Using numerical simulations and a simple scaling theory, we study the microphase separation of a mixture of polymer brushes with different chain lengths tethered to surfaces with nonuniform curvature. We measure the free energy difference of the phase separated configurations as a function of spheroid eccentricity and ordering of the microdomains formed on them. We find that there is a preference for the longer chains to locate in high curvature regions, and identify and quantify the driving forces associated with this phenomenon. We also find that nonuniform curvature typically limits the number of striped domains that would normally form on a spherical surface under identical physical conditions. Finally, we generalize the scaling theory developed for brushes on spherical surfaces to include prolate and oblate spheroids, and show explicitly that while immiscibility between the chains is required for phase separation to occur on spheroids, it is unnecessary for certain surfaces with regions of positive and negative curvature. We present a phase diagram showing the conditions under which curvature-driven phase separation of miscible, but lengthwise asymmetric chains is expected to occur.
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