The diagonal bond method: A new lattice polymer model for simulation study of block copolymers

Abstract

A new approach to an old algorithm for the Simulation of Isinglike Systems

Discovering New Ordered Phases of Block Copolymers

“…More important, it removes any possible constraints imposed by the fixed cell dimension on a periodic microphase, which generally create strains in the system and, thus, bias the system toward structures with lower strain energy. This point has been clearly demonstrated in Monte Carlo simulations of lattice models where it was shown that certain patterns appear only at a particular box size [7].…”

“…This limitation is especially accentuated when exploring the large parameter space and various molecular designs of multiblock copolymers. On the other hand, Monte Carlo simulation methods, though free of assumptions about the symmetry of the phases, are computationally expensive and limited by finite size effects [6,7].In this paper we propose an alternative approach for studying the morphology of multiblock copolymers without the need to assume the symmetry of the ordered phase. Drolet and Fredrickson [8] have recently proposed a numerical implementation of SCF theory that, similarly, does not require the assumption of the microphase symmetry.…”

“…This limitation is especially accentuated when exploring the large parameter space and various molecular designs of multiblock copolymers. On the other hand, Monte Carlo simulation methods, though free of assumptions about the symmetry of the phases, are computationally expensive and limited by finite size effects [6,7].…”

A mesoscopic Archimedean tiling having a new complexity in an ABC star polymer

“…1b), being assumed that three polymer chains are totally incompatible and all chains are long enough. For this three-component polymeric system, theoretical work by Dotera and Hatano 14 pointed out the formation of hexagonal (6 3 ) pattern, while Bohbot-Raviv and Wang 15 reported on ( 6 3 ) and (4.8 2 ) structures. Later it has been summarized that only three patterns, (6 3 ), (4.8 2 ), and (4.6.12), are allowed to exist, since only three polygons should meet on a vertex and only even polygons should appear as proposed in the even polygon theorem.…”

“…16 Of course, real structures have curved domain boundaries and volume fractions are not exactly the same as those of the surface fractions of the Archimedean tilings. However, using the idea of the minimal fundamental triangles, 14 it is easily shown that these three Archimedean tilings are representatives of the real structures. As for experimental results, (4.8…”