Polymer Characterization

(a work in progress)

The fundamental question in polymer science:
"OK. I started out with a bottle of clear liquid, and I ended up with a bottle of clear liquid. So what have I really accomplished, and is it any different from what I accomplished last week?"

The field of polymer characterization is about answering that question: Have I made anything, is it what I wanted to make, and is it the same as what I made last week. Along the way, however, you can find ways to answer some other pretty cool questions that don't have anything to do with the above.

To characterize is, according to Funk and Wagnall, to describe by qualities or peculiarities. So how might I describe a polymer? Well, I could describe every atom at a every position, their bond lengths and angles in every conformation, and do this for every molecule in a polymer solution ... I hope you have some time on your hands. It is a simple fact of life that we will have to settle for averages of whatever qualities we decide we want to measure. So what might some of those qualities be?

Polymer Properties that you might want to measure

· Mass (Molecular Weight)
This would be the molecular weight of a particular polymer molecule.  But it is no stretch to see that the odds of EVERY polymer molecule having hte SAME number of subunits are pretty steep.  In general, any sample of polymer molecules will have a RANGE of molecular weights. This is referred to generally as POLYDISPERSITY.  (The rarer event of ALL polymers having about the same molecular weight is called MONODISPERSITY).  Hence, we will generally measure some average of the molecular weight (and any other property, for that matter).  And the type of average we measure will depend heavily on the technique we employ to make the measurement.

· Polydispersity
To repeat, there is generally a range of molecular weights in a given polymer sample, so we must also find a way to characterize the distribution of molecular weights. One way is to measure and record the entire distribution of molecular weights (fraction of polymer molecules with a particular molecular weight). A simpler method (simpler both in the technique and in the resulting information) is to express the polydispersity as a ratio of different molecular weight averages (MW/Mn or MZ/MW, for example).

· Size (Radius of Gyration)
Here, size refers to the physical extent of the molecule – how much room it takes up. With a little thought, it may be clear that a "stiffer" molecule takes up more room for a given molecular weight than a "floppier" molecule. As we discuss this issue, we will be forced to define more carefully what we mean by "size". For example, does an electrostatically charged molecule take up more room than a neutral one? And what happens then when you change the ionic strength of the environment?

· Degree of Association
Strandedness (single strand, double strand, etc)
Aggregation
Degradation
We have talked mostly about linear molecules (another class is branched molecules, in which there is a central trunk and many "branches" extending from it), but many polymers occur in multiple strands. That is, they consist of two or more simple linear molecules bonded together. DNA's double helix is the most famous example, but other examples are a polymer called schizophylan (a triple strand) and xanthan (which some claim is a double strand, while others contend it is single).
In addition, there are less organized forms of association between polymers. This is termed aggregation, and may sometimes be desirable (as when a pharmacologist wants an antibody to aggregate with a liposome) or undesirable, (as when a solution of dissolved polymer molecules slowly aggregates and precipitates from solution).
The opposite of aggregation (when polymers come together) is degradation, when they fall apart. Again, this can be desired (when plastic bags degrade under the influence of ultraviolet light) or not (when collagen in skin degrades under the influence of ultraviolet light).

· Conformation
The most common polymer conformation is the random coil conformation, in which each bit of the molecule is oriented randomly with respect to the others.  A rarer conformation is the aptly named linear conformation, in which all the bits are lined up in a straight line.  It is generally of interest to know what the conformation of a polymer is, and how that conformation might change in different environments (varying ionic strength, varying pH, etc.).

· Interactions
Polymers clearly interact with one another. In order to aggregate, there must be an attractive interaction. But when they get too close, there is clearly a repulsive interaction (the steric repulsion). Furthermore, when polymers carry an electric charge (this type of polymer is called a polyelectrolyte), electrostatic forces come into play (both attractive, which cause aggregation, and repulsive, which do not).

So, how do I measure it already!?

Polymers are clearly too small to measure directly. A large polymer consists of maybe 100,000 repeat units, each of which might a molecular weight of about 200 g/mole. The entire molecule then has a molecular weight of say 20,000,000 g/mole (really big!). It's mass is then ~10-17 grams. In the analytical lab, I think we can measure about 10-3 g. Optical tweezer guys are crowing about measuring forces in the pN = 10-12 N range – this corresponds to a mass of about 10-13 kg = 10-10 g. Not even close. And this is a big polymer.

Consider the size, then. We know that the size is of the order of the RMS end-to-end distance. That is given, for a random coil polymer, by r = N½ l. Using the previously mentioned generic big polymer, N = 105. Estimate l as about 10 Å (using 20 Da/Å as a generic mass per unit length). Then r is about 3200 Å = 320 nm. It is a general principle that you can see a thing only by bouncing something off of it that has a wavelength much smaller than the thing you want to see. So we can just about make out a polymer molecule with an x-ray microscope (none laying around that I have seen). How about a rodlike molecule? The size is then just N·l = 106 Å = 105 nm = 0.1 mm. Plenty big enough to see (except remember that it is only a few Angstroms across). It seems clear that due to the tiny scales involved, we will generally not be able to view polymers directly, but rather we will have to do so indirectly. That is, we will measure some other (more accessible) property from which we will be able to infer the polymer quality of interest (for example, measuring viscosity allows us to infer something about the size of the molecules making up the viscous material).

What follows is an evolving discussion of various methods, concentrating upon those that I know something about.

· End group analysis (count the polymers)
The idea behind end group analysis is straightforward. If I know the total mass of a polymer sample, and I know the number of molecules in the sample, the determination of the molecular weight is straightforward (right?). The former determination is made in the normal way – weigh the sample. The latter takes advantage of the fact that the ends of a polymer chain will generally be different from the interior. It will generally involve some type of titration to determine the number of molecule ends. For example, the dye Rhodamine 6G can be used to reveal the existence of COOH groups on the ends of polymer molecules (although there are radiochemical methods as well).
The end group technique works best for low molecular weight polymers (why?), and is generally limited to polymers no bigger than about 105 g/mol. With a bit of thought, it becomes clear that when the polymer sample is polydisperse, the end group technique gives the number average molecular weight, Mn(which is why we bring it up in the first place).
 

(the following topics will be expanded in the fullness of time...)
· Osmometry

· Cryoscopy/Ebulliometry
(freezing point depression/boiling point elevation)

· Viscometry / Transport Methods / Chromatography

· Laser light scattering

· Integrated techniques