Ring-like curved surfaces confined

SSL theory for diblock copolymers confined in ring-like curved surfaces... 

Figure 30 shows the symmetrical concentric-ring barrel structure (A-B-A)m confined between two ring-like curved surfaces (cylinders). It is assumed that the fringe thickness is the same for both the exterior and interior layers, while that of the middle layers is nearly twice in size regardless of A domain or B domain. This assumption has been proved to be valid via MC simulation mentioned above. 

In this work, a framework of the SSL theory for diblock copolymer melts confined in ring-like curved surfaces has been proposed. When the curvature approaches to zero, it reduces to the well-known SSL theory for the parallel lamellar phases. In the case of the equal confined thickness to the exterior radius, it can also be extended to the system with a nanopore confinement. Moreover, the Helmholtz energy of the concentric cylinder barrel, sector column and CMSC phases in 2D confinements based on this SSL theoretical framework can be evaluated in the convenient manner. The calculated results show that the diblock copolymer melts exhibit a layer-type transition with a similar mechanism, regardless of ring-like curved surfaces, planar surfaces, and nanopores. 

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