(4as) Computational Studies of Phase Transition in Systems of Anisotropic Building Blocks With Applications to in Silico Design of Functional Materials | AIChE

(4as) Computational Studies of Phase Transition in Systems of Anisotropic Building Blocks With Applications to in Silico Design of Functional Materials

Authors 

Haji-Akbari, A. - Presenter, Yale University



Phase transitions are ubiquitous in nature. The very existence of life on earth would not have been possible without the multitude of thermodynamic and kinetic phase transitions that take place both in vitro and in vivo. Computational studies of phase transition are not only important from a theoretical perspective, but can also help us gain a better understanding of profoundly important natural processes such as climate change or protein folding. Studies of phase transition have gained further momentum in light of recent advents in nanotechnology and material sciences, which has made the bottom-up assembly of complex functional materials possible. Most notable are the wide range of anisotropic nano- and colloidal building blocks that can spontaneously assemble into complex structures with interesting mechanical, electrical, magnetic and/or optical properties. Bottom-up assembly of such complicated structures from the corresponding building blocks usually involves one or several phase transitions. Computational studies of such transitions can help us devise engineering guidelines for designing new building blocks and new structures. The main focus of my research is to study the phenomenology, thermodynamics and kinetics of phase transitions in systems of anisotropic building blocks or molecules, or in systems with confined geometries. In the following paragraphs, I mention different flavors of phase transition problems that are of particular interest to me.

1- Entropy-driven disorder-order transitions in hard particle sysrems: From a theoretical perspective, hard particles are suitable model systems for studying the exclusive effect of building block geometry on the thermodynamic phase behavior, because the thermodynamics of a hard particle system is purely determined by its shape. In addition, hard particles closely mimic colloidal particles that interact via short-range repulsive interactions, and can be used for in silico prediction of the experimental behavior of such colloidal systems. Theoretical and computational studies of hard particles are also intimately related to the problem of packing in discrete geometry, since the densest packing of a given shape is the most stable structure of the corresponding hard particle system in the limit of infinite pressure. Since it is generally difficult to obtain analytical solutions for the packing problem, numerical approaches- based on hard particle simulations- are becoming popular heuristic ways solving packing problems. Although entropy-driven transitions can happen in energetic systems as well, all disorder-order transitions in hard particle systems are entropy-driven [1].

Hard tetrahedra, the main focus of my PhD dissertation, are the simple yet perplexing examples of geometrically anisotropic building blocks that self-assemble into complicated structures.  The regular tetrahedron is the simplest of the five Platonic solids.  In my research, Monte Carlo simulations revealed that these geometrically simple building blocks assemble into a dodecagonal quasicrystal, at sufficiently high densities due to entropy alone [2]. These quasi-periodic arrangements are surprisingly dense. An approximant of the quasicrystal that we constructed manually is an even denser packing and constituted the world record at the time of its discovery.  Quasicrystals are an exotic class of solids with long-range order that lack periodicity. In 2011, the Nobel Prize in Chemistry was awarded to Danieh Schechtman for the discovery of the first quasicrystal [3]. We found that the quasicrystal forms robustly from hard tetrahedra, and subsequently found the phase again in a system of hard triangular bipyramids (TBPs), which are dimers of hard tetrahedra [4]. We also confirm that in both systems, the quasicrystal approximant is more stable at intermediate densities than the now known densest packing of these polyhedra [4, 5].  This research suggests the rich and subtle role that entropy plays in stabilizing complex structures and the potential that geometric anisotropy has in inducing complex forms of order.

2- Homogeneous Nucleation of Ice and Gas Hydrates: I am also interested in phase transitions in systems of small anisotropic molecules such as water, CO2 and small organic molecules such as hydrocarbons. I use advanced sampling techniques such as umbrella sampling and forward-flux sampling for calculating the free energy profiles and nucleation rates for these crystallization processes. I am particularly interested in studying homogeneous nucleation in confined geometries such as droplets, films and porous media since such confined environments are usually more relevant to what really happens in nature, and are therefore more interesting to atmospheric, oceanic and geological sciences. The knowledge obtained from these studies will be extremely helpful in designing materials for energy storage and sequestration. 

1. Daan Frenkel. Entropy-driven phase transitions. Physica A, 263:26–38, 1999.

2. Amir Haji-Akbari, Michael Engel, Aaron S. Keys, Xiaoyo Zheng, Rolfe Petschek, Peter Palffy-Muhoray, and Sharon C. Glotzer. Disordered, quasicrystalline and crystalline phase of densely-packed tetrahedra. Nature, 462:773-777, 2009.

3. D. Shechtman, I. Blech, D. Gratias, and J. W.Cahn. Metallic phase with long- range orientational order and no translational symmetry. Phys. Rev. Lett., 53:1951–1953, 1984.

4. Amir Haji-Akbari, Michael Engel, and Sharon C Glotzer. Degenerate quasicrystal of hard triangular bipyramids. Phys. Rev. Lett., 107:215702, 2011.

5. Amir Haji-Akbari, Michael Engel, and Sharon C Glotzer. Phase diagram of hard tetrahedra. J. Chem. Phys., 135:194101, 2011.