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Entropy favours open colloidal lattices

Abstract

Burgeoning experimental and simulation activity seeks to understand the existence of self-assembled colloidal structures that are not close-packed1,2,3,4,5,6,7,8,9. Here we describe an analytical theory based on lattice dynamics and supported by experiments that reveals the fundamental role entropy can play in stabilizing open lattices. The entropy we consider is associated with the rotational and vibrational modes unique to colloids interacting through extended attractive patches10. The theory makes predictions of the implied temperature, pressure and patch-size dependence of the phase diagram of open and close-packed structures. More generally, it provides guidance for the conditions at which targeted patchy colloidal assemblies in two and three dimensions are stable, thus overcoming the difficulty in exploring by experiment or simulation the full range of conceivable parameters.

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Figure 1: Examples of 2D open lattices.
Figure 2: Predicted entropy in 2D open colloidal structures and comparison with experiment.
Figure 3: Predicted phase diagram and comparison with experiment.
Figure 4: Predicted 3D structures.

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Acknowledgements

X.M. was supported by NSF under grant DMR-1104707. Q.C. and S.G. were supported by the US Department of Energy Division of Materials Science, under award number DE-FG02-07ER46471 through the Frederick Seitz Materials Research Laboratory at the University of Illinois at Urbana-Champaign. For equipment, we acknowledge the National Science Foundation, CBET-0853737. We thank K. Chen for help with particle tracking, and J. Whitmer and T. C. Lubensky for useful discussions.

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Contributions

X.M. and Q.C. initiated this work; X.M. developed the theory and did calculations based on the theory; Q.C. and S.G. designed and performed the experiment; X.M., Q.C. and S.G. wrote the paper.

Corresponding author

Correspondence to Xiaoming Mao.

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The authors declare no competing financial interests.

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Mao, X., Chen, Q. & Granick, S. Entropy favours open colloidal lattices. Nature Mater 12, 217–222 (2013). https://doi.org/10.1038/nmat3496

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