Systems far from equilibrium can exhibit complex transitory structures, even when equilibrium fluctuations are mundane1,2. A dramatic example of this phenomenon has recently been demonstrated for thin-film solutions of passivated nanocrystals during the irreversible evaporation of the solvent3,4,5,6,7,8,9,10,11,12,13,14. The relatively weak attractions between nanocrystals, which are efficiently screened in solution, become manifest as the solvent evaporates, initiating assembly of intricate, slowly evolving structures4. Although certain aspects of this aggregation process can be explained using thermodynamic arguments alone6, it is in principle a non-equilibrium process7. A representation of this process as arising from the phase separation between a dense nanocrystal ‘liquid’ and dilute nanocrystal ‘vapour’ captures some of the behaviour observed in experiments3, but neglects entirely the role of solvent fluctuations, which can be considerable on the nanometre length scale15. Here we present a coarse-grained model of nanoparticle self-assembly that explicitly includes the dynamics of the evaporating solvent. Simulations using this model not only account for all observed spatial and temporal patterns, but also predict network structures that have yet to be explored. Two distinct mechanisms of ordering emerge, corresponding to the homogeneous and heterogeneous limits of evaporation dynamics. Our calculations show how different choices of solvent, nanoparticle size (and identity) and thermodynamic state give rise to the various morphologies of the final structures. The resulting guide for designing statistically patterned arrays of nanoparticles suggests the possibility of fabricating spontaneously organized nanoscale devices.
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This work was supported by the United States–Israel Binational Science Foundation. L.E.B. is supported by the Columbia MRSEC. P.L.G. was an MIT Science Fellow throughout most of this work. D.R.R. is a Sloan Fellow and Camille Dreyfus Teacher-Scholar.
The authors declare that they have no competing financial interests.
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Rabani, E., Reichman, D., Geissler, P. et al. Drying-mediated self-assembly of nanoparticles. Nature 426, 271–274 (2003). https://doi.org/10.1038/nature02087
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