Kelvin's Tetrakaidecahedron as a Wigner–Seitz Cell Found in Spherically Microphase-Separated BCC Lattice from AB Diblock Copolymer by Monte Carlo Simulation

Abstract

Metropolis Monte–Carlo simulation is carried out for microphase-separated bulk state of AB diblock copolymers with various compositions. The distribution probability of end segments in long B-block chain are explored to determine the Wigner–Seitz(WS) cells as primitive cells for four known periodic structures, lamellar-, Gyroid-, cylindrical-, and spherical ones. The end segments are commonly turned to be localized at the several distinct far sites from the lattice points of WS cells for all morphologies investigated. Among them, when the fraction of A segments is 0.25, a hexagonal prism type column appears as a WS, while when the fraction is much lower at 0.1, body-centered cubic(BCC) lattice is formed and its end segments are found to be localized at hexagonal frames and also on the six square faces of truncated octahedron or Kelvin's Tetrakaidecahedron(KT), which has rarely been found in real soft material ever. This achievement is strongly pointing that each micelle formed by self-assembled diblock coplymers in bulk have essentially the framework of equivolume KT in real material systems.