858 resultados para Triangle Inequality
Resumo:
By using a combinatorial screening method based on the self-consistent field theory, we investigate the equilibrium morphologies of linear ABCBA and H-shaped (AB)(2)C(BA)(2) block copolymers in two dimensions. The triangle phase diagrams of both block copolymers are constructed by systematically varying the volume fractions of blocks A, B, and C. In this study, the interaction energies between species A, B, and C are set to be equal. Four different equilibrium morphologies are identified, i.e., the lamellar phase (LAM), the hexagonal lattice phase (HEX), the core-shell hexagonal lattice phase (CSH), and the two interpenetrating tetragonal lattice phase (TET2). For the linear ABCBA block copolymer, the reflection symmetry is observed in the phase diagram except for some special grid points, and most of grid points are occupied by LAM morphology. However, for the H-shaped (AB)(2)C(BA)(2) block copolymer, most of the grid points in the triangle phase diagram are occupied by CSH morphology, which is ascribed to the different chain architectures of the two block copolymers. These results may help in the design of block copolymers with different microstructures.
Resumo:
By using a combinatorial screening method based on the self-consistent field theory (SCFT) for polymers, we have investigated the morphology of H-shaped ABC block copolymers (A(2)BC(2)) and compared them with those of the linear ABC block copolymers. By changing the ratios of the volume fractions of two A arms and two C arms, one can obtain block copolymers with different architectures ranging from linear block copolymer to H-shaped block copolymer. By systematically varying the volume fractions of block A, B, and C, the triangle phase diagrams of the H-shaped ABC block copolymer with equal interactions among the three species are constructed. In this study, we find four different morphologies ( lamellar phase ( LAM), hexagonal lattice phase ( HEX), core-shell hexagonal lattice phase (CSH), and two interpenetrating tetragonal lattice (TET2)). Furthermore, the order-order transitions driven by architectural change are discussed.
Resumo:
Geometries, vibrational frequencies, electron affinities, ionization potentials and dissociation energies of the title clusters in both neutral and positively and negatively charged states were studied by use of density functional theory. For both neutral and charged species, different initial isomers were studied in order to determine the structure with the lowest energy. Vibrational analysis was also performed in order to characterize these isomers. For Ta-2, Ta-Ta metallic bond is strengthened by adding or removing an electron, i.e. the charged species are much more stable than the neutral counterpart. For Ta-3, equilateral triangle with D-3h symmetry has the lowest energy for both neutral and charged species (near equilateral triangle for cation). TaO and its charged species have much larger dissociation energy compared with other tantalum oxides. For Ta2O and TaO2. structure with C-2v symmetry is much more stable than linear chains. For Ta3O, planar structure with doubly bridging oxygen atoms of C-2v, symmetry is the global minimum for both neutral and charged species. While for TaO3, three-dimensional structures are favored for both neutral (C-1 symmetry) and charged species (C-3v symmetry).