This page is all about polymer crystals. No, this page has nothing to do
with polymers as used by the new age community. We're talking about
another kind of crystal here. The kind of crystal we're talking about
here is any object in which the molecules are arranged in a regular
order and pattern. Ice is a crystal. In ice all the water molecules are
arranged in a specific manner. So is table salt, sodium chloride.
(Oddly, your mother's good crystal drinking glasses are not crystal at
all, as glass is an amorphous solid, that is, a solid in which the molecules have no order or arrangement.)
To understand all this talk of crystals and amorphous solids, it helps
to go home. Go home? Why? So you can look in your sock drawer, that's
why. You see, some people are very neat and orderly. When they put their
socks away they fold them and stack them very neatly. Like this:
Other people don't really care about how neat their sock drawers look.
Such folk will just throw their socks in the drawer in one big tangled
mess. Their sock drawers look like this:
Polymers are just like socks in that sometimes they are arranged in a
neat orderly manner, like the sock drawer in the top picture. When this
is the case, we say the polymer is crystalline
. Other times there
is no order, and the polymer chains just form a big tangled mess, like
the socks in the bottom picture. When this happens, we say the
polymer is amorphous
We're going to talk about the neat and orderly crystalline polymers on this page.
So what kind of arrangements do the polymers like to form?
They like to line up all stretched out, kind of like a neat pile of new boards down at the lumber yard.
But they can't always stretch out that straight. In fact, very few polymers can stretch out perfectly straight, and those are ultra-high molecular weight polyethylene, and aramids like Kevlar and Nomex. Most polymers can only stretch out for a short distance before they fold back on
themselves. You can see this in the picture.
For polyethylene, the length the chains will stretch before they fold is about 100 angstroms.
But not only do polymers fold like this. Polymers also form stacks of
these folded chains. There is a picture of a stack, called a lamella,
Of course, it isn't always as neat as this. Sometimes part of a chain is
included in this crystal, and part of it isn't. When this happens we
get the kind of mess you see below. Our lamella is no longer neat and
tidy, but sloppy, with chains hanging out of it everywhere!
Of course, being indecisive, the polymer chains will often decide they
want to come back into the lamella after wandering around outside for
awhile. When this happens, we get a picture like this:
This is the switchboard model of a polymer crystalline lamella.
Because we like you, we're going to tell you that when a polymer chain
doesn't wander around outside the crystal, but just folds right back in
on itself, like we saw in the first pictures, that is called the adjacent re-entry model.
Amorphousness and Crystallinity
Are you wondering about something? If you look at those pictures up
there, you can see that some of the polymer is crystalline, and some is
not! Yes folks, most crystalline polymers are not entirely crystalline.
The chains, or parts of chains, that aren't in the crystals have no
order to the arrangement of their chains. We fancy bigshot scientists
say that they are in the amorphous state. So a crystalline
polymer really has two components: the crystalline portion and the
amorphous portion. The crystalline portion is in the lamellae, and the
amorphous potion is outside the lamellae. If we look at a wide-angle
picture of what a lamella looks like, we can see how the crystalline and
amorphous portions are arranged.
As you can see, lamella grow like the spokes of a bicycle wheel from a
central nucleus. (Sometimes we bigshot scientists like to call these
spokes "lamellar fibrils".) The fibrils grow out in three dimensions, so
they really look more like spheres than wheels. The whole assembly is
called a spherulite. In a sample of a crystalline polymer weighing only a few grams, there are many billions of spherulites.
In between the crystalline lamellae, there are regions where there is no
order to the arrangement of the polymer chains. These disordered
regions are the amorphous regions we were talking about.
As you can also see in the picture, a single polymer chain may be partly
in a crystalline lamella, and partly in the amorphous state. Some
chains even start in one lamella, cross the amorphous region, and then
join another lamella. These chains are called tie molecules.
So you see, no polymer is completely crystalline. If you're making plastics,
this is a good thing. Crystallinity makes a material strong, but it
also makes it brittle. A completely crystalline polymer would be too
brittle to be used as plastic. The amorphous regions give a polymer toughness, that is, the ability to bend without breaking.
But for making fibers, we like our polymers to be as crystalline as
possible. This is because a fiber is really a long crystal. Want to
know more? Then visit the Fiber Page!
Many polymers are a mix of amorphous and crystalline regions, but some
are highly crystalline and some are highly amorphous. Here are some of
the polymers that tend toward the extremes:
As you can see on the lists above, there are two kinds of polystyrene. There is atactic polystyrene, and there is syndiotactic
polystyrene. One is very crystalline, and one is very amorphous.
Syndiotactic polystyrene is very orderly, with the phenyl groups falling
on alternating sides of the chain. This means it can pack very easily
But atactic styrene has no such order. The phenyl groups come on any
which side of the chain they please. With no order, the chains can't
pack very well. So atactic polystyrene is very amorphous.
Other atactic polymers like poly(methyl methacrylate) and poly(vinyl chloride) are also amorphous. And as you might expect, stereoregular polymers like isotactic polypropylene and
polytetrafluoroethylene are highly crystalline.
Polyethylene is another good example. It can be crystalline or
amorphous. Linear polyethylene is nearly 100% crystalline. But the
branched stuff just can't pack the way the linear stuff can, so it's
Polyesters are another example. Let's look at the polyester we call poly(ethylene terephthalate).
The polar ester groups make for strong crystals. In addition, the
aromatic rings like to stack together in an orderly fashion, making the
crystal even stronger.
How Much Crystallinity?
Remember we said that many polymers contain lots of crystalline material
and lots of amorphous material. There's a way we can find out how much
of a polymer sample is amorphous and how much is crystalline. This
method has its own page, and it's called differential scanning calorimetry
first order transition
glass transition temperature,
second order transition,
Note: Before you read this page, make sure you've read the glass transition page and the polymer crystallinity page.
Differential scanning calorimetry is a technique we use to study what
happens to polymers when they're heated. We use it to study what we call
the thermal transitions of a polymer. And what are thermal
transitions? They're the changes that take place in a polymer when you
heat it. The melting of a crystalline polymer is one example. The
glass transition is also a thermal transition.
So how do we study what happens to a polymer when we heat it? The first
step would be to heat it, obviously. And that's what we do in differential scanning calorimetry, or DSC for short.
We heat our polymer in a device that looks something like this:
It's pretty simple, really. There are two pans. In one pan, the sample
pan, you put your polymer sample. The other one is the reference pan.
You leave it empty. Each pan sits on top of a heater. Then you tell
the nifty computer to turn on the heaters. So the computer turns on the
heaters, and tells it to heat the two pans at a specific rate, usually
something like 10 oC per minute. The computer makes absolutely sure that the heating the rate stays exactly the same throughout the experiment.
But more importantly, it makes sure that the two separate pans, with
their two separate heaters, heat at the same rate as each other.
Huh? Why wouldn't they heat at the same rate? The simple reason is
that the two pans are different. One has polymer in it, and one
doesn't. The polymer sample means there is extra material in the sample
pan. Having extra material means that it will take more heat to keep
the temperature of the sample pan increasing at the same rate as the
So the heater underneath the sample pan has to work harder than the
heater underneath the reference pan. It has to put out more heat. By
measuring just how much more heat it has to put out is what we measure in a DSC experiment.
Specifically what we do is this: We make a plot as the temperature increases. On the x-axis we plot the temperature. On the y-axis we plot difference in heat output of the two heaters at a given temperature.
We can learn a lot from this plot. Let's imagine we're heating a polymer.
When we start heating our two pans, the computer will plot the difference
in heat output of the two heaters against temperature. That is to say,
we're plotting the heat absorbed by the polymer against temperature. The
plot will look something like this at first.
The heat flow at a given temperature can tell us something. The heat flow
is going to be shown in units of heat, q supplied per unit time, t. The
heating rate is temperature increase T per unit time, t. Got it?
Let's say now that we divide the heat flow q/t by the heating rate T/t. We end up with heat supplied, divided by the temperature increase.
Remember from the glass transition page that when you put a certain
amount of heat into something, its temperature will go up by a certain
amount, and the amount of heat it takes to get a certain temperature
increase is called the heat capacity, or Cp.
We get the heat capacity by dividing the heat supplied by the resulting
temperature increase. And that's just what we've done in that equation
up there. We've figured up the heat capacity from the DSC plot.
The Glass Transition Temperature
Of course, we can learn a lot more than just a polymer's heat capacity
with DSC. Let's see what happens when we heat the polymer a little
more. After a certain temperature, our plot will shift upward suddenly,
This means we're now getting more heat flow. This means we've also got an
increase in the heat capacity of our polymer. This happens because the
polymer has just gone through the glass transition. And as you learned
on the glass transition page, polymers have a higher heat capacity above
the glass transition temperature than they do below it. Because of this
change in heat capacity that occurs at the glass transition, we can use
DSC to measure a polymer's glass transition temperature. You may notice
that the change doesn't occur suddenly, but takes place over a temperature
range. This makes picking one discreet Tg kind of tricky, but we
usually just take the middle of the incline to be the Tg.
But wait there is more, so much more. Above the glass transition, the
polymers have a lot of mobility. They wiggle and squirm, and never stay
in one position for very long. They're kind of like passengers trying to
get comfortable in airline seats, and never quite succeeding, because
they can move around more. When they reach the right temperature, they
will have gained enough energy to move into very ordered arrangements,
which we call crystals, of course.
When polymers fall into these crystalline arrangements, they give
off heat. When this heat is dumped out, it makes the little
computer-controlled heater under the sample pan really happy. It's happy
because it doesn't have to put out much heat to keep the temperature of
the sample pan rising. You can see this drop in the heat flow as a big
dip in the plot of heat flow versus temperature:
This dip tells us a lot of things. The temperature at the lowest point of
the dip is usually considered to be the polymer's crystallization temperature, or Tc.
Also, we can measure the area of the dip, and that will tell us the
latent energy of crystallization for the polymer. But most importantly,
this dip tells us that the polymer can in fact crystallize. If you
100% amorphous polymer, like atactic polystyrene,
you wouldn't get one of these dips, because such materials don't crystallize.
Also, because the polymer gives off heat when it crystallizes, we call crystallization an exothermic transition.
Heat may allow crystals to form in a polymer, but too much of it can be
their undoing. If we keep heating our polymer past its Tc, eventually we'll reach another thermal transition, one called melting. When we reach the polymer's melting temperature, or Tm,
those polymer crystals begin to fall apart, that is they melt. The
chains come out of their ordered arrangements, and begin to move around
freely. And in case you were wondering, we can spot this happening on a
Remember that heat that the polymer gave off when it crystallized? Well
when we reach the Tm, it's payback time. There is a
latent heat of melting as well as a latent heat of crystallization. When
the polymer crystals melt, they must absorb heat in order to do so.
Remember melting is a first order transition. This means that when you
reach the melting temperature, the polymer's temperature won't rise until
all the crystals have melted. This means that the little heater under the
sample pan is going to have to put a lot of heat into the polymer in order
to both melt the crystals and keep the temperature rising at the
same rate as that of the reference pan. This extra heat flow during
melting shows up as a big peak on our DSC plot, like this:
We can measure the latent heat of melting by measuring the area of this
peak. And of course, we usually take the temperature at the top of the
peak to be the polymer's melting temperature, Tm.
Because we have to add energy to the polymer to make it melt, we call
melting an endothermic transition.
Putting It All Together
So let's review now: we saw a step in the plot when the polymer was heated
past its glass transition temperature. Then we saw a big dip when the
polymer reached its crystallization temperature. Then finally we saw a
big peak when the polymer reached its melting temperature. To put them
all together, a whole plot will often look something like this:
Of course, not everything you see here will be on every DSC plot. The
crystallization dip and the melting peak will only show up for polymers
that can form crystals. Completely amorphous
polymers won't show any crystallization, or any melting either. But
polymers with both crystalline and amorphous domains, will show all the
features you see above.
If you look at the DSC plot you can see a big difference between the glass
transition and the other two thermal transitions, crystallization and
melting. For the glass transition, there is no dip, and there's no peak,
either. This is because there is no latent heat given off, or absorbed,
by the polymer during the glass transition. Both melting and
crystallization involve giving off or absorbing heat.
The only thing we do see at the glass transition temperature is a change
in the heat capacity of the polymer.
Because there is a change in heat capacity, but there is no latent heat
involved with the glass transition, we call the glass transition a second order transition. Transitions like melting and crystallization, which do have latent heats, are called
first order transitions.
How much crystallinity?
DSC can also tell us how much of a polymer is crystalline and how much is
amorphous. If you read the page dealing with polymer crystallinity,
you know that many polymers contain both amorphous and crystalline
material. But how much of each? DSC can tell us. If we know the latent
heat of melting, ΔHm, we can figure out the answer.
The first thing we have to do is measure the area of that big peak we
for the melting of the polymer. Now our plot is a plot of heat flow per
gram of material, versus temperature. Heat flow is heat given off per
second, so the area of the peak is given is units of heat x
temperature x time-1 x mass-1. We usually would put this in units such as joules x kelvins x (seconds)-1 x (grams)-1:
Got that? Don't worry. It gets simpler. We usually divide the area
by the heating rate of our dsc experiment. The heating rate is in units
of K/s. So the expression becomes simpler:
Now we have a number of joules per gram. But because we know the mass of
the sample, we can make it simpler. We just multiply this by the mass of
Now we just calculated the total heat given off when the polymer melted.
Neat, huh? Now if we do the same calculation for our dip that we got on
plot for the crystallization of the polymer, we can get the total heat
absorbed during the crystallization. We'll call the heat total
heat given off during melting Hm, total, and we'll call
the heat of the crystallization Hc, total.
Now we're going to subtract the two:
Why did we just do that? And what does that number H' mean?
H' is the heat given off by that part of the polymer sample which
was already in the crystalline state before we heated the polymer
above the Tc. We want to know how much of the polymer
was crystalline before we induced more of it to become crystalline.
That's why we subtract the heat given off at crystallization. Is everyone
Now with our magic number H' we can figure up the percent
crystallinity. We're going to divide it by the specific heat of melting,
The specific heat of melting? That's the amount of heat given off by a
certain amount, usually one gram, of a polymer. H' is in joules,
and the specific heat of melting is usually given in joules per gram, so
we're going to get an answer in grams, which we'll call
This is the total amount of grams of polymer that were crystalline below
the Tc. Now if we divide this number by the weight of
our sample, mtotal, we get the fraction of the sample
that was crystalline, and then of course, the percent crystallinity:
And that's how we use DSC to get percent crystallinity.
Reference of this text is: www.pslc.ws