It would seem that polymer chains constructed from monomers as a result of random chemical reactions should have a rather wide distribution in their lengths. This is indeed true, and the name for this phenomenon when chains of various lengths coexist in a polymer substance is polydispersity.
Polydispersity has to be borne in mind when analyzing polymer properties.
In practice, there are some ways to reduce polydispersity by separating chains with di↵erent length.
An interesting method to obtain polymers with relatively narrow poly-dispersity without additional separation processes is based on the so-called living polymerization. This is a polymerization for which the ability of a growing chain end to terminate or to transfer its active species to another molecule has been removed. To reduce polydispersity the rate of chain initiation should be much larger than the rate of chain propagation. As a result practically all the chains grow simultaneously at a more or less constant rate until the monomer is exhausted. Living polymerization is a popular method for synthesizing block copolymers (see Sections 2.5 above and 4.7 below), since growing chain ends remain active after the process
How are Polymers Made? 25
with initial monomer is completed (no chain termination). Therefore, at this stage it is possible to add another monomer, and a new chain block will start to grow.
First example of living polymerization was discovered by Michael Szwarc (1909–2000) in 1956 in the anionic polymerization of styrene in special cat-alytic system. In this type of polymerization active chain end is negatively charged which prevents most of termination processes.
Anionic and later cationic polymerization gave most of examples of liv-ing polymerization systems until recently, when more sophisticated methods of manipulation with free-radical polymerization processes become avail-able. These methods are based on the use of the compounds which re-versibly react with propagating radical and convert it to the so-called “dor-mant species”. When the equilibrium between the active and dor“dor-mant species is regulated by special catalysts based on a transition metal, this process is called atom transfer radical polymerization (ATRP). If this equi-librium is provided by stable radicals such as nitroxides, the process is called stable free-radical polymerization (SFRP). In the case when dor-mant species are formed via a chain transfer rather than reversible ter-mination reactions, this process is referred to as reversible addition frag-mentation chain transfer (RAFT) polymerization. All these techniques allow to produce macromolecules of desired architecture and molecular masses.
3.5 Branched Polymers
Let’s now talk briefly about branched polymers. If, say, polycondensation is going on, and initial monomers have only two functional groups each, then we shall end up with linear polymer chains (with a small proportion of loops). However, if the monomers have three or more functional groups, a branched macromolecule can be synthesized (see Figure 2.8 c). Given plenty of “multifunctional” monomer units at the start, one can even obtain a polymer network (Figure 2.8 d ).
Branched macromolecules and polymer networks can also be formed by the linking of linear chains. There are various chemical ways of cross-linking. Sometimes chemically active cross-linking agents are used; they establish covalent bonds between di↵erent chain strands. Alternatively, ionization in a polymer system can be stimulated by radiation, etc. The simplest everyday life example of cross-linking is vulcanization — during
this process viscous natural rubber becomes a highly elastic polymer net-work (see Chapter 7 for more details).
Chapter 4
What Kinds of Polymer Substances are There?
. . . they knew how to weave stu↵s of the most beautiful colors and elaborate patterns . . .
Hans Christian Andersen, The Emperor’s New Clothes
4.1 “Traditional” States of Matter and Polymers
We now can easily visualize polymer molecules — they are long chains tangled up into coils. However, even knowing the molecular structure of a substance, it may still be hard to predict for sure all its properties. For example, water, consisting always of the same well-known molecules H2O, depending on the conditions can be a liquid, a solid (ice), or a gas (steam).
So what about polymer substances? How do they look, and what states can they exist in?
Everyone is familiar with the three simplest ordinary states of matter:
solid (crystal), liquid and gaseous. There is also a fourth one, a plasma.
Normally it emerges at extremely high temperatures when thermal motion is so intense that it leads to the ionization of the atoms. If a polymer is heated up to such a temperature, its molecular chains will merely fall apart.
So the substance will not be polymeric any longer, or, in other words, the destruction of the polymer will occur. Thus, the state of a high-temperature plasma is not possible for polymers.
It seems we are left with the three “traditional” states of matter after all. This sounds too small a number though, if we try to imagine all the diversity of polymer substances in everyday life: there are plastics and
27
rubber, fibers and fabrics, timber and paper, polymer films and varnishes, dyes and paints, not to mention the various polymers found in nature! You would be right to suspect therefore that the common concept of the three states of matter is not quite applicable to polymers, especially as two of the three states, a gas and a crystal, are not really typical for polymers.
Indeed, if one wanted to create a polymer gas, one would have to make long heavy molecules (like the ones in Figure 2.1) “fly” around. This would only be possible if there were no gravity, and also if you could maintain a low pressure in the container (i.e. you would have to provide a high vacuum there). Obviously, such exotic conditions are very hard to achieve;
this is exactly why polymer gases have not been heard of so far.
b
a c
Fig. 4.1 A cartoon of molecular arrangements in typical polymeric substances: (a) a liquid;
(b) a perfect crystal; (c) a partially crystallized polymer.
Perfect single crystals (see Figure 4.1) cannot be obtained from polymers for another reason. Let’s experiment with a liquid of polymer molecules (Figure 4.1 a). If we cool it down to below the crystallization tempera-tures, then the perfect crystal (Figure 4.1 b) will be energetically the most favorable state. It cannot be formed straightaway, though. Crystallization goes on totally independently in di↵erent parts of the system. So what ap-pears at the start is a number of crystalline “nuclei” randomly orientated with respect to each other. Clearly, when the nuclei grow big enough the entire structure becomes somewhat “frozen”. (This is because, in the crys-talline phase, in order to move with respect to each other polymer chains have to overcome enormous energetic barriers.) Hence, further evolution towards the perfect structure of Figure 4.1 b appears hardly possible. This
What Kinds of Polymer Substances are There? 29
is why crystallizing polymers normally form a semi-crystalline phase so that crystalline regions are separated by amorphous layers (Figure 4.1 c). Some-times perfect single crystals of a polymer can still be obtained by special techniques, but they have not found any broad practical use.
4.2 Possible States of Polymer Substances
Do we have to class all polymers as liquids, now we know that they can be neither gases nor, except rarely, crystals?! In the broad sense, we would — if we only regard a liquid as a dense substance that has no long-scale or-der in the atoms’ positions. However, this definition would not be terribly informative. This is why there is another, more fruitful way to classify poly-mers’ phases. A distinction is normally made between a semi-crystalline state, a polymer glass, an elastic, and a viscous polymer. Which of the four phases occurs depends on the kind and strength of interactions between the monomers.
We have already talked about semi-crystalline polymers. Let’s now de-scribe in brief the other three states. A polymer in a viscous state is purely a liquid of macromolecules as sketched in Figure 4.1 a. Long chains all mingle together, but, in thermal motion, they can rather easily move with respect to each other. If an external stress is applied, some overall motion of the molecules occurs, i.e. the polymer starts to flow. The flow develops quite slowly, due to a great number of entanglements. This explains why the viscosity of polymeric liquids is normally rather high. Naturally, this state of a polymer is called viscous; another name for it is a polymer melt.
Let’s now see what will happen if molecular chains of a polymer melt are joined together with covalent chemical bonds (cross-links) to form a network (see Figure 2.8 d). (We talked about di↵erent techniques of how to synthesize a polymer network in Chapter 3.) Clearly, the chains will no longer be able to move long distances relative to each other (simply because they will all be tied together into a network). Thus it becomes impossible for the polymer to flow. Meanwhile, on a smaller scale (i.e. shorter than an average distance between two neighboring cross-links) the mobility of the chains will not be constrained by the cross-links. This is why, if you apply tension to a polymer network, its chains, which were originally coiled up (Figure 2.8 d), stretch quite considerably, resulting in exceptionally large elastic reversible deformations. This state of a polymer is called elastic.
Rubber is, obviously, a well-known example of it.
Cross-linking of chains in an elastic polymer does not necessarily have to be caused by covalent bonds between neighboring molecules, however.
The role of e↵ective cross-links can be performed by nuclei of a crystalline phase (Figure 4.1 c), or by topological entanglements (Figure 2.10 c and d). It can also be played by some small regions where, due to particular local conformations of the chains, there are comparatively high potential barriers for the chains to move with respect to each other (“glassy” or
“frozen” regions). Thus, an elastic polymer substance can in principle be produced without chemical cross-linking.
If the temperature decreases, many polymers tend to change from a melt to a semi-crystalline state. However, far from all polymers crystallize when they are cooled. The crystal formation begins when little crystalline seeds start developing. This happens when, on the one hand, the crystalline phase is thermodynamically favorable but, on the other hand, the thermal motion is enough to enable the rearrangement of the polymer chains to form seeds. If the cooling is fast enough, we can easily avoid that stage, and so a crystal does not form. This statement is also true for substances with low molecular weights. The new thing for polymers is that the “fast” cooling does not necessarily have to be very fast in the usual sense of the word. As you can see from Figure 4.1 c, it takes much more time to form a crystalline seed for heavily entangled chains than for atoms or small molecules which are not chained together.
Moreover, some polymers cannot be crystallized even in principle. In-deed, crystallization may only appear if there is long-scale order in the molecules’ positions (as in Figure 4.1 b). However, say, for a statistical copolymer whose chains consist of two types of units, A and B, long-scale order is impossible. (This is simply because the sequences ofA and B along the chains are totally random.) Such copolymers can never crystallize on cooling.
The same e↵ect is observed for homopolymers whose monomers, al-though chemically identical, may appear in a few di↵erent spatial configu-rations, with high barrier for the inter-conversion between these states. As an example, Figure 4.2 shows two possible configurations of the repeat unit of propylene. If the synthesis is carried out under usual conditions, these two configurations will be present in roughly equal proportions, and will alternate randomly along the chains. This kind of polypropylene is called atactic; obviously, it cannot crystallize. Yet there is a special technique for synthesizing the so-called isotactic polypropylene instead, whose monomers
What Kinds of Polymer Substances are There? 31 of the monomer unit of propylene.
are all arranged in only one of the two possible configurations. Crystalliza-tion is then quite straightforward.
There are many other polymers that, like polypropylene, are atactic (i.e. unable to crystallize) if synthesized under normal conditions. This includes, for instance, polystyrene, polymethyl methacrylate (perspex), and polyvinyl chloride (PVC), to mention but a few from everyday life.
So crystallization does not happen, but what kind of processes do hap-pen in the “noncrystallizable” polymers if the temperature is reduced?
Since thermal motion becomes less, energy barriers for relative motion of the molecules grow e↵ectively higher and higher. Gradually, this motion becomes “frozen out”, first of all at the largest scale, and then at increas-ingly smaller ones. In the end, any thermal motion at any scale larger than the size of a monomer ceases to exist. Polymers in such a “frozen” state are known as polymeric glasses, and the process that we have just described is called a glass transition. It normally occurs in a rather narrow temperature range around the “glass transition temperature” Tg.
Thus, polymers which are unable to crystallize tend to become a glass at low temperatures. You may be quite familiar with those more or less transparent glasses made from the atactic polymers already mentioned — polystyrene, perspex and PVC. (For the first two of them Tg 100 C, whereas for the last one Tg 80 C.) However, ordinary silicate glasses (used for windows, for example) are not polymeric; they are made of low molecular weight compounds such as silicon dioxide, oxides of boron, sodium and calcium. Such a mixture forms a glass on cooling, roughly in the same way as polymers.
The very term “glass” leaves no doubt that the substances are mainly used as transparent partitions. You may wonder why the majority of polymeric glasses are actually transparent, whereas semi-crystalline poly-mers are normally not. The reason is that the structure shown in
Figure 4.1 c has a great number interfaces between the crystalline and amorphous phases. Light gets reflected by the interfaces many, many times, and eventually gets totally “lost” between them. As a result, the sample does not let light out, hence the lack of transparency. Meanwhile, so-called acrylic glasses, say, have a much more uniform structure, or at least the scale of inhomogeneities is much smaller than the wavelengths of visible light. Therefore, light can penetrate through such substances without be-ing scattered — which is why some nice tableware is made of this material.
4.3 Plastics
All four states of polymers are very important from the practical point of view. Rubber substances are used in their elastic state, for example; we shall talk about them in detail in Chapter 7.
In this section we are going to look at plastics, the materials that we know very well from everyday life. Over the last few decades they have become widely used in industry too. The worldwide yearly production of plastics exceeds now 150 million tons. We hardly imagine life without these materials: what else can we use to make pens or water bottles? At the same time, plastics are endangering the environment: about 10 million tons of them are now floating in the Ocean alone, and no one knows how to deal with that. Concentrate on usefulness or on dangers — one thing is clear:
we have to understand plastics. Thus, what are they?
By definition, plastics are those polymers which whilst being processed are either elastic or viscous, whereas the materials in the actual use have to be either glasses or semi-crystalline substances. How can a polymer be transformed from one state into another? In many cases, it is done by changing the temperature: A polymer can be processed at elevated tem-peratures, where it is a viscous liquid, and afterwards cooled to become glassy or semi-crystalline. Materials produced in such a way are called thermosoftening plastics. However, some polymers tend to show the op-posite behavior — they become solid with increasing temperature. For instance, epoxy resin mixed up with a hardener very quickly becomes solid if heated up. This is simply because cross-links are formed more rapidly at higher temperatures. Such materials are sometimes called thermosetting plastics.
Thus, all four states of polymers share “responsibility” for the properties of plastics. Some of them are involved at the production stage, and others
What Kinds of Polymer Substances are There? 33
come into play when the plastic is put to practical use. We should also point out in what way the properties of glassy and semi-crystalline plastics di↵er from each other. Semi-crystalline thermosoftening materials (such as polyethylene, terylene, nylon, and teflon) are much more deformable and elastic, and much less fragile, than polymeric glasses. Normally they are not transparent either, but, in contrast to rubber, they tend to retain their shape under moderate deformation.
The extent to which solid materials can be deformed is described in physics by Young’s modulus, E. It is defined in the following way. Let’s imagine that we are stretching a cylindrical rod of length ` and cross-sectional area S, applying a force f along the axis. As the English scientist Robert Hooke noticed as early as 1660, the deformation ` of the rod (i.e. variation of its length) is proportional to the force (provided that ` is not too big),
= f
S = E `
` . (4.1)
In this formula is the stress, i.e. it is the force per unit cross-sectional area, and E is Young’s modulus. The value of E depends on the material of the rod, but not on its shape or size.
Let’s now look at some materials that we are going to talk about later in this chapter, and see what sort of values of E they have at room tem-perature. As a point of reference, it makes sense to choose the hardest inorganic substances, such as steel, cermet alloys, etc. Their Young’s mod-uli range from 1011–1012 Pa1 Inorganic glasses (as used in windows) have E in the range of 1010–1011 Pa. Meanwhile, for polymeric glasses typical values are E 109–1010 Pa which means that their deformability is two orders of magnitude higher than that of steel. As we have already said, semi-crystalline plastics are even more easily deformed; indeed, they have E 108–109Pa. As for various sorts of rubber, as well as other polymers which are normally used in their elastic state, their Young’s moduli tend to be exceptionally low: E < 106Pa.
How can we account for such a great di↵erence in values of E for di↵er-ent polymeric materials? Thermal motion in an elastic polymer is intense enough to enable the chains to move freely with respect to each other. How-ever, long-distance movements of the chains (i.e. flow) are much harder to
1As formula (4.1) indicates, E has units of pressure — force per unit area. This is why we express it in Pascals. Let’s remind that the unit Pa is defined as one Newton per m2, and that normal atmospheric pressure is very close to 105Pa. Since we are going to understand the molecular world, it is also useful to realize that one MPa (megaPascal) can be thought of as 1nmpN2, where pico Newton is 1 pN = 10 12N and 1 nm = 10 9m.
perform because of the cross-links. Under an external tension, the chains
perform because of the cross-links. Under an external tension, the chains