Simulating the Structure of Amorphous Polymers via the Random Walk Model
Class: Mathematical Methods for Materials Science (3.016), continued through Fundamentals of Scientific Programming (aka Code Your Major) (3.s06)
Term: Fall 2017, continued through Winter 2018
The structure of an amorphous polymer resembles a random walk. This work examines random walks of varying complexity, culminating with a three-dimensional self avoiding, variable angle random walk.
Monomer tacticity and R-group length affect a polymer's ability to form dense, semi-crystalline regions. Both of these factors, by extension, limit the angle at which a monomer can attach to a previous monomer, thereby limiting the variable angle walk. Root mean square (RMS), the average spatial dimension traversed by a polymer from end to end, increases as bond angle increases. This is observed via simulation.
Modeled in Mathematica by Sara L. Wilson.