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note
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While the absolute free energies of the structures are sensitive to the discretization used, the differences between free energies are only slightly influenced by discretization. As a consequence, the phase boundaries are not significantly changed. In our study of intermediate structures, we find that the shift in the absolute free energies is smaller on going from a 256 × 256 lattice to a 512 × 512 lattice than it is on going from a 128 × 128 lattice to a 256 × 256 lattice.
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31644448969
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note
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B = q = q† = 0 is imposed at these lattice points. We have chosen this approach over other approaches which use incompressibility conditions that smoothly approach zero as the pore wall is approached (ref 5, for example) for simplicity.
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31644439383
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note
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We caution the reader that we use the word "cylinders" only as a convenient term to describe these domains. Although these structures exist in a parameter region that overlaps with the region where hexagonally coordinated cylinders are in equilibrium in the bulk phase diagram, our two-dimensional study does not determine whether in three dimensions, under confinement, these domains are cylinders, spheres, helices, or some other three-dimensional morphology.
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