Catalysis of Conversion Between the Spin Isomers of H 2 by MOF-74. Brian S. Burkholder

Transcription

1 Catalysis of Conversion Between the Spin Isomers of H 2 by MOF-74 Brian S. Burkholder April 1, 2009

2 CONTENTS 1. Introduction Hydrogen Storage The Ortho and Para Species of Hydrogen Background Why Do We Care? Infrared Spectroscopy Raman Spectroscopy Going Cold Metal-Organic Frameworks Theory and Background Ortho and Para Hydrogen Spin Isomers The Symmetrization Requirement The Rotational State The Rotational Symmetries The Equilibration of H 2, D 2, and HD The Improbability of Homogeneous Conversion The Forbidden J = ±1 Transition Interaction of H 2 and H H 2 -H 2 Interactions Catalyzed Conversion Conversion by Gaseous Impurities Conversion of a Fluid by a Solid Catalyst Conversion by a Paramagnetic Lattice Infrared Absorption Raman Scattering Experimental Methods Infrared Spectroscopy

3 Contents iii The Spectrometer The Gas Loading System The Sample Chamber and Cryostat Ortho-Para Conversion The Dipstick Converter The Closed-Cycle Converter Raman Spectroscopy MOF Infrared Cold Procedure Results Characteristics of the MOF-74 Infrared Spectrum Demonstration of Conversion Identification of Peaks through Conversion Conversion with Concentration Fast Loading Low Temperature Back Conversion D 2 and HD The Infrared Mechanisms Raman Spectra Discussion and Analysis Ortho-Para Conversion The Rate of Conversion The Equilibrium Ratio Applications Low Temperature Back Conversion D 2 and HD The Infrared Mechanisms Conclusions and Future Work Ortho-Para Conversion Other Materials Further Work in MOF The Dipstick Raman The Gas Cell

4 Contents iv Use with the Infrared Spectrometer Use with the Closed-Cycle Refrigerator

5 LIST OF FIGURES 1.1 Crystal structure of MOF Modes of molecular motion The axis system for the hydrogen molecule The axes for proton exchange The equilibrium ratios of H 2, D 2, and HD The gas loading system The sample chamber and coldfinger The DRIFTS rig The dipstick conversion system The closed-cycle converter The Raman gas T-cell The infrared spectrum of MOF Conversion in MOF-74 with time Fast loading of H 2 with no secondary band Fast loading of H 2 with secondary band Fits to equilibrium data Low temperature back conversion The Q regions of D 2 and HD Raman spectrum of unmirrored test tube Raman spectrum of mirrored test tube Raman spectrum of Erlenmeyer flask Raman spectrum of T-cell Neutron diffraction Gaussian and Lorentzian fits The spectra of different adsorption materials

6 LIST OF TABLES 2.1 The two-proton spin states The J dependence of rotational state symmetry Rotational constants of the hydrogen isotopes The spin degeneracies of H 2, D 2, and HD Gas phase peak locations System volumes Ortho-para ratio and para concentration with time Fits for ortho-para equilibration Measured equilibrium ortho-para behavior Relative strengths of infrared mechanisms Gas pressure v. loading Separation of H 2 Binding Sites S peak location predictions Summary of conversion timescales in various materials Time for preparation of parahydrogen in MOF

7 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.

8 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.

9 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, H 2 and O 2 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 Background In 1926, Heisenberg theorized the existence of two different spin isomers of molecular hydrogen, called ortho and para[25]. The Pauli exclusion principle

10 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 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-

11 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] 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 H 2 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)

12 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 H 2 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 H 2, D 2, 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 Second, as indicated in Table 3.1, the pure rotational transitions of H 2 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 H 2 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-

13 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 H 2 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 H 2 concentration. However, we want to limit H 2 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-

14 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 e 1/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

15 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.

16 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 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.

17 2. THEORY AND BACKGROUND 2.1 Ortho and Para Hydrogen Spin Isomers The Symmetrization Requirement Recall that protons have spin of 1 2. The two protons of the hydrogen molecule can thus each individually be in the state s = 1 2 m s = or s = 1 2 m s = 2 1. For the sake of concision these will henceforth be referred to as and 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 m S = 0, while the latter can have m S = +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 a and b, then we must have Ψ(a, b) 2 = Ψ(b, a) 2 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 H 2 we have Ψ(a, b) = Ψ(b, a). S = 1 S = 0 m = +1 m = m = 1 Tab. 2.1: The two-proton spin states.

18 2. Theory and Background 10 (a) The vibrational mode. (b) The rotational mode. (c) The translational mode. Fig. 2.1: The ways in which H 2, D 2, 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.

19 2. Theory and Background 11 Note that since a b = b a (2.1) 1 a b + a b = 1 b a + b a (2.2) 2 2 a b = b a (2.3) 1 2 a b a b = 1 2 b a b a (2.4) all the S = 1 states are symmetric under exchange, while S = 0 is antisymmetric. There are three ways in which H 2 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 The total wavefunction has a component for each of these motions and the spin, and so has the form Ψ(a, b) = ψ x (a, b)ψ ν (a, b)ψ J (a, b)χ(a, b) (2.5) where ψ x (a, b) is the translational state, ψ ν (a, b) is the vibrational state, ψ J (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 r a r b, 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 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 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 = p2 x 2m + p2 y 2m + p2 z 2m (2.6)

20 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 ( ) T = 1 p 2 θ + p2 φ 2I sin 2, (2.7) φ where I is the H 2 moment of inertia and θ and φ are as in Fig Note that we have reduced from three to two variables since we are assuming no change in r, and hence p r = 0. This treatment so far is purely classical. To transition to the quantum universe, we simply replace the classical angular momenta p φ and p θ with the appropriate operators and let Ĥ = T. Then we solve the Schrödinger equation: 1 sin θ ( sin θ ψ J θ θ Ĥψ J = Eψ J (2.8) ) ψ J sin 2 θ φ 2 = 2I h 2 Eψ J. (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

21 2. Theory and Background 13 harmonics, and we obtain energy eigenvalues E J = h2 J(J + 1) (2.10) 2I where J is the quantum number giving the nuclei s total orbital angular momentum. We define the rotational constant B h2 2I. (2.11) Note that E J depends only on J, but the spherical harmonics and in turn the rotational wavefunctions ψ J also depend on the azimuthal quantum number m J. This leads to the rotational degeneracy of 2J + 1, since m J 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 The Rotational Symmetries It will be instructive to explicitly give the form of ψ J. The spherical harmonics have the form where Y m J J e im J φ sin m J θp m J J (cos θ) (2.12) P m J J (x) = dm J P J (x) dx m J and P J (x) dj (x 2 1) J dx J (2.13) are the associated Legendre polynomials. Note that P m J J (x) is even if J m J is even and odd if it is odd. We now consider exactly what it means to interchange the protons of H 2. 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 = 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, φ = φ + π and θ = π θ. This is illustrated by Fig We examine the effect of this on Eq term by term. We have e im J φ = e im J (φ+π) = e im J φ e im J π = { e imφ, e imφ, if m J is even if m J is odd (2.14)

22 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. m J J ψ J Even Even + Even Odd - Odd Even + Odd Odd - Tab. 2.2: The J dependence of rotational state symmetry. and sin m J θ = sin m J (π θ) = sin m J θ. (2.15) The final term is P m J J (cos θ ) = P m J J (cos(π θ)) = P m J J ( cos θ) = { P m J J (cos θ), if J m J is even P m J J (cos θ), if J m J is odd. (2.16) The total sign of ψ J as a function of the evenness and oddness of J and m J is given in Table 2.2. Note that if J is even then ψ J is unchanged by exchange of the nuclei, while if J is odd then ψ J 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 H 2 into the two distinct ortho and para spin isomers we need only explain

23 2. Theory and Background 15 B (mev) B (cm 1 ) B (K) H D HD 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 k B. why one spin species does not readily convert to the other. 2.2 The Equilibration of H 2, D 2, 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: H 2, D 2, 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 E J can be produced by 2J + 1 distinct m J values. Thus the degeneracy of each rotational level is g J = 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-spin 1 species of H 2 has spin degeneracy g o = 3 and even-spin state degeneracy g e = 1. In D 2, 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. by The population of an energy state in thermal equilibrium is given in general N i = N T g i e Ei/k BT Z (2.18) 1 In this section we use the terms odd and even in place of ortho and para, since in D 2 the terms ortho and para refer to the even and odd states, respectively, and HD has no ortho or para species at all.

24 2. Theory and Background 16 Ortho-Para Ratio H 2 D 2 HD Temperature (K) (a) Ortho-Para Ratio Temperature (K) (b) Fig. 2.4: The equilibrium ratios of H 2, D 2, 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).

25 2. Theory and Background 17 g o g e H D HD 1 1 Tab. 2.4: The spin degeneracies of H 2, D 2, and HD. where Z is the partition function and N T is the total number of particles. In this case, the total population of the even and odd states are respectively given by N e = N T Z g e Thus, Jeven g J e BJ(J+1)/k BT N o N e = and g o g J e BJ(J+1)/k BT g e Jodd Jeven N o = N T Z g o g J e BJ(J+1)/kBT. Jodd (2.19) g J e BJ(J+1)/k BT. (2.20) 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 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.

26 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 = 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 E 1 = 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 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 Interaction of H 2 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.

27 2. Theory and Background 19 It makes sense that this process is dependent on the frequency of H 2 -H 2 collisions and should therefore depend on H 2 concentration. However, Farkas found that the back conversion rate actually depends on the concentration of H atoms. He calculated that his sample of H 2 at these high temperatures contained between 10 8 and 10 6 % H atoms, and found that this was sufficient to sustain the reaction H 2,p + H H 2,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 H 2 -H 2 Interactions Conversion from H 2 -H 2 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 H 2,o + H 2,o H 2,p + H 2,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 H 2 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

28 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 dn o dt = kn 2 o (2.21) where k is the rate constant and n o 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 n o 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 n o. 2.4 Catalyzed Conversion 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 dn o dt = kn O2 n o (2.22) where n O2 is the concentration of O 2, n o is the concentration of the odd-j species of H 2, and k is a constant. This makes sense considering the discussion of Section The conversion rate is dependant on the concentration of material to be converted, n o, and concentration of catalyst, n O2. 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 O 2 is about 2000 times that of orthohydrogen[15]. Thus the presence of nearly any O 2 will drastically increase the conversion rate above that for H 2 -H 2 interactions. Water impurities behave

29 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 = 2µ2 aµ 2 pi 3 h 2 l 6 k B T (2.23) where µ a is the magnetic moment of the paramagnetic molecule, µ p is the proton magnetic moment, I is the H 2 moment of inertia, k B is Boltzmann s constant, T is temperature, and l is the mean free path of an H 2 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 l is inversely proportional to 3 n, this probability will increase with concentration 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 H 2 around Nd 2 O 3. This situation is analogous to the gaseous impurity. The conversion rate will still depend linearly on n o, 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 H 2 is still v rms = 5kB T m = 561 m/s. (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 Conversion by a Paramagnetic Lattice To begin, we will derive the behavior of Larmor precession, following the method of Griffiths[24]. Start with a single proton in a magnetic field B = B 0 ẑ. The

30 2. Theory and Background 22 Hamiltonian of this system is Ĥ = µ B (2.25) where µ is the magnetic dipole moment µ = γ S (2.26) where S is the proton s spin vector and γ is its gyromagnetic ratio. Thus Ĥ = γb 0 Sz (2.27) where S z = h 2 ( ). (2.28) We already know that the spin eigenstates of a single proton are and. 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/ h + βe ie t/ h. (2.29) But we know = ( 1 0 ) and = ( 0 1 ), (2.30) so, since by the Schrödinger equation Ĥψ = Eψ, E = γb 0 h 2 and E = +γb 0 h. (2.31) 2 Thus, χ(t) = ( αe iγb0t/2 βe iγb0t/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, that is a 2 + b 2 = 1. It is convenient to say α = cos ( ) δ 2 and β = sin ( ) δ. (2.33) 2

31 2. Theory and Background 23 We want to know what effect the magnetic field is having on the spin. We thus calculate the expectation values Sx, Sy, and Sz. This process is calculation is just algebra and is omitted. We find Sx = h 2 sin δ cos(γb ot) (2.34) Sy = h 2 sin δ sin(γb ot) (2.35) Sz = h cos δ (2.36) 2 It is clear from these expectation values that S is at a fixed angle δ to the z-axis. The projection of S onto the xy-plane traces out a circle as time develops. Thus S precesses around the z-axis with the Larmor frequency ω = γb 0. (2.37) In molecular hydrogen, the two protons spins are ordinarily coupled. If we were to put H 2 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 are respectively located at r a and r b in fields B a and B b. Thus Hamiltonian becomes Ĥ = µ a B a µ b B b (2.38) where µ a and µ b are the magnetic moments of the a and b protons. Note that Ĥ acts only on the spin state of H 2. Thus the spin state develops as χ(t) = e iht χ(0). (2.39)

32 2. Theory and Background 24 By exploiting power series, the time development can be written as e iht = cos(ω a t) + i sin(ω a t) σ a B a B + cos(ω b t) + i sin(ω b t) σ b B b a B b (2.40) where σ a and σ b are the components of the respective protons in the direction of their respective fields (equivalent to S z in the one proton case) and ω a and ω b are the individual Larmor frequencies of the protons[39]. This can yield the probability of para to ortho conversion ( P (t) = sin 2 (ω a ω b )t+sin 2 η ) sin(2ω a t) sin(2ω b t)+sin 2 (η) sin 2 (ω a t) sin 2 (ω b t), 2 (2.41) where η is the angle between B a and B b. This behavior is complicated, but it can be productively examined in two limiting cases. First, take the case where B a and B b are parallel but of different magnitude. Then η = 0 and ω a ω b. The probability reduces to P (t) = sin 2 (ω a ω b )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. In the second case, we take B a and B b to have the same magnitude but different direction. Then η 0 and ω a = ω b. This gives ( P (t) = sin 2 (2ωt) sin 2 η ) + sin 4 (ωt) sin 2 (η) (2.43) 2 where we have made the replacement ω = ω a = ω b. This situation is more difficult to visualize, but also results in the two protonic spins precessing out of phase and eventually flipping. Note that the limit where B a and B b are parallel gives a rough estimate of the time required for conversion. For appreciable conversion we want (ω a ω b )t nπ (2.44) B 0 t nπ γ. (2.45)

33 2. Theory and Background 25 If we can estimate the change in field strength across H 2 and the lifetime of H 2 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 H 2 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 ψ a to another state ψ b is give by P a b ψ a µ ψ b 2 (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 P a b µ 2 ψ a ψ b 2. (2.48) This is zero because ψ a and ψ b 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.

34 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 H 2 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 H 2 can be expressed as the spherical harmonic Y m 2. The result is that the matrix element ψ a Q ψ b 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 = E 0 sin(ωt) (2.51)

35 2. Theory and Background 27 where ω is the frequency of the incident radiation. The induced dipole of the hydrogen molecule is thus µ = αe 0 sin(ωt). (2.52) This time varying dipole produces electromagnetic radiation, which is proportional to the amplitude of µ 2. We take r to be the displacement between the molecule s positive and negative charges. molecule, and expand it as a Taylor series in r. Then We assume that α varies over the α = α 0 + r α r +. (2.53) We approximate the variation of α with the first two terms of this expansion. Thus α µ = α 0 E 0 sin(ωt) + re 0 sin(ωt). (2.54) r Classically, we take r to vary with the frequency of vibration of the molecule, ω ν. Then µ = α 0 E 0 sin(ωt) + r 0 E 0 α r sin(ωt) sin(ω νt) = α 0 E 0 sin(ωt) + r 0E 0 2 α r [cos(ω ω ν) cos(ω + ω ν )]. (2.55) We see that the molecule can produce scattered radiation at the frequencies ω, ω ω ν, and ω + ω ν. 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 H 2 possesses[32]. We can thus use Raman scattering to probe H 2.

36 3. EXPERIMENTAL METHODS 3.1 Infrared Spectroscopy 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, CaF 2 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 H 2, D 2, 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. ν = 0 ν = +1 S(0) S(1) Q(0) Q(1) S(0) S(1) H D HD Tab. 3.1: The rotational, vibrational, and ro-vibrational transitions of H 2, D 2, 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.

37 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 D 2 primary site. The InSb detector is also supposed to be more sensitive in the 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, H 2 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 The Gas Loading System The gas loading system transfers gas from H 2, D 2, and HD high pressure cylinders to the sample, and is illustrated in Fig 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 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

38 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. H 2, D 2, and HD can be loaded from the main tank, He from another tank, and pure para H 2 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 cm 3. 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 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

39 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 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 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 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

40 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)caf 2 windows at the entrance and exit of the cryostat. f)plane mirrors that direct light into and out of the cryostat.