Diagram of the model used in our simulations.
(a) and (b) Snapshots of microphase-separated configurations taken from MD trajectories. Short and long brushes have heights of 4 and 8 monomers, respectively. From left to right: oblate spheroid, same configuration showing only the adsorbed monomers; prolate spheroid, same configuration showing only the adsorbed monomers. Long brushes concentrate on regions of high curvature, short brushes concentrate on flatter regions.
Pairs of phase-separated, three-striped configurations from thermodynamic integration simulations. Left pair (a and b): Oblate long-on-pole, oblate short-on-pole. Right pair (c and d): Prolate long-on-pole, prolate short-on-pole.
Free energy differences from simulation between opposite pairs of striped configurations on oblate and prolate spheroids. Snapshots of these pairs are shown in Fig. 3 . Pairs of oblate spheroids have positive values and pairs of prolate spheroids have negative values because the free energy difference is defined as ΔF = F LOP − F SOP . The line at zero height difference illustrates that the free energy for two equal-length brushes on different spheroids is the same regardless of the configuration.
Scaling picture of a polymer brush on a spheroid. ξ, the blob size, and h, the brush height, are functions of the polar angle θ, and depend on the radius of curvature at the grafting point.
(a) Free energy differences between pairs of three-striped configurations on oblate and prolate spheroids, using the analytical expression in Eq. (6) for the free energy of brushes on spheroids. Differences increase with eccentricity and with brush heights, in agreement with our results from simulations shown in Fig. 4 . (b) Free energy differences between pairs of striped configurations as a function of eccentricity for different number of stripes. With more stripes, the overall free energy gain decreases.
(a)–(c) Snapshots of phase-separated configurations taken from equilibrium MD trajectories. Only the adsorbed monomers are shown. Red monomers are from the long brush, yellow monomers are from the short brush. Systems spontaneously microphase-separate into configurations with long brushes on high curvature regions and short brushes on low curvature regions.
(a) Drawing of a Pac-Man-like surface with positive and negative curvature obtained by overlapping a large sphere of radius R 1 and a smaller sphere of radius R 2. The location of the center of the smaller sphere is such that R 2 = R 1sin α. (b) Phase diagram for the Pac-Man-like object depicted in Fig. 8 , showing phase-separated and mixed coexistence curves as a function of chain length ratio and chain mixing ratio. Phase separation occurs for values of to the right of the coexistence curves. As the length of the short chain decreases, phase separation occurs at lower volume fractions.
Snapshot from simulations of two miscible chains having different lengths while they phase separate on a surface with regions of positive and negative curvature. Red monomers correspond to the long chain, yellow to the short chain. The surface is defined by Eq. (11) .
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