# Why must polymers have a repeating unit?

In organic chemistry, we learned that small molecules can form a polymer via a process called polymerization. For example, $\ce{CH2=CH-Br}$ molecules can form the polymer

\begin{align} \ce{nCH2=CH-Br-> -[-CH2 -}&\ce{CH -]_n -}.\\ &\;\ce{|}\\ &\ce{Br} \end{align}

So the polymer is a periodic chain $\ce{-CH2-CHBr-CH2-CHBr-\cdots}$. But since every monomer can have two orientations ($\ce{-CH2-CHBr -}$ or $\ce{-CHBr-CH2 -}\!$), there is no requirement that all monomers must be in the same orientation, does the polymer have to be a peroidic chain? Can it be a random chain with a structure that looks like

$$\ce{-CH2-CHBr-CHBr-CH2-CHBr-CH2-CH2-CHBr-CH2-\cdots}\,?$$

Most textbooks emphasize that $n$ is random, but still assume that the unit repeats.

• I recommend you look at the roots of ‘polymer’ poly means many, mer means segment, mono means one. Monomer - one segment. Polymer - many segments. – JSCoder says Reinstate Monica Jan 16 '18 at 3:36
• @JavaScriptCoder, the discussion is periodic vs random. I'm not sure if a random chain is actually possible, or it is simply energetically not favorable on the scale of thermal fluctuations $k_BT$. – Zhuoran He Jan 16 '18 at 4:14
• honestly I can’t see why it couldn’t be random, I mean DNA could be random and still considered a polymer – JSCoder says Reinstate Monica Jan 16 '18 at 4:18
• Random chains are very much possible. Then again, this particular one is probably repeating. – Ivan Neretin Jan 16 '18 at 4:20
• Well, that's what happens in practice, too. Related reading: en.wikipedia.org/wiki/Tacticity. – Ivan Neretin Jan 16 '18 at 5:45

Entropy would favour a random orientation of each monomer unit when building up the chain, however whenever you have two different substituents at the ethylene unit, then electrostatics and sterical hindrance will make one side be preferred to make the connection to the growing chain end.

Polymers that do grow via chain growth therefore have a regular structure, but there can be defects. The defect density depends on how strong the preference for one side is during the polymerisation reaction. You can have as little as one in ten thousand. That's actually a bit of a problem, because the regularity often allows polymers to crystallise, which is important for the technical application. You want the number of defects always to be the same, because too high crystalinity makes your material brittle, too low makes it soft.

Polymers that make step growth (any two molecules randomly connect with their end groups, until you have a long chain) could be different, but also there often a regular structure occurs, because of A-B + A-B , either the A+B like to react, or A+A and B+B.

• I realize this problem is related to a 1D Ising model with nearest neighbor interactions. Since the Ising model in 1D does not have a ferromagnetic phase transition at nonzero temperatures, defects are inevitable once the chain grows long (to approach the thermodynamic limit). – Zhuoran He Jan 16 '18 at 16:28
• @ZhuoranHe No, that doesn't really apply afaik. We are not talking about a 1D crystal. The chain is flexible (rotation around sp3-bonds, ), so there is a lot of room for entropy in it. Isotactic polypropylene for example can be made practically defect-free, much less than one defect per molecule at several thousand monomers per molecule, and you could also (not only theoretically) sort out chains with a defect. – Karl Jan 16 '18 at 20:28
• I know the chain is not straight. In a simplified model that only cares whether adjacent monomers have the same or opposite orientations, the rotational degrees of freedom of the sp3 bonds would be uncoupled to the ordering of the orientations. To make the mean defect-free length long, we need to reduce $\exp(-\Delta E/k_BT)$ by increasing $\Delta E$, the energy cost of having a defect. If $\Delta E=10k_BT$, then the defect-free length could be $\sim 10^4$. – Zhuoran He Jan 16 '18 at 21:01
• @ZhuoranHe The orientation of repeating units cannot reach thermodynamic equillibrium, because the activation energy to flip one unit cannot be reached without completely destroying the chain. The ends of a long gaussian chain have no way of knowing they belong the same chain. A fixed, known defect imo is not even a defect in the way Ising is looking at it. (?) – Karl Jan 16 '18 at 22:01
• I think they still can reach equilibrium during the reaction. You see the number $n$ can randomly change. What this means is that the bonds between monomers are forming and breaking all the time. To preserve the defectless chains sifted from the reaction system, the temperature would then have to be lowered. – Zhuoran He Jan 17 '18 at 16:11