Anisotropic fluctuations, ordered block copolymers

Shi A C, Noolandi J and Desai R C 1996 Theory of anisotropic fluctuations in ordered block copolymer phases Macromolecules 29 6487... 

The mean-field SCFT neglects the fluctuation effects [131], which are considerably strong in the block copolymer melt near the order-disorder transition [132] (ODT). The fluctuation of the order parameter field can be included in the phase-diagram calculation as the one-loop corrections to the free-energy [37,128,133], or studied within the SCFT by analyzing stability of the ordered phases to anisotropic fluctuations [129]. The real space SCFT can also applied for a confined geometry systems [134], their dynamic development allows to study the phase-ordering kinetics [135]. 

Because of the softness of interactions in block copolymers (here we restrict our consideration to flexible molten blocks above the glass transition temperature), thermal fluctuation in these systems is expected to be significant, especially near the order-disorder transition temperatures (Fredrickson and Helfand, 1987). In addition, the long relaxation times, due to the slowness of the motion of polymers, often lead to metastable and other kinetic states. Thus, full understanding of the self-assembly in block copolymers requires understanding of the nature of fluctuation, metastability, and kinetic pathways for various transitions. Most of this article is focused on theoretical studies of these issues in the simpler AB block copolymers. A key concept that emerges from these studies is the concept of anisotropic fluctuations first, these fluctuations determine the stability limit of an ordered phase second, they are responsible for the emergence of new structures... 

Fig. 3. Computer simulation results using a time-dependent Ginzburg-Landau approach, showing the microstructural evolution after a temperature jump from the lamellar phase to the hexagonal cylinder phase for a moderately asymmetric diblock copolymer. The time units are arbitrary. (Reprinted with permission from Polymer 39, S. Y. Qi and Z.-G. Zheng, Weakly segregated block copolymers Anisotropic fluctuations and kinetics of order-order and order-disorder transitions, 4639-4648, copyright 1998, with permission of Excerpta Medica Inc.)...

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