We will verify the PolyFTS calculation by comparing to the Polyorder results. The SCFT model we will test is miktoarm star block copolymer and homopolymer blends (AB3 + A).

# Polyorder Configuration File

The configuration file for Polyorder can be either in INI or in YAML format. Sample configuration files can be found in the `example`

folder in the Polyorder project.

# Simpson's Rule and Other Fourth-Order Quadrature Formulas

## 1. Closed formulas

By dividing the closed interval into uniform subintervals with length of , the extended Simpson’s rule is given by (1)

where for , and is in . The number of points, , must be **odd**, meaning that there are even number of subintervals. This requirement is a consequence of the fact that the coefficients alternate in a specific pattern, namely there are pairs of coefficient terms plus an extra -coefficient term and two end-point terms. Therefore, there are terms in total, while is always odd.

# mpltex: A Tool for Creating Publication Quality Plots

Creating a publication-quality plot is not an easy job. One needs to consider a dozen of factors:

- The figure size should be set explicitly to match journal specific value. For exmaple, journals published by American Chemical Society (ACS) allows a maximum 3.25-inch width figure for single-column and a maximum 7-inch width figure for double-column.
- The font family should be customized. Most of the time, “Times New Roman” is a safe choice. You should consult the journal author guide for more information.
- The font size also needs to be set properly.
- The linewdith of axis, axis ticks, line arts, the format of legend, the colors are all important factors affects the final looking of a plot.
- The file format of a figure should be chosen carefully. For most publishers, EPS is a good choice for line arts and other simple 2D arts, such as histograms, power spectra, bar charts, errorcharts, scatterplots.

# A Quick Guide to the Self-Consistent Field Theory in Polymer Physics

## 1. Introduction

The self-consistent field theory (SCFT) for many-chain systems is obtained by imposing a mean-field approximation to simplify the statistical field theories. The statistical field theories can be constructed from the particle-based model by carrying out a particle-to-field transformation.

The general approach for a particle-to-field transformation is to invoke formal techniques related to Hubbard-Stratonovich transformations, which have the effect of decoupling interactions among particles (or polymer segments) and replacing them with interactions between the particles and one or more auxiliary fields.