Understanding shape entropy through local dense packing
Engel M, van Anders G, Klotsa D, Ahmed NK, Glotzer SC (2014)
Publication Language: English
Publication Status: Published
Publication Type: Journal article, Original article
Publication year: 2014
Journal
Publisher: National Academy of Sciences
Book Volume: 111
Pages Range: E4812-E4821
Journal Issue: 45
Abstract
Entropy drives the phase behavior of colloids ranging from dense suspensions of hard spheres or rods to dilute suspensions of hard spheres and depletants. Entropic ordering of anisotropic shapes into complex crystals, liquid crystals, and even quasicrystals was demonstrated recently in computer simulations and experiments. The ordering of shapes appears to arise from the emergence of directional entropic forces (DEFs) that align neighboring particles, but these forces have been neither rigorously defined nor quantified in generic systems. Here, we show quantitatively that shape drives the phase behavior of systems of anisotropic particles upon crowding through DEFs. We define DEFs in generic systems and compute them for several hard particle systems. We show they are on the order of a few times the thermal energy (k(B)T) at the onset of ordering, placing DEFs on par with traditional depletion, van der Waals, and other intrinsic interactions. In experimental systems with these other interactions, we provide direct quantitative evidence that entropic effects of shape also contribute to self-assembly. We use DEFs to draw a distinction between self-assembly and packing behavior. We show that the mechanism that generates directional entropic forces is the maximization of entropy by optimizing local particle packing. We show that this mechanism occurs in a wide class of systems and we treat, in a unified way, the entropy-driven phase behavior of arbitrary shapes, incorporating the well-known works of Kirkwood, Onsager, and Asakura and Oosawa.
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APA:
Engel, M., van Anders, G., Klotsa, D., Ahmed, N.K., & Glotzer, S.C. (2014). Understanding shape entropy through local dense packing. Proceedings of the National Academy of Sciences of the United States of America, 111(45), E4812-E4821. https://dx.doi.org/10.1073/pnas.1418159111
MLA:
Engel, Michael, et al. "Understanding shape entropy through local dense packing." Proceedings of the National Academy of Sciences of the United States of America 111.45 (2014): E4812-E4821.
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