The self-assembly of asymmetric diblock copolymers confined within cylindrical pores is studied using the self-consistent-field theory. The cylinder-forming asymmetric diblock copolymer is chosen to be near the cylinder-gyroid phase boundary in the intermediate segregation region. This choice makes the self-assembled cylindrical structure highly deformable, leading to very rich morphologies under confinement. A rich variety of structures, such as helices, stacked toroids, and perforated tubes, is observed as a function of the degree of confinement characterized by the ratio between the pore diameter D and bulk period L (D/L) as well as pore surface-polymer interactions. The origin of these confinement-induced structures is elucidated. The theoretical results are in good agreement with available experimental observations.

We have used lattice Monte Carlo simulations to investigate the molecular assembly of symmetric diblock copolymer melts within cylindrical nanochannels. We studied the effect that the surface field has on the copolymer morphology in three cylinders having different diameters. Upon varying the strength of the surface field, we observed a variety of morphologies, including stacked-disk, single-helix, catenoid-cylinder, gyroidal, stacked-circle, and concentric cylindrical barrel structures. The results of these simulations should be helpful when designing polymeric nanomaterials confined in cylindrical nanochannels.

Self-assembly of cylinder-forming diblock copolymers under spherical confinement is studied using real-space self-consistent field theory calculations (SCFT). Various microstructures are found at different confinement dimensions and surface fields. Most of these microstructures are center-symmetric and they could not be formed in bulk or under planar and cylindrical confinements. It is also observed that the interactions between the confinement surface and the polymers have a large effect on the self-assembly. When the spherical confinement's surface attracts the short blocks, the self-assembled structures become similar to those under a neutral surface field. On the other hand, when the spherical confinement's surface attracts the long blocks, the equilibrium structures become different from those under a neutral surface field.

The strategy of constraining the lepton flavor mixing from remnant CP symmetry is investigated in a rather general way. The neutrino mass matrix generally admits four remnant CP transformations which can be derived from the measured lepton mixing matrix in the charged lepton diagonal basis. Conversely, the lepton mixing matrix can be reconstructed from the postulated remnant CP transformations. All mixing angles and C\P-violating phases can be completely determined by the full set of remnant CP trans formations or three of them. When one or two remnant CP transformations are preserved, the resulting lepton mixing matrix would depend on three real parameters or one real parameter, respectively, in addition to the parameters characterizing the remnant CP. The concrete form of the mixing matrix is also presented. The phenomenological predictions for the mixing parameters are discussed. The conditions leading to vanishing or maximal Dirac CP violation are studied.