Module 8 Self-avoid chains

Monomer units in a polymer chain cannot overlap in space. How does this factoer influence the size of the chain?

Like a snake, avoid running into yourself!

2 Module objectives

  • Compare the root mean square (RMS) end-to-end distances and radii of gyration of polymers with the same degree of polymerization (\(DP\)) based on hindered rotation model and self-avoid hindered rotation model.
  • Derive the scaling rule between the size of the polymer chain and the degree of polymerization (\(DP\)) for self-avoid chains given the self-avoid criteria.
  • Explore the influence of self-avoid criteria on the scaling rule.

3. Classroom implementation ideas

Experiments:

Set the self avoid threshold as 1.5 and bond angle as 109.5 \(^\circ\), perform simulations with different chain lengths, record the results in the table.

DP \(h_{nsa}\) \(h_{sa}\) \(R_{g,nsa}\) \(R_{g,sa}\)
25
50
100
200
400

The subscript “nsa” means non-self-avoid and “sa” means self-avoid.

Questions:

  1. Does the self-avoid chain model have the same scaling factor as non-self-avoid model? What is the scaling factor of the self-avoid chain under the simulation conditions?

  2. Change the self avoid threshold and perform the simulations again. How does the self-avoid threshold influence the scaling factor?

  3. Change the bond angles and perform the simulations again. How does the bond angle influence the scaling factor?

4. Example practice questions

  1. Which of the statement is true?
  1. Given the same \(DP\), a self-avoid chain always have larger end-to-end distance than a non-self-avoid chain.
  2. Given the same \(DP\), the RMS end-to-end distance of self-avoid chains is larger than that of non-self-avoid chains.
  3. With \(DP=50\), the RMS end-to-end distance of self-avoid chains is \(a\) times larger than that of non-self-avoid chains; for \(DP=500\), the factor \(a\) should be the same comparing the RMS end-to-end distance of self-avoid chains and non-self-avoid chains.
  4. Given the same \(DP\), a self-avoid chain always have larger radius of gyration than a non-self-avoid chain.
  1. Why self-avoid chain model does not have the same scaling rule as non-self-avoid chain model, i.e., \(\langle h\rangle \propto DP^{0.5}\)?