(a) Monolayer of block-copolymer spherical micelles with a near-neighbor spacing of confined between two conducting plates separated by a distance of . (b) An applied voltage creates an external field of strength , transforming the spherical nanodomains into perpendicular cylinders.
Region denotes the conditions under which a monolayer of hexagonally packed spheres has a lower free energy than either disordered or cylindrically ordered films, in the case of no external electric field. Most of our calculations focus on the point and denoted by the cross, but we also investigate the effects from changes in segregation and composition along the two dotted paths.
Deformation of a spherical nanodomain [defined by ] as the electric-field strength is increased. Note that the hexagonal packing of the domains has little effect on the rotational symmetry about their vertical axes. Therefore, we only show a single cut through the sphere, where the horizontal axis points in the direction of a nearest neighbor.
Free energy along the kinetic pathway from the minimum corresponding to a monolayer of spheres up to the top of the energy barrier , and down to the minimum corresponding to perpendicular cylinders , plotted for external electric fields of various strengths . All four paths are calculated for block-copolymer films of segregation and composition , with a dielectric contrast of .
Evolution of the minority domain along the kinetic pathway shown in Fig. 4 for the field strength of . The positions , , and along the pathway correspond to the free-energy minimum of the phase, the top of the energy barrier, and the minimum of the phase, for which the free energies are denoted by , , and , respectively.
(a) Energy barrier, , preventing the transformation from spheres to cylinders and (b) relative stability of the cylinders, , plotted as a function of increasing field strength for several values of the dielectric contrast . To combine results for different , the horizontal axes have been scaled by .
(a) Energy barrier, , preventing the transformation from spheres to cylinders and (b) relative stability of the cylinders, , plotted as a function of segregation for several different field strengths . The diblock composition and dielectric contrast are fixed at and , respectively. (c) Number of molecules per nanodomain (solid curve) along with the dimensions of its unit cell (dashed curves).
Analogous plots to those in Fig. 7, but showing the effect of changing the diblock-copolymer composition . In order that the monolayer of spheres remains stable under zero electric field, the segregation is adjusted according to , which is denoted by a dotted curve in Fig. 2.
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