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Stability of the Gyroid Phase in Diblock Copolymers at Strong Segregation

Eric Cochran, Chemical and Biological Engineering, Iowa State University, 1035 Sweeny Hall, Ames, IA 50011-2230, Carlos J. Garcia-Cervera, Department of Mathematics, University of California, Santa Barbara, Santa Barbara, CA 93106-5121, and Glenn H. Fredrickson, Materials Research Laboratory, University of California, Santa Barbara, Santa Barbara, CA 93106-5121.

We report high resolution self-consistent field theory (SCFT) calculations that show the gyroid phase, Q230, to be stable in conformationally symmetric linear diblock copolymer melts prepared within the strong segregation regime, cN = 100, over a composition window of ~ 1.5%. This window broadens with the introduction of conformational asymmetry. The SCFT equations were solved using a novel pseudospectral approach with a plane wave basis and periodic boundary conditions. Saddle point field configurations were obtained using a semi-implicit Seidel relaxation algorithm. The modified diffusion equation was solved using a fourth-order backward differentiation formula and implicit treatment of the Laplacian operator. Our calculations are consistent with recent experimental observations of Q230 in strongly segregated diblocks.