Paraffin melting transition studied with X-ray diffraction

With teachers from the Cornell RET summer program, we studied the melting behavior of commercially bought paraffin wax using our X-ray beamlines. One of the teachers had noted that his students had observed that paraffin had multiple phase transitions, evidenced by multiple temperature plateaus in time when the wax was melted with constant heating.

This intrigued us, because this suggests that the substance has at least two very distinct components. As we go through the data, we’ll try to explain this conclusion.

We have a Rigaku rotating Cu anode X-ray source, operating at 40 kV filament voltage and 50 mA. Electrons boil off from the filament, are accelerated by the 40 kV electrical potential, and then slam into the Cu anode. As the electrons slow down in the Cu, X-rays are produced. The X-rays are then focused using two mirrors. The entire beamline is filled with Helium gas, to prevent absorption of the X-rays by air.

The sample was mounted in a glass capillary tube, 1.5 mm in diameter with wall thickness about 0.1 mm. Scattered X-rays were detected using a modified CCD camera, similar to what are used in modern digital cameras. A “beam stop” is in place to prevent the direct X-ray beam from striking the detector.

At 0 Celsius, this is the x-ray scattering pattern we observe.

At least three distinct rings are visible. Remember that in diffraction, a wide ring corresponds to short length scales, and smaller rings correspond to long length scales in the sample. So the image is “reciprocal” to the actual spacing of atoms or molecules. We see this from Bragg’s Law for diffraction:

nq = 2k sin(2*theta)

where n is any integer, q is the reciprocal of the distance between two atoms that scatter x-rays, k is 2*pi/x-ray wavelength, and theta is the angle measured between the scattered x-ray and the main beam.

Returning to the image, the two wider rings correspond to length scales in the paraffin of about 4 angstroms (1 angstrom is 1 ten billionth of a meter). There is a much smaller ring (in the left center of the image) which corresponds to a length scale of about 40 angstroms. The beam stop can be seen inside this ring as a sharp edge.

While it is difficult to say exactly what these rings correspond to without further work, we can make a few rough guesses.

The rings at 4 angstroms are most likely representative of the spacing between long carbon-chain molecules. That should come as no surprise, since paraffin is indeed made up of long carbon chain molecules. Why there are two rings of about this spacing is more interesting.

The likely explanation is that as the paraffin cools from the liquid state, it adopts a configuration where the hydrocarbon chains are all aligned along one direction. But they do not pack like square boxes; instead, if we look down that alignment direction, we see that the layers are offset, and the chains look to be on the corners of a parallelogram.

So we see that in one direction, the chain spacing is slightly different than in the other direction. This structure is called orthorhombic. This probably accounts for the two wide rings.

The narrow ring close to the beam is likely an impurity, like lecithin, and is probably indicative of a lamellar structure (like a stack of papers).

Let’s see what happens as we raise the temperature.

At 35 Celsius, we can see that the rings are less intense, and the outermost ring has nearly disappeared. The paraffin is starting to undergo a phase transition. In this case, it looks like the orthorhombic structure is disintegrating, giving way to a slightly more fluid phase.

At 40 Celsius, the outer ring is completely gone, and the other paraffin ring is starting to spread out. Referring to Bragg’s Law above, this smearing out in angle corresponds to a smearing out in the length scale on which we see correlations between molecules. What does that mean?!? As temperature increases, the hydrocarbon chains become more flexible, and start to squirm around. When they were cold, they were rigid and mostly straight, like garden hoses all lined up neatly. But as they warm up, they start to bend. So our garden hoses aren’t so neat anymore. What do we notice? The distance between chains (hoses) changes as we go along the length of the chain (hose): we get a distribution of distances between chains. That is exactly what we see in the above image: a distribution of angles implies a distribution of distances!

Now we’ve heated to 55 Celsius, and that broadening is even greater. The chains bend and squirm more as they get hotter. We are now well into melting. As we heat past this point, the ring disappears completely, indicating that the carbon chains are no longer correlated with each other. In fact, the chains themselves are now fluid, waving back and forth.

(The splotches in the image are due to water droplets on the face of the detector.)

It is nice to view the data as a complete temperature series. We have taken a pie slice of each image and integrated it. This allows us to look at each ring as a peak in a plot with axes of scattered x-ray intensity versus angle. That data is then put back into a “3-D” plot where one axis is angle, one axis is temperature and the third (color) axis is x-ray intensity. This way we can follow what happens to the peaks as we go along in temperature.

The bottom of the figure is the highest angle, the top is the lowest angle. Temperature increases from left to right from 0 to 80 Celsius. You can see the bottom (highest angle) peak disappear first, then the next peak blur out as the chains melt completely. Upon cooling, we see similar things:

Again, temperature increases from left to right, from 0 to 80 Celsius, but now this data was taken as we cooled the sample slowly. Note that the transition temperatures are slightly different. This “hysteresis” is due to “meta-stability” of the different phases of the paraffin. This rather complicated sounding term has a simple meaning: the states are reluctant to change from what they are into something else. So even though the system ought to be in a different state, it lingers in the state it is in, until it cannot do so any longer. The reasons for this effect are varied, and in some cases, not fully understood.