Eur. Phys. J. E (2009) 30: 361-369
https://doi.org/10.1140/epje/i2009-10534-3

Regular Article

Fast and accurate SCFT calculations for periodic block-copolymer morphologies using the spectral method with Anderson mixing

Department of Mathematics, University of Reading, Reading RG6 6AX, Whiteknights, UK

^* e-mail: m.w.matsen@reading.ac.uk

Received: 27 August 2009
Accepted: 13 October 2009
Published online: 3 December 2009

Abstract

We study the numerical efficiency of solving the self-consistent field theory (SCFT) for periodic block-copolymer morphologies by combining the spectral method with Anderson mixing. Using AB diblock-copolymer melts as an example, we demonstrate that this approach can be orders of magnitude faster than competing methods, permitting precise calculations with relatively little computational cost. Moreover, our results raise significant doubts that the gyroid (G) phase extends to infinite N . With the increased precision, we are also able to resolve subtle free-energy differences, allowing us to investigate the layer stacking in the perforated-lamellar (PL) phase and the lattice arrangement of the close-packed spherical ( S _cp phase. Furthermore, our study sheds light on the existence of the newly discovered Fddd ( O⁷⁰ morphology, showing that conformational asymmetry has a significant effect on its stability.