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کریستالیزاسیون در پلیمرها و DSC

    Such folk will just throw their socks in the drawer in one big tangled mess. If you read the page dealing with polymer crystallinity, you know that many polymers contain both amorphous and crystalline material. We want to know how much of the polymer was crystalline before we induced more of it to become crystalline.

Crystallinity and polymer structure

A polymer's structure affects crystallinity a good deal.

Polyesters are another example. These disordered regions are the amorphous regions we were talking about. Go home? Why? So you can look in your sock drawer, that's why. So the expression becomes simpler:

Of course, not everything you see here will be on every DSC plot. And that's what we do in differential scanning calorimetry, or DSC for short.
Differential scanning calorimetry is a technique we use to study what happens to polymers when they're heated.

Crystallization

But wait there is more, so much more.ws/macrog/images/stal04.ws/macrog/images/dsc11. But most importantly, this dip tells us that the polymer can in fact crystallize. This means we've also got an increase in the heat capacity of our polymer.

Polyethylene is another good example. The only thing we do see at the glass transition temperature is a change in the heat capacity of the polymer.pslc. Then we saw a big dip when the polymer reached its crystallization temperature.pslc. That's why we subtract the heat given off at crystallization.


Differential Scanning Calorimetry In between the crystalline lamellae, there are regions where there is no order to the arrangement of the polymer chains. They wiggle and squirm, and never stay in one position for very long. The crystallization dip and the melting peak will only show up for polymers that can form crystals.ws/macrog/images/dsc06.gif" /> And that's how we use DSC to get percent crystallinity. When we start heating our two pans, the computer will plot the difference in heat output of the two heaters against temperature. Completely amorphous polymers won't show any crystallization, or any melting either. When this is the case, we say the polymer is crystalline.gif" /> This is the total amount of grams of polymer that were crystalline below the Tc. We'll call the heat total heat given off during melting Hm, total, and we'll call the heat of the crystallization Hc, total. They form strong hydrogen bonds. The heating rate is temperature increase T per unit time, t.gif" />

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. But how much of each? DSC can tell us.ws/macrog/images/stal01.pslc.

But more importantly, it makes sure that the two separate pans, with their two separate heaters, heat at the same rate as each other.ws/macrog/images/stal10. Got it?

So you see, no polymer is completely crystalline. You leave it empty.ws/macrog/images/dsc03. 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.pslc. It has to put out more heat. Most polymers can only stretch out for a short distance before they fold back on themselves.gif" />

Of course, it isn't always as neat as this.gif" /> Now we just calculated the total heat given off when the polymer melted. Because we have to add energy to the polymer to make it melt, we call melting an endothermic transition.

Now we're going to subtract the two:

Let's say now that we divide the heat flow q/t by the heating rate T/t.gif" />

Crystallinity and intermolecular forces

Intermolecular forces can be a big help for a polymer if it wants to form crystals.

To understand all this talk of crystals and amorphous solids, it helps to go home.

We're going to talk about the neat and orderly crystalline polymers on this page.

But for making fibers, we like our polymers to be as crystalline as possible.pslc. When this heat is dumped out, it makes the little computer-controlled heater under the sample pan really happy. This is because a fiber is really a long crystal. There is atactic polystyrene, and there is syndiotactic polystyrene. 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. And in case you were wondering, we can spot this happening on a DSC plot. You can see this drop in the heat flow as a big dip in the plot of heat flow versus temperature:

As you can see, lamella grow like the spokes of a bicycle wheel from a central nucleus.ws/macrog/images/dsc00.ws/macrog/images/stal03.

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.pslc. The heat flow is going to be shown in units of heat, q supplied per unit time, t. 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.

Crystallinity in Polymers

As you can see on the lists above, there are two kinds of polystyrene. It's happy because it doesn't have to put out much heat to keep the temperature of the sample pan rising. 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.pslc.gif" />

For polyethylene, the length the chains will stretch before they fold is about 100 angstroms.ws/macrog/images/dsc07. So a crystalline polymer really has two components: the crystalline portion and the amorphous portion. If you're making plastics, this is a good thing.gif" /> 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. Now our plot is a plot of heat flow per gram of material, versus temperature. The heating rate is in units of K/s.

This dip tells us a lot of things. With no order, the chains can't pack very well.gif" />

The heat flow at a given temperature can tell us something.gif" />

This page is all about polymer crystals. 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:

This is the switchboard model of a polymer crystalline lamella.ws/macrog/images/dsc12. When we reach the polymer's melting temperature, or Tm, those polymer crystals begin to fall apart, that is they melt.pslc. Linear polyethylene is nearly 100% crystalline.

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. In addition, the aromatic rings like to stack together in an orderly fashion, making the crystal even stronger. Neat, huh? Now if we do the same calculation for our dip that we got on the DSC plot for the crystallization of the polymer, we can get the total heat absorbed during the crystallization.

Melting

Heat may allow crystals to form in a polymer, but too much of it can be their undoing. If you analyzed a 100% amorphous polymer, like atactic polystyrene, you wouldn't get one of these dips, because such materials don't crystallize. Let's imagine we're heating a polymer.

This means we're now getting more heat flow.ws/macrog/images/stal02.pslc. 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.ws/macrog/images/fiber02.gif" /> Now we have a number of joules per gram.

The Glass Transition Temperature

Of course, we can learn a lot more than just a polymer's heat capacity with DSC. The chains, or parts of chains, that aren't in the crystals have no order to the arrangement of their chains. The whole assembly is called a spherulite. Let's look at the polyester we call poly(ethylene terephthalate).jpg" />

Polymers are just like socks in that sometimes they are arranged in a neat orderly manner, like the sock drawer in the top picture. The phenyl groups come on any which side of the chain they please. By measuring just how much more heat it has to put out is what we measure in a DSC experiment. (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.) The fibrils grow out in three dimensions, so they really look more like spheres than wheels.gif" />

Keywords:
amorphous, crystal, first order transition
glass transition temperature, heat capacity, latent heat
second order transition, thermal transition


Note: Before you read this page, make sure you've read the glass transition page and the polymer crystallinity page. 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.ws/macrog/images/dsc14. Also, we can measure the area of the dip, and that will tell us the latent energy of crystallization for the polymer. We're going to divide it by the specific heat of melting, Hc*.gif" /> Got that? Don't worry.pslc. On the x-axis we plot the temperature. Let's see what happens when we heat the polymer a little more. Each pan sits on top of a heater. The other one is the reference pan.gif" />

How Much Crystallinity?

Remember we said that many polymers contain lots of crystalline material and lots of amorphous material.

Other atactic polymers like poly(methyl methacrylate) and poly(vinyl chloride) are also amorphous.gif" />

Syndiotactic polystyrene is very orderly, with the phenyl groups falling on alternating sides of the chain. These chains are called tie molecules.ws/macrog/images/stal07. Here are some of the polymers that tend toward the extremes:

Some Highly Crystalline Polymers: Some Highly Amorphous Polymers:
Polypropylene Poly(methyl methacrylate)
Syndiotactic polystyrene Atactic polystyrene
Nylon Polycarbonate
Kevlar and Nomex Polyisoprene
Polyketones Polybutadiene

Why?

So why is it that some polymers are highly crystalline and some are highly amorphous? There are two important factors, polymer structure and intermolecular forces. Polymers also form stacks of these folded chains. And that's just what we've done in that equation up there.pslc. Then finally we saw a big peak when the polymer reached its melting temperature.

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.

The polar ester groups make for strong crystals. One is very crystalline, and one is very amorphous.

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. We use it to study what we call the thermal transitions of a polymer. We just multiply this by the mass of the sample:

 Reference of this text is: www.

The first thing we have to do is measure the area of that big peak we have for the melting of the polymer.pslc.

Also, because the polymer gives off heat when it crystallizes, we call crystallization an exothermic transition.jpg" />

Other people don't really care about how neat their sock drawers look.

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. We fancy bigshot scientists say that they are in the amorphous state.pslc. (Sometimes we bigshot scientists like to call these spokes "lamellar fibrils". Like this:

It's pretty simple, really. When this happens, we say the polymer is amorphous. That is to say, we're plotting the heat absorbed by the polymer against temperature. On the y-axis we plot difference in heat output of the two heaters at a given temperature.pslc.ws/macrog/images/dsc01. This means it can pack very easily into crystals. There's a way we can find out how much of a polymer sample is amorphous and how much is crystalline. Their sock drawers look like this:

But atactic styrene has no such order. Is everyone following me?

Now with our magic number H' we can figure up the percent crystallinity. Transitions like melting and crystallization, which do have latent heats, are called first order transitions.

So the heater underneath the sample pan has to work harder than the heater underneath the reference pan.pslc. This happens because the polymer has just gone through the glass transition.pslc. 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. It gets simpler.

Of course, being indecisive, the polymer chains will often decide they want to come back into the lamella after wandering around outside for awhile.

But they can't always stretch out that straight. The melting of a crystalline polymer is one example. And what are thermal transitions? They're the changes that take place in a polymer when you heat it. When they put their socks away they fold them and stack them very neatly. If we know the latent heat of melting, ΔHm, we can figure out the answer. We usually divide the area by the heating rate of our dsc experiment. A good example is nylon.

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. A completely crystalline polymer would be too brittle to be used as plastic. 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. The glass transition is also a thermal transition.ws/macrog/images/dsc13.pslc.

But not only do polymers fold like this. When the polymer crystals melt, they must absorb heat in order to do so.

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