2.1. Stopped Flow SEOP

The experimental setup is sketched in Fig. 1. Mixtures containing various concentrations of ¹²⁹Xe and ⁸³Kr were hyperpolarized in borosilicate glass SEOP cells (length = 120 mm, inner diameter = 28 mm) containing ∼1 g Rb (99.75%; Alfa Aesar, Heysham, England, UK). The SEOP cell was housed in an aluminum oven with quartz windows and temperature controlled using heated air. The fringe field of a 9.4 T superconducting magnet provided the magnetic field of for the SEOP process. Unless otherwise specified, a line narrowed diode-array laser system (30 W, 0.25 nm linewidth Comet Module, Spectral Physics, Santa Clara, CA, USA) tuned to the D₁ transition of Rb (794.7 nm) was used to irradiate the SEOP cell with collimated, circularly polarized light of 23.3 W power (incident at SEOP cell).

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Figure 1. The experimental setup used for stopped flow SEOP.

A. Shuttling to high-field detection. The hp mixture is transferred to the detection cell by pressure equalization after the noble gas mixtures are hyperpolarized in the SEOP cell for a time period of t_d by the stopped flow SEOP method. B. Outline of the optical elements used in Fig. 1A. The elements λ/2 plate and second beam splitter were used to control the laser irradiation (B₄) to the SEOP cell (i.e. adjustment of the B₄/B₃ ratio - for details of power dependent measurements see section 2.2).

https://doi.org/10.1371/journal.pone.0049927.g001

Steady state, nuclear spin polarization was reached after 6 minutes for ¹²⁹Xe SEOP and after approximately 18 minutes for ⁸³Kr SEOP. However, due to time restraints ⁸³Kr SEOP times of only 8 minutes were used resulting to 80% completion of the built up, as verified by measurements at both high and low SEOP pressure. During SEOP, the gas mixture was contained within the SEOP cell with valve 2 closed (see Fig. 1A). Valve 1 was kept open initially to allow for pressure monitoring but was closed approximately 2 minutes before delivery. The borosilicate detection cell and PFA transfer tubing were evacuated (valve 3 open) during the SEOP duration. After SEOP completion, valve 3 was closed and valve 2 opened. Pressure equalization caused rapid hp gas transfer via 1.5 mm (inner diameter) PFA tubing into the 15 mm borosilicate detection cell. The detection cell located within a 9.4 T superconducting magnet and a Magritek Kea 2 spectrometer (Wellington, NZ) with custom-built probes tuned to the resonance frequencies of ¹²⁹Xe (110.5 MHz) and ⁸³Kr (15.4 MHz) where used for detection.

2.2. Laser Power Adjustment and Optical Measurements

In addition to the line narrowed Comet laser, two broadband 30 W Coherent (Santa Clara, CA, USA) fiber array packaged (FAP) lasers were also used as a non-narrowed laser system (2 nm linewidth) for SEOP efficiency comparison with the line narrowed Comet laser. Due to the experimental setting only 15.6 W of FAP laser power was used to irradiate the SEOP cell. To have a proper comparison between the narrowed and broadband laser systems the laser power of the narrowed laser was reduced to approximately match the power of the broadband system. Fig. 1B displays the optical elements used to reduce the power of the Comet laser. The first beam splitter in the path of the laser light was present in all experiments in this work and ensured that only a single plane of linearly polarized light would continue toward the SEOP cell. It was found that B₂ = 19 B₁ for the highly linear polarized Comet system and B₂ = B₁ for the FAP system (i.e. no linear polarization remaining due to passage through the long fibre optic cable of the FAP system). Laser power control was obtained through a λ/2 wave plate followed by a second beam splitter. By rotating the λ/2 wave plate the laser rejection (B₃) was controlled, thus enabling the power control for the laser irradiation (B₄) of the SEOP cell without changes in the irradiation profile (i.e. wavelength and spatial distribution). The incident laser power was measured at the SEOP cell using a Coherent PM150-50C water-cooled power meter. The same power adjustment procedure was also used for the power dependent measurements described in section 4.9.

The rubidium absorption linewidth in the presence of pure krypton, xenon, N₂, and a Xe - N₂ mixture was measured through absorption experiments similar to those by Driehuys and co-workers [46]. An incandescent light source with a consistent emission over the observed wavelengths irradiated the SEOP cell in place of the laser. A fibre optic cable leading to the optical spectrometer, HR2000+ Ocean Optics (Dunedin, Fl, USA) with a spectral resolution of 0.04 nm was placed at the rear of the SEOP cell to measure the D₁ absorption line width at 794.72–795.15 nm.

2.3. Temperature Control

The temperature of the SEOP cell inside the oven was maintained by an inflow of heated air near the back of the cell. Two thermocouples attached to the SEOP cell were used to measure the cell temperature. The first thermocouple was placed at the frontal region of the cell (i.e. in approximately 10 mm distance from the laser illuminated window) where it was carefully shielded from IR radiation, while the second thermocouple was positioned near the back region of the cell. The data from the two thermocouples were fed into a temperature controller. With this setup, the temperature controlled incoming air provided sufficiently stable temperature conditions, although the actual temperature inside the cell could not be determined. The temperature was measured on the surface of the SEOP cell at the thermocouple locations during ramping and steady-state processes. Typical temperature difference across the cell was less than 10 K after the steady–state conditions were reached.

2.4. Gas Mixtures

Research grade Xe (99.995% natural abundance, 26.4% ¹²⁹Xe; Airgas, Rednor, PA, USA), Kr (99.995% natural abundance, 11.5% ⁸³Kr; Airgas, Rednor, PA, USA), and N₂ (99.999% pure, Air Liquide, Coleshill, UK) were used to prepare the gas mixtures used in this study. The mixtures with varying noble gas contents were prepared prior to the SEOP experiments using a custom built gas mixing system. The ‘standard mixture’ described in section 2.6 required the use of research grade He (99.999% pure, Air Liquide, Coleshill, UK) in addition to other gases.

2.5. Determination of Obtained Polarization Values

For the determination of the actual polarization value, the integrated signal intensities of the hp noble gases were compared to the integrated signal intensity of a thermally polarized sample of the respective gas. For the thermal ⁸³Kr NMR measurement, a 15 mm borosilicate sample tube was pressurized to 560 kPa of natural abundance Kr gas leading to at 298 K [47]. Data were averaged from 360 acquisitions with a 360 s recycle delay time between pulses. Similarly, for the ¹²⁹Xe thermal measurement, a sample tube was pressurized to 500 kPa containing 4 amagat of natural abundance Xe gas and approximately 1 amagat of O₂ in order to reduce the longitudinal relaxation time to ( at 4.7 T [48]). Data were averaged from 120 acquisitions with 120 s recycle delay time between pulses. Taking into account the differences in concentration, pressure, and number of scans the integrated intensities from the thermal samples were compared with the integrated intensity of the hp samples to obtain the polarization enhancement over the thermal spin polarization.

For nuclei with arbitrary spin I the spin polarization P in a thermal equilibrium is given [45]:(1)with as the gyromagnetic ratio, as the Boltzmann constant, and as the Planck constant. Eq. 1 assumes Boltzmann population distribution at high temperatures where , a condition that is fulfilled for the thermally polarized samples described above. Note that the thermal samples and the ‘standard mixture’ (described in section 2.6) where rerecorded with another NMR system (Bruker, Avance III at 9.4 T) in order to confirm the obtained hyperpolarization values with the Kea 2 spectrometer.

2.6. Accuracy of Polarization Measurements

The SEOP generated polarization can be measured with high precision through high field NMR spectroscopy. However, the polarization values will scatter due to fluctuations in the SEOP cell. For example, the cell surface will ‘cure’ after reloading with rubidium metal, probably due to redistribution of surface condensed Rb, and the obtained hyperpolarization will increase initially for up to a few hours for cells newly loaded with rubidium. Further, contamination with oxygen, CO₂, or H₂O will lead to a slow decrease in the obtainable hyperpolarization. Some of the cells that appear to be nearly identical lead to slightly different hyperpolarization values. Because of the many factors that may influence these measurements data sampling was randomized during parts of the experiment. To characterize experimental variation in cell performance over time a polarization value was obtained for a standard mixture (5% Xe, 5% N₂, 90% He at 230±20 kPa and 373 K). This polarization value, averaged over a few experiments, was measured to be 44.0±5.4% and was further used for the ‘quality control’ test of a given SEOP cell. Three different SEOP cells that consistently achieved polarization values in this range were used during the course of the experiments. If the achievable polarization of a cell fell outside this range, it was cleaned and refilled with rubidium. Errors reported for the polarization measurements are based on the ±5.4% error of the standard mixture and scaled accordingly.

2.7. Data Analysis

Data analysis was performed using Igor Pro Version 6.2 from Wavemetrics (Lake Oswego, OR, USA). Fitting parameters for spin-exchange optical pumping were extracted using built-in non-linear least squares fitting algorithms.

Background to the ⁸³Kr and ¹²⁹Xe SEOP Experiments

The unit ‘amagat’ for the number density [M_i] of gas phase atoms or molecules is often used for convenience. In this work an amagat is defined as the density of an ideal gas at standard pressure and temperature of 101.325 kPa and 273.15 K and therefore . Note that the amagat was historically defined as the density of the specific gas at standard pressure and temperature resulting to the slightly different value for instance for xenon with [49]. The small difference of less than 1% between the two definitions indicates almost ideal gas behavior for xenon at this condition.

3.1. Expected Pressure Dependence

The increase of the noble gas spin polarization as a function of the total pressure decrease is expected from [21], [50]:(2)where is the optical pumping rate caused by laser irradiation of the alkali metal atoms (i.e. by irradiation of rubidium (Rb) atoms with circular polarized light at the D₁ transition at 794.7 nm for all experiments described in this work). In principle, the rate is a function of position within the pump cell due to the weakening of the laser in the optically thick medium [39], [51], however for the purpose of this work an averaged value is assumed for simplicity, noting also the presence of significant gas convection in the SEOP cell [52]. The rate constant describes the spin exchange rate and is the longitudinal relaxation rate of the noble gas atoms. The polarization, P_NG, increases with increasing SEOP time, t_p, until the contribution from the exponential term in Eq. 2 becomes negligible and the steady state value of polarization P_NG has been reached. The Rb electron spin polarization is limited by spin depolarizing collisions with inert gas atoms described by the gas (M_i) specific rate constants multiplied by the number density of the corresponding gas, . A further limitation is through radiation trapping described by the rate constant [30] that is further discussed below (see section 3.3) and by the rate constant that is caused by spin rotation interactions (i.e. interaction of the Rb 5s electron spin with Rb-M_i molecular rotation - see section 3.4). A major contribution to the Rb depolarization in the gas phase at SEOP pressures is caused by binary atomic collision. The rate constants caused by these interactions are directly dependent on the density of the respective atoms [33]. The rate constant of xenon is and is about 500 times larger than that of molecular nitrogen and more than 3 orders of magnitude larger than that of helium (see Table 1). Similarly, the rate constant of krypton, , is a factor of 100 higher than that of molecular nitrogen. Therefore, even in the 95% nitrogen and 5% krypton gas mixture the contribution of molecular nitrogen to the overall Rb electron spin relaxation is only about 14% of the total gas phase relaxation caused by binary collisions. Moreover, in all other mixtures used in this work the nitrogen contribution to rubidium 5s electron spin depolarization through binary collisions is assumed to be below 4%.

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Table 1. ⁸³Kr and ¹²⁹Xe literature rate constants used in Eq. 2.

https://doi.org/10.1371/journal.pone.0049927.t001

3.2. Contribution of Rb-Rb Collisions

Unlike typical experiments at high SEOP pressure, depolarization of the rubidium electron spin due to rubidium-rubidium atom collisions may contribute significantly to Rb depolarization in the gas phase at low SEOP gas densities. The fairly large corresponding rate constant indicates that electron magnetic dipole – dipole interactions are responsible for the relaxation mechanism [51]. Depolarization due to Rb-Rb collisions depends on the rubidium number density [Rb] and is therefore a function of the SEOP cell temperature. An empirical equation (replacing an older, similar equation by Killian [53]) for [Rb] in m⁻³ as a function of temperature T in Kelvin is [54], [55]:(3)

Using Eq. 3 one obtains that at 373 K. However Eq. 3 should be used with caution for Rb concentration calculations as uncertainties arise from the difficulty of proper temperature monitoring inside the SEOP cell during on-resonance irradiation with a high-powered laser as explained further in the text (see section 4.3 for discussion of the correction factor, c^Rb, to [Rb]).

The potential uncertainty in temperature is quite inconsequential for the rubidium depolarization in ¹²⁹Xe SEOP since the rubidium density at a temperature of 373 K leads to a relaxation rate of that contributes less than 2% to the Rb gas phase relaxation at the lowest pressure (5 kPa) and the lowest xenon concentration (5.0%) used. The significance of Rb-Rb collisions to the Rb depolarization decreases further as the total gas pressure and the xenon concentration increase. However, the situation is quite different in ⁸³Kr SEOP. Firstly, the rate constant is about 5 times smaller than , thus increasing the relative importance of for the rubidium depolarization. Secondly, ⁸³Kr SEOP produces the highest nuclear spin polarization at 433 K and, according to Eq. 3, . This translates into 27 fold increase in Rb concentration as compared to and Rb-Rb collisions contribute therefore significantly to the rubidium depolarization, in particular at low SEOP pressures. For example, at 30 kPa total gas pressure the contribution of to the Rb gas phase depolarization ranges from approximately 2% (for the 74% krypton mixture) to 5% (for the 25% krypton mixture) to about 20% for the leanest (5%) krypton mixture. Therefore uncertainties in SEOP temperature (and therefore [Rb]) can affect the second term in Eq. 2 for ⁸³Kr SEOP.

3.3. Radiation Trapping

Molecular nitrogen is an important component of an SEOP gas mixture because it can, unlike mono-atomic noble gasses, dissipate energy from excited rubidium electronic states into vibrational modes [32], [56]. This non-radiative relaxation pathway reduces rubidium fluorescence, depending on the N₂ number density [30]. In SEOP mixtures with high rubidium density [Rb], fluorescence may be detrimental to the Rb spin polarization because it can lead to radiation trapping where a single incident circularly polarized photon gives rise to multiple scattered photons that are arbitrarily polarized. Wagshul and Chupp [56] have reported a formula based on earlier experimental work [57] that quantifies the extent of quenching through N₂. A slight modification of this formula, i.e. multiplication with the term from SEOP in the absence N₂, leads to an expression similar to the one reported by Brunner and co-workers [52]:(4)where was obtained in an earlier ¹²⁹Xe SEOP measurement [30]. Unfortunately, the effect of laser power, cell temperature, [Rb], and cell geometry on are little explored to date. For this work is assumed to provide a good approximation for ¹²⁹Xe SEOP at 373 K but is expected to be significantly higher for ⁸³Kr SEOP at 433 K due to the strongly increased rubidium density. Radiation trapping can be important at low pressure SEOP and is therefore included in Eq. 2.

3.4. Rb Depolarization Caused by Spin-rotation Interactions

At lower pressures with correspondingly longer lifetimes of the Rb-Xe van der Waals complexes, a significant Rb polarization loss is induced by spin rotation interaction [58]. In Eq. 2 this effect is represented by the rate . The functional dependence of on SEOP gas pressure and composition is difficult to quantify. For an SEOP gas mixture with fixed concentration in the long-lifetime pressure regime (i.e. at very low pressures), the relaxation rate will increase with the pressure increase due to the intensified complex formation. At sufficiently high pressure the short molecular lifetime regime is reached and the further increase of complex formation with increasing pressure will be offset by higher breakup rates, thus resulting in pressure independent . In this regime, the Rb nuclear-electron hyperfine interaction limits the influence of spin-rotation relaxation. At further pressure increase however, the very short lifetime regime is reached with a diminished hyperfine interaction and therefore, starts to increase again with increasing pressure until the hyperfine interaction has become completely negligible. For a 1% Xe, 1% N₂, and 98% He SEOP mixture, a rate of at 423 K (and an approximately 60% higher value at 353 K) has been reported for the short lifetime limit [58]. This value is comparable to that of caused by binary collisions in ¹²⁹Xe SEOP at 40 kPa and 373 K in the 5% Xe - 95% N₂ mixture. The relaxation rate is however mixture dependent. For instance completely replacing helium by nitrogen should considerably reduce [59] as N₂ facilitates the break-up of the Rb-NG van der Waals dimer better than helium. Unfortunately literature data of for the mixtures used in this work are not available. SEOP conditions in the current work are likely to create short to very short lived Rb-NG van der Waals complexes. Therefore, to a first approximation and within the scope of this work, will be considered as pressure independent because of its general pressure independence in the short lifetime limit and because of its relatively small pressure dependence compared to binary relaxation, in the very short lifetime limit. In the lower pressure regime, where actually dominates Rb depolarization rate this crude approximation is destined to fail, therefore experimental data fitting with Eq. 2 (or modifications thereof) was not attempted in this pressure limit.

3.5. The Spin Exchange Rate

The spin exchange rate results from the added contributions of (1) spin exchange in rubidium - noble gas van der Waals complexes that is characterized by the rate constant, and (2) from spin exchange caused by binary collisions quantified by the velocity averaged binary spin-exchange cross section . Literature values of and for ⁸³Kr and ¹²⁹Xe are listed in Table 1 [18], [27], [60], [61], while Eq. 5 shows the contribution of both rates to [27]:(5)

The rates and are comparable to their corresponding rates at a densities of 0.25 amagat and 0.4 amagat respectively (in the absence of nitrogen). In this density range, van der Waals dimers (mediated through three-body collisions) and binary collisions contribute about equally to the spin exchange. However, binary collisions will eventually dominate in the spin exchange process as the contributions from van der Waals complexes is expected to decline with the increase of the noble gas concentration and therefore its density [NG].

The N₂ molecules in the SEOP mixture also contribute to the Rb-NG dimer break up. This contribution is quantified by the characteristic pressure ratio listed in Table 1 with the specific values for xenon and krypton [18], [27], [62]. The parameter r in Eq. 5 is the partial pressure ratio (or density ratio) in a mixture. The ratio b shows that a dilution of xenon in nitrogen can be beneficial to . However, a dilution of krypton in nitrogen can be detrimental to because the break up of van der Waals complexes is facilitated by nitrogen more than by krypton. Note however, that nitrogen is still beneficial for ⁸³Kr SEOP because of its radiation quenching effect (section 3.3) and because (section 3.1).

4.1. Noble Gas Polarization as a Function of SEOP Gas Pressure

Steady state, or near steady state spin polarization was obtained for the ¹²⁹Xe mixtures after about 6 min of SEOP at 373 K and a near steady state (approximately 80%) was reached after 8 min of SEOP for ⁸³Kr mixtures at 433 K. The steady state polarization P is shown as a function of the total SEOP pressure in Figs. 2 and 3 for hp ⁸³Kr and hp ¹²⁹Xe respectively. The noble gas polarization P of both isotopes in all mixtures increased as the total gas pressure was decreased from 350 kPa to below ambient in all studied mixtures. The maximum steady state polarization for hp ⁸³Kr was obtained at a total gas pressure , in the range of 35–50 kPa, depending on the krypton concentration used. Similarly, a polarization maximum was observed for hp ¹²⁹Xe, however at a lower total pressure range of . Reducing the pressure below these values resulted to a rapid drop in the steady state polarization of the noble gases. In order to facilitate the following discussions, the SEOP pressure that resulted to the highest observed steady state polarization , will be labeled as . Table 2 lists for various mixtures, the corresponding total SEOP pressure , and the corresponding SEOP partial pressure .

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Figure 2. ⁸³Kr spin polarization, P, as a function of SEOP pressure.

⁸³Kr spin polarization as a function of SEOP cell pressure and combined number density ([Kr]+[N₂]) at 433 K for four different gas mixtures. See the legend in the figure for symbol explanation. Polarization data are detailed in Table 2. Data analysis using Eq. 8 with and as fitting parameters is shown in solid lines and resulting values are reported in Table 4. Fitting of the data was also not attempted for values much lower than ; the dotted lines are extrapolations to pressure ranges outside the fitting region.

https://doi.org/10.1371/journal.pone.0049927.g002

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Table 2. Maximum noble gas polarization , maximum apparent noble gas polarization , and corresponding gas pressures extracted from data of Figs. 2 and 3.

https://doi.org/10.1371/journal.pone.0049927.t002

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Figure 3. ¹²⁹Xe spin polarization, P, as a function of SEOP pressure.

¹²⁹Xe spin polarization as a function of the SEOP cell pressure and combined number density ([Xe]+[N₂]) at 373 K for four different gas mixtures. Please refer to the legend in the figure for symbol explanation. Polarization data are detailed in Table 2. A. Solid lines represent data analysis with Eq. 8. Extrapolation of these theoretical curves to pressure ranges outside the fitted region are shown by dotted lines. B. Same experimental data as in (A) but the solid lines represent now the data analysis using Eq. 8 with the pressure dependence of the Rb D₁ absorption taken into account through Eq. 9. Extrapolation to pressure ranges outside the fitted region are shown by dotted lines. Fitting parameters for (A) and (B) are reported in Table 5A and 5B, respectively.

https://doi.org/10.1371/journal.pone.0049927.g003

As can be seen from Table 2, the maximum ⁸³Kr polarization of was reached for the 5% krypton - 95% nitrogen mixture at an SEOP pressure of 54 kPa. This is a remarkably high spin polarization for a quadrupolar spin system observed at ambient temperature. ¹²⁹Xe SEOP at a pressure of 46 kPa using a 5% xenon mixture resulted to spin polarization. Both results were obtained with a 23.3 W laser irradiation that resulted in a power density of 2.6 W/cm² at the SEOP cell front window.

Since hp noble gasses remain diluted without cryogenic separation process, the obtained polarization does not enable easy comparison with experiments that utilize cryogenic separation. It is therefore useful to define an apparent polarization, P_app, scaled to the polarization, P, in the pure hp noble gas that would result to the same MRI signal.(6)

The apparent polarization, P_app, provides a measure of the ‘usable’ spin polarization in MR experiments if the hp noble gas is not separated from the nitrogen after SEOP. Table 2 also lists the apparent maximum steady state polarization . The highest was obtained for krypton with the 25% and 50% krypton mixtures leading in both cases to . Mixtures with 40% and 50% of xenon lead to the highest values with . In cases where similar values are obtained for different SEOP mixtures, economical considerations will prefer the mixture with lower noble gas concentration, in particular when expensive isotopically enriched gases are used.

Note the maximum polarizations listed in Table 2 were generated every 6 minutes for hp ¹²⁹Xe and every 8 minutes for hp ⁸³Kr (and with slightly increasing values for P_Kr at SEOP times up to 18 min). The ideal pumping time for MRI applications however may be shorter than these values if polarization can be compromised in favor for faster experimental repetition.

4.2. SEOP Temperature

The three-body spin exchange rate and the binary cross section are both more than two orders of magnitude smaller for the Rb-⁸³Kr system than for the Rb-¹²⁹Xe system. The resulting small rate has two adverse consequences for ⁸³Kr SEOP as predicted by Eq. 2. Firstly, a smaller in the presence of a higher relaxation rate leads to a reduced steady state polarization P for ⁸³Kr compared to that for ¹²⁹Xe under otherwise identical SEOP conditions. Secondly, smaller values further result in slower ⁸³Kr SEOP polarization build up as compared to ¹²⁹Xe SEOP, thus increasing the repetition time in MRI applications. In order to, at least partially, offset this effect [Rb] needs to be raised through elevated ⁸³Kr SEOP temperatures. In addition to the increased [Rb], a further advantage of elevated ⁸³Kr SEOP temperatures comes from reduced quadrupolar relaxation of ⁸³Kr on the cell surface, as discussed in Appendix 2 in Supporting Information S1. It was found that up to a temperature of 433 K the benefit from the increased spin exchange rate for ⁸³Kr SEOP outweighs other detrimental effects arising from elevated temperatures. In contrast, a temperature of 373 K was found to produce the highest ¹²⁹Xe spin polarization in this work. Examples of adverse effects at higher temperatures are increased Rb-Rb collision rates, as discussed in the section 3.2, and increased laser absorption in the rising optical density of the rubidium vapor phase.

4.3. Results from Inversion Recovery ⁸³Kr SEOP Experiments

The noble gas self-relaxation rate is difficult to obtain from published data as it is specific to some SEOP conditions, for example SEOP cell dimensions and its surface temperature. However, the combined rate constants can be extracted from the time dependence of the polarization obtained in SEOP experiments according to Eq. S1 in Appendix 1 in Supporting Information S1 (i.e. utilizing the time dependence of Eq. 2). In principal, build up curves can be measured directly inside the SEOP cell [28], [61], [63]. However, in this work the SEOP time dependence is determined through remotely detected NMR experiments (i.e. after hp gas transfer into the high field magnet) as no further experimental modification was required for the existing instrumentation. The drawback of this procedure was that the measurement of the build up curves required time-consuming point-by-point experiments. The data from inversion recovery ⁸³Kr SEOP experiments (see Appendix 1 in Supporting Information S1) are shown in Fig. 4A and the rate constants, , obtained from fitting with Eq. S1 are listed in Table 3.

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Table 3. ⁸³Kr and ¹²⁹Xe values for obtained from fitting of inversion recovery build up data (see Fig. 4) with Eq. S1.^A.

https://doi.org/10.1371/journal.pone.0049927.t003

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Figure 4. Inversion recovery ⁸³Kr and ¹²⁹Xe SEOP.

A. Inversion recovery of ⁸³Kr polarization after SEOP time, t_p, for two krypton-nitrogen gas mixtures at different SEOP pressures. Please refer to the legend in the figure for symbol explanation. B. Inversion recovery of ¹²⁹Xe polarization after SEOP time, t_p, for two xenon-nitrogen gas mixtures at different SEOP pressures. The inversion recovery data from both (A) and (B) were analyzed using Eq. S1. Polarization data were normalized to their values at for ⁸³Kr and for ¹²⁹Xe to visually compare the rate differences of the mixtures and pressures. The obtained rate constants from fitting of both (A) and (B) are reported in Table 3.

https://doi.org/10.1371/journal.pone.0049927.g004

The spin exchange rates listed in Table 3 were calculated using Eq. 5 with the relevant literature values reported in Table 1. However, the experimental value obtained from the inversion recovery experiments for ⁸³Kr SEOP below 200 kPa presents a problem when combined with the calculated spin exchange rate values in order to determine the first fraction in Eq. 2, . Using , Eq. 2 predicts an upper limit for the ⁸³Kr polarization of . In reality, any experimentally measured value for P_Kr would be further reduced because of P_Rb <1 and due to incomplete (approximately 80%) build up at min in SEOP. In remarkable disagreement, the experimental data show polarization values of up to and for the 5% krypton and 25% krypton mixtures, respectively (see Fig. 2 and Table 2).

The discrepancy between predicted maximum possible polarization and observed polarization may be due to incorrect literature data in Table 1 used for determining . Note that the literature data was obtained at temperature conditions different from the ones used in this work. Another potential culprit is a wrong value of [Rb] obtained from Eq. 3 based on temperature measurements outside the cell. The temperature inside the cell under high power laser irradiation in the presence of the liquid rubidium metal is unknown. Wagshul and Chupp [51] noted a discrepancy of a factor of two or more in [Rb] under ¹²⁹Xe SEOP conditions from the prediction by the equilibrium vapor equation. Further doubt about [Rb] determination through external temperature measurements arises from Raman spectroscopical experiments by Happer and co-workers that provide access to the in situ temperature distribution within the SEOP cell by measuring the rotational - vibrational N₂ temperature [64]. The internal temperatures were found to substantially exceed those measured externally at the cell outside surface. Finally, a numerical simulation study [52] also draws a very complex picture about a non-uniform temperature distribution within a static SEOP cell with significantly elevated internal temperatures. The same, perhaps amplified problem may occur for ⁸³Kr SEOP experiments that are run at the cell outside temperature of 433 K. A correction factor c^Rb for the rubidium concentration from Eq. 3 is therefore introduced for this work. It follows from the discrepancy between observed and calculated described above, that c^Rb >2. An upper limit for the correction factor c^Rb <8 is obtained from the fact that cannot be negative. Further, the upper limit can be reduced to c^Rb <6 if one assumes that relaxation rate of ⁸³Kr is not significantly lower than typical rates found for ¹²⁹Xe under SEOP conditions. Further determination of c^Rb for ⁸³Kr SEOP was not possible from the data in this work, however the qualitative outcome of the fittings in Fig. 2 is not strongly affected within the range 2< c^Rb <6. The correction factor was set to for further data analysis in Fig. 2.

The similarity in the values in Table 3 for ⁸³Kr SEOP is caused by the [Kr] independent rate constant that dominates over the term even at the low pressures of for all krypton mixtures. As pressure , the van der Waals contributions will be even further marginalized. As a consequence, the inversion recovery ⁸³Kr SEOP curves in Fig. 4A all display similar time dependence at SEOP pressures below 200 kPa. At 310 kPa, the combined rate constant is increased due to the increased relaxation rate constant . The functional form of the pressure dependence of is explored in Appendix 2 in Supporting Information S1. Rewriting Eq. S4 as a function of the krypton number density and using leads to:(7)

4.4. ⁸³Kr Polarization vs. SEOP Pressure Dependence above

The pressure dependence of the ⁸³Kr polarization, shown in Fig. 2, should be described in principle by Eq. 2 for SEOP pressures above . Most of the relevant parameter are listed either in Table 1 or described by Eqs. 3, 4, 5, and 7. The equation used for fitting of the data in Fig. 2 is:(8)where and (in Eq. 4) were used as fitting parameters. The correction factor was used for [Rb], as described in section 4.3. A functional form of is given by Eq. 7 (also based on ). The scaling factor f = 0.8 in Eq. 8 accounts for the limited SEOP duration of 8 min that caused the polarization build up to be approximately 80% completed. The rubidium electron spin relaxation due to spin-rotation interaction in van der Waals complexes is represented by the rate that is assumed to be constant under the SEOP conditions used in this work (see section 3.4). When used as a third fitting parameter, consistently emerged with negative or near zero values with little influence on the other fitting parameters, indicating small to negligible spin-rotation interactions for ⁸³Kr. It was therefore set to zero and the results for and are listed in Table 4.

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Table 4. Values for and from fitting experimental data of ⁸³Kr spin polarization as a function of SEOP cell pressure in Fig. 2 using Eq. 8.^A.

https://doi.org/10.1371/journal.pone.0049927.t004

At a first glance, the fitting result in Fig. 2 (solid lines) appear to demonstrate that Eq. 8 qualitatively describes the dependence of the ⁸³Kr SEOP polarization on [Kr] at pressures above . The obtained function describes the experimental observation reasonably well beyond the fitting range (see dashed line). The resulting rate constants are fairly consistent but are about three fold increased compared to previously reported ¹²⁹Xe SEOP data [30]. These values are quite high but an increase in with increasing rubidium density is expected. The rates listed in Table 4 are low and indicate low pumping rates as it would be expected for an optically thick medium with high [Rb]. The 2.8 fold decrease of with increasing krypton concentration is further discussed in section 4.8.

4.5. Results from Inversion Recovery ¹²⁹Xe SEOP Experiments

In contrast to ⁸³Kr SEOP, the time behavior of the ¹²⁹Xe SEOP polarization shown in Fig. 4B depends strongly on total pressure and gas composition (see Table 3). This observation is in agreement with previous work [28] and was expected since , i.e. the van der Waals contribution to the spin exchange rate caused by three-body collisions, plays a more dominant role for ¹²⁹Xe SEOP than for ⁸³Kr SEOP. An increased relative to the rate caused by two body collisions will result in a stronger noble gas density dependency for in Eq. 5. Furthermore, the time scale of the inversion recovery is accelerated at low xenon density compared to that of ⁸³Kr (Fig. 4A). However, at high [Xe], is reduced and the ¹²⁹Xe SEOP time dependence (i.e. the rate constant ) becomes similar to that of ⁸³Kr SEOP at high [Kr]. The reason for the similar B values at high noble gas densities are of course different for the two isotopes: The dominating term in ¹²⁹Xe SEOP is that decreases with [Xe], whereas is assumed to be pressure independent. The ⁸³Kr SEOP time dependence, on the other hand is controlled through that increases with [Kr] while rate of ⁸³Kr is mostly pressure independent.

The combined rate constants and the rates for ¹²⁹Xe, as listed in Table 3, imply that the correction factor for [Rb], if needed at all, must be because of the requirement . Once again, cannot be further determined and the average of the range is taken. Furthermore, the assumption is made that is caused mainly by interactions with the surface and is therefore pressure and gas composition independent. This seems to be indeed the case with the exception of the data taken at 50 kPa that scatter widely. However, for ¹²⁹Xe SEOP at this pressure the values for are relatively small compared to B and a significant error is not unlikely. Excluding 50 kPa data and averaging the 180 kPa and 300 kPa data one obtains _using . Note, for it follows that in better agreement with data by Goodson et al. [28] who previously determined in a coated SEOP cell. However, as will be discussed in the following section, the exact value is not very important for the description of ¹²⁹Xe SEOP in this work.

4.6. P_Xe vs. SEOP Pressure Dependence above

A qualitative analysis of the data shown in Fig. 3A was attempted with Eq. 8 derived from Eq. 2 with the inclusion of the correction factor for the rubidium density, . During the fitting procedure the rates and were used as the fitting parameter with the correction factor set to and the nuclear relaxation term to . Unlike for ⁸³Kr SEOP that is run at a temperature of 433 K, the radiation trapping term for ¹²⁹Xe SEOP could be taken from literature data with [30]. Furthermore, the SEOP duration was long enough to reach the steady state polarization value and therefore one could set f = 1. The rest of the constants used in the fitting procedure were taken from Table 1, in the case of the multiple choices of the literature data the constants from reference [27] were used. The resulting fits over the pressure range from 45 to 240 kPa are displayed (solid lines) in Fig. 3A (see also Table 5A for the relevant fitting parameters). The theoretical curves were further extended over the entire pressure range using the values for and obtained from fitting (dotted lines). Although, fitting curves using Eq. 8 seem to qualitatively describe the experimental behavior in Fig. 3A, the results listed in Table 5A are not within the expected range. The optical pumping rate constant are quite high and, the rate constant values are about one order of magnitude higher than a previous literature value for a 1% Xe, 1% N₂, and 98% He SEOP mixture with at 353 K [58] (see section 3.4). Furthermore, increasing [Xe] and decreasing [N₂] should lead to increasing , however the value for the mixture 78.2% Xe drops below for all other mixtures and exhibits an unacceptably high error.

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Table 5. Values for , and rates obtained from the fitting of experimental data of ¹²⁹Xe spin polarization as a function of SEOP cell pressure (Fig. 3) using Eq. 8.^A.

https://doi.org/10.1371/journal.pone.0049927.t005

Note that the general appearance of the overall shape of the fitting curves is not dramatically affected by (at least within the range ), nor do the resulting values for the fitting parameters change significantly. Generally, the larger ratio makes the first term in Eq. 8 less important for ¹²⁹Xe SEOP compared to ⁸³Kr SEOP. However, the unsatisfactory results of the data fitting with Eq. 8 will need some further considerations. The rubidium D₁ absorption linewidth may hold important information for the second term in Eq. 8 and may provide a better understanding of the experimental data. The effect of the D₁ linewidth is discussed in the following section.

4.7. Non-linear Pressure Broadening of the Rb D₁ Absorption Linewidth

Fig. 5A shows IR absorption spectra of rubidium within the SEOP cell when illuminated by an incandescent light source. Spectra were acquired at 433 K with pure krypton for three pressures: 9 kPa, 68 kPa and 434 kPa. Only the D₁ transition (i.e. the transition at 794.7 nm) and its linewidth are relevant for the SEOP studied in the present work. The pressure behavior of the D₁ linewidth is depicted in Fig. 5B. Further theoretical analysis suggests that a [Xe]^1/3, [Kr]^1/3, and [N₂]^1/3 functional form provides a reasonably good description of the absorption linewidth behavior over the studied pressure range. The non-linear Rb D₁ line dependence on gas density dependence is in contrast to the linear gas density dependence usually found for alkali metal D₁ or D₂ transitions (see for instance [46], [65]). The cause for this unexpected behavior was not further investigated and the exact functional description would benefit from refinement in future research.

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Figure 5. Rubidium IR absorption linewidth as a function of gas pressure.

A. IR absorption spectrum of Rb in the SEOP cell containing pure krypton gas at 433 K at three different pressures as detailed in the figure legend. The absorption lines experience a pressure broadening and, to a lesser extent, a shift to higher wavelengths with increasing pressure. B. Rb D₁ absorption linewidth as a function of SEOP cell pressure at 433 K for pure krypton (solid red triangles), for pure N₂ at 433 K (solid green squares), for pure xenon at 373 K (solid black circles), and for a mixture of 50% xenon with 50% N₂ (open black circles). The pressure dependence of the absorption linewidth can be approximately described by (dashed lines). Eq. 9 was concluded from the observed linewidth dependence. The linewidth of the narrowed laser and the broadband laser are 0.25 nm and 2.0 nm respectively, and are indicated in the figure by horizontal dotted lines.

https://doi.org/10.1371/journal.pone.0049927.g005

Fig. 5B shows that the linewidth in the presence of either krypton or N₂ at 433 K is much broader than that in the presence of xenon at 373 K. The Rb absorption linewidth with N₂ at 373 K was too close the resolution limit of the optical spectrometer used (i.e. 0.04 nm). The data demonstrates that all krypton-nitrogen mixtures at 433 K should lead to a D₁ broadening that is much larger than the laser linewidth (0.25 nm – dashed line in Fig. 5B) at all pressures above .

However, a different situation occurs for xenon at 373 K, in particular in mixtures with N₂. In these cases the laser linewidth may exceed the D₁ linewidth and thus not all of the laser power will be absorbed. The effect of the linewidth is difficult to quantify, in particular since exact on-resonance irradiation can be disadvantageous as explored in detail by Wagshul and Chupp [51] and recently observed for high power irradiation by Wild and co-workers [66] and by Goodson and co-workers [67]. However, for this work the simple assumption is made that laser irradiation with a wider linewidth than the D₁ linewidth will lead to a pressure dependent pumping rate that follows the same dependence as the D₁ linewidth itself:(9)with as the optical pumping rate at 1 amagat total gas density. The density dependent rate constant as defined in Eq. 9 replaces in Eq. 8. Using and as fitting parameters with all other parameters kept identical to the ones used in section 4.6, fitting with Eq. 8 leads to the solid lines depicted in Fig. 3B with the values for rate constants listed in Table 5B. Once again, the theoretical curves were further extended over the entire pressure range using the values for and obtained from fitting (dotted lines). The results for listed in Table 5B are similar to previous literature values [30] obtained under similar conditions and seem to be constant for different gas compositions except for the highest xenon concentration where a clear drop in results. The value for at 373 K for the mixture with 5% in Table 5 is identical to the literature value for a 1% Xe, 1% N₂, and 98% He SEOP mixture at 353 K [58]. Further, with increasing [Xe] the values for show a monotone increase. Overall, the consideration of the pressure dependence of the Rb D₁ (Eq. 9) in Eq. 8 appears to result to more realistic values for and . While there is little effect on the qualitative appearance between the fitted curves in Figs. 3A and 3B, the extended curve (dotted line) in Fig. 3B provides a better description of the observed data compared to the one in Fig. 3A.

It should be noted again that Eq. 9 should be handled with care since it is based on a number of simplifying assumptions. Firstly, neither the line shape of the pressure broadened Rb D₁ transition nor the emission line shape of the frequency narrowed diode-array laser are Lorentzian or otherwise straightforwardly defined. Further, at high xenon concentration and pressure, the adsorption linewidth starts to exceed the laser linewidth causing the validity of the underlying concept in Eq. 9 to end. This may be the case in particular at high SEOP pressures for the mixture containing 78.2% xenon. Another factor, not considered here, is the pressure dependent shift of the D₁ transition. For ¹²⁹Xe SEOP at 373 K this shift is small with 0.13 nm over the used pressure range for pure xenon. Although the shift is larger at 433 K with 0.43 nm over the used pressure range for krypton (see Fig 5A) it is still small compared to the D₁ line broadening. Despite the limitation of Eq. 9, requiring more refinement in future research, the current work suggests that the effect of pressure broadening needs to be considered for a correct description of variable pressure ¹²⁹Xe SEOP with narrowed lasers.

4.8. Thermal Properties of SEOP Gases

The values for ⁸³Kr SEOP listed in Table 4 of change by a factor of approximately 2.8 between the gas mixtures used. The rates found in ¹²⁹Xe SEOP summarized in Table 5B are less affected by [Xe] except for the mixture containing 78.2% xenon where the rate drops significantly. However, nothing in the general theory outlined in section 3 gives rise to the expectation that is affected by the noble gas-nitrogen ratio of the various mixtures. Nevertheless, at the same time it has been noted that the temperature gradient between the front and the back of the SEOP cell changed when SEOP mixture was altered.

The mixture dependent changes in the temperature gradient across the SEOP cell may have been induced by the different thermal conductivity of the used gas mixtures. Under the experimental SEOP conditions, N₂ has an approximate 2.5 times larger thermal conductivity than krypton (and 4.5 times larger than xenon) [68]. Therefore, as the krypton or xenon concentration in the SEOP cell is increased, the decreasing thermal conductivity allows for higher temperature difference between the laser-illuminated front of the SEOP cell and its back. The consequences of this temperature gradient are unknown but changes in local rubidium concentration, thermal convection, and laser penetration are likely to lead to different convection patterns within the cell [52], [69]. Note also, that the heat capacity, of N₂ is more than 5/3 larger than that of a mono-atomic noble gas. Therefore, the corresponding changes between the gas mixtures may potentially have a profound impact on quantitative SEOP measurements and comparison of data between different noble gas mixtures needs to be handled with great caution. Due to the higher temperature, ⁸³Kr SEOP may be stronger affected than ¹²⁹Xe SEOP.

Thermal conductivity and heat capacity effects may explain the mixture dependent values but would of course also require mixture dependent values. Unfortunately, the limited data in this work does not make the usage of a further fitting parameter reasonable in particular since the differences between the values are not too excessive.

However, a serious concern for the fitting of the experimental data would be SEOP gas pressure of the temperature, , and . Fortunately, no effect on the pump cell temperature gradient with pressure changes has been noted. Moreover, the well-known equation for the thermal conductance, , of an ideal gas is(10)where is the mean average velocity of the gas molecules, is the mean free path, is the molar heat capacity at constant volume, [M] the density of the gas, and N_A is Avogadro’s number. The thermal conductivity of an ideal gas is pressure independent because the gas density is directly proportional to the pressure, whereas and is also pressure independent.

4.9. Effect of Laser Power and Laser Linewidth

The effects of laser power on the polarization curves are shown in Fig. 6. The power of the laser irradiation was adjusted in the linear polarized part of the laser beam rotating the plate positioned in front of a beam splitter (see experimental section or Fig. 1B). This procedure allowed for the control of the laser irradiation power (incident at the SEOP cell) without changing the linewidth, the line shape, and irradiation pattern (i.e. beam shape). Fitting of the data was performed using Eq. 8 in the same fashion as in section 4.7 using as defined in Eq. 9. The parameter at 23.3 W power was taken from literature [30] and was scaled linearly with the relative decrease of laser power.

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Figure 6. ¹²⁹Xe polarization, P, dependence on laser power.

¹²⁹Xe spin polarization as a function of SEOP cell pressure for two different gas mixtures at four different SEOP laser power levels. Please refer to the figure legend for symbol explanation. The laser power was measured in the front of the SEOP cell. Data were analyzed using Eq. 8 (utilizing Eq. 9) within the fitting region (solid lines). Extrapolations to pressure ranges outside the fitted region are shown by dotted lines. The fitting procedure is discussed in section 4.9 and the results of the data analysis are listed in Table 6.

https://doi.org/10.1371/journal.pone.0049927.g006

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Table 6. Values of rates from fitting of the ¹²⁹Xe spin polarization data for different laser powers and laser linewidths in Figs. 6 and 7 using Eq. 8.^A.

https://doi.org/10.1371/journal.pone.0049927.t006

Measurements at 23.3 W power were performed redundantly under the same pumping conditions as the ones used for 5% and 50% Xe mixtures displayed Fig. 3. The resulting rates, , are listed in Table 6 for the two mixtures at various laser power levels.

The increase in as the laser power is raised from 5.7 W to 23.3 W is 3.0 fold for the 50% mixture and is 2.6 fold for the 5% xenon mixture. However, the dependence of on laser power (see Fig. 6) is more pronounced for the 50% mixture (approximately 2.0 fold increase in the polarization between 5.7 W to 23.3 W) compared to the 5% xenon gas mixture (1.3 fold increase). The increasing importance of laser power for SEOP with higher noble gas concentration is due to the second fraction in Eq. 8 that makes the (or ) values more relevant for the obtained polarization, , if the destructive rates are high. Therefore higher laser power is particularly beneficial for higher noble gas concentration SEOP. This is an important observation for the concept of cryogen-free SEOP.

Fig. 7 depicts a comparison of SEOP results obtained with a line narrowed (0.25 nm) Comet laser module using reduced laser power (17.3 W) and with a similar power (15.6 W) but using much larger linewidth (Coherent FAP, approximately 2 nm line width). Data were analyzed with Eq. 8 in identical fashion as above and the resulting for broadband laser ¹²⁹Xe SEOP are listed in Table 6. Clearly, laser line narrowing is beneficial for SEOP as it leads to a 9.3 fold increase of for the 50% xenon mixture and to the 6.4 fold increase for the 5% xenon mixture. Similar to the laser power trend, the resulting improvement of through line narrowing is particularly strong for SEOP with high xenon concentration. A 4.7 fold increase of is observed in Fig. 7 for the 50% xenon mixture as compared to the 2.7 fold increase for the 5% xenon mixture.

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Figure 7. ¹²⁹Xe polarization, P, dependence on laser linewidth.

¹²⁹Xe spin polarization as a function of SEOP cell pressure with the line narrowed (0.25 nm linewidth, 17.3 W) and FAP laser irradiation (2 nm linewidth, 15.6 W). Data were analyzed using Eqs. 8 and 9 for fitting region indicated by the solid lines as discussed in section 4.9. Extrapolation using the obtained values of the fitting coefficients to pressure ranges outside the fitting range are shown by dotted lines. Results of this data analysis are listed in Table 6.

https://doi.org/10.1371/journal.pone.0049927.g007

4.10. Rapid Decrease of P_NG with Decreasing Pressure below

When the SEOP pressure was reduced below (i.e. for ¹²⁹Kr SEOP and for ⁸³Kr SEOP) a sharp decrease in polarization was observed. Note, that data fitting was limited to pressures above , however simple extrapolation of the (high-pressure) fitting curves into the lower pressure region are shown as dotted lines in Figs. 2 and 3. These extensions seem to provide a remarkably good description of the low-pressure behavior. This result should however not be over-interpreted, in particular since the assumption of a constant will fail in the low-pressure regions (see section 3.4). The rate , caused by spin-rotation interaction, will lead to significant depolarization at lower pressure but its effect is overestimated in this work because its absolute value will decrease with decreasing pressure.

There are further effects that contribute to the rapid polarization drop below . Radiation trapping, discussed in section 3.3, reduces the rubidium electron spin polarization. Radiation trapping will increase with lower values, in particular in mixtures with high noble gas concentration (i.e. low N₂ concentration) as described by Eq. 4.

A contribution to the polarization drop at pressures below , that is not accounted for in Eq. 8, may be caused by an optically dense boundary layer of rubidium at the cell window that is illuminated by the laser. This layer will reduce the resonant laser light penetrating the SEOP cell at any pressure. As demonstrated by Wagshul and Chupp [51] its effect is particularly detrimental at low pressures when the resonant absorption cross section of the rubidium is very high, leading to an almost complete absorption of the resonant laser light. The situation can be alleviated by detuning the laser to (slight) off-resonant illumination (not attempted in this work) and by the usage of very high laser power densities [51]. This effect was not investigated in this work.

Furthermore, the sudden drop in P_NG with decreasing SEOP pressure may be caused by a dramatic increase in rubidium relaxation due to the combination of increased diffusion and wall relaxation [33], [51]. The contribution of diffusion modes on the Rb relaxation in pure nitrogen becomes dominant and increases dramatically at pressures below 50 kPa of N₂ [51], i.e. at a pressure slightly above in the current work. This effect was also not further investigated in this work.

Recompression of Low Pressure hp Noble Gases, Equivalent Flow Rates and Storage

This work demonstrated that SEOP with mixtures containing high noble gas concentrations can produce high spin polarization. This concept may be used as a pathway to hp noble gas MRI without the need for cryogenic separation. However, the drawback of this technique is that the hp noble gases need to be recompressed after SEOP. As shown previously by Imai et al. [36], diaphragm pumps can be utilized for low pressure ¹²⁹Xe SEOP without significant depolarization. In the current work, recompression was found to maintain about 80% of the ¹²⁹Xe polarization and approximately 60% of ⁸³Kr polarization thus reducing from 4.4% to approximately 2.6%.

Further development is needed to make recompression of larger volumes routinely available. The SEOP cell used in this work has approximately 75 cm³ volume and the ¹²⁹Xe SEOP is complete every 6 min. Assuming 80% gas transfer, SEOP with the 50% xenon mixture at 22 kPa (see Table 2) leads to 1.8 cm³/min hp gas (at 298 K delivery temperature) with 12.4% apparent spin polarization, . Similarly, SEOP with 25% krypton at 40 kPa results to an equivalent flow rate of 2 cm³/min hp gas with 2.6% apparent spin polarization.

The polarization and rates above have been obtained with a single 23.3 W laser (incident beam power at SEOP cell entry) and scaling of the volume should be possible by increasing laser power and SEOP cell volume. In any case the usage of multiple cells and lasers would increase the volume of hp gas per time unit. Furthermore, temporary storage of hp ¹²⁹Xe at ambient temperature has previously been successfully demonstrated by Saam and co-workers [70] as a viable alternative to cryogenic storage. Further studies are required to explore temporary storage of hp ⁸³Kr.

Conclusions

Cryogen free production of hp ⁸³Kr and hp ¹²⁹Xe for practical MRI applications is possible through stopped flow SEOP with high noble gas concentrations at low total gas pressures. Without cryogenic separation the apparent polarization (as defined in Eq. 6) was for hp ¹²⁹Xe at a production rate of 1.8 cm³/min hp gas (volume at 298 K). Respectively, an apparent polarization of at a rate of 2 cm³/min was produced for hp ⁸³Kr. These results were obtained using 23.3 W of laser power (incident at the SEOP cell) and a laser linewidth of 0.25 nm. Recompression of the hp gases after SEOP is a necessary step with this technique and preliminary work resulted to (for ¹²⁹Xe) and (for ⁸³Kr) after recompression.

Current theory (Eq. 2) appears to provide a reasonable qualitative description of the SEOP gas pressure dependence of the polarization although several simplifications were used in this work. Overall, the practical application of current theory would benefit if more studies and published data were available. For instance, little is known about the actual spin-rotation parameter for various gas mixtures. Further, an experimental procedure to measure the temperature distribution within the SEOP cell would be very useful. In this work, a corrected value for the rubidium density [Rb] was used for ⁸³Kr SEOP analysis (Eq. 8) that is 4 times higher than its predicted equilibrium value at the (externally) measured SEOP cell temperatures. A correction factor of 1.3 was used for ¹²⁹Xe SEOP analysis, although correction proved to be less important compared to ⁸³Kr SEOP. The rubidium density (and the pumping rate due to associated changes in laser penetration) also appeared to be dependent on the SEOP mixture, an effect attributed to different thermal conductivity of the various gas mixtures. Furthermore, the Rb D₁ absorption linewidth dependence upon the SEOP gas pressure at 373 K was taken into account for the hp ¹²⁹Xe data fitting (Eq. 9). The pressure dependence of the Rb D₁ transition appeared not to be relevant for ⁸³Kr SEOP because the D₁ linewidth at 433 K is much wider than that of the narrowed diode array laser. However, a non-linear pressure broadening of the Rb D₁ linewidth was observed in all cases and this unexpected behavior warrants further study.

High SEOP temperature is needed for ⁸³Kr in order to increase the spin exchange rate for ⁸³Kr and to decrease the ⁸³Kr relaxation rate . The results from ⁸³Kr SEOP inversion recovery experiments suggest that surface relaxation is a strong contributor to at SEOP below 200 kPa (see Appendix 2 in Supporting Information S1 for discussions). Therefore, higher ⁸³Kr spin polarization may be obtained through a reduction in surface to volume ratio using larger SEOP cells that reduce and thus increase the ratio in Eq. 2.

The technique would benefit from future development focusing on practical gas recompression units, in particular for hp ⁸³Kr, and on larger SEOP cell volumes to produce larger quantities of hp noble gas within a given time interval. Larger SEOP cells, that may also improve the polarization in ⁸³Kr SEOP, will require increased laser power. Further increased laser power density at narrow laser line widths may be particularly advantageous for SEOP with high noble gas concentrations, as demonstrated in this work. Laser line narrowing to approximately 0.25 nm provides a crucial increase in ¹²⁹Xe polarization compared to SEOP with a 2 nm laser and further narrowing would likely be helpful for ¹²⁹Xe SEOP at low pressures. Finally, the general concepts of cryogen free hp noble gas production are by no means restricted to SEOP with rubidium. SEOP with cesium vapor [59], [71], [72] has recently been shown to increase the ¹²⁹Xe polarization significantly compared to SEOP with rubidium [29]. The benefits of cesium vapor SEOP at low gas pressures, in particular with ⁸³Kr, are still unexplored.