Cubic phases of block copolymers under shear and electric fields by cell dynamics simulation. I. Spherical phase

Abstract

Cell dynamics simulation is used to investigate pathways of sphere-to-cylinder transition in block copolymer melt under applied simple shear flow and electric field. Both fields can induce the transition when their strength is above some critical value. At weak fields the spherical phase is preserved, with spheres being deformed into ellipsoids. Weak shear flow is found to improve order in the spherical phase. Observed sliding of layers of spheres under shear is very similar to the experimental finding by Hamley et al. [J. Chem. Phys. 108, 6929 (1998)]. The kinetic pathways are sensitive to the degree of microphase separation in the system and hence affected by temperature. The details of the pathways are described by means of Minkowski functionals.

Mechanisms of electric-field-induced alignment of block copolymer lamellae

“…The time evolution of the order parameter is given by the Cahn-Hilliard-Cook (or the time-dependent Ginzburg-Landau) equation, [10][11][12][13][14][15][16][17][18] which in the presence of an applied electric field (along the y direction) becomes:…”

“…We implement a Ginzburg-Landau approach in a cell dynamics simulation (CDS), which is a very fast computational technique [10][11][12][13][14][15][16][17][18] and can serve as a research precursor for more elaborate but slow methods like SCFT. For a symmetric AB diblock copolymer the structure can be described by an order parameter …”

Diblock copolymer sphere morphology in ultra thin films under shear

“…We observe that as the shear proceeds, the overall number of spheres slightly drops, analogous to what we observed before for the sheared spheres in the bulk. 18 Therefore, there is a similarity between the defect annihilation kinetics in the films of two layers and in the two neighbouring layers in the bulk.…”

“…Fig. 4d shows the Euler characteristic (one of the Minkowski functionals 18 ), which in this case is equal to the number of spheres. We observe that as the shear proceeds, the overall number of spheres slightly drops, analogous to what we observed before for the sheared spheres in the bulk.…”

“…16 Cell dynamics simulation (CDS) of larger simulation boxes confirmed these findings and also found alignment of spheres in hexagonally packed sliding layers. 18 Molecular dynamics simulation of a bilayer film revealed shear-induced ordering of hexagonally arranged spheres in a shear flow.…”