Broadly accessible SCFT for block polymer materials discovery

This website accompanies the paper:

Akash Arora, Jian Qin, David C. Morse, Kris T. Delaney, Glenn H. Fredrickson, Frank S. Bates and Kevin D. Dorfman, "Broadly accessible self consistent field theory for block polymer materials discovery," Macromolecules 49, 4675-4690 (2016). pdf

This is an open access article published under an ACS AuthorChoice License, which permits copying and redistribution of the article or any adaptations for non-commercial purposes.

The problem

Many fields of condensed matter physics have robust, widely distributed software that is used by experimentalists in the design of experiments and interpretation of data. Key examples include Lumerical FDTD for plasmonics, ANSYS for fluid mechanics, and COMSOL for a wide variety of typical physical phenomena. 

This is not the case for modeling the phase behavior of block polymers. Here, the key computational tool is self-consistent field theory (SCFT). While the methodology is well developed and known within the polymer community, there are two key barriers limiting its widespread use:

The computational barrier: Efficient SCFT calculations require a relatively sophisticated inner loop, comprising time integration along the time contour using a half-stepping algorithm and a pseudo-spectral method (via fast Fourier transform), and an outer global optimization loop. While these tools are not a major obstacle for groups well versed in computation, they are a significant barrier to entry for new users, particularly those without computational expertise.

The implementation barrier:  A single SCFT calculation obtains a local free energy minimum for a given polymer chemistry. The challenge is that there are many such local minima, so starting from an arbitrary initial condition rarely leads to the desired ordered phase. As such, it is difficult for a new user (and sometimes even an experienced user) to compare the free energies of different candidate phases to determine which has the lowest free energy (the thermodynamically stable state). 

Our solution

This website, along with the accompanying paper, aim to address both the computational barrier and the implementation barrier, thereby making SCFT an easily accessible tool for new users, in particular those working in experimental groups.

The computational solution: We have made several improvements to the open-source Polymer Self-Consistent Field (PSCF) code that allow for (i) computing the equilibrium composition for complicated phases, like the Frank-Kasper σ phase, using modest desktop resources and (ii) interface with our initialization algorithm. A compiled executable for OS X and a binary installer for Linux are available on the software page of this website. You can get started with SCFT with a simple double-click. We also have an executable for linux and the source code is openly available

The implementation solution: We have developed a protocol that allows users to start from a typical experimental scenario that includes the structure factor and symmetry of an ordered phase, as well as the form factor for particles in the ordered phase. We have developed software that converts this information into inputs for PSCF, which then refines the initial data into the local SCFT free energy minimum.  We also have a level set method for handling network phases, like gyroid. Importantly, the initial inputs only need to be approximate. The examples page has step-by-step instructions for our protocol for several different phases in diblock polymers and tetrablock terpolymers. 

What is available on this website?

This website consists of four major sections:

  1. The development of this website was motivated by a DMREF grant from the National Science Foundation as part of the Materials Genome Initiative. The MGI tab provides more information about our project, including novel tools that may eventually be included. 
  2. The key theoretical basis is self-consistent field theory, which is described qualitatively on the SCFT tab. The idea here is explain why the calculation is challenging, without getting into either the mathematical or numerical details. We also provide background on our initialization approaches, as well as the Polymer Self-Consistent Field code used for our calculations. 
  3. In order to implement SCFT, you will need to have the relevant software. We have a dmg file that you can easily install on OSX, a linux distribution, and related software that runs in Matlab. We are sorry if you are running Windows - this version is still a work in progress.
  4. The various examples from our paper are described in detail on the examples tab. These include particle-forming phases in diblock polymers and tetrablock terpolymers, as well as a level set example for the gyroid phase. As we produce more examples, we will add them to the examples tab. 

A more detailed, formal description of the content of this website appears in our paper.