The bar for getting the suffix of PhD after your name is high – you have to fundamentally change the philosophy in a field. As a faculty member responsible for training some of these individuals, I’m sometimes faced with the conundrum that advancing the philosophy implies that I have to change the way I was doing things. Thanks to newly minted Dr. Carl Bunge, I’m now trying to re-teach myself statistical thermodynamics while learning optics from scratch.

Carl’s dissertation was the design and operation of a continuous, cryogenic, Raman spectroscopy system for measuring ortho-parahydrogen concentrations of a flow. In the August 2020 issue of Cold Facts Vol. 36, Issue 4, “Is It Parahydrogen or Para-Hydrogen,” I gave you a preview of his room temperature measurements showing that the Raman system could resolve each of the J = 0, 1, 2, and 3 rotational modes of ortho- and parahydrogen. We had previously used the traditional method of using a hot-wire anemometer to back out the composition from the differences in thermal conductivity near 140 K. That system was a challenge, to say the least, as we were always having to replace all of the hot wires we busted.

Carl’s spectrometer used a 532 nm green argon laser with horizontal polarization, 2-meter-long multimode fiber optics, and fused silica quartz lenses mounted in a ¼” Swagelok SS 316 cross. He found three of the lasers at my university’s surplus in what may have been the find of the century. After tweaking the power levels and optical filter system Carl started generating spectrographs like the one in Figure 1 taken at 290 K and 16.7 bar pressure. You can see each of the four lower ro-vibrational energy transitions of hydrogen as the molecules are excited and then re-emit light read by the spectrometer. Compared to the old hot-wire anemometry method, this new method was like being able to see for the first time.

The room temperature values were acceptably near the anticipated 3:1 ratio of ortho-parahydrogen and the liquid hydrogen values were near 99.1% parahydrogen, also expected. We were excited. This is also when trouble began and how Carl learned why PhD’s are hard. At any temperature in between ambient and 20 K his values were deviating significantly (<10%) and repeatedly from the expected ortho-parahydrogen equilibrium concentration predicted by statistical mechanics. Based on some recent publications in physics journals (that shall go unnamed), we were led to believe that the cause of deviations was due to only basing the equilibrium percentage of para-orthohydrogen on the J = 0 and J = 1 distribution, as those were the only peaks that could be resolved when the Raman technique was first developed. Now that we could resolve the higher peaks, were the statistical methods of old now wrong?

To resolve the source of discrepancies Carl decided to watch ortho-parahydrogen migration between energy levels during cooling from room temperature to 77.5 K in a non-catalytic measurement cell. This would tell us if hydrogen was moving uniformly between energy modes as sensed by the Raman probe, or if re-emission was mode specific. Figure 2 shows the migration of ortho- from 31 and para- from 20 as the temperature is reduced. Carl made the observation that the total ortho-parahydrogen concentration changed from 73.5% to 63.3% at 77.5 K when it should have remained constant. Natural ortho-parahydrogen conversion can only account for 0.02% of this conversion in 140 minutes at these low densities. NIST-calibrated sources showed the system was spot on. Raman spectroscopy would not be as easy as hoped.

Probing some old textbooks on the topic we found that even the simple differences in energy states of the hydrogen molecule have differing spectral intensities. More statistical thermodynamics. But once accounted for, Carl got his spectrometer agreeing with the ortho-parahydrogen percentages predicted by statistical thermodynamics. From what we can tell it’s the first time anyone has done it with a continuous flow system and corrected for the differing spectral intensities between modes. With some post processing we hope to have a program to help others simply correct their Raman measurements to accurately agree with the statistical thermodynamic predictions.

Given the simplicity of Carl’s setup, and the ability to measure composition at any temperature within the cryogenic regime, we don’t plan to go back to the old thermal anemometry or other relative methods any time soon. And the statistical thermodynamic sages who developed the science of cryogenic hydrogen can rest at ease knowing that they still got it right. ■