NON-CRYOGENIC STORAGE CELL FOR HYPERPOLARIZED 129XE

Abstract

A system is disclosed for producing and storing gaseous spin polarized 129Xe including: a polarizer configured to produce gaseous spin polarized 129Xe, and a storage apparatus for non-cryogenically storing gaseous spin polarized 129Xe.

Description

CROSS REFERENCE TO RELATED APPLICATIONS

The application claims benefit of U.S. Provisional Patent Application Ser. No. 61/055819, filed May 23, 2008, the content of which is incorporated herein by reference in its entirety.

STATEMENT REGARDING FEDERALLY SPONSORED R&D

This invention was made with government support under PHY-0134980 awarded by National Science Foundation. The Government has certain rights to this invention.

BACKGROUND

This disclosure is related to the storage of spin polarized (e.g. hyperpolarized) gasses (e.g. ¹²⁹Xe).

Noble-gas isotopes having non-zero nuclear spin may be optically polarized to levels approaching unity via the techniques such as of spin-exchange optical pumping (SEOP) [1, 2], whereby the notoriously weak signal generated by nuclear moments is enhanced by several orders of magnitude. Even after several decades of work by many groups, hyperpolarized gasses continue to be studied and applied in a wide variety of magnetic-resonance experiments; we cite a few recent examples [3-5]. In a typical implementation, circularly polarized laser light is incident on a glass cell containing a macroscopic amount of an alkali-metal (usually Rb), the noble gas, and a small quantity of nitrogen to promote collisional de-excitation of the excited states generated by resonant absorption of the laser light by the alkali-metal vapor at the first principle (D₁) electric-dipole transition [6]. (This corresponds to a wavelength of 795 nm for Rb.) The alkali-metal vapor density is controlled by adjusting the cell temperature from room temperature up to ≈500 K in the presence of a macroscopic amount of alkali metal in the closed cell. The selection rule for absorption of circularly polarized light and collisional mixing of the excited-state magnetic sublevels lead to rapid and efficient spin polarization of the valence electron of the alkali-metal vapor. Collisions with noble-gas atoms then lead to an exchange of angular momentum between the alkali-metal electron and the noble-gas nucleus. The time-dependent build-up of nuclear polarization P_N(t) in such a sample that occurs while the laser is on is given by:

$P_N\left(t\right)-〈P_A〉\frac{{\gamma }_{\mathrm{se}}}{{\gamma }_{\mathrm{se}}+\Gamma }\left[1-\exp \left(\frac{-t}{{\gamma }_{\mathrm{se}}+\Gamma }\right)\right],$

where P_A is the time- and volume-averaged alkali-metal polarization, γ_se is the spin-exchange rate, and Γ is the longitudinal relaxation rate of the noble gas due to to all other mechanisms. Note, in Eq. (1) we have ignored the anomalous excess relaxation that scales with alkali-metal density recently observed for SEOP of ³ He [7].

It is clear from Eq. (1) that F limits the ultimate nuclear polarization for a fixed value of γ_se, the latter being limited by available laser power and the photon efficiency (the number of polarized nuclei produced per photon absorbed in the cell volume) [8] for a given alkali-metal-noble-gas pair and laser/cell geometry, whereby one generally maintains P_A close to unity. An understanding of the mechanisms responsible for the relaxation rate r is thus essential to the efficient production of hyperpolarized gasses. Note,

While SEOP is typically used to polarize either of the stable spin-½ noble-gas isotopes, ³He and ¹²⁹Xe, the examples presented below will deal specifically with the relaxation mechanisms that limit the polarization of ¹²⁹Xe. The relaxation rate F may be written [9]:

Γ=Γ_t+Γ_p+Γ_g+Γ_w,

where Γ_i=Γ_t+Γ_p is the intrinsic rate due to the sum of contributions from transient and persistent Xe₂ dimers; and Γ_e=Γ_g+Γ_w is the extrinsic rate due to the sum of contributions from atomic diffusion through gradients in the applied magnetic field [10, 11] and interactions with the cell surface (wall relaxation). In most cases involving SEOP of xenon, some combination of Γ_p and Γ_w dominates the relaxation. For xenon densities as low as 0.1 amagat, Γ_g is usually negligible [9], although there is size limitation for hyperpolarized-xenon storage cells in a given Helmholtz geometry due to this mechanism (see Sec. 4.5). For xenon densities ≈1 amagat and larger, Γ_t sometimes makes a small but non-negligible contribution to the total relaxation rate. Based on the present and previous work [9, 12, 13], we have developed a semi-empirical formula for the intrinsic relaxation rate l_i of ¹²⁹Xe as a function of xenon density [Xe] (amagats), temperature T (Kelvin), applied magnetic field B₀ (Tesla), and gas composition. This formula applies for [Xe]>0.3 amagat at all reasonable values of B₀:

${\Gamma }_i^{-1}=\frac{\left[\mathrm{Xe}\right]}{56.1h}{\left(\frac{T_0}{T}\right)}^{1/2}+\frac{1}{4.59h}{\left(\frac{T_0}{T}\right)}^2\left[1+\left(3.65\times {10}^{-3}\right)B_0^2\right]\left(1+r\frac{\left[B\right]}{\left[\mathrm{Xe}\right]}\right),$

where the first teen is clue to persistent dimers and the second is due to transient dimers; T₀=293 K, [B] is the density of a second gas in the mixture, and r≡k_B/k_Xe is the ratio of the persistent-dimer breakup coefficient for the second gas to that for xenon. We have measured r=0.51 for nitrogen, which, along with helium, is most often present with xenon in SEOP situations. For helium, Chann, et al. have measured r=0.25. The transient-dimer term in Eq. (3) is based on the results of Moudrakovski, et al. [13]; we have estimated its temperature dependence by considering that, in the weak-interaction limit, the probability for a spin transition is approximately proportional to the rate of binary collisions and to the square of the collision duration. Hence, we should have θ, ∝1/ν, where ν∝T^1/2 is the mean thermal velocity of the xenon atoms. The uncertainty in the relaxation time calculated from Eq. (3) is about 10%.

Longitudinal relaxation also plays a key role in the accumulation and storage of hyperpolarized gasses. Storage times of several hours or more are directly relevant to applications such as magnetic resonance imaging (MRI), where the gas must often be transported to the MRI scanner with minimal polarization loss. In the case of ¹²⁹Xe, a relatively long longitudinal relaxation time T₁≡Γ⁻¹ is also important for the accumulation stage in a flow-through xenon polarizer [14, 15], the current state-of-the-art scheme for the versatile production of liter-quantities of highly polarized ¹²⁹Xe for any application. In these devices, a gas mixture lean in xenon is passed continuously through a glass cell, in which it is polarized by SEOP with a laser, and subsequently frozen as a polycrystalline solid at 77 K in a liquid-nitrogen trap. This basic scheme has proven effective in dealing with the inherently low (7%) Rb—Xe spin-exchange efficiency. i.e., the rate at which angular momentum is transferred to the noble-gas nucleus divided by the rate at which it is lost by the alkali-metal atoms [16]. The source of this low efficiency is the strong spin-rotation interaction of the rubidium valence electron with the electron cloud of the xenon atom, whereby P_A begins to plummet for xenon densities [Xe]>1 amagat. Hence, ¹²⁹Xe (unlike ³He) is not readily polarized in large batches at high density. Cryogenic accumulation of xenon as it flows out of the polarizing cell serves two purposes. First, it separates out the other gasses, typically nitrogen and helium, making it possible to prepare pure xenon samples. Second, since most or all of the polarization survives the phase transition [15, 17], large quantities of hyperpolarized xenon can be accumulated from the low-density flow and stored for times on the order of T₁≈2.5 h at 77 K in an applied magnetic field B₀≧0.1 T [18] before being revolatilized. This method evolved, in part, because of the reliable 2.5 h storage time, although it became clear in later work the gas must be quickly and completely frozen to 77 K [15]; at higher temperatures, particularly those approaching the xenon melting point (161 K), relaxation rates increase dramatically due to vacancy diffusion in the solid [19], resulting in polarization losses in the freeze/thaw cycle.

Hyperpolarized ¹²⁹Xe is now used for research variety of disciplines such as medical imaging, biological assays, and pore characterization [1A, 2A, 3A]. Many of these experiments require on-demand production of large (liter-per-hour and more) quantities of hyperpolarized ¹²⁹Xe. The state-of-the-art method for such production is the flow-through polarizer/accumulator [4A, 5A]. One manufacturer claims the ability to produce 10 L/h of hyperpolarized xenon [6A]. These techniques require diluting Xe to a small percent of gas mixture, usually of order 1%.

Presently, the only method for separating the hyperpolarized Xe from the other buffer gasses is using cryogenic freezing. This method capitalizes on the high Xe melting temperature (161 K) compared with other gasses in the mixture. Xenon freezes out of the gas stream as a polycrystalline solid and deposits in some holding cell; the hyperpolarization generally survives the phase transition. The cryogenic cell is also used to store the Xe, as the relaxation time of Xe at 77 K in an applied field of 2 kG is of order 2 hours [7A]. The xenon can be accumulated and stored as a solid for about this amount of time before it is revolatilized and used as a gas in an experiment or application.

Cryogenic separation is disadvantageous because it is a stepped method. One must accumulate Xe for some amount of time from a flow through polarizer and then divert or stop the flow when ready to volatilize the solid. It would advantageous for a number of experiments to have the ability to separate the Xe continuously, so that a steady stream of pure hyperpolarized Xe could be directed to an experiment or application. Further disadvantantages of cryo separation are discussed below.

SUMMARY OF THE INVENTION

Techniques are described for storing large quantities of hyperpolarized (HP) ¹²⁹Xe gas. In various embodiments, an apparatus may include a large (10 cm diam or larger) valved glass container (cell), the interior of which is coated with a silicone or paraffin-like compound to inhibit longitudinal relaxation of the ¹²⁹Xe nuclei. The cell contains no alkali-metal. The cell sits in a modest magnetic field (about 3 millitesla) generated by a Helmholtz coil pair. The cell is designed to receive HP xenon gas from a current state-of-the-art device, a ¹²⁹Xe flow-through polarizer/accumulator based on the established method of spin exchange optical pumping, whereby laser light and an alkali-metal vapor are used to transfer spin angular momentum to ¹²⁹Xe in the gas phase. The inventors have developed a thorough understanding of gas-phase relaxation of ¹²⁹Xe nuclei in the presence of other xenon atoms (intrinsic relaxation), as well as due to collisions with the cell wall (extrinsic relaxation). Part of this understanding is that the wall relaxation rate scales as the surface-to-volume ratio of the cell: larger spherical cells have slower relaxation rates. Cells may be produced in which the storage lifetime of the HP xenon gas is 2-3 times longer than the current state-of-the-art storage method and requires no cryogenic freezing of the xenon or associated large magnetic fields. Moreover, such cells may be used in conjunction with gas centrifuge separators to provide pure hyperpolarized xenon without need for cryogenic separation.

In one aspect, a storage apparatus is disclosed for non-cryogenically storing gaseous spin polarized ¹²⁹Xe including: a storage vessel including an interior surface substantially surrounding a storage volume; and a magnet which produces a substantially uniform magnetic field within the storage volume; where the interior surface is characterized in that the longitudinal spin relaxation rate of the gaseous spin polarized ¹²⁹Xe due to interactions with the interior surface is about equal to or less than the longitudinal spin relaxation rate of the gaseous spin polarized ¹²⁹Xe due to intrinsic mechanisms.

Some embodiments include a heater for maintaining the storage vessel at a temperature greater than room temperature. In some embodiments, the heater is configure to maintain the storage vessel at a temperature greater than about 100 degrees centigrade.

In some embodiments, the magnet includes a pair of coils in the Helmholtz configuration.

In some embodiments, the interior surface consists of a layer of material substantially free of alkali-metal.

In some embodiments, the vessel includes glass, and the interior layer is on the glass. In some embodiments, the interior layer includes a silane- or siloxane-based coating.

In some embodiments, the vessel includes a plastic material and the interior surface consists of the plastic material. In some embodiments, the plastic material includes Teflon.

In some embodiments, the ratio of the area of the interior surface to the storage volume is less than about 1 cm⁻¹. In some embodiments, ratio of the area of the interior surface to the storage volume is less than about 0.5 cm⁻¹.

In some embodiments, the substantially uniform magnetic field within the storage volume has a magnitude of about 3 milliTesla or less.

In some embodiments, the storage vessel is characterized by a relaxation time for the gaseous spin polarized ¹²⁹Xe of greater than about five hours, the relaxation time corresponding to a density of the spin polarized ¹²⁹Xe of greater than about one amagat.

In some embodiments, the storage vessel is characterized by a relaxation time for the gaseous spin polarized ¹²⁹Xe of greater than about seven hours, the relaxation time corresponding to a density of the spin polarized ¹²⁹Xe of greater than about one amagat.

In another aspect, a system is disclosed for producing and storing gaseous spin polarized ¹²⁹Xe including: a polarizer configured to produce gaseous spin polarized ¹²⁹Xe; and a storage apparatus for non-cryogenically storing gaseous spin polarized ¹²⁹Xe as described above. The storage apparatus is in communication with the polarizer to receive and store the spin polarized ¹²⁹Xe.

In some embodiments, the polarizer is a spin exchange optical pumping polarizer. In some embodiments, the polarizer includes one or more volumes in which Xe is in the presence of alkali-metal, and the storage apparatus stores the gaseous spin polarized ¹²⁹Xe received from the polarizer in a substantially alkali-metal free environment.

Some embodiments include: a gas centrifuge separator. The separator is in communication with the polarizer to receive a mixture of gaseous spin polarized ¹²⁹Xe and other gasses from the polarizer. The separator is configured to separate substantially pure gaseous spin polarized ¹²⁹Xe from the mixture. The storage apparatus is in communication with the separator to receive and store the substantially pure gaseous spin polarized ¹²⁹Xe.

In some embodiments, the substantially pure gaseous spin polarized ¹²⁹Xe is at least about 90% pure. In some embodiments, the substantially pure gaseous spin polarized ¹²⁹Xe is substantially free of alkali-metal.

In another aspect, a method of non-cryogenically storing gaseous spin polarized ¹²⁹Xe is disclosed including: providing storage vessel including an interior surface substantially surrounding a storage volume; providing a substantially uniform magnetic field within the storage volume; and introducing gaseous spin polarized ¹²⁹Xe into the storage volume. The interior surface is characterized in that the longitudinal spin relaxation rate of the gaseous spin polarized ¹²⁹Xe due to interactions with the interior surface is about equal to or less than the longitudinal spin relaxation rate of the gaseous spin polarized ¹²⁹Xe due to intrinsic mechanisms.

Some embodiments include maintaining the storage vessel at a temperature greater than room temperature. In some embodiments, the temperature greater than room temperature is greater than 100 degrees centigrade or greater than 200 degrees centigrade, or more.

In some embodiments, introducing gaseous spin polarized ¹²⁹Xe into the storage volume includes polarizing gaseous ¹²⁹Xe in a polarizer to produce gaseous spin polarized ¹²⁹Xe and transferring the gaseous spin polarized ¹²⁹Xe to the storage vessel.

In some embodiments, transferring the gaseous spin polarized ¹²⁹Xe to the storage vessel includes: passing a mixture of gaseous spin polarized ¹²⁹Xe through one or more gas centrifuge separators to produce substantially pure gaseous spin polarized ¹²⁹Xe; and introducing the substantially pure gaseous spin polarized ¹²⁹Xe into the storage volume. In some embodiments, the centrifuge is configured separate polarized xenon without substantially destroying the polarization.

Various embodiments may include any of the above described features, either alone or in combination.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1A is a schematic of a cell for non-cryogenic storage of gaseous spin polarized ¹²⁹Xe.

FIG. 1B a schematic of a system for producing and storing gaseous spin polarized ¹²⁹Xe.

FIG. 1C is a flow diagram of a process for producing and storing gaseous spin polarized ¹²⁹Xe.

FIG. 1 is a plot of persistent dimmer relaxation rate versus total gas density.

FIG. 2 shows a plot of 2K(M^sr+M^csa) extracted from the fits in FIG. 1 (see Table I) vs. the square of the applied magnetic field B₀.

FIG. 3 is a plot of the ¹²⁹Xe persistent-dimer relaxation rate Γ_p at 8.0 T vs. 1/T².

FIG. 4 is a plot of NMR signal intensity vs. time for cell 113B at room temperature in an applied field of 14.1 T.

FIG. 5 shows a plot of Γ_w vs. B₀ at room temperature.

FIG. 6 shows pressure profiles in stages of the centrifugation process, for 1 stage (A), 3 stages (B), 5 stage(C), and 8 stages (D) of centrifugation.

FIG. 7 shows the time evolution of the concentration of Xe gas in a cylinder.

FIGS. 8a-8g are photographs showing exemplary storage cells.

DETAILED DESCRIPTION

FIG. 1A shows a storage cell 100 or non-cryogenically storing gaseous spin polarized¹²⁹. Cell 100 includes a storage vessel 102 including an interior surface 104 substantially surrounding a storage volume 106. Storage volume 106 may be accessed using valve 107.

A magnet 108 produces a substantially uniform magnetic field within the storage volume 106. As shown, the magnet 108 is an electromagnet which includes a pair of coils in the Helmholtz configuration, driven by power source 110. In other embodiments, and suitable type of magnet may be used including e.g. a permanent magnet or an electromagnet in another configuration (e.g. a solenoid surrounding all or a portion of vessel 102). In some embodiments, the substantially uniform magnetic field within the storage volume has a magnitude of about 3 milliTesla or less, or about 1 milliTesla or less.

As described in detail below, interior surface 104 is made of a material which inhibits longitudinal spin relaxation caused by interactions (e.g. collisions) between the ¹²⁹Xe and the surface. For example, in some embodiments, surface 104 is characterized in that the longitudinal spin relaxation rate of the gaseous spin polarized ¹²⁹Xe stored in volume 106 due to interactions with the interior surface is about equal to or less than the longitudinal spin relaxation rate of the gaseous spin polarized ¹²⁹Xe due to intrinsic mechanisms.

In some such embodiments, the interior surface 104 is wholly or partially made up of material which is substantially free of alkali-metal. For example the vessel 102 may be made of glass, and the interior surface 104 may be material layer on the glass. In some embodiments, the material layer includes a silane- or siloxane-based coating. Suitable coatings may be provided using any techniques know in the art.

In some embodiments, the vessel 102 is made of an alkali-metal free plastic material (e.g. Teflon) and the interior surface 104 consists of this plastic material (e.g. no coating is provided on the layer).

Some embodiments of cell 100 include a heater 112 for maintaining the storage vessel at a temperature greater than room temperature. The heater 112 may operate to heat vessel 102 using any suitable method including contact heating, convection heating, radiative heating, etc. Heater 112 may include a control system, e.g. a thermostat for maintaining a set temperature. In some embodiments, the heater 112 maintains the storage vessel at a temperature, e.g., greater than room temperature, or greater than about 100 degrees centigrade, 200 degrees centigrade, 300 degrees centigrade, or more.

Although, as shown, the vessel 102 is a spherical bulb, in various embodiments the vessel 102 may be formed as any suitable shape. As described in detail below, it is advantageous to minimize the ratio of the area of the interior surface 104 to the storage volume 106. For example. In some embodiments, the ratio of the area of the interior surface to the storage volume is less than about 1 cm⁻¹, less than about 0.5 cm⁻¹, or even less. FIGS. 8a through 8g show exemplary vessels having various dimensions.

Cell 100 can be used for long term, non-cryogenic storage of gaseous spin polarized ¹²⁹Xe. As describe in detail below, the use of an alkali free interior surface and applied the magnetic field reduces extrinsic relaxation, and allows for long storage times. For example, in some embodiments, the storage vessel is characterized by a relaxation time for the gaseous spin polarized ¹²⁹Xe of greater than about five hours, greater than about seven hours, or even more at a of greater than about one amagat or more.

Referring to FIG. 1B, a system 200 may be used for producing and storing gaseous spin polarized ¹²⁹Xe. System 200 includes a polarizer 202 which operates on gas mix 203 to produce gaseous spin polarized ¹²⁹Xe. In some embodiments, the polarizer 202 is a spin exchange optical pumping polarizer, e.g. of the type described in detail below.

Spin polarized ¹²⁹Xe is transferred from the polarizer to a storage cell 100 of the type described above for non-cryogenically storage. Thus, the storage cell 100 is in communication, directly or indirectly, with the polarizer 202 to receive and store the spin polarized ¹²⁹Xe. The polarizer may include one or more volumes in which Xe is in the presence of alkali-metal, while storage cell 100 stores the gaseous spin polarized ¹²⁹Xe received from the polarizer in a substantially alkali-metal free environment. Any suitable system, e.g. system of valves and transfer chambers, may be employed to transfer the spin polarized ¹²⁹Xe from the polarizer 202 to the storage cell 100 while maintaining the alkali free environment of the cell 100.

Some embodiments optionally include separator 204, which may be a gas centrifuge separator. The separator 204 is in communication with the polarizer 202 to receive a mixture of gaseous spin polarized ¹²⁹Xe and other gasses from the polarizer 202. The separator 204 separates substantially pure gaseous spin polarized ¹²⁹Xe from the mixture. As described in detail below, the separator 204 may operate to effect the separation without substantially reducing the spin polarization of the polarized ¹²⁹Xe. For example, in some embodiments, the separator 204 may be constructed with substantially alkali-metal free inner surfaces to reduce extrinsic relaxation resulting from collisions of the gas with these surfaces.

The storage cell 100 is in communication with the separator 202 to receive and store the substantially pure gaseous spin polarized ¹²⁹Xe. For example, the substantially pure gaseous spin polarized ¹²⁹Xe may be at least about 80%, about 90% pure, about 95% pure, about 99% pure, or more. In some embodiments, the substantially pure gaseous spin polarized ¹²⁹Xe transferred to cell 100 is substantially free of alkali-metal.

FIG. 1 C shows a flow diagram illustrating steps for a process 300 of polarizing and storing ¹²⁹Xe using the system 200. In step 301, polarizer 202 receives an un-polarized gas mix 203 containing Xe. In step 302, polarizer 202 polarizes at least portion of the gas mix to produce gaseous spin polarized ¹²⁹Xe. In optional step 303, separator 204 separates the gaseous spin polarized ¹²⁹Xe from other gasses present in the mix 203. In step 304, the gaseous spin polarized ¹²⁹Xe is stored in storage cell 100. Step 304 may include the following substeps. In substep 304a, the gaseous spin polarized ¹²⁹Xe is contained in the alkali-metal free environment of vessel 102. In substep 304b and 304c, a desired magnetic field and temperature is maintained in the vessel 102.

While not intending to be bound by theory, the following provides additional detail regarding devices and techniques for non-cryogenic storage of gaseous spin polarized ¹²⁹Xe.

Accumulation and storage of hyperpolarized xenon near room temperature in the gas phase is desirable in that it would eliminate the need for large magnetic fields, the cryogenic apparatus, and freeze/thaw cycles. The historical problem with this approach has been that ¹²⁹Xe gas-phase relaxation is relatively fast and notoriously irreproducible, whereby wall relaxation plays a crucial role. Some progress was made in understanding wall interactions, particularly in cells treated with silane- or siloxane-based surface coatings in fields on the order of 1 mT [20, 21], where T₁=20-60 min was observed. Others observed T₁>3 h for some coated cells at 9.4 T, an indication that wall relaxation is suppressed at high field [13, 22]. These studies all had in common relatively small cells (1-3 cm dia.) that contained macroscopic amounts of rubidium along with the coating, meaning that the gas was polarized by SEOP in the same cell in which T₁ was subsequently measured. While it is well known that ³He relaxation on uncoated glass is reliably suppressed by the presence of alkali metal [23, 24, 25], this is apparently not the case for ¹²⁹Xe, where in fact, the interaction of the alkali metal with the surface coating, particularly when heated to 100° C. or more during SEOP can lead to erratic and generally increasing relaxation rates [9]. Wall relaxation in xenon cells is not relaxation-site limited at the usual SEOP densities, i.e., xenon atoms are not inhibited from interacting with wall sites due to their occupation by other xenon atoms. Hence, in the regime for which the wall contribution to T₁ is long compared to the mean time for a xenon atom to diffuse across the cell (easily realized in all of our experiments and most others), the wall-relaxation rate is independent of [Xe] and depends linearly on the surface-to-volume ratio S/V. Accordingly larger-diameter coated cells containing no alkali metal may be used as a way of reducing the ¹²⁹Xe gas-phase wall-relaxation rate.

Gas-phase ¹²⁹Xe relaxation due to persistent Xe₂ dimers has been shown[12]. These van der Waals molecules are formed in three-body collisions and have a mean lifetime τ_p˜1 ns [12, 9] before being destroyed by another collision. The maximum relaxation time for a pure xenon sample due to this mechanism alone was shown to be ≈4 h and independent of [Xe] for low applied magnetic field B₀ (a few millitcsla). The density independence arises both because the fraction of xenon atoms bound in molecules and the molecular formation/breakup rate τ_p⁻¹ have the same linear dependence on [Xe], and because the fast-fluctuation limit Ω²τ_p²<<1, where Ω is the ¹²⁹Xe Larmor frequency, holds for all reasonable values of [Xe] and B₀<1 T; see Eq. (4) below. This density independence effectively mimics wall relaxation, and it has undoubtedly confounded some earlier work in measuring Γ_w, particularly since the the minimum intrinsic rate Γ_p is much larger than previously believed [13, 26]. We have verified and extended this work at low [Xe] and B₀=8.0 T, which straddles the fast- and slow-fluctuation regimes. We showed that persistent-dimer relaxation is strongly suppressed at this field for sufficiently low xenon densities 0.1 amagat) and large magnetic fields. Indeed, we observed extraordinarily small gas-phase relaxation rates in our alkali-metal-free, coated cells, with measured T₁'s exceeding 25 h in some cases.

Increased understanding of gas-phase relaxation of ¹²⁹Xe allowns for significant improvements in cell performance vis-à-vis hyperpolarized gas production, accumulation, storage, and transport for the various applications. We have extended our study of this relaxation to a wide range of applied magnetic fields and temperatures, with an eye towards a large-diameter (≧20 cm) coated cell that could store several liters of hyperpolarized xenon with a T_1≧7 h in an applied magnetic field of ≈3 mT, tripling the storage time of solid xenon at 77 K and eliminating the need for high-field cryogenic accumulation. The work is divided into three main parts described herein:

(1) The study of the magnetic suppression of the persistent-dimer mechanism in a range of magnetic fields from 1.5 T to 14.1 T. This data allowed us to deduce the relative strength of the spin-rotation (SR) and chemical-shift-anisotropy (CSA) interactions via the B₀²-dependence of the CSA contribution. This, in turn, generates an independent estimate for the maximum low-field pure-xenon relaxation time of T₁=4.6 h.

(2) The study of wall relaxation over the same range of B₀ and further on down to 3 mT. This is made possible by a thorough understanding of the persistent-dimer mechanism with which wall relaxation often competes. Wall-relaxation times in our alkali-metal-free coated cells varied from ≈10 h at 3 mT to >100 h at 14.1 T, suggesting a high-field decoupling of a wall mechanism that has to do with interactions of ¹²⁹Xe atoms with unpaired electrons at the surface or inside of the coating [20].

(3) The study of the temperature dependence of the persistent-dimer rate Γ_p in the fast-fluctuation limit in the range of 20-100° C. The inverse-square dependence of Γ_p on temperature T is consistent with our theoretical model and results in an increase of ≈60% in the relaxation time due to persistent dimers at 100° C. compared to room temperature.

Intrinsic longitudinal relaxation of ¹²⁹Xe gas in the SEOP regime of pressure and temperature is dominated by the SR [27] and CSA [28, 29] interactions modulated by the formation and breakup of persistent Xe² dimers in three-body collisions. The theory is discussed in detail in Refs. [9, 12]. In brief, the persistent-dimer relaxation rate is given by

${\Gamma }_p=\left(2K\left[\mathrm{Xe}\right]\right)\left(M^{\mathrm{sr}}+M^{\mathrm{csa}}\right)\left(\frac{{\tau }_p}{1+{\Omega }^2{\tau }_p^2}\right),$

where K≡[Xe₂]/[Xe]² is the chemical equilibrium coefficient, M^sr and M^csa are the interaction strengths (second moments) of the SR and CSA interactions, respectively, and τ_p⁻¹ is the molecular formation rate (equal to the breakup rate in chemical and thermal equilibrium). This equation can be reparameterized and added to the wall relaxation rate Γ_w to obtain for the total relaxation rate:

$\Gamma \left(\left[G\right]\right)={\Gamma }_w+2K\left(M^{\mathrm{sr}}+M^{\mathrm{csa}}\right)\left(\frac{\alpha {k_{\alpha }\left[G\right]}^2}{{k_{\alpha }^2\left[G\right]}^2+{\Omega }^2}\right),$

where [G] is the total gas density, α≡=[Xe]/[G] is the xenon concentration, and k_α is the molecular breakup coefficient for the particular gas composition. In this work, nitrogen is the only other gas in the mixture, and

$\frac{1}{{\tau }_p}=k_{\alpha }\left[G\right]=k_{\mathrm{Xe}}\left[\mathrm{Xe}\right]+k_N\left[N_2\right],$

where k_Xe and k_N are the breakup coefficients for xenon and nitrogen as third bodies, respectively.

At high gas densities, in the fast-fluctuation limit Ω²<<k_α²┌G┐² of Eq. (5), the persistent-dimer relaxation rate is independent of [G] for a given gas composition, as first observed by Chann, et al. [12] for B₀=2.0 mT and also by our group for B₀=8.0 T [9]. At lower densities the rate is suppressed due to the increasing relevance of the Ω² term in Eq. (5). Whereas M^st is independent of the applied field B₀ [27], M^csa is proportional to B₀². Hence, acquiring a set of relaxation curves as a function of [G] that are fitted to Eq. (5), where each curve is at one of several values of B₀, allows M^sy to be separated from M^csa.

The temperature dependence to Γ_p comes predominantly through chemical equilibrium coefficient K and the mean persistent-dimer lifetime τ_p in Eq. (4). The chemical equilibrium coefficient is given by [30]

$K=\frac{1}{2}{\left(\frac{h^2}{2\pi \mu \mathrm{kT}}\right)}^{3/2}Z,$

where h is the Planck constant, k is the Boltzmann constant, Z=Σ_i(2N_i+1)e^−Ei/kT is the partition function for the internal ro-vibrational states of the Xe₂ dimer, and μ is its reduced mass. The portion of this expression that multiplies Z is the ratio of translational partition function for a single dimer to that for two free atoms in the classical high-temperature and low-density limit. We neglect here the weak temperature dependence of Z at room temperature and above, where T>E_i/k≈280 K [31]. Classically, τ_p is inversely proportional to the mean relative velocity of the gas molecules, which is proportional to T^1/2. We treat here only the fast-fluctuation limit, Ω²τ_p²<<1, relevant to high-density xenon storage cells in small magnetic fields. Since the product Kτ_p appears in this limit, we expect the relaxation rate Γ_p to depend on T⁻². We have ignored here any temperature dependence of the collisional cross sections or of the interaction strengths M^sr and M^csa.

As will be understood by those skilled in the art, some of the experimental procedures described here are related to those described in detail in our previous work [9]. Some of the measurements of the longitudinal relaxation time T₁ for ¹²⁹Xe in xenon gas were done in a single borosilicate-glass (Pyrex) “measurement” cell, designated 113B shown in FIGS. 8d-e. It is a 6.7 cm diam sphere connected via a 10 cm length of capillary (0.5 mm diam) to a glass valve and sidearm used for evacuation and refilling. A 4 cm length of 6 mm glass tubing (the stem) extends from the sphere opposite the capillary entrance. The cell contains no alkali-metal, but the interior was coated with dimethyldichlorosilane, which inhibits wall relaxation in a manner similar to silicone coatings previously introduced [20, 21].

Hyperpolarized xenon was generated in one of several “pumping” cells, which have a geometry similar to the measurement cells and also contain Rb metal for SEOP. Our high-vacuum gas-handling system [32] is used to measure cell volumes, evacuate cells, and to refill pumping cells with a precise mixture of xenon (isotopically enriched to 86%; Spectra Gasses, West Branchburg, N.J.) and nitrogen. Unless otherwise noted, the xenon concentration α=0.91±0.02 throughout this work, where the error reflects variation in multiple preparations of the mixture in the pumping cells. The effects of varying a are consistent with the theory presented above and were studied previously [9, 12].

Xenon gas, polarized by SEOP to 10% in a pumping cell was then transferred (at the known value of α) to the measurement cell using a glass transfer manifold and mechanical vacuum pump for evacuating dead space. In the case of the 1.5 T and 8.0 T fields, the cell was immediately inserted into a NMR probe and the probe assembly was inserted into the magnet. In the case of the 4.7 T and 14.1 T fields, the polarized measurement cell was transported in a portable 2 mT battery-powered solenoidal coil to an NMR facility. (Less than 10% of the magnetization was lost during transport.) All magnets (with the exception of the 1.5 T magnet) had a wide-bore (89 mm diam) vertical configuration. The probes were capacitively tuned saddle coils (one to two turns) placed along the stem of the cell; the respective resonance frequencies corresponded to the ¹²⁹Xe gyromagnetic ratio of 11.8 MHz/T. In the 1.5 T field (provided by a 30 cm diam horizontal-bore imaging magnet), the cell was situated horizontally at the magnet isocenter with a surface-coil probe placed underneath it.

NMR measurements were conducted with an Aries (Tecmag) spectrometer with a homebuilt rf section (1.5 T and 8.0 T), Chemagnetics CMX200 (4.7 T), and Varian

Infinityplus 600 (14.1 T). For measurements above room-temperature, the 8.0 T probe was insulated and heated with air flowing across a filament heater located away from the magnet. In addition, several low-field (B₀≈3 mT) measurements were made using a homebuilt low-frequency spectrometer [33], whereby the cell and NMR probe were placed in a oven (similarly heated with flowing hot air) located at the isocenter of a Helmholtz pair. In all cases the longitudinal relaxation rate Γ was measured by periodic acquisition of a free-induction decay (FID) induced by a single rf pulse. A negligible fraction of the magnetization was destroyed by each pulse. Either the height or the area under the the peak of each Fourier-transfoinied FID was plotted as a function of time and a least-squares fit was used to extract Γ.

The relaxation rate Γ was measured as a function of total gas density [G] for the four different magnetic fields. The data were fit in each case to Eq. (5) using the appropriate value of the Larmor frequency Ω, with the wall-relaxation rate F the interaction-strength term 2K(M^sr+M^csa) extracted as free parameters; see Table 1. Since the xenon concentration α and, hence, the breakup coefficient k_α are field-independent, the value

k_α=(3.54±0.28)×10⁻¹⁰ cm³/s,

was determined from a global fit to the four data sets, and this value was then used as a fixed parameter for each of the fits to the individual data sets.

FIG. 1 shows a plot of the room-temperature ¹²⁹Xe persistent-dimer relaxation rate vs. total gas density for a fixed xenon concentration α=0.912 at four different applied magnetic fields. The wall relaxation rate 64 _w and the product 2K(M^sr+M^csa) are extracted from fits of the measured relaxation rates Γ([G]) to Eq. (5) for each field (see Table 1). The corresponding value of Γ_w has been subtracted from all the data sets in this plot to show clearly the behavior of the persistent-dimer rate Γ_p. The high-density fast-fluctuation limit results in a density-independent relaxation rate (asymptote) that increases with field due to the increasing strength of the CSA interaction; the magnetic suppression of the persistent-dimer mechanism with decreasing density starts at higher densities and happens more gradually for higher fields. The field-independent molecular breakup coefficient k_α=(3.54±0.28)×10⁻¹⁰ cm³/s was extracted from a global fit to all four data sets.

The plot in FIG. 1 shows the persistent-dimer rate Γ_p=Γ−Γ_w plotted vs. [G] for all four fields along with the respective best fits. The errors in the free parameters were, in general, underestimated by our non-linear fitting routines and had to be handled with some care. They were determined for a given field and temperature by allowing k_α to vary over its error range and observing the effect in the fit on 2K(M^sr+M^csa) and Γ_w.

TABLE I
Free parameters extracted from the fits of the data shown in FIG. 1 to
Eq. (5). Errors are given in parentheses for the least significant figure(s).
B0	2K(Msr + Mcsa)	Γw
(T)	(10−14 cm3/s2)	(10−6 s−1)
1.5	2.02(17)	18.5(9)
4.7	2.53(14)	4.1(5)
8.0	2.87(15)	3.70(8)
14.1	3.86(9)	1.60(19)

The effect of the CSA interaction is shown in FIG. 1 by the monotonic increase of the asymptotic high-density rate with increasing magnetic field. To determine the relative contributions of the SR and CSA interactions, the interaction-strength parameter 2K(M^sr+M^csa) is plotted vs. the square of the applied field B₀ in FIG. 2. FIG. 2 shows a plot of 2K(M^sr+M^csa) extracted from the fits in FIG. 1 (see Table I) vs. the square of the applied magnetic field B₀. A linear fit to the data yields the relative contributions of the SR and CSA interactions as a function of B₀, as given in Eqs. (9) and (10), where the intercept is proportional to the field-independent spin-rotation interaction strength M^sr, which can then be used to deduce the limiting low-field pure-xenon relaxation rate due to persistent dimers.

The data are consistent with a linear B₀² dependence. The slope and intercept from a linear least-squares fit yield, respectively,

2KM^csa[(8.26±0.73)×10⁻¹⁷ cm³/s²T²]B₀²,

2KM^sr=(2.24±0.10)×10⁻¹⁴ cm³/s².

The inset graph to FIG. 2 shows the fraction of the the total interaction strength that is due to the SR interaction as a function of B₀; the SR and CSA interactions contribute equally for B₀≈16.5 T. A correction to the empirical formula based on this result appears as a factor in the persistent-dimer term of the empirical formula in Eq.(3). Moudrakovski, et al. [13] made a similar measurement at very high xenon densities (>30 amagat), in the transient-dimer regime, and found that the SR and CSA interactions contribute equally for B₀=12 T. Although our measurement was made at much lower density in the persistent-dimer regime, there is no apparent reason that the relative strength of the two interactions should be different in the two cases.

The result in Eq. (10) can be used to calculate the density-independent persistent-dimer relaxation rate for pure xenon gas in the high-density low-field limit, where only the SR interaction contributes; this is almost always the relevant regime for SEOP. Here we follow the notation originally introduced by Chann, et al. [12] for this characteristic limiting rate:

${\Gamma }_{\mathrm{vdW}}^{\mathrm{Xe}}=\frac{2{\mathrm{KM}}^{\mathrm{sr}}}{k_{\mathrm{Xe}}}.$

We use the value of k_α in Eq. (8) and the value of the nitrogen breakup coefficient k_N=(1.9+0.2)×10⁻¹⁰ cm³/s measured in our previous work [9] in Eq. (6) to calculate k_Xe=(3.70+0.31)×10⁻¹⁰ cm³/s. This represents only a small correction to our value of k_α, since our samples are over 90% xenon. Finally, using Eqs. (10) and (11), we obtain

Γ_vdW^Xe=(6.05±0.57)×10⁻⁵ s⁻¹,

corresponding to a relaxation time of 4.59±0.43 h, which is the value that appears in the persistent-diener term of Eq. (3). This value is in good agreement with 4.1 h measured by Chann, et al. [12]. It is smaller than 5.45 h deduced from measurements in our previous work [9]; however, most of this discrepancy can be traced to using different data to calculate the relative contributions of the SR and CSA interactions to the total interaction strength. Some of our previous work was done at B₀=8.0 T, where we took the measured rate and divided it by the fraction of the interaction strength that is due to the SR interaction in order to obtain a value appropriate in the low-field limit. This fraction was determined from the measurements of Moudrakovski, et al. [13], to be 71% at 8.0 T. A similar calculation based on the data presented here [see Eqs. (9) and (10)] yields an 81% contribution for the SR interaction at 8.0 T, which would lower the relaxation time in our previous work [9] to 4.8 h, in much better agreement with the present result.

We performed a series of individual relaxation measurements in temperature range 20-100° C. at 8.0 T for [G]=0.35 amagat, well into the density-independent fast-fluctuation limit. Relaxation due to transient dimers is negligible for this low density, but the measured rates at all temperatures have been corrected by subtracting the room-temperature wall-relaxation rate at 8.0 T (see Table I). The higher-temperature points are likely over-corrected, since Γ_W should become smaller at higher temperatures due to decreasing residence time on the coating, assuming that this time is governed by an Arrhenius relationship [20]. However, the correction is small in any case, corresponding to a relaxation time of ≈75 h, so we use it as a best approximation at all temperatures.

FIG. 3 is a plot of the ¹²⁹Xe persistent-dimer relaxation rate Γ_p at 8.0 T vs. 1/T², where the absolute temperature T ranges between 293 K and 373 K. The measured rates were corrected by subtracting the relatively small room-temperature wall-relaxation rate Γ_w. The quality of the one-parameter fit forced through the origin indicates that this simple inverse-square model for the temperature dependence of Γ_p based on the arguments presented herein is reasonably valid at and above room temperature.

The corrected data are plotted in FIG. 3 vs. the inverse-squared absolute temperature. The one-parameter least-squares linear fit to this data (forced through the origin) supports the simple theory of a linear dependence of the persistent-dimer relaxation rate on 1/T², which comes from the temperature dependence of the product Kτ_p in the fast-fluctuation limit of Eq. (4). The slope of fitted line is 6.2±0.2 s⁻¹K² . The slope can be corrected for the low-field limit by multiplying by 81%, the fraction of the interaction strength due to SR at 8.0 T (see end of previous section and FIG. 1). Using the corrected slope to calculate Γ_p at T=293 K yields 5.85×10⁻⁵ s⁻¹, in good agreement with the minimum relaxation rate for pure xenon given in Eq. (12). We performed these measurements at 8.0 T to clearly separate Γ_p from any temperature-dependent wall relaxation, but the results should be equally valid in the low-field limit and contribute to longer overall relaxation times at higher temperatures. Based on these results, we include the factor of (T₀/T)² in the persistent-dimer term of Eq. (3), which predicts an intrinsic maximum T₁ for pure xenon of 7.45 h at T=100° C.

The extracted wall-relaxation rates Γ_w in Table I decrease dramatically with increasing applied field. At 14.1 T, in the low-density regime where the persistent-dimer rate is highly suppressed, we measured T₁=99.4 h for [G]=0.012 amagat. The wall-relaxation time extracted from the fit is an extraordinary 174 h.

FIG. 4 is a plot of NMR signal intensity vs. time for cell 113B at room temperature in an applied field of 14.1 T. The cell contains xenon at 12.0 mbar and nitrogen at 1.09 mbar. To our knowledge, this is by far the longest gas-phase relaxation time ever recorded for ¹²⁹Xe and results from the simultaneous suppression of the intrinsic persistent-dimer mechanism and the wall-relaxation mechanism at 14.1 T.

The plot of recorded NMR signal intensity vs. time in FIG. 4 and shows that the slope actually trends slightly downward over the course of this measurement, corresponding to T₁=105 h for the first 50 h and T₁=82 h for the last 45 h. This may have to do with a gradual increase in oxygen concentration (due to very slow outgassing or leakage) into the cell over the course of the long measurement. If this gradual increase in relaxation rate were due solely to collisions with paramagnetic oxygen atoms, it would correspond to an oxygen partial pressure of ≈10⁻³ mbar [34] developing over the course of the measurement.

FIG. 4: Plot of NMR signal intensity vs. time for cell 113B at room temperature in an applied field of 14.1 T. The cell contains xenon at 12.0 mbar and nitrogen at 1.09 mbar. To our knowledge, this is by far the longest gas-phase relaxation time ever recorded for ¹²⁹Xe and results from the simultaneous suppression of the intrinsic persistent-dimer mechanism and the wall-relaxation mechanism at 14.1 T.

FIG. 5 shows a plot of Γ_w vs. B₀ at room temperature. In an attempt to obtain a more complete picture of the field-dependence of Γ_w, data were acquired for three additional values of the applied field B₀ made in an electromagnet (0.91 T, and 2.0 T) and a Helmholtz pair (2.8 mT). For these three data points, Γ_w was not extracted from a fit. Instead, cell 113B was filled with nearly pure xenon (a from a flow-through xenon polarizer (built in our laboratory) to a density ≈1 amagat. In this density and magnetic-field regime, the persistent dimer rate Γ_p=Γ_vdW^Xe. According to Eq. (2), Γ_w was then determined by subtracting our deduced value of Γ_vdW^Xe in Eq. (12) from the measured rate for each of the three additional values of B₀.

Note that in FIG. 5 the points with small error bars are extracted from the density-dependence curves shown in FIG. 1; the weighted fit to Eq. (13) is almost entirely determined by these points. The other points result from single measurements on pure xenon in the fast-fluctuation limit, where the persistent dimer relaxation rate ⊖_vdW^Xe=(6.05±0.57)×10⁻⁵ s¹ has been subtracted from the measured relaxation rate. The error propagation from this subtraction leads to much larger error bars. The fit yields a correlation time for the wall interaction of ≈4 ns, consistent with interaction of ¹²⁹Xe with fluctuating paramagnetic sites on or in the wall coating.

We model the high-field wall relaxation as

${\Gamma }_w=M^w\left(\frac{{\tau }_c}{1+{\Omega }^2{\tau }_c^2}\right),$

where M^w is the strength of the wall interaction and τ_c^{31 1} is its correlation time, presumed to be due to fluctuating paramagnetic spins at the surface. This is a simplified version of the model proposed by Driehuys, et al. [20] based on the expected field dependence of the relaxation due to the coupling of the ¹²⁹Xe spin I with a wall spin S [35], which contains additional terms in the power spectrum of Eq. (13) involving the Larmor frequency of the spin S in addition to the ¹²⁹Xe Larmor frequency SZ. In the range of applied field B₀<10 mT studied in that work, Driehuys, et al. [20] were able to fit their relaxation data to a sum of two terms involving protons and paramagnetic sites, respectively, as the spin S . They determined that ¹²⁹Xe relaxes due to coupling with the protons in the surface coating with an associated correlation time τ_c≈8 μs. The proton-induced relaxation, which was directly verified with a double-resonance experiment, cannot be explained by a simple adsorption model; rather, xenon atoms must be trapped within the coating for times ≧8 μs. The second term yielded a much shorter correlation time τ_c≈8 ns, which is a reasonable relaxation time for paramagnetic surface spins at room temperature.

For the much larger applied fields in our work, the relaxation due to protons is completely suppressed. For relaxation due to paramagnetic sites, the terms in the power spectrum involving the paramagnetic resonance frequency are negligible, due to the ≈10³ larger gyromagnetic ratio for electrons compared to ¹²⁹Xe, leading to the simple form of Eq. (13). A least-squares fit of the data to this functional form is also shown in FIG. 4, and yields a correlation time τ_c≈4 ns (corresponding to a characteristic decoupling field ≈3 T), in reasonable agreement with the predicted correlation time for interaction with paramagnetic spins at the surface or inside of the coating.

To explore the implications of the above results for a practical low-field hyperpolarized-xenon storage cell at ambient pressures, additional experiments were done at B₀≈3 mT at both room temperature and T=100° C. Again, the flow-through xenon polarizer provided nearly pure xenon (α=1), and cells were filled to a density ≈1 amagat. We also used three additional alkali-metal-free coated cells. Two of these (designated 105B and 113A) were similar in size to cell 113B; the other was also similar except that its diameter (12.7 cm) is double that of the other cells. The cells all showed increases in the measured relaxation time T₁ of 50-100% at the elevated temperature. Our results are summarized in Table II, which displays measured relaxation times T₁ and the inferred wall-relaxation times based on subtracting from the measured rate both Γ_p and Γ_t (the latter is a 10% correction at most), as calculated from Eq. (3). It is difficult to extract precise information concerning wall-relaxation times, particularly at the elevated temperature, since Γ_p and Γ_w are comparable at these low fields (unlike at B₀=8.0 T) and both decrease with increasing temperature (see Sec. 4.3 above). However, it is clear that a significant improvement was realized for the cell with larger S/V; the measured T₁ in this cell of 5.75 h at T=100° C. approaches our predicted limit of 7.45 h and is a factor of two or more longer than any previously recorded ¹²⁹Xe relaxation time in the low magnetic fields typical of SEOP.

Table II shows low-field relaxation times (in hours) of four cells at both room temperature and 100° C. The first three have a diameter ≈6.7 cm and were measured at B₀=2.8 mT; the last cell has a diameter ≈12.7 cm and was measured at B₀=3.1 mT. The cells all contained pure xenon at the indicated density (in amagats). Uncertainties are given in parentheses for the least significant figure(s). The last two columns show the room-temperature wall-relaxation time derived from subtracting the relevant persistent- and transient-dimer rates [Eq. (3)] from the measured rate. The elevated temperature increases the measured T₁ by 50-100%.

TABLE II
		T1	T1	T1 (wall)	T1 (wall)
Cell	[Xe]	293 K	373 K	293 K	373 K
105B	1.5(1)	2.40(5)	3.66(11)	5.8(8)	8.7(1.1)
113A	≈1.5	1.30(4)	2.45(5)	1.9(1)	4.0(2)
113B	1.1(1)	2.57(15)	4.53(13)	6.6(1.3)	14.5(3.0)
139	0.7(1)	3.40(22)	5.75(23)	16(7)	35(18)

Even larger cells with a correspondingly larger xenon storage capacity are possible.

In some embodiments, the size will eventually be limited by magnetic field gradients far away from the center of a pair of Helmholtz coils, but this limit is not terribly stringent for xenon. As a guideline, we assume Helmholtz pair of radius (and separation) R and a cell having radius no larger than R/3 . We have estimated the gradient-induced relaxation for such a cell to be [36]

${\Gamma }_g\approx 0.01\frac{D}{R^2}.$

Although the calculation is done for an ideal Helmholtz geometry (actual gradients might be larger), the estimate in Eq. (14) applies only to the outer edge of a cell whose radius is as large as R/3, and so remains fairly conservative for the entire cell. For [Xe]=0.1 amagat at (a conservative estimate of the density during the filling process), D=8.2×10⁻⁵ m² /s at 100° C. [37]. If we take R=0.50 m, a 0.33 m diam spherical cell containing pure-xenon should have Γ_g⁻¹≧85 h from the gradient mechanism alone; this time would increase by an order of magnitude as the cell is filled to 1 amagat. Such a cell would have a 19 L storage capacity.

For completeness, we note that dilution of xenon with a second gas lowers the rate Γ_p significantly for those gasses that can form and break up persistent Xe₂ dimers with an efficiency comparable to Xe itself. Referring to Eq. (4), the second gas decreases the persistent-dimer lifetime τ_p without changing the fraction of xenon atoms bound in molecules. The effects of adding a second gas were studied thoroughly by Chann, et al.

[12] and in our previous work [9]. Nitrogen has the largest breakup coefficient measured (besides xenon); Γ_p is reduced by about one-third for a 50-50 mixture. We have included the effects of a second gas in our semi-empirical formula for the total intrinsic relaxation rate in Eq. (3).

In summary, we have presented a systematic study of both intrinsic persistent-dimer relaxation and wall relaxation of ¹²⁹Xe, including temperature and magnetic-field dependence; we conclude that it should be possible to develop a xenon storage cell that has a measured T₁≧7 h at 3.0 mT and 100° C. for pure xenon at densities up to a few amagats. These cells are silicone-coated but alkali-metal-free and show relatively long and robust wall-relaxation times of up to tens of hours. They can be utilized in state-of-the-art flow-through xenon polarizers, whereby storage times for polarized xenon can be increased by a factor of three or more compared with state-of-the-art cryogenic schemes, and cryogenic storage and associated freeze/thaw cycles can be eliminated. We note that if producing pure hyperpolarized xenon is required for a given experiment, then separation of xenon from other gasses in the mixture (which comes naturally with cryogenic accumulation) might be a limitation of the room-temperature accumulation scheme proposed here. One approach would be to use the cryogen for gas separation only, followed by immediate volatilization and transfer to a storage cell. However, other cryogen-free separation schemes are possible, as described below. The use of a small gas centrifuge (on the order of 0.1 m diam) has already been demonstrated for the continuous separation of methane from CO₂ on the time scale of minutes [38, 39]; such a device utilizing suitable materials and/or a surface coating that does not depolarize ¹²⁹Xe could presumably accomplish continuous separation of xenon from the other much lighter gasses typically found in a flow-through polarizer.

As noted above, non-cryogenic storage does not allow for easy separation of ¹²⁹Xe from other gasses through cryogenic solidification. However, Gas-centrifuge separation may be used in conjunction with a non-cryogenic storage cell to provide purification. This is a process where separation is brought about by rotating the gasses at high speed. Gasses with higher molecular weights are pushed to the walls of the centrifuge, while lighter gasses remain in the center. This is usually done in a continuous-flow mode. One typically flows the gas mixture through several centrifuge stages in order to achieve desired separation. Gas centrifuges have been used to separate uranium isotopes for use in nuclear fission [8A]. Such separations are time intensive because of the small mass separation between the two isotopes of uranium. Gasses with greater mass ratio separate more easily.

Centrifuge devices are most effective when using an axial countercurrent flow, whereby one gains both enhanced separation and shorter equilibrium times [9A]. We present a simple centrifuge model with no countercurrent flow for use in separating hyperpolarized Xe from buffer gasses. Systems using axial countercurrent flow would perform better than what is presented here. The radial partial pressures of gasses in a centrifuge are given by [10A]

p_i=p_i0e^Air2,

where p_i is the partial pressure of the i^th gas in the mixture, p_i0 is its pressure in the center of the centrifuge, r is the radial distance from the center, and

$A_i=\frac{M_i{\omega }^2}{2\mathrm{RT}},$

where M_i the molar mass of the i^th gas in the mixture, and ω is the angular speed of the centrifuge. It can be shown that the relationship between the center pressure and the partial pressure of the gas when not rotating is [10A]

$p_{0i}=\frac{A_iR^2}{{}^{A_iR^2}-1}p_{\mathrm{fi}},$

where R is the radius the centrifuge chamber.

Using these equations, we can determine the final gas fraction profiles for a given set of initial gas partial pressures. We apply this to a typical mixture of Xe in a flow-through polarizer. The simulated centrifuge was spinning at 5×10⁴ RPM and had a radius of 10 cm. We simulated removing the gas between 9 cm and 10 cm radius and injecting the mixture into another centrifuge stage with the same parameters. After a single stage, the Xe concentration is increased from 1% to about 3%. After three stages, the concentration increased to 27%, and after eight stages, the concentration has increased to 98%. FIG. 6 shows some of the resulting pressure profiles in stages of the centrifugation process. In particular, FIG. 6 shows the normalized gas pressure for 1 stage (A), 3 stages (B), 5 stage(C), and 8 stages (D) of centrifugation. The intial gas mixture is composed of 1% Xe, 10% N₂, and 89% He. Xe is in grey, N ₂ is in black, and He is in lighter grey.

In some embodiments, it is important to understand how long the gas mixture will spend in each stage of the centrifuge so that one can plan the volume of the stages and estimate losses in Xe polarization due to relaxation. The gas mixture will quickly gain angular momentum and establish a pressure gradient. Diffusion will then establish the equilibrium concentration profile.

The diffusion equation for the heavy gas in two-component system in a cylindrical centrifuge is given by [11A]

$\frac{\partial }{\partial t}\left(\frac{\mathrm{Px}}{\mathrm{RT}}\right)+\frac{1}{r}\frac{\partial }{\partial r}\left\{\frac{P}{\mathrm{RT}}D\left[\left(A_{\mathrm{heavy}}-A_{\mathrm{light}}\right)r^2x\left(1-x\right)-r\frac{\partial x}{\partial r}\right]\right\}=0.$

This is a nontrivial partial differential equation typically requiring numerical methods to approximate the solution. A simpler approach is to have the initial conditions be the known equilibrium profile of the rotating system and then use the non-rotating diffusion equation to determine the time it takes for the system to relax. It is reasonable to assume that these two processes take place on similar time scales.

The diffusion equation for a non-rotating system is

$\frac{\partial x}{\partial t}-D\left(\frac{{\partial }^2x}{\partial r^2}+\frac{1}{r}\frac{\partial x}{\partial r}\right)=0.$

Using Comsol FEMLAB 3.1 diffusion package, we started with the pressure profile given in Eq. 1a and allowed the system to relax to equilibrium. Xenon was taken to have a uniform concentration of 1% at equilibrium. FIG. 7 shows the time evolution of the concentration of Xe gas in a 10 cm radius cylinder at r=9.9 cm. The concentration profile in initially that of Xe in a centrifuge spinning at 50000 rpm. The system relaxes with a characteristic time on the order of ≈10 s and should be completely relaxed in ≈60 s, comparable with numerical simulations done on other gasses in similar centrifuge systems.

Centrifuge gas separation of hyperpolarized ¹²⁹Xe from flow-through systems is a feasible alternative to cryogenic separation. The above analysis indicates that one could reasonably enrich an initial 1% Xe mixture to >90% purity using 8 centrifuge stages in about 8 minutes. In order to realize a separator, one needs to find a material that is sufficiently strong to take the stress of high speed rotation and has long enough wall relaxation rates such that the polarized ¹²⁹Xe does not appreciably decay. Alternatively, a suitable high-strength material could be coated with a silane- or siloxane-based coating, such as those used with glass polarization cells [12A, 13A], or with some other suitable non-relaxivc coating.

A number of embodiments of the invention have been described. Nevertheless, it will be understood that various modifications may be made without departing from the spirit and scope of the invention. For example, although the storage cells described above are made of glass with an interior coating free of alkali-metals, any material may be used which is characterized in that the longitudinal spin relaxation rate of the gaseous spin polarized ¹²⁹Xe due to interactions with the interior surface (the wall rate) is about equal to or less than the longitudinal spin relaxation rate of the gaseous spin polarized ¹²⁹Xe due to intrinsic mechanisms. For example, plastic materials (e.g. fluoropolymer plastics) such as Teflon of UItem 1000 should have a wall rate comparable to or less than that of the coated glass surfaces used in the examples above.

Although devices described in the examples above operate at a defined temperatures (e.g. room temperature or 100° C.), other temperatures or temperature ranges may be used. As demonstrated in the examples above, feasible storage times increase with increasing temperature. Thus, in some embodiments, storage cells may be maintained at temperatures of, for example, a few hundred degrees centigrade or more to provide improved performance. In general, this operating temperature is limited only by the material properties (e.g. melting point) of the storage cell.

Although the devices described above feature storage cells with substantially spherical volumes, any other shape may be used.

Although the devices described above employ Helmholtz coils to provide a uniform magnetic field, it is to be understood that any other suitable magnet may be used (e.g. a solenoid, a permanent magnet, etc.). Although specific magnetic field strengths are described in the examples above, a field may be provided with any suitable strength, e.g. 3 mT or more, 100 mT or more, 1000 mT or more, etc. In general, increased field strength will improve the performance of the storage cell by decreasing the hyper-polarization relaxation rate.

Any of the techniques described above may be used in conjunction with known applications of hyperpolarized gasses, including but not limited to medical imaging (e.g. medical MRI).

In some embodiments storage cells of the type described above may be used in conjunction with a cryogenic apparatus used for separation of hyperpolarized xenon, but not for storage. For example, one could receive a polarized gas mixture in small batches, freeze it long enough to separate the xenon from the other gasses in the mixture (e.g., a minute or two), and then immediately volatilize it into a storage cell.

The devices and techniques described herein may be extended to the non-cryogenic storage of hyperpolarized materials other than 1²⁹Xe, e.g. any other material which experiences inhibited wall relaxation in an alkali free environment.

Additional discussion related to the devices and technique B.C. Anger, et al., Gas-phase spin relaxation of 129Xe, Phys. Rev. A 78 043406 (2008), which is incorporated by reference herein it its entirety.

Additional material is attached in an appendix and/or incorporated by reference. It is to be understood that in the case that any technical definitions presented in the main body of this application conflict with those presented in the appendix or incorporated references, the definition in the main body holds.

REFERENCES

[1] T. G. Walker and W. Happer, Rev. Mod. Phys. 69, 629 (1997).

[2] S. Appelt, A. Ben-Amar Baranga, C. J. Erickson, M. V. Romalis, A. R. Young, and W. Happer, Phys. Rev. A 58, 1412 (1998).

[3] B. Driehuys, J. Walker, J. Pollaro, G. P. Cofer, N. Mistry, D. Schwartz, and G. A. Johnson, Magn. Reson. Med. 58, 893 (2007).

[4] L. Schroder, T. J. Lowery, C. Hilty, D. E. Wemmer, and A. Pines, Science 314, 446 (2006).

[5] S. Pawsey, I. Moudrakovski, J. Ripmeester, L.-Q. Wang, G. J. Exarhos, J. L. C. Rowsell, O. M Yaqhi, J. Phys. Chem. C 111, 6060 (2007).

[6] W. Happer, Rev. Mod. Phys. 44, 169 (1972).

[7] E. Babcock, B. Chann, T. G. Walker, W. C. Chen, and T. R. Gentile, Phys. Rev. Lett. 96, 083003 {2006).

[8] E. Babcock, I. Nelson, S. Kadlecek, B. Driehuys, L. W. Anderson, F. W. Hersman, and T. G. Walker, Phys. Rev. Lett. 91, 123003 (2003).

[9] B. N. Berry-Pusey, B. C. Anger, G. Laicher, and B. Saam, Phys. Rev. A 74, 063408 (2006).

[10] G. D. Cates, S. R. Schaefer, and W. Happer, Phys. Rev. A 37, 2877 (1988).

[11] L. D. Shearer and G. K. Walters, Phys. Rev. 139, A1398 (1965).

[12] B. Charm, I. A. Nelson, L. W. Anderson, B. Driehuys, T.G. Walker, Phys. Rev. Lett. 88, 113201 (2002).

[13] I. L. Moudrakovski, S. R. Breeze, B. Simard, C. I. Ratcliffe, J. A. Ripmeester, T. Seideman, and J. S. Tse, J. Chem. Phys. 114, 2173 (2001).

[14] B. Driehuys, G. D. Cates, E. Miron, K. Sauer, D. K. Walter, and W. Happer, Appl. Phys. Lett. 69, 1668 (1996).

[15] I. C. Ruset, S. Ketel, F. W. Hersman, Phys. Rev. Lett. 96, 053002 (2006).

[16] X. Zeng, Z. Wu, T. Call, E. Miron, D. Schreiber, and W. Happer, Phys. Rev. A 31, 260 (1985).

[17] G. D. Cates, D. R. Benton, M. Gatzke, W. Happer, K. C. Hasson, and N. R. Newbury, Phys. Rev. Lett. 65, 2591 (1990).

[18] M. Gatzke, G. D. Cates, B. Driehuys, D. Fox, W. Happer, and B. Saam, Phys. Rev. Lett. 70, 690 (1993).

[19] N. N. Kuzma, D. Babich, and W. Happer, Phys. Rev. B 65, 134301 (2002).

[20] B. Driehuys, G. D. Cates, and W. Happer, Phys. Rev. Lett, 74, 4943 (1995).

[21] X. Zeng, E. Miron, W. A. van Wijngaarden, D. Schreiber, and W. Happer, Phys. Lett. 96A, 191 (1983).

[22] S. R. Breeze, S. Lang, I. Moudrakovski, C. I. Ratcliffe, J. A. Ripmeester, G. Santyr, B. Simard, and I. Zuger, J. Appl. Phys. 87, 8013 (2000).

[23] W. A. Fitzsimmons, L. L. Tankersley, and G. K. Walters, Phys. Rev. 179, 156 (1969).

[24] W. Heil, H. Humblot, E. Otten, M. Schafer, R. Surkau, and M. Leduc, Phys. Lett. A 201, 337 (1995).

[25] R. E. Jacob, S. W. Morgan, B. Saam, and J. C. Leawoods, Phys. Rev. Lett. 87, 143004 (2001).

[26] E. R. Hunt and H. Y. Can, Phys. Rev. 130, 2302 (1963).

[27] P. S. Hubbard, Phys. Rev. 131, 1155 (1963).

[28] H. M. McConnell and C.H. Holm, J. Chem. Phys. 25, 1289 (1956).

[29] H. W. Spiess, D. Schweizer, U. Haeberlen, and K. H. Hausser, J. Magn. Reson. 5, 101 (1971).

[30] F. Reif, Fundamentals of Statistical and Thermal Physics (McGraw-Hill, N.Y., 1965).

[31] M. Hanni, P. Lantto, N. Runeberg, J. Jokisaari, and J. Vaara, J. Chem. Phys. 121, 5908 (2004).

[32] R. E. Jacob, S. W. Morgan, and B. Saam, J. Appl. Phys. 92, 1588 (2002).

[33] B. Saam and M. S. Conradi, J. Magn. Reson. 134, 67 (1998).

[34] C. J. Jameson, A. K. Jameson, and J. K. Hwang, J. Chem. Phys 89, 4074 (1988).

[35] A. Abragam, Principles of Nuclear Magnetism (Oxford Science Publications, New York, N.Y., 1961).

[36] See EPAPS Document No. TBD for a discussion of gradient-induced relaxation in a Helmholtz-coil geometry. For more information on EPAPS, see http://www.aip.org/pubservs/epaps.html.

[37] J. Kestin, K. Knierim, E. A. Mason, B. Najafi, S. T. Ro, and M. Waldman, J. Phys. Chem. Ref Data 13, 229 (1984).

[38] R. van Wissen, M. Golombok and J. J. H. Brouwers, Chem. Eng. Sci. 60, 4397 (2005).

[39] M. Golombok and L. Chewter, Ind. Eng. Chem. Res. 43, 1743 (2004).

[1A] Li-Qoing Wang, Yongsoon Shin, W. D. Samuels, Gregory J. Exarhos, I. L Moudrakovksi, V. V. Terskikh, and Ripmeester. Magnetic resonance studies of hierarchically ordered replicas of wood cellular structures prepared by surfactant-mediated mineralization. J. Phys. Chem. B, 107(50):13793-13802, 2003.

[2A] Thomas J. Lowery, Seth M. Rubin, E. Janette Ruiz, Megan M. Spence, Nicolas Winssinger, Peter G. Schultz, Alexander Pines, and David E. Wemmer. Applications of laser-polarized ¹²⁹Xe to biomolecular assays. Mag. Res. Imag., 21:1235-1239, 2003.

[3A] R. W Mair, M. I. Hrovat, S. Patz, M. S. Rosen, I. C. Ruset, G. P. Tupulos, L. L. Tsai, J. P. Butler, F. W. Hersman, and R. L. Walsworth. ₃ He lung imaging in an open access, very-low-field human magnetic resonance imaging system. Mag. Res. Med., 53:745-749, 2005.

[4A] B. Driehuys, G. D. Cates, E. Miron, K. Sauer, D. K. Walter, and W. Happer. High-volume production of laser-polarized ¹²⁹Xe. Appl. Phys. Lett., 69:1668-1670, 1996.

[5A] I. C. Ruset, S. Ketel, and F. W. Hersman. Optical Pumping System Design for Large Production of Hyperpolarized ¹²⁹Xe. Phys. Rev. Lett., 96: 053002, 2006.

[6A] F. W. Hersman. Xemed webpage. http://xemedllc.com/.

[7A] N. N. Kuzma, B. Patton, K. Raman, and W. Happer. Fast nuclear spin relaxation in hyperpolarized solid ¹²⁹ xe. Phys. Rev. Lett., 88(14):147602, March 2002.

[8A] W. E. Groth, Konrad Beyerle, Erich Nann, and K. H. Welge. Enrichment of uranium isotopes by the gas centrifuge method. In Peaceful Uses of Atomic Energy, page 439, 1958.

[9A] Ralph van Wissen, Micheal Golmbok, and J. J. H. Brouwers. Separation of carbon dioxide and methan in continuous contercurrent gas centrifuges. Chem. Eng. Sci., 60:4397-4407, 2005.

[10A] Michael Golombok and Les Chewter. Centrfugal separation for cleaning well gas streams. Ind. Eng. Chem. Res., 43:1743-1739, 2004.

[11A] Steven R. Auvil and Bruce W. Wilkinson. The steady and unsteady state analysis of a simple gas centrifuge. AIChE J., 22(3):564-568, 1976.

[12A] X. Zeng, Z. Wu, T. Call, E. Miron, D. Schreiber, and W. Happer. Experimental determination of the rate constants for spin exchange between optically pumped K, Rb, and Cs atoms and ¹²⁹Xe nuclei in alkali-metal-noble-gas van der Waals molecules. Phys. Rev. A, 31: 260-278, 1985.

[13A] B. Driehuys, G. D. Cates, and W. Happer. Surface Relaxation Mechanisms of Laser-Polarized ¹²⁹Xe. Phys. Rev. Lett, 74:4943-4946, 1995.

Claims

1. A storage apparatus for non-cryogenically storing gaseous spin polarized by 129Xe comprising:

a storage vessel comprising an interior surface substantially surround a storage volume; and

a magnet which produces a substantially uniform magnetic field within the storage volume;

wherein the longitudinal spin relaxation rate of gaseous spin polarized 129Xe contained in the storage volume due to interactions with the interior surface is about equal to or less than the longitudinal spin relaxation rate of the gaseous spin polarized 129Xe due to intrinsic mechanisms.

2-25. (canceled)