@Article{CiCP-17-1360,
author = {Kai Jiang, Weiquan Xu and Pingwen Zhang},
title = {Analytic Structure of the SCFT Energy Functional of Multicomponent Block Copolymers},
journal = {Communications in Computational Physics},
year = {2018},
volume = {17},
number = {5},
pages = {1360--1387},
abstract = {<p style="text-align: justify;">This paper concerns the analytic structure of the self-consistent field theory
(SCFT) energy functional of multicomponent block copolymer systems which contain
more than two chemically distinct blocks. The SCFT has enjoyed considered success
and wide usage in investigation of the complex phase behavior of block copolymers.
It is well-known that the physical solutions of the SCFT equations are saddle points,
however, the analytic structure of the SCFT energy functional has received little attention
over the years. A recent work by Fredrickson and collaborators [see the monograph
by Fredrickson, <em>The Equilibrium Theory of Inhomogeneous Polymers</em>, (2006), pp.
203–209] has analysed the mathematical structure of the field energy functional for
polymeric systems, and clarified the index-1 saddle point nature of the problem caused
by the incompressible constraint. In this paper, our goals are to draw further attention
to multicomponent block copolymers utilizing the Hubbard-Stratonovich transformation
used by Fredrickson and co-workers. We firstly show that the saddle point character
of the SCFT energy functional of multicomponent block copolymer systems may be
high index, not only produced by the incompressible constraint, but also by the Flory-Huggins
interaction parameters. Our analysis will be beneficial to many theoretical
studies, such as the nucleation theory of ordered phases, the mesoscopic dynamics.
As an application, we utilize the discovery to develop the gradient-based iterative
schemes to solve the SCFT equations, and illustrate its performance through several
numerical experiments taking ABC star triblock copolymers as an example.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.281113.271114a},
url = {http://global-sci.org/intro/article_detail/cicp/11015.html}
}