What Is Microcalorimetry?

Calorimetry is the science of heat. It is not about how many calories are in a Big Mac, but about how a given material responds to temperature changes on both the atomic and macroscopic level. This varies widely from substance to substance, and reveals important information about the arrangement and interaction of the atoms.

Microcalorimetry is the calorimetry of small samples, specifically microgram samples (or thereabouts). These are much more challenging to study than big chunks of material because (1) the time scale for changing the temperature is much faster and (2) the probes you attach to the sample to measure it suck away a greater proportion of the heat involved (see the comments on the pages below about "addenda".)

Both chemists and physicists perform microcalorimetry experiments. Since I am a physicist, my emphasis will be on the way we think about this subject. Don't be surprised if you talk to a chemist who does calorimetry and it sounds like a different language! (Language barriers between scientists are actually quite a big problem). What my old group at UCSD works on is the measurement of heat capacity.

OK.... so what's Heat Capacity?

If I apply heat to a mass of rock, its temperature rises a bit. If I apply the same heat to the same mass of copper, its temperature will rise more. The heat capacity describes this effect: it is the proportionality between heat applied and subsequent temperature rise.

Heat capacity=(change in heat)/(change in temperature)

Copper has a lower heat capacity than rock because it has a larger change in temperature for the same change in heat. The heat capacity is different at different temperatures; in general it is flat above room temperature and drops toward zero at lower temperatures because the material's ability to absorb and transmit heat changes with temperature.

This is interesting (trust me, it is). The way the material deals with heat involves the electrons, the ionic cores, and the interaction between the two. What really distinguishes materials (like copper and rocks) from each other is where electrons are and how they interact with the ions and the other electrons. Heat capacity alone cannot tell you everything, of course, but it's an important piece of the whole picture.

How is heat capacity measured?

You might suspect that the way to measure heat capacity is to make two measurements: the added heat and the temperature rise. Then you just divide them and get the heat capacity. Certainly this works, but it is not always possible. Think about how you would make the measurement. To determine the temperature, you need a thermometer. When you add the heat, you warm up both the thermometer and the sample. That's one source of error. Also, to add the heat, you must have something connected to the sample, like heater leads. As you add the heat, some of it leaks back down the leads-- more error. Another consideration is the time scale of the heating (how long will it take the whole sample to heat up?) and the temperature measurement (how quickly does my thermometer respond?). Such concerns are easily accomodated when measuring large samples like rocks, but what if you can only make a few thousandths of a gram of the material of interest? What if you can only make a thin film, which has a mass of a few millionths of a gram? Many materials studied today indeed come in such small packages. Suddenly the heater leads, the substrate that the film is grown upon, and the thermometer contribute extra heat capacity that is the same size (or even larger) than what you're trying to measure (jargon: this extra heat capacity is called "addenda"). And time considerations require the use of fast electronics to measure the temperature changes.

People have developed a variety of methods for measuring heat capacity, appropriate for various masses and types of sample. I can't go into all of them, so I'll just describe the one I used, which is called the relaxation method (that's what the links below will lead you to).

Since my samples were only about 10 micrograms (10 millionths of a gram), I probed them with a microcalorimeter. I have measured thin films of pure C₆₀ and K₃C₆₀, C₈₂, C₈₄, and two "endohedral" fullerenes (materials where there are atoms inside the fullerene cage).

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