A single polymer chain can adopt countless conformations due to the flexibility of the C-C single bond, which allows rotational freedom. The idea came from a student who chose polymer behavior, like end-to-end distance or flexibility of the polymeric chain as a part of their Physics Class Project. With that, students are introduced to these principles through a random walk model, helping them connect abstract mathematical concepts to actual physical phenomena in polymer science.

Real-World Application: This project bridges theoretical modeling with practical engineering skills. For example, simplified models like random walk model is commonly used in Materials Science, Mathematics, Brownian Motion to approximate behaviors that otherwise require complex and rigorous computations. Through this project, students can explore real world applications in fields such as thermal conduction, structural analysis, and even epidemiology models. However, the model seems somewhat simplified but understanding its limitations is important in practical applications.

Model Limitations: Through the application of random walk model in polymeric chains, students realize that this model does not account for self-interaction (or overlapping steps, i.e. C-C chain collapsing in itself) or side chain electron restrictions in C-C bonds. However, understanding these limitations when simplifying complex systems, provide students with an opportunity to reflect on this and other instances where simplified models can effectively provide practical and viable solutions within the bounds of balanced accuracy.

Technical Depth and Background

This project was developed for students who have completed coursework in advanced mathematics (including vector analysis, multivariable calculus, physics) and introductory materials science. Although no perquisite was placed for statistical modeling, but a basic understanding of programming was required either in MATLAB or in Python. We found that this foundational knowledge supports understanding of vector-based calculations and material and chemical properties, making the project both accessible yet challenging.

Dimensionality of the Model

For now, the initial understanding of this model for this project is constrained to 2D only. For ambitious students, instructors may consider extending the project to 3D, bringing additional complexity to help challenge students to appreciate dimensional effects on polymer chain interactions.

Mindset Matters: 3Cs and KEEN Framework

• Curiosity: Students explore the connection and inclusion of mathematics, vector analysis and materials science by simulating random walks and investigating deviations from real polymer dynamics while realizing the practicality of the model.
• Connections: Through this project we encouraged students to connect simplified modeling in polymers to similar simplifications in engineering, fostering interdisciplinary thinking.
• Creating Value: By understanding the practical limitations of the simplified models, students learn to apply abstract concepts effectively, creating insights applicable across all engineering disciplines.