Continuous flow production of concentrated hyperpolarized xenon gas from a dilute xenon gas mixture by buffer gas condensation

Abstract

We present a new method for the continuous flow production of concentrated hyperpolarized xenon-129 (HP ¹²⁹Xe) gas from a dilute xenon (Xe) gas mixture with high nuclear spin polarization. A low vapor pressure (i.e., high boiling-point) gas was introduced as an alternative to molecular nitrogen (N₂), which is the conventional quenching gas for generating HP ¹²⁹Xe via Rb-Xe spin-exchange optical-pumping (SEOP). In contrast to the generally used method of extraction by freezing Xe after the SEOP process, the quenching gas separated as a liquid at moderately low temperature so that Xe was maintained in its gaseous state, allowing the continuous delivery of highly polarized concentrated Xe gas. We selected isobutene as the candidate quenching gas and our method was demonstrated experimentally while comparing its performance with N₂. Isobutene could be liquefied and removed from the Xe gas mixture using a cold trap, and the concentrated HP ¹²⁹Xe gas exhibited a significantly enhanced nuclear magnetic resonance (NMR) signal. Although the system requires further optimization depending on the intended purpose, our approach presented here could provide a simple means for performing NMR or magnetic resonance imaging (MRI) measurements continuously using HP ¹²⁹Xe with improved sensitivity.

Introduction

Nuclear magnetic resonance (NMR) of hyperpolarized xenon-129 (HP ¹²⁹Xe) atoms has been widely used in a variety of research areas, such as physics, chemistry, material science, and biomedical imaging^{1, 2}. HP ¹²⁹Xe gas is usually produced via a spin-exchange optical-pumping (SEOP) method, in which a hyperpolarized nuclear spin state is achieved based on the transfer of the angular momentum carried by photons from circularly polarized laser light^{3, 4}. For this transfer process, an alkali metal (typically rubidium, Rb) is used as an intermediate. One of the two spin states of the valence electron of a vaporized Rb atom becomes populated abundantly by absorbing circularly polarized laser light with a wavelength matched to the Rb D1 transition (~795 nm). Through subsequent Rb-Xe interactions, such as binary collision between a spin-polarized Rb atom and a Xe atom or the formation of an Rb/Xe van der Waals molecular complex, the transfer of spin polarization from a Rb electron to the ¹²⁹Xe nuclei occurs.

In order to obtain highly polarized ¹²⁹Xe gas, two types of buffer gases are generally added to the Xe gas to promote efficient SEOP. The first, and the most important for optical pumping is to add a quenching gas such as molecular nitrogen (N₂), which prevents the excited state of Rb atoms from re-radiating unpolarized photons, enabling the avoidance of radiation trapping. Nitrogen has a large quenching cross section^{5, 6} and a moderate spin destruction cross section for Rb (${k}_{{\rm{SD}}}^{{\rm{Rb}}-{{\rm{N}}}_{2}}$ = 1.3 × 10⁻²⁵  T ³ cm³ s^{−1  7}, where T is the temperature in K) and, therefore, it is typically used as a quenching gas in SEOP, where several tens of kPa of N₂ are added to Xe gas to provide sufficient quenching effect. A second buffer gas is added in order to broaden the absorption line of Rb to better match the spectral profile of the laser⁸. Generally, several hundreds of kPa of helium (He) are added to the Xe/N₂ gas mixture for this purpose. Helium is chosen because it has the smallest spin destruction cross section for Rb (${k}_{{\rm{SD}}}^{{\rm{Rb}}-{\rm{He}}}$ = 1.0 × 10⁻²⁹  T ^4.26 cm³ s^{−1  9}) and, therefore, causes little loss of Rb spin polarization while broadening. Xe, in contrast, has a large spin destruction cross section for Rb (${k}_{{\rm{SD}}}^{{\rm{Rb}}-{\rm{Xe}}}$ = 6.3 × 10⁻¹⁷(T-273.15)^1.17 cm³ s^{−1  10}) and, therefore, causes a significant loss of Rb spin polarization in condition with higher Xe number density, leading to a reduction in ¹²⁹Xe nuclear spin polarization, P _Xe. Based on these characteristics, a highly diluted Xe gas mixture composed of a small amount of Xe and N₂, and a large amount of He gas has been used for generating highly polarized ¹²⁹Xe gas^{8, 10,11,12,13}.

The buffer gases needed for SEOP cause a side-effect of signal reduction through dilution of the Xe gas. By separating the HP ¹²⁹Xe gas from the buffer gases, HP ¹²⁹Xe gas can be concentrated. Because Xe freezes well above the boiling point of both N₂ and He, the buffer gases can be removed by freezing out the Xe. At present, the only effective way to concentrate HP ¹²⁹Xe for further use in NMR or magnetic resonance imaging (MRI) is freeze-thaw separation, in which Xe in the continuously flowing gas mixture is frozen and accumulated until it reaches a sufficient amount for use, and then the solid Xe is thawed to return it to a gaseous state^{8, 10, 11, 14, 15}. The freeze-thaw approach, however, has some drawbacks, such as the accumulation of a sufficient quantity of solid HP ¹²⁹Xe taking a considerable time (e.g., several tens of minutes). Although the longitudinal relaxation time T ₁ of solid ¹²⁹Xe at liquid N₂ temperature in the presence of a magnetic field is reasonably long for accumulation¹⁶, it often results in an extra significant loss of P _Xe in the process of solidification, accumulation, and volatilization of Xe, and this process complicates the system and its operation. Furthermore, this approach is not compatible with the continuous flow production of HP ¹²⁹Xe gas because the Xe gas has to be stored in a solid state. Therefore, its use is limited to NMR or MRI experiments conducted in a batch mode.

Depending on the purpose, it is possible to forgo the cryogenic accumulation step to directly deliver highly or moderately dilute HP ¹²⁹Xe mixtures to the target by continuous flow^{12, 17, 18} or stopped flow^{19,20,21,22,23}. However, it is obvious that the use of fully concentrated ¹²⁹Xe gas from highly dilute HP ¹²⁹Xe mixture enables MRI applications with significantly increased signal intensity¹². Most recently, Meersmann and coworkers demonstrated that molecular hydrogen (H₂) can be used as a quenching gas in SEOP and it can be reactively removed via catalytic combustion for the purpose of purifying HP ⁸³Kr as well as HP ¹²⁹Xe after SEOP²⁴. However, the continuous flow production of purified HP noble gas, to the best of our knowledge, has not been demonstrated previously.

The aim of this work is to develop a new method to concentrate HP ¹²⁹Xe gas from a dilute Xe gas mixture using a new buffer gas for SEOP that is capable of continuously delivering highly spin polarized undiluted ¹²⁹Xe gas for use in performing NMR or MRI measurement continuously with improved sensitivity. We reported a study on pulmonary functional imaging in mice using HP ¹²⁹Xe generated using a system based on the concept described here²⁵. In the present study, we focus on the basic aspects of the methodology based on a detailed analysis of Xe polarization, Rb polarization and Rb-Xe spin exchange process in the use of a new quenching gas comparing them with the conventional N₂. Furthermore, we investigate the current shortcoming to improve the system by analyzing observed enhancement of MR signal strength and loss of polarization encountered in a concentration process of dilute Xe gas.

Results and Discussion

Selection of a quenching gas

Our proposal for concentrating HP ¹²⁹Xe gas from a dilute Xe gas mixture was to use a high boiling point gas as a quenching gas that condenses at a higher temperature than Xe. In order to achieve this objective, the candidate quenching gas requires sufficient quenching ability, a higher boiling point than Xe, a small contribution to the spin destruction of Rb, and low chemical reactivity with highly reactive Rb. To quench the fluorescent emission, it is required to transfer the excitation energy of Rb atoms to kinetic energy of the quenching gas. Molecular gases with a chemical double bond possess a large quenching cross section and can effectively quench fluorescence through energy transfer into its vibrational mode⁶. Among the previously reported data regarding quenching cross section, a hydrocarbon gas ethylene (ethene, H₂C=CH₂) has a larger quenching cross section (σ(P _1/2 → S _1/2) = 139 Ų) than that of N₂ (σ(P _1/2 → S _1/2) = 58 Ų)^{5, 6}, and has a slightly higher boiling point (169.5 K) than Xe (165.0 K). Ethylene, however, was not suitable for our purpose because of the very small difference in boiling point, and, therefore, a gas with a substantially different boiling point was required in order to enhance the separation efficiency from Xe gas. In the present study, isobutene (2-methylpropene, H₂C=C(CH₃)₂) was selected as the first candidate quenching gas because its boiling point is 266.2 K, which is over 100 K higher than Xe, and it has a chemical double bond favorable for effective quenching similar to N₂ and ethylene.

Continuous flow production of concentrated HP ¹²⁹Xe gas by isobutene condensation

In order to demonstrate that Xe was concentrated continuously from the dilute Xe gas mixture, the ¹²⁹Xe NMR signal was measured repeatedly from the continuously flowing Xe/isobutene gas mixture before and after condensing of isobutene. The Xe/isobutene gas mixture was flowed through a polarizer²⁶ for hyperpolarization, a tubular spiral glassware as a cold trap (Fig. 1a), and an NMR tube in a 9.4-T superconducting magnet for measuring the ¹²⁹Xe NMR signal. More details about the experimental set-up and NMR measurement are given in Methods section. Figure 1b shows a time course of the ¹²⁹Xe signal-to-noise ratio (SNR) of the NMR spectrum measured during the continuous flow production of HP ¹²⁹Xe using a binary gas mixture of Xe/isobutene before and after the concentration of HP ¹²⁹Xe by application of the cold trap. Results from the Xe/N₂ mixture are shown for comparison. For a dilute Xe/isobutene mixture without a cold trap, a stable HP ¹²⁹Xe signal was observed continuously, although the SNR was slightly lower than that of the Xe/N₂ mixture. For repeated acquisitions of ¹²⁹Xe spectra, the spiral glass was put in a cold Dewar at after 150 s. Immediately after this, the ¹²⁹Xe signal intensity began to increase, then increased further gradually with some fluctuations, and finally reached a steady state. The enhanced ¹²⁹Xe signal continued to be measured with sufficient stability similar to the Xe/N₂ mixture. Representative NMR spectra showing spectral enhancement by concentrating Xe are shown in Fig. 1c. After the measurement, it was confirmed that liquid isobutene was stored in the storage vessel attached to the lower side of the spiral glassware (Fig. 1d), and, therefore, isobutene had been removed from the Xe gas, and the concentrated Xe gave the enhanced signal.

Figure 1

Dynamics of ¹²⁹Xe NMR signal enhancement by removing isobutene. (a) Diagram of the glassware for condensing and storing isobutene using a cold trap and schematic diagram of the production of concentrated HP ¹²⁹Xe gas from the Xe/isobutene gas mixture. (b) Time course of SNR of ¹²⁹Xe spectrum using gas mixtures with Xe/isobutene (diamonds) and Xe/N₂ (rectangles). Spiral glass piping was immersed in a Dewar at the time point indicated by the black allow to trap isobutene at 203 K. The Xe fraction in both mixtures was f _Xe,SEOP = 0.20. Gas flow rates of Xe, isobutene, and N₂ were F _Xe = 17, F _ib = 69 and ${F}_{{{\rm{N}}}_{2}}$ = 69 sccm, respectively. (c) HP ¹²⁹Xe NMR spectrum acquired from a Xe/N₂ gas mixture (left) and a Xe/isobutene gas mixture recorded before (center) and after separation of isobutene using the cold trap (right). (d) Photograph of the liquid isobutene separated from Xe gas and stored in the storage vessel.

Comparison between isobutene and N₂ as a quenching gas for Rb-Xe SEOP

In order to maximize a benefit from signal enhancement by concentrating HP ¹²⁹Xe, it is important that the use of isobutene did not cause a significant loss of P _Xe compared with using conventional N₂. The influence of using isobutene as an alternative quenching gas to conventional N₂ on P _Xe was investigated by comparing with that of N₂. The details of calculations of P _Xe are given in Methods section. The P _Xe for each diluted Xe gas mixture (i.e., Xe/isobutene or Xe/N₂) was measured for the five conditions with the gas mixture. The Xe flow rate (F _Xe) varied from 2.2 to 30 sccm (cubic centimeter per minute at standard temperature and pressure (STP)) whereas that of isobutene (F _ib) or N₂ $({F}_{{{\rm{N}}}_{2}})$ was kept constant at 69 sccm; therefore, the volume fraction of Xe in the source gas mixture, f _Xe,SEOP, ranged from 0.03 to 0.30 (Table 1). Figure 2a compares P _Xe between isobutene and N₂ in the gas mixture without a cold trap. Here, the volume fraction of Xe in the gas mixture at measurement region, f _Xe,meas, was equal to that in the source gas mixture, f _Xe,SEOP. When using the isobutene mixture, P _Xe was 2–17% lower than that observed with the N₂ mixture in these experimental conditions. A similar tendency between the two mixtures was observed for the dependence of P _Xe on f _Xe,SEOP; namely, P _Xe increased with decreasing f _Xe,SEOP because the lower Xe number density in SEOP process as is well-known.

Table 1 Flow rates and volume fractions of the gas mixture, and partial pressures and number densities of atoms in SEOP cell at a temperature of 383 K and total pressure of 15 kPa.

Figure 2

Comparison between isobutene and N₂ as the quenching gas for Rb-Xe SEOP. Plot of P _Xe (a), P _app (b), P _Rb (c), γ _SE (d), and τ _SU (e) as a function of f _Xe,SEOP for a Xe/N₂ mixture (rectangles) and Xe/isobutene mixture (circles) without the separation procedure. The residency time of atoms in SEOP cell, τ _cell, is also shown in (e). (f) Plot of the ratio of P _Xe, P _Rb, γ _SE τ _SU, and a factor of $1-{e}^{-{\tau }_{{\rm{cell}}}/{\tau }_{{\rm{SU}}}}$ for isobutene mixture relative to those for N₂ mixture as a function of f _Xe,SEOP. Gas flow conditions used in these experiments were listed in Table 1.

In order to compare the ¹²⁹Xe signal intensities in the various experimental conditions, the apparent polarization, P _app, was defined as refs 19 and 20:

$${P}_{{\rm{app}}}={P}_{{\rm{Xe}}}\cdot {f}_{{\rm{Xe}},{\rm{meas}}}$$

(1)

Details of P _app are given in Methods section. The f _Xe,SEOP dependence of P _app was also observed to have a similar tendency between the two mixtures (Fig. 2b). Owing to a dilution effect, P _app decreased with decreasing f _Xe,SEOP even though P _Xe increased.

The use of isobutene resulted in a slight loss of P _Xe compared with N₂. In order to understand how isobutene affects the Rb-Xe SEOP process and clarify the rationale of the polarization loss, we further analyzed the experimental data using a standard model of SEOP and compared several factors affecting P _Xe between isobutene and N₂ mixtures. The nuclear spin polarization of ¹²⁹Xe at the output of the SEOP cell in the flow-though polarizer is given by ref. 27

$${P}_{{\rm{Xe}}}({\tau }_{{\rm{cell}}})={\gamma }_{{\rm{SE}}}{\tau }_{{\rm{SU}}}\langle {P}_{{\rm{Rb}}}\rangle \,(1-{e}^{-{\tau }_{{\rm{cell}}}/{\tau }_{{\rm{SU}}}})$$

(2)

where γ _SE is the Rb-¹²⁹Xe spin-exchange rate, which includes the contributions of spin exchange induced by Rb-Xe van der Waals molecules, ${\gamma }_{{\rm{SE}}}^{{\rm{vdW}}}$, and spin exchange caused by Rb-Xe binary collisions, ${\gamma }_{{\rm{SE}}}^{{\rm{BC}}}$, according to refs 10 and 27

$${\gamma }_{{\rm{SE}}}={\gamma }_{{\rm{SE}}}^{{\rm{vdW}}}+{\gamma }_{{\rm{SE}}}^{BC}=(\frac{1}{{\sum }_{j}({n}_{j}/{\xi }_{j})}+\langle \sigma v\rangle )\,{n}_{{\rm{Rb}}}$$

(3)

where ξ _j denotes the van der Waals-specific rate for each gas atom with density n _j , and 〈σv〉 is the velocity averaged binary spin-exchange cross section. τ _SU is the spin-up time constant defined as ref. 27

$${\tau }_{{\rm{SU}}}^{-1}={\gamma }_{{\rm{SE}}}+{{\rm{\Gamma }}}_{{\rm{Xe}}}$$

(4)

where Γ_Xe is the ¹²⁹Xe spin relaxation rate, which is though to be dominated by wall relaxation^{8, 10}. The wall relaxation rate is pressure independent and depends on the cell geometry (surface/volume) and its surface properties (paramagnetic impurities). 〈P _Rb〉 is the volume-averaged Rb polarization in the cell. τ _cell is the mean ¹²⁹Xe residence time in the cell, which is related to the total flow rate, F _tot, according to

$${\tau }_{{\rm{cell}}}=\frac{{V}_{{\rm{cell}}}}{{F}_{{\rm{tot}}}}\cdot \frac{{p}_{{\rm{cell}}}}{{p}_{{\rm{s}}}}$$

(5)

where V _cell is the cell volume and p _cell is the total pressure of the gas in the cell. Among the two contributions to the Rb-Xe spin exchange, the formation and break up of Rb/Xe van der Waals molecular complex is affected by the difference in gas atoms or molecules, which is characterized by van der Waals specific rate, ξ _j according to Eq. 3. We could estimate the ξ for isobutene as ξ _ib = 2.61 × 10³ s⁻¹ (see Methods section) and found that the ξ _ib is less than half of ${\xi }_{{{\rm{N}}}_{2}}$ (=5.70 × 10³ s^{−1  28, 29}). The low ξ results in low spin exchange rate, γ _SE, which was 40–48% lower for isobutene mixture than for N₂ mixture under our experimental conditions summarized in Table 1 (Fig. 2d). According to Eq. 2, P _Xe reaches γ _SE τ _SU〈Rb〉 after a sufficiently long SEOP time compared to the spin up time, τ _SU. Therefore, if Γ_Xe is sufficiently small compared to γ _SE, the difference in γ _SE has a small influence on P _Xe. In our system, sufficiently small Γ_Xe was measured as 1.84 × 10⁻⁴ s⁻¹ (see Methods section). Indeed, the γ _SE τ _SU was calculated as 0.986–0.987 for isobutene mixture and 0.992–0.993 for N₂ mixture; therefore, the effect of the difference between two mixtures is less than 1% (Fig. 2f). The lower γ _SE prolong the spin up time, τ _SU, and requires longer residency time for P _Xe to reach sufficiently high value. Since the nuclear spin polarization of ¹²⁹Xe builds up with a time constant of τ _SU according to Eq. 2, especially for the continuous flow system at a low cell pressure, we need to take into account that the residency time becomes short according to Eq. 5. The spin up time, τ _SU, for isobutene was calculated as raged from 69.4 to 78.4 s and from 40.9 to 41.8 s for N₂. Although these spin up times for both gas mixtures were shorter than τ _cell (Fig. 2e), which was ranged from 76.1 to 105.8 s for our experimental condition (V _cell = 848 cc, p _cell = 15 kPa, and F _tot ranging from 71.2 to 99.0 sccm), the SEOP time was insufficient for isobutene compared to N₂ as a factor of $1-{e}^{-{\tau }_{{\rm{cell}}}/{\tau }_{{\rm{SU}}}}$ for isobutene mixture (0.666–0.741) was ~20% lower than that for N₂ mixture (0.838–0.925) (Fig. 2f).

Interestingly, in all experimental conditions, 〈P _Rb〉 for isobutene mixture was 4–24% higher than that for N₂ mixture (Fig. 2c,f). The Rb electron spin polarization at a position z in the SEOP cell along the laser propagation direction is given by refs 8, 10 and 27

$${P}_{{\rm{Rb}}}\,(z)=\frac{{\gamma }_{{\rm{OP}}}\,(z)}{{\gamma }_{{\rm{OP}}}\,(z)+{{\rm{\Gamma }}}_{{\rm{SD}}}}$$

(6)

where γ _OP is the optical pumping rate, which is determined by the overlap of the frequency- and position-dependent laser intensity profile Φ(ν,z) and the alkali-metal D ₁ absorption cross section σ _s(ν) according to

$${\gamma }_{{\rm{OP}}}\,(z)=\int \,{\rm{\Phi }}\,(\nu ,z)\,{\sigma }_{{\rm{s}}}\,(\nu )\,d\nu $$

(7)

Γ_SD is the Rb spin polarization destruction rate, which can be attributed to spin depolarizing binary collisions with atoms in the gas mixture, the formation and breakup of Rb-Xe van der Waals molecules and radiation trapping^{19, 30}:

$${{\rm{\Gamma }}}_{{\rm{SD}}}=\sum _{j}\,{n}_{j}{k}_{{\rm{SD}}}^{{\rm{Rb}}-j}+{{\rm{\Gamma }}}_{{\rm{SD}}}^{vdW}+{{\rm{\Gamma }}}_{{\rm{SD}}}^{{\rm{trap}}}$$

(8)

where ${k}_{{\rm{S}}{\rm{D}}}^{{\rm{R}}{\rm{b}}-j}$ is the Rb spin-destruction cross section for Rb binary collisions with each gas atom with an atomic density n _j . Therefore, the Rb polarization is limited by the Rb spin destruction processes characterized by a rate constant of Γ_SD (Eq. 6). Since the difference in gases alters all the rate constants involved in these processes, the higher value of 〈P _Rb〉 for isobutene mixture indicates that the isobutene has a valuable property of sufficiently small contribution to the spin destruction of Rb compared to N₂. The optical pumping rate, γ _OP includes the effects of pressure broadening of the Rb absorption line and shift of its central line by buffer gases. The pressure-broadening and shift coefficients for Rb have been measured for He, Xe and N₂ and they are slightly different ranging from 18.0 to 18.9 GHz/amg for broadening and from −8.3 to 5.6 GHz/amg for shift³¹. Although the difference in gases may be less effective for the behavior of broadening and shift as reported for these three gases, the use of isobutene has a possibility to change the γ _OP compared to the case of N₂. In order to understand how isobutene affects spin destruction of Rb and optical pumping rate, further study is required, in which important physical quantities such as the absorption line broadening factor and each rate constant related to spin depolarizing binary collisions, van der Waals molecules and radiation trapping should be quantified. At this stage, our results suggested that isobutene seems to act as a quenching gas effectively because observed Rb polarization was higher than that for N₂ mixture.

In terms of the reactivity of hydrocarbon gases coexisting with highly reactive Rb in the SEOP cell, Rb does not seem to readily react with saturated hydrocarbon gases such as methane^{21, 32}, ethane³² and butane³³. Any reaction also seems to be very slow for the unsaturated hydrocarbon isobutene used here. In fact, degradation of the SEOP cell using the isobutene mixture was adequately slow and at an acceptable level to complete in vivo experiments with a sufficient number of mice, e.g., 50 mice²⁵.

Dependence of ¹²⁹Xe signal enhancement on the volume fraction of Xe in the diluted gas mixture

In the same gas flow conditions as described in the previous section, the enhancement of ¹²⁹Xe signal by removing isobutene was investigated. Figure 3a shows dependence of P _app on f _Xe,SEOP measured from concentrated Xe and that from diluted Xe using Xe/isobutene mixtures. Here f _Xe,meas was different from f _Xe,SEOP for the concentrated Xe because isobutene was removed from the source gas mixture. For all conditions, the removal of isobutene from Xe gas enabled P _app to increase (i.e., the enhancement was due to the increase in f _Xe,meas in Eq. 1). The highest value of P _app = 11.9% was obtained at f _Xe,SEOP = 0.20, whereas P _app = 3.7% was observed for diluted Xe at f _Xe,SEOP = 0.30.

Figure 3

Dependence of ¹²⁹Xe signal enhancement on the Xe fraction in a dilute gas mixture. (a) Plot of P _app as a function of f _Xe,SEOP for a Xe/isobutene mixture. Data were obtained for a dilute Xe mixture without the separation (circles, the same data as shown in Fig. 2b) and for concentrated Xe after separation from isobutene at 196 K (diamonds). (b) Plot of enhancement factor ε as a function of f _Xe,SEOP. Gas flow conditions used in these experiments were listed in Table 1. (c) Comparison of ¹²⁹Xe signal enhancement between experimental results and ideal conditions. Asterisks: observed enhancement factor, which are the same data as shown in (b) solid line: ideal enhancement factor; dashed line: ideal enhancement factor including residual isobutene at 196 K; dotted line: fitted curve using Eq. 11 with f _ib,res = 0.13. Inset shows the expanded plot of the main figure for clarify. (d) Plot of ¹²⁹Xe polarization loss factor, LP, as a function of f _Xe,SEOP. The flow rate of Xe is indicated above the plot. The plotted values were calculated using a relation of Eq. 10 with f _ib,res = 0.13. The dotted line was drawn based on Eq. 13 using the values of α estimated from the fit as shown in c and f _ib,res = 0.13.

In order to assess the effectiveness of concentrating Xe from the dilute Xe gas mixture, an enhancement factor, ε, was defined as the ratio of the amplitude of ¹²⁹Xe signal obtained from concentrated Xe relative to that from diluted Xe with the same gas mixture used. Details about ε are given in the Methods section. The enhancement factor can be expressed by using the index P _app as:

$$\varepsilon =\frac{{P}_{{\rm{app}},{\rm{conc}}}}{{P}_{{\rm{app}},{\rm{dil}}}}$$

(9)

where P _app,conc and P _app,dil are the apparent polarization observed from concentrated Xe and diluted Xe, respectively. Figure 3b shows dependence of ε on f _Xe,SEOP. The maximum enhancement factor of ε = 3.9 was observed at f _Xe,SEOP = 0.11.

Although the ¹²⁹Xe NMR signal was enhanced by the proposed method, the observed enhancement did not reach the value expected. From Eqs 1 and 9, the enhancement factor can be further rewritten as:

$$\varepsilon =\frac{{P}_{{\rm{Xe}},{\rm{conc}}}}{{P}_{{\rm{Xe}},{\rm{dil}}}}\cdot \frac{1-{f}_{{\rm{ib}},{\rm{res}}}}{{f}_{{\rm{Xe}},{\rm{SEOP}}}}$$

(10)

where P _Xe,conc and P _Xe,dil are the polarization for concentrated Xe and diluted Xe, respectively, and f _ib,res is the fraction of residual isobutene in the gas mixture after the removal process. Note that P _Xe,conc and P _Xe,dil are the polarization observed in the measured region (i.e., in the NMR magnet) and, therefore, there is a possibility of a difference between them, although the polarization at the exit of the SEOP cell was the same for both concentrated and diluted conditions. According to Eq. 10, the specific relation ε = 1/f _Xe,SEOP holds true in conditions that satisfy the following two assumptions: (I) isobutene is completely removed from the gas mixture by the cold trap (i.e., f _ib,res = 0), and (II) the separation process has no influence on P _Xe (i.e., P _Xe,conc = P _Xe,dil). In this ideal condition, it was expected that extremely high ε can be obtained at lower f _Xe,SEOP. Figure 3c compares ε between the ideal (solid line) and the observed values (asterisks). At the lower f _Xe,SEOP, the observed ε was far lower than the ideal one, whereas it was closer to the ideal one with increasing f _Xe,SEOP (e.g., ε~33 and ε~1.7 at f _Xe,SEOP = 0.03 for ideal case and measured value, respectively, whereas ε~3.3 and ε~2.4 at f _Xe,SEOP = 0.30 for ideal case and measured value, respectively). The first assumption described above (I) was not established in our experiments. f _ib,res can be estimated from the vapor pressure of isobutene, which is related to the cold trap temperature, and the total pressure at the separation region. The vapor pressure of isobutene at 196 K is ~2.0 kPa³⁴, leaving 13% of isobutene in the gas mixture at 15 kPa total pressure, which was our experimental condition. This caused an increase in f _ib,res from the ideal value of 0 to 0.13, and thus ε decreased 13% from the ideal one (Fig. 3c, dashed line). With regard to the second assumption above (II), there were three possible causes to induce a difference in P _Xe between the concentrated and diluted conditions: (i) a reduction in ¹²⁹Xe magnetization at the gas–liquid surface in the concentrated condition. The depolarization was expected when gaseous Xe atoms contact with a liquid surface, where an interaction occurs between the ¹²⁹Xe atoms and ¹H of the dense liquid isobutene molecules. In addition, an exchange phenomenon of Xe atoms between gaseous Xe and depolarized dissolved Xe caused a loss of gaseous Xe magnetization. (ii) A difference in relaxation time between concentrated and diluted conditions downstream of the separation region. Because Xe interacts with Xe in concentrated conditions whereas Xe interacts with both Xe and isobutene in diluted condition, the difference in gas composition could cause a difference in relaxation time. (iii) A difference in time needed for gas transport from the separation region to the measurement region. The reduced total flow rate due to the removal of isobutene could cause extra depolarization before the measurements. In order to analyze our experimental data in relation to these possibilities, ε was rewritten to include relaxation and flow rate:

$$\varepsilon =\frac{\exp \,(-{\alpha }_{{\rm{conc}}}/{F}_{{\rm{tot}},{\rm{conc}}})}{\exp \,(-{\alpha }_{{\rm{dil}}}/{F}_{{\rm{tot}},{\rm{dil}}})}\cdot \frac{{F}_{{\rm{t}}ot,dil}}{{F}_{{\rm{t}}ot,conc}}$$

(11)

with

$${F}_{{\rm{tot}},{\rm{conc}}}={F}_{{\rm{Xe}}}+{F}_{{\rm{ib}},{\rm{res}}},\,{F}_{{\rm{tot}},{\rm{dil}}}={F}_{{\rm{Xe}}}+{F}_{{\rm{ib}}},\,{\alpha }_{{\rm{conc}}}=\sum _{i}\,\frac{{V}_{i}}{{T}_{1,i,{\rm{conc}}}}\cdot \frac{{p}_{i}}{{p}_{{\rm{s}}}},\,{\alpha }_{{\rm{dil}}}=\sum _{i}\,\frac{{V}_{i}}{{T}_{\mathrm{1,}i,{\rm{dil}}}}\cdot \frac{{p}_{i}}{{p}_{{\rm{s}}}}$$

where the suffixes “dil” and “conc” denote the parameters related to the diluted Xe gas mixture and concentrated Xe gas, respectively, F _tot is the total flow rate downstream from the separation region, F _ib,res is the flow rate of residual isobutene after the removal process, α is a constant involved in ¹²⁹Xe relaxation, i denotes a site in which the relaxation occurs, T _1,i is the ¹²⁹Xe T ₁ at site i, V _i is the volume at site i, and p _i and p _s are the total pressure of the gas at site i and standard-state pressure, respectively. The total flow rate was measured at ambient pressure. The depolarization effects described for (i) and (ii) were included in α _conc and α _dil in Eq. 11 as a difference in the number of sites, where the relaxation is occurred, and difference in the relaxation time. Details about the relationship between Eqs 10 and 11 are given in the Methods section. By fitting the observed ε to Eq. 11, α _conc and α _dil were estimated as 8.6 and 8.4 sccm, respectively, with a coefficient of determination of R ² = 0.733 (Fig. 3c, dotted line). From these values, the degree of relaxation in the concentrated condition could be similar to that in diluted conditions. Here, we introduce a polarization loss factor (LP) defined as:

$$LP=1-RP$$

(12)

where a retained polarization fraction (RP) is a factor that describes the fraction of polarization retained when the gas passes through the buffer gas separation procedure and expressed using Eqs 10 and 11 (see also the Methods section for RP):

$$RP=\frac{{P}_{{\rm{Xe}},{\rm{conc}}}}{{P}_{{\rm{Xe}},{\rm{dil}}}}=\frac{\exp \,(-{\alpha }_{{\rm{conc}}}/{F}_{{\rm{tot}},{\rm{conc}}})}{\exp \,(-{\alpha }_{{\rm{dil}}}/{F}_{{\rm{tot}},{\rm{dil}}})}$$

(13)

Figure 3d shows a plot of the LP as a function of f _Xe,SEOP as well as F _Xe. LP increased with decreasing f _Xe,SEOP because of the reduced flow rate for the concentrated condition. Therefore, the discrepancy of ε between our experimental results and the ideal case could be mainly attributed to the reduced total flow rate because of the removal of isobutene described in (iii).

Requirements for improving the system

In order to improve the system and produce HP ¹²⁹Xe gas with higher P _app, LP needs to be minimized. Based on our results, higher F _Xe was required to suppress the reduction in P _Xe,conc (i.e. the increase in LP) and attain higher signal enhancement. In fact, it was confirmed experimentally that ε was improved by increasing F _Xe because of the partial suppression of relaxation during the concentrated Xe gas transfer, as shown in Table 2, where the results using a 3% Xe/97% isobutene mixture with different total flow rates of F _tot = 71.2 and F _tot = 142.3 sccm (i.e. F _Xe = 2.2 and F _Xe = 4.3 sccm, respectively) were compared. In this case, LP was improved from 0.94 to 0.88. However the improved ε~3.4 was still far lower than that for the ideal value of ~33 because LP remained high value. Additionally, the achievable P _Xe,dil was low for the higher flow rate because of the short residency time of Xe atoms in SEOP cell (τ _cell = 53 s) compared to the spin up time of this mixture (τ _SU = 78 s), resulting in low P _app.

Table 2 Effect of the total gas flow rate on P _Xe, P _app, and ε using 3% Xe/97% isobutene mixture.

In order to further suppress the relaxation effect and obtain higher P _app, it will be necessary to adopt much higher F _Xe while keeping f _Xe,SEOP low. By improving SEOP efficiency, the reduction in P _Xe at the outlet of the SEOP cell caused by the increasing total flow rate may be suppressed. A simple solution could be to introduce spectrally line-narrowed laser diode array (LDA) to improve the absorption efficiency of Rb. The effectiveness of using the line-narrowed LDA to improve P _Xe has been shown by other group¹⁹ and by our group as well for our own SEOP system³⁵. Another approach to prevent P _Xe,conc from reduction was to suppress depolarization during HP ¹²⁹Xe gas transfer from the SEOP cell to the measurement region. For this purpose, the material or inner surface coating as well as the shape of all regions from the outlet of the SEOP cell to the measurement region and any effect of the magnetic field that the HP gas is passing through should be taken into account to prolong the relaxation time of ¹²⁹Xe^36,37,38. An additional requirement for improving this system is to optimize the temperature of the cold trap. In this study, isobutene was condensed and removed from Xe gas at only a single temperature around 195 K. At this temperature, ~13% of isobutene remained in the gas mixture, resulting in a reduction in the achievable Xe concentration. Lowering the cold trap temperature can reduce the vapor pressure of isobutene and could improve the separation efficiency.

Conclusion

We have demonstrated the continuous flow production of nearly pure HP ¹²⁹Xe gas concentrated from dilute HP ¹²⁹Xe gas mixture with higher P _Xe, which could be realized using isobutene as a quenching gas in Rb-Xe SEOP. Useful properties of isobutene as a quenching gas for generating HP ¹²⁹Xe was revealed by the comparison of several parameters related to SEOP with conventional N₂. Utilizing the large difference in boiling point between isobutene and Xe, isobutene could be condensed and removed from HP ¹²⁹Xe/isobutene gas mixture, resulting in enhancement of the ¹²⁹Xe NMR signal owing to the increased concentration of Xe. By optimizing further the system for better performance, this approach could provide a simple means for performing NMR or MRI measurements continuously using HP ¹²⁹Xe with extremely improved sensitivity in a wide range of research fields.

Methods

Polarizer

A schematic overview of the experimental setup is shown in Fig. 4, which is a modified system of our low-pressure and flow-through polarizer²⁶. Approximately 0.5 g of Rb (EP grade, over 99.5% purity; Nacalai Tesque Inc., Kyoto, Japan) was deposited into a cylindrical Pyrex glass cell (6 cm diameter, 30 cm length). The SEOP cell was placed vertically in a fringe field of 12 mT near a vertical 9.4-T superconducting magnet and housed in an oven. The temperature of the oven was maintained at 383 K using a hot-air blower (CH-6056 HOTWIND S; Leister Technologies AG, Kaegiswil, Switzerland) to increase the Rb vapor pressure. Laser light from two fiber-coupled broadband LDA systems (FAP system, output power ~30 W, linewidth ~2 nm full width at half maximum (FWHM); DUO-FAP system, ~60 W and <6 nm FWHM; COHERENT Inc., CA, USA) were coupled via a transport glass fiber to the circular polarizing unit (COHERENT Inc.). Two circularly polarized beams output from the unit were emitted into the SEOP cell.

Figure 4

Schematic diagram of the experimental setup. Details are given in the text.

Natural abundance Xe (26.44% ¹²⁹Xe; Air Liquide Japan Ltd., Tokyo, Japan), N₂ (Air Liquide Japan Ltd.), and isobutene (Tokyo Chemical Industry Co., Ltd., Tokyo, Japan) were used. The gas flow rates were controlled independently using individual mass flow controllers (Model 3660, Kojima Instruments Inc, Kyoto, Japan) calibrated for each gas. By adjusting the each flow rate, we controlled the volume fraction of each gas in the gas mixture. Different gases from the outlets of the mass flow controllers were mixed, dried, and then passed into the SEOP cell. The SEOP process was conducted at a pressure of 15 kPa, which was monitored using a pressure gauge (Handy Manometer Model PG-100 102RP, Nidec Copal Electronics Corp., Tokyo, Japan). The resulting HP gas was compressed to atmospheric pressure using a diaphragm pump (LABPORT N86KV.18, KNF Neuberger GmbH, Freiburg, Germany) and delivered into a ϕ 10-mm NMR tube placed in an NMR probe via a polyethylene tube (1.4 mm inner diameter, 1.9 mm outer diameter; SP102, Natsume Seisakusho Co., Ltd., Tokyo, Japan). After passing through the NMR tube, the gas flow rate was checked by a water displacement method.

Gas separation

In order to separate isobutene from the Xe gas, a cold trap was introduced within the system, where isobutene gas was condensed, collected, and stored. The HP gas mixture exiting the SEOP cell was transferred into Pyrex tubular spiral glassware (Fig. 1a), where the gas mixture flowed around and down the spiral, deposited liquid isobutene, and exited up through the vertical return tube. The liquid isobutene dropped down through the spiral and entered a storage vessel placed on the lower side of the spiral. The glassware was cooled by immersing it in dry ice/methanol mixture in a Dewar and maintained at a constant temperature of around 195 K while being monitored using a thermocouple. This temperature was well below the boiling point of isobutene and well above that of Xe (the vapor pressures of isobutene and Xe at 195 K are ~2 kPa and ~428 kPa, respectively), allowing Xe gas to pass through.

Because the solubility of Xe and the relaxation rate of ¹²⁹Xe in organic solvent both increase with decreasing temperature^{39, 40}, the separation process was conducted at low pressure to suppress volume loss and polarization loss of ¹²⁹Xe. That is, by reducing the partial pressure of Xe gas, the amount of Xe atoms dissolved into liquid isobutene can be reduced. In addition, shorter residence time of Xe gas in this region can suppress the polarization loss of gaseous ¹²⁹Xe by coming in contact with ¹H of liquid isobutene at the gas–liquid interface as well as by exchange phenomenon at the liquid surface with dissolved Xe, which relaxed by dipole–dipole interaction with ¹H of liquid isobutene.

NMR measurement

All NMR measurements were performed in a vertical 9.4-T superconducting magnet (bore width 89 mm; Oxford Instruments plc., Oxford, UK) with a high-resolution NMR spectrometer, Agilent Unity INOVA 400WB with software VNMR 6.1 C installed (Agilent Technologies, Inc., Santa Clara, CA). A ϕ 10-mm NMR probe (Agilent Technologies, Inc.) tuned to the resonant frequency of ¹²⁹Xe (110.6 MHz) was used for detection. The NMR signal of HP ¹²⁹Xe was measured at room temperature with a pulse width of 1 μs, flip angle of 8°, spectral width of 49321.8 Hz, and 16384 data points, without accumulating multiple free induction decay (FID) transients. The FID was recorded repeatedly with a repetition interval of 5 s while the HP gas flowed continuously. The acquired FIDs were phase and baseline corrected and an exponential line broadening of 3 Hz was applied, and then, Fourier transformed to obtain NMR spectra. An SNR was calculated from each spectrum, in which a range from 50 ppm to 100 ppm (with respect to the ¹²⁹Xe spectrum at 0 ppm) was set as the noise region. FWHM of the spectrum, ν _FWHM, was also measured. These processing steps were carried out using VNMR 6.1 C software.

Polarization

To calculate the P _Xe of HP ¹²⁹Xe, the signal was compared with that measured for a standard sample of Xe gas at thermal equilibrium according to:

$${P}_{{\rm{Xe}},{\rm{p}}}=\frac{{{\rm{SNR}}}_{{\rm{p}}}}{{{\rm{SNR}}}_{{\rm{e}}}}\cdot \frac{{\nu }_{{\rm{FWHM}},{\rm{p}}}}{{\nu }_{{\rm{FWHM}},{\rm{e}}}}\cdot \frac{{f}_{{\rm{Xe}},{\rm{e}}}}{{f}_{{\rm{Xe}},{\rm{p}}}}\cdot \frac{\sqrt{{{\rm{NA}}}_{{\rm{e}}}}}{\sqrt{{{\rm{NA}}}_{{\rm{p}}}}}\cdot {P}_{{\rm{Xe}},{\rm{e}}}$$

(14)

where suffixes p and e denote the parameters for hyperpolarized and thermal equilibrium state, respectively, and f _Xe and NA are the fraction of Xe in the gas mixture and the number of FID accumulation, respectively. As the standard sample, a gas mixture of 50% Xe/50% O₂ was enclosed at atmospheric pressure within a ϕ 10-mm NMR tube. O₂ was included to promote the efficiency of FID accumulation by reducing ¹²⁹Xe T ₁ ⁴¹. For the thermal equilibrium gas, 10,000 FID transients were accumulated with the same acquisition parameters as HP ¹²⁹Xe except for a repetition interval of 3 s. Post-processing of the FID was performed in the same manner as HP ¹²⁹Xe. ¹²⁹Xe polarization at thermal equilibrium was calculated from Boltzmann’s distribution law for nuclei with spin I = 1/2 according to ref. 42:

$${P}_{{\rm{Xe}},{\rm{e}}}\approx \frac{\hslash |\gamma |{B}_{0}}{2{k}_{{\rm{B}}}T}$$

(15)

where ħ = h/2π, γ, B ₀, k _B and T are Plank constant, gyromagnetic ratio of ¹²⁹Xe nuclei, static magnetic field strength (B ₀ = 9.4 T), Boltzmann constant, and temperature (typically T = 292 K), respectively. For HP ¹²⁹Xe, ten P _Xe,p calculated from repeatedly acquired spectra were averaged to give final values.

Enhancement factor

In order to assess the effectiveness of concentrating Xe from a dilute Xe gas mixture, an enhancement factor, ε, was defined as the ratio of the amplitude of the ¹²⁹Xe signal, A, obtained from concentrated Xe relative to that from diluted Xe with the same gas mixture used. ε was calculated from SNR and ν _FWHM of ¹²⁹Xe spectra according to:

$$\varepsilon =\frac{{A}_{{\rm{conc}}}}{{A}_{{\rm{dil}}}}=\frac{{{\rm{SNR}}}_{{\rm{conc}}}}{{{\rm{SNR}}}_{{\rm{dil}}}}\cdot \frac{{\nu }_{{\rm{FWHM}},{\rm{conc}}}}{{\nu }_{{\rm{FWHM}},{\rm{dil}}}}$$

(16)

where the suffixes “dil” and “conc” denote the parameters related to experiments with diluted Xe gas mixture without a separation procedure and experiments with concentrated Xe gas by removing isobutene using a cold trap, respectively. The amplitude of the ¹²⁹Xe NMR signal obtained from a Xe gas mixture was proportional to the ¹²⁹Xe polarization, P _Xe, and the number density of ¹²⁹Xe in the gas mixture at the measurement region, n _Xe,meas. In the present study, because the signal was measured at constant temperature and atmospheric pressure, n _Xe,meas was only the function of a fraction of Xe in the gas mixture at the measurement region, f _Xe,meas, and therefore:

$$A\propto {P}_{{\rm{Xe}}}\cdot {f}_{{\rm{Xe}},{\rm{meas}}}$$

(17)

For the diluted condition, f _Xe,meas was equal to the fraction of Xe in the gas mixture in the SEOP region, f _Xe,SEOP, whereas for the concentrated condition, f _Xe,meas becomes 1 − f _ib,res with f _ib,res as a fraction of residual isobutene in the gas mixture after the removal process. Therefore, the enhancement factor can be expressed as Eq. 10.

Apparent polarization

In order to compare the ¹²⁹Xe signal intensities between diluted and concentrated conditions for various gas mixtures, the fraction of Xe in the gas mixture needs to be taken into account together with the polarization of ¹²⁹Xe^{17, 19, 20}. Apparent polarization, P _app, has been proposed by Meersmann and coworkers^{19, 20} in this regard as Eq. 1. P _app is a measure of the polarization taking into account the fraction of Xe in the gas mixture and scaled to the polarization in pure HP ¹²⁹Xe gas, allowing direct comparison of the signal intensity of dilute Xe gas mixture with that of pure Xe gas at polarization P _Xe. By using the P _app, the enhancement factor is also expressed as the ratio of apparent polarization as Eq. 9. The apparent polarization for the diluted condition, P _app,dil, was calculated from a measured P _Xe,dil and a setup condition of f _Xe,SEOP as:

$${P}_{{\rm{app}},{\rm{dil}}}={P}_{{\rm{Xe}},{\rm{dil}}}\cdot {f}_{{\rm{Xe}},{\rm{SEOP}}}$$

(18)

whereas that for the concentrated condition, P _app,conc, was calculated from P _app,dil and ε using relations of Eqs 10 and 18 as:

$${P}_{{\rm{app}},{\rm{conc}}}={P}_{{\rm{Xe}},{\rm{conc}}}\cdot \mathrm{(1}-{f}_{{\rm{ib}},{\rm{res}}})={P}_{{\rm{app}},{\rm{dil}}}\cdot \varepsilon $$

(19)

because P _Xe,conc cannot be determined due to uncertainty of f _ib,res.

Retained polarization fraction

In the experimental setup used in this study, Xe gas mixture polarized at the SEOP cell was transferred to the NMR tube in which the ¹²⁹Xe NMR signal is measured. During this transfer process, the nuclear spin polarization of ¹²⁹Xe was depolarized by various factors. This polarization loss was simply defined here as:

$${P}_{{\rm{Xe}},{\rm{meas}}}={P}_{{\rm{Xe}},{\rm{SEOP}}}\cdot \exp \,(-\sum _{i}\,\frac{{\tau }_{i}}{{T}_{\mathrm{1,}i}})$$

(20)

where P _Xe,meas and P _Xe,SEOP are ¹²⁹Xe polarization at the measurement region and at the exit of the SEOP cell, respectively, i denotes a site in which the relaxation occurs, T _1,i and τ _i are the longitudinal relaxation time of ¹²⁹Xe at site i and the residence time of the gas mixture at site i, respectively. τ _i is related to the total gas flow rate at STP, F _tot, according to:

$${\tau }_{i}=\frac{{V}_{i}}{{F}_{{\rm{tot}}}}\cdot \frac{{p}_{i}}{{p}_{{\rm{s}}}}$$

(21)

where V _i is the volume at site i, and p _i and p _s are the total pressure of the gas at site i and standard-state pressure, respectively. The total gas flow rate is the sum of each flow rate for constituents included in the gas mixture, F _j :

$${F}_{{\rm{tot}}}=\sum _{j}\,{F}_{j}$$

(22)

The fraction of each constituent in the gas mixture was defined as:

$${f}_{j}=\frac{{F}_{j}}{{F}_{{\rm{tot}}}}$$

(23)

When the polarized gas mixture was transferred to the measurement region without separation procedure, the fraction of Xe in the gas mixture at the measurement region, f _Xe,meas, was equal to that at the SEOP region, f _Xe,SEOP:

$${f}_{{\rm{Xe}},{\rm{meas}}}={f}_{{\rm{Xe}},{\rm{SEOP}}}=1-\sum _{k}\,{f}_{k,{\rm{SEOP}}}$$

(24)

where f _k,SEOP is the fraction of buffer gases in the SEOP region. If the buffer gases were removed after the SEOP process, f _Xe,meas would increase with the following relation:

$${f}_{{\rm{Xe}},{\rm{meas}}}=1-\sum _{k}\,{f}_{k,\mathrm{res}}$$

(25)

where f _k,res is the fraction of residual buffer gases in the mixture after the removal process, and has a value ranging from 0 to f _k,SEOP. That is, if the buffer gases are removed completely from Xe gas, f _Xe,meas becomes unity, whereas if the buffer gases are not removed at all, f _Xe,meas = f _Xe,SEOP, which is the same as for the case described in Eq. 24. A retained polarization factor (RP) was defined as a polarization obtained from concentrated Xe, P _Xe,meas,conc, divided by that from diluted Xe mixture, P _Xe,meas,dil. This index means a factor that describes the fraction of polarization retained when the gas passes through the buffer gas separation procedure, and is expressed by using relations of Eqs 20 and 21 as:

$$RP=\frac{{P}_{{\rm{Xe}},{\rm{meas}},{\rm{conc}}}}{{P}_{{\rm{Xe}},{\rm{meas}},{\rm{dil}}}}=\frac{\exp \,(-{\alpha }_{{\rm{conc}}}/{F}_{{\rm{tot}},{\rm{conc}}})}{\exp \,(-{\alpha }_{{\rm{dil}}}/{F}_{{\rm{tot}},{\rm{dil}}})}$$

(26)

with:

$${\alpha }_{{\rm{conc}}}=\sum _{i}\,\frac{{V}_{i}}{{T}_{1,i,{\rm{conc}}}}\cdot \frac{{p}_{i}}{{p}_{{\rm{s}}}},\quad {\alpha }_{{\rm{dil}}}=\sum _{i}\,\frac{{V}_{i}}{{T}_{1,i,{\rm{dil}}}}\cdot \frac{{p}_{i}}{{p}_{{\rm{s}}}}$$

Here we assumed that the P _Xe,SEOP is the same value regardless of the use of the cold trap, because the SEOP process, and hence P _Xe,SEOP, was assumed not to be affected by the separation process in the experiments. Therefore, from Eqs 23 to 26, Eq. 10 can be further rewritten as Eq. 11.

Estimation of van der Waals-specific rate for isobutene

In order to estimate a van der Waals-specific rate for isobutene, ξ _ib, we conducted the following experiments. By using a gas mixture of single composition, 3% Xe/97% isobutene, the total flow rate dependence of P _Xe were measured for the two pressures in SEOP cell of p _cell = 15 kPa and p _cell = 101 kPa. The total flow rate was varied ranging from 35.1 sccm to 285 sccm. The results were analyzed by using following equation. Including a relaxation effect during the transfer process from the output of the SEOP cell to the measurement region into Eq. 2 (see also Retained polarization section), we can express the ¹²⁹Xe polarization at the measurement region as a function of total flow rate as follows:

$${P}_{{\rm{Xe}},{\rm{meas}}}\,({F}_{{\rm{tot}}})={P}_{0}\,(1-{e}^{-\beta /{F}_{{\rm{tot}}}})\,{e}^{-\alpha /{F}_{{\rm{tot}}}}$$

(27)

with:

$${P}_{0}={\gamma }_{{\rm{SE}}}{\tau }_{{\rm{SU}}}\langle {P}_{{\rm{Rb}}}\rangle ,\quad \beta =\frac{{V}_{{\rm{cell}}}}{{\tau }_{{\rm{SU}}}}\cdot \frac{{p}_{{\rm{cell}}}}{{p}_{{\rm{s}}}},\quad \alpha =\sum _{i}\,\frac{{V}_{i}}{{T}_{\mathrm{1,}i}}\cdot \frac{{p}_{i}}{{p}_{{\rm{s}}}}$$

where α is the same definition as the one described in Eq. 26. The experimental data were fitted by using Eq. 27 with P ₀ and ${\tau }_{{\rm{SU}}}^{-1}$ as fitting parameters. The α was also set as a fitting parameter for the data obtained from the experimental data at p _cell = 101 kPa whereas α = 8.4 sccm was used for that at p _cell = 15 kPa, which was measured as α _dil as described in the previous section. The values of V _cell = 848 cc was used in the analysis. The observed P _Xe,meas and fitted curves are shown in Fig. 5, and the estimated values from the fit are listed in Table 3 (upper). The van der Waals-specific rate for isobutene and ¹²⁹Xe spin relaxation rate can be calculated from the values of ${\tau }_{{\rm{SU}}}^{-1}$ for two cell pressures using relations of Eqs 3 and 4. In the calculation, literature values of ξ _Xe and 〈σv〉, and the number densities of atoms calculated for our experimental condition listed in Table 3 (lower) were used. The estimated values were ξ _ib = 2.61 × 10³ s⁻¹ and Γ_Xe = 1.84 × 10⁻⁴ s⁻¹.

Figure 5

Dependence of P _Xe on total gas flow rate using 3% Xe/97% isobutene mixture polarized at 15 kPa and 101 kPa. The experiments were performed without a separation procedure. The solid and dashed lines are the result of the fit using Eq. 27. The coefficient of determination of the fit was R ² = 0.9991 for 15 kPa and 0.9998 for 101 kPa.

Table 3 Parameters estimated from the analysis of the total gas flow dependence of P _Xe using 3% Xe/97% isobutene mixture polarized at 15 kPa and 101 kPa (upper).

Data Availability

All data generated or analysed during this study are included in this published article.