Module 9 Star and branched polymers

What do star and branched polymers look like? How do their radii of gyration change with the degree of polymerization?

2 Module objectives

  • Compare the radii of gyration of polymers with the same degree of polymerization but with different architectures, i.e., linear, star shapped, and branched.
  • Derive the scaling rule between the radii of gyration and the degree of polymerization for star shapped polymers and branched polymers.
  • Explore the influence of the number of branching points on the radii of gyration.

3. Classroom implementation ideas

Experiments:

Set the number of branching point as 10, perform simulations with different degree of polymerization (\(DP\)), record the root mean square (RMS) radii of gyration for linear, star and branched polymers.

\(DP\) Linear Star Branched
100
200
400
800

Questions:

  1. What are the scaling factors for star and branched polymers, respectively?

  2. For the same \(DP\), which type of polymer has the smallest \(R_g\) and which has the largest? Explain why?

  3. In general, the radius of gyration of which type of polymer has narrower distribution? Explain why.

4. Example practice questions

  1. Which of the statements is true?
  1. Given the same \(DP\), introducing branching points to the polymers would result in smaller RMS radius of gyration.
  2. As long as the \(DP\) are the same, linear, star shaped and branched polymers have the same RMS radius of gyration.
  3. A linear polymer always has larger radius of gyration than star shaped or branched polymers given their \(DP\) are the same.
  4. For the same \(DP\), more branching points would not affect the RMS radius of gyration of the polymers.
  1. Are the scaling rules for star and branched polymers the same as that of linear polymers? Why?