Cell dynamics simulations of curvature driven grain boundary migration using halfloop bicrystal geometry
Abstract
Experiments on thin films of sphereforming diblock copolymers demonstrate that at late times, the orientational correlation length ξ_{6} of the hexagonal pattern in these systems follows a power law in time, ξ_{6} ∼ t^α, with α = 0.25. In an effort to understand this unusually low coarsening exponent, we have modeled the system using cell dynamics simulations based on the time dependent GinzburgLandau equation and the CahnHilliard model. In simulations of coarsening from random disorder, we find that the coarsening exponent α varies roughly linearly from 0 to 0.5 with the amount of noise η. We have also performed simulations using the halfloop bicrystal geometry of Shvindlerman et al., in which we measure the steadystate velocity v of grain boundaries as a function of their curvature κ. Where the standard result predicted by absolute reaction rate theory is v ∼ κ, we instead find v ∼ κ^m, where m ≥ 1, again depending on η. We further find that for different noise levels, the two different exponents are related by α = (m + 1)^{1}, suggesting that the anomalously slow ξ_{6} ∼ t^0.25 coarsening is a consequence of the peculiar scaling of curvature driven grain boundary velocity.
 Publication:

APS March Meeting Abstracts
 Pub Date:
 March 2004
 Bibcode:
 2004APS..MARU29004T