We examine nucleation of the stable body-centred-cubic (BCC) phase from the metastable uniform disordered phase in an asymmetric diblock copolymer melt. Our comprehensive, large-scale simulations of the time-dependent, mean-field Landau-Brazovskii model find that spherical droplets of the BCC phase nucleate directly from disorder. Near the order-disorder transition, the critical nucleus is large and has a classical profile, attaining the bulk BCC phase in an interior that is separated from disorder by a sharp interface. At greater undercooling, the amplitude of BCC order in the interior decreases and the nucleus interface broadens, leading to a diffuse critical nucleus. This diffuse nucleus becomes large as the simulation approaches the disordered phase spinodal. We show that our simulation follows the same nucleation pathway that Cahn and Hilliard found for an incompressible two-component fluid, across the entire metastable region. In contrast, a classical nucleation theory calculation based on the free energy of a planar interface between coexisting BCC and disordered phases agrees with simulation only in the limit of very small undercooling; we can expand this region of validity somewhat by accounting for the curvature of the droplet interface. A nucleation pathway involving a classical droplet persists, however, to deep undercooling in our simulation, but this pathway is energetically unfavourable. As a droplet grows in the simulation, its interface moves with a constant speed, and this speed is approximately proportional to the undercooling.
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A high-accuracy self-consistent mean-field theory calculation [M. W. Matsen, Eur Phys. J. E 30, 361 (2009) and Macromolecules 45, 2161 (2012)] indicates that the direct DIS-to-BCC transition is interrupted by a very narrow region of hexagonally close-packed (HCP) micelles for fA < 0.24. Neither the HCP phase, nor the FCC phase [Y.-Y. Huang, J.-Y. Hsu, H.-L. Chen, and T. Hashimoto, Macromolecules 40, 406 (2007)], appear in our simulations of nucleation, which are performed at fA = 0.386.
We use the parameters given in R. K. W. Spencer, Ph.D. thesis, University of Guelph, Guelph, Ontario, Canada, 2014, and the formula for χ for SI in Ref. 50, with N = 200. The region where the nucleus is classical, Δτ < 2.5 × 10−4, corresponds to an undercooling of about 1 K, for fA = 0.386 (γ = 0.1). For fA = 0.2 (γ = 0.3), relevant to Ref. 50, the estimate becomes 8 K, assuming the width of the CNT region grows as γ2.
