Non-cryogenic storage cell for hyperpolarized ¹²⁹ Xe

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.

CROSS REFERENCE TO RELATED APPLICATIONS

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

BACKGROUND

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

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 (D ₁ ) 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 angulai momentum between the alkali-metal electron and the noble-gas nucleus The time-dependent build-up of nuclear polarization P _N (I) in such a sample that occurs while the laser is on is given by

where (P _A ) is the time- and volume-averaged alkali-metal polarization, γ _se is the spin- exchange rate, and F 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 F is thus essential to the efficient production of hyperpolaπzed gasses Note,

While SEOP is typically used to polarize either of the stable spin- 1/2 noble-gas isotopes, ³ He and ¹²⁹ Xe, the examples presented below will deal specifically with the relaxation mechanisms that limit the polarization of ¹²⁹ Xe The relaxation rate F may be written [9]

γ = γ _/ +γ _/ , +γ, +γ _W ,

where F ₁ = F, + F is the mtπnsic rate due to the sum of contributions from transient and persistent Xe ₂ dimers, and F _e = F + F _w is the extπnsic rate due to the sum of contπbutions 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 T and T _w dominates the relaxation Foi xenon densities as low as 0 1 amagat, T is usually negligible [9], although there is size limitation for hyperpolaπzed- xenon storage cells m a given Helmholtz geometry due to this mechamsm (see Sec 4 5) For xenon densities « 1 amagat and larger, T ₁ 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-empiπcal formula for the intrinsic relaxation rate T ₁ of ¹²⁹ Xe as a function of xenon density [Xe] (amagats), temperature T (Kelvin), applied magnetic field B ₀ (Tesla), and gas composition This formula applies for [Xe] > 0 3 amagat at all reasonable values of B ₀

where the first term is due to persistent dimers and the second is due to transient dimers, T ₀ = 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 m Eq (3) is based on the results of Moudrakovski, et al [13], we have estimated its temperature dependence by consideπng that, in the weak-mteraction 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 T ₁ oc l/v , where v ∞ T ¹¹² is the mean thermal velocity of the xenon atoms The uncertainty m the relaxation time calculated from Eq (3) is about 10%

Longitudinal relaxation also plays a key role m 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 ¹²⁹ Xe, a relatively long longitudinal relaxation time Tj ≡ T ' 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 ¹²⁹ Xe for any application In these devices, a gas mixture lean m xenon is passed continuously through a glass cell, in which it is polaπzed by SEOP with a laser, and subsequently frozen as a polycrystalline solid at 77 K m a liquid-nitrogen trap This basic scheme has proven effective m dealing with the inherently low (7%) Rb-Xe spm-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, ¹²⁹ Xe (unlike ³ He) is not readily polaπzed 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 hyperpolaπzed xenon can be accumulated from the low-density flow and stored for times on the order of T _x « 2 5 h at 77 K in an applied magnetic field B ₀ ≥ 0 1 T [18] before being revolatihzed This method evolved, in part, because of the reliable 2 5 h storage time, although it became clear m 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 m the solid [19], resulting m polarization losses m the freeze/thaw cycle

Hyperpolaπzed ^l29 Xe is now used for research variety of disciplines such as medical imaging, biological assays, and pore characterization [IA, 2A, 3A] Many of these experiments require on-demand production of large (hter-per-hour and more) quantities of hyperpolarized ¹²⁹ Xe The state-of-the-art method for such production is the flow-through polanzer/accumulator [4 A, 5A] One manufacturer claims the ability to produce 10 L/h of hyperpolaπzed 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 m the mixtuie Xenon freezes out of the gas stream as a polycrystalline solid and deposits in some holding cell, the hyperpolanzation 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 revolatihzed 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 expeπments to have the ability to separate the Xe continuously, so that a steady stream of pure hyperpolarized Xe could be directed to an expeπment or application Further disadvantantages of cryo separation are discussed below

SUMMARY OF THE INVENTION

Techniques are described for storing large quantities of hyperpolarized (HP) ¹²⁹ Xe 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 ¹²⁹ Xe nuclei The cell contains no alkali- metal The cell sits in a modest magnetic field (about 3 millitesla) generated by a Helmholtz coil parr The cell is designed to receive HP xenon gas from a current state-of-the-art device, a ¹²⁹ Xe 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 ¹²⁹ Xe m the gas phase The inventors have developed a thorough understanding of gas-phase relaxation of ¹²⁹ Xe nuclei m 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 spheπcal cells have slower relaxation rates Cells may be produced m 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 ^" Xe 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 characteπzed in that

the longitudinal spin relaxation rate of the gaseous spin polarized ¹²⁹ Xe due to interactions with the interior surface is about equal to or less than the longitudinal spin relaxation rate of the gaseous spin polaπzed ¹²⁹ Xe 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 inteπor surface consists of a layer of mateπal 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 mateπal and the interior surface consists of the plastic mateπal 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 ' In some embodiments, ratio of the area of the inteπor surface to the storage volume is less than about 0 5 cm '

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 polaπzed ¹²⁹ Xe of greater than about five hours, the relaxation tune corresponding to a density of the spin polanzed ¹²⁹ Xe of greater than about one amagat

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

hi another aspect, a system is disclosed for producing and storing gaseous spin polaπzed ¹²⁹ Xe including a polarizer configured to produce gaseous spin polarized ¹²⁹ Xe, and a storage apparatus for non-cryogemcally stoπng gaseous spin polarized ¹²⁹ Xe as

descπbed above The storage apparatus is in communication with the polarizer to receive and store the spin polarized ¹²⁹ Xe

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

Some embodiments include a gas centrifuge separator The separator is m communication with the polaπzer to receive a mixture of gaseous spin polaπzed ¹²⁹ Xe and other gasses from the polaπzer The separator is configured to separate substantially pure gaseous spin polaπzed ¹²⁹ Xe from the mixture The storage apparatus is in communication with the separator to receive and store the substantially pure gaseous spin polaπzed ^P9 Xe

hi some embodiments, the substantially pure gaseous spin polaπzed ¹²⁹ Xe is at least about 90% pure In some embodiments, the substantially puie gaseous spin polaπzed ' ²⁹ Xe is substantially free of alkali-metal

In another aspect, a method of non-cryogenically storing gaseous spin polaπzed

¹²⁹ Xe 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 ¹²⁹ Xe into the storage volume The interior surface is characteπzed in that the longitudinal spin relaxation rate of the gaseous spin polarized ¹²⁹ Xe due to interactions with the interior surface is about equal to or less than the longitudinal spin relaxation rate of the gaseous spm polaπzed ¹²⁹ Xe 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

hi some embodiments, introducing gaseous spin polaπzed ¹²⁹ Xe into the storage volume includes polarizing gaseous ¹²⁹ Xe m a polaπzer to produce gaseous spin polaπzed ¹²⁹ Xe and transferring the gaseous spin polaπzed ¹²⁹ Xe to the storage vessel

In some embodiments, transferπng the gaseous spm polaπzed ¹²⁹ Xe to the storage vessel includes passing a mixture of gaseous spm polarized ¹²⁹ Xe through one or more gas

centrifuge separators to produce substantially pure gaseous spin polarized ¹²⁹ Xe, and introducing the substantially pure gaseous spin polaπzed ¹²⁹ Xe 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 descπbed features, either alone or m combination

BRIEF DESCRIPTION OF THE DRAWINGS

Fig IA is a schematic of a cell for non-cryogenic storage of gaseous spin polaπzed ¹²⁹ Xe

Fig IB a schematic of a system for producing and stoπng gaseous spin polarized ¹²⁹ Xe

Fig 1C is a flow diagram of a process for producing and storing gaseous spm polaπzed ¹²⁹ Xe

Fig l 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 B ₀

Fig 3 is a plot of the ¹²⁹ Xe persistent-dimer relaxation rate F ₀ at 8 0 T vs I /T ²

Fig 4 is a plot of NMR signal mtensity vs time for cell 113B at room temperature in an applied field of 14 I T

Fig 5 shows a plot of T _w vs B ₀ at room temperature

Fig 6 shows pressure profiles m stages of the centπfugation process, for 1 stage (A), 3 stages (B), 5 stage(C), and 8 stages (D) of centπfugation

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 IA shows a storage cell 100 or non-cryogemcally storing gaseous spin polarized ^l29 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 m the Helmholtz configuration, dπven by power source 110 hi other embodiments, and suitable type of magnet may be used including e g a permanent magnet or an electromagnet m another configuration (e g a solenoid surrounding all or a portion of vessel 102) hi some embodiments, the substantially uniform magnetic field withm the storage volume has a magnitude of about 3 milliTesla or less, or about 1 milliTesla or less

As described m detail below, interior surface 104 is made of a material which inhibits longitudinal spm relaxation caused by mteractions (e g collisions) between the ¹²⁹ Xe and the surface For example, m some embodiments, surface 104 is characterized in that the longitudinal spin relaxation rate of the gaseous spin polarized ¹²⁹ Xe 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 ¹²⁹ Xe due to intrinsic mechamsms

In some such embodiments, the interior surface 104 is wholly or partially made up of material which is substantially free of alkali-metal For examplethe vessel 102 may be made of glass, and the interior surface 104 may be mateπal layer on the glass In some embodiments, the mateπal 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 mateπal (e g Teflon) and the mteπor surface 104 consists of this plastic mateπal (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 1 12 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 1 OO 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 descπbed m 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 ', less than about 0 5 cm ', or even less Figs 8a through 8g show exemplary vessels having various dimensions

Cell 100 can be used for long term, non-cryogemc storage of gaseous spin polaπzed 1 ²⁹ Xe As describe in detail below, the use of an alkali free interior surface and applied the magnetic field reduces extπnsic relaxation, and allows for long storage times For example, m some embodiments, the storage vessel is characterized by a relaxation time for the gaseous spin polaπzed ¹²⁹ Xe 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 IB, a system 200 may be used for producing and storing gaseous spin polaπzed ¹²⁹ Xe System 200 includes a polarizer 202 which operates on gas mix 203 to produce gaseous spin polarized ¹²⁹ Xe In some embodiments, the polaπzer 202 is a spin exchange optical pumping polaπzer, e g of the type descπbed m detail below

Spin polarized ¹²⁹ Xe is transferred from the polaπzer to a storage cell 100 of the type descπbed 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 ¹²⁹ Xe The polaπzer 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 ¹²⁹ Xe received from the polaπzer m a substantially alkali-metal free environment Any suitable system, e g system of valves and transfer chambers, may be employed to transfer the spin polaπzed ¹²⁹ Xe from the polanzer 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 m communication with the polarizer 202 to receive a mixture of gaseous spin polaπzed ¹²⁹ Xe and other gasses from the polaπzer 202 The separator 204 separates substantially pure gaseous spin polaπzed ¹²⁹ Xe from the mixture As descπbed m detail below, the separator 204 may operate to effect the separation without substantially

reducing the spin polarization of the polarized ¹²⁹ Xe For example, in some embodiments, the separator 204 may be constructed with substantially alkali-metal free inner surfaces to reduce extπnsic relaxation resulting from collisions of the gas with these surfaces

The storage cell 100 is m communication with the separator 202 to receive and store the substantially pure gaseous spin polaπzed ¹²⁹ Xe For example, the substantially pure gaseous spin polarized ¹²⁹ Xe 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 ' ²⁹ Xe transferred to cell 100 is substantially free of alkali-metal

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

Accumulation and storage of hyperpolanzed 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 histoπcal problem with this approach has been that ¹²⁹ Xe gas-phase relaxation is relatively fast and notoriously irreproducible, whereby wall relaxation plays a crucial role Some progress was made m understanding wall interactions, particularly m cells treated with silane- or siloxane-based surface coatings m fields on the order of 1 mT [20, 21], where T _x = 20 -60 mm was observed Others observed T ₁ > 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 m common relatively small cells (1 -3 cm dia ) that contained macroscopic amounts of rubidium along with the coating, meaning that the gas was polaπzed by SEOP m the same cell m which T ₁ was subsequently measured While it is well known that He relaxation on uncoated glass is reliably suppressed by the presence of alkali metal [23, 24, 25], this is apparently not the case for ¹²⁹ Xe, where m fact, the

interaction of the alkali metal with the surface coating, particularly when heated to 100 ⁰ 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, m the regime for which the wall contπbution to T ₁ 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 SIV Accordingly larger-diameter coated cells containing no alkali metal may be used as a way of reducing the ¹²⁹ Xe gas-phase wall- relaxation rate

Gas-phase ¹²⁹ Xe relaxation due to persistent Xe ₂ dimers has been shown[12] These van der Waals molecules are formed m three-body collisions and have a mean lifetime r _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 B ₀ (a few millitesla) The density mdependence arises both because the fraction of xenon atoms bound m molecules and the molecular formation/breakup rate r ^~ ' have the same linear dependence on [Xe], and because the fast- fluctuation limit ω ^' -T _p « 1 , where ω is the ¹²⁹ Xe Larmor frequency, holds for all reasonable values of [Xe] and B ₀ < 1 T, see Eq (4) below This density independence effectively mimics wall relaxation, and it has undoubtedly confounded some earlier work m measuring T _w , particularly smce the the minimum intrinsic rate T is much larger than previously believed [13, 26] We have veπfied and extended this work at low [Xe] and B ₀ = 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 T _x 's exceeding 25 h m some cases

Increased understanding of gas-phase relaxation of ¹²⁹ Xe allowns for significant improvements m cell performance vis-a-vis hyperpolanzed 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 hyperpolaπzed xenon with a T _x ≥ 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 mam parts descπned herein

(1) The study of the magnetic suppression of the persistent-dimer mechanism in a range of magnetic fields from 1 5 T to l4 1 T This data allowed us to deduce the relative strength of the spin-rotation (SR) and chemical-shift-amsotropy (CSA) interactions via the

B ₀ -dependence of the CSA contπbution This, m turn, generates an independent estimate for the maximum low-field pure-xenon relaxation time of T _x = 4 6 h

(2) The study of wall relaxation over the same range of B ₀ 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 m our alkali-metal-free coated cells vaπed 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 ¹²⁹ Xe 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 F m the fast-fluctuation limit m the range of 20-100 ⁰ C The mverse-square dependence of T 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 ⁰ C compared to room temperature

Intrinsic longitudinal relaxation of ¹²⁹ Xe 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 Xe ₂ dimers in three-body collisions The theory is discussed in detail m Refs [9, 12] In brief, the persistent-dimer relaxation rate is given by

r = (2K[Xe])(M ^sr + M ^c c ^s s ^a a

where K ≡ [Xe, ]/[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 ^~] is the molecular formation rate (equal to the breakup rate in chemical and thermal equilibrium) This equation can be reparameteπzed and added to the wall relaxation rate T _w to obtam for the total relaxation rate

r([G]) = r _w +2K(M ^sr +M- χ _; , c ^t k " _a [G ^J ? j,

where [G] is the total gas density, a ≡ [Xe]/[G] is the xenon concentration, and k _a is the molecular breakup coefficient for the particular gas composition In this work, nitrogen is the only other gas m the mixture, and

— = MG] = * _Xe [Xe] + fc _N [N, ], r

where k _Xe and & _N are the breakup coefficients for xenon and nitrogen as third bodies, respectively

At high gas densities, in the fast-fluctuation limit ω ² « £ ² [G] ² of Eq (5), the persistent-dimer relaxation rate is independent of [G] for a given gas composition, as first observed by Charm, et al [12] for B ₀ = 2 0 mT and also by our group for B ₀ = 8 0 T [9] At lower densities the rate is suppressed due to the increasing relevance of the ω ^" term m Eq (5) Whereas M ^sτ is independent of the applied field i? ₀ [27], M ^csa is proportional to

B ₀ 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 B ₀ , allows M ^sr to be separated from M ^csa

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

l yiπμkτ)

where h is the Planck constant, k is the Boltzmann constant, Z = /J (2N ₁ + l)e ' is the partition function for the internal ro-vibrational states of the Xe ₂ 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 > EJk ~ 280 K [31] Classically, r is inversely proportional to the mean relative velocity of the gas molecules, which is proportional to T ^xa We treat here only the fast-fluctuation limit, ω ² τ ² « 1 , relevant to high-density xenon storage cells m small magnetic fields Since the product Kr appears in this limit, we expect the relaxation rate T to depend on T ^" 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 desciibed here are i elated to those described m detail in our previous work [9] Some of the measurements of the longitudinal relaxation time T ₁ for ¹²⁹ Xe m xenon gas were done m a single borosilicate-glass (Pyrex) "measurement" cell, designated 113B shown m 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 m a manner similar to silicone coatings previously introduced [20, 21]

Hyperpolaπzed xenon was generated m 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-handlmg 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, NJ) and nitrogen Unless otherwise noted, the xenon concentration α = 0 91 ± 0 02 throughout this work, where the error reflects variation m multiple preparations of the mixture m 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 % m a pumping cell was then transferred (at the known value of a ) to the measurement cell usmg 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 mto the magnet In the case of the 4 7 T and 14 1 T fields, the polaπzed 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 duπng 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 ¹²⁹ Xe 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 Vaπan

Infimtyplus 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 ( B ₀ « 3 mT) measurements were made using a homebuilt low-frequency spectrometer [33], whereby the cell and NMR probe were placed m a oven (similarly heated with flowing hot air) located at the isocenter of a Helmholtz pair

In all cases the longitudinal relaxation rate F was measured by periodic acquisition of a free-induction decay (FED) 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-transformed FID was plotted as a function of time and a least-squares fit was used to extract T

The relaxation rate T was measured as a function of total gas density [G] for the four different magnetic fields The data were fit m each case to Eq (5) using the appropriate

value of the Larmor frequency ω , with the wall-relaxation rate T _w and the interaction- strength term 2K(M ^sr + M ^csa ) extracted as free parameters, see Table 1 Since the xenon concentration a and, hence, the breakup coefficient k _a are field-mdependent, the value

k _a = (3 54 + 0 28) ^χ l(T ^lu cm Vs,

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 ' ²⁹ Xe persistent-dimer relaxation rate vs total gas density for a fixed xenon concentration a = 0 912 at four different applied magnetic fields The wall relaxation rate T _w and the product 2K(M ^sr + λ/ ^csa ) are extracted from fits of the measured relaxation rates F([G]) to Eq (5) for each field (see Table 1) The corresponding value of T _w has been subtracted from all the data sets in this plot to show clearly the behavior of the persistent-dimer rate T The high-density fast- fluctuation limit results m 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 _a = (3 54 ± 0 28) x l O ^~10 cm ³ /s was extracted from a global fit to all four data sets

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

Table I Free parameters extracted from the fits of the data shown in Fig 1 to Eq (5) Errors are given m parentheses for the least significant figure(s)

The effect of the CSA interaction is shown in Fig 1 by the monotomc 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 B ₀ m Fig 2 Fig 2 shows a plot of 2K(M ^sr + M ^csa ) extracted from the fits m Fig 1 (see Table I) vs the square of the applied magnetic field B ₀ A linear fit to the data yields the relative contributions of the SR and CSA interactions as a function of B ₀ , 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 B ₀ dependence The slope and intercept from a linear least-squares fit yield, respectively,

2KM ^csa = [(8 26 + 0 73) x lθ ^~17 CmVs ² T ² ]s ² ,

2KM ^sr = (2 24 ± 0 10) x l0 ^"14 cm ³ /s ²

The mset graph to Fig 2 shows the fraction of the the total interaction strength that is due to the SR interaction as a function of B ₀ , the SR and CSA interactions contribute equally for 5 ₀ « 16 5 T A correction to the empincal 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), m the transient- dimer regime, and found that the SR and CSA interactions contπbute equally for B _ϋ = 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 m 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 Charm, et al [12] for this characteristic limiting rate

We use the value of k _a m Eq (8) and the value of the nitrogen breakup coefficient k _N = (1 9 + 0 2) x l0 ^~10 cm ³ /s measured in our previous work [9] m Eq (6) to calculate k _Xe = (3 70 ± 0 31) x 10 ^~ '° cm ³ /s This represents only a small correction to our value of k _a , since our samples are over 90% xenon Finally, using Eqs (10) and (1 1 ), we obtain

r _v ^x / _w = (6 05 ± 0 57) x l0- ⁵ sλ

corresponding to a relaxation time of 4 59 ± 0 43 h, which is the value that appears m the persistent-dimer term of Eq (3) This value is m good agreement with 4 1 h measured by

Chann, et al [12] It is smaller than 5 45 h deduced from measurements m 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 B ₀ = 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 m order to obtain a value appropriate m 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% contπbution 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 seπes of individual relaxation measurements m temperature range 20- 100 ⁰ 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, smce T _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 w 75 h, so we use it as a best approximation at all temperatures

Fig 3 is a plot of the ¹²⁹ Xe persistent-dimer relaxation rate Y _p at 8 0 T vs MT ² , 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 T _w The quality of the one-parameter fit forced through the ongm indicates that this simple inverse- square model for the temperature dependence of T based on the arguments presented herein is reasonably valid at and above room temperature

The corrected data are plotted m Fig 3 vs the inverse-squared absolute temperature The one-parameter least-squares linear fit to this data (forced through the oπgin) supports the simple theory of a linear dependence of the persistent-dimer relaxation rate on l/T ² , which comes from the temperature dependence of the product Kr _p in the fast-fluctuation limit of Eq (4) The slope of fitted line is 6 2 ± 0 2 s ^~ ' K ² 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 F at T = 293 K yields 5 85 x lO ^~5 s ^" ' , m good agreement with the minimum relaxation rate for pure xenon given m Eq (12) We performed these measurements at 8 0 T to clearly separate T from any temperature-dependent wall relaxation, but the results should be equally valid m the low-field limit and contnbute to longer overall relaxation times at higher temperatures Based on these results, we mclude the factor of (T ₀ IT ) ² m the persistent- dimer term of Eq (3), which predicts an intrinsic maximum T _x for pure xenon of 7 45 h at T = I OO ⁰ C

The extracted wall-relaxation rates T _w m 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 T _x = 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 m 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 ¹⁷⁹ Xe 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 m Fig 4 and shows that the slope actually trends slightly downward over the course of this measurement, corresponding to

T _x = 105 h for the first 50 h and T _x - 82 h for the last 45 h This may have to do with a gradual increase in oxygen concentration (due to very slow outgassmg or leakage) into the cell over the course of the long measurement If this gi adual 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] developmg 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 ¹²⁹ Xe 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 T _w vs B ₀ at room temperature In an attempt to obtain a more complete picture of the field-dependence of T _w , data were acquired for three additional values of the applied field B ₀ made m an electromagnet (0 91 T, and 2 0 T) and a Helmholtz pair (2 8 mT) For these three data points, T _w was not extracted from a fit Instead, cell 113B was filled with nearly pure xenon (a « 1 ) 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 F = T^ _w According to Eq (2), T _w was then determined by subtracting our deduced value of T^ _w m Eq (12) from the measured iate for each of the three additional values of B ₀

Note that in Fig 5 the points with small error bars are extracted from the density- dependence curves shown m 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 (6 05 + 0 57) x lO ^~5 s ' 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 ¹²⁹ Xe with fluctuating paramagnetic sites on or in the wall coating

We model the high-field wall relaxation as

where M ^w is the strength of the wall interaction and r _c ' 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 Dπehuys, et al [20] based on the expected field dependence of the relaxation due to the coupling of the ¹²⁹ Xe spin / 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 m addition to the ¹²⁹ Xe Larmor frequency ω In the range of applied field B ₀ < 10 mT studied m that work, Dπehuys, 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 £ They determined that ¹²⁹ Xe relaxes due to couplmg with the protons m the surface coating with an associated correlation time τ _c « 8 μ s The proton-mduced relaxation, which was directly verified with a double-resonance expeπment, cannot be explained by a simple adsorption model, rather, xenon atoms must be trapped within the coating for times > 8 μ s 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 m 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 « 10 ³ larger gyromagnetic ratio for electrons compared to ¹²⁹ Xe, leading to the simple form of Eq (13) A least-squares fit of the data to this functional form is also shown m 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 hyperpolaπzed- xenon storage cell at ambient pressures, additional experiments were done at B ₀ « 3 mT at both room temperature and T = IOO ⁰ C Again, the flow-through xenon polaπzer provided nearly pure xenon (a — I ), 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 m 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 m the measured relaxation time T _x of 50-100% at the elevated temperature Our results are summarized in

Table II, which displays measured relaxation times T _x and the inferred wall-relaxation tunes based on subtracting from the measured rate both T and T ₁ (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 T and T _w are comparable at these low fields (unlike at B ₀ = 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 SIV , the measured T _x in this cell of 5 75 h at T = 100 ⁰ C

approaches our predicted limit of 7.45 h and is a factor of two or more longer than any previously recorded ¹²⁹ Xe 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 ⁰ C. The first three have a diameter « 6.7 cm and were measured at B ₀ = 2.8 mT; the last cell has a diameter « 12.7 cm and was measured at 5 ₀ = 3.1 niT.

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 T _x by 50-100%.

Table II

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]

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 x 10 ^~5 m ² /s at 100 ⁰ C [37]. If we take R = 0.50 m, a 0.33 m diam spherical cell containing pure-xenon should have F ^~ > 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 r significantly for those gasses that can form and break up persistent Xe ₂ dimers with an efficiency comparable to Xe itself. Referring to Eq. (4), the second gas decreases the persistent-dimer lifetime τ without changing the fraction of xenon atoms bound in molecules. The effects of adding a second gas were studied thoroughly by Charm, et al. [12] and in our previous work [9]. Nitrogen has the largest breakup coefficient measured (besides xenon); T 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 ' ²⁹ Xe, including temperature and magnetic-field dependence; we conclude that it should be possible to develop a xenon storage cell that has a measured T ₁ ≥ 7 h at 3.0 mT and 100 ⁰ 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 descπbed 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 CO ₂ on the time scale of minutes [38, 39], such a device utilizing suitable materials and/or a surface coating that does not depolaπze ¹²⁹ Xe could presumably accomplish continuous separation of xenon from the other much lighter gasses typically found m a flow-through polarizer

As noted above, non-cryogenic storage does not allow for easy separation of ¹²⁹ Xe from other gasses through cryogenic solidification However, Gas-centrifuge separation may be used m 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 m the center This is usually done in a continuous-flow mode One typically flows the gas mixture through several centrifuge stages m order to achieve desired separation Gas centrifuges have been used to separate uramum isotopes for use m 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 gams both enhanced separation and shorter equilibrium times [9A] We present a simple centrifuge model with no countercurrent flow for use in separating hyperpolaπzed 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 ₁ = P,o ^e ' > where p _: is the partial pressure of the ι ^Ul gas m the mixture, p _ι0 is its pressure in the center of the centrifuge, r is the radial distance from the center, and

M ω ²

A =

2RT where M ₁ is the molar mass of the i ^ϋ> gas in the mixture, and CO 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]

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 x lO ⁴ 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% N , , 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 [1 IA]

This is a nontπvial partial differential equation typically requiring numeπcal 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-rotatmg 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-rotatmg system is

Using Comsol FEMLAB 3 1 diffusion package, we started with the pressure profile given in Eq Ia 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 m a 10 cm radius cylinder at r = 9 9 cm The concentration profile m initially that of Xe in a centrifuge spinning at 50000 rpm The system relaxes with a characteπstic time on the order of ~ 10 s and should be completely relaxed in « 60 s, comparable with numerical simulations done on other gasses m similar centrifuge systems

Centrifuge gas separation of hyperpolaπzed ' ²⁹ Xe from flow-through systems is a feasible alternative to cryogenic separation The above analysis indicates that one could reasonably ennch an initial 1% Xe mixture to > 90% purity using 8 centrifuge stages m about 8 minutes In order to realize a separator, one needs to find a mateπal that is sufficiently strong to take the stress of high speed rotation and has long enough wall relaxation rates such that the polarized ^I29 Xe 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- relaxive coating

A number of embodiments of the invention have been descnbed Nevertheless, it will be understood that various modifications may be made without departing from the spiπt and scope of the invention For example, although the storage cells descnbed above are made of glass with an intenor coating free of alkali-metals, any material may be used which is characterized m that the longitudinal spin relaxation rate of the gaseous spm polaπzed

¹²⁹ Xe 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 ¹²⁹ Xe due to intrinsic mechanisms For example, plastic materials (e g fluoropolymer plastics) such as Teflon of Ultem 1000 should have a wall rate comparable to or less than that of the coated glass surfaces used in the examples above

Although devices descπbed in the examples above operate at a defined temperatures (e g room temperature or 100 ⁰ C), other temperatures or temperature ranges may be used As demonstrated m 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 mateπal 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-polaπzation relaxation rate

Any of the techniques described above may be used m 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 descπbed above may be used m 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 m the mixture (e g , a mmute or two), and then immediately volatilize it into a storage cell

The devices and techniques descπbed herein may be extended to the non-cryogenic storage of hyperpolarized materials other than I ²⁹ Xe, e g any other mateπal which expeπences 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 m an appendix and/or incorporated by reference It is to be understood that m the case that any technical definitions presented in the mam body of this application conflict with those presented m the appendix or incorporated references, the definition m the mam body holds

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