Symmetric diblock copolymer thin films confined between homogeneous and patterned surfaces: Simulations and theory
J. Chem. Phys. 112, 9996 (2000); doi:10.1063/1.481635
Issue Date: 8 June 2000
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We have investigated the ability of a simple phenomenological theory to describe the behavior of symmetric diblock copolymer thin films confined between two hard surfaces. Prior knowledge of the morphology in the confined films is crucial for applying this theory to predict the phase diagram of such systems. Taking advantage of our observations in Monte Carlo simulations, we use the theory to construct phase diagrams for thin films confined between patterned-homogeneous surfaces, and obtain good agreement with our results of simulations. Two conditions are essential for obtaining long-range ordered perpendicular lamellae: a lower stripe-patterned surface with the surface pattern period Ls comparable to the bulk lamellar period L0, and an upper neutral or weakly preferential surface. We have also examined the undulation of perpendicular lamellae between two hard surfaces. For the cases of two homogeneous (preferential) surfaces and patterned-preferential surfaces, our calculations using the phenomenological theory indicate that the amplitudes of the undulation are on the same order of magnitude as observed in our Monte Carlo simulations, and are one order of magnitude larger than previously reported. The theory, however, is unable to capture the shape of the undulation. For the case of patterned-neutral surfaces, we find that an earlier analysis is unable to yield the undulations that would stabilize the perpendicular lamellar morphology. We have addressed this issue and obtained undulations that are consistent with our observations from Monte Carlo simulations. ©2000 American Institute of Physics.
| History: | Received 15 November 1999; accepted 13 March 2000 |
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- Strictly speaking, Eq. (21) only represents the hard surface confinement at the surfaces, but not near the surfaces. According to the assumptions that chain trajectories are perpendicular to the AB interface and that chains terminate at the interfaces between adjacent lamellae, the corresponding boundary conditions for the lower hard surface should be
and for the upper hard surface,
We find that the solution using Eq. (21) may not satisfy the above equations in some regions in the case of relatively strong surface preference, for example, the case of
H = 1 (
S = 2 and d = 4) studied in Sec. III B 1 and in Ref. 19. In Fig. 6 such a region is shown by a thick dashed line. Note, however, that perpendicular lamellae are not actually preferred in this case. Therefore, this problem might be of little practical significance; the fixed boundary conditions Eq. (21) could be sufficient for the solution to satisfy the above equations when perpendicular lamellae are actually preferred.








