Download Catalysis of Conversion Between the Spin Isomers

Catalysis of Conversion Between the Spin Isomers
of H2 by MOF-74
Brian S. Burkholder
April 1, 2009
CONTENTS
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1
1.1
Hydrogen Storage . . . . . . . . . . . . . . . . . . . . . . . . . . .
1
1.2
The Ortho and Para Species of Hydrogen . . . . . . . . . . . . .
1
1.2.1
Background . . . . . . . . . . . . . . . . . . . . . . . . . .
1
1.2.2
Why Do We Care? . . . . . . . . . . . . . . . . . . . . . .
3
1.3
Infrared Spectroscopy . . . . . . . . . . . . . . . . . . . . . . . .
3
1.4
Raman Spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . .
4
1.5
Going Cold . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5
1.6
Metal-Organic Frameworks . . . . . . . . . . . . . . . . . . . . .
6
2. Theory and Background . . . . . . . . . . . . . . . . . . . . . . . . . .
9
2.1
Ortho and Para Hydrogen Spin Isomers . . . . . . . . . . . . . .
9
2.1.1
The Symmetrization Requirement . . . . . . . . . . . . .
9
2.1.2
The Rotational State . . . . . . . . . . . . . . . . . . . . .
11
2.1.3
The Rotational Symmetries . . . . . . . . . . . . . . . . .
13
2.2
The Equilibration of H2 , D2 , and HD . . . . . . . . . . . . . . . .
15
2.3
The Improbability of Homogeneous Conversion . . . . . . . . . .
17
2.4
2.3.1
The Forbidden ∆J = ±1 Transition . . . . . . . . . . . .
18
2.3.2
Interaction of H2 and H . . . . . . . . . . . . . . . . . . .
18
2.3.3
H2 -H2 Interactions . . . . . . . . . . . . . . . . . . . . . .
19
Catalyzed Conversion . . . . . . . . . . . . . . . . . . . . . . . .
20
2.4.1
Conversion by Gaseous Impurities . . . . . . . . . . . . .
20
2.4.2
Conversion of a Fluid by a Solid Catalyst . . . . . . . . .
21
2.4.3
Conversion by a Paramagnetic Lattice . . . . . . . . . . .
21
2.5
Infrared Absorption . . . . . . . . . . . . . . . . . . . . . . . . .
25
2.6
Raman Scattering . . . . . . . . . . . . . . . . . . . . . . . . . .
26
3. Experimental Methods . . . . . . . . . . . . . . . . . . . . . . . . . . .
28
3.1
Infrared Spectroscopy . . . . . . . . . . . . . . . . . . . . . . . .
28
Contents
iii
3.1.1
The Spectrometer . . . . . . . . . . . . . . . . . . . . . .
28
3.1.2
The Gas Loading System . . . . . . . . . . . . . . . . . .
29
3.1.3
The Sample Chamber and Cryostat . . . . . . . . . . . .
31
3.2
Ortho-Para Conversion . . . . . . . . . . . . . . . . . . . . . . . .
3.2.1 The Dipstick Converter . . . . . . . . . . . . . . . . . . .
34
34
3.2.2
The Closed-Cycle Converter . . . . . . . . . . . . . . . . .
38
3.3
Raman Spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . .
39
3.4
MOF-74 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
40
3.5
Infrared Cold Procedure . . . . . . . . . . . . . . . . . . . . . . .
41
4. Results
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
43
4.1
Characteristics of the MOF-74 Infrared Spectrum . . . . . . . . .
43
4.2
Demonstration of Conversion . . . . . . . . . . . . . . . . . . . .
46
4.3
Identification of Peaks through Conversion . . . . . . . . . . . . .
46
4.4
Conversion with Concentration . . . . . . . . . . . . . . . . . . .
46
4.4.1
Fast Loading . . . . . . . . . . . . . . . . . . . . . . . . .
46
4.5
Low Temperature Back Conversion . . . . . . . . . . . . . . . . .
53
4.6
D2 and HD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
53
4.7
The Infrared Mechanisms . . . . . . . . . . . . . . . . . . . . . .
53
4.8
Raman Spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . .
55
5. Discussion and Analysis . . . . . . . . . . . . . . . . . . . . . . . . . .
60
5.1
Ortho-Para Conversion . . . . . . . . . . . . . . . . . . . . . . . .
60
5.1.1
The Rate of Conversion . . . . . . . . . . . . . . . . . . .
60
5.1.2
The Equilibrium Ratio . . . . . . . . . . . . . . . . . . . .
62
5.1.3
Applications . . . . . . . . . . . . . . . . . . . . . . . . .
65
5.2
Low Temperature Back Conversion . . . . . . . . . . . . . . . . .
66
5.3
D2 and HD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
67
5.4
The Infrared Mechanisms . . . . . . . . . . . . . . . . . . . . . .
67
6. Conclusions and Future Work . . . . . . . . . . . . . . . . . . . . . . .
70
6.1
6.2
Ortho-Para Conversion . . . . . . . . . . . . . . . . . . . . . . . .
70
6.1.1
6.1.2
Other Materials . . . . . . . . . . . . . . . . . . . . . . . .
Further Work in MOF-74 . . . . . . . . . . . . . . . . . .
70
72
6.1.3
The Dipstick . . . . . . . . . . . . . . . . . . . . . . . . .
73
Raman . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
73
6.2.1
73
The Gas Cell . . . . . . . . . . . . . . . . . . . . . . . . .
Contents
iv
6.2.2
Use with the Infrared Spectrometer
. . . . . . . . . . . .
74
6.2.3
Use with the Closed-Cycle Refrigerator . . . . . . . . . .
74
LIST OF FIGURES
1.1
Crystal structure of MOF-74 . . . . . . . . . . . . . . . . . . . .
7
2.1
Modes of molecular motion . . . . . . . . . . . . . . . . . . . . .
10
2.2
The axis system for the hydrogen molecule
. . . . . . . . . . . .
12
2.3
The axes for proton exchange . . . . . . . . . . . . . . . . . . . .
14
2.4
The equilibrium ratios of H2 , D2 , and HD . . . . . . . . . . . . .
16
3.1
The gas loading system . . . . . . . . . . . . . . . . . . . . . . .
30
3.2
The sample chamber and coldfinger . . . . . . . . . . . . . . . . .
31
3.3
The DRIFTS rig . . . . . . . . . . . . . . . . . . . . . . . . . . .
32
3.4
The dipstick conversion system . . . . . . . . . . . . . . . . . . .
35
3.5
The closed-cycle converter . . . . . . . . . . . . . . . . . . . . . .
37
3.6
The Raman gas T-cell . . . . . . . . . . . . . . . . . . . . . . . .
39
4.1
The infrared spectrum of MOF-74 . . . . . . . . . . . . . . . . .
44
4.2
Conversion in MOF-74 with time . . . . . . . . . . . . . . . . . .
45
4.3
Fast loading of H2 with no secondary band . . . . . . . . . . . .
47
4.4
Fast loading of H2 with secondary band . . . . . . . . . . . . . .
48
4.5
Fits to equilibrium data . . . . . . . . . . . . . . . . . . . . . . .
50
4.6
Low temperature back conversion . . . . . . . . . . . . . . . . . .
52
4.7
The Q regions of D2 and HD . . . . . . . . . . . . . . . . . . . .
54
4.8
Raman spectrum of unmirrored test tube . . . . . . . . . . . . .
56
4.9
Raman spectrum of mirrored test tube . . . . . . . . . . . . . . .
56
4.10 Raman spectrum of Erlenmeyer flask . . . . . . . . . . . . . . . .
4.11 Raman spectrum of T-cell . . . . . . . . . . . . . . . . . . . . . .
57
57
5.1
Neutron diffraction . . . . . . . . . . . . . . . . . . . . . . . . . .
63
5.2
Gaussian and Lorentzian fits . . . . . . . . . . . . . . . . . . . .
68
6.1
The spectra of different adsorption materials . . . . . . . . . . .
71
LIST OF TABLES
2.1
The two-proton spin states . . . . . . . . . . . . . . . . . . . . .
9
2.2
The J dependence of rotational state symmetry . . . . . . . . . .
14
2.3
Rotational constants of the hydrogen isotopes . . . . . . . . . . .
15
2.4
The spin degeneracies of H2 , D2 , and HD . . . . . . . . . . . . .
17
3.1
Gas phase peak locations . . . . . . . . . . . . . . . . . . . . . .
28
3.2
System volumes . . . . . . . . . . . . . . . . . . . . . . . . . . . .
38
4.1
Ortho-para ratio and para concentration with time . . . . . . . .
51
4.2
Fits for ortho-para equilibration . . . . . . . . . . . . . . . . . . .
51
4.3
Measured equilibrium ortho-para behavior . . . . . . . . . . . . .
52
4.4
Relative strengths of infrared mechanisms . . . . . . . . . . . . .
55
5.1
Gas pressure v. loading . . . . . . . . . . . . . . . . . . . . . . .
60
5.2
Separation of H2 Binding Sites . . . . . . . . . . . . . . . . . . .
61
5.3
S peak location predictions . . . . . . . . . . . . . . . . . . . . .
62
5.4
Summary of conversion timescales in various materials . . . . . .
65
5.5
Time for preparation of parahydrogen in MOF-74 . . . . . . . . .
66
ACKNOWLEDGMENTS
I would like to thank Stephen FitzGerald for his advice and guidance throughout
this project, and for introducing me to the world of research. I also thank Jesse
Hopkins and Peter Zhang for their help with both the work and fun of being in
the lab. Additionally, I thank Bill Mohler for keeping our equipment running
and Bill Marton for building anything we needed. Finally, I would like to thank
my sister Grace for her help with some old German articles.
SUMMARY
As the use of petroleum to power automobiles becomes increasingly problematic,
attention has turned to hydrogen as a potential alternative energy source. One
of the major difficulties facing the widespread adoption of hydrogen as a fuel
is the problem of storage. This has led to the discovery and investigations of
lightweight, porous materials capable of holding large quantities of hydrogen.
A particularly promising class of these materials are metal-organic frameworks.
We have studied one particular such framework, MOF-74, and its interactions
with the hydrogen that it stores.
This thesis is concerned with the quantum mechanical behavior of hydrogen
trapped in MOF-74. All hydrogen molecules are one of two types, called ortho
and para. The amount of each type present depends on temperature. At room
temperature, hydrogen gas is composed of 75% ortho molecules and 25% para
molecules. At temperatures near absolute zero, we expect to find only para
molecules. However, a molecule can only convert from one type to the other
in the presence of a magnetic field. Thus, when hydrogen is cooled from room
temperature to near absolute zero, 75% of the molecules get “stuck” as ortho.
We cool hydrogen in this way, and observe the “stuck” molecules. We then
supply a magnetic field and watch the ortho molecules convert to para.
We have found that MOF-74 produces a magnetic field capable of causing
conversion in the hydrogen that it stores. This conversion occurs on the order
of a minute, which is faster than the rate observed in many other materials.
Additionally, MOF-74 appears to alter the way in which the concentration of
ortho and para molecules depends on temperature. This makes MOF-74 unique
and exciting among metal-organic frameworks.
1. INTRODUCTION
1.1 Hydrogen Storage
Concerns over the personal automobile’s contributions to global warming, depleting worldwide petroleum reserves, and political instability in the world’s
primary petroleum-producing regions have led to the search for a replacement
for the internal combustion engine[37]. One promising prospect is to use hydrogen as a substitute for petroleum, as it is clean burning and its production is
not under the control of any particular nation or organization. However, there
are numerous technical barriers to the development and production of hydrogen
powered vehicles. One of the most pressing, and the one that we focus on, is the
problem of storage. The United States Department of Energy has determined
that economical operation requires the weight of usable hydrogen stored be at
least 9% of the total weight of the gas storage and delivery system, referred to
as 9 wt%[38]. Hydrogen is traditionally stored as either gas in high pressure
tanks or liquid in cryogenic tanks. The state of the art for these two methods
currently provides between 3.4 and 4.7 wt%[38].
Our work focuses on analyzing storage materials for use in hydrogen fuel
cells. In a fuel cell, H2 and O2 interact to produce water and electrical energy[44,
30]. A substrate of some kind, herein referred to as the host or the lattice,
holds hydrogen in the cell until it is released to power a car. The interaction
between the hydrogen and host provides the basis for both our use of infrared
spectroscopy and the quantum mechanical effects that will be the bulk of this
discussion.
1.2 The Ortho and Para Species of Hydrogen
1.2.1
Background
In 1926, Heisenberg theorized the existence of two different spin isomers of
molecular hydrogen, called ortho and para[25]. The Pauli exclusion principle
1. Introduction
2
requires that the combined wavefunction of two fermions, such as protons, be
antisymmetric. For our purposes here, we are concerned with the spin and rotational components of the wavefunction. Thus a symmetric rotational state
requires an antisymmetric spin state, and vice versa. Heisenberg found that a
pair of protons (the hydrogen molecule) has two possible spin states. One is
symmetric with S = 1, the ortho state, while the other is antisymmetric with
S = 0, the para state. Here S is the total nuclear spin quantum number. The
overall antisymmetrization requirement means that each rotational state (indicated by the angular momentum quantum number J) is exclusively associated
with either the ortho or para spin state. We show in Section 2.1.2 that states
with even J are para, and those with odd J are ortho. At room temperature,
75% of a sample of hydrogen is in odd-J states and 25% is in even-J states.
Since the ground rotational state J = 0 is a para state, at sufficiently low
temperatures (below about 20 K) essentially all of the hydrogen should be the
para spin species[36, 45]. The first attempts to confirm this experimentally were
done by measuring the thermal conductivity of a sample of hydrogen[15, 36].
The two spin states have different and well known specific heats, and so a
measurement of thermal conductivity gives the relative concentration of the
ortho and para species. However, when this experiment was conducted it was
found that ratio of the species did not correspond to the thermal equilibrium
value. Rather, at all temperatures, the hydrogen behaved as if it still had its
room temperature concentration[6].
The hydrogen was incapable of equilibrating because a transition from the
J = 1 to J = 0 state requires flipping a spin. It is a violation of conservation
of angular momentum for one of the nuclear spins to flip spontaneously. Since
their spins cannot flip, ortho molecules are constrained to fall no lower than the
lowest ortho state. Thus, all molecules in the ortho state at room temperature
get “stuck” in the J = 1 state when the hydrogen is cooled down. A sample of
hydrogen cooled from room temperature retains its room temperature ortho to
para ratio, no matter how low the temperature gets[6, 15, 36].
In order to flip a spin, a hydrogen molecule must experience a magnetic field
that is inhomogeneous over the length of the molecule. Classically (and inexactly) speaking, this field gradient produces a torque on the nuclear spin and
allows it to flip. This process is the catalysis of conversion, and is treated more
rigorously in Section 2.4. Once an ortho molecule has its spin flipped, it can
relax to the J = 0 state[8, 39]. This process of turning the ortho species into the
para will henceforth be referred to as ortho-para conversion. In practice the in-
1. Introduction
3
homogeneous field is supplied by a paramagnetic catalyst. Catalyzed conversion
was first accomplished by Bonhoeffer and Harteck in 1929 with charcoal[8, 7, 6].
1.2.2
Why Do We Care?
The measurement of the ortho-para ratio is desirable for numerous reasons.
First, it is fascinating in and of itself to see the quantum mechanical properties
of hydrogen in action. More practically, the equilibrium ortho-para ratio at a
given temperature is dependent on the separation between the J = 0 and J = 1
levels. Comparisons of hydrogen adsorbed on a lattice to that in the gas phase
allow us to observe perturbations of hydrogen’s rotational energy levels. This
gives an indication of how hydrogen interacts with its host.
Because the ortho and para species exhibit different infrared transitions,
the absorption spectra for converted and unconverted hydrogen are different.
Comparing the two helps identify characteristics of the spectrum, and in turn
of the host. The host lattice is often able to catalyze conversion, so we are able
to observe conversion in situ. Measuring the rate of this conversion gives a sense
of the kinetics of the process.
There are two mechanisms by which we can see infrared absorption. They
each give different absorption peak intensities and affect the ortho and para
species differently. The behavior of these mechanisms is unknown in general.
If, however, we know the ortho-para ratio, then we can calculate the relative
intensity of the two mechanisms, providing information about how H2 interacts
with its host.
Finally, one of the fundamental problems of working at cryogenic temperatures is the difficulty of measuring temperature. How do we know for certain
that our thermometer and our sample are at the same temperature? Since
ortho-para conversion is temperature dependent, an accurate measurement of
the equilibrium ratio in principle produces an accurate measurement of temperature, provided we already know how conversion behaves in a particular
material.
1.3 Infrared Spectroscopy
Infrared spectroscopy is usually inappropriate for studying molecular hydrogen. For a molecule to absorb an infrared photon its electric dipole moment
must change. Hydrogen, as a homonuclear diatomic (and therefore symmetric)
1. Introduction
4
molecule, has no dipole moment and therefore no infrared activity[10].
The hydrogen we are interested in, however, is adsorbed on a lattice, which
induces a dipole in the guest molecule. The adsorbed hydrogen becomes infrared
active and can be observed. Any hydrogen gas that does not get adsorbed and
remains in the gas phase is still transparent in the infrared. Thus the inherent
infrared inactivity is an advantage, as we see only what is in the lattice.
We use infrared spectroscopy to detect changes in the vibrational and rotational modes of the H2 nuclei. When a molecule absorbs a photon, it makes
a transition equal to the energy of that photon. We probe our sample with a
range of frequencies, and the ones that get absorbed correspond to molecular
transitions. Our infrared apparatus can detect absorption between about 1000
and 6000 cm−1 , and is therefore capable of detecting the ν = 0 → 1 vibrational
transition and associated J = 0 → 2 and J = 1 → 3 rotational sidebands of H2 ,
D2 , and HD. Note that ν is the vibrational quantum number. The locations of
these transitions are given in Table 3.1.
According to Beer’s law, Eq. 2.46, the intensity of an absorption peak is
proportional to the concentration of the matter doing the absorbing. Since we
only see hydrogen that has been adsorbed, the strength of our IR peaks gives a
measurement of the amount of hydrogen contained in our host. By comparing
the intensities of peaks associated with the ortho species and those associated
with the para species we can measure the ortho-para ratio in our material. This
method will be the foundation of our analysis of ortho-para conversion.
There are some challenges to using this technique. First, we obtain infrared
absorption from two different mechanisms, making concentration values harder
to obtain than suggested by Eq. 2.46. Second, as indicated in Table 3.1, the pure
rotational transitions of H2 are well below 1000 cm−1 and are thus unobservable
by our spectrometer. Third, since hydrogen’s energy levels are perturbed by the
host lattice, we are unable to observe H2 transitions apart from the influence
of the host lattice. Finally, our effective use of infrared spectroscopy requires
liquid helium. Liquid helium is expensive and not always available, limiting how
often productive experiments can be performed.
1.4 Raman Spectroscopy
Some of the challenges facing infrared spectroscopy can be overcome with Raman spectroscopy. In the Raman effect, photons (generally from a laser) are
scattered inelastically from the target molecule. In the scattering process en-
1. Introduction
5
ergy is transferred from the photon to the molecule, exciting a transition. The
scattered photon’s frequency is reduced (to conserve energy), and this change
is measured against the known frequency of the incident radiation.
Where infrared absorption requires a change in the molecule’s electric dipole
moment, Raman spectroscopy requires a variable electric polarizability[35, 10].
While H2 has no dipole moment, it does have a polarizability. Thus molecular
hydrogen is Raman active, and can be observed in the gas phase. This allows us
to avoid many of the problems of infrared spectroscopy. Only one mechanism
governs the scattering, so signal intensity is directly proportional to concentration. We are also able to observe transitions absent the perturbations of the
host lattice. The Raman spectrometer can examine as low as 100 cm−1 , and so
observe the pure rotational transitions. Raman spectroscopy can be performed
effectively at room temperature, so the need for liquid helium is obviated.
Finally, and most importantly to this examination, since infrared spectroscopy can only be performed on adsorbed hydrogen and the lattice catalyzes
ortho-para conversion, we cannot observe hydrogen without conversion. This
increases the difficulty of measuring the concentration of the ortho and para
species. Even if we know the concentrations initially present in the hydrogen, it
has converted to some other ratio by the time any data are taken. Additionally,
if we load hydrogen that has been previously converted by the external system,
it is impossible to distinguish between conversion extrinsic and intrinsic to the
lattice. Since Raman spectroscopy is done on unadsorbed gas, very little conversion occurs during the data taking process, and so any difference from room
temperature values must be the result of extrinsic effects. Raman spectroscopy
is thus complementary to infrared spectroscopy, and we hope to use the two in
parallel.
Raman spectroscopy presents its own challenges. Since signal intensity is
proportional to the number of molecules in the laser beam path, we get increased signal strength with increased path length and increased H2 concentration. However, we want to limit H2 usage by the Raman system as much
as possible. The goal is to create a gas cell that maximizes path length and
minimizes volume. This process is ongoing.
1.5 Going Cold
All the infrared data that will be presented were taken at cryogenic temperatures, usually 30 K. This is obviously more difficult and expensive than opera-
1. Introduction
6
tions at room temperature, but is required to obtain useful data. First, since the
ratio between the adsorbed and gas phases goes as e1/T (simply from the Boltzmann factor), decreasing temperature by a factor of 10 from room temperature
dramatically increases hydrogen uptake by the host.
Second, the width of absorption lines scales with the magnitude of thermal
fluctuations, so cold temperatures sharpen our peaks considerably. This improves the precision with which we can determine the location and size of these
peaks, and prevents nearby peaks from superimposing on each other. Also, most
hydrogen hosts have multiple binding sites, each with a different binding energy.
At room temperature, the difference in energy between sites is small compared
to the hydrogen’s thermal energy, so all binding sites fill simultaneously. At 30
K the energy difference between sites is significant, and the sites fill sequentially.
This makes it possible to investigate the behavior of sites individually rather
than in aggregate. This ends up being particularly important in the analysis of
conversion behavior, which we found to vary between binding sites.
1.6 Metal-Organic Frameworks
There are two broad categories of materials useful for hydrogen storage: those
that form chemical bonds with the hydrogen (chemisorption), and those that
physically adsorb hydrogen on their surface (physisorption). The former bonds
hydrogen strongly, much more so than the Department of Energy’s 40 kJ/mol
target[38]. The sorption process in this case is not easily reversible, and so the
energy stored cannot be practically extracted to power an automobile. Finding materials that chemisorb more weakly and relinquish their hydrogen more
readily has been a major focus of study.
Physisorbent materials produce lower binding energies than desirable, usually less than 10 kJ/mol[34, 22, 5, 42]. It is much easier to extract physisorbed
hydrogen, though in many cases too easy. Many physisorbent materials have
little to no hydrogen uptake at room temperature and atmospheric pressure.
They require either low temperatures (< 100 K) or high pressure (> 100 atm),
making long term storage under practical conditions impossible[20, 19, 34]. The
hope is to find physisorbent materials with higher binding energies, so that they
might be able to store efficiently under practical conditions. It is this sort of
material that we focus on.
Given the 9 wt% Department of Energy goal, it is essential to minimize
the mass of all components of the storage system. Thus materials with the
1. Introduction
7
Fig. 1.1: This is MOF-74, viewed along its primary axis. It forms a honeycomb structure. The purple atoms are Zn , which bind the hydrogen. The hydrogen
binding sites are indicated in green. There are four different sites, with six
of each per hexagon. They fill from the outside in, as indicated.
1. Introduction
8
highest possible ratio between the mass of stored hydrogen and mass of storage material are desirable. For materials that use physisorption, this means we
want a lightweight, porous material with high surface area. This has historically meant the use of carbon allotropes and zeolites[20, 34, 42, 9]. In the last
decade, attention has turned to a new class of materials called Metal-Organic
Frameworks (MOFs), which consist of metallic clusters connected by organic
links[33, 51, 40]. They feature tunable structure, allowing for substantial customization of adsorption materials and giving cause for optimism about the long
term viability of MOFs[41].
Herein we consider MOF-74. It is a zinc-based compound, and has been
shown to exhibit a binding energy between 8.3 and 8.8 kJ/mol[42, 34]. Liu
et al. found its maximum hydrogen uptake to be 4.8 wt% theoretically and
2.8 wt% experimentally[34]. This makes MOF-74 one of the better observed
materials for binding energy, but less exciting for uptake. Little work has been
done on MOF-74 in the infrared, and to the author’s knowledge no one has
considered its behavior as a catalyst for ortho-para conversion.
MOF-74 exhibits hexagonal symmetry and takes on a honeycomb structure,
as shown in Fig. 1.1. It has four distinct sites where hydrogen can be adsorbed.
This structure was established by neutron diffraction experiments at NIST[34].
Throughout this thesis we will refer to site 1 as the primary site and the other
three as the secondary sites. Note that the viewing angle of Fig. 1.1 was selected
to highlight the hexagonal symmetry of MOF-74. The four binding sites do not
lie in the same plane.
MOF-74 exists as a dry, yellow powder and is extremely air sensitive, being
destroyed immediately on contact. It must be stored at an overpressure of argon
in a glove box while waiting to be used. When it is in our spectrometer, we
keep it at an overpressure of either hydrogen or helium between runs.
2. THEORY AND BACKGROUND
2.1 Ortho and Para Hydrogen Spin Isomers
2.1.1
The Symmetrization Requirement
Recall that protons have spin of 21 . The two protons of the hydrogen molecule
can thus each individually be in the state s = 1 ms = + 1 or s = 1 ms = − 1 .
2
2
2
2
For the sake of concision these will henceforth be referred to as |↑i and |↓i
respectively. To consider the hydrogen molecule’s two nuclei together, we first
recognize that the molecule’s total nuclear spin can be either S = 0 (singlet)
or S = 1 (triplet). The former can have only mS = 0, while the latter can
have mS = +1, 0, −1. This gives four possible states, each of which is a linear
combination of the possible single particle states. They are given in Table 2.1.
The two protons are indistinguishable, so our system can undergo no observable change if we interchange the two protons. That is, if we call our protons
2
2
a and b, then we must have |Ψ(a, b)| = |Ψ(b, a)| where Ψ(a, b) is the total
wavefunction of protons a and b. This is only possible if Ψ(a, b) = Ψ(b, a) or
Ψ(a, b) = −Ψ(b, a). If the former case obtains, then the state Ψ(a, b) is said to be
symmetric, while if the latter it is said to be antisymmetric. The Pauli exclusion
principle requires that the total wave function of two fermions, such as protons,
be antisymmetric. Thus for the nuclei of H2 we have Ψ(a, b) = −Ψ(b, a).
m = +1
m=0
m = −1
S=1
|↑↑i
√1 |↑↓ + ↓↑i
2
|↓↓i
S=0
√1 |↑↓
2
− ↓↑i
Tab. 2.1: The two-proton spin states.
2. Theory and Background
10
(a) The vibrational mode.
(b) The rotational mode.
(c) The translational mode.
Fig. 2.1: The ways in which H2 , D2 , and HD can move. They are the (a) H-H bond
stretching, (b) rotation perpendicular to the molecular axis, and (c) translation of the molecule relative to the host lattice.
2. Theory and Background
11
Note that since
|↑a ↑b i = |↑b ↑a i
1
1
√ |↑a ↓b + ↓a ↑b i = √ |↑b ↓a + ↓b ↑a i
2
2
(2.1)
|↓a ↓b i = |↓b ↓a i
1
−1
√ |↑a ↓b − ↓a ↑b i = √ |↑b ↓a − ↓b ↑a i
2
2
(2.3)
(2.2)
(2.4)
all the S = 1 states are symmetric under exchange, while S = 0 is antisymmetric.
There are three ways in which H2 can move: the whole molecule can translate, the protons can vibrate, and the protons can rotate about the molecular
center of mass, as indicated in Fig. 2.1. The total wavefunction has a component
for each of these motions and the spin, and so has the form
Ψ(a, b) = ψx (a, b)ψν (a, b)ψJ (a, b)χ(a, b)
(2.5)
where ψx (a, b) is the translational state, ψν (a, b) is the vibrational state, ψJ (a, b)
is the rotational state, and χ(a, b) is the spin state. It must be that an odd
number of these states are antisymmetric.
However, the translational state depends only on the center of mass coordinates of the molecule, which are indifferent to exchange. The vibrational state
depends on |ra − rb |, which is also indifferent to exchange[36]. Thus the vibrational and translational states are always symmetric, and so to have total
antisymmetrization exactly one of the rotational and spin states is antisymmetric. In the next section we consider the symmetry properties of the rotational
state.
2.1.2
The Rotational State
The hydrogen molecule has two axes of rotation, perpendicular to each other as
well as to the molecular axis as shown in Fig. 2.2. We will treat the molecule as
a rigid rotor. That is, the protons are each a point mass m with fixed separation
R. There is no potential in this situation, so all the energy comes from the three
kinetic energy components
T =
p2y
p2
p2x
+
+ z
2m 2m 2m
(2.6)
2. Theory and Background
12
Fig. 2.2: The axis system for the hydrogen molecule. In the rigid rotor model the
masses are points and the internuclear distance R is fixed. The x and z axes
are the axes of rotation.
of each proton. We can rewrite this in spherical form as
1
T =
2I
p2θ
+
p2φ
sin2 φ
!
,
(2.7)
where I is the H2 moment of inertia and θ and φ are as in Fig. 2.2. Note that we
have reduced from three to two variables since we are assuming no change in r,
and hence pr = 0. This treatment so far is purely classical. To transition to the
quantum universe, we simply replace the classical angular momenta pφ and pθ
with the appropriate operators and let Ĥ = T . Then we solve the Schrödinger
equation:
⇒
ĤψJ = EψJ
1 ∂
∂ψJ
1 ∂ 2 ψJ
−2I
sin θ
+ 2
= 2 EψJ .
2
sin θ ∂θ
∂θ
∂φ
sin θ
h̄
(2.8)
(2.9)
However, down to a constant, this is identical to the familiar angular component
of the hydrogen atom wavefunction. The answers are the same, the spherical
2. Theory and Background
13
harmonics, and we obtain energy eigenvalues
EJ =
h̄2
J(J + 1)
2I
(2.10)
where J is the quantum number giving the nuclei’s total orbital angular momentum. We define the rotational constant
B≡
h̄2
.
2I
(2.11)
Note that EJ depends only on J, but the spherical harmonics and in turn the
rotational wavefunctions ψJ also depend on the azimuthal quantum number mJ .
This leads to the rotational degeneracy of 2J + 1, since mJ can take on all the
values {−J, −J + 1, . . . , J − 1, J}. The establishment of these rotational states
and energies will enable us to both examine the statistical mechanics of the
ortho and para species of hydrogen and explain why there is not autonomous
conversion between them.
2.1.3
The Rotational Symmetries
It will be instructive to explicitly give the form of ψJ . The spherical harmonics
have the form
|mJ |
YJmJ ∝ eimJ φ sin|mJ | θPJ
where
|mJ |
PJ
(x) =
(cos θ)
(2.12)
dmJ PJ (x)
dJ (x2 − 1)J
and
P
(x)
∝
J
m
dx J
dxJ
|mJ |
are the associated Legendre polynomials. Note that PJ
(2.13)
(x) is even if J − |mJ |
is even and odd if it is odd.
We now consider exactly what it means to interchange the protons of H2 .
We follow the method of Farkas, and start by inverting the direction of the
molecular axis. Using the scheme of Fig. 2.2, we say ŷ 0 = −ŷ. We then reflect
the electron positions about the molecular center[15]. Thus proton a now has
the coordinates and electronic environment of proton b and vice versa. This
has effectively exchanged the protons. Geometrically, then, φ0 = φ + π and
θ0 = π − θ. This is illustrated by Fig. 2.3. We examine the effect of this on
Eq. 2.12 term by term. We have
(
0
eimJ φ = eimJ (φ+π) = eimJ φ eimJ π =
eimφ ,
−e
imφ
if mJ is even
, if mJ is odd
(2.14)
2. Theory and Background
14
Fig. 2.3: The exchange of protons. The y-axis has changed direction. Note that either
the x or z-axis also has to change direction in order to preserve the righthandedness of the coordinate system. The z-axis is chosen arbitrarily.
mJ
Even
Even
Odd
Odd
J
Even
Odd
Even
Odd
ψJ
+
+
-
Tab. 2.2: The J dependence of rotational state symmetry.
and
sin|mJ | θ0 = sin|mJ | (π − θ) = sin|mJ | θ.
(2.15)
The final term is
(
|m |
PJ J (cos θ0 )
=
|m |
PJ J (cos(π−θ))
=
|m |
PJ J (− cos θ)
=
|mJ |
PJ
(cos θ),
|m |
−PJ J (cos θ),
if J − |mJ | is even
if J − |mJ | is odd
(2.16)
The total sign of ψJ as a function of the evenness and oddness of J and mJ
is given in Table 2.2. Note that if J is even then ψJ is unchanged by exchange of
the nuclei, while if J is odd then ψJ is multiplied by −1. Thus the odd-J states
are antisymmetric and the even-J states are symmetric. In order for the total
wavefunction Ψ(a, b) to be antisymmetric under the interchange of protons, we
need either an even-J rotational state with the singlet spin state or an odd-J
rotational state with the triplet spin state. This dichotomy is the basis for all
the data that will be presented. To complete the description of the separation
of H2 into the two distinct ortho and para spin isomers we need only explain
.
2. Theory and Background
H2
D2
HD
B (meV)
7.35
3.71
5.54
B (cm−1 )
59.3
29.9
44.7
15
B (K)
85.3
43.0
40.7
Tab. 2.3: Rotational constants in the ground vibrational state of hydrogen isotopes
in various units[46]. To obtain actual units of energy, the numbers of column two should be multiplied by hc and those of column three should be
multiplied by kB .
why one spin species does not readily convert to the other.
2.2 The Equilibration of H2 , D2 , and HD
Before we examine the potential methods of conversion, we explore the theoretical behavior of the species from a statistical mechanics perspective. We will
consider the rotational levels of three isotopes of molecular hydrogen: H2 , D2 ,
and HD. The rotational constants of these isotopes are given in Table 2.3.
As seen in Eq. 2.11, the energy levels of each isotope are determined by B.
Note that B behaves qualitatively as we would expect, given that B ∝ I −1 ,
where I is the molecular moment of inertia. To analyze the relative populations
of the rotational states, we need to know the states’ degeneracies in addition
to their energies. As we have seen in Section 2.1.3, each rotational energy level
EJ can be produced by 2J + 1 distinct mJ values. Thus the degeneracy of each
rotational level is
gJ = 2J + 1.
(2.17)
This is the same for every isotope. Each level also has a spin degeneracy, which
is different for each isotope. As we saw in Section 2.1.1, the odd-spin1 species of
H2 has spin degeneracy go = 3 and even-spin state degeneracy ge = 1. In D2 , the
presence of neutrons changes the nature of the spin states and their degeneracies.
HD has distinguishable particles and thus no symmetrization requirement or
spin degeneracy. The spin degeneracies are summarized in Table 2.4.
The population of an energy state in thermal equilibrium is given in general
by
Ni = NT
gi e−Ei /kB T
Z
(2.18)
1 In this section we use the terms ‘odd’ and ‘even’ in place of ‘ortho’ and ‘para’, since in
D2 the terms ‘ortho’ and ‘para’ refer to the even and odd states, respectively, and HD has no
ortho or para species at all.
2. Theory and Background
16
3.5
Ortho-Para Ratio
3.0
H2
D2
HD
2.5
2.0
1.5
1.0
0.5
0.0
0
40
80
120
160
200
240
280
Temperature (K)
(a)
0.35
Ortho-Para Ratio
0.30
0.25
0.20
0.15
0.10
0.05
0.00
15
20
25
30
35
40
45
50
Temperature (K)
(b)
Fig. 2.4: The equilibrium ratios of H2 , D2 , and HD based on statistical mechanical
considerations of the rotational level splittings. In (b) we see a magnification
of the cold temperature region of (a).
2. Theory and Background
go
3
1
1
H2
D2
HD
17
ge
1
2
1
Tab. 2.4: The spin degeneracies of H2 , D2 , and HD.
where Z is the partition function and NT is the total number of particles. In
this case, the total population of the even and odd states are respectively given
by
Ne =
X
NT
ge
gJ e−BJ(J+1)/kB T
Z
and No =
Jeven
X
NT
go
gJ e−BJ(J+1)/kB T .
Z
Jodd
(2.19)
Thus,
go
X
gJ e−BJ(J+1)/kB T
No
Jodd
X
=
.
Ne
ge
gJ e−BJ(J+1)/kB T
(2.20)
Jeven
We are now able to calculate the equilibrium ratio of even to odd states, which
would always be attained if conversion were not usually forbidden. Figure 2.4
gives the equilibrium ratios for the three isotopes in the range of temperatures
from 0 - 300 K. It is to these ratios that all data will be compared.
2.3 The Improbability of Homogeneous Conversion
As seen in the previous section, the equilibrium ratio between the ortho and
para species of molecular hydrogen is 3:1 at room temperature and essentially 0
at 30 K. It would thus be expected that a sample of hydrogen cooled from room
temperature to 30 K will equilibrate at the lower ratio. In practice this does
not occur. It turns out that hydrogen on its own converts between the ortho
and para spin species extremely slowly. We will call this process homogeneous
conversion. It is disallowed because to transition from the J = 1 to the J = 0
state requires a transition from the triplet to singlet spin state in order to
maintain overall antisymmetrization. However, a spin cannot flip on its own,
as that would violate the conservation of angular momentum. Thus the Pauli
exclusion principle keeps ortho molecules in the rotationally excited J = 1 state,
no matter how low the temperature is. Difficulties with specific processes are
elaborated on below.
2. Theory and Background
18
A catalyst is necessary in order to efficiently equilibrate a sample of hydrogen. This is heterogeneous conversion. The interaction between hydrogen and a
paramagnetic lattice can produce a magnetic field gradient over the length of a
hydrogen molecule. This allows a spin to flip and thus a relaxation from J = 1
to J = 0.
2.3.1
The Forbidden ∆J = ±1 Transition
As the J = 1 rotational state is excited compared to the J = 0 state, we expect that at sufficiently low temperatures the molecule will relax to the ground
rotational state. Indeed, ∆J = ±1 is usually a selection rule for infrared absorption in gases. Additionally, the energy difference between the two states is
E1 = 2B = 119 cm−1 , which is in the far infrared region of the electromagnetic
spectrum. It is thus reasonable to expect that the molecule might relax by infrared radiation. However, we do not observe this. Instead we find the selection
rule to be ∆J = ±2. This is explained in Section 2.5.
Wigner found a spontaneous transition probability on the order of 10−10 s[49].
Bonhoeffer and Harteck attempted to measure this rate of conversion and found
the half-life of the J = 1 state to be at least a year[7, 6]. For all practical purposes, this transition is forbidden and does not occur.
2.3.2
Interaction of H2 and H
Molecular hydrogen can also be converted by the chemical exchange of protons[15].
Farkas used catalyzed conversion to produce a sample of hydrogen containing
47% para species[13, 14]. He then heated the sample to a range of temperatures between 700 and 900 o C so that the sample was far out of its thermal
equilibrium ratio and observed the back conversion of para hydrogen to ortho
hydrogen.
He was able to establish this back conversion as homogeneous by varying
the hydrogen’s container. Since the system contained just hydrogen, the only
possible catalyst for the conversion was the wall of the gas chamber. Farkas used
both quartz and porcelain tubes to contain the converted gas, and observed no
change between the materials. He also inserted a second tube inside the first,
increasing the total tube surface area exposed to the gas. This also had no
effect on the conversion rate. This implies that the gas tube is not catalyzing
the back conversion and any change from J = 0 to J = 1 occurs as a result of
interactions within the hydrogen.
2. Theory and Background
19
It makes sense that this process is dependent on the frequency of H2 -H2
collisions and should therefore depend on H2 concentration. However, Farkas
found that the back conversion rate actually depends on the concentration of H
atoms. He calculated that his sample of H2 at these high temperatures contained
between 10−8 and 10−6 % H atoms, and found that this was sufficient to sustain
the reaction
H2,p + H
→
H2,o + H
↑↓ + ↑
→
↑↑ + ↓ .
This result was confirmed by Geib and Harteck, who used an electrical discharge
to produce a concentration of hydrogen atoms between 3 and 19% and were thus
able to see the effect more dramatically[21].
However, at the temperatures we are concerned with, between 15 and 300
K, the concentration of dissociated H atoms is essentially zero, and so this effect
can be ignored, and is not a potential source of conversion.
2.3.3
H2 -H2 Interactions
Conversion from H2 -H2 interactions was first discovered in the liquid and solid
phases[15]. Both Bonhoeffer and Harteck and Keesom, Bijl, and van der Horst
observed conversion in the liquid phase on the order of hours[7, 31]. None of the
previously discussed mechanisms are capable of this effect. Might this process
be chemical, as in the case of the atomic interaction? This would have the form
H2,o + H2,o
→
H2,p + H2,p
↑↑ + ↓↓
→
↑↓ + ↑↓
However, such a reaction would have a temperature dependent activation energy,
which is not observed[15, 12]. Because the ortho state possesses a nonzero spin,
it also possesses a net magnetic moment. Thus if two ortho molecules are in
close enough proximity, each will produce a substantial magnetic field gradient
on the other, which can cause conversion as described in more detail below. In
this way, hydrogen is able to catalyze its own conversion.
At what rate can H2 convert itself? Since the conversion is a random process,
it must be dependent on the concentration of unconverted (ortho) molecules.
However, it also depends on the number of other ortho molecules that each
2. Theory and Background
20
ortho molecule is exposed to, since the orthohydrogen is catalyzing itself. If we
take the molecules to be free to move, then each ortho molecule is exposed to
all the others. The conversion thus takes the form
dno
= −kn2o
dt
(2.21)
where k is the rate constant and no is the concentration of ortho hydrogen[15,
16, 11, 43]. This qualitative form is the same in the solid and liquid, though
the conversion is faster in the solid. The intermolecular spacing is smaller, and
therefore the magnetic field gradient is greater, producing a greater conversion
rate.
In the limit no → 0, the solid and liquid forms diverge[15]. In the liquid phase
individual molecules move freely, and thus the distribution of the ortho and para
species is isotropic. In the solid, however, at temperatures below about 3 K the
diffusion rate of ortho hydrogen through the solid is smaller than the conversion
rate and ortho molecules can become isolated from other ortho molecules. An
isolated molecule is unable to have its conversion catalyzed or catalyze the
conversion of another molecule. This causes a cut-off in the conversion of the
solid for small no .
2.4 Catalyzed Conversion
2.4.1
Conversion by Gaseous Impurities
Farkas and Sachsse found in 1933 that conversion could be catalyzed by the
presence of oxygen impurities in a sample of hydrogen[15, 17, 18]. They observed
conversion of the form
dno
= −knO2 no
dt
(2.22)
where nO2 is the concentration of O2 , no is the concentration of the odd-J
species of H2 , and k is a constant. This makes sense considering the discussion
of Section 2.3.3. The conversion rate is dependant on the concentration of
material to be converted, no , and concentration of catalyst, nO2 . Oxygen makes
an effective catalyst because it is paramagnetic. Since its magnetic field is, of
course, produced on a molecular scale, this field is inhomogeneous on a molecular
scale. Also note that the magnetic moment of O2 is about 2000 times that of
orthohydrogen[15]. Thus the presence of nearly any O2 will drastically increase
the conversion rate above that for H2 -H2 interactions. Water impurities behave
2. Theory and Background
21
similarly[15]. It is vital that all traces of air be removed from our system before
we attempt conversion. When we remove the converted hydrogen from our
conversion system, it is stored at 77 K before being loaded into MOF-74. If
there are gaseous impurities present, then the 97% parahydrogen that we have
produced will back convert to 50% parahydrogen, which is equilibrium at 77 K.
The probability of conversion from this process was found by Wigner to be
W =
2µ2a µ2p I
3h̄2 `6 kB T
(2.23)
where µa is the magnetic moment of the paramagnetic molecule, µp is the proton
magnetic moment, I is the H2 moment of inertia, kB is Boltzmann’s constant,
T is temperature, and ` is the mean free path of an H2 molecule[49, 50, 15].
Note that the probability is inversely proportional to temperature. This makes
sense because at lower temperatures, the intermolecular interaction time will
be greater, giving greater opportunity for conversion. Additionally, since ` is
√
3
n, this probability will increase with concentration.
inversely proportional to
2.4.2
Conversion of a Fluid by a Solid Catalyst
There are two catalysts that we use to intentionally convert hydrogen. In the
conversion system, we place liquid H2 around Nd2 O3 . This situation is analogous to the gaseous impurity. The conversion rate will still depend linearly
on no , and the orthohydrogen to be converted is still free to move. The only
difference is that the catalyst is not free to move. However, note that at 15 K,
the root-mean-square speed of H2 is still
r
vrms =
5kB T
= 561 m/s.
m
(2.24)
Collisions will still be extremely frequent, and the immobility of the catalyst
should not hamper conversion. Note that this process also governs the interaction of gas with the walls of our gas system, various parts of which are stainless
steel or copper. To avoid back conversion in the warm parts of our gas system,
we thus want to use materials with small magnetic moments.
2.4.3
Conversion by a Paramagnetic Lattice
To begin, we will derive the behavior of Larmor precession, following the method
~ = B0 ẑ. The
of Griffiths[24]. Start with a single proton in a magnetic field B
2. Theory and Background
22
Hamiltonian of this system is
~
Ĥ = −~
µ·B
(2.25)
where µ
~ is the magnetic dipole moment
~
µ
~ = γS
(2.26)
~ is the proton’s spin vector and γ is its gyromagnetic ratio. Thus
where S
Ĥ = −γB0 S~z
where
h̄
S~z =
2
1
0
0
−1
(2.27)
!
.
(2.28)
We already know that the spin eigenstates of a single proton are |↑i and |↓i.
Then at any given time t, the proton’s spin state is given by a linear combination
of these eigenstates:
χ(t) = αe−iE↑ t/h̄ |↑i + βe−iE↓ t/h̄ |↓i .
But we know
1
|↑i =
!
0
and |↓i =
0
(2.29)
!
−1
,
(2.30)
so, since by the Schrödinger equation Ĥψ = Eψ,
E↑ =
+γB0 h̄
−γB0 h̄
and E↓ =
.
2
2
(2.31)
Thus,
χ(t) =
αeiγB0 t/2
βe−iγB0 t/2
!
.
(2.32)
The coefficients α and β are constrained by χ(0). We do not care what particular
spin state the proton is initially in, so we only require that χ(0) be normalized,
2
2
that is |a| + |b| = 1. It is convenient to say
α = cos
δ
δ
and β = sin
.
2
2
(2.33)
2. Theory and Background
23
We want to know what effect the magnetic
D E DfieldE is having
D Eon the spin. We
~
~
thus calculate the expectation values Sx , Sy , and S~z . This process is
calculation is just algebra and is omitted. We find
h̄
sin δ cos(γBo t)
(2.34)
2
−h̄
sin δ sin(γBo t)
(2.35)
2
h̄
cos δ
(2.36)
2
D E
~ is at a fixed angle δ to the
It is clear from these expectation values that S
D E
~ onto the xy-plane traces out a circle as time
z-axis. The projection of S
D E
~ precesses around the z-axis with the Larmor frequency
develops. Thus S
D E
S~x =
D E
S~y =
D E
S~z =
ω = γB0 .
(2.37)
In molecular hydrogen, the two protons’ spins are ordinarily coupled. If we
were to put H2 in a constant magnetic field, the protonic spins would precess in
phase with each other, with no net spin flip. A large inhomogeneous magnetic
field can break this coupling and allow ortho to para conversion[28]. We will
follow the method of Petzinger in examining this process[39]. In general we are
interested in the process both from the ortho to para state and the para to ortho
state. However, since the singlet state is simpler to treat than the triplet, we
will here examine the case of para to ortho transition. The reverse process will
have the same qualitative form, if not the exact mathematical construction.
Thus we start with a hydrogen molecule in the singlet spin state. When we
say that the field is inhomogeneous, we mean that each proton experiences a
different magnetic environment. We call the protons a and b, and say that they
~b . Thus Hamiltonian
are respectively located at r~a and r~b in fields B~a and B
becomes
~b
Ĥ = −µ~a · B~a − µ~b · B
(2.38)
where µa and µb are the magnetic moments of the a and b protons. Note that
Ĥ acts only on the spin state of H2 . Thus the spin state develops as
χ(t) = e−iHt χ(0).
(2.39)
2. Theory and Background
24
By exploiting power series, the time development can be written as

e−iHt
 

~
~
σ
~
·
B
σ
~
·
B
a
a
b
b
= cos(ωa t) + i sin(ωa t)  + cos(ωb t) + i sin(ωb t) 
~
~
Ba Bb (2.40)
where σa and σb are the components of the respective protons in the direction
of their respective fields (equivalent to S~z in the one proton case) and ωa and
ωb are the individual Larmor frequencies of the protons[39]. This can yield the
probability of para to ortho conversion
P (t) = sin2 (ωa − ωb )t + sin2
η
2
sin(2ωa t) sin(2ωb t) + sin2 (η) sin2 (ωa t) sin2 (ωb t),
(2.41)
~
~
where η is the angle between Ba and Bb . This behavior is complicated, but it
can be productively examined in two limiting cases. First, take the case where
~b are parallel but of different magnitude. Then η = 0 and ωa 6= ωb .
B~a and B
The probability reduces to
P (t) = sin2 (ωa − ωb )t.
(2.42)
This answer makes sense if we imagine the spins as classical vectors rotating
out of phase. This equation measures how much out of phase the two spins are.
When they are maximally out of phase, the probability of conversion is 1, and
when they are momentarily in phase the probability is 0.
~b to have the same magnitude but
In the second case, we take B~a and B
different direction. Then η 6= 0 and ωa = ωb . This gives
P (t) = sin2 (2ωt) sin2
η
2
+ sin4 (ωt) sin2 (η)
(2.43)
where we have made the replacement ω = ωa = ωb . This situation is more
difficult to visualize, but also results in the two protonic spins precessing out of
phase and eventually flipping.
~b are parallel gives a rough estimate of
Note that the limit where B~a and B
the time required for conversion. For appreciable conversion we want
(ωa − ωb )t ≈nπ
nπ
⇒ ∆B0 t ≈ .
γ
(2.44)
(2.45)
2. Theory and Background
25
If we can estimate the change in field strength across H2 and the lifetime of H2
adsorbed on a surface, we have an estimate of the efficiency with which we will
convert.
Note that we made no assumptions about the source of the magnetic field.
This theory is equally valid for any field source. Practically, this field is supplied
by a paramagnetic molecule, which can be an orthohydrogen molecule, a gaseous
impurity, or a lattice.
2.5 Infrared Absorption
The intensity of an absorption peak is governed by Beer’s Law. It simply gives
I = An
(2.46)
where I is the intensity of the absorption peak, n is the concentration of the
absorbing material, and A is a constant dependant on the material and the absorption mechanism. It is this relationship that allows us to use infrared spectroscopy to measure the concentration of the adsorbed ortho and para species.
We use infrared radiation, which has a wavelength on the order of 1 µm. The
internuclear spacing of H2 is on the order of 1 Å. We will thus take the electric
field from the photons to be spatially constant over the hydrogen molecule.
These photons interact with a molecule primarily through the molecule’s dipole
moment[10]. From Griffiths, the probability of a transition from some state ψa
to another state ψb is give by
2
Pa→b ∝ |hψa | µ |ψb i|
(2.47)
where µ is the dipole moment of the molecule[24]. Clearly if µ = 0 then the
probability of transition is zero. If µ is constant, then
2
Pa→b ∝ µ2 |hψa |ψb i| .
(2.48)
This is zero because ψa and ψb are orthogonal. Thus the only transitions that
occur are ones where the electric dipole moment of the molecule changes.
This makes sense for the vibrational and ro-vibrational transitions that we
observe. When a molecule makes a vibrational transition, the internuclear spacing changes. This changes the charge separation, which changes the dipole
moment.
2. Theory and Background
26
Hydrogen is a symmetric molecule and so has no electric dipole moment, and
under ordinary circumstances has no infrared activity. However, when hydrogen
is adsorbed on a lattice (MOF-74 in this case), a dipole can be induced. The
adsorbed hydrogen therefore has a dipole of the form
µ = αE
(2.49)
where α is the polarizability of H2 and E is the electric field from the photon.
We refer to this as the overlap term. Since α is isotropic, there is no θ or φ
dependence to µ, and hence the overlap mechanism cannot produce a change in
angular momentum. The Q(0) and Q(1) peaks are produced in this way.
The hydrogen molecule can also induce a dipole in the lattice through its
quadrupole. This has the form
µ = Qα
(2.50)
where Q is the quadrupole moment of hydrogen and α is the polarizability of
MOF-74. Note that the J = 0 state is spherically symmetric and so has no
quadrupole. Thus the Q(1) peak is also activated by the quadrupole term,
while the Q(0) is not. Since the Q(1) peak is activated by two mechanisms, it
is more intense than the Q(0) for the same concentration. The implications of
this will be discussed below. Note that the quadrupole of H2 can be expressed
as the spherical harmonic Y2m . The result is that the matrix element hψa | Q |ψb i
is nonzero only for J = 0 or J = ±2. This gives us our J selection rules. The
J = 0 case is the Q(1) peak, while the J = +2 case gives us the S peaks. We
do not see the J = −2 transition because there is no appreciable population of
any state with J > 1 at the temperatures we are concerned with. Note that due
to the complicated symmetries of the MOF-74 binding sites, we are unable to
determine the m selection rules.
2.6 Raman Scattering
The intensity of a Raman peak depends on the target molecule’s polarizability.
We show this following the method of Colthup et al[10]. While we assume the
electric field experienced by a hydrogen molecule to be constant with space, it
is not constant with time. We take the electric field to have the form
E = E0 sin(ωt)
(2.51)
2. Theory and Background
27
where ω is the frequency of the incident radiation. The induced dipole of the
hydrogen molecule is thus
µ = αE0 sin(ωt).
(2.52)
This time varying dipole produces electromagnetic radiation, which is proportional to the amplitude of µ2 . We take r to be the displacement between the
molecule’s positive and negative charges. We assume that α varies over the
molecule, and expand it as a Taylor series in r. Then
α = α0 + r
∂α
+ ··· .
∂r
(2.53)
We approximate the variation of α with the first two terms of this expansion.
Thus
µ = α0 E0 sin(ωt) + rE0
∂α
sin(ωt).
∂r
(2.54)
Classically, we take r to vary with the frequency of vibration of the molecule,
ων . Then
∂α
sin(ωt) sin(ων t)
∂r
r0 E0 ∂α
= α0 E0 sin(ωt) +
[cos(ω − ων ) − cos(ω + ων )] .
2 ∂r
µ = α0 E0 sin(ωt) + r0 E0
(2.55)
We see that the molecule can produce scattered radiation at the frequencies
ω, ω − ων , and ω + ων . These are respectively Rayleigh scattering, Stokes
Raman scattering, and anti-Stokes Raman scattering. It is clear that Rayleigh
scattering only requires that a molecule be polarizable, while Raman scattering
requires a spatially varying polarizability, which H2 possesses[32]. We can thus
use Raman scattering to probe H2 .
3. EXPERIMENTAL METHODS
3.1 Infrared Spectroscopy
3.1.1
The Spectrometer
Our primary method for investigating a sample is by Diffuse Reflectance Infrared Fourier Transform Spectroscopy (DRIFTS). A light source illuminates
our sample, and photons corresponding to characteristic energy level transitions in the sample are absorbed while the rest are reflected at a random angle.
By comparing the absorption lines from the sample under different conditions
(i.e. with and without hydrogen), we are able to examine the characteristics of
both our material and the hydrogen stored within it.
Our spectrometer is a Michelson interferometer, and its capabilities are governed by the choice of light source, beamsplitter, and detector. The configuration used for most of the data presented here was a quartz halogen lamp,
CaF2 beamsplitter, and mercury cadmium telluride (MCT) detector. These
collectively allow for high signal intensity and low noise in the region of approximately 2000 cm−1 and 6000 cm−1 . As has been discussed, we are primarily
concerned with the vibrational and ro-vibrational transitions. Table 3.1 shows
where these peaks occur in the gas phase of H2 , D2 , and HD. The bulk of these
peaks are perturbed by no more than 100 cm−1 from their gas phase value. It is
clear that our spectrometer’s range is appropriate for investigating these peaks.
H2
D2
HD
∆ν
S(0)
354.4
179.1
267.1
=0
S(1)
587.1
297.5
443.1
Q(0)
4161.1
2993.5
3632.1
∆ν = +1
Q(1)
S(0)
4155.2 4497.2
2991.4 3166.3
3628.2 3887.6
S(1)
4712.8
3278.4
4055.6
Tab. 3.1: The rotational, vibrational, and ro-vibrational transitions of H2 , D2 , HD
in cm−1 [1, 46]. The Q transitions are ∆J = 0 while the S transitions are
∆J = +2. The number in parentheses indicates the initial J value of the
transition.
3. Experimental Methods
29
We also have a globar source. It is cooler, and the peak of its emission
spectrum is at a lower frequency. It can be used for excursions to the far infrared,
to about 200 cm−1 . This lets us attempt to see direct rotational transitions,
the frequencies for which are listed in Table 3.1. However, the globar suffers a
factor of four reduction in intensity from the quartz lamp. Going that low in
frequency also pushes the limit of the MCT detector, which reduces the signal
to noise ratio. Finally, many host lattices, including MOF-74, have lots of peaks
in the far infrared, making extracting hydrogen peaks difficult.
To study higher frequencies, we have a quartz beamsplitter and InSb detector. The hope is to be able to examine the doubled frequencies of the vibrational and ro-vibrational peaks we already see. Not only does this provide
another way to corroborate our data, but when the peak frequencies double so
do the splittings. This allows the deconvolution of peaks that ordinarily overlap.
Unfortunately, we have only observed this double peak for the D2 primary site.
The InSb detector is also supposed to be more sensitive in the 4000-6000 cm−1
range of primary interest, but in practice has been comparable to the MCT.
The spectrometer directs light into a cryostat, where our sample resides. The
light reflected from the sample then exits the cryostat after passing through a
series of collecting optics and is picked up by the detector. The detector produces
a voltage signal which is passed through a preamplifier. The preamplifier can
multiply this signal by a factor of 1, 2, 12, or 24. The amplified signal is put
through a Fourier transform and then collected by a PC, where it can be stored
and manipulated.
As discussed in Section 2.5, H2 O has a strong infrared signal, which can interfere with our data collection. The spectrometer is thus operated at a vacuum.
A mechanical pump keeps the system at approximately 1 Torr.
3.1.2
The Gas Loading System
The gas loading system transfers gas from H2 , D2 , and HD high pressure cylinders to the sample, and is illustrated in Fig. 3.1. Only one cylinder can be
connected at a time, though they can be switched easily. Our pressure gauge is
accurate from vacuum up to 1 atm, with resolution 2 × 10−4 atm. This allows
fine control of the amount of gas entering the sample.
Impurities in the gas line can destroy the MOF-74, back convert our parahydrogen, and give inaccurate measures of the amount of hydrogen loaded into the
system. A mechanical pump, connected to the system by valve D, can achieve
3. Experimental Methods
30
Fig. 3.1: This is the gas loading system, which transfers hydrogen to our sample.
Valves are indicated by the red boxes. H2 , D2 , and HD can be loaded from
the main tank, He from another tank, and pure para H2 from the conversion
system. These can be loaded as necessary into the sample chamber. Volumes
of this system’s components are given in Table 3.2.
pressure low enough as to be indistinguishable from zero by our gauge. Since
MOF-74 is a dry powder, it is important to have a slow flow rate into or out of
the sample chamber to avoid dislodging the sample. All the gas system valves
can attain a flow rate on the order .2 mbar. In order to reduce the impurity
levels in the line low enough to keep MOF-74 from being destroyed, we pump
and flush. In this process the line is pumped down to a vacuum, refilled to an
atmosphere with helium, and pumped down again. Performing this process several times reduces impurities to trace levels and prevents damage to the sample
and back conversion. The helium also serves as an exchange gas, the importance
of which is explained below.
In order to know exactly how much hydrogen has been introduced to the
sample, the gauge’s pressure reading must be converted to the number of moles
loaded. The calibrated volume provides this capability. It is machined to have
a volume of 25 cm3 . From this we can learn the volumes of the system’s other
components, which in turn allows us to know how a pressure reading corresponds
to an amount of hydrogen.
The introduction of hydrogen to MOF-74 is controlled by three valves,
marked in Fig. 3.1. Valve A controls the flow rate from the main hydrogen
tank and valve F from the conversion system. Valve G controls the flow rate
from the main body of the gas system to the sample chamber. By loading the
3. Experimental Methods
31
Fig. 3.2: The sample chamber bolted onto the coldfinger, courtesy of Hugh
Churchill[9]. a)Connects to the gas loading system, and corresponds to valve
F in Fig. 3.1. b)The vertical and angular alignment system. c)Connects
to the diffusion the pump that keeps the cryostat evacuated. d)The optical
amount that holds the DRIFTS mirrors. e)The ellipsoidal DRIFTS mirrors.
f)The sapphire dome which covers the sample. g)The copper sample platform
which bolts to the cold finger. h)The cold finger.
system in stages, from the tank or conversion system to the line pictured in
Fig. 3.1 to the sample chamber, precise amounts of hydrogen can be introduced
to the sample.
3.1.3
The Sample Chamber and Cryostat
The sample chamber is located inside the cryostat, contains the MOF-74, and
is accessed through the lid of the cryostat. The chamber consists of a copper
platform bolted to the bottom of a cold finger, as can be seen in Fig. 3.2. On
this platform is a post, into which can be screwed any of a number of different
sample holders. These holders are shallow (a few millimeters) copper cups
which contain the dry powder that is the sample. This allows for quick and
3. Experimental Methods
32
Fig. 3.3: The DRIFTS rig around the sample, courtesy of Hugh Churchill[9]. Note
that light travels from left to right. a)The ellipsoidal mirrors that direct
the light onto MOF-74 and collect the reflected light. b)The sample holder.
c)MOF-74. d)The sample platform. e)CaF2 windows at the entrance and
exit of the cryostat. f)Plane mirrors that direct light into and out of the
cryostat.
3. Experimental Methods
33
easy transfer of materials into and out of the spectrometer.
The platform is then covered by a dome consisting of sapphire windows
fused to a stainless steel body. The windows are transparent in the infrared and
are capable of withstanding both cryogenic temperatures and extreme pressure
differentials. A lead gasket keeps the connection between the dome and platform
gas tight.
The sample platform is surrounded by two ellipsoidal mirrors, indicated in
Fig. 3.2. One focuses the beam from the spectrometer on the sample. The other
collects the diffuse reflections from the sample and focuses them on the detector.
The sample chamber must be connected to the gas system. This connection
is a way for heat to leak from the lab into the sample chamber, kept at 30 K for
most experiments. It is therefore necessary to use a conductor that is minimally
thermally conductive. For a solid, heat transfer takes the form
PQ = k∆T
A
,
l
(3.1)
where PQ is the rate of heat transfer, ∆T is the temperature difference between
the sample and environment, A is the connector’s cross-sectional area, l is the
connector’s length, and k is the connector’s thermal conductivity. We therefore
use a long, one-sixteenth inch diameter stainless steel capillary. Stainless steel is
a poor thermal conductor, so the total heat brought from the environment into
the sample is very small. This capillary feeds into the sample chamber through
the bottom of the sample platform, as seen in Fig. 3.2. The capillary exits the
cryostat through its lid and connects to the gas loading system. Valve A in
Fig. 3.2 corresponds to valve G in Fig. 3.1.
The cryostat is also capable of transferring heat through its walls. To prevent
this, it must be kept at a vacuum. The cryostat is kept at a pressure on the
order of 10−5 or 10−6 Torr by a diffusion pump, which prevents heat from the
walls to reach the cold sample through conduction or convection.
A schematic of this apparatus is seen in Fig. 3.2. The box is constructed
of aluminum and is inserted directly into the body of the spectrometer, with
which it seals via an o-ring. CaF2 windows allow the spectrometer’s beam to
pass into the cryostat and out again into the detector. The top of the cryostat
allows the insertion of a transfer tube to bring liquid helium from a storage tank
into our system. This cools down the cold finger, which in turn cools the sample
platform and sample holder. This series of good thermal conductors allows heat
to be effectively drawn from the sample into the helium.
3. Experimental Methods
34
Direct manipulation of the sample is of course impossible when it is under
vacuum. The sample platform contracts substantially upon cooling and moves
the sample out of the beam path. In order to correct for this, the cryostat has
vertical and angular alignment controls, as indicated in Fig. 3.2. These allow
the sample platform to be moved up and down and side to side, optimizing the
optical configuration in situ.
There are two silicon diode thermometers and a heater in the cryostat. One
thermometer and the heater are at the base of the cold finger, while the other
is at the end of the sample platform. These measure and control the sample’s
temperature, so that we can perform our experiments isothermically.
3.2 Ortho-Para Conversion
3.2.1
The Dipstick Converter
The conversion system consists of two separate components, which are collectively connected to the gas storage system by valve F. The dipstick does the
actual conversion, and the storage coil holds the pure para hydrogen which has
been produced. These components can be isolated from each other and the gas
loading system as a whole. The system is designed after that of Andrews[3].
As has been explained in Section 2.4, converting the ortho species of hydrogen to the para requires the presence of an inhomogeneous magnetic field.
The dipstick provides this with the paramagnetic catalyst Nd2 O3 , which is a
pale lavender powder. It was selected as our catalyst based on the advice of
a colleague. Five grams of this powder was placed in a 10 cm3 stainless steel
volume, which is connected by one-eighth inch diameter stainless steel tubing
to the rest of the conversion system, as seen in Fig. 3.4. There is a silicon diode
thermometer attached to the side of the volume. The whole dipstick assemblage
is then be inserted inside a dewar of liquid helium and sealed. Hydrogen can
then be loaded into the dipstick from the gas loading system.
In order to obtain appreciable amounts of conversion, the interaction time
between hydrogen and catalyst must be long, as discussed in Section 2.4. Thus
we want our hydrogen in the liquid phase. In the gas phase, the hydrogen’s
average interaction time is short, so the probability of flipping a spin in any
particular interaction is small. Additionally, the catalyst is concentrated in the
bottom of the dipstick, while the gas fills it evenly. This reduces the frequency
of interactions. The resultant conversion rate is too slow to be practical. If
3. Experimental Methods
35
Fig. 3.4: The dipstick conversion system, which converts normal hydrogen into pure
para species. Red boxes indicate valves. The conversion cell is suspended in
the cold vapor over liquid helium and is kept at about 15 K. The converted
hydrogen is then removed from the cell and kept in the storage coil, submerged in liquid nitrogen. The whole apparatus connects to the gas loading
system.
3. Experimental Methods
36
the hydrogen solidifies on the other hand, the conversion can cut off before
reaching thermal equilibrium, as discussed in Section 2.3.3. Thus to achieve the
maximum possible conversion in the shortest possible time, we want the liquid
phase.
This process requires that we operate the dipstick between about 12 and 20
K. To control the temperature we control the vertical position of the catalyst
chamber. The volume is not immersed in the liquid helium, which would be too
cold, but is instead suspended in the vapor above the liquid. We can increase
the temperature of the dipstick by raising it in the dewar and decrease the
temperature by lowering it. We are able to attain stability within about two
degrees over the course of twelve hours, with no manipulation of the apparatus.
This allows us to perform conversions overnight.
After the conversion is complete, we remove the hydrogen from the conversion cell by extracting the dipstick from the helium dewar and heating it to room
temperature. The resultant gas is then trapped in the storage coil, which has a
volume of 20 cm3 . Once the para hydrogen is out of the helium it is drastically
out of thermal equilibrium, and great care must be taken to keep it isolated
from magnetic field gradients which would cause it to back convert. The coil is
therefore made of copper, because copper is generally free from magnetic impurities (as opposed to stainless steel) and so will not catalyze back conversion.
The coil is kept submerged in liquid nitrogen. The equilibrium ratio of ortho
to para hydrogen at 77 K is 1:1[45]. This is much worse than the essentially
pure para hydrogen that can be produced at 15 K, but far superior to the 3:1
ratio obtained at room temperature. The liquid nitrogen assures that if back
conversion does occur the parahydrogen will not be completely lost. However,
this temperature decrease increases the interaction time, which will increase the
reaction rate. It may be that while we prevented our hydrogen from returning
to 75% ortho, we increased the speed with which it left 3% ortho.
The converted hydrogen can be introduced into the gas loading system via
valve F. Note that to get hydrogen from the storage coil to the sample chamber
requires passing through stainless steel tubes. However, the gas is in contact
with room temperature stainless steel only briefly (on the order of a minute)
and has brief interaction times. We believe that very little back conversion is
able to occur in this process.
3. Experimental Methods
37
Fig. 3.5: The closed-cycle converter. The valve is marked with a red box. Gas is loaded
and removed from the top. The converted hydrogen can be transferred to
any system desirable.
3. Experimental Methods
Component
Calibrated Volume
Gas Line
Sample Chamber
Conversion Cell
Storage Coil
38
Volume (cm3 )
25
7
1
10
20
Tab. 3.2: Volumes of the components of the gas loading system, sample chamber,
and dipstick conversion system. The gas line is the tubing connecting the
hydrogen tank and conversion system to the sample system. Note that it
includes the volume of the pressure gauge.
3.2.2
The Closed-Cycle Converter
The dipstick converter has two substantial practical drawbacks resulting from
its use of liquid helium. First, liquid helium is expensive and not always readily
available. Any time it is possible to eliminate it from a procedure, we should.
Second, keeping the spectrometer at 30 K requires the constant transfer of
helium into the cryostat. It is therefore impossible to convert new hydrogen
while running an experiment on the spectrometer. If during an experiment we
use all the converted hydrogen or contaminate it, then the experiment is over.
We can potentially solve both of these problems by adapting a closed-cycle
helium refrigerator with a conversion cell.
Substantial progress has been made in designing and implementing such a
cell. The system consists of a helium compressor which cools down a copper
cold finger. This cold finger is insulated from the environment by a vacuum
jacket which, like the spectrometer’s cryostat, is kept at 10−5 or 10−6 Torr by
a diffusion pump. A copper conversion cell was constructed to be placed inside
this vacuum jacket. It has a volume of 1.5 cm3 and contains .25 grams of Nd2 O3 .
It is screwed directly onto the cold finger, making good thermal contact. A onesixteenth inch diameter stainless steel capillary runs from this cell, through the
wall of the vacuum jacket, and to an external valve that can be connected to a
hydrogen tank.
As in the cryostat, the use of thin stainless steel tubing is vital. With no
cell in place, the closed-cycle refrigerator can achieve temperatures as low as 10
K. In the first version of this system, one-eighth inch diameter tubing was used
instead of the capillary. When this cell was placed in the system, the refrigerator
could get no lower than 50 K, much higher than necessary for conversion. With
the switch to the capillary, the refrigerator was again able to reach baseline
3. Experimental Methods
39
Fig. 3.6: The Raman gas T-cell. The red square indicates a valve. The cell is constructed of glass and is four inches long.
values.
Unfortunately, this system remains untested. It was completed after we
exhausted our most recent supply of liquid helium, without which we cannot
examine converted hydrogen in the infrared spectrometer. Furthermore, Raman
spectroscopy, the other method of examining conversion, has failed to yield
useful results.
The hope, though, is that this system will be usable with both the infrared
and Raman spectrometers. In the former case, we will be able to convert hydrogen while the system is cold. In the latter case, we will be able to do
measurements of conversion without any liquid helium at all. And since any
material can be placed in the conversion cell, this will allow the testing of any
material at any time.
3.3 Raman Spectroscopy
While DRIFTS is excellent for examining hydrogen that has been adsorbed by
a lattice, there are some drawbacks which have been discussed. The Raman
spectrometer passes a beam of 9394 cm−1 from a Nd:YAG laser through a
sample. Some of the scattered photons are collected by a mirror into either
an Indium-Gallium-Arsenide (InGaAs) or Germanium (Ge) detector. The former can operate at room temperature. The latter operates at 77 K, but is
approximately twice as sensitive.
The intensity of signal is, of course, proportional to the number of photons
scattered off the target hydrogen and, therefore, to the number of hydrogen
molecules in the beam path. Thus we want high concentration (that is to
say high pressure) of hydrogen and a long path length through the hydrogen.
3. Experimental Methods
40
However, we also want to minimize the amount of hydrogen used in order to
save converted hydrogen for either infrared experiments or further Raman experiments and to avoid homogeneous back conversion. Therefore in practice we
keep the pressure as low as reasonably possible (about 1 atm), while minimizing
the gas cell’s volume and maximizing its path length.
The first attempt at a gas cell was just a stoppered test tube. We then tried
depositing a copper mirror on the test tube. We also tried an Erlenmeyer flask.
The current gas cell, which has yet to be fully implemented, is a 4 inch long, onequarter inch diameter glass tube with closed ends, as in Figure 3.6. An open
branch in the middle of the tube can be connected to either the closed-cycle
converter or the gas loading system.
Raman experiments can be run in parallel with infrared. Because the relationship between concentration and signal strength is unambiguous for the
Raman effect, Raman spectroscopy can be used to measure the ortho-para ratio
inside the infrared system. Raman can also be used with the closed-cycle conversion cell to investigate the conversion mechanism in any number of materials.
3.4 MOF-74
There are four different batches of MOF-74 that we have experimented on. Was
obtained from NIST. The other three were synthesized at Oberlin College by
Jesse Rowsell. X-Ray diffraction was performed on the batches and showed
them to be extremely similar, though not quite identical.
The work described herein was done on one of the batches synthesized at
Oberlin. At the end of the synthesis process, the MOF-74 is suspended in
solvent, which saturates MOF-74’s binding sites. Before the material can be
used for adsorption experiments, the MOF-74 must be degassed to remove all
the solvent. This is accomplished by baking the material at about 540 K for 6
hours under a constant flow of inert nitrogen gas.
One batch was air-exposed in the baking process and ruined. Another was
baked at too high a temperature and partially burned. The sample worked on
here was taken from a portion that was most likely to be fully degassed and
undamaged.
After the degassing process is complete, the material is transferred to a glove
box for storage. The glove box is kept at an overpressure of argon and contains
less than .1 ppm of O2 and H2 O.
The cryostat lid, sample platform, and gas line from the sample chamber up
3. Experimental Methods
41
to valve G can be removed from the cryostat and placed in the glove box. The
MOF-74 is loaded in the sample and sealed under the sapphire dome. The dome
and valve collectively keep the sample under an overpressure of argon once it
is removed from the glove box. This apparatus is then replaced in the cryostat
and reattached to the gas loading system. The gas system is then pumped and
flushed, and the MOF-74 can then be safely exposed to the gas system.
3.5 Infrared Cold Procedure
Once the sample chamber has been safely reintegrated with the gas loading
system, the argon is pumped out. The spectrometer and cryostat are also
evacuated. Helium exchange gas is then loaded into the sample. This is required
to insure that the sample is in thermal equilibrium with the sample chamber.
If the sample chamber is evacuated, then heat transfer up through the post
that connects the sample platform to the sample holder is slow. Thus helium is
loaded in the sample chamber in order to transfer heat between the sample and
sample platform.
Helium is transferred into the cryostat via a port at the top of the cold
finger in Fig. 3.2. Most data are taken at 30 K. To achieve equilibrium at this
temperature, both the liquid helium flow rate and heater power can be adjusted.
The heater is adjusted automatically by a PID controller, while the helium
flow rate is adjusted manually by a throttle valve. In all cases temperature is
controlled from the thermometer at the base of the cold finger, which is generally
about 3 K colder than the thermometer at the end of the sample platform.
Once thermal equilibrium is reached, hydrogen is transferred into the gas
loading system from either the main tank or the conversion system. This gas
can then be slowly leaked into the sample chamber. The amount of gas loaded
at once is referred to as a jolt. A typical jolt contains about .06 mmol of
hydrogen, though we occasionally use ones as much as ten times larger. This
gas is adsorbed by the sample over the course of about a minute. Smaller jolts
are completely adsorbed by the MOF-74. When larger jolts are used, some
hydrogen stays in the gas phase.
A single infrared spectrum is an average of many scans. Increasing the number of scans taken reduces noise in the spectrum but increases the time required
to take it. Most data is a composite of between 50 and 100 scans. We can also
vary resolution between 4 cm−1 and .5 cm−1 . A higher resolution provides
sharper peaks and is often necessary to adequately distinguish two adjacent
3. Experimental Methods
42
peaks. However, higher resolution requires the Michelson interferometer’s adjustable mirror to move through a greater distance, which takes more time. It
also introduces more noise to the spectrum. Most data is taken at 1 cm−1 ,
which is necessary to resolve some features.
We examine variations in our spectra as a function of time, temperature, and
concentration. Watching things change with time lets us measure conversion. If
we take very short spectra as we load hydrogen, we can also see the hydrogen as
it is being adsorbed. Temperature changes also show conversion, as they induce
equilibrium changes. Concentration changes are how we initially identify peaks.
Watching a peak grow as hydrogen is loaded is what distinguishes it from any
host peaks that might be present.
4. RESULTS
4.1 Characteristics of the MOF-74 Infrared Spectrum
Before we begin discussing the data at large, it will be important to identify
the major characteristics of the MOF-74 infrared spectrum. None of the qualities of the features will be justified here. Some will be discussed below, and
others are beyond the scope of this thesis. See Jesse Hopkins’ thesis for more
information[27].
As was discussed in Section 1.6, MOF-74 has four sites where hydrogen can
be loaded. In principle, these can each be observed as separate absorption bands.
In practice, we see only two strong absorption bands, referred to as the primary
and the secondary. There are three major groupings of peaks. Figure 4.1 4.1(a)
shows the Q region, which contains peaks resulting from the pure vibrational
ν = 0 → 1 transition. We see two Q(1) and one Q(0) peak in the primary band,
and one of each in the secondary. There are indications of small peaks that may
be associated with the third and fourth binding sites.
Approximately 100 cm−1 higher than these pure vibrational transitions is
the translational sideband, indicated in Fig. 2.1 (c). It arises from H2 making a
translational center of mass transition concurrently with a vibrational transition.
The S(0) region is the left half of Fig. 4.1 (b). It contains the peaks from
J = 0 → 2 region occurring with the vibrational transition. There are peaks
associated with both the primary and secondary vibrational bands.
The S(1) region is the right half of Fig. 4.1 (b). It contains the peaks from
J = 1 → 3 region occurring with the vibrational transition. Again, there are
peaks associated with the primary and secondary bands. Note that this region
is very weak in MOF-74.
4. Results
44
0.8
Q(0)
0.7
Absorbance
0.6
Normal
Converted
Q(0)
Q(1)
0.5
0.4
Q(1)
0.3
0.2
translational
0.1
0.0
4080
4100
4120
4140
4160
4180
4200
4220
4240
-1
Frequency (cm )
(a) The Q region
1.0
S(0)
S(0)
Absorbance
0.8
0.6
0.4
S(1)
S(1)
0.2
0.0
4300
4400
4500
4600
-1
Frequency (cm )
(b) The S region
Fig. 4.1: The infrared spectrum of MOF-74.
4700
4800
4. Results
45
0.50
Absorbance
0.40
0.30
1 min
10 min
20 min
30 min
40 min
60 min
Q(1)
Q(0)
Q(1)
0.20
0.10
0.00
4070 4075 4080 4085 4090 4095 4100 4105 4110 4115 4120
-1
Frequency (cm )
(a) The Q region
0.70
S(0)
Absorbance
0.60
0.50
0.40
0.30
0.20
0.10
0.00
4360
4370
4380
4390
4400
4410
-1
Frequency (cm )
(b) The S(0) region
0.70
Absorbance
0.60
0.50
0.40
S(1)
0.30
S(1)
0.20
0.10
0.00
4560
4570
4580
4590
4600
4610
4620
4630
-1
Frequency (cm )
(c) The S(1) region
Fig. 4.2: Conversion in MOF-74 over time. The Q(1) and S(1) peaks decrease with
time, while the Q(0) and S(0) increase. The legend gives time after loading
H2 into the sample chamber.
4. Results
46
4.2 Demonstration of Conversion
The functionality of the dipstick converter is verified by loading gas from the
storage cylinder into our sample. We can see the results of this in Fig. 4.1. The
character of the spectrum is dramatically changed from when normal hydrogen
is used, with half of the peaks disappearing and those remaining growing substantially. This indicates that the hydrogen underwent ortho-para conversion
in the dipstick system.
We verify the ability of MOF-74 to catalyze ortho-para conversion by loading
the cold sample with room temperature hydrogen and observing the behavior
of the hydrogen over time. The intensity of the Q(1) and S(1) peaks (associated
with odd rotational states) decreases, while that of the Q(0) and S(0) (associated
with even rotational states) increases, as seen in Fig. 4.2. The result of this
is a spectrum markedly similar to that obtained with the dipstick converter.
We interpret this to mean that MOF-74 is capable of catalyzing ortho-para
conversion.
4.3 Identification of Peaks through Conversion
Figure 4.1 also shows one of the major practical benefits of using converted
hydrogen. Examining how peaks respond to ortho-para conversion helps us
identify them. The locations of peaks in the gas phase are well known, but
are perturbed by the lattice. If the energy level splittings change, then the observed peak positions change. The host is also capable of causing more dramatic
changes, breaking degeneracies and change the selection rules of H2 transitions.
This causes peaks to appear and disappear relative to the gas phase, complicating the identification process.
4.4 Conversion with Concentration
4.4.1
Fast Loading
If the ortho and para species had identical infrared behavior, we would expect
the intensity ratio between the Q(1) and Q(0) peaks to be 3:1 for normal,
unconverted hydrogen. However, as was discussed in Section 2.5, there are
two mechanisms that activate the Q(1) transition, and only one that activates
Q(0). We thus expect to observe an intensity ratio higher than 3:1. In Fig. 4.2,
however, the very first spectrum taken after hydrogen is loaded seems to exhibits
4. Results
0.7
Q(0)
0.6
Absorbance
47
37 s
68 s
115 s
167 s
383 s
577 s
Q(1)
0.5
0.4
0.3
0.2
0.1
0.0
4080
4100
4120
4140
4160
-1
Frequency (cm )
(a) The Q region
0.24
S(0)
S(1)
Absorbance
0.20
0.16
0.12
0.08
0.04
0.00
4300
4400
4500
4600
4700
-1
Frequency (cm )
(b) The S region
Fig. 4.3: The fast loading of normal hydrogen into MOF-74 with no population of the
secondary band.
4. Results
48
0.70
Q(0)
0.60
Q(0)
Q(1)
Absorbance
0.50
Q(1)
0.40
0.30
55 s
95 s
135 s
178 s
280 s
440 s
45 min
0.20
0.10
0.00
4080
4100
4120
4140
4160
-1
Frequency (cm )
(a) The Q region
1.0
S(0)
Absorbance x 10
0.8
S(0)
0.6
0.4
S(1)
S(1)
0.2
0.0
4300
4400
4500
4600
4700
-1
Frequency (cm )
(b) The S region
Fig. 4.4: The fast loading of normal hydrogen into MOF-74 with population of the
secondary band.
4. Results
49
an intensity ratio much less than 3:1. This suggests that substantial orthopara conversion occurs before even a single spectrum can be taken. It is thus
profitable to try to get data as soon as possible after hydrogen is let into the
sample chamber, faster than two minutes. This requires reducing both the
resolution of the spectra and the number of scans averaged over, which reduces
the quality of the data. We found that by taking 10 scans at 1 cm−1 resolution
we were able to get a complete spectrum approximately every 15 seconds. We
did this twice. Figure 4.3 shows the results when enough hydrogen is loaded to
nearly saturate the primary site, while Fig. 4.4 shows results for the primary
and secondary sites loaded.
It appears, simply by inspection, that conversion occurs more quickly with
the secondary site filled than without it. As has been discussed in Section 2.5,
both the Q(0) and Q(1) transitions are activated by the dipole term, while the
Q(1) transition is also activated by the quadrupole term. Therefore, for a given
concentration of molecules, the Q(1) peak will be more intense than the Q(0).
If we want to be able to use infrared spectroscopy to measure the ortho-para
ratio in our sample, then we need to be able to separate these effects.
This is accomplished by looking at the S peaks. Both the S(0) and S(1)
are only activated by the quadrupole term. Thus the relationship between
concentration and intensity should be the same for both of them. To get at this
relationship, we look at in situ conversion. We know that if no loading is taking
place, then any change in peak intensity is the result of conversion. At 30 K, the
only populated rotational states are the J = 0 and J = 1. Thus as conversion
occurs, we see the S(0) intensity increase and the S(1) decrease, which is the
result of the transfer of some number of molecules from the J = 1 to the J = 0
state. By choosing some fixed length of time to observe this conversion over,
we create a calibration between intensity (which is measured as the area under
a peak) and concentration. We call these calibration values Icalb (S(0)) and
Icalb (S(1)) for the S(0) and S(1) peaks respectively. If I0 and I1 are the S(0)
and S(1) intensities at some particular time, then we calculate the ratios
I1
I0
= M0 and
= M1 .
Icalb (S(0))
Icalb (S(1))
(4.1)
M1
= Ro−p
M0
(4.2)
Finally,
is the ortho-para ratio for the spectrum from which we found I0 and I1 . By
4. Results
50
3.5
Ortho-Para Ratio
3.0
Primary Alone
Primary with Secondary
Secondary
2.5
2.0
1.5
1.0
0.5
0.0
0
400
800
1200
1600
2000
2400
2800
Time (s)
Fig. 4.5: Exponential fits to conversion for H2 , D2 , and HD.
applying this method to the data, we obtain the results of Table 4.1. Note that
the equilibrium is roughly the same in all cases, but that it is reached much
more quickly with the second site filled.
We use the least-squares method to fit the exponential model of Eq. 2.22.
The concentration of the ortho state as a function of time is therefore
no (t) = no (∞) + Ae−kt
(4.3)
where no (∞) is the ortho concentration as t → ∞ and A and k are constants.
We performed three individual fits, for the primary band when no secondary
sites are loaded, for the primary band in the presence of the secondary band,
and for the secondary band. The values of the fits are given in Table 4.2 and
plotted in Fig.4.4.1 along with the data of Table 4.1.
Note that no (∞) is the equilibrium ortho-para ratio under the conditions
measured and τ = k −1 is the lifetime of a molecule in the J = 1 state. We can
extract the fraction of they hydrogen in the para state, fp = 1/(1 + no ).
4. Results
51
(a) Primary band only.
Time (s)
37
51
68
91
115
140
167
233
383
577
Ortho-Para Ratio
1.04
.76
.80
.83
.66
.61
.64
.52
.48
.28
% Para
49.0
57.0
55.5
54.7
60.4
62.1
61.2
65.9
67.7
78.3
(b) Primary band with secondaries loaded.
Time (s)
55
95
135
178
280
440
1200
2700
Ortho-Para Ratio
1.33
.83
.40
.44
.33
.24
.27
.27
% Para
42.9
54.8
71.4
69.4
75.0
80.5
78.6
78.6
(c) Secondary band.
Time (s)
55
95
135
178
280
440
1200
2700
Ortho-Para Ratio
.95
.63
.45
.39
.26
.22
.20
.21
% Para
51.2
61.2
68.9
72.2
79.2
81.7
83.2
82.6
Tab. 4.1: Ortho-para ratio and para concentration with time.
Primary Alone
Primary with Secondary
Secondary
no (∞)
.31 ± .1
.26 ± .07
.21 ± .03
k
.0055 ± .002
.018 ± .004
.014 ± .002
A
.76 ± .1
2.0 ± .3
1.2 ± .1
Tab. 4.2: The fit values of the conversion data from Table 4.1.
4. Results
(b) Primary
ondary.
(a) Primary Alone.
min
mid
max
% Para
71
77
83
τ
130
180
320
52
with
(c) Secondary.
% Para
76
80
84
min
mid
max
sec-
τ
45
55
70
min
mid
max
% Para
81
83
85
τ
66
74
83
Tab. 4.3: The equilibrium para concentrations and J = 1 lifetimes for various loadings
and sites. These numbers are derived from Table 4.2. The label mid indicates
the value derived from the center of the uncertainty ranges. Min and max
are the extrema of the uncertainty ranges.
0.60
0.50
1 min
10 min
20 min
40 min
60 min
Q(0)
Absorbance
Q(1)
0.40
0.30
Q(0)
0.20
Q(1)
0.10
0.00
4060
4070
4080
4090
4100
4110
4120
4130
4140
4150
-1
Frequency (cm )
Fig. 4.6: Parahydrogen back converting at 30 K. Times after loading H2 into the sample chamber is given. Note the different behavior of the primary and secondary bands.
4. Results
53
4.5 Low Temperature Back Conversion
At 30 K, we have shown that H2 in MOF-74 equilibrates to about 80% parahydrogen. The dipstick converter produces essentially 100% parahydrogen at 15
K. We thus expect to observe a sample of parahydrogen loaded into MOF-74
from the dipstick back convert to a para concentration of about 80%. Figure 4.5
shows this clearly. This data was taken at 30 K, with enough hydrogen to load
the primary and secondary sites. A substantial amount of the H2 transitions
from the J = 0 to J = 1 state, contrary to what we predict for the gas phase.
4.6 D2 and HD
The D2 and HD isotopes exhibit different conversion behavior from H2 , as seen
in Fig 2.4. At 30 K, we expect HD to contain 4% J = 1 species and D2 to
contain 8% J = 1 species. Thus HD should look roughly similar to H2 , while
D2 should be noticeably different.
The observation of these isotopes is hindered by their reduced intensity. The
intensity of an absorption peak is inversely proportional to the reduced mass
of the molecule. Thus the HD peaks are weaker by a factor of 4/3 and the D2
peaks are weaker by a factor of 2. Additionally, host peaks are more numerous
below around 3500 cm−1 , where Table 3.1 shows the D2 and HD transitions to
be located. This makes the guest from the host more difficult. The spectra for
these two isotopes are visible in Figs. 4.6(a) and 4.6(b).
4.7 The Infrared Mechanisms
As has been discussed, there are two different mechanisms by which we observe
infrared transitions. The Q(0) peak is produced solely by the overlap term,
while the Q(1) peak is produced by both the overlap and quadrupole terms.
This causes the relationship between intensity and concentration for the Q(0)
and Q(1) peaks to be different. We can use the measured ortho-para ratio to
get at the relative strength of the overlap and quadrupole mechanisms.
If the Q(0) and Q(1) peaks were produced by the same transition, then they
would have the same concentration dependence. A ratio of the area under the
two peaks would thus give the ortho-para ratio in the sample. We thus begin
by using the GRAMS computer program to deconvolve the overlapping peaks
of the Q region, allowing us to get the areas. We then take the appropriate
4. Results
54
0.24
Q(0)
Absorbance
0.20
0.16
Q(0)
0.12
0.08
0.04
0.00
2930
2940
2950
2960
2970
2980
2990
-1
Frequency (cm )
(a) D2
0.35
Q(0)
0.30
Q(0)
Absorbance
0.25
0.20
Q(1)
0.15
Q(1)
0.10
0.05
0.00
3550
3560
3570
3580
3590
3600
3610
3620
3630
-1
Frequency (cm )
(b) HD
Fig. 4.7: The Q regions of D2 and HD. The S regions of both isotopes are too small
to be worth examining here.
4. Results
(a) Gaussian fits.
Time
95 s
280 s
45 min
IQ(1) /IQ(0)
.93
.63
.54
55
(b) Lorentzian fits.
β/α
.12
.91
1.0
Time
95 s
280 s
45 min
IQ(1) /IQ(0)
.74
.38
.32
β/α
-.11
.15
.19
Tab. 4.4: Fits to some of the data of Fig. 4.4. Note the marked difference between the
Gaussian and Lorentzian fits.
ratio and compare it to that calculated from the S peaks, which is the actual
ortho-para ratio. If IQ(0) and IQ(1) are the intensities of the respective peaks,
then Beer’s law gives us
IQ(1)
αno + βno
β no
=
= (1 + )
IQ(0)
αnp
α np
(4.4)
where α and β are the constants of proportionality between concentration and
intensity for the overlap and quadrupole terms, respectively. Thus the strength
of the quadrupole term relative to the overlap term is
IQ(1) np
β
=
− 1.
α
IQ(0) no
(4.5)
The results of this calculation for data from the series of Fig. 4.4 are given in
Table 4.4. These results are contradictory, and the full implications of this are
discussed in Section 5.4. However, based on experimental and theoretical work
done on H2 in C6 0, we believe that the Lorentzian fits are more accurate[9, 26].
4.8 Raman Spectra
The Raman spectrometer unfortunately has yet to produce concentration data.
We will therefore here be concerned with detailing the experimental progress
that has been made toward a working Raman gas phase cell.
The first iteration of the gas cell was simply a test tube. It had a diameter
of 12 mm and length of 150 mm, for a total volume of approximately 17 cm3 .
A rubber stopper was used to seal the tube, and a piece of one-eighth inch steel
tubing was put through the center of the stopper to allow the introduction and
removal of hydrogen to the tube. A valve on the end of the tubing allowed the
tube to be closed of to the environment and could be attached to either the gas
loading system or the closed-cycle conversion system.
4. Results
56
0.50
S(1)
0.45
0.40
Absorbance
0.35
0.30
S(0)
0.25
0.20
0.15
0.10
0.05
0.00
300
350
400
450
500
550
600
650
700
-1
Frequency (cm )
Fig. 4.8: Raman spectrum of 1 bar of H2 in an unmirrored Pyrex test tube. A Ge
detector was used. Arrows indicate the expected peak locations.
2.4
Absorbance
2.0
1.6
S(0)
1.2
S(1)
0.8
0.4
0.0
200
400
600
800
1000
1200
1400
-1
Frequency (cm )
Fig. 4.9: Raman spectrum of 1 bar of H2 in a Pyrex test tube that has been mirrored
with copper. A Ge detector was used. Arrows indicate the expected peak
locations.
4. Results
57
0.70
S(1)
0.60
Absorbance
0.50
0.40
0.30
S(0)
0.20
0.10
0.00
300
350
400
450
500
550
600
650
700
-1
Frequency (cm )
Fig. 4.10: Raman spectrum of 1 bar of H2 in a Pyrex Erlenmeyer flask. A Ge detector
was used. Arrows indicate the expected peak locations.
1.0
0.9
S(1)
0.8
Absorbance
0.7
S(0)
0.6
0.5
0.4
0.3
0.2
0.1
0.0
400
800
1200
1600
2000
2400
2800
-1
Frequency (cm )
Fig. 4.11: Raman spectrum of 1 bar of H2 in the glass T-cell. An InGaAs detector was
used. Arrows indicate the expected peak locations.
4. Results
58
Raman spectroscopy should reveal the pure rotational (∆ν = 0) transitions
listed in Table 3.1. Figure 4.8 shows a spectrum from that region taken with the
test tube at approximately 1 bar of H2 . This used the more sensitive germanium
detector. As can be seen, there is hardly any hydrogen signal, certainly not
enough to be usable.
In the next iteration, thin film deposition was used to put a copper mirror on
the test tube surface. This should, in principle, enhance the signal in two ways.
First, the laser gets a second pass through the hydrogen, doubling the number
of scattering events that occur. Second, any photons that scatter away from the
collecting mirror (forward scattering on the first laser pass, backscattering on
the second) are not brought to the detector. The presence of a mirror redirects
these photons to the collecting optics.
Figure 4.9 shows that the background noise with this cell is on the order
of the signal from the plain test tube. The reason for this is suggested by
the steep increase in signal at low frequencies. While the mirror does perform
the functions mentioned above, it also reflects the Raman laser back into the
collecting mirror. The Raman spectrometer contains a filter in front of the
detector that removes the frequency of the laser. This is in place to prevent
the detection of photons that have undergone Rayleigh scattering (and thus
still have the frequency of the laser). However the unscattered laser beam is
vastly more intense than the Rayleigh scattered photons. The filter is not 100%
efficient, and though the amount of radiation that gets through is small relative
to the amount incident on the filter, it is much greater than what is Raman
scattered off the hydrogen. Thus there is a substantial intensity spike at the
frequency of the laser. Because the spectrometer has limited resolution, this
delta function at the laser frequency is transformed into a broad peak. We are
interested in the region of frequency space very near to zero cm−1 , and so the
H2 peaks come in on the shoulder of the broad laser peak and are completely
washed out. The mirror is hence not an appropriate way to increase intensity.
The third iteration used an Erlenmeyer flask. When the laser is passed
through the bottom of the flask, we get a path length in the hydrogen of just
under two inches (5 cm), which is a factor of two improvement over the mirrored
test tube, and a factor of four improvement over the plain test tube. As is seen
in Fig. 4.10, the flask allows us to observe usable ortho and para peaks with 1
bar of H2 . However, for reasons still not understood, we were not able to get
consistent results. Loading the same amount of hydrogen did not always produce
the same peak intensities. Additionally, the volume of the Erlenmeyer flask is
4. Results
59
greater than 50 cm3 and requires a large amount of hydrogen to pressurize to 1
bar. We do not want to consume this much hydrogen in one Raman experiment,
so this cell is not acceptable.
The current iteration of the gas cell is the T-cell pictured in Fig. 3.6. It is
four inches long and one quarter inch in diameter, for a volume of approximately
3 cm3 . This is obviously a vast improvement over the Erlenmeyer flask, and is
even a factor of five improvement over the test tube. Meanwhile, we are able to
get a path length double that of the flask. Data taken on the T-cell loaded to 1
bar of H2 is shown in Fig. 4.11. There is a large fluorescence peak that washes
out our hydrogen peaks. We have yet to understand the source of this peak or
how to mitigate it.
5. DISCUSSION AND ANALYSIS
5.1 Ortho-Para Conversion
5.1.1
The Rate of Conversion
By Table 4.3, we see that the rate of conversion increases by a factor of 3 when
the secondary sites are loaded. There are a number of possible explanations for
this phenomenon, which will be discussed.
Initially, nearly all the hydrogen loaded into the sample chamber is adsorbed
by the sample. However, as the total amount of hydrogen taken up by the
sample increases, the amount remaining in the gas phase also increases, as seen
in Table 5.1. Thus, by Eq. 2.21, the gaseous hydrogen in the sample chamber can
convert itself. Note that the equilibrium between the gas and adsorbed phases is
dynamic, there is a constant interchange of particles between the two. From the
data in Fig. 4.4, we believe the lifetime of H2 in MOF-74 to be on the order of a
minute. Any conversion that occurs in the gas phase could conceivably manifest
in the adsorbed phase (and thus in our infrared spectra) in the same time scale
that we see. However, Farkas observed timescales for liquid and solid hydrogen
H2 Adsorbed (mmol)
.16
.29
.42
.54
.60
.66
.71
H2 Gas Pressure (Torr)
.61
.76
.91
1.5
3.3
9.0
21.
Tab. 5.1: The pressure of H2 gas remaining in the sample chamber for given amounts
of hydrogen adsorbed by MOF-74. This data is from a single experimental
run, and is not intended to imply a specific quantitative result. Rather, it is
meant to suggest the general qualitative pattern observed when hydrogen is
loaded in MOF-74.
5. Discussion and Analysis
Distance (Å)
2.847
2.896
3.061
4.180
4.391
4.411
4.705
5.342
61
Site
3
2
3
4
2
3
2
1
Tab. 5.2: The type of binding sites to nearest to one of MOF-74’s primary sites. The
numbers of column two refer to the labels of Fig. 1.1. Clearly, the proximity
of H2 molecules increases dramatically when the secondary sites are loaded.
This gives credence to the idea that the increased conversion rate observed
when the secondary band appears is the result of H2 -H2 interactions.
on the order of hours, as seen in Table 5.4[15]. Given the longer interaction
times of the liquid and solid phases, conversion should proceed faster in them
than in the gas phase. Thus self-catalyzed conversion on the order of minute is
not a reasonable explanation for what we see.
It is also possible that the gas phase hydrogen could be catalyzed by something other than MOF-74, by some element of the sample chamber. However,
the only materials in the immediate vicinity of the sample are copper, aluminum, and sapphire, none of which have an appreciable magnetic moment.
They should therefore be ineffective as catalysts. The only material in our sample besides MOF-74 that we believe to have appreciable conversion capability
is stainless steel, which can posses magnetic impurities. The only stainless steel
accessible to hydrogen when the sample chamber is closed to the gas system is a
one-sixteenth inch diameter capillary, with total volume approximately .5 cm3 .
The volume of the sample chamber is three times this, and so hydrogen will
disproportionately occupy the copper and aluminum sample chamber instead
of the stainless steel capillary. Additionally, because stainless steel has a very
low thermal conductivity, the capillary is likely to be warmer than the sample
chamber. This makes hydrogen even less likely to occupy the capillary (since
its average speed will be higher), and also less likely to convert during any individual collision with the capillary wall. The capillary seems an unlikely source
of conversion.
The increased conversion rate when the secondary band is filled must be
the result of processes inside MOF-74. There are two likely options. First, the
5. Discussion and Analysis
S(0)
S(1)
Observed (cm−1 )
4359
4602
62
Predicted (cm−1 )
4290
4434
Tab. 5.3: The predictions of primary S peaks with secondary sites loaded. Observation
and prediction are dramatically different.
secondary site may produce a greater inhomogeneous magnetic field than the
primary site. This would enable faster conversion in the secondary site than
in the primary. As seen in Fig. 4.4, the separation between the Q peaks of
the primary and secondary sites is approximately 50 cm−1 . At 30 K, for low
hydrogen loadings, the probability of a molecule being in the secondary site
rather than the primary is
e−∆E/kB T ≈ .09.
(5.1)
Thus until we have saturated the primary site, any effect from the secondary
will be minimal, which would lead to a sudden “turn on” of the conversion rate
once the secondary site is populated.
Another option is that the secondary site itself does not convert any faster
than the primary, but facilitates H2 -H2 interactions. Distances from the primary
site to some of its nearest neighbors are given in Table 5.2. These were obtained
by neutron diffraction experiments at NIST[34]. The distance between molecules
adsorbed on primary sites is over twice that for the intermolecular distance in
solid hydrogen. Thus with only the primary site loaded, H2 -H2 interactions are
much reduced.
When the secondary sites are loaded, however, the intermolecular distance is
less than in solid hydrogen. The field from a magnetic dipole goes as r−3 , and so
its gradient goes as r−4 [23]. Decreased intermolecular separation substantially
increases the magnetic field gradient that the hydrogen molecules experience
from each other, and hence the rate of conversion. We thus expect that the rate
of homogeneous conversion in adsorbed hydrogen increases with the loading of
the secondary sites.
5.1.2
The Equilibrium Ratio
The data of Table 4.3 show that the hydrogen in MOF-74 fails to reach the
expected 97% para species equilibrium. The approximately 80% that it actually achieves would be consistent with a temperature of about 47 K. However,
a helium isotherm performed on our system confirms the accuracy of our ther-
5. Discussion and Analysis
63
Fig. 5.1: Neutron diffraction data from Liu et al.[34]. There is data for two different
hydrogen loadings, one with the secondaries filled and one without. We here
consider only the data with .8 H2 /Zn. The J = 0 → 1 peaks are the first two
on the left.
mometer and its 30 K reading to within a few Kelvin. Thus the observed ratio
must be the result of changes to the hydrogen’s behavior induced by the host.
The relative concentrations of the ortho and para species is determined by
the separation between the J = 0 and J = 1 rotational states. For H2 in the
gas phase, this separation is
2B = 171 K = 14.7 meV
(5.2)
where B is the rotational constant from Table 2.3. For H2 to equilibrate to 80%
para at 30 K, we need this separation to be 108 K or 9.5 meV.
There are two ways to achieve this change in separation. First, the adsorbed
H2 can retain the physical characteristics of the gas phase, populating the same
energy states and exhibiting the same transitions. In this case, the host changes
nothing but the energy eigenvalues associated with each state. The second option is for the host to induce a change in hydrogen’s physical properties (most
probably the internuclear separation), thereby changing the energies of its transitions.
This separation can also be studied with neutron diffraction, for which the
∆J = ±1 transition is allowed. Figure 5.1 shows neutron data taken by Liu
5. Discussion and Analysis
64
et al. at NIST[34]. The labeled peaks are attributed to the ∆J = ±1 peaks.
There are two such peaks because the degeneracy of the J = 1 level has been
broken. There are three individual states that make up the J = 1 state (for
mJ = −1, 0, +1). As we see only two peaks, one of the two must still have a
degeneracy of two. To find the separation between the J = 0 and J = 1 states,
we need what the energy of the J = 1 state would be if it were not split. We
know
X
∆Ei = 0
(5.3)
i
where ∆Ei is the shift in energy from the unsplit energy level to the ith split
level. For the two transitions observed in Fig. 5.1, we do not know which
has degeneracy two and which has degeneracy one. Thus we consider both
possibilities. For E1 = 8.3 mev and E2 = 11.0 mev, if E1 has degeneracy two,
then E0→1 = 9.2 meV. If E2 has degeneracy two, then E0→1 = 10.1 meV. Both
values are in good agreement with the observed conversion behavior.
It only remains to determine whether this reduced separation comes from
a perturbation of the gas phase energy eigenvalues or a change in the physical
properties of H2 . If the physical properties have changed, then we expect that
the change in J = 0 → 1 separation comes from a change in the rotational
constant B. Recalling Eq. 2.11, B can only change if the moment of inertia
I changes, which in turn only changes if the internuclear separation changes.
Note that E0→1 = 2B, so we have B = 4.6 meV or B = 5.1 meV, which is a
reduction of about 35% from the gas phase. Since B ∝ R−2 , where R is the
internuclear separation, this decrease in B would result in a 24% increase in R.
On its face, this seems much larger than is probable.
To test this, we use the decreased value of B to try to predict the locations
of the ro-vibrational S peaks. We first need to estimate the value of B in the
first excited vibrational state, which is what matters for the ro-vibrational transitions. We get this from the separation of the Q(0) and Q(1) peaks. Table 3.1
shows that the gas phase separation of these peaks is 6 cm−1 . This is because
R is larger in the ν = 1 state than in ν = 0, meaning that B1 < B0 , where we
now use B = 0 to refer to the rotational constant in the ν = 0 state and B1
is in the ν = 1 state. Thus, since the rotational energy EJ = BJ(J + 1), the
transition ν = 0 → 1 reduces the rotational energy for all states with J 6= 0,
even though no change in J occurs. The energy difference between the Q(0)
and Q(1) transitions is therefore 2(B0 − B1 ). As seen in Fig. 4.4, this energy
5. Discussion and Analysis
Material
Liquid H2
Solid H2
MOF-74 Primary
MOF-74 Secondary
Silver(111)
Copper(100)
APACHI
65
Timescale
2.3 h[15]
1.4 h[15]
3 min
1 min
1 min[4, 29]
1.7 h[2, 29]
7.5 min[48, 47]
Tab. 5.4: A summary of conversion timescales from this and other work. Note that for
silver and copper the numbers indicate the lattice orientation. The vastly
different values for copper and silver are attributed to solid state effects due
the different lattice orientations, and not from differences between the two
elements’ atoms[29]. APACHI is a nickel silica compound[48, 47].
difference in MOF-74 is about 8 cm−1 . Therefore
B1 = B0 − 4 cm−1 = 34 cm−1 = 4.2 meV.
(5.4)
To predict the S peak locations, we start with the observed Q peak locations,
and add on 6B1 to get the S(0) peak and 10B1 to get the S(1) peak. The results
of this are given in Table 5.3. Clearly, the observed S peaks are far closer to the
gas phase values than to the predicted values. We interpret this to mean that
the rotational constant has not actually changed by 35%. Rather, B is at or
near its gas phase value, but the J = 0 → 1 separation has been decreased by
the host. The exact mechanism for this remains unknown, though we suspect it
to be the result of anisotropic interactions between guest and host, since none
of the binding sites are at points of spherical symmetry.
5.1.3
Applications
It is worthwhile to compare the conversion timescale MOF-74 to other catalysts.
As can be seen in Table 5.4, MOF-74 is able to convert hydrogen substantially
faster than other materials. This indicates that MOF-74 might be effectively
adapted for use as a catalyst. Before any such system were implemented however, some challenges would need to be addressed. The extreme air-sensitivity
of MOF-74 makes it difficult to use a single sample for extended periods of
time. We have found that MOF-74 can only be stored safely at an overpressure
of inert gas. This would make a conversion cell utilizing MOF-74 substantially
more difficult to use than our current Nd2 O3 model, which can be air-exposed
5. Discussion and Analysis
% Para
90
99
99.9
99.99
66
Time (s)
60
190
330
470
Tab. 5.5: Amount of time required to produce various concentrations of parahydrogen
with MOF-74 as a catalyst. These numbers assume that there is enough
hydrogen present to populate the secondary sites and that the temperature
is low enough to achieve 100% para concentration at infinite time.
without permanent harm, and for which a simple vacuum is sufficient for long
term storage.
Another issue facing the use of MOF-74 is the lower than expected equilibrium para percentage. The hope would be that in the temperature range
around 15 K that we usually operate the dipstick converter MOF-74 would be
able to attain a concentration closer to 100% parahydrogen. Unfortunately this
remains untested.
If MOF-74 were adapted as a catalyst, it would be productive to know what
timescales various concentrations of parahydrogen could be produced in. These
values are presented in Table 5.5.
5.2 Low Temperature Back Conversion
As discussed in Section 5.1.2, it is reasonable that we should see back conversion
at 30 K. However, the data of Fig. 4.5 were taken on a different batch of MOF74 than the other spectra exhibited in this thesis. Simply by comparing the Q
peaks of Fig. 4.5 to those of Fig. 4.4, it seems that this back conversion returns
to a parahydrogen concentration on the order of 50%, which is dramatically
different than the 20% observed in the rest of our data. It is difficult to explain
this conclusively, as we cannot yet in any detail explain the reason for the
observed perturbation to the J = 0 → 1 separation.
However, we believe that the sample that the data of Fig. 4.5 is from was
likely contaminated with air. Clearly the sample was not destroyed, as it was
still able to take up appreciable amounts of hydrogen and produce a spectrum
qualitatively similar to those from other samples. But if this sample of MOF74 was damaged, there may have been substantial impurities present. This
could easily alter the adsorbed hydrogen’s behavior in unpredictable ways. This
therefore remains an open area of study.
5. Discussion and Analysis
67
5.3 D2 and HD
Figure 4.7(b) is qualitatively similar to Fig. 4.4. This is expected for 30 K, as
HD equilibrates to 96% J = 0 species as opposed to the 97% of H2 . The case
here is more ambiguous, since H2 does not behave as if it is at 30 K. However, if
the J = 0 → 1 separation for HD changes in proportion to H2 , then we expect
HD to contain 83% J = 0 species, compared to 80% for H2 . It is thus reasonable
that HD and H2 should look the same in MOF-74.
The case of D2 is more difficult. Figure 4.7(a) shows only peaks associated
with the J = 0 species. At 30 K, we expect D2 to contain about 92% J = 0
species, while if the J = 0 → 1 separation scales as the H2 separation does, then
we expect 80% J = 0. Thus we expect D2 to exhibit peaks associated with the
J = 1 species that are at least as strong as those of H2 . However we see none
at all. This is explained by the smaller separation between the Q(1) and Q(0)
peaks for D2 compared to H2 . For D2 , B0 = 29.9 cm−1 and B1 = 28.8 cm−1 [46].
The resulting separation is 2(B0 − B1 ) = 2.2 cm−1 . But the FWHM for the
primary Q peaks is about 6 cm−1 . We therefore believe that the Q(1) peaks are
present, but get overwhelmed by the much larger and very nearby Q(0) peaks.
5.4 The Infrared Mechanisms
The data of Table 4.4 show a marked disparity between the results from the
Gaussian and Lorentzian fits. If we believe the Gaussian fits, then the quadrupole
mechanism might have strength comparable to the overlap term. If we believe
the Lorentzian fits, then the quadrupole term is insignificant compared to the
overlap mechanism.
For two reasons, we put greater faith in the Lorentzian fits. First, the
Lorentzian fits are self-consistent. The measurements of the Q peak intensities
are fairly rough due to the difficulty of deconvolving the closely overlapping
peaks, and the uncertainty in the ratio is about 15%. Within that margin, the
Lorentzian fits show an essentially nonexistent quadrupole term. The Gaussian
peaks provide no consistent conclusion.
Second, Fig. 5.4 shows the higher quality of the Lorentzian fit over the
Gaussian. The Q(0) peak possesses a substantial tail on the high frequency
side, which is lost by a fit to a Gaussian peak. Thus IQ(0) is underestimated,
which leads to overestimation of β/α. The Lorentzian fit more accurately models this tail, and so we expect it produces a more accurate estimate of β/α.
5. Discussion and Analysis
68
0.60
Absorbance
0.50
Data
Peak 1
Peak2
Peak3
Fit
0.40
0.30
0.20
0.10
0.00
4080
4100
4120
4140
4160
4140
4160
-1
Frequency (cm )
(a) Gaussian fit.
0.60
Absorbance
0.50
0.40
0.30
0.20
0.10
0.00
4080
4100
4120
-1
Frequency (cm )
(b) Lorentzian fit.
Fig. 5.2: The Gaussian and Lorentzian fits to the primary site from Fig. 4.4 at 45
minutes. Only two Q(1) peaks and one Q(0) peak are fit here. It is difficult
to separate the primary Q(0) peak from the area between the primary and
secondary bands, and so we do not try to fit anything higher than the primary
Q(0). Displayed are the data, the three fitted peaks (two Q(1) peaks and
1 Q(0) peak), and the sum of the peaks. It can be clearly seen that the
Gaussian fit underestimates the area of the Q(0) peak, which can explain the
large quadrupole effect estimated by the Gaussian data.
5. Discussion and Analysis
69
Additionally, experimental and theoretical work have suggested that Lorentzian
curves provide better fits and are more physically reasonable[9, 26]. Therefore,
we believe the quadrupole mechanism in MOF-74 is substantially weaker than
the overlap mechanism.
6. CONCLUSIONS AND FUTURE WORK
6.1 Ortho-Para Conversion
6.1.1
Other Materials
We have thus far been able to measure the rate and equilibrium ratio of orthopara conversion in MOF-74. In the future we hope to expand this study to other
materials. Materials studied previously by our lab include MOF-5, HKUST1, and ZIF-8. We hope to expand the methods herein to these materials, to
hopefully correlate the conversion properties in a material with its other physical
and chemical properties. This is an exciting venture, because MOF-74 is the first
material in which we have observed conversion as quickly as demonstrated here,
as well as the first material in which we have observed a change in hydrogen’s
thermal equilibrium.
We also hope to expand our study of the infrared mechanisms to these materials. The relative strength of these mechanisms is highly dependent on the
crystal structure of the host lattice. We have seen preliminary indications of
this in the relative strengths of the S peaks in different materials. As seen in
Fig. 6.1, the strength of the S peaks varies dramatically from one material to the
next. MOF-74 has fairly small S peaks, whereas those of MOF-5 are as large as
the Q peaks and those of HKUST-1 are almost non-existent. Since the S peaks
are produced solely by the hydrogen quadrupole mechanism, we expect that the
two infrared mechanisms should behave substantially differently in each of these
materials, and we hope to be able to extract that information.
As has been mentioned, the measurement of the sample temperature is a
difficult to do accurately. We want to make more accurate measurements of
temperature, to find whether our current measurement system is adequate, and
if not how it can be adapted. This will involve an attempt to get a thermometer
inside the sample dome. We also can use helium to observe the behavior of
our system when no adsorption or condensation occurs (possible since helium
in almost completely noninteractive). Getting this information will allow us to
6. Conclusions and Future Work
Q(0) and Q(1)
S(0)
71
S(1)
Absorbance
MOF-74
MOF-5
HKUST-1
ZIF-8
4000
4200
4400
4600
4800
-1
Frequency (cm )
Fig. 6.1: A comparison of the spectra of different materials. All the spectra were taken
at large H2 loadings, but other than that the conditions are not necessarily
the same. Note how the strength of the S peaks varies substantially between
materials. The dotted lines give gas phase peak locations.
6. Conclusions and Future Work
72
make more precise measurements of the equilibrium ratio and hydrogen capacity
of the sample. Additionally, once conversion behavior is well understood in a
material, it can be used as an accurate measure of that materials temperature.
6.1.2
Further Work in MOF-74
We hope to expand our work in MOF-74 to other temperature regimes. Performing the experiments that have been done here at temperatures between
30 and 70 K will allow us to get a much clearer view of hydrogen’s conversion
behavior in MOF-74. There are obstacles to these experiments. As we go to
higher temperatures, our peaks broaden from thermal variations of the hydrogen. This makes it more difficult to accurately measure the intensity of peaks,
particularly for the closely spaced Q peaks. Additionally, at higher temperatures MOF-74 does not load as efficiently. We have to load a larger amount
of gas into the sample chamber to get the sample to take up the same amount
of hydrogen. This will increase the magnitude of any conversion that occurs
outside the sample, obscuring that which occurs in the sample.
Going to temperatures below 30 K will sharpen our peaks and also allow us
to get closer to 100% parahydrogen. This presents its own challenges. Because
the rate of heat transfer into the cryostat from the laboratory is proportional
to the temperature difference, it becomes more difficult to maintain a constant
temperature at colder temperatures. We must use more liquid helium, which
is expensive and impractical. In our excursions to 20 K thus far, we also have
not observed notable improvement in our spectra. We suspect that though our
thermometer, positioned on the cold finger, attains 20 K, the sample does not.
We hope to find ways to further reduce the heat transfer into our system and
achieve 20 K.
It is also desirable to have more extensive data with D2 and HD. Such
data provides confirmation of the behavior observed in H2 . It also allows us
to examine the quantum mechanical behavior of the three species. Each of the
isotopes has unique quantum mechanical behavior; different spin states, different
masses, different zero-point energies. Unfortunately, the data collected on D2
and HD thus far are much less clear than H2 . This is largely intrinsic. Those
two isotopes absorb infrared at lower frequencies, which leads to lower intensity.
They also absorb in a region of the electromagnetic spectrum where MOF-74
happens to have substantial peaks. This is further complicated by the increased
cost of D2 and HD (particularly HD) compared to H2 . It remains unclear if
6. Conclusions and Future Work
73
these obstacles can be overcome to produce more precise data from these two
isotopes.
6.1.3
The Dipstick
The dipstick conversion system has yet to be fully vetted, and it would be
productive to have more qualitative information about how it converts. Our
practice of converting overnight was chosen because it produces the desired results. We do not know how long is actually necessary to produce nearly 100%
parahydrogen with Nd2 O3 . This work’s progress in quantitatively analyzing
ortho-para conversion will enable accurate, quantitative investigations of the
conversion capability of Nd2 O3 . This will allow us to improve the efficiency of
our conversion procedure, and also evaluate whether Nd2 O3 might be advantageously replaced by a different catalyst.
We also want data on the storage coil’s ability to keep parahydrogen stored
above liquid helium temperatures. Up to now we have been keeping the storage
coil in a liquid nitrogen bath, in the belief that this was the best way to keep
the hydrogen at its very low temperature ratio. However, it seems that this
may actually lead to faster back conversion (though to a lower final ortho-para
ratio). We plan to obtain quantitative data on the relative merits of the two
possible storage temperatures. We also want to measure the effect of increased
concentration on back conversion in the coil. Since the dipstick cannot be used
to produce additional parahydrogen while the infrared spectrometer is in use,
we want to produce as much parahydrogen as possible at once. However, homogeneous back conversion goes as n2o . We want to know the maximum amount of
parahydrogen that can be stored without catalyzing substantial back conversion
over the course of an infrared experiment.
6.2 Raman
6.2.1
The Gas Cell
We have yet to find a design for the Raman gas cell that provides a large signal
for reasonably small amounts of hydrogen. The current T-cell should provide
for a long path length through the H2 for small quantities of gas. However, we
observe a large fluorescence peak. We have yet to be able to explain the reason
for this peak, which has not been observed in any of our previous gas cells. If we
are able to remove this peak, then we expect the T-cell to provide a better than
6. Conclusions and Future Work
74
factor of two improvement over the Erlenmeyer flask, our best signal producer.
There is also the possibility of using a system of prisms to enable multiple passes
of the laser through the gas cell without ultimately reflecting the beam into the
collecting optics.
6.2.2
Use with the Infrared Spectrometer
Once we obtain usable signal from the Raman spectrometer, we can use it in
parallel with the infrared experiments already being done. Glass should be
a very stable material for holding converted hydrogen[15]. Therefore any gas
removed from the infrared system for analysis in the Raman spectrometer should
retain the ratio it held upon its removal for the duration of a Raman experiment
(about an hour). This allows us to take a snapshot of the infrared system’s
concentration information at any given instant. The Raman effect allows direct
observation of hydrogen’s pure rotational lines. These lines are produced by a
single mechanism and result only from the internal properties of the hydrogen,
with no guest-host interactions. This means that we in a Raman spectrum,
we can measure the ortho-para ratios simply by taking the ratio of the S(1) to
S(0) peaks[35]. This is a dramatic improvement over the method used in this
work, and would allow for much greater precision in ratio measurements. And
since these measurements can be performed simultaneously with the infrared
experiment, we can observe the ortho-para behavior of our sample in nearly
real time, and adjust the experiment as necessary.
6.2.3
Use with the Closed-Cycle Refrigerator
We have been able to install a conversion cell in the closed-cycle refrigerator and
attain temperatures as low as 10 K. This system should be able to effectively
perform ortho-para conversion without the use of liquid helium. The system will
remain untested, however, until the Raman gas cell is working. Once the two
systems are working together, we will be able to study the conversion behavior
of whatever material is loaded in the closed-cycle conversion cell. This will
initially allow us to perform precise measurements of Nd2 O3 , which will help
in analyzing the dipstick. After that, the closed-cycle system allows for finer
temperature control than the infrared system. This will enable us to study the
temperature dependent conversion behavior of a wide range of materials.
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