Radiolytic Degradation of Uranyl-Loaded Tributyl Phosphate by High and Low LET Radiation

ABSTRACT Understanding and characterizing the radiolytic degradation of solvents used for treatment of used nuclear fuel is an ongoing topic of research. In the work presented here, degradation constants for the radiolysis of tributyl phosphate (TBP) as a function of various process variables, such as the inclusion of nitric acid and uranyl ions on the TBP, were determined. Degradation constants were determined for both high linear energy transfer (LET) and low LET (gamma) radiation exposure. Results indicate that susceptibility to gamma radiolysis is roughly twice that of high LET and that acid uptake by TBP has little effect on the overall degradation for both high and low LET irradiations. The inclusion of a metal ion affects the degradation of TBP by forming complexes that absorb a portion of the energy deposited by radiation. These TBP–metal complexes break down during irradiation, and the degradation constants for the complex were found to be higher compared to free TBP, for both high and low LET radiations suggesting that the TBP–uranyl complex is more susceptible to radiation than free TBP.


Introduction
Foremost among solvent extraction processes aimed at the reduction of spent nuclear fuel inventories by partitioning and transmutation is the plutonium uranium reduction extraction (PUREX) process. [1,2]This entails liquid-liquid extraction of plutonium and uranium from an aqueous phase of spent nuclear fuel dissolved in moderately concentrated nitric acid by an organic phase of ~30% by volume tributyl phosphate (TBP) in kerosene.Radiation-induced degradation of both the TBP and the organic diluent during contact with the radioactive metal-laden aqueous feed is an issue of great concern. [3,4]In addition to requiring eventual addition to make up for lost TBP, some of the degradation products such as dibutyl and monobutyl phosphoric acid (HDBP and H 2 MBP, respectively) have high affinities for some of the fission products resulting in poor process performance.This, combined with radiolysis products of the diluent, can form interfacial cruds or additional phases that retain fission products and other metals. [5]Conventional process equipment such as centrifugal contactors are designed to only handle two distinct phases, and therefore, additional phases can cause reduction in product stream purity.Because of this, the study of the interactions between ionizing radiation and TBP is of great interest to improve process stability.
With the advances in computing technology, predictive and process design models are continuously being developed.For the PUREX process, as well as other processes for treatment of used nuclear fuel, the possibility of modeling the degradation of TBP by radiolysis with regard to dose dependence as well as dose rate dependence and type of incident radiation is of interest.As such, there is a need for data on how TBP behaves in response to radiation.Numerous studies in the past have investigated the degradation of TBP under certain conditions using low linear energy transfer (LET) radiation, mostly gamma radiation.Mincher et al. has provided a thorough review of the literature on TBP radiolysis [6] ; however, few studies exist for alpha radiation.Recently, Pearson et al.  compiled and reported on the degradation constants for the radiolysis of TBP from several research groups by high LET (alpha particles) as well as gamma radiation. [7]s in previous work from our research group, we utilize the 10 B(n,α) 7 Li reaction to induce high LET degradation in our samples.This method has been shown to adequately reflect the degradation due to alpha particles by correcting for the LET value based on the energy of the particle. [8]rovided that the boron is well distributed within the sample, the high LET (alpha) radiation field is considered uniform across the sample.This method bypasses the limitations of conventional helium ion beam irradiations, which are inhibited by low penetration depth and impermeability with respect to the encapsulation material.
The degradation constants from the previous work by Pearson et al. [7] represent a system of 30% TBP in n-dodecane in the absence of nitric acid or metal ions.As such, it would be beneficial to determine degradation constants that are more relatable to the PUREX process.In this work, we investigate high and low LET irradiations of TBP loaded to different degrees with uranyl, extracted from nitrate media, to elucidate the role that metal ligand complex plays in the radiolysis of TBP.

Sample preparation
Separate organic solutions containing 0.1 or 1 M TBP (99%, Fluke, New Jersey, USA) or 0.25 M HDBP (97%, Sigma Aldrich, St. Louis, Missouri, USA) in n-dodecane (99+%, Alfa Aesar, Haverhill, Massachusetts, USA) were prepared.Aqueous phases of 3 M nitric acid (Macron, Randor, Pennsylvania, USA) containing varying concentrations of uranium as follows: 0, 0.0125, 0.025, 0.05, and 0.1 M for low TBP concentration; 0, 0.025, 0.05, 0.1, and 0.25 M for high TBP concentration; and 0, 0.0075, 0.015, 0.0225, and 0.03 M for HDBP.The uranium was added by mass as uranyl nitrate hexahydrate and consisted of depleted uranium of ~0.2 mol% 235 U (ACS grade, International Bio-Analytical Industries, Inc., Boca Raton, Florida, USA).Approximately 5 mL aliquots of the organic phase were contacted in borosilicate glass vials with equal volumes of the various aqueous phases.The vials were shaken by way of a vortex mixer (Model 02215365, Fisher Scientific, Waltham, Massachusetts, USA) at ~160 rpm for 15 min and then centrifuged at 3000 rpm for 5 min to allow the phases to separate.The organic phase was then removed from contact with the aqueous and visually inspected to ensure no presence of aqueous-phase bubbles were detected.For the samples that would be exposed to high LET radiation, after separation of the phases, bis(pinacolato) diboron (99%, Sigma Aldrich) was added to all organic phases for a final concentration of 0.4 M boron.The boron used in this work was of natural abundance.

Low LET irradiations
For low LET irradiations, a Cs-137 source (Cs137 Irradiator Mark-I, Model 68, JL Shepherd & Associates, San Fernando, California, USA) with 661 keV gamma rays was used.The source was calibrated for dose to water by Fricke dosimetry [9,10] prior to the start of the irradiation.The dose rate at the position of our samples was 2.14 ± 0.06 kGy/h.The organic solutions were irradiated for intervals of 0-28 days to achieve doses of 0-1,440 kGy.Solutions of TBP in n-dodecane that had not been contacted with an aqueous phase were also placed in the Cs-source to benchmark this experiment to previous work.Identical samples to those irradiated were kept outside of the Cs-source to serve as standards.Large volumes of each solution were irradiated, and at the end of each interval, a small sample of 150 μL of each organic solution was removed for analysis by gas chromatography (GC).After the sample was removed, the container with the remainder of the solution was placed back in the gamma cell.During the irradiations, the solutions are sealed, and opening the containers for sampling will introduce air back in the container.However, any oxygen is assumed to be consumed very rapidly once the solution is placed back in the irradiation field, and we assume that the effect of oxygen to our irradiated solutions is negligible.

High LET irradiations
Organic solutions were exposed to a mix of high and low LET by introducing samples in the neutron flux of the UC Irvine TRIGA® reactor (General Atomics, San Diego, California, USA).Details of the method have been presented in previous work from our group. [7,8]The background low LET dose rate from the core has been verified to be approximately 40.4 kGy/h during normal reactor operations at 250 kW.The organic phases were irradiated for intervals of 0 (for standard samples) up to 6.8 h at 250 kW of reactor power, in the rotating Lazy Susan specimen rack.In this position, the samples receive a thermal neutron flux of approximately 8 × 10 11 neutrons/cm 2 /s which translate to a high LET dose of ~211 kGy/h due to the 4 He and 7 Li recoils from the 10 B(n,α) 7 Li reaction.The Lazy Susan specimen rack is located in the reflector outside the core, and thus, the epithermal neutron flux is at least one order of magnitude lower than the thermal and is expected to make a negligible contribution to the dose under the conditions used here.The irradiation times were chosen in order to achieve total doses comparable to the gamma irradiation in the Cs-source.Organic samples without boron were irradiated simultaneously to correct for the low LET contribution from the core.At the end of each interval, the samples were removed, and 150 μL of each irradiated organic solution was removed for analysis by GC.
Although industrial application of the PUREX process calls for 30 vol% TBP in kerosene (~1 M TBP), our high LET study was performed only with 0.1 M TBP and a maximum aqueous-phase concentration of 0.1 M uranium.This allowed us to work with lower concentrations of uranium, as the reactor irradiations would produce significant amount of activation products.

Determination of TBP and HDBP concentrations
Post irradiation, samples were diluted 1:150 in hexane (95%, Sigma Aldrich) containing triphenyl phosphate as an inert internal standard to monitor the performance and consistency of the GC.For additional calibration and standardization purposes, stock solutions of HDBP were prepared.A derivatization agent, diazomethane, was added to the solution.This derivatization is done in order to add methyl groups to acidic radiolysis products that might react with and be retained by the silica within the GC column.Diazomethane was prepared within a diazomethane generator kit (Sigma Aldrich) using diazald (99%, Sigma Aldrich), Carbitol (99%, Sigma Aldrich), and potassium hydroxide (Fischer Scientific).The diazomethane gas was captured in hexane.All samples were analyzed by a Hewlett Packard 5890 Gas Chromatograph using a flame-ionization detector.The GC was equipped with a 30-m DB-5ms column (Agilent Technologies, Santa Clara, California, USA) and an associated Hewlett Packard Controller 7673A integrator.The heating program began at 60°C and increased at a rate of 10°C/min until a final temperature of 350°C and a final hold time of 10 min.

Determination of uranium concentrations
Neutron activation analysis (NAA) was used to measure the uranium uptake by the TBP.Known concentration standards for uranium ranging from 0.0125 to 0.5 M UO 2 2+ in 3 M HNO 3 were irradiated at 250 kW in the Lazy Susan position in the UC Irvine TRIGA® reactor for 1 h.Alongside of the standards, aqueous and organic samples of phases from extraction experiments using varying total uranyl concentration that had been contacted for 15 min with organic phases of 0.1 or 1 M TBP in n-dodecane followed by separation were irradiated.During the irradiation, 238 U captures a neutron and forms 239 U, which will decay with a half-life of 23.45 min to 239 Np.The irradiated samples were analyzed the day following the irradiation to ensure that all 239 U had decayed to 239 Np.The activity of 239 Np was measured using a high-purity germanium detector (30% relative efficiency, Canberra, Meriden, Connecticut, USA) with Genie 2000 software.Samples were counted for 15 min each and corrected for decay.A calibration curve relating corrected count rates to known concentrations was made using the uranium standards.This curve was then used to determine uranium concentrations of both the aqueous and organic phases after extraction.
The samples of HDBP contacted with 3 M HNO 3 and varying concentrations of uranyl proved not to be stable during the irradiation, forming a gelatinous phase below the liquid organic phase and rendering quantification of the HDBP-metal complex degradation constant futile.

Tbp/n-dodecane irradiations
The solutions of TBP in n-dodecane were irradiated to benchmark our studies and compare to previous work.The results from the irradiation of 0.1 M TBP/n-dodecane in the Cs-source are shown in Fig. 1.The value of G - TBP was determined by taking the slope of the plot of concentration (µmoles/kg) of TBP remaining in the solution versus dose (Gy, i.e., J/kg).G - TBP was found to be 0.036 ± 0.001 µmol/J.For 1 M TBP, we found G - TBP to be 0.38 ± 0.012 µmol/J, which agrees well with Pearson et al. who reported a value of 0.36 µmol/J [6] for a system of 1 M TBP/n-dodecane.Since G-values are concentration dependent, the values from 0.1 M TBP or 1 M TBP found in our study differ by a factor of 10.
Figure 2 shows the result of low LET irradiation by background gamma rays and beta particles in the reactor.Using a value of the background dose rate of 40.4 kGy/h (established in previous studies) yielded results consistent with the low LET results from the 137 Cs source.The value of G - TBP caused by background radiation was found to be 0.038 ± 0.001 µmol/J and is within error identical to the value corresponding to the 137 Cs source.Due to the difference in low LET dose rates between the 137 Cs source and the reactor background, there could be a potential dose-rate effect.However, given the overlapping values of the degradation, this does not appear to be the case.Figure 2 also shows the linear degradation trend calculated using the G-value established by the 137 Cs irradiations for comparison.
To estimate the degradation of TBP from high LET, the decrease in TBP concentration that was observed in the corresponding samples (samples that had been exposed to the same total neutron flux) without boron can be used to correct the concentration found in the samples that contained boron.The assumption that the high and low LET are additive was used in previous work [7] and was shown to yield results comparable to past literature.The decrease in TBP concentration due to predominantly high LET with background low LET included is plotted in Fig. 3.The value for G - TBP by the combination of a total of 1,440 kGy high LET and 299 kGy background low LET was found to be 0.017 ± 0.002 µmol/J, which again is about 1/10th of the value determined by Pearson using the same method (0.14 µmol/J).Again, it is worth noting here that the order-of-magnitude difference is due to initial concentration differences.
The results show a slightly more than twofold increase in the TBP consumption for low LET compared to high LET.This is attributed to the increased likelihood of recombination of radical species (that would otherwise attack TBP [11,12] ) in the more condensed tracks caused by high LET radiation.
G-values calculated by fitting a straight line to the concentration profile of TBP can vary greatly as a function of where the linear fit is drawn.This may account for some of the discrepancies seen when comparing literature values.In addition to this, as discussed before, the G-value depends on specific initial conditions and is not a universal measure.For this reason, some authors [7,13] have endeavored to express the radiolysis yield as degradation constants.
In this work, we encountered trouble expressing the effect of metal complexes in terms of G-values, whereas degradation constants provide a better fit and allow for easier estimation of the  individual contributions from low and high LET.The aforementioned G-values are reported along with corresponding degradation constants in Table 1.The degradation constants are found by treating the decrease in TBP with dose as a function of the degradation constant multiplied by the TBP concentration, providing an expression for exponential decrease in TBP concentration, see Eq. ( 1) and ( 2) for example.The experimental values of TBP concentration determined by chromatography were used to fit the corresponding equations and to find degradation constants for low and high LET following procedures outlined by Pearson et al. [6] d Tbp Tbp/acid/n-dodecane irradiations Literature values provided by Adamov et al. [13] indicated that the presence of 3 M HNO 3 enhanced the degradation of TBP under gamma radiation.However, their study did not separate the aqueous and organic phases after contact but rather irradiated both phases together.Our results, Fig. 4, show that the irradiation of TBP with nitric acid uptake has no significant difference in G - TBP compared to the system without acid.The degradation constants are shown in Table 1.

Tbp/uranium/acid/n-dodecane irradiations
Prior to any irradiation, all samples were analyzed for TBP content in order to establish a baseline.As can be seen in Figs. 5 and S1 in the electronic supplementary information (ESI), when metal concentration in the aqueous phase increases, there was a proportional decrease in the amount of TBP observed based on GC analysis.This indicates that as the TBP-uranyl complexes form, the amount of TBP detected by the flame-ionization detector decreases, suggesting that GC on metalloaded TBP shows only the TBP that is not complexed to a metal ion.This unbound TBP will be referred to as "free TBP" for the purposes of this work.In order to validate this assumption, neutronactivation analysis of the organic phases was conducted to determine the UO 2 2+ concentration extracted in each organic phase.The results of the NAA are shown in Figs. 6 and S2 (ESI) for 0.1 M TBP and 1 M TBP, respectively.
If the amount of free TBP in solution is governed by the amount of UO 2 2+ present in the organic phase, the relationship should follow the previously reported stoichiometry of two TBP molecules per extracted UO 2 2+ ion. [14]Hence, for every uranyl ion extracted, two TBP molecules become bound, and the relationship for free TBP at any given metal loading must be Table 1.G-values and degradation constants for TBP radiolysis.Results compared to those reported previously by Pearson et al. [7].
System G -TBP (µmol/J) k γ or k α (1/kGy)    3) and show an almost identical slope as the experimental values from GC analysis but a discrepancy in the intercept with the y-axis.However, this calculation is based on an upper limit of TBP in the organic phase and as such does not account for any TBP that may have been lost to the aqueous phase during the extraction process, or uptake of water, nitric acid, and uranium into the organic phase, which may cause a change in the volume of the organic phase.Furthermore, the measurements have some uncertainty associated with them that are partly reflected in the error bars in the figures.Nevertheless, these results verify that varying the uranium uptake into the organic phase accounts for the discrepancy in the concentrations of TBP that can be analyzed by the GC.The free TBP concentration as a function of gamma radiation of the organic solutions containing the highest concentration of uranium can be seen in Fig. 7.As the metal ion concentration increases, the trend of free TBP, based on the GC analysis, as a function of dose changes.At the highest metal loading of 17 and 200 mM uranyl (for 0.1 M TBP and 1 M TBP, respectively), there is a sharp increase in the amount of free TBP as compared with the lower metal loading, which looks more similar to the trend with pure TBP or from contact with HNO 3 , namely, a more typical exponential decay trend.It is worth noting that the trends for 0.1 M TBP and 1 M TBP are very similar.Additional data for low LET degradation of 1 M TBP solutions with varying concentrations of uranyl are shown in the ESI (Figs.S3-S6).Figure 8 shows the corresponding trends for the 0.1 M TBP samples irradiated in the reactor and exposed to a mixed field of high and low LET radiations.

Radiolysis of TBP-UO 2 2+ complexes by low LET radiation
The initial increase in TBP concentration with dose at higher metal loading, Figs.7 and 8, can be explained as radiation disrupting the metal-ligand complex and freeing up previously bound TBP.Hence, this reaction should have a corresponding degradation constant.As a starting point, it is assumed that the reaction whereby the complex breaks to free up TBP depends on dose and on the amount of complex at any given time, in analogy with Eq. ( 1) for free TBP.Because the free TBP also undergoes radiolysis, this process can be treated as a sequence of first-order reactions.Written only with consideration for TBP (i.e., metal and nitrate ions are disregarded in the balance for the equation): where k 1 and k 2 are the corresponding degradation constants for the complex and free TBP, respectively.(UO 2 )(NO 3 ) 2 (TBP) 2 will henceforth be referred to as "complex", or "comp", in subsequent equations.The necessary equations would then be  8) with fitted degradation constants k 1γ = 6.9 (±0.25) × 10 -3 kGy -1 and k 1γ = 6.6 (±0.90) × 10 -3 kGy -1 , for the 0.1 and 1 M TBP case, respectively.
In these equations, the dose rate, _ D γ , is used instead of dose.The dose and dose rate are easily interchangeable using the irradiation time.The dose rate is constant during an irradiation, and it allows one to use time as a variable rather than dose.This is especially useful for a source of mixed high and low LET radiations where the dose rates of each type can be different.The degradation of free TBP by low LET radiation, k 2γ , was determined before and is listed as k γ in Table 1.Integration of Eq. ( 5) and ( 6) yields the concentration of both complex and TBP at any given time: Here, the unknowns are [Complex] and k 1γ .The model for TBP presented in Eq. ( 8) was fit to experimental data at each metal concentration to determine k 1γ for each concentration.Figure 7 above shows the examples at the highest metal loading of 17 and 200 mM uranyl uptake, where k 1γ was found to be 6.9 × 10 -3 and 6.6 × 10 -3 kGy -1 , respectively.It can be seen in Fig. 7 that the model fit well with the experimental values, and the fitted degradation constants for 0.1 and 1 M TBP overlap within one standard deviation.
Although there are slight variations in the determined values of k 1γ as metal loading is varied, the constants are identical within error, and an average gamma degradation constant for the complex was determined.The results for 1 M TBP contacted with a higher range of uranyl concentrations, also shown in Table 2, are in excellent agreement with the low LET degradation constant from 0.1 M indicating that the TBP concentration dependency can be overcome by using degradation constants rather than G-values.An overall degradation constant for the breakdown of the TBP-uranyl complex due to low LET radiation was calculated and is listed in Table 2.

Radiolysis of TBP-UO 2 2+ complexes by high LET radiation
Because the reactor contains a mixed field of gamma and beta radiations in addition to the high LET radiation within the sample, it is important to represent the contribution of low and high LET separately in order to see the true effect each has.Hence, Eq. ( 5) and ( 6) require the addition of two terms, k 1α and k 2α for the corresponding reactions caused by high LET.Because of the difference in dose rates between high and low LET, time is used as a variable, as discussed above.The resulting equations for describing the TBP-metal complex and free TBP concentration become In these equations, k 1γ is known from the previous fit at low LET only.Both D α and D γ ; the alpha and gamma dose rates, were determined by dosimetry.Again, we can then substitute the degradation constants shown in Table 1 for both low and high LET as k 2γ and k 2α , respectively.Hence, the only unknowns are [Complex] and k 1α .
As before, the model from Eq. ( 9) and (10) was fit against the experimental data.The data from this fit can be seen in Fig. 8, while the degradation constants at each metal loading can be seen in Table 2.As for the low LET degradation constants, there are slight discrepancies between each metal loading, but overall, the constants are within error of each other, and an average was calculated as before.Overall, the model provides a good fit to the experimental data for all conditions investigated.
Similar to the studies of LET effects on free TBP radiolysis, when examining the degradation constants for the complex, low LET appears to have twice the effect compared to high LET.The reason for this is likely the same as for free TBP.The high LET radiation causes the formed radicals to recombine in a dense track and are, therefore, less probably to interact with the TBP or TBP-UO 2 2+ complex.For low LET, the radicals produced are more sparsely distributed, and the probability of them interacting with TBP or the complex increases.
Few authors have published on the topic of the effect of metal uptake on TBP degradation.However, the few that do agree that the presence of metal ions inhibits TBP degradation and HDBP formation, though differences in experimental systems make direct comparison difficult. [15,16]Our studies show a highly nonlinear response to the free TBP concentration with increasing radiation dose, which was described as the TBP-UO 2 2+ complex broken by incident radiation to free the previously bound TBP.Overall, it seems that the susceptibility of radiation of the complex is about an order of magnitude greater than that of free 3.5 (±0.15) × 10 -3 1.0 0.02 7.3 (±0.7) × 10 -3 -1.0 0.04 6.2 (±0.9) × 10 -3 -1.0 0.12 6.4 (±1.2) × 10 -3 -1.0 0.20 6.6 (±0.9) × 10 -3 -Average for 1 M TBP 6.6 (±0.63) × 10 -3 -Average (all combinations) 6.9 (±0.60) × 10 -3 -TBP.One possible explanation is the relative differences in enthalpy.For example, the enthalpy associated with the C-O bond that, when broken, yields HDBP is on the order of 355 kJ/mole, while Stas et al. [17] reported an enthalpy value for the extraction of UO 2 2+ from 0.5 and 1 M HNO 3 by TBP in kerosene as ~16 and ~23 kJ/mole, respectively, and Orabi et al. report 55.72 kJ/mole [18] using 25 vol% TBP in kerosene at a phase ratio 1:1.It is important to note that these values reflect the energy of transfer between the aqueous and organic phases in addition to the energy of complex formation and are likely overestimates for the electrostatic bond itself.What is certain, however, is that the TBP-metal complex is held together by relatively weak electrostatic forces, and energy deposited in the solution can affect the stability of the complex.This explanation does not necessarily take into account a reaction pathway that includes indirect radiolysis where a radical or reactive species formed by the incoming radiation reacts with the free TBP or TBP-metal complex.Based on the difference in low and high LET degradation constants, it appears that the indirect radiolysis is more likely at the conditions studied here.Further work is needed to identify the degradation paths of the various species.

HDBP formation and degradation
In order to assess the formation and degradation rates of HDBP in these systems, it was important to first establish that our methods were viable.To this end, we analyzed samples of 1 M TBP without contact with an aqueous phase for HDBP production and compared our results to degradation constants for HDBP given by Pearson et al. [7] The model used to fit the experimental data is represented by Eq. ( 11), where k (+HDBPγ) represents the formation of HDBP from TBP by gamma radiolysis, k (-HDBPγ) represents the subsequent degradation constants for HDBP, and k γ is the TBP degradation constant from Eq. ( 2).The comparison of a model using the values for k (+HDBPγ) and k (-HDBPγ) , determined by Pearson et al. [7] , of 1.48 × 10 -4 and 2.49 × 10 -4 kGy -1 , respectively, is shown in Fig. S7 (ESI).
In order to see what role the uptake of nitric acid from contact with an aqueous phase would play on HDBP formation and degradation, we performed irradiations on two solutions, 1 M TBP/n-dodecane as well as a solution of 0.25 M HDBP in n-dodecane, both contacted with an aqueous phase of 3 M HNO 3 .The degradation constant of HDBP in an organic solution contacted with 3 M nitric acid, k (-HDBPγH + ), was determined to be 4.18 × 10 -4 kGy -1 using Eq. ( 12).The fit of Eq. ( 12) to the experimental data is shown in Fig. 9.After fitting k (-HDBPγH + ), we analyzed the irradiated TBP after contact with nitric acid using Eq. ( 13) to find the value of the formation constant of HDBP by TBP degradation, k (+HDBPγH+) .The constant was determined to be k (+HDBPγH+) = 9.81 (±0.08) × 10 -5 kGy - 1 for the formation of HDBP in irradiated 1 M TBP contacted with 3 M HNO 3 .Figure 10 shows the fit of Eq. ( 13) to the experimental data for HDBP concentration found in the irradiated solutions.

HDBP
We were able to determine the concentrations of HDBP in the irradiated solutions of 1 M TBP with various concentrations of uranium.(The results of this can be found in Figs.S3-S6 in the ESI.)From these results, we observe that less HDBP is present as the metal ion concentration in the organic phase increases.This may be due to complexation of HDBP to uranyl effectively reducing the "free" HDBP that we would observe in the GC analysis.Hence, to accurately model the formation of HDBP, we would need to account for the likelihood of the formed HDBP competing with TBP for coordination to the uranium.In addition to this, we would also need to determine the degradation constant for the HDBP-uranium complex, similar to what was done for TBP.However, as mentioned in the experimental section, upon irradiation, the solutions of HDBP containing extracted uranyl showed significant third-phase formation, and the experiment was aborted.The presence of the third phase was not unsurprising, as it is well known that significant amounts of HDBP may promote third-phase formation during the PUREX process. [19]Due to this complication, no degradation constants of the metal-HDBP complex were determined.

Conclusions
G-values for the destruction of TBP in TBP/n-dodecane systems by both low and high LET were determined.The values for G TBP with both gamma and alpha radiations were in good agreement with prior studies done by Pearson et al. with low LET being roughly twice as potent as high LET.
However, due to a factor of 10 difference in initial concentration, G-TBP varied by a factor of 10.This is an indication that G-values, while being a simple approximation, might not be the most adequate descriptor of radiolysis yield.Instead of G-values, degradation constants were calculated based on exponential fit.The degradation constants for radiolysis by low and high LET were 2.93 (±0.08) × The "TBP Model" was plotted using Eq. ( 2) with k γ = 3.13 (±0.25) 10 -4 kGy -1 for acid contacted TBP radiolysis.The "HDBP Model" was plotted using Eq. ( 11) with k (+HDBPγH+) found to be 9.81 (±0.25) × 10 -5 kGy -1 .
10 -4 and 1.29 (±0.15) × 10 -4 kGy -1 , respectively, which agree well with previous values reported by Pearson et al. [7] While some sources state that the inclusion of an aqueous phase has been known to increase the rate of TBP consumption [15,20,21] , our studies indicate that the nitric acid uptake by TBP during extraction had little effect on TBP degradation.This result was consistent across both low and high LET studies.It should be noted, however, that results from different literature have different methodology in the irradiations which may result in slight changes.The formation of HDBP appears to be inhibited by acid uptake at 3 M HNO 3 , which seems to confirm the observations of Gao et al. [22] We observed a decrease from 1.48 (±0.04) × 10 -4 to 9.81 (±0.08) × 10 -5 kGy -1 for the formation constant of HDBP by gamma radiolysis of 1 M TBP when comparing "dry" versus solutions contacted with 3 M HNO 3 .
The breakdown of the TBP-uranyl complex was found to happen at a higher rate than free TBP.Degradation constants of 6.9 (±0.6) × 10 -3 and 3.5 (±0.15) × 10 -3 kGy -1 for the TBP-uranyl-nitrate complex in n-dodecane were found for low and high LET, respectively.These degradation constants are a first step toward a mathematical description of the radiolysis of TBP during the PUREX process, and the methodology can be easily implemented for other extraction processes.

Figure 1 .
Figure 1.TBP concentration versus dose for the 137 Cs low LET gamma radiolysis of TBP in n-dodecane.The degradation model is a linear fit of the data and G - TBP determined from the slope of the dashed line.

Figure 2 .
Figure 2. TBP concentration versus dose for the low LET irradiation of TBP in n-dodecane using the UC Irvine reactor and a comparison between reactor background (40.4 kGy/h) degradation with degradation model derived from the 137 Cs source (2.14 kGy/h) degradation data.The lines are linear fits of the data, and the G-values represent the slope.

Figure 3 .
Figure 3. TBP concentration versus dose for the mixture of high and low LET irradiation of TBP in n-dodecane using the UC Irvine reactor.The degradation model is a linear fit of the experimental data, and the G-values represent the slope of the dashed line.

Figure 4 .
Figure 4. (Top) Result of 137 Cs low LET irradiation of TBP after acid uptake.(Bottom) Result mixture of high and low LET irradiations of TBP after acid uptake.The degradation model is a linear fit of the data, and the G-values represent the slope of the dashed lines.

Figure 5 .
Figure 5. Organic-phase TBP concentration as a function of aqueous-phase condition.Sample type, from left to right: TBP denotes "dry" organic phase; acid denotes organic phase contacted with 3 M nitric acid; each number corresponds to the concentration of uranyl in the aqueous phase before contact.

Figure 6 .
Figure 6.Experimental values of nonirradiated TBP versus organic-phase UO 2 2+ concentration.The experimental data represent the raw data taken from GC analysis.Predicted represents the initial TBP concentration of 0.1 M with a decrease calculated from Eq. (3) based on the uranium concentration obtained from neutron activation analysis.Deviations in initial values are attributable to extraction of water and nitric acid into the organic phase as well as losses of TBP to the aqueous phase.

Figure 8 .
Figure 8. Experimental data of the evolution of free TBP as a function of mixed high and low LET radiation dose.The lines correspond to theoretical calculations using the model in Eq. (10).

Table 2 .
Compilation of degradation constants for the breakup of TBP-UO 2 2+ complexes by both low (0.1 and 1 M TBP) and high LET (0.1 M TBP).