ratio, and the compression rate, and then watch how ellipsoid jamming varies with these parameters.

The user will also be able to choose between monodisperse systems which tend to crystallize in 2D and the 50:50 bidisperse systems typically employed in jamming studies. This app should be of interest to both K-12 students and young researchers.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.