Lattice Self-consistent Field Calculations of Phase Behavior of Symmetric Star Block Copolymers AmBm Confined between Two Parallel Surfaces

We studied the lamellar structures formed by incompressible melts of symmetric star block copolymer (BCP) A(m)B(m) confined between two identical, homogeneous and parallel surfaces with their separation equal to the bulk lamellar period, using the self-consistent field calculations on a simple cubic lattice. All the star BCPs have the same chi N-AB value, where chi is the Flory-Huggins parameter characterizing the repulsion between two nearest-neighbor A and B segments, and N-AB is the number of segments on one pair of A- and B-arms. The effects of total chain length N and the number of A or B arms m in each A(m)B(m) chain on the lamellar structure and orientation were investigated in detail. We found that the normalized A-B interfacial widths of the confined lamellae increase with decreasing m at fixed N or N-AB = (N - 1)/m. The calculated Helmholtz free energy per chain shows that perpendicular lamellae are stable over parallel lamellae when the two confining surfaces are neutral. As the surface preference Lambda (e.g., for B-segments) increases, all systems exhibit a first-order phase transition from perpendicular to parallel lamellae. At a fixed m value, the star BCPs with smaller N have larger Lambda range to form perpendicular lamellae. At a fixed N (or N-AB), the star BCPs with larger m have larger Lambda range to form perpendicular lamellae. These findings may provide useful information for the lithographic applications of BCPs.