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Modeling the anisotropic self-assembly of spherical polymer-grafted nanoparticles
17.G. Malescio and G. Pellicane, Nature Mater. 2, 93 (2003).
24.P. Akcora, H. Liu, S. K. Kumar, J. Moll, Y. Li, B. C. Benicewicz, L. S. Schadler, D. Acehan, A. Z. Panagiotopoulos, V. Pryamitsyn, V. Ganesan, J. Ilavsky, P. Thiyagarajan, R. H. Colby, and J. F. Douglas, Nature Mater. 8, 354 (2009).
26.We note that this form is a pure mean-field expression, whereas the other scaling expressions used include phenomenological corrections for the fluctuation/blob picture. This inconsistency is expected to only marginally modify the phase diagrams presented.
28.The in the theoretical model represents the energy gained on contact between the particles. Explicitly, it is related, but not identical, to the used in simulations.
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Recent experimental results demonstrated that polymer grafted nanoparticles in solvents display self-assembly behavior similar to the microphase separation of block copolymers and other amphiphiles. We present a mean-fieldtheory and complementary computer simulations to shed light on the parametric underpinnings of the experimental observations. Our theory suggests that such self-assembledstructures occur most readily when the nanoparticle size is comparable to the radius of gyration of the polymer brush chains. Much smaller particle sizes are predicted to yield uniform particle dispersions, while larger particles are expected to agglomerate due to phase separation from the solvent. Selected aspects of our theoretical predictions are corroborated by computer simulations.
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