  The order-disorder transition of a sphere-forming block copolymer thin film
was numerically studied through a Cahn-Hilliard model. Simulations show that
the fundamental mechanisms of pattern formation are spinodal decomposition and
nucleation and growth. The range of validity of each relaxation process is
controlled by the spinodal and order-disorder temperatures. The initial stages
of spinodal decomposition are well-approximated by a linear analysis of the
evolution equation of the system. In the metastable region, the critical size
for nucleation diverges upon approaching the order-disorder transition, and
reduces to the size of a single domain as the spinodal is approached. Grain
boundaries and topological defects inhibit the formation of superheated phases
above the order-disorder temperature. The numerical results are in good
qualitative agreement with experimental data on sphere-forming diblock
copolymer thin films.
