Eur. Phys. J. E (2014) 37: 18
https://doi.org/10.1140/epje/i2014-14018-1

Regular Article

Self-consistent field theory of block copolymers on a general curved surface

The State Key Laboratory of Molecular Engineering of Polymers, Department of Macromolecular Science, Fudan University, 200433, Shanghai, China

^* e-mail: lijf@fudan.edu.cn

Received: 20 July 2013
Revised: 17 December 2013
Accepted: 17 March 2014
Published online: 26 March 2014

Abstract

In this work, we propose a theoretical framework based on the self-consistent field theory (SCFT) for the study of self-assembling block copolymers on a general curved surface. Relevant numerical algorithms are also developed. To demonstrate the power of the approach, we calculate the self-assembled patterns of diblock copolymers on three distinct curved surfaces with different genus. We specially study the geometrical effects of curved surfaces on the conformation of polymer chains as well as on the pattern formation of block copolymers. By carefully examining the diffusion equation of the propagator on curved surfaces, it is predicted that Gaussian chains are completely unaware of the extrinsic curvature but that they will respond to the intrinsic curvature of the surface. This theoretical assertion is consistent with our SCFT simulations of block copolymers on general curved surfaces.