Overview

When you think of the word “polymer”, what do you envision — what comes to mind? My guess is that you immediately think “plastics”. Indeed, the materials we call plastics are polymers, but not all polymers are plastics, not by a long shot! Through this course, we will discover how diverse polymer materials really are, in terms of both their chemistry and structure and explore some of the unique properties that make polymers so useful in our daily lives.

Take a moment and look around you — can you identify some materials that are made of polymers? Perhaps you are wearing a shirt that has cotton (a natural polymer, cellulose) or pants that are stretchy because they have Spandex (a synthetic polymer)? Are you wearing contacts or glasses? Both are polymers — contact lenses are made of crosslinked 2-hydroxyethylmethacrylate and the lenses of most glasses are polycarbonate. Do you have hair and fingernails? (I hope so!) They are made of keratin, another polymer. You are “you” because of your DNA — yet another example of a polymer! In fact, it may be hard for you to find materials around you that aren’t made of polymers, at least in part. Polymer materials have revolutionized our world — don’t you want to know what they are and why they’re so special?

Figure 1.1: Common ploymers

Learning Outcomes

By the end of this lesson, you should be able to:

• Provide examples of polymer materials in daily life.
• Define monomer, dimer, trimer, oligomer, polymer.
• Describe the difference between monomer and repeat unit.
• Define and compare homopolymer, copolymer, and blend.
• Draw skeletal structures of linear polymers, branched polymers, network polymer.
• Compare statistical copolymer, random copolymer, alternating copolymer, block copolymer, graft copolymer, and draw schematics of each.
• Compare and contrast the properties and structure of thermoplastics, elastomers, thermosets.
• Define glass transition temperature and melting temperature, compare and contrast.
• Calculate the degree of polymerization
• Calculate the mean repeat unit molar mass
• Calculate and contrast number average molar mass, weight-average molar mass
• Define and calculate  molar mass dispersity

Lesson Checklist

Please refer to the Canvas Calendar for specific timeframes.

Questions?

If you have questions, please feel free to post them to the General Questions and Discussion forum. While you are there, feel free to post your own responses if you, too, are able to help a classmate.

The name of this course is “Introduction to Polymer Materials”. Let’s break it down.

Introduction:
I assume that this is the first class you have ever had teaches you what a polymer is – no background knowledge about polymers specifically is needed for this course. That being said, this course builds upon basic principles in general chemistry, organic chemistry, and math that you will need to know.

Polymer:
What is it? You’ll find out soon!

Materials:
This class is not a polymer “physics” course, nor is it a polymer “chemistry” course – it’s a polymer materials course. To me, “materials” means that we are going to emphasize an understanding of how the molecular, atomic level structure of a polymer affects its macroscale properties as a material. This structure – functional relationship, as you will see, is especially important and fascinating for polymers. And, we are going to emphasize not just the fundamental science, but also delve into some applications and explore how these unique properties of polymers are useful.

Figure 1.2: Materials Thought Flow Chart

Source: Lauren Zarzar

Within the “materials” world, you may hear the distinction “soft” versus “hard” materials. Typically, one would lump inorganic materials like metals or ceramics into “hard” materials that are strong and tough, while polymers and other organic materials evoke thoughts of “soft” materials – materials that are squishy, flexible, and weak. And while maybe this categorization is applicable to many materials, there are numerous cases in which these assumptions fail. For example, mercury is a metal – but it’s a liquid (a soft material). Kevlar is a polymer used for making many products including bullet proof vests, but it is extremely strong – stronger than steel in fact. Diamond, one of the hardest materials known to man, is organic and made entirely of carbon. So dispel any preconceived notions about the physical properties of polymers – in fact, one of the unique aspects of polymers that makes them so useful is how tunable and diverse the physical properties are. We will discuss in detail how the physical properties of a polymer are related to the chemistry and molecular structure of a polymer.

Given how ubiquitous polymers are in our lives today, it’s rather incredible to think that the concept of a polymer did not exist until relatively recently. People used to think that polymer materials were actually colloids – they described the material properties they observed by saying that there were “lots of small molecules that were interacting strongly with each other”. If you told scientists 100 years ago that there were actually really long, huge, molecules in there that were strung together with covalent bonds, they would have said you were crazy. The concept of such “macro molecules” just did not exist. So even though people have been using polymers for millennia (wood, silk etc.) and even more recently (do you know those really old telephones made of Bakelite?) – the concept of a polymer did not exist until Staudinger came along in the 1920s – it’s that recent! So it also just goes to show you that a lot of materials science, in terms of applications – you can get pretty far sometimes without understanding the fundamentals, but once people understood polymers on a molecular level, both research and applications exploded.

Figure 1.3: Bakelite

Source: Telephone image (pxhere)

As stated previously, natural polymers have been used for ages – wood and cotton, for example, are made of natural polymer. But the earliest examples of actual polymer chemistry really start in the 1830s, when people began experimenting with reactions of cotton – cotton, of course, being cellulose. This work led to the discovery of various nitrated cellulose products. Nitrocellulose, also called Celluloid, was used as an early replacement material for billiard balls. At the time, billiard balls were made from elephant ivory, and it was getting really expensive (and environmentally unsustainable), so there was a push to find a suitable substitute. The problem was that the “sound” billiard balls made when they hit each other was really important, and difficult to replicate in other materials. John Wesley Hyatt used one of these modified cellulose polymers to create billiard balls, and it was quite successful! However, there was a slight problem with nitrated cellulose polymers in that there were quite flammable and legend has it that occasionally the billiard balls exploded! So clearly, more work needed to be done. Along came Bakelite – which is the first example of a truly synthetic polymer (the rest were just modifications of cellulose). Bakelite, formed from the condensation reaction of phenol with formaldehyde, became hugely popular – perhaps you have seen products with Bakelite, such as those old telephones. Keep in mind that all this time, people still didn’t really know what a polymer was.

Hermann Staudinger was the first to suggest in 1920 that a polymer is actually a very large molecule, a macromolecule, where the atoms in the molecule were held together by covalent bonds. Recall from general chemistry that a covalent bond is made when atoms share their electrons – this is distinct from a simple attraction between molecules, which is what up until this point, was what everyone thought was what was giving these materials their unique properties. The general consensus was that the materials were simply colloids, where the particles were small molecules held together by attractive intermolecular forces. So this idea that there was actually a giant molecule in there was at the time incomprehensible. It took over a decade for Staudinger’s ideas to fully catch on, and he received the Nobel Prize for his contributions in 1953.

There have been lots of amazing discoveries about polymers since then. For example, even more recently, conductive polymers were discovered – again, at the time, it was difficult for people to believe that an organic material like a polymer could be conductive like a metal, but it's true! Polymers have found even more uses than you could imagine. They are replacing traditional metals and semiconductors, they are being used in solar cells and electronics. There are polymer formulations that are being used in composites for building materials, medicine, drug delivery, adhesives, paints, packaging, clothing. Everywhere.

As just mentioned, a polymer is a large macromolecule. The word “polymer” can be broken down into the Greek components: poly (many) + mer (part). “One part” would then be called a monomer, “two parts” would be a dimer, “three parts” a trimer, “a few parts” is an oligomer. Polymers can be made of a single repeating unit, over and over, there can be many different monomers in a polymer, you can have ordered repeats, random repeats, there are infinite combinations, and we will talk about the structure of the polymer in detail.

Figure 1.4: Linking monomers together to create polymers

Source: Lauren Zarzar

To create a polymer, imagine linking together a bunch of monomer units by sequentially reacting each monomer together. Table 1.1 in the textbook shows examples of chemical structures of common monomers and the polymers that result from their polymerization. Notice the nomenclature for how we name the polymer from the monomer, also pay attention to the notation used for describing the repeat unit of the polymer, which is the structure appearing in the brackets [ ]. Let’s use styrene as an example (Figure 1.5).

Figure 1.5: Styrene

Source: Lauren Zarzar

Styrene is the name of the monomer, but the repeat unit is the part that is “repeated” (in the brackets) that make up the polymer. The repeat unit is not necessarily the same as the monomer; a repeat unit can be made from multiple monomers for example. If the number of atoms, and hence the molecular weight, of the monomer is the same as the repeat unit, then we call this a polyaddition polymerization. However, the number of atoms in the repeat unit is not always the same as the monomer, if there are chemical byproducts of the polymerization reaction (and we would call this a polycondensation polymerization). A good example of this would be nylon 6,6 produced from the polymerization of hexamethylenediamine and adipic acid (Figure 1.6). Notice that the repeat unit of nylon 6,6 is a combination of both monomers, and that some atoms were lost during the polymerization so that the chemical structure of the repeat unit is not just the simple addition of both monomers; we have lost H₂O in this reaction. Can you identify the bond formed between the hexamethylenediamine and the adipic acid in the nylon polymer?

Figure 1.6: Hexamethylenediamine combines with adipic acid to form nylon 6,6

Source: Lauren Zarzar

Depending on how many different monomers are combined into a polymer, and in what order and structure, we have different ways of generally classifying polymers (Table 1.2 in text). If the polymer is made up of a single monomer, we call it a homopolymer (Figure 1.7) (e.g., if our monomer is A, the polymer would be poly(A)). If a polymer is derived from the polymerization of multiple different monomers, we call it a copolymer (Figure 1.8) (e.g., if our monomers are A and B, our polymer would be poly(A-co-B). There are many varieties of copolymers. If the positions of monomers is randomly distributed within the polymer, then we call that poly(A-ran-B). Here, “random” does not mean the same thing as “I didn’t intentionally put the monomers in a specific order”; to be random, there truly has to be a random distribution over the entire length of the polymer, which in many cases does not happen even if you do not intentionally control monomer order. More often, “statistical” is correct; since each monomer may have a different reactivity, one monomer may be more readily incorporated in the polymer than the other and so the distribution of each monomer along the polymer MAY be different. So in the cases where the monomers follow such statistical distributions (that are not random) we call them statistical copolymers, poly(A-stat-B). Figure 1.8 shows drawings of alternating copolymers poly(A-alt-B), block copolymers poly(A-block-B), and graft copolymers polyA-graft-polyB. A blend is a mixture of different polymers.

Figure 1.7: Homopolymer

Source: Lauren Zarzar

Figure 1.8: Copolymers

Source: Lauren Zarzar

So now we know that monomers can be ‘strung’ together to form a long molecule called a polymer. Perhaps you are imaging that it looks like a tiny piece of string or spaghetti – and in many cases, we can simplify the drawing of the polymer by just drawing the skeletal structure as a squiggly line. In such drawings of skeletal structures, like those shown in Figure 1.9, we don’t draw out the specific chemical structure, but the lines are supposed to represent the polymer backbone and can help us visualize higher order structure. Because a polymer doesn’t just have to be a linear – it can be much more complicated than that. It can be branched – like a tree – or it can be network, where all the strings are connected to each other at linking points called crosslinks. The skeletal structure of a polymer significantly affects its properties. For example, network polymers tend to hold their 3D shape much better than linear polymers; can you imagine trying to build a sculpture out of spaghetti?

Figure 1.9: Skeletal structures

Source: Based on figures from Young, Robert J., and Peter A. Lovell.
Introduction to Polymers, Third Edition, CRC Press, 2011.

In addition to classifying polymers by their chemical structure, we also classify them based on their physical properties (Figure 1.3 in the text). There are three main types: thermoplastics, elastomers, and thermosets. Elastomers are stretchy – think “elastic”, like a rubber band. They can be stretched and deformed and return to their original shape because their 3D structure is held together by crosslinks (i.e. most elastomers are network polymers). Their unique properties are a function of their 3D network structure. Things like crosslink density affect their macroscale material properties. Thermosets are rigid that usually have a very high degree of crosslinking. When they are heated, they don’t often flow or soften, they usually just degrade (i.e., the bonds in the polymer are broken). This is in contrast to thermoplastics or thermosoftening polymers, which do flow upon heating. Thermoplastics are typically linear or branched and do not have that network structure to hold their shape (hence they flow when heated). Most commercial polymers are thermoplastics. They can be crystalline, semi-crystalline, or amorphous. Crystalline phases have a melting temperature (T_m). Amorphous phases can’t really “melt” because they are already amorphous (it’s not considered a phase transition), so we use the term glass transition temperature (T_g) to characterize their softening point. T_g might be a range of temperature over which the transition occurs.

Some polymers have characteristics of more than one of these classes. In a sense, it’s a continuum. For example, some elastomers can also be characterized either as a thermoplastic or thermoset.

Usually, "short" polymers are called oligomers. When we start getting to tens, hundreds, thousands of repeat units or more, we have polymers. They can be huge. Remember back to general chemistry, where you learned how to calculate the molar mass of a molecule? Similarly, we can describe the "size" of a polymer using molar mass (or molecular weight) which is typically defined in units of g/mol and abbreviated as "M". Another way of describing the size of a polymer is by its degree of polymerization. Degree of polymerization (described by "x") is the number of repeat units in a polymer. If we know the molar mass of a polymer, how can we figure out the degree of polymerization? Similarly, if we know degree of polymerization, how can we figure out molar mass? All we need to know is the molar mass of the repeat unit!

Let us set up this relationship, where the new variable M₀ is the molar mass of the repeat unit:

$$M=x{\overline{M}}_0$$

Where:

• $M$ = molar mass
• $x$ = degree of polymerization
• $M_0$ = molar mass of the repeat unit

We see that the total molar mass of the polymer is just a function of the degree of polymerization and the molar mass of the repeat unit.

PROBLEM 2

A polymer with molar mass of 35,200 g/mol. has a degree of polymerization of 800. Which polymer, of the ones shown below, could it be?

Click here for the answer.

ANSWER 2

D. poly(vinyl alcohol)

PROBLEM 3

What is the molar mass of polyethylene (shown below) which has a degree of polymerization of 100?

Click here for the answer.

ANSWER 3

$$M=x{\overline{M}}_0= 100*\frac{28g}{mol}=\frac{2,800g}{mol}$$

PROBLEM 4

The following monomer is polymerized (condensation polymerization with loss of water). If the degree of polymerization is 100, what is the molar mass of the polymer?

Click here for the answer.

ANSWER 4

$M$ = 7,200 g/mol

1. First, draw the polymer in terms of the repeat unit:
   
2. Determine the molecular formula of the repeat unit:
   3 Carbon, 2 Oxygen, 4 Hydrogen
3. Calculate the molar mass of the repeat unit, ${\overline{M}}_0$:
   3 (12 g/mol) + 2 (16 g/mol) + 4 (1 g/mol) = 72 g/mol
4. Calculate polymer molar mass, $M=x{\overline{M}}_0$:
   $M=100\ast \frac{72\text{g}}{\text{mol}}=\text{7,200 g/mol}$

What if our polymer has more than one monomer, or more than one type of repeat unit? In that case, we define the mean ${\overline{M}}_0$ of the copolymer as just a weighted average of the repeat unit, where the weights are the mole fraction (X) of each type of repeat unit.

$${\overline{M}}_0={{\displaystyle \sum }}^{\text{}}{X}_j{M}_0^j$$

Where:

• $M$ = molar mass
• $x$ = degree of polymerization
• $M_0$ = molar mass of the repeat unit

Example:

What is the mean molar mass of the repeat unit for a copolymer comprised of 20 mol% styrene, 30 mol% methyl methacrylate, and 50% vinyl chloride? The chemical structures of the monomers and the resulting copolymer are shown below.

$${\overline{M}}_0=0.2*\frac{104g}{mol}+0.3*\frac{100g}{mol}+0.5*\frac{62.5g}{mol}=\frac{82.05g}{mol}$$

When you first learned about the molar mass of molecules, you learned that the molar mass is linked to the identity of the compound; for example, H₂O always had a molar mass of 18 g/mol. If the molar mass wasn't 18g/mol, it couldn't be water! The situation is very different for polymers. Take polypropylene, for example:

Polypropylene

Source: Lauren Zarzar

The molar mass of this polymer could be 420 g/mol (if degree of polymerization is 10) or 21,000 g/mol (if the degree of polymerization is 500). Although vastly different in molar mass, both of these molecules are polypropylene. For polymers, there is almost always a molar mass distribution. An example distribution is given in Figure 1.10. Although this curve looks continuous, we know that in fact it cannot be - the mass of the polymer does change in discreet units, depending on the size of the repeat unit. However, we do typically draw the distributions as continuous function.

Figure 1.10: A typical weight-fraction molar mass distribution curve for a polymer with the most probable distribution of molar mass and a repeat unit molar mass 100 g mol^-1.

Source: Based on figure 1.4 from Young, Robert J., and Peter A. Lovell.
Introduction to Polymers, Third Edition, CRC Press, 2011.

Because there is a distribution in molar mass, we have a choice as to how to actually define a characteristic molar mass for a sample. There are three general approaches for calculating the molar mass from a distribution, giving us three different values: ${\overline{M}}_n$(number average molar mass), ${\overline{M}}_w$, (weight average molar mass) and ${\overline{M}}_z$(z-average molar mass). You'll notice from Figure 1.10 that $M_n<M_w<M_z$. Each value of molar mass is defined differently.

$M_n$ is defined as the sum of the products of the molar mass of each size of polymer multiplied by its mole fraction (X). Recall from general chemistry that a mole fraction is equal to the ratio of number of moles (or molecules) of a type of polymer (N) divided by the total number of moles (or molecules). Basically, this is the same as your "average" arithmetic mean!

$${\overline{M}}_n={{\displaystyle \sum }}^{\text{}}{X}_i{M}_i=\frac{{{\displaystyle \sum }}^{\text{}}{N}_i{M}_i}{{{\displaystyle \sum }}^{\text{}}{N}_i}$$

Sometimes it's easier for us to work in weight fractions ($w_i$) rather than mole fractions, since mass is often easier to measure. The weight fraction $w_i$ is defined as the mass of molecules of molar mass $M_i$ divided by the total mass of all the molecules present:

$$w_i=\frac{N_i{M}_i}{{{\displaystyle \sum }}^{\text{}}{N}_i{M}_i}$$

Thus, we can define $M_w$:

$${\overline{M}}_w={{\displaystyle \sum }}^{\text{}}{w}_i{M}_i=\frac{{{\displaystyle \sum }}^{\text{}}{N}_i{M}_i^2}{{{\displaystyle \sum }}^{\text{}}{N}_i{M}_i}$$

Compare ${\overline{M}}_w$ to ${\overline{M}}_n$ — do you notice how ${\overline{M}}_w$ is a function if $M_i$ squared? Therefore, bigger polymers have a greater influence on ${\overline{M}}_w$ than they do on ${\overline{M}}_n$, skewing the value of ${\overline{M}}_w$ to be larger than ${\overline{M}}_n$.

The dispersity is an indication of the breadth of the molar mass distribution. Consider the two mass distributions shown below in Figure 1.11. The orange curve is broader than the blue, hence we would say that the orange polymer sample has greater dispersity.

Figure 1.11 - Sample Molar Mass Distributions

Source: Lauren Zarzar

We define the dispersity as the ratio of $M_w$ and $M_n$:

$$\mathrm{dispersity=\; Đ } =\frac{{\overline{M}}_w}{{\overline{M}}_n}$$

If your polymer is completely uniform, and every polymer molecule is exactly the same size, your dispersity would be 1. If there is any distribution in molar mass, then dispersity will be greater than 1 because $M_w$ is always greater than $M_n$.

Earlier in the lesson, we learned about degree of polymerization. Well, if there is a distribution in polymer molar mass, then there must also be a distribution of degree of polymerization. So to describe the degree of polymerization for a polydisperse polymer we use degree of polymerization averages, and similarly to molar mass distributions, we have both a number average and a weight average for degree of polymerization.

$${\overline{x}}_n=\frac{{\overline{M}}_n}{{\overline{M}}_0}$$

$${\overline{x}}_w=\frac{{\overline{M}}_w}{{\overline{M}}_0}$$

Summary

In Lesson One you have learned the very basics of polymers - how we describe the composition (monomer, repeat unit, homopolymer, copolymer, etc.), the skeletal structure (linear, branched, network), and the polymer size (degree of polymerization, number and weight average molar mass). You will have hopefully noticed how different polymer molecules are than molecules you are most familiar with. In particular, the polymer molar mass does not define its composition unlike other molecules, because a polymer have any degree of polymerization. Polymers are also so much higher molar mass than other molecules and as we will see in upcoming lessons, this gives polymers some unique material properties. Next, we will be learning about what is necessary to make a polymer in the first place, because not all molecules are monomers. How do we link together these monomers, and what determines the skeletal structure?

Reminder - Complete all of the Lesson 1 tasks!

You have reached the end of Lesson 1! Review the checklist on the Lesson 1 Overview / Checklist page to make sure you have completed all of the activities listed there before you begin Lesson 2.

Overview

Now that you know what a polymer is, how do we make one, and how do we categorize all the many types of polymers that can be formed? We know that in order to create a polymer, we need to link together monomers, and in this lesson we will begin to discuss how that happens. We will find that there are two general pathways by which monomers can be added together: chain growth and step growth. Each mechanism is characterized by different reactions that take place. In this lesson, you will learn the general characteristics of these polymerization pathways, what is necessary for a molecule to actually be considered a monomer, and how the functionality of the monomer contributes to the skeletal structure of the polymer.

Learning Outcomes

By the end of this lesson, you should be able to:

• describe the principle of equal reactivity;
• define and compare/contrast step growth vs chain growth; condensation with addition polymerization;
• identify functionality of a monomer and how it affects the skeletal structure of polymer formed;
• name the class of polymer formed based on the chemical structure;
• When presented with a polymer, be able to suggest monomers that can be used to produce it.

Lesson Checklist

Please refer to the Canvas Calendar for specific time frames.

Questions?

If you have questions, please feel free to post them to the General Questions and Discussion forum. While you are there, feel free to post your own responses if you, too, are able to help a classmate.

Polymerization requires chemical reactions, and chemical reactions happen as a consequence of collisions of molecules; if monomers never encounter each other, they can never react! Therefore, we would expect that the rate of a reaction has dependence on collision frequency. This is an especially important consideration for polymers, because polymers can be really big which means they diffuse slowly, leading to a lower rate of collision, providing fewer opportunities for reactions. However, because the polymer is large and diffuses more slowly, each encounter between reactants actually has a longer duration, which favors a reaction. These two effects — less overall collisions but longer collision duration — are assumed to balance each other out. Analyses of polymer reaction kinetics suggest that this is a reasonable assumption in most cases. We are therefore going to make this very key assumption called the principle of equal reactivity, which is that reactivity does not vary as a function of polymer size. This assumption underlies all of our future analysis of polymerization, and is important to keep in mind.

Now to actually make a polymer in the first place, you have to have the correct degree of functionality. Clearly, for a polymer to form and grow, 1) there has to be an initial reaction between monomers, and 2) there has to be reaction between monomers and the growing polymer molecule. Consider the two molecules in Figure 2.1, where A and B are able to react together to form a bond. Because each molecule only has one A or B group, once they react, there is no more functionality left to continue the polymerization. Thus, these molecules don’t have enough functionality to form a polymer.

Figure 2.1: Reaction between monomers without functionality

Source: Lauren Zarzar

What if instead you had molecules with both an A and B group, as shown in Figure 2.2. Now, after A and B react, there is still enough functionality on the molecules to continue adding monomers to the polymer chain. There is sufficient functionality for a polymer to form.

Figure 2.2: Reaction between monomers with functionality of two

Source: Lauren Zarzar

In Figure 2.2 the monomers have a functionality of two, and so the polymer that forms is a linear polymer (We first learned about skeletal structures in Lesson 1). But what if the monomer had even more functionality? Consider Figure 2.3 where the monomer has a functionality of 4. Now we see that we can get formation of branched polymers and/or network polymers.

Figure 2.3: Reaction between monomers with functionality of four

Source: Lauren Zarzar

So identifying the functionality in a monomer — and whether it has enough to form a polymer in the first place — is going to be key. But let’s say you already know that your monomer can form a polymer — what happens next? How does a monomer actually add to another monomer, or add to a dimer, or add to an existing polymer? There are two general mechanisms for how this can happen: step growth polymerization and chain growth polymerization.

Consider this exercise: you have a bag of pop beads, and each bead represents a monomer. You reach into the bag, pick up two beads, and put them together (they “react”) to form a dimer. Then you put this dimer back into the “solution” of monomers (the bag). Reach in, and grab two more beads at random. Most likely, you pick two single beads - put them together, and throw the dimer back. After you do this a bunch of times, perhaps you reach in and grab a monomer and a dimer. Put them together, you’ve made a trimer. Throw it back! If you do this for long enough, pretty soon your bag will be full of short oligomers, and lots of them, without many monomers left. Only after a long time of doing this exercise will you actually start to piece together these short oligomers to create longer polymers.

This mechanism is characteristic of step growth polymerization. Step polymerization is characterized by:

• loss of monomer early on in the reaction (remember, you turned all those monomers into dimers, trimers, and other short oligomers);
• growth of polymers throughout the reaction;
• the average molar mass increases slowly (for the majority of the exercise, your bag had only very short oligomers in it — only after very long times did you start to get longer polymers);
• high extents of reactions are necessary to get long chain lengths (lots and lots of beads had to be combined into those dimers and trimers before you started to get longer polymers);
• no initiator is used (the bead monomers were inherently reactive with each other).

Now try this variation of the bead exercise. In the bag, put a bunch of similarly colored beads (monomers) and a few differently colored beads (which will be our initiator molecules). The difference between this and the previous exercise is that monomer can only add to the initiator or a growing polymer containing the initiator. So reach in and grab two beads until you pull out an initiator and a monomer. Put them together, throw them back! Grab two more; if you grab two monomers, they won’t react with each other. Eventually, you will grab a monomer and a growing polymer fragment that has the initiator bead; keep adding monomers to that. What you find is that, in comparison to the step polymerization exercise, here you are forming relatively few numbers of polymers but each polymer chain that does form will grow longer, faster. You will also not use up your monomer as quickly; even when your polymers grow large, you’ll still have lots of monomer beads left. This exercise is similar to chain growth polymerization. Chain growth polymerization has the following characteristics (compare to step growth polymerization!):

• growth of polymer occurs by adding monomers to relatively few polymer chains;
• monomer remains even at long reaction times;
• average molar mass increases quickly;
• initiation is required.

We will be considering step and chain polymerization independently, and in great depth, in the coming lessons, but for now you should have a good idea of the similarities and differences between these two mechanisms.

We will first consider polymerization in which a linear polymer is formed, and the mechanism is step growth, i.e., linear step polymerization. We already have seen an example of what this could look like (Figure 2.2). Linear step polymerization occurs from polymerization of either bifunctional or difunctional monomers, which have a functionality of two. A difunctional monomer has two of the same reactive groups capable of forming bonds (e.g. two “A” groups), while a bifunctional monomer has two reactive groups, although they are not the same moieties (but can still react to form bonds, e.g. an “A” and “B” group) (Figure 2.4).  We have terminology to describe each of these various combinations of reactions, as depicted in Figure 2.4. For example, if we have monomers that are bifunctional (A-B) and A reacts with B,  we call this type of polymerization “ARB” type. (The “R” represents whatever chemical structure is between the reactive functional groups of the monomer). If we have difunctional monomers that react with themselves (A-A reacts with A-A) we call this “RA2”. And if we have difunctional monomers (A-A and B-B) where A reacts with B, then this is an “RA2+RB2” type reaction.

Figure 2.4 Polymerization of bifunctional and difunctional monomers

Source: Lauren Zarzar

PROBLEM

Consider polycarbonate, formed from the reaction between bisphenol A and phosgene. What “type” of polymerization is this?

Bisphenol A combines with phosgene to form polycarbonate

Source: wikimedia

1. RA₂ + RB₂
2. RA₂
3. RB₂
4. ARB

Click here for the answer.

ANSWER

A. RA₂ + RB₂

So what exactly are A and B? What functional groups can we use to create polymers, and what sorts of polymers do they produce?

Polymers are often distinguished by the structure of the linkages that are produced. Table 3.1 in the text provides seven common classes of polymers that can be produced by step growth polymerization. We will consider each of these in depth, and identify the functional groups that are needed in the monomers to produce the desired polymers. Be conscious of whether the reactions are polycondensation or polyaddition reactions (refer back to Lesson 1 - What is a Polymer).

Polyesters

Polyesters can be produced from the reaction between carboxylic acids or acid halide groups with alcohols (Figure 2.5). Notice that when a carboxylic acid is used, water is a product; when an acid halide is used, acid is a product.

Figure 2.5 Polyesters

Source: Lauren Zarzar

A very common polyester is polyethylene terephthalate, or PET (Figure 2.6). If you see recycling symbol #1 on your container, it's PET! PET is the most common thermoplastic polymer and is frequently used in synthetic fibers. Even though there are many different polyesters, PET is so common - 18% of world polymer production - that it is often just identified by the general name, "polyester". So if you look on your clothing label and find that it says "polyester", now you know that it's PET. The inclusion of aromatic groups in the backbone lends the polymer more mechanical and thermal stability. University of Liverpool - Chem Tube 3D.

Figure 2.6 Polyethylene terephthalate (PET)

Source: Lauren Zarzar

Polyamides

Polyamides are produced from the reaction between carboxylic acids or acid halides with amine groups that creates amide bonds (Figure 2.7).

Figure 2.7 Polyamides

Source: Lauren Zarzar

Nylon is a great example of a polyamide. Nylon 6,6 is shown in Figure 2.8; the "6,6" part comes from the fact that each monomer has 6 carbons; there are many other kinds of nylon as well, depending on the specific monomers used. Nylons have extensive hydrogen bonding between polymer chains which generates a relatively high degree of order (and crystallinity) contributing significantly to nylon's strength and rigidity. This ordering also makes nylon great for fibers. Nylon 6,6 can be easily made from interfacial polymerization, because the adipic acid (or sebacoyl chloride) is water soluble and the hexamethylenediamine is oil soluble. (VIDEO/www.youtube.com/watch?v=VtCBarLbHRM)

Figure 2.8 Nylon 6,6

Source: Lauren Zarzar

Other important examples of polyamides are polypeptides or proteins. Proteins are polypeptides, produced from the polymerization of amino acid monomers. The generic structure of an amino acid is shown in Figure 2.9. Do you see how the polymerization of an amino acid would create an ARB type polymer?

Figure 2.9 Polypeptides or proteins

Source: Wikipedia - Amino acid ball.

Polyethers

Polyethers are formed from reactions between diols in an RA₂ type polymerization.

Figure 2.10 Polyethers

Source: Lauren Zarzar

Polyurethanes

Polyurethanes are formed from the reaction between diisocyanates with diols (Figure 2.11).

Figure 2.11 Polyurethanes

Source: Lauren Zarzar

Polyurea

Polyurea is formed from the reaction between diisocyanates with diamines (Figure 2.12)

Figure 2.12 Polyurea

Source: Lauren Zarzar

Directions: Drag the polymer diagrams into the box indicating the proper polymer type. When you have placed all of the polymers, click on the Check button to see how you did.

Hint: You should end up with three polymers in each group.

Note: You may want to zoom out to help you see the whole activity window. Ctrl + – on Windows or Command + – on a Mac. To return to the default zoom level, use Ctrl + 0 on Windows or Command + 0 on a Mac.

Summary

Hopefully, you now feel comfortable identifying classes of polymers based on the linkages in the backbone and suggesting monomers with appropriate functionality to make polymers of a targeted type and skeletal structure. The various classes of polymers we learned (polyester, polyether, etc.) and the specific reactions we discussed to produce them are all examples of step polymerizations. In Lesson 3, we will continue to dive deeper in step growth mechanisms and especially start to consider the kinetics of polymerization.

Reminder - Complete all of the Lesson 2 tasks!

You have reached the end of Lesson 2! Review the checklist on the Lesson 2 Overview / Checklist page to make sure you have completed all of the activities listed there before you begin Lesson 3.

Overview

In this Lesson, we will take a close look at step polymerization. If we know the number of reactive groups in our monomer mixture, and we can control how many groups react, then can we predict the number average degree of polymerization? We can! First we consider if we have stoichiometric balance of reactive groups, then we consider if we have a non-stoichiometric balance and what effects that has on the polymer produced. Finally, we end with a statistical analysis of step polymerization, which gives us insight into the distributions of the molar masses produced.

Learning Outcomes

By the end of this lesson, you should be able to:

• Define extent of reaction and reactant ratio
• Apply Carothers theory to step polymerization reactions
• Calculate the probability of finding a polymer of specific degree of polymerization, and the weight fraction or number fraction of polymers of a specific degree of polymerization

Lesson Checklist

Please refer to the Canvas Calendar for specific time frames.

Questions?

If you have questions, please feel free to post them to the General Questions and Discussion forum. While you are there, feel free to post your own responses if you, too, are able to help a classmate.

We will now consider in greater depth the theoretical treatment of linear step-growth polymerization. Specifically, we will examine the Carothers equation, which relates degree of polymerization to extent of reaction. We learned about degree of polymerization in Lesson 2, but what is extent of reaction?

If we assume equal amounts of mutually reactive groups (e.g., $A$ and $B$ groups), then we can define the extent of reaction $\left( p \right)$as

$$p=\frac{\#functionalgroupsreacted}{\#functionalgroupsinitially}$$

Extent of reaction is really just the probability that any single functional group that was present at the start has reacted. Consider the mixture of bifunctional monomers in Figure 3.1.

Figure 3.1: Stoichiometric balance of A and B

Source: Lauren Zarzar

What is the extent of reaction shown in Figure 3.1? $A$ and $B$ each represent a functional group, so there were 16 functional groups (2 on each of 8 molecules) initially. Looking at the products, we find that 6 of those functional groups are now part of new bonds, so they reacted. We plug these values our equation for extent of reaction:

$$p=\frac{\#functionalgroupsreacted}{\#functionalgroupsinitially}=\frac{6}{16}=0.375$$

But notice, there is another way to represent extent of reaction in terms of number of molecules, where $N$ is the number of molecules left after the reaction and $N_O$ is the number of molecules initially. Again, using Figure 3.1, where our initial number of molecules is 8 and our final number of molecules is 5:

$$p=\frac{N_O-N}{N_O}=\frac{8-5}{8}=0.375$$

Let’s rearrange this new expression for extent of reaction:

$$\frac{N_O}{N}=\frac{1}{1-p}$$

This value, $N_O/N$, should be familiar, because it’s the same as the number average degree of polymerization!

$${\overline{x}}_n=\frac{N_O}{N}$$

We combine the equations for extent of reaction with number average degree of polymerization to yield the Carothers equation for stoichiometric balance of reactive groups:

$${\overline{x}}_n=\frac{1}{1-p}$$

So what does this equation tell us?

If you want polymers of any significant length (i.e., high degree of polymerization, ${\overline{x}}_n$) you need very high extent of reaction $\left( p \right)$!

If there is a stoichiometric imbalance, we consider the reactant ratio, r:

$$r=\frac{N_A}{N_B}$$

We always have a choice of which groups are $A$ and which groups are $B$; here, we must define the reactant ratio such that it is equal to or less than 1. The way we have defined $r$, then the $A$ groups would be in the minority.

Now because we are still confining our analysis to linear polymerization, each monomer has only 2 reactive groups. So, the total number of molecules initially present can be represented as:

$$N_O=\frac{N_A+N_B}{2}$$

Let’s simplify this expression, and try to represent $N_O$ as a function of only the number of $B$ groups for instance, but substituting in $r$:

$$N_O=\frac{N_B\left( 1+r \right)}{2}$$

Consider the following example, which is a modification of Figure 3.1. Notice, we now have a different number of $A$ and $B$ groups:

Figure 3.4: Stoichiometric imbalance of A and B

Source: Lauren Zarzar

Our minority functional group is $A$. So our reactant ratio is:

$$r=\frac{N_A}{N_B}=\frac{7}{9}$$

We can still define an extent of reaction:

$$p=\frac{\text{\#}minorityfunctionalgroupsreacted}{\text{\#}minorityfunctionalgroupsinitially}=\frac{3}{7}$$

Let’s keep our eye on the prize: we want to be able to define ${\overline{x}}_n$ as a function of $r$ and $p$. How can we do this?  Similarly to our derivation with the case of stoichiometric balance, we need to have an expression for $N$, the number of molecules remaining. The number of molecules remaining is:

$$N=\frac{\#unreactedfunctionalgroups}{\text{\#}functionalgroupspermolecule}$$

Convince yourself with our example that this is true. There are 10 unreacted $A$ and $B$ groups, and 2 functional groups per molecule. Thus, we have 5 molecules remaining; and indeed we do! But how can we write $N$ as a function of $r$ and $p$? Let’s rewrite our expression for $N$, taking into account that we already know there are 2 functional groups per molecule, and we only have $A$ and $B$ unreacted groups:

$$N=\frac{\left( \#unreactedA \right)+\left( \#unreactedB \right)}{2}$$

We can define $\#unreactedA$ as:

$$\#unreactedA\text{ = \# }Apresentinitially-\text{ \# }Areacted$$

$$\#unreactedA\text{ = r}{N}_B\left( 1-p \right)$$

We can define $\#unreactedB$ as:

$$\#unreactedB\text{ = }{N}_B-p{N}_A\text{= }{N}_B\left( 1-rp \right)$$

Notice that the because $A$ only reacts with $B$, the number of $A$ groups that react $\left( p{N}_A\right)$ is the same as the number of $B$ groups that react.

Try plugging some numbers in from our example in Figure 3 to convince yourself these expressions hold.

$$\#unreactedA\mathrm{groups}\text{ = }r{N}_B\left( 1-p \right)=\frac{7}{9}\left( 9 \right)\left( 1-\frac{3}{7}\right)=4$$

$$\#unreactedB\mathrm{groups}\text{ = }{N}_B\left( 1-rp \right)=9\left( 1-\frac{7}{9}\ast \frac{3}{7}\right)=6$$

Ultimately, we wanted to write our expression for $N$ in terms of $r$ and $p$. So:

$$N=\frac{\left( \#unreactedA \right)+\left( \#unreactedB \right)}{2}=\frac{r{N}_B\left( 1-p \right)+N_B\left( 1-rp \right)}{2}$$

We can simplify:

$$N=\frac{N_B\left( 1+r-2rp \right)}{2}$$

Now, finally, we have expressions for $N$ and $N_O$ which we substitute into our general expression for ${\overline{x}}_n$

$${\overline{x}}_n=\frac{N_o}{N}=\frac{\frac{N_B\left( 1+r \right)}{2}}{\frac{N_B\left( 1+r-2rp \right)}{2}}=\frac{1+r}{1+r-2rp}$$

Finally, we have a more general Carothers equation that is now applicable to polymerization with non-stoichiometric balance of reactive groups. And what does this equation tell us? If you want polymers of any significant length (high degree of polymerization) you need VERY HIGH extent of reaction AND to control $r$ as close to 1 as possible!

Table 3.1 (Table 3.3 in the text) calculates values of degree of polymerization for varying values of extent of reaction and reactant ratio. Take a look; you may be surprised really how high extent of reaction needs to be in order to get polymers of any significant length, especially as your reactant ratio deviates more greatly from 1.

$${\overline{x}}_n=\frac{1+r}{1+r-2rp}$$

These short chains are barely polymers!

PROBLEM

You’re polymerizing the two monomers shown below. You want to limit your number average degree of polymerization to 39. Assuming you can achieve a quantitative reaction (p approaching 1), and you start with 2 moles of phenolphthalein as your limiting reagent, then how many moles of terephthaloyl chloride should you use?

Phenolphthalein (left) and terephthaloyl chloride (TCL) (right)

Source: Lauren Zarzar

Click here for the answer.

ANSWER

We are told degree of polymerization, x_n is 39. We can therefore use the Carothers equation to solve for reactant ratio:

$${\overline{x}}_n=39=\frac{1+r}{1+r-2r\left( 1 \right)}$$

$$r=\frac{38}{40}=0.95$$

Once we know the reactant ratio, that tells us the mole ratio of reactive groups that we should use. Since the reactant ratio always has to be 1 or less, and we are told that phenolphthalein is the limiting reagent (and we have 2 moles of it, with 2 functional groups per molecule), we define the reactant ratio as:

$$r=0.95=\frac{N_A}{N_B}$$

$$=\frac{molphenolphthalein\ast 2}{molterephthaloylchloride\ast 2}$$

$$=\frac{2}{molterephthaloylchloride}$$

We solve for moles of terephthaloyl chloride, which equals 2.1 moles.

With Carothers theory, we were dealing with number-average quantities. But how do we predict the molar mass distributions? If we treat each reaction between A and B groups in a step of polymerization as a random event, we can start to apply probability and statistics to the reaction and get an estimation of the distribution of the degrees of polymerization of the polymers formed for a given extent of reaction. Essentially, we are trying to find $P\left( x \right)$, which is the probability of existence of a molecule containing exactly x units at time t with extent of reaction p. Without going into the derivation here, we find the probability of finding a sequence of x units:

$$P\left( x \right)=\left( 1-p \right)p^{\left( x-1 \right)}$$

Since $P\left( x \right)$ is the probability of finding an “x-mer”, it must also be representative of the mole fraction of x-mers:

$$molfraction\text{ x-mer}=\frac{N_x}{N}=\left( 1-p \right)p^{\left( x-1 \right)}$$

Where $N_x$ is number of x-mers and $N$ is total number of molecules at time $t$. Often, it’s hard to measure the number of molecules present at any given time $\left( N \right)$, but it’s easy to find $N_0$, which is the number of molecules we initially start with . Can we substitute in $N_0$? In order to relate $N$ to $N_0$ we use a familiar equation:

$${\overline{x}}_n=\frac{1}{1-p}=\frac{N_0}{N}$$

If we solve this above equation for $N$, we find $N=N_0\left( 1-p \right)$. We substitute this relationship into $N_x=N\left( 1-p \right)p^{\left( x-1 \right)}$ and find an expression for the number of “x-mers” at a given extent of reaction:

$$N_x=N_0{\left( 1-p \right)}^2{p}^{\left( x-1 \right)}$$

We may also be interested in the weight fraction of x-mers, in addition to the number fraction. How do we solve for that? We start with the standard definition of weight fraction:

$$w_x=\frac{massofmoleculeswithdegreeofpolymerizationx}{totalmassofallmolecules}$$

$$=\frac{N_x\left( x{\overline{M}}_0\right)}{N_0{\overline{M}}_0}=\frac{x{N}_x}{N_0}$$

We substitute into this with $\frac{N_x}{N_0}={\left( 1-p \right)}^2{p}^{\left( x-1 \right)}$ and get the weight fraction of x-mers at a given extent of reaction:

$$w_x=x{\left( 1-p \right)}^2{p}^{\left( x-1 \right)}$$

PROBLEM

You are polymerizing the below monomers (1 mole of each) by step growth polymerization. When you stop the reaction, there are 0.1 moles of acid chloride groups left. What weight fraction of monomer do you have left?

Phenolphthalein (left) and terephthaloyl chloride (TCL) (right)

Source: Lauren Zarzar

Click here for the answer.

ANSWER

First, we find the extent of reaction:

$$p=\frac{N_A}{N_B}=\frac{\left( 2mol-0.1mol \right)}{\left( 2mol \right)}=0.95$$

Then we can find the weight fraction of monomer (because x=1 is monomer!)

$$w_x=x{\left( 1-p \right)}^2{p}^{\left( x-1 \right)}$$

$$=1{\left( 1-0.95 \right)}^2{0.95}^{\left( 1-1 \right)}$$

$$=0.0025$$

PROBLEM 2

You are polymerizing the below monomers (1 mole of each) by step growth polymerization. You stop the reaction when it's 99% complete. What fraction of the mixture is monomer, on a per mole basis?

Phenolphthalein (left) and terephthaloyl chloride (TCL) (right)

Source: Lauren Zarzar

Click here for the answer.

ANSWER 2

We can plug directly into the $P\left( x \right)$ equation:

$$P\left( x \right)=\left( 1-p \right)p^{\left( x-1 \right)}$$

$$=\left( 1-0.99 \right){0.99}^{\left( 1-1 \right)}$$

We can use these relationships we have learned from the statistical theory to plot the most probable distributions for $P\left( x \right)$ and $w_x$:

Figure 3.5: Probable distributions for $P\left( x \right)$ and $w_x$

Source: Figure 3.1 from Young, Robert J., and Peter A. Lovell.
Introduction to Polymers, Third Edition, CRC Press, 2011.

What can we learn from these plots? First, consider the plot of $P\left( x \right)$ for a few different values of extent of reaction (which is the left graph). Notice that $P\left( x \right)$, even for the high extents of reaction, is always larger for the lower values of $x$. This is telling us that even if we go to high extents of reaction, polymers with low degrees of polymerization are still more likely to be found than those with high degrees of polymerization. Now look at the second graph, at right, which is a plot of $w_x$. In contrast, this plot has a peak, which is actually very close to $M_n$. As extent of reaction increases, we see that the peak weight fraction moves to high values of $x$– this makes sense, because the polymers with higher degrees of polymerization are formed at higher extents of reaction. We also notice that the breadth of the curve increases as extent of reaction increases, which tells us that the dispersity of the polymer is increasing.

From these distributions, we can solve for the number average molar mass using this relationship:

$${\overline{M}}_n={\displaystyle \sum P\left( x \right) }{M}_x$$

Doing a series of substitutions (i.e. substitute in $P\left( x \right)=\left( 1-p \right)p^{\left( x-1 \right)}$, $M_x=x{\overline{M}}_0$, and then simplify) we find:

$${\overline{M}}_n=\frac{{\overline{M}}_0}{1-p}$$

Does this look familiar? It’s the same relationship as we got from Carothers theory!

Without going through the derivation, we can apply a similar analysis to get information about the weight average molar mass as well. We find:

${\overline{M}}_w={\overline{M}}_0\frac{1+p}{1-p}$ and ${\overline{x}}_w=\frac{1+p}{1-p}$ and $dispersity=1+p$

Summary

In Lesson 3, we got a more in depth look at step polymerization. Using the Carothers equation, we now understand the relationship between extent of reaction, reactant ratio, and the degree of polymerization. Out of these relationships, we learned that in order to achieve high degrees of polymerization, we need to go to high extents of reaction and have a reactant ratio as close to 1 as possible. We also used statistical theory to derive expressions for the probability of finding an x-mer, the weight fraction of x-mers, and the number fraction of x-mers. From these, we can learn about the distribution of the polymer molar mass for different extents of reaction.

Reminder - Complete all of the Lesson 3 tasks!

You have reached the end of Lesson 3! Review the checklist on the Lesson 3 Overview / Checklist page to make sure you have completed all of the activities listed there before you begin Lesson 4.

Overview

In this Lesson, we are going to learn how free radical polymerization works, what the actual mechanism of the reaction is like, and why it happens. Free radical polymerization is a type of chain growth polymerization, but not the only one – in coming lessons we will cover other kinds of chain growth mechanisms, including ionic polymerization and ring opening polymerization. For now, in Lesson 4 and 5, we are going to focus on free radical, which is one of the most common types of polymerization. We are breaking down the topic of free radical polymerization into two lessons: Lesson 4 focuses on the reaction mechanisms and Lesson 5 focuses on the reaction kinetics.

Learning Outcomes

By the end of this lesson, you should be able to:

• Identify monomers that can undergo free radical polymerization.
• Draw arrow pushing mechanisms for polymerization by free radical polymerization, including initiation, propagation, termination (by combination or disproportionation), and chain transfer.
• Name and describe the stages of the free radical polymerization mechanism.
• Identify the head and tail of a monomer and whether a reaction occurred in a head to tail, head to head, or tail to tail fashion in a polymer and why
• Describe the effects of chain transfer on polymer skeletal structure

Lesson Checklist

Please refer to the Canvas Calendar for specific timeframes.

Questions?

If you have questions, please feel free to post them to the General Questions and Discussion forum. While you are there, feel free to post your own responses if you, too, are able to help a classmate.

Recall from Lesson 2 that we learned about two types of polymerizations: step growth and chain growth. In Lesson 3, we explored in depth the monomers that undergo step growth polymerization and Carothers theory for linear step polymerization. In Lesson 4, we now begin to examine the details of chain growth polymerization. More specifically, in this lesson, we are going to focus on free radical polymerization, which is a specific type of chain growth polymerization.

First, we should probably refresh our memory of what a radical actually is! A radical species is characterized by having an unpaired electron. From general chemistry, we recall that it is much more stable to have electrons paired in orbitals rather than unpaired — so as you may expect, radicals tend to be highly reactive and relatively short-lived. Radicals are denoted by a single dot (representing the electron), such as in Figure 4.1.

Figure 4.1: Various ways of representing a radical in a chemical structure.

Source: Section 4.1 from Young, Robert J., and Peter A. Lovell.
Introduction to Polymers, Third Edition, CRC Press, 2011.

The radical is shown as the single dot in Figure 4.1. In (i) the geometry and the hybridization of the central carbon is emphasized. The carbon is sp² hybridized, and the radical exists in the unhybridized p orbital that is perpendicular to the plane containing the substituents. Usually, the orbital is not drawn, as in (ii) or (iii).

Free radical polymerization makes use of this unstable radical by sequentially adding unsaturated monomers to the active center (radical end) of a growing polymer. Let's break that idea down further. As a refresher, recall that unsaturated molecules are characterized by not having the greatest possible number of hydrogens based on the carbon content. Usually, this means that the molecule contains a double or triple bond. Monomers that are most frequently used for free radical polymerization have a double bond, and more specifically, often a vinyl group or acryloyl group (Figure 4.2). Examples of a few common monomers are shown in Figure 4.3.

Figure 4.2: Common functional groups that can undergo free radical polymerization

Source: Lauren Zarzar

Figure 4.3: Examples of monomers that can be polymerized with free radical polymerization

Source: Lauren Zarzar

We already stated that we are going to use the radical to react with unsaturated monomers and this is going to create a polymer — but how? We can represent this reaction, and where the electrons go within the molecules, by using arrow pushing mechanisms which you learned in organic chemistry. In free radical polymerization, monomers are sequentially added together and the reactive radical end (the active center) attacks double bonds of monomers as shown in Figure 4.4.

Figure 4.4: Mechanism of free radical polymerization

Source: Lauren Zarzar

There is actually a lot going on in Figure 4.4. First of all, you may want to refresh your memory regarding the conventions of arrow pushing mechanisms. The arrows show where the electrons start (at the arrow tail), and where they go (the arrow head); single headed arrows represent the movement of one electron, while double-headed arrows represent movement of an electron pair. Here, we will be using lots of single headed arrows because we are dealing with radicals, which are unpaired electrons. As shown in Figure 4.4, we have broken down the "overall reaction" into two steps for clarity. Let's look in detail at Step 1 in Figure 4.4. Note that the π bond of the double bond is broken (the σ bond still remains) and that the π bond is broken homolytically. By homolytically, we mean that the two electrons in that bond are split evenly between the two carbons in the bond, one electron going to each carbon. Then, one of those new radicals that is generated can react with the radical on the other monomer, forming a new carbon-carbon bond (step 2). In the future, when writing reaction mechanisms, all you would need to show is the "overall reaction" as shown in bottom of Figure 4.4. Notice that after this reaction takes place, our product now has one additional monomer linked to the polymer chain, and our radical is still at the end of the molecule (this is called the active center). Building upon this general mechanism of free radical polymerization, we move on to more in depth understanding of the process. For example, how do we even get these radicals in the first place? How do we get rid of the radicals if we want to stop our reaction to make polymers of a specific length? These are the sorts of questions that we will soon address.

There are three general stages of free radical polymerization: 1) initiation, 2) propagation, 3) termination. Let's consider these stages in the order which they occur.

1. Initiation

This step involves the creation of the radical, i.e., creation of the active center. Usually, we need to add a special molecule called an initiator to our reaction to generate these radicals in the first place. By using a trigger like an input of light (hv) or heat (Δ), we induce the initiator to homolytically decompose into fragments containing radicals that can be used to initiate polymerization. Common molecules that are used as initiators include peroxides (containing a peroxide bond, -O-O-) and azo compounds (containing R-N=N-R'). Examples of common initiators include benzoyl peroxide, with is thermally triggered, and benzophenone, which is UV triggered. Note that for each bond that is broken, you get two radicals formed.

Figure 4.5: Initiation mechanism for radical generation

Source: Lauren Zarzar

Figure 4.6: Examples of common radical initiators

Source: Lauren Zarzar

Once we generate the radical, it has to be transferred to a monomer to create an active center. It's worth pointing out that not all radicals generated during initiation actually get transferred to the monomer. Some molecules with radicals may further decompose, and the radicals recombine, before they ever get a chance to react with the monomer. But assuming we do have transfer to monomer, there are actually two ways that a radical can add to the double bond of a monomer. There are two ways because the two carbons involved in the double bond may not be equivalent (i.e., they may have different substituents). Figure 4.7 depicts the two ways that the initiator radical can add to a monomer.

Figure 4.7: A radical can add to a monomer in two different ways where "X" represents any substituent (except hydrogen, in which case these pathways would be equivalent)

Source: Lauren Zarzar

The first reaction (Mode I) typically predominates in free radical polymerization. Why do you think this might be the case? Comparing Mode 1 and Mode 2, we notice that difference is whether the initiator radical forms a bond with the carbon attached to the "X" group or not. Remember that for a reaction to occur, two reagents have to be able to get close to each other, which is why consideration of steric effects is important. Hopefully you learned some about steric hindrance in organic chemistry, but to quickly summarize, the basic idea is that bulky substituent groups (i.e., bulky, large "X" groups) prevent the radical from being able to approach the other molecule closely enough to react. Well, in Mode 1, the only substituents on the reacting carbon are hydrogens (since it is a methylene group), which are small, so there's really not much steric hindrance. For Mode 2, "X" could be anything —  imagine a tert-butyl group that's big and bulky — the radical will have a harder time approaching that carbon. Thus, Mode 1 tends to be favored based just on steric considerations. But there is another reason as well, which is that the radical in Mode 1 ends up on the carbon with more substituents, which can help to make that radical more stable than the radical on the methylene group.

2. Propagation

Propagation involves the growth of the polymer chains, where monomers are sequentially added to the active center. The mechanism of propagation looks like what we already discussed in Figure 4.4, so refer back to that if you get confused about the movement of the electrons. Similarly to initiation, there are actually multiple ways in which a monomer can add to the active center (again, because the two carbons in the vinyl group of the monomer may be non-equivalent). Figure 4.8 depicts the two ways in which the monomer can add to the active center. We name these configurations depending on how the "head" or "tail" of the monomer is connected to the active center. The "head" of the monomer is the side where the substituent is attached, while the "tail" is the methylene. Because of the reasons discussed in the section on initiation (sterics, and stabilization of the radical), we expect that the active center is usually found on the "head" group and preferentially reacts with the "tail" of another monomer (i.e., "head to tail"). Less frequently, we would see head to head addition; if head to head addition occurs, it will most likely be followed immediately by a tail to tail addition, such that the active center again ends up on the head side.

Figure 4.8: Configurations in which a monomer can add to an active center during the propagation step of free radical polymerization

Source: Lauren Zarzar

CASE STUDY

Consider the polymerization of vinyl fluoride (Figure 4.9). Do you think this monomer will still preferentially add in a head to tail fashion?

Figure 4.9: Vinyl fluoride

Source: Introduction to Polymers Section 4.1

The tail (the methylene) is less sterically hindered, so in terms of steric effects, we still expect head to tail addition. But, you may recall from organic chemistry, that fluorine is strongly electron withdrawing which would actually destabilize a radical on the head carbon (which is electron deficient). So, we have competing effects - which wins out? Turns out that 90% of the linkages in poly(vinyl fluoride) are still head to tail, emphasizing the importance of steric considerations.

3. Termination

Termination involves destruction of the radical active centers, thus preventing any further propagation. But, what happens to those radicals then? There are few different possibilities for where they go. Often, termination occurs via combination of radicals (Figure 4.10).

Figure 4.10: Termination by combination

Source: Lauren Zarzar

Also notice in Figure 4.10 that upon termination by combination, the final polymer has a final degree of polymerization of x+y, and there are two initiator fragments on each end. Termination by combination is not the only pathway for termination. In termination by disproportionation, an H atom is extracted from the end of a growing chain and the leftover electron combines with another radical, generating a terminal π bond (Figure 4.11).

Figure 4.11: Termination by disproportionation

Source: Lauren Zarzar

In termination by disproportionation, we have created two polymers, one with an unsaturated end, and both have one end with an initiator fragment.

Chain transfer is a process that occurs during polymerization, in which the active center is transferred from one species to another (Figure 4.12).

Figure 4.12: Chain transfer
TA can be initiator, monomer, polymer, the solvent, or something you add to purposefully transfer the radical (i.e., a transfer agent). Often, T is a hydrogen atom or halogen atom

Source: Lauren Zarzar

In Figure 4.12, we use T and A to just represent fragments of a molecule that are linked by a single bond. TA can be initiator, monomer, polymer, the solvent, or something you add to purposefully transfer the radical (i.e., a transfer agent). Often, T is a hydrogen atom or halogen atom. Notice that breakage of the single bond in TA happens by homolytic cleavage, as we have seen before, such that the radical has been transferred from one species to another. Chain transfer - the rates at which it happens, and the species between which the radical is transferred - can have dramatic effects on the structure of the resulting polymer. First, we will consider the impact of chain transfer to polymer.

Chain transfer to polymer

Chain transfer to polymer means that the radical is transferred to somewhere in or on a polymer - it can be the same polymer where the radical was initially (intramolecular chain transfer, or backbiting), or the active center can be transferred to a different polymer chain (intermolecular chain transfer). Both of these processes are shown in Figure 4.13.

Figure 4.13: Intramolecular and intermolecular chain transfer to polymer. Intramolecular chain transfer to polymer, sometimes called backbiting, most often leads to short branches. Intermolecular chain transfer to polymer tends to lead to longer branches.

Source: Lauren Zarzar

If we were to polymerize a monomer with a functionality of two (e.g., a monomer with a vinyl group) we expect to create a linear polymer, without branching. But if there is chain transfer to polymer, then we get a very different polymer skeletal structure that does have branching. If there is intramolecular chain transfer to polymer, sometimes called backbiting, the active center is transferred to somewhere else along the same polymer chain where the active center originated. Usually, it's transferred to a position pretty close to the polymer end resulting in the formation of a short branch. If there is intermolecular chain transfer to polymer, then the active center is transferred to another polymer chain. It could be transferred anywhere along the polymer; usually, this mechanism leads to branches that are longer.

Summary

Free radical polymerization is one of the most important types of polymerizations, and now you should feel comfortable indenting monomers that will undergo free radical polymerization, drawing the free radical polymerization mechanism, and describing how chain transfer affects skeletal structure. It is very key that you understand how the monomers react to give the polymer so that you can draw an accurate repeat unit for any monomer(s) that you start with. Next, we are going to be building upon the foundation we learned in Lesson 4 and apply that to the kinetics of free radical polymerization in Lesson 5.  

Reminder - Complete all of the Lesson 4 tasks!

You have reached the end of Lesson 4! Review the checklist on the Lesson 4 Overview / Checklist page to make sure you have completed all of the activities listed there before you begin Lesson 5.

Overview

In this Lesson, we continue learning about free radical polymerization, with a focus on the kinetics of the polymerization. We describe the rate of reaction for initiation, propagation, and termination, and how those reactions play into the overall rate of polymerization. Introduction of inhibitors or retarders can be used to modulate the rate or onset of polymerization. We also learn about how to calculate the number average degree of polymerization for free radical polymerization and how it relates to factors such as concentration of monomer, initiator, and chain transfer.

Learning Outcomes

By the end of this lesson, you should be able to:

• Calculate rates of initiation, propagation, and termination, and how these influence rate of polymerization
• Describe the effect of monomer concentration, initiator concentration, radical concentration, and rate of chain transfer on rate of polymerization and degree of polymerization
• Determine the polymer skeletal structure from monomers that can be polymerized by free radical pathways
• Describe steady state conditions
• Describe the effects of inhibitors and retarders on polymerization.

Lesson Checklist

Please refer to the Canvas Calendar for specific timeframes.

Questions?

If you have questions, please feel free to post them to the General Questions and Discussion forum. While you are there, feel free to post your own responses if you, too, are able to help a classmate.

Now that we have a working understanding of the reactions and processes that can happen during free radical polymerization, we can begin to discuss the polymerization kinetics for free radical polymerization. We start from the very beginning and define the rate of polymerization:

As shown in Eq. 5.1, we are defining the rate of polymerization as the rate at which monomer M is consumed. Note the negative sign, which is there because we are defining the rate as the disappearance or consumption of monomer.

You may want to refresh your memory of rate equations before going much further!

Rate of Initiation:

We should be able to write a rate equation for each "step" in free radical polymerization: initiation, propagation, and termination. Let's start with initiation; there are actually two parts to initiation: 1) the formation of the radical from decomposition of the initiator and 2) transfer of the radical to a monomer.

Figure 5.1:

Source: Lauren Zarzar

The first step of initiation, generation of the radicals, is generally much slower than transfer of the active center to the monomer. Thus, the first step of initiation is the rate determining step, meaning that the rate of initiation is really only a function of the slow step, formation of radicals. Thus, we can represent the rate of initiation as the rate of formation of radicals:

Notice that we don't have anything about monomer concentration in rate of initiation. Because we consume so little monomer during initiation, we neglect any changes in monomer concentration here. But we can make this more specific. Let's say we generate two radicals per initiator molecule, which is common, and that the rate of dissociation of the initiator has a rate constant of k_d.

Figure 5.2:

Source: Lauren Zarzar

We can thus re-write the rate for first step of initiation as:

However, we also know that not all the radicals that are produced actually get transferred to monomer; only some fraction of them make it through step 2 of initiation. Radicals may combine, react with solvent, etc. To account for the fact that not all radicals produced in step 1 are actually used, we introduce the concept of initiator efficiency, f. For example, If half of our radicals produced actually get used and transferred to monomer, then f =0.5. We can update our description of the rate of initiation:

Rate of Propagation:

Propagation involves the transfer of the radical from one monomer to another monomer, or to polymer. We are using up lots of monomer in this step.

Figure 5.3:

Source: Lauren Zarzar

The rate of disappearance of monomer (note the negative sign in the rate!) is a function of the rate constant, the monomer concentration, and concentration of active centers (M·)

Note that this is the only place where we directly account for the rate as consumption of monomer (but NOT the radical species).

Rate of Termination:

Recall that we have two different pathways for termination: combination and disproportionation.

Figure 5.4:

Source: Lauren Zarzar

We write the rate equations for these two termination pathways:

The coefficient of two results from the fact that two growing polymers are consumed by either pathway.

Add up these two rates (ktc +ktc = kt ) to get an overall rate equation:

We have now written rate equations for initiation (generation of radicals), propagation (growth of polymer), and termination (consumption of radicals). At the very beginning of the reaction, the rate of formation of radicals is faster than consumption of monomer. But the number of radicals cannot keep growing forever! Eventually, the rate of formation of radicals and consumption of radical monomer/active centers reaches a steady state — radicals are formed as quickly as they are consumed/propagated in the reaction. Radicals are consumed just as fast as they are created. This is called steady state. We work under this assumption for the rest of our derivation of steady state polymerization rates.

The rate of production of radicals is the same as the consumption of radicals:

Substitution of our previous expressions:

Rearrange to solve for the steady state concentration of radicals:

OK great, why do we care? Well, we ultimately want to figure out the rate of polymerization, which recall that we defined at the very beginning of the section. To refresh your memory, we defined rate of polymerization as rate of consumption of monomer. Where else have we seen rate of consumption of monomer? We saw it in the expression for the rate of propagation!

While we can measure the concentration of monomer, it's not easy to measure the concentration of radical. But if we are under steady state conditions, we can substitute for $\left[ M· \right]$ using $\left[ M· \right]={\left( \frac{R_i}{2k_t}\right)}^{1/2}$

Note: the upper limit for $\left[ M \right]$ is pure monomer. When pure monomer is used, it's called bulk polymerization

We have already introduced the idea of number average degree of polymerization. Recall:

We are going to try to describe number average degree of polymerization using the concentration of monomer and initiator, and for now let's neglect chain transfer. Can we substitute for the numerator, moles of monomer consumed in time $t$? What's the rate of monomer consumption? We know that, it's the rate of propagation: $R_{prop}=-\frac{d\left[ M \right]}{dt}=k_p\left[ M \right]\left[ M· \right]$. What about the denominator, moles of polymer formed in time $t$? Think about in what step we actually form a complete polymer — it's the termination step. In Figure 5.4, and we noticed that for termination by combination we form one polymer, and for termination by disproportionation we form 2 polymers. Thus the total rate of polymer formation is the sum of formation from combination and disproportionation. We write rate equations for this:

Let's substitute for the numerator and denominator in our number average degree of polymerization. We are going to use the subscript '0' for ${\overline{x}}_n$ to denote that this is the degree of polymerization in the absence of chain transfer.

Again, we can't do so much with radical concentrations in that expression. So let's substitute the steady state concentration of radicals, $\left[ M· \right]={\left( \frac{R_i}{2k_t}\right)}^{1/2}$ and we get:

$q$ is the fraction of termination happening by disproportionation. If there is only termination by combination then $q=0$. If there is only termination by disproportionation then $q=1$. We can further substitute with $R_i=2f{k}_d\left[ I \right]$:

This equation looks a little complicated. But importantly, we want to gain insight as to how the number average degree of polymerization is affected by inputs we can control, namely the concentration of monomer and concentration of initiator. We find: ${\left( {\overline{x}}_n\right)}_0\propto \left[ M \right]{\left[ I \right]}^{-1/2}$

We call the equations for ${\text{R}}_{\text{p}}$ and ${\left( {\overline{x}}_n\right)}_0$ that we derived instantaneous equations because they apply to a specific concentration of $\left[ \text{M} \right]$ and $\left[ \text{I} \right]$ (which change over time). As a refresher: $R_p\propto \left[ M \right]{\left[ I \right]}^{1/2}$ and ${\left( {\overline{x}}_n\right)}_0\propto \left[ M \right]{\left[ I \right]}^{-1/2}$. Thus, both go up with increasing $\left[ \text{M} \right]$, and the expressions are oppositely correlated with $\left[ \text{I} \right]$. Thus, we can predict how changing $\left[ \text{M} \right]$ and $\left[ \text{I} \right]$, which we can control, will affect our resulting polymer. Remember $\left[ \text{M} \right]$ is limited to pure monomer in bulk polymerization. So there are constraints on the degrees of polymerization that you can achieve.

How accurate are these expressions as compared to experimental values of ${\overline{x}}_n$? We find that experimental values of ${\overline{x}}_n$ tend to be lower than expected based on these derived relationships. Why? What have we neglected in our derivations? Chain transfer! Chain transfer can contribute significantly to the termination of growing polymer chains. Even though the transferred radical can still continue to react, the chain from which it was transferred is now shorter (lower ${\overline{x}}_n$) than would have been expected (Figure 5.5). The rate of polymerization may not be so greatly affected if $A·$ reacts quickly with monomer (Figure 5.5).

Figure 5.5: Chain transfer effect on rate of polymerization and degree of polymerization

Source: Lauren Zarzar

We can account for chain transfer, including chain transfer to solvent, monomer, and initiator, in addition to termination by combination and disproportionation by building this into the "moles of polymer formed at time t" part of the denominator in our expression for ${\overline{x}}_n$. We thus update our previous expression, which was ${\left( {\overline{x}}_n\right)}_0=\frac{k_p\left[ M \right]\left[ M· \right]}{ 2k_{td}{\left[ M· \right]}^2+k_{tc}{\left[ M· \right]}^2}$, and we alter it:

Notice that the $k_{trM}\left[ M· \right]\left[ M \right]$ takes into account chain transfer to monomer, $k_{trI}\left[ M· \right]\left[ I \right]$ is for chain transfer to initiator, and $k_{trS}\left[ M· \right]\left[ S \right]$ is for chain transfer to solvent. This is a more accurate description of degree of polymerization. Notice that we didn't include a term for chain transfer to polymer in our updated description of degree of polymerization because if the active center is transferred between polymers, then there is actually no effect on "moles of polymer formed at time t". Rearrange, substitute with ${\left( {\overline{x}}_n\right)}_0$ (which we previously derived without chain transfer) to generate the Mayo Walling Equation:

We have thus introduced transfer constants $C_M$, $C_I$, $C_S$ are $k_{tr}/k_p$ for each type of chain transfer reaction (transfer to monomer, initiator, and solvent, respectively). Notice that while chain transfer to polymer can greatly affect skeletal structure, it doesn't affect degree of polymerization because the number of polymers before and after chain transfer are the same.

See Table 5.1 below for a list of example transfer constants of various solvents for the free radical polymerization of styrene. Solvents with high transfer constants would prevent propagation and growth of long polymers, but can be added in small quantities to produce smaller polymers if they are desired (i.e., used as a chain transfer agent).

PROBLEM

A solution of 100 g/L acrylamide in methanol is polymerized at 25°C with 0.1 mol/L diisobutyryl peroxide whose half life is 9.0 h at this temperature and efficiency in methanol is 0.3. For acrylamide, $k_p{ }^2/k_t=22Lmo{l}^{-1}{s}^{-1}$ at 25°C and termination is by coupling alone.

What is the initial steady state rate of polymerization?
(half life for a first order reaction: $t_{1/2}=\frac{\text{ln}\left( 2 \right)}{k_d}$)

Click here for the answer.

ANSWER

We are looking to solve for the initial steady state rate of polymerization, thus $R_p=k_p\left[ M \right]{\left( \frac{f{k}_d\left[ I \right] }{k_t}\right)}^{1/2}$

To solve this equation, we need to substitute for many variables. Can we pull all of that necessary information out of the question? Let's start with the concentration of the monomer, acrylamide. It's density is given, but we need the concentration in mol/L:

$$\left[ M \right]=\left[ acrylamide \right]=\frac{100g}{L}\text{*}\frac{mol}{71g}=1.408 mol/L$$

Let's move on to $k_d$. We can get this rate constant for decomposition of the initiator from the half life. We are going to solve for this with the time units of seconds, because in the problem we are given $k_p{ }^2/k_t=22Lmo{l}^{-1}{s}^{-1}$ and we want to make sure all our units are going to be consistent throughout the problem.

$$k_d=\frac{\text{ln}\left( 2 \right)}{9hr*3600s/hr}=2.139x{10}^{-5}/s$$

In order to actually make sure of $k_p{ }^2/k_t=22Lmo{l}^{-1}{s}^{-1}$ we are going to have to rearrange our expression for $R_p$ a little.

$$R_p=k_p\left[ M \right]{\left( \frac{f{k}_d\left[ I \right] }{k_t}\right)}^{\frac{1}{2}}= \frac{k_p}{k_t^{1/2}}\left[ M \right]{\left( f{k}_d\left[ I \right] \right)}^{\frac{1}{2}}$$

Now it looks like we have all the numbers we need to plug into this equation!

$$R_p={\left( \frac{22 L}{mol*s}\right)}^{\frac{1}{2}}\left( \frac{1.408 mol}{L}\right)\left[ 0.3\left( \frac{2.139x{10}^{-5}}{s}\right)\left( \frac{0.1\text{ mol}}{\text{L}}\right) \right]{}^{\frac{1}{2}}=5.292x{10}^{-3}mol/\left( L*s \right)$$

We can add specific molecules to our reaction if we want to prevent or slow down polymerization. For example, when you purchase a commercially available monomer from a supplier, you may read on the bottle that the monomer is stabilized, perhaps by a molecule such as MEHQ (monomethyl ether hydroquinone). Such inhibitors are added to extend the shelf life of the monomer by preventing unwanted, premature polymerization. Inhibitors work by "trapping" any radicals that are generated in a very stable molecule that does not further react. If a "normal" polymerization follows a trajectory such as in Figure 5.6 (Figure 4.7 in the textbook), then that same polymerization with an inhibitor present would follow a trajectory like Figure 5.6 (c); the inhibitor prevents polymerization for a certain amount of time (the induction time), which depends on how much inhibitor is present. As soon as all the inhibitor is used up, then the reaction proceeds as normal.

A retarder works slightly differently than an inhibitor, and serves to slow down a polymerization rather than prevent it, as shown in Figure 5.6 (b). Retarders act in a similar way as inhibitors in that they stabilize radicals, but are not quite as good as preventing further reactions of the radicals as inhibitors. Hence, polymerization can still proceed in the presence of active retarder.

FIGURE 5.6: Schematic examples of inhibition and retardation: (a) normal polymerization; (b) polymerization in the presence of a retarder; and (c) polymerization in the presence of an inhibitor (where Δt is the induction period).

Source: Figure 4.7 from Young, Robert J., and Peter A. Lovell.
Introduction to Polymers, Third Edition, CRC Press, 2011.

Reaction rates typically depend on temperature, so what about polymerization reactions? More specifically, how are rate of polymerization and degree of polymerization dependent on temperature? As with any other reaction, temperature changes the rate constants associated with the polymerization. But there are many rate constants that affect polymerization, so the effect of temperature is not necessarily straightforward. If the temperature increased, we expect there to be more radicals generated in a shorter time frame, so the concentration of active centers will go up. Because rate of polymerization is directly correlated with concentration of radicals, the rate of polymerization will also go up with temperature. Can we simply keep increasing the temperature to increase $R_p$ indefinitely? That's not really an effective strategy, because depolymerization, which is the polymer reverting to monomer, is favored at elevated temperatures. At the ceiling temperature, the rate of polymerization and depolymerization are equal. Also consider that at higher temperatures, with higher concentration of radicals, that also means that termination rates will be higher. As the rate of termination increases, the degree of polymerization decreases, and the polymers will be shorter. Thus, the temperature at which you run a polymerization reaction can have significant impact on the resulting polymer formed and should be considered carefully.

Thus far, we have primarily considered free radical linear polymerizations of monomers containing a functionality of 2. With the exception of branching that can occur from chain transfer to polymer, a monomer with a functionality of 2 can only lead to linear polymers. But what if we use a monomer that has a functionality greater than 2? Much like what we discussed for step polymerization, we will get branching and possible formation of crosslinks leading to a network structure. In fact, many monomers for free radical polymerization that have a functionality higher than 2 are often called crosslinkers. Examples of common crosslinkers are shown in Figure 5.7 and Figure 4.2 in the textbook.

Figure 5.7: Examples of crosslinkers for free radical polymerization

Source: Lauren Zarzar

Polymerization of a monomer and crosslinker would create a network polymer, such as diagramed in Figure 5.8. The monomers that have a functionality of 2 form linear polymers, that are linked by the crosslinker.

Figure 5.8: Schematic diagram of a network polymer formed from monomer 'X' and crosslinker 'Z'.

Source: Replicated from Figure 4.19 from Young, Robert J., and Peter A. Lovell.
Introduction to Polymers, Third Edition, CRC Press, 2011

Overview

In this Lesson, we will learn about two additional chain growth polymerization mechanisms: cationic and anionic. These ionic polymerization mechanisms have several similarities to the radical chain growth polymerization in terms of the general mechanism (initiation, propagation, termination). An important distinction is that there will be a charged active center in ionic polymerization (while the radical active center is neutral). This charge is what primarily causes any differences we observe between ionic and radical chain growth. The different charge between cationic (positive charge) and anionic (negative charge) further leads to even more variation among ionic polymerization. Try to compare and contrast the three chain growth mechanisms as you go through the lesson to put in perspective and context how the various pathways are related to monomer chemistry, polymer skeletal structure, and reaction mechanism.

Learning Outcomes

By the end of this lesson, you should be able to:

• Predict if a monomer with polymerize via anionic or cationic pathways
• Compare and contrast ionic polymerization with free radical polymerization
• Draw the arrow pushing mechanism for cationic, anionic, and living anionic polymerization
• Describe the characteristics of living anionic polymerization
• Explain how the solvent and counter ions affect ionic polymerization rates

Lesson Checklist

Please refer to the Canvas Calendar for specific timeframes.

Questions?

If you have questions, please feel free to post them to the General Questions and Discussion forum. While you are there, feel free to post your own responses if you, too, are able to help a classmate.

In Lesson 6, we will continue to talk about chain polymerizations, but we will be exploring new reaction mechanisms: ionic polymerization. In contrast to free radical polymerization, in which the reactive species was a radical (which is neutral), in ionic polymerizations, the active center will be either an anion or a cation, thus carrying charge. Because of the charge associated with ionic polymerization, stabilization of that charge on the active center is going to be a much more critical factor to consider when deciding whether monomers will tend to polymerize with anionic or cationic pathways.

Figure 6.1 - Examples of monomers that can be polymerized by cationic pathways

Source: Lauren Zarzar

Think back to organic chemistry, where you learned about carbocations and carbanions. How were the carbocations and carbanions best stabilized? By substituents that could help distribute or delocalize charge! A carbocation is stabilized by substituents that donate electron density, since the carbocation is electron deficient. On the other hand, carbanions are best stabilized by substituents that withdraw electrons, since carbanions are electron rich. In most cases, a monomer will have a preference for whether it’s easier to polymerize by anionic or cationic pathways, depending on which active center intermediate is more stable. There are a few monomers, such as styrene, which distribute the charge so well that they can be polymerized by both pathways.

Let’s refresh your memory on electron withdrawing and electron donating groups:

PROBLEM

Do you expect acrylonitrile to proceed via anionic or cationic polymerization?

Acrylonitrile

1. Cationic
2. Anionic
3. Neither, free radical only

Click here for the answer.

ANSWER

B. Anionic

Because –CN is strongly electron withdrawing.

Before diving into the specifics of both anionic and cationic polymerization, here is a general comparison of ionic polymerization with free radical polymerization:

• A propagating chain active center is accompanied by a counter ion (opposite charge) in ionic polymerization, but not with free radical polymerization.
• The counter ion can affect stereochemistry and rate of polymerization in ionic polymerization, which is not a consideration for free radical polymerization.
• The polarity of the solvent is more important in ionic polymerization than in free radical polymerization, because now we have charge to stabilize at the active center.
• Termination can’t occur by reaction between active centers because they are the same charge, whereas in free radical polymerization it is common to have termination by combination of radicals.

Let’s first consider cationic polymerization in depth. Cationic polymerization goes through initiation, propagation, chain transfer, and termination, much like free radical polymerization. But cationic polymerization is of course characterized by having an active center that is a positively charged cation. Thus, we look for monomers that have substituents to help stabilize that positive charge and which are electron donating. Example monomers that can be polymerized by cationic polymerization are:

Figure 6.2 - Examples of monomers that can be polymerized by cationic pathways

Source: Lauren Zarzar

Initiation:

Cationic active centers are created by reaction of the monomer with an electrophile. Examples of good initiators are H₂SO₄ or HClO₄; BF₃, AlCl₃, SnCl₃ with ‘co-catalyst’ (water or organic halide, makes for more stable counter ion). The general steps of initiation are shown in Figure 6.3. As typical, there are two steps in the initiation process.

Figure 6.3 - Showing the steps of initiation for cationic polymerization.

Source: Lauren Zarzar

R⁺ is an electrophile and A^- is the counter-ion. Note that a double headed arrow is used to show the reaction mechanism because we are pushing two electrons (as compared to with reactions in free radical polymerization, where our single headed arrows signified the movement of individual electrons).

Propagation:

Propagation usually takes place by head to tail addition because of the stability of the carbocation and steric considerations. Again, note the double headed arrows in Figure 6.3 and that the counter-ion is always present.

Figure 6.4 - Propagation in cationic polymerization

Source: Lauren Zarzar

Termination and chain transfer:

Unlike in free radical polymerization, termination by two propagating chains reacting is not possible, because they have the same charge. Instead, termination occurs usually by ion pair rearrangement, releasing H⁺ and generating a terminal C=C as shown in Figure 6.4. Even though the terminated chain still has a double bond which in principle can continue to polymerize, due to the substitution on that terminal carbon, sterics will reduce the reactivity.

Figure 6.5 - Termination by ion pair rearrangement during cationic polymerization

Source: Lauren Zarzar

Chain transfer can also occur, similarly resulting in a terminated chain with an end C=C. Again, due to the substitution on the terminal carbon of the terminated chain, even though there is a double bond which can in principle continue to react, sterics will prevent reactivity. The chain that now contains the active center will continue to polymerize. Similar to free radical polymerization, chain transfer to polymer can affect the skeletal structure. Also like free radical polymerization, chain transfer to solvent can still occur and would reduce the degree of polymerization.

Figure 6.6 - Chain transfer during cationic polymerization

Source: Lauren Zarzar

Solvent and Counter-ion effects:

Because we now have charge at our active center and have a counter-ion associated with our active center, we have to take into account effects of solvent and that counter-ion that we didn’t have to consider for free radical polymerization. As follows from our general understanding of how added steric bulk prevents reactions, then it’s no surprise that “freer” carbocationic active centers propagate faster (higher k_p) than if associated closely with a counter ion. Polar solvents will help to separate ion pairs. Not only can propagation occur faster, but more ion pair separation will also reduce ion pair rearrangement and rate of termination.

Figure 6.7 - Effect of counter-ion association with active enter on rate of propagation

Source: Lauren Zarzar

We now move onto anionic polymerization where we have a negative charge at our active center. To stabilize our active center, we then want to have electron withdrawing substituents on the active center carbon in order to help delocalize the excess charge.

Initiation:

Anionic polymerizations are often initiated by strong nucleophilic initiators, such as potassium amide. As we often see, there are two steps for initiation:

Figure 6.8 - Initiation of anionic polymerization of styrene using potassium amide.

Source: Lauren Zarzar

Styrene is one of the monomer most commonly polymerized by anionic polymerization.

Propagation:

Again, looks similar to what we have seen before for propagation but with an anion at the active center. Similarly to initiation, we are showing the propagation for polymerization of styrene.

Figure 6.9 - Propagation for polymerization of styrene

Source: Lauren Zarzar

Termination and Chain Transfer:

Like other chain polymerizations we have seen, we can get chain transfer to solvent. However, for anionic polymerization, we do not see ion pair rearrangement, and there is no formal termination. Why? Well, it would require transfer of a hydride (H^-), rather than an H⁺ which we saw for cationic polymerization; this is unfavorable. Therefore, there is no formal pathway for termination. In order to terminate the polymerization, special molecules would need to be added to cap the polymer with non-reactive functional groups. In the absence of any termination, we call this kind of anionic polymerization a living polymerization.

Kinetics of Living Anionic Polymerization:

It is interesting to compare the kinetics of living polymerization with the free radical polymerization kinetics to see the effect that removing chain transfer and termination have on the kinetics. When carried out in a polar solvent, it is generally true for these anionic polymerizations that k_i is much greater than k_p since pretty much all our initiator is in the active form very early on. So, the total concentration of carbanionic active centers equals the concentration of initiator used initially ${\left[ I \right]}_0$. And we can write the rate of propagation:

$$R_p=-\frac{d\left[ M \right]}{dt}=k_p{\left[ I \right]}_0\left[ M \right]$$

where $K_p{\left[ I \right]}_0$ is a constant, so we see there is only dependence on ${\left[ M \right]}_0$, concentration of monomer. We can also easily describe the degree of polymerization:

$${\overline{x}}_n=\frac{molesmonomerconsumed}{molesofpolymerproduced}=\frac{cK{\left[ M \right]}_0}{{\left[ I \right]}_0}$$

where c=fractional conversion of monomer and K equals the number of active centers generated per initiator (often, this is 1 for initiators like KNH₂ but there are some initiators that generate 2 active carbanions per initiator molecule, which case K=2). We find from this equation that degree of polymerization increases linearly with monomer conversion (which is very different than for free radical polymerization!)

Because the mechanisms for living polymerizations without terminations are quite different from step or chain mechanisms, the derivation for the molar mass distribution is different. (we will not go into depth here). For living polymerization, the molar mass dispersity is given below and a plot of the distributions for various values of ${\overline{x}}_n$ is given in Figure 6.10 below (textbook Figure 5.1). Notice that the distributions are relatively narrow, which is different from what we have seen previously for step polymerization and free radical polymerization.

$$\frac{{\overline{M}}_w}{{\overline{M}}_n}=1+\frac{1}{{\overline{x}}_n}$$

Figure 6.10 - Weight-fraction Poisson distribution w_x of chain lengths for values of x̄_n in a polymerization without termination. For comparison, the dotted line shows the weight-fraction most probable distribution of chain lengths when ${\overline{x}}_n$ =50 (See Sections 3.1.3.2 and 4.3.8). Thus, polymerization without termination produces far narrower distributions of chain length than either step polymerization or conventional free-radical polymerization.

Source: Derived from Introduction to Polymers Figure 5.1

Overview

In this Lesson, we consider some intricacies of chain polymerization which we have disregarded to this point. For example, you all have learned about the concept of chirality in organic chemistry - is there such a thing for polymers, and how is it controlled? There is, and we call it tacticity - and the tacticity of the polymer has very important ramifications for the polymer properties. What about monomers that are conjugated and can have resonance? We will look at what happens when we polymerize dienes, which have conjugated double bonds, both of which can participate in polymerization. Lastly, we consider a special type of chain growth polymerization where are monomers are actually cyclic, called ring opening polymerization.

Learning Outcomes

By the end of this lesson, you should be able to:

• Identify the tacticity of a polymer.
• Draw the mechanisms for polymerization of dienes leading to 1,2 addition, 3,4 addition, and cis/trans 1,4 addition products.
• Describe the benefits of coordination polymerization and why Ziegler Natta polymerization is used.
• Draw mechanisms and describe the tacticity for cationic and anionic ring opening polymerization.

Lesson Checklist

Please refer to the Canvas Calendar for specific timeframes.

Questions?

If you have questions, please feel free to post them to the General Questions and Discussion forum. While you are there, feel free to post your own responses if you, too, are able to help a classmate.

Many commercially important polymers that you may use in your daily lives, such as epoxy glue, rely on ring opening polymerization. Ring opening polymerization is characterized by using a monomer that is cyclic (a ring) and the mechanism can proceed by radical, anionic, or cationic pathways depending on the specific monomer and initiator. During polymerization, the ring opens and creates a linear polymer. In many ways, ROP is familiar to our other mechanisms, and we can use it to make many of the same polymers (and some new ones). It still requires initiation, it still goes through propagation and termination, it still follows the same rules for electron donating and electron withdrawing groups as we learned for cationic and anionic polymerization.

FIgure 7.1: Examples of ring opening polymerizations

Source: Lauren Zarzar based on figures from Young, Robert J., and Peter A. Lovell.
Introduction to Polymers, Third Edition, CRC Press, 2011.

So why use a cyclic monomer instead of a non-cyclic one? Well, one important thing going for cyclic monomers (with small rings) is that they have ring strain, which makes them somewhat less stable (and hence more reactive) than non-cyclic monomers. For larger rings, they have less ring strain, but more steric repulsion between the ring substituents, which also makes them unstable.

Let's first look at a cationic ring opening polymerization of epoxides, which are very common cyclic monomers, and are used to produce polyethers. We can use the same initiator molecules. Note the use of double-headed arrows for moving pairs of electrons. We see some equilibrium structures here as well that are new - the cationic intermediates are in equilibrium between the ring open and ring closed state. Termination can occur by rearrangement, just as we saw before in cationic polymerization.

Figure 7.2: Cationic ring opening polymerization of epoxides

Source: Lauren Zarzar based on figures from Young, Robert J., and Peter A. Lovell.
Introduction to Polymers, Third Edition, CRC Press, 2011.

We can also consider ring opening polymerization of epoxides by anionic polymerization, as shown below.

Figure 7.3: Anionic ring opening polymerization of epoxides

Source: Lauren Zarzar based on figures from Young, Robert J., and Peter A. Lovell.
Introduction to Polymers, Third Edition, CRC Press, 2011.

Notice that again we see the same kinds of initiators as was typical for anionic polymerization. We have added an "R" group onto the epoxide to help stabilize the anion, and because of this substitution, the nucleophilic attack will occur on the least hindered carbon. We also see no inherent termination process, unlike cationic polymerization.

In addition to epoxides, another common class of cyclic monomers are lactones:

Figure 7.4: Anionic ring opening polymerization of lactones

Source: Lauren Zarzar based on figures from Young, Robert J., and Peter A. Lovell.
Introduction to Polymers, Third Edition, CRC Press, 2011.

PROBLEM 1

Of the monomers shown below, which would yield a polyether when polymerized by ring opening polymerization?

1. Isotactic polybutadiene
2. Syndiotactic polybutadiene
3. Atactic polybutadiene

Click here for the answer to Problem 1.

ANSWER 1

A. Isotactic polybutadiene

Isotactic polybutadiene would yield a polyether

PROBLEM 2

Of the monomers shown below, which one would you choose to make this polymer?

Click here for the answer to Problem 2.

ANSWER 2

D.

Because we usually draw polymers as flat 2D structures on a piece of paper, it's easy to forget that actually polymers are three-dimensional and the structure often has very important ramifications on the polymer properties and chemistry. For example, in organic chemistry, you learned about chirality or the "handedness" of molecules, where the position of the atoms in 3D space differ by mirror images of one another. Molecules that are chiral have the same connectivity of the atoms, but are not the same molecules - the structures would not be able to be overlaid with each other when the 3D structure is considered. We use a similar concept for polymers, tacticity.

Figure 7.5: Using 3D notation to show polymer tacticity

Source: Dr. Lauren Zarzar based on figures from Young, Robert J., and Peter A. Lovell.
Introduction to Polymers, Third Edition, CRC Press, 2011.

Look at the two repeat units shown in Figure 7.5. Recall from organic chemistry that we used the dashed lines to indicate a bond that goes "into" the page, and a bold line to indicate a bond "coming out of" the page, to give a 3D representation of the molecule. We see in Figure 7.5 that the connectivity of all the atoms is identical between the two structures, but the X and Y substituents are flipped in their 3D orientation. (The carbon that has the X and Y substituents is called an asymmetric carbon.) Therefore, these repeat units are actually not exactly the same; they cannot be overlaid with each other, no matter what orientation you choose. So even though the same monomer could be used to make both of these repeat units, these repeat units are different! In order to describe this difference in 3D structure, we use the concept of tacticity.

There are three terms we use to describe polymer tacticity. Isotactic means that all asymmetric carbons in the polymer have the same configuration. Syndiotactic means that the asymmetric carbons have alternating configuration. Atactic means that the asymmetric carbons have random orientation. Drawings of each of these is shown below. Notice that in order to have tacticity, you must have asymmetric carbons. If X=Y in Figure 7.5, then there is no asymmetric carbon, and no relevant tacticity. Also realize that the entire polymer does not have to be just one of these categories, there may be short stretches along the polymer which can take on any tacticity. Tacticity is important because it can affect the chemistry, reactivity, and mechanical properties of polymers. You can imagine that if the polymer structure is more "regular", such as an isotactic polymer versus an atactic polymer, that the isotactic polymer may be able to pack better, and thus crystallize more easily, which would significantly affect its material properties.

Figure 7.6: Three variations of polymer tacticity

Source: Dr. Lauren Zarzar based on figures from Young, Robert J., and Peter A. Lovell.
Introduction to Polymers, Third Edition, CRC Press, 2011.

So how does this tacticity arise? To understand this, we have to remember what the 3D structure of our active center looks like. Recall that the radical on our active center is in an unhybridized p orbital that is perpendicular to the plane with the sp² orbitals bonded to the substituents, as shown in Figure 7.7 below. In a slight oversimplification, we can imagine that the orientation of the next repeat unit will depend on whether the next monomer approaches the active center from above or below. If you are interested, for a more detailed figure depicting how this orientation gets translated to the tacticity, please see Figure 6.2 in the text.

Figure 7.7: Tacticity varies depending on the approach of the monomer

Source: Dr. Lauren Zarzar based on figures from Young, Robert J., and Peter A. Lovell.
Introduction to Polymers, Third Edition, CRC Press, 2011.

PROBLEM

The polymer below was formed from ring opening polymeriztion of the below monomer. What is the tacticity of this polymer?

1. Isotactic
2. Syndiotactic
3. Atactic

Click here for the answer.

ANSWER

A. Isotactic

Notice that isotactic and syndiotactic refer to the stereoisomerism of the asymmetric carbons, not necessarily the direction those bonds are "pointing". Here, we see the R groups alternate between going into and out of the page, so our first instinct is likely to say that this is a syndiotactic polymer - but also notice that if you were to rotate all the carbons so that they are pointing in the same direction, that in fact, all the carbons with the R group have the same stereochemistry, making it isotactic.

There are multiple variables that can affect the resulting stereochemistry of the polymer, such as counter ion, solvent, or temperature. However, it is still very difficult to make highly regular structures by any of the polymerization mechanisms we have discussed thus far. If we need to make highly stereoregular structures, we need a different approach: coordination polymerization. Coordination polymerization involves the addition of monomers to an organometallic active enter.

One of the most important coordination polymerization catalysts is the Ziegler-Natta catalyst. The Ziegler-Natta catalyst allows for the synthesis of highly linear, stereoregular polymers. For example, at the beginning of the course, we introduced both high and low density polyethylene; well, to make the high density polyethylene (HDPE), we noted that you had to have very highly linear polyethylene that packed together well. Such HDPE is often made using coordination polymerization, and cannot be accomplished by other polymerization routes. Similarly, polypropylene can also be produced with a highly steroregular structure (isotactic or syndiotactic) through coordination polymerization. A simplified mechanism of how this works is shown using a Zr catalysts is shown in Figure 7.8.

Figure 7.8: Simplified mechanism for a simplified catalyst for ethylene polymerization.

Source: Wikipedia - Ziegler–Natta catalyst

Since you have not likely taken inorganic chemistry, and for coordination polymerization we are dealing with organometallic molecules, I am not going to expect you to learn or understand exactly how the polymerization mechanism works. But there are a couple important differences to note. First, we see that the organometallic catalyst is located at our active center and "holds on" to the monomer. It holds on to the monomer is a very specific orientation, and so every monomer reacts in the same orientation. Recall how in Figure 7.7, we showed that the stereochemistry is controlled by whether the monomer approaches the active center from above or below? Well, we are basically using this organometallic catalyst to help us control that. But we also see that since the Zr has to coordinate to the monomer that the monomer has to be able to approach the catalyst and that bulky groups are going to prevent this coordination from happening. Therefore, we can't use this technique for every polymer, and those with bulky substituents are going to be less active towards coordination polymerization.

Thus far, we have only considered chain polymerization of monomers that have isolated reactive groups. But we also recall from general chemistry and organic chemistry that double bonds are conjugated and can participate in resonance (depending on the molecular structure). So what happens if we have a conjugated monomer? For example, 1,3-butadiene and isoprene are common monomers (shown below) which have conjugated double bonds. How do these monomers react?

Figure 7.9: 1,3-isobutadiene and isoprene

Source: Dr. Lauren Zarzar based on figures from Young, Robert J., and Peter A. Lovell.
Introduction to Polymers, Third Edition, CRC Press, 2011.

There are going to be multiple ways in which these unsaturated bonds can react. To keep track of which carbon is where, we need to number our carbons. Following tradition from the naming of organic molecules, we number our carbons along the carbon chain with the diene and start counting with the carbon nearest the substituent. Take this generic diene as an example, where "R" represents some substituent. We number the carbons as follows:

Figure 7.10: Generic diene with numbered carbons

Source: Dr. Lauren Zarzar based on figures from Young, Robert J., and Peter A. Lovell.
Introduction to Polymers, Third Edition, CRC Press, 2011.

It is very important that you number your carbons correctly, or you will end up drawing the wrong polymerization products. Please note that you do not necessarily number from left to right, it just depends on where that substituent "R" is located. We see we have two unsaturated bonds that we could polymerize: the 1,2 and 3,4 bonds. Figure 7.11 shows the products we get if we polymerize through those bonds:

Figure 7.11: Products of polymerizing through the 1,2 and 3,4 bonds

Source: Dr. Lauren Zarzar based on figures from Young, Robert J., and Peter A. Lovell.
Introduction to Polymers, Third Edition, CRC Press, 2011.

We see we get two very different polymer depending on whether we react the 1,2 or 3,4 bond. (Also, don't forget that each of these polymers can have tacticity!) But we aren't quite done, because these dienes have conjugated double bonds, which we know can have resonance. This means, if we generate an active center, that it can move through the molecule via resonance and this will also affect our products. To make things even more complicated, single bonds can rotate, and the bond rotation in the diene will also affect our polymer! As shown in Figure 7.12, because of these resonances and bond rotation we can also get cis 1,4 addition and trans 1,4 addition. (Remember the "cis" and "trans" geometric isomers from general chemistry and organic chemistry?).

Figure 7.12: Polymerization of dienes showing the formation of the cis and trans 1,4 addition products. The * signifies the active center.

Source: Dr. Lauren Zarzar based on figures from Young, Robert J., and Peter A. Lovell.
Introduction to Polymers, Third Edition, CRC Press, 2011.

Just as tacticity was important to the polymer structure and properties, so is the mode of addition for dienes. Depending on whether you have primarily cis or trans addition, you can have polymers with very different mechanical properties.

PROBLEM

Shown below are (A) trans, (B) cis, and (C) vinyl polybutadiene (from left to right). Which one is most crystalline?

1. Trans polybutadiene
2. Cis polybutadiene
3. Vinyl polybutadiene

Click here for the answer.

ANSWER

A. Trans polybutadiene

The regular zig zag structure of the backbone will allow the polymer to pack better giving it more crystallinity.

Summary

After this lesson, you should now feel comfortable identifying the tacticity of a polymer, describing how the tacticity impacts the polymer properties, and suggesting methods by which to control tacticity. Additionally, you should be able to draw the products of polymerization of dienes, and describe the mechanism of the various products are formed. Lastly, you now can suggest cyclic monomers to use to create polymer via ring opening polymerization, and notice how many of those polymers you can also make by step growth! Next, we move onto copolymers – where we have not just one type of monomer, but two or more. We will find that when we mix monomers, it’s likely that one monomer is more reactive (and incorporated more quickly into the polymer). How do we measure that, and determine which monomers will actually end up in the polymer? All coming soon, in Lesson 8!

Reminder - Complete all of the Lesson 7 tasks!

You have reached the end of Lesson 7! Review the checklist on the Lesson 7 Overview / Checklist page to make sure you have completed all of the activities listed there before you begin Lesson 8.

Overview

You now have a great toolbox of monomers and polymerization mechanisms by which you can make all sorts of exciting polymer materials! You can decide what sorts of monomers and polymerization mechanisms to use, when and how to control tacticity, and how polymerization mechanism impacts skeletal structure for both step growth and chain growth (radical, cationic, anionic, and ring opening). Let’s expand that breadth even more, and think about how we can mix monomers together to create copolymers. In Lesson 1, we learned the difference between homopolymer and copolymer, but most of the polymers we have actually talked about up until now have been homopolymers which incorporate a single type of monomer. In this Lesson, we learn how to predict the ratios in which a monomer will be incorporated into a polymer, and how that composition might drift over the course of a reaction.

Learning Outcomes

By the end of this lesson, you should be able to:

• Explain under what circumstances, and why, the composition of a polymer changes with extent of reaction
• Distinguish between homopropagation and cross propagation reactions
• Describe kinetics of binary chain copolymerization
• Define reactivity ratio
• Apply copolymer composition equations to predict polymer compositions
• Describe, in terms of reactivity ratios, the conditions leading to random copolymerization, azeotropic copolymerization; block copolymers, alternating copolymers, or homopolymers
• Interpret plots of F_A vs f_A
• Explain composition drift using reactivity ratios

Lesson Checklist

Please refer to the Canvas Calendar for specific timeframes.

Questions?

If you have questions, please feel free to post them to the General Questions and Discussion forum. While you are there, feel free to post your own responses if you, too, are able to help a classmate.

n this lesson, we will consider what happens in terms of kinetics and skeletal structure when we polymerize two or more different monomers together to create a copolymer. We already learned in general what a copolymer is in Lesson 1 “what is a polymer?”. Make sure to refresh your memory on the difference between homopolymer and copolymer, and the definitions of alternating copolymer, block copolymer, random copolymer, and statistical copolymer.

Let’s consider a copolymer formed from reacting two monomers together. We consider a system in which the different monomers can react with each other, and they can also react with themselves. An example would be in the case of chain growth polymerization of two different monomers with vinyl groups. (This is an important point, because we saw some examples of step polymerization in which you could only get an alternating copolymer, RA₂+RB₂, just because of the specific functional groups that had to react. We are not considering that situation right now.) Consider the situation shown in Figure 8.1 where we have a purple and green monomer, and the purple happens to be incorporated faster into the polymer than the green one. Well, then at the start of our reaction, the polymer we form is going to contain mostly purple monomers. Later in the course of reaction, we find we have used up most of the purple monomers but have lots of green monomers left, so we begin to incorporate the green monomers more often than purple. As you can see, this leads to a distribution of the purple and green monomers along the polymer that is uneven; we have more repeat units of purple at one end of our polymer and more green at the other. You could also imagine that you stop the reaction before getting to a high extent of reaction, and end up with a polymer that has almost no green monomers at all! So what factors influence this distribution of purple and green along the length of the polymer? Can we predict and describe how various monomers will be incorporated when they are polymerized together?

Figure 8.1: Schematic representation of how two different monomers can be incorporated at different rates into the copolymer and the effect that could have on the polymer composition

Source: Lauren Zarzar

Let’s narrow our focus to 1) chain growth polymerization and 2) binary copolymerization. The chain growth part you already know, and for binary copolymerization we mean that there will only be two different monomers, which we will call A and B. Now because we have two different monomers, that means we can also have two different active centers: -A* and –B*. We designate the active enter with an * because it could be any number of species, such as radical, anion, or cation. Since A can react with A, A can react with B, and B can react with B, we have several different modes of addition that can occur:

$$\begin{array}{c}\text{Homopropagation reactions} \\ \text{ 1) }\sim \text{A*+A}\stackrel{{\text{ k}}_{\text{AA}}}{\to }\sim \text{AA*} \\ \text{ 2) }\sim \text{B*+B}\stackrel{{\text{ k}}_{\text{BB}}}{\to }\sim \text{BB*}\end{array}$$

$$\begin{array}{c}\text{Cross-propagation reactions} \\ \text{ 3) }\sim \text{B*+A}\stackrel{{\text{ k}}_{\text{BA}}}{\to }\sim \text{BA*} \\ \text{ 4) }\sim \text{A*+B}\stackrel{{\text{ k}}_{\text{AB}}}{\to }\sim \text{AB*}\end{array}$$

When an active center on A reacts with another A, or when an active center on B reacts with another B, we call these homopropagation reactions. When an active center on B reacts with A, or when an active center on A reacts with B, these are called cross-propagation reactions. We can describe the rate of monomer consumption for both A and B monomers as the sum of the processes that consume those monomers. For example, A is consumed in reactions (1) and (3) as outlined above. B is consumed in reactions (2) and (4). We then write the rate of consumption for each A and B monomer:

For any point during the reaction, we now have expressions that describe how much A or B is being incorporated. What about the ratio of incorporation? By looking at a ratio of the rates of incorporation of A and B, we can immediately have a sense of which monomer is being preferentially consumed:

This equation for d[A]/d[B] looks a little scary, but if we could just substitute for the concentration of active centers, we could simplify it….. How can we figure out the steady state concentration of active centers?

To start, we can describe the rate of change of [A*] and [B*], which are the active centers, very similarly to how we described the change in [A] and [B]. A* is consumed in reaction (4) but created in reaction (3). (Homopropagation reaction (1) also involves A* but there is no net change in the concentration of A* in reaction (1), thus we do not need to consider it). B* is consumed in reaction (3) and produced in reaction (4). (Again, homopropagation reaction (2) has net zero effect on [B*] so we don’t consider it). Therefore, we can write the change in concentration of active centers: