Simulation of grain coarsening of block copolymer cylindrical microdomains which are perpendicularly oriented by using the phase field crystal model

Abstract

We have conducted computer simulation to understand the feature of the grain coarsening of polymer microdomains. For this purpose, the phase field crystal model was utilized with the conserved potential field and perpendicularly oriented cylindrical microdomains were simulated, being evoluted from the disordered state. As a result, the power-law behavior was confirmed as the grain size is proportional to t¡, where t is the simulation time. The growth exponent ¡ was further found to be dependent on the noise strength ¦ in the simulation. Two different power-law behaviors were found for early and late stages for all of the results except for zero noise strength for which a single power-law behavior was observed over the entire time range. ¡ increased from 0.16 to 0.33 (for the late stage) with increasing noise strength. Although the result (0.16 ≤ ¡ ≤ 0.33) contradicts our previous experimental result (¡ = 0.45) obtained by atomic force microscopy and small-angle X-ray scattering [Polymer Journal, 2017, 49, 655.], simulated images are rigorously examined to understand the features of the grain coarsening. The following features are found. First of all, not only point defects but also line defects can exist in a grain. Both of them can trigger to create a new grain boundary or a small grain. Such formation of small grains was just transient so that they disappeared immediately. The reason why such transient grains are necessarily formed may be due to an instability in larger grains in the course of their growth. Such instability is caused by the localized energy due to a heavy distortion of the hexagonal lattice. As an example of the slow process of grain coarsening, it is suggested that slow movement of the grain boundaries can be driven by the change of the position of individual cylinders from the original grain to a neighboring grain. Furthermore, heavily curved grain boundaries are forced to be immediately straightened due to the high energy of the bent grain boundaries. Thus, we can recognize that the grain coarsening is driven by a dynamic movement and exchange of grain boundaries, as we have speculated in our previous publication.