There are many
types of polymers: natural polymers such as wood, rubber, cotton, wool,
leather, and silk; biological polymers such as proteins, enzymes, starch, and
cellulose; and synthetic polymers such as polypropylene (PP), polyvinyl
chloride (PVC), and polystyrene (PS). In this chapter, we will discuss the
various structural elements of polymers, such as their chemistry and
crystallinity. The effect of structure on polymer properties will be discussed
in the next chapter.
Chemistry of polymers
The term polymer means “many
mers,” where mer originates from the
Greek word meros, which means “part.”
Thus, polymers are chains of repeat units. The chain forms by the sequential
addition of monomer units, as illustrated in the figure below:
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| Callister, William D. Materials Science and Engineering: An Introduction. New York: John Wiley & Sons, 2007. Print |
In this example, polyethylene is formed as an unpaired electron is transferred to each ethylene monomer that is added to the chain. When all the repeat units are the same, like in this case, the resulting chain is called a homopolymer. When two or more different repeat units are involved, the result is called a copolymer. The table below shows the repeat units of some of the most common polymers.
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| Callister, William D. Materials Science and Engineering: An Introduction. New York: John Wiley & Sons, 2007. Print |
Molecular weight
Since the lengths of polymer chains will all be different,
molecular weights of polymers are described as average molecular weights. There
are two ways to do this: number-average molecular weight and weight-average
molecular weight. The number-average molecular weight can be computed using:
where
Mi is the mean molecular weight in the interval i and xi
is the fraction of the total number of chains within that interval. On the
other hand, weight-average molecular weight can be calculated using:
where Mi is the again the mean molecular
weight in the interval i and wi is the weight fraction of molecules
in that interval. Number-average molecular weight will be more sensitive to low
molecular weight species while the weight-average molecular weight will be more
sensitive to higher molecular weight molecules. The polydispersity index, which
is a measure of the breadth of molecular weight distribution, is the
weight-average molecular weight divided by the number-average molecular weight.
Another parameter that is used to describe polymer size it the degree of
polymerization. This can be calculated by:
where m is the molecular weight of the repeat unit.
Molecular
shape
Polymer chains can take on different
configurations depending on the degree of twisting and bending that occurs
along the backbone. As depicted in the carbon backbone examples below, each
successive carbon atom can lie on any point of the cone of revolution that has
a 109 degree angle with the previous bond. In the middle example, the chain is
fairly linear, whereas in the example on the right, the rotation of the carbon
atoms into other positions results in a more twisted shape. Rotational
flexibility depends on factors such as the repeat unit structure or the
existence of bulky side chains. Quantitatively, chain conformations can be
described using models such as the free-jointed chain, the freely-rotating
chain, or the hindered rotating chain.
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| Callister, William D. Materials Science and Engineering: An Introduction. New York: John Wiley & Sons, 2007. Print |
Some definitions related to molecular
shape are the end-to-end distance and the persistence length. For a polymer
made up of monomer “vectors”
li, the end-to-end distance h is the sum of li.
The persistence length, on the other
hand, is the characteristic length scale for the exponential decay of the
correlations of backbone tangents. Essentially, the persistence length is how
long it takes for the backbone to bend, on average, at a right angle.
Molecular structure
There are different types of molecular structures found in polymers, such as linear, branched, crosslinked, and network. They are shown below:
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| Callister, William D. Materials Science and Engineering: An Introduction. New York: John Wiley & Sons, 2007. Print |
Linear polymers can be described as a
“mass of spaghetti.” They are fairly flexible and the chains are held together
by Van der Waals forces and hydrogen bonding. Branched polymers are harder to
pack together and thus have lower density. Crosslinked polymers are formed when
chains are joined together by covalent bonds. Rubbers are often crosslinked
through the process of vulcanization. Finally, network polymers are
three-dimensional and are the result of multiple covalent bonds.
Thermoplastics are linear or branched and
soften when heated and harden when cooled. Thermosets are crosslinked or
network and, once hardened, will not soften upon heating.
Isomers
Stereoisomers can be isotactic,
syndiotactic, or atactic. An isotactic configuration is when R groups are found
on the same side of the chain. A syndiotactic configuration is when the R
groups alternate sides. An atactic configuration is when the R groups are
randomly positioned.
There are also geometrical isomers, which
occur within polymers with double bonds in the backbone. When side groups are
on the same side of the double bond, the polymer is said to be in the cis structure.
When the side groups are diagonally across from each other, the polymer is in
the trans structure.
Copolymers
When chains are composed of more than one
type of repeat unit, the resulting polymer is called a copolymer. Copolymers
can be advantageous because they allow polymer chemists to combine properties
from different homopolymers. Below are the different types of copolymers. For a
more detailed discussion on block copolymers, check out this post.
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| Callister, William D. Materials Science and Engineering: An Introduction. New York: John Wiley & Sons, 2007. Print |
Crystallinity
in polymers
A polymer is said to be crystalline when
its molecular chains are aligned and packed in an ordered arrangement. On the
other hand, it is amorphous when the chains are misaligned and disordered.
Generally, it is easier to achieve crystallinity in polymers that have simple
and/or regular chemical structures. Often, polymers will have crystalline
regions interspersed within an amorphous matrix. The degree of crystallinity
can be determined using the following equation:
where ρs is the density of a
specimen for which the percent crystallinity is to be determined, ρa
is the density of the amorphous part, and ρc is the density of the perfectly
crystalline part.
Crystalline regions can be described
using the chain-folded model, depicted below. In this model, chains within a
platelet are aligned and fold back and forth on themselves.
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| Callister, William D. Materials Science and Engineering: An Introduction. New York: John Wiley & Sons, 2007. Print |
Many semicrystalline polymers form spherulites. As shown
in the figure below, spherulites grow radially outwards and consist of lamellar
chain-folded fibers with amorphous regions between them.
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| Callister, William D. Materials Science and Engineering: An Introduction. New York: John Wiley & Sons, 2007. Print |
Defects in
polymers
Due to the chainlike nature of polymers, the concept of
defects is different than in metals and ceramics—though they still exist. As
shown in the figure below, defects such as impurities and screw dislocations
follow very similar definitions as they did in other materials. However, besides
traditional defects, chain ends are also considered defects (usually associated
with vacancies). Also, the surfaces of chain-folded layers and boundaries between
crystalline regions are considered interfacial defects.
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| Callister, William D. Materials Science and Engineering: An Introduction. New York: John Wiley & Sons, 2007. Print |
Diffusion in
polymers
Small foreign molecules can diffuse between the molecular chains of
polymers. The mechanism for this diffusion is similar to the interstitial diffusion
that occurs in metals, although in polymers diffusion occurs through small
voids between chains, from one open region to another. Thus, rates of diffusion
are greater in more “open” amorphous regions than through crystalline regions.
Smaller molecules also diffuse faster than larger ones.
Diffusion in polymers is often characterized by the permeability coefficient, PM. Steady-state diffusion through a polymer membrane can be described using a modified Fick’s first law:
where J is the diffusion flux , ΔP is the difference in
pressure of the gas across the membrane, and Δx is the membrane thickness.
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