Chain-growth Polymerization

Polymerization refers to any process which forms polymers. There are two main types: chain-growth polymerization and step-growth polymerization. The former is discussed on this page and the latter on the next page.

Chain-grown polymerization

In a chain-grown reaction, there are three steps illustrated in Figure 9.7.1 for the case of polyethylene.

Step 1: Initiation

A free radical (a molecule with an unpaired valence electron, making it highly reactive) is formed, usually by splitting some initiator molecule into two radicals:

$$\ce{I ->2R.}$$

A radical then bonds with a monomer, completing its own valence shell but leaving the mer with an unpaired electron, making it a radical mer:

$$\ce{R. + M ->RM_{1}.}$$

Step 2: Propagation

The radical mer at the end of the chain bonds with another monomer, completing its valence shell but leaving the newly bonded mer with an unpaired electron:

$$\ce{RM_{1}. + M -> RM_{2}.}$$

This process repeats until termination.

Step 3: Termination

A reaction occurs which gets rid of the free radical. There are two main possibilities for this:

  1. Recombination: two chains react to form a single molecule that no longer has a free radical (and hence no longer grows). This is the first termination option shown in Figure 9.7.1.
  2. Disproportionation: A hydrogen atom is transferred from one chain to the other, bonding with the free radical on that chain. The chain that lost the Hydrogen forms a double bond and also becomes unreactive.

Chain-growth polymerization is used to produce many common polymers including polyethylene, polypropylene, polyvinyl chloride (PVC) and more.

The three steps of a chain-grown polymerization reaction.

Figure 9.7.1 The three steps of a chain-grown polymerization reaction.

An Agent-based Model of Chain-growth Polymerization

NetLogo model 9.7.1 is a model of chain-growth polymerization. The model starts with some radical initiator molecules and some mers. Then each time step they random walk and:

  • Initiation
    • If a monomer runs into a radical initiator, they bond. The mer becomes a radical-mer and the radical-initiator becomes just an initiator (bonds are saturated).
  • Propogation
    • If a radical-mer runs unto a monomer, they bond. The radical-mer becomes a saturated mer, and the monomer becomes a radical mer.
  • Termination
    • If two radical-mers run into each other, they bond and both become saturated-mers (if disproportionation-prob is > 0, then with the probability they disproportionate instead which means they don't bond, but they both become saturated).
    • If a radical-mer runs into a radical-initiator, they bond and both saturate (this is also a form of recombination).

Explore the model and answer the questions below.

Exercise 9.7.1: Let's Grow!
Due: Wed, Oct 02, 12:30 PM

Using NetLogo model 9.7.1, answer the questions below. Take about 10 minutes on this exercise.

  1. Observe what's happening after you press go and let the system run for about 1000-2000 ticks. Do your best to describe the distribution in sizes of the molecules.

  2. Increase the number of initiators so that they're about the same as the number of monomers (100:100 or so). Before pressing go, explain how you'd expect the size distribution of the polymer chains to change.

    Run the model. Does your predication pan out?

  3. Now, decrease the number of initiators to a very small number, and increase the number of monomers (5:1000 ratio). What do you expect to happen? What happens?

Simplified ABM of Chain-Growth Polymerization

NetLogo model 9.7.1 is nice because it explicitly shows chains growing in a pretty realistic way. However, this can get computationally expensive if we want to simulate large numbers of chains. So, NetLogo model 9.7.2 introduces a simplification: instead of keeping track of chains, polymers are just treated as single agents in the model which grown when they incorporate a new monomer (which then disappears from the model). This allows us to simulate many molecules.

This model starts with some initiators and monomers. Again, they random walk and each tick:

  • Initiation
    • With probability $K_i$ each initiator splits into two radicals
  • Propogation
    • If a monomer runs into a radical, it increases the chain-length of the radical by 1 and "dies" (because it was incorporated into the growing chain which still has a radical on the end and thus still called a "radical" in this model).
  • Termination
    • If two radicals run into each other, with probability $K_m$, they bond together and become a non-growing polymer.

Explore the model to investigate chain length distributions. If you pause the model, you can press the arrange-by-size button to line up the polymers by size in the x-direction (the y-direction is random just to spread them out).

Exercise 9.7.2: Let's Grow - With a Different Model!
Due: Wed, Oct 02, 12:30 PM

Let's keep this one short - about 5 minutes.

  1. Press go and explain what you're observing on the chain length plots. Does the trend make sense? Describe specifically the low-length and high-length regions.

  2. How might the model in NetLogo model 9.7.2 prove more useful than that of NetLogo model 9.7.1 when considering the size distributions of the polymers?