Proceedings of the National Conference
On Undergraduate Research (NCUR) 2007
Dominican University of California
San Rafael, California
April 12 – 15, 2007
The Determination of Relative Concentrations of Hydrogen Isotopes
Laurence A. Lewis
Department of Physics and Astronomy
James Madison University
800 S. Main Street
Harrisonburg, VA 22807
Faculty Advisor: Dr. C. Steven Whisnant
Abstract
James Madison University's hydrogen distillery produces hydrogen deuteride (HD) gas with purity greater than
99.99%. This purified gas is polarized and used to make a frozen spin target with polarization relaxation times that
approach one year. These targets are ideal for use in polarized gamma ray beams for the study of the spin-dependent
properties of nucleons. To affect the polarization of the target a small, known concentration of orthonormal-H2 and
minimal D2 must be present. Thus, it is important to quantify the H 2 and D2 concentrations present in the distilled
HD gas to determine the optimal amount of H2 relative to the other isotopes to achieve the longest relaxation time.
Low-temperature gas chromatography (GC) is implemented for this purpose. The GC utilizes the isotopic variances
in column transit time and produces three overlapping asymmetric Gaussian peaks with areas proportional to the
concentrations present in the sample. Numerical algorithms using functions modeled on fitting these asymmetric GC
peaks are implemented which minimize the value of the function. The results of the algorithms are high quality fits
which allow for the extraction of the relative concentrations of each of the isotopes of hydrogen. The method and
results of such fits will be discussed. In addition, the use of the GC to determine the spin isomer fraction of
molecular hydrogen within the HD sample will be addressed.
Keywords: Gas Chromatography, Hydrogen Isotopes, Least-Squares Fitting
1. Introduction
James Madison University (JMU) purifies 98% hydrogen deuteride (HD) to a concentration greater than 99.99% by
use of a multi-stage low-temperature hydrogen distillery. The product of the distillation is a gas used to create a
strongly polarized hydrogen ice target (SPHICE) kept at ~2mK in a ~17T magnetic field. This target is used in
inelastic scattering experiments to determine the spin-dependent properties of the nucleon and provide data for
intermediate energy one and two photopion production. To polarize the target a small, known amount of
orthonormal H2 (o-H2) must be added. This allows for a spin exchange between the o-H2 and the HD, decreasing the
polarization time for the SPHICE target become polarized. Once the o-H2 decays to its energetically favored
paranormal H2 (p-H2), the p-H2 couples to the lattice increasing the spin relaxation time of the polarized neutrons
and protons to a few months. To optimize the polarization and relaxation times the concentration of the o-H2 present
must be 2-3 parts per ten thousand.
1.1 methodology
To analyze the distilled HD gas, gas chromatography is implemented. Gas chromatography capitalizes on the time
difference between different chemicals to transit a capillary column, in this case the variances in hydrogen isotope
and spin-state determine the transit time through the column. The GC system currently in use is a Varian 3800 Gas
Chromatograph with a Single Channel 1041 gas injection valve and Thermal Conductivity Detector (TCD) (Figure
1). The GC uses Ne as a carrier gas as opposed to He to prevent errors in data collection due to the similar thermal
conductivity of He and H2. The column (currently 50m in length and 0.32mm in diameter) is a fused silicate tubing
coated with CP-MolSieve 5A, a porous (~5 Angstroms) adsorbent stationary phase polymer. Analysis of distilled
HD gas and hydrogen gas in general has occurred with two separate column configurations, the previous setup and
current setup.
Figure 1. Schematic of GC with TCD 1.
Schematic of the GC with red lines and arrows indicating sample gas (HD), blue lines and arrows indicating
carrier gas (Ne), and red and blue lines and arrows indicating carrier gas transporting sample through GC. The Ne
travels to the reference TCD and also transports the sample gas through the capillary column (previously in an oven
at 120 C but currently in a liquid nitrogen dewar; see Figure 3). Separation of the different gases (hydrogen isotopes
and isomers) occurs in the capillary column. The signal generated is the difference between the signal obtained from
the reference thermal conductivity (top TCD) and the sample and reference thermal conductivity (bottom TCD).
1.2 previous setup
The previous setup of the GC had the column (100m in length) mounted in an oven while timed injections of liquid
N2 (LN2) vapor (at 77K) by solenoid attempted to maintain a steady temperature in the column oven. Sample spectra
are given in Figure 2. Analyzing samples in this setup proved difficult due to the noise created by the thermal
fluctuations in the column oven. This results in the low purity isotopes being lost in the thermal noise caused by the
solenoid injections.
.
Figure 2. Distilled HD GC spectra in previous setup.
Note the periodicity of the noise fluctuations in the baseline. These events correspond to the injections of LN2
vapor by solenoid into the capillary column. The main peak is HD while the H2 and D2 peaks would normally reside
on the left and right of the HD peak, respectively. However, due to the noise, the peaks may not be extracted using
iterative fitting techniques outlined later in this paper.
1.3 current setup
The aim of the current GC setup is to reduce the noise caused by thermal fluctuations within the column. As a result,
the entire column is submerged in LN2 vapor in a stainless steel Dewar (Figure 3).
Figure 3. Schematic of Dewar-column system.
The capillary column (reduced to 50m in length) now rests on two polystyrene insulating rafts, floating above LN2
inside a stainless steel Dewar. The capillary column sinks with the evaporating LN 2, which may help maintain a
fairly static temperature of the entire column during a GC run. The temperature of the column in the Dewar as a
function of depth (as measured from the top of the Dewar to the top of the insulating raft) is mapped and plotted in
Figure 4. A typical spectrum of an undistilled hydrogen mixture (random amounts of H2, HD, and D2) is given in
Figure 5.
190
temp (K)
180
170
160
3
4
5
depth (in)
6
7
8
Figure 4. Temperature of the column plotted as a function of depth in the Dewar with best fit exponential.
To minimize temperature fluctuations in the Dewar as a sample is being run, it is necessary to maintain a LN 2 level
corresponding to the flattest local temperature gradient in the Dewar.
Figure 5. Hydrogen mixture spectrum obtained from GC in current setup.
1.4 fitting
When analyzing the spectra, it is possible to integrate between the observed limits of the peaks and obtain an
estimate of the relative concentrations of hydrogen isotopes present in the sample. However, when dealing with such
high concentrations, the uncertainty associated with a fitting method becomes more and more important. In addition,
the peak overlap prevents any truly accurate integration by observation of limits. As a result, numerical least-squares
fitting is implemented using the IGOR package by WaveMetrics 2. The numerical fitting procedure of the
optimization of nonlinear function parameters in least-squares fitting was reported independently by Levenberg 3
and Marquardt 4.To fit the asymmetric Gaussian peaks, an accepted chromatographic fitting function, the
exponentially-modified Gaussian (EMG) is used. The causes of asymmetry from the heterogeneity of stationary
phase, tailing injection, and column overload have been shown to produce exponential tailing in the signal 5. Thus,
the EM is a physically justifiable fitting function. The function is given by
(1)
where A is the area (corresponding to the concentration of isotope present), τ represents the time constant of the
exponential tail, σg is the standard deviation of the Gaussian, and tg is the time of Gaussian maximum (which usually
does not correspond with the gas retention time within the column). The asymmetry of the EMG can be
characterized by τ /σg. It should noted that at low asymmetries the EMG becomes unstable because it begins to rely
heavily on the relative accuracy of contributions of small values from the error function, which, in most numerical
programs, is approximated by a polynomial expansion 6.
2. Data and Analysis
The peaks in the hydrogen mixture in Figure 5 correspond to p-H2, o-H2, and HD respectively with D2 in the
magnified window. In Figure 6, the two previous spectra have been superimposed. The top corresponds to distilled
HD and the bottom to a hydrogen mixture.
Figure 6. Superimposed spectra of distilled HD (top) and hydrogen mixture (bottom).
Notice the minimal noise, even when magnification is increased 175x to show the D2 peak (Figure 5). In addition,
notice the separation of the isomers of H2 (which did not occur when testing hydrogen mixtures in the previous
setup), overall increased separation of isotopes (separated by approximately 1min as opposed to several seconds in
the previous setup), longer retention time of the HD peak (~9.3min vs. ~8.2min with the previous setup), and the
band broadening. Due to a lower column temperature, the gas remains in the stationary phase longer. This leads to
longer retention times which results in more separation between peaks and the broadening of peaks due to the
amplification of isotopic and spin-state variances in transit times.
To capitalize on the diatomic isotope separation obtained in the new GC setup, the aim of the current research is to
map the relative spin isomer concentration as a function of temperature. During experimentation, no D2 spin isomer
separation was achieved. For hydrogen however, isomer peaks readily separated under the current setup. Due to the
three-fold degeneracy of the o-H2 state, at room temperature the ratio of o-H2: p-H2 is 3:1 7. The spectrum for a H2
sample equilibrated at 300K is shown in Figure 7.
Figure 7. H2 sample equilibrated at 300K with EMG fit.
The ratio obtained by the fits of o-H2:p-H2 is 3.00196 ± 0.01856, which is in good agreement with theoretical
predictions and previous results 7.
To obtain different spectra for different values of o-H2:p-H2 equilibration must occur fairly quickly. To allow the
ortho-para conversion to equilibrate quickly, the gas was allowed to adsorb onto activated charcoal, in a sample
bottle, in a Dewar of LN2 for several days 7. At 77K, the ratio o-H2:p-H2 should be 1.017:1 [7]. The spectrum for the
H2 sample equilibrated at 77K is shown in Figure 8.
Figure 8. H2 sample equilibrated at 77K with EMG fit.
The o-H2:p-H2 ratio given by the fits is 1.20300 ± 0.007768. The obtained data slightly conflicts with the accepted
result of 1.017 7. Conflicts with previous data may result due to quick reconversion into the orthonormal state as a
result of rapid temperature increase. Additionally, it may be the case that equilibration is not being reached. Further
investigation and mapping of the hydrogen spin isomer relative concentrations as a function of temperature is
necessary above and below 77K to complete the picture and understand the behavior spin isomer equilibration and
conversion, determine the temperature at which D2 isomer separation occurs, comprehend the full fitting capabilities
of the EMG (at low and high asymmetries), and optimize the current column configuration of the GC.
3. Acknowledgments
The author would like to acknowledge the generous contributions of time, effort, and funds from the faculty advisor,
Dr. C. Steven Whisnant, as well as the LEGS collaboration at Brookhaven National Laboratory.
4. References
1
Sheffield Hallam University, “Gas Chromatography,” www.shu.ac.uk/,
teaching.shu.ac.uk/hwb/chemistry/tutorials/chrom/gaschrm.htm.
2
IGOR Pro from WaveMetrics Inc, 10200 SW Nimbus, G-7, Portland, OR 97223, www.wavemetrics.com
3
K Levenberg, “A Method for the Solution of Certain Problems in Least-Squares,” Quarterly Applied
Mathematics 2 (1944): 164.
4
D Marquardt, “An Algorithm for Least-Squares Estimation of Nonlinear Parameters,” Journal of Applied
Mathematics 11 (1963): 431
5
A Felinger, Data Analysis and Signal Processing in Chromatography (New York: Elservier Press, 1998).
6
K Lan, JW Jorgenson, “A Hybrid of Exponential and Gaussian Functions as a Simple Model of
Asymmetric Chromatographic Peaks,” Journal of Chromatography A 915 (2001): 1.
7
A Farkas, Orthohydrogen, Parahydrogen, and Heavy Hydrogen (Cambridge: Cambridge University Press,
1935).