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Title: Understanding shape entropy through local dense packing

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. In this paper, 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 BT) 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.more » Finally, 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.« less
Authors:
 [1] ;  [1] ;  [1] ;  [1] ;  [2]
  1. Univ. of Michigan, Ann Arbor, MI (United States). Dept. of Chemical Engineering
  2. Univ. of Michigan, Ann Arbor, MI (United States). Dept. of Chemical Engineering. Dept. of Materials Science and Engineering
Publication Date:
Grant/Contract Number:
FG02-02ER46000; W911NF-10-1-0518; N00244-09-1-0062; PIOF-GA-2011-302490 Actsa
Type:
Accepted Manuscript
Journal Name:
Proceedings of the National Academy of Sciences of the United States of America
Additional Journal Information:
Journal Volume: 111; Journal Issue: 45; Journal ID: ISSN 0027-8424
Publisher:
National Academy of Sciences, Washington, DC (United States)
Research Org:
Univ. of Michigan, Ann Arbor, MI (United States)
Sponsoring Org:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22); US Army Research Office (ARO); USDOD; European Commission (EC)
Country of Publication:
United States
Language:
English
Subject:
36 MATERIALS SCIENCE; colloids; entropy; nanoparticles; self-assembly; shape
OSTI Identifier:
1348368

van Anders, Greg, Klotsa, Daphne, Ahmed, N. Khalid, Engel, Michael, and Glotzer, Sharon C.. Understanding shape entropy through local dense packing. United States: N. p., Web. doi:10.1073/pnas.1418159111.
van Anders, Greg, Klotsa, Daphne, Ahmed, N. Khalid, Engel, Michael, & Glotzer, Sharon C.. Understanding shape entropy through local dense packing. United States. doi:10.1073/pnas.1418159111.
van Anders, Greg, Klotsa, Daphne, Ahmed, N. Khalid, Engel, Michael, and Glotzer, Sharon C.. 2014. "Understanding shape entropy through local dense packing". United States. doi:10.1073/pnas.1418159111. https://www.osti.gov/servlets/purl/1348368.
@article{osti_1348368,
title = {Understanding shape entropy through local dense packing},
author = {van Anders, Greg and Klotsa, Daphne and Ahmed, N. Khalid and Engel, Michael and Glotzer, Sharon C.},
abstractNote = {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. In this paper, 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 (kBT) 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. Finally, 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.},
doi = {10.1073/pnas.1418159111},
journal = {Proceedings of the National Academy of Sciences of the United States of America},
number = 45,
volume = 111,
place = {United States},
year = {2014},
month = {10}
}