A Self-Optimised Approach to Synthesising DEHiBA for Advanced Nuclear Reprocessing, Exploiting the Power of Machine-Learning

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Reagents were made up to their desired concentrations in the stock solutions, loaded into glass bottles and primed on the dual piston reciprocating JASCO PU-2800 HPLC pumps.These solutions were then pumped where streams would be mixed using Swagelok SS-100-3 tee-pieces according to Figure 2. Tubular reactors were made from PFA, PTFE and 316 stainless steel tubing (1/16" OD), these were fitted to cylindrical aluminium blocks and heated via a Eurotherm 3200 temperature controller, this enabled the reaction mixtures to be heated rapidly.After the reactor, the tubing enabled rapid cooling back to roughly ambient temperature prior to an aliquot of the reaction solution being sampled using a VICI Valco EUDA-CI4W sample loop (4-port) with 0.5 and 0.06 μL injection volume.The sample was then fed directly into an Agilent 1260 Infinity II series HPLC instrument fitted with an Agilent Poroshell 120 EC-C18 reverse phase column (5 cm length, 4.6 mm ID and 2.7 μm particle size) for quantitative analysis.The flow system was maintained under a constant back pressure using an Upchurch Scientific back pressure regulator (100/250 psi) for all setups however route (e) also employed the Tescom TM 26-1762-22 control pressure regulator to achieve a pressure of 210 bar.The automated system was controlled using a custom written MATLAB program to enable real-time control and monitoring of all the optimisation variables.The machine-learning algorithms in MATLAB were initiated with Latin hypercube sampling where the number of experiments for this was 2n+1, n being the number of variables.This formula guarantees that each dimension is divided into n + 1 subintervals, and that there will be one sample in each subinterval.This helps achieve a more even coverage of the parameter space, thus reducing the risk of missing important regions.The analytical data from this and following experiments enabled the generation of new conditions for the optimisation to proceed.To determine process metrics, biphenyl was included as an internal standard in reservoir 1 solutions, here the internal standard and compound signal areas allow for accurate calculations to be completed using calibration data previously obtained.During the process, Microsoft Teams screen sharing capability is also utilised to allow for the user to monitor the equipment remotely.

Reagent Costs
The lowest cost for each reagent was acquired as of March 2022 for the cost calculations used by this research.Figure S2: Six 4/5D plots demonstrating the reagent cost for routes (a-f), the synthetic route for each is defined above the plots for ease of comparison.A consistent colour bar is illustrated throughout, ranging between 0-80%, whilst the x, y, z and size ranges are subject to the parameter space for each optimisation, finally a reduced dataset has been presented for clarity.Figure S3: Six 4/5D plots demonstrating the space-time yield for routes (a-f), the synthetic route for each is defined above the plots for ease of comparison.A consistent colour bar is illustrated throughout, ranging between 0-80%, whilst the x, y, z and size ranges are subject to the parameter space for each optimisation, finally a reduced dataset has been presented for clarity.Figure S4: Six 4/5D plots demonstrating the product yield for routes (a-f), the synthetic route for each is defined above the plots for ease of comparison.A consistent colour bar is illustrated throughout, ranging between 0-80%, whilst the x, y, z and size ranges are subject to the parameter space for each optimisation, finally a reduced dataset has been presented for clarity.

The Optimum Conditions for Each Route Combined
A combination of tables 1-6 in the paper but with the colour scale normalised for better comparison of process metrics Table S2: The optimum conditions from routes (a-f) with a normalised colour scale across each route 2 Experimental

HPLC and GC-FID Methods
HPLC analysis was performed on an Agilent 1260 Infinity II series HPLC instrument fitted with an Agilent Poroshell 120 EC-C18 reverse phase column (5 cm length, 4.6 mm ID and 2.7 μm particle size) with a binary pump and a variable wavelength detector.
The same HPLC method was used for all routes and calibrations.Water (A, 18.2 MΩ) and acetonitrile (B) HPLC mobile phases were used, starting with a 50:50 method of A:B, the amount of A was reduced to 5% over 3 minutes and held here for a further 3 minutes before returning to 50:50 over 0.5 minutes at a flow rate of 1.50 mL min -1 and a column temperature of 30 °C.210 nm was used to detect the product DEHiBA, whilst 254 nm was used to detect biphenyl.
GC analysis was carried out on an Agilent 7890B instrument fitted with an Agilent Technologies 7693 Autosampler and a HP-5 column (30 m x 0.32 mm, 0.25 µm film thickness), H 2 carrier gas, FID detector.
The same GC method was used throughout, starting at 40 °C and holding at this for 1 minute, then the temperature was ramped up to 55 °C over 1 minute and held here for a further 1 minute.The temperature was then gradually increased to 150 °C over 3.8 minutes.Finally the temperature was raised to 300 °C over 3 minutes before cooling to 40 °C.

Calibrations for Quantitative Analysis
All raw materials were purchased from suppliers and calibrated where possible via GC-FID and HPLC.N,N-di-(2-ethylhexyl)isobutyramide (DEHiBA) was synthesised as well as purchased from a commercial supplier (Technocomm) for analytical calibrations to enable the quantitative analysis of all reactions for calculating key process metrics.Two calibration curves are shown in Figure S2 for HPLC and GC-FID:
An example chromatogram is shown in Figure S3.Three flow setups were investigated for route (a), each an attempt to improve on the last setup, with setup (iii) being discussed in the paper.The reservoir configuration and concentrations define the feasible parameter space for each self-optimisation, therefore this screening provides an insight into feasible reservoir configurations whilst allowing access to different parameter spaces to further the optimisation in the search for improved process metrics.The setups investigated here differed the location and amount of triethylamine in the reservoirs:  Setup (i) combined a large excess of triethylamine with DiEHA in reservoir 1, to match the maximum possible equivalents of iBCl (3 with respect to DiEHA).
 Setup (ii) combined equal amounts of triethylamine and iBCl into reservoir 2.
 Setup (iii) separated each reagent into individual reservoirs for the optimisation of both the equivalents of iBCl and triethylamine.
Figure S7 illustrates these setups as well as the setups for routes (b-f).Despite the convenience and simplicity offered by setup (i), the optimisation was limited by its inability to vary the equivalents of triethylamine, this large and constant excess of triethylamine limited the RME to a theoretical maximum of 39.5%.Nevertheless setup (i) performed exceedingly well with minimal trade-off between the key process metrics.
All the reactions conducted were high yielding at > 90%, and an optimum RME of 38.8% was achieved at just 40 °C, with 0.95 equivalents of iBCl, the large excess of triethylamine, and a 10 minute residence time which substantially diminished the STY.Impressively, several conditions were close to this optimum RME, but to their advantage, far outperformed in terms of productivity with the optimum requiring only a 0.5 minute residence time at 150 °C, achieving an RME of 38.4% and an exceptional improvement in STY to 367 g L -1 h -1 .This condition provided little trade-off between key process metrics, proving itself as the overall optimum condition in this case.
A clear trend between temperature and residence time was observed, with higher temperatures favouring lower residence times for the best conversion due to thermal degradation of starting materials.Therefore, in addition to improving the STY, shorter residence times aided to improve the RME.Overall route (a), setup (i) showed great promise, with the maximum RME and STY just 0.7% and 6 g L -1 h -1 from their theoretical maximum, in addition to the insignificant trade-off as demonstrated by the insignificant Pareto front (figure S4, ESI).
However, in an attempt to improve on this, setup (ii) was designed so that only a slight excess of triethylamine was maintained with respect to iBCl.This was initially promising, however starting material degradation over a period of just 6 hours resulted in a loss of reproducibility, with large yield losses in some cases, verifying the impracticality of combining triethylamine and iBCl.This degradation is caused by ketene formation which is highly reactive and in this case has degraded somewhat in the reservoir.
A plot comparing the RME and STY metrics for setups (i) and (iii) was produced and can be found in Figure S4.A plot demonstrating the performance of route (a) even at 12 second residence times is shown in Figure S5 where little trade-off is observable even at these flow rates.

Reaction Mass Efficiency (%) Space Time Yield (g L-1 h-1)
Figure S9: STY, RME Pareto fronts for routes (a-c) with the additional data from route (a) exploring residence times below 0.5 minutes the limit that was set in Figure 4 and shown by the dashed line as the upper STY limit To further add to the data provided in the paper we have hereby included the entirety of the reaction conditions explored for route (a) and the outcome of each experiment.

Batch Chemistry:
Batch studies were initially conducted to ensure homogeneity and product formation via this route.Whilst later batch experiments were employed for kinetic understanding.
Water and a range of common organic solvents including methanol, ethanol, tetrahydrofuran, N,N-dimethylformamide, dichloromethane, toluene, hexane, ethyl acetate, acetone, acetonitrile, and diethyl ether were screened to ensure the solubility of reagents.Acetonitrile, water, methanol, ethanol, N,N-dimethylformamide and chloroform were the only reagents to solubilise EDC.HCl, thus the only suitable solvents to transition this route into flow hence these were trialled in batch first.
Di-2-ethylhexylamine (0.2976 g, 1.22 mmol) and isobutyric acid (0.1157 g, 1.30 mmol) were combined in a round bottom flask, note the exotherm of this combination.EDC.HCl (0.2769 g, 1.43 mmol) and DMAP (0.0079 g, 0.07 mmol) were then combined with solvent (see above) in a 10 mL volumetric flask.Once the di-2ethylhexylamine and iBA solution had cooled to room temperature the EDC.HCl solution was charged, the reaction was stirred at 30 °C for repeatability over 24 hours to yield a colourless and homogenous solution.HPLC analysis confirmed yields of 96.3%, 99.9%, 55.5%, 9.0%, 2.1%, and 0% for acetonitrile, dichloromethane, N,N-dimethylformamide, ethanol, methanol and water respectively.
Although dichloromethane was best yielding the environmental impact of this solvent and the low boiling point causing cavitation in the HPLC pumps as well as a restrictive temperature range meant that acetonitrile was best suited for this reaction in flow.
Studies without DMAP saw a reduction in yield for reactions in acetonitrile to 45.8%.Replacement with DIPEA resulted in yields between 31.4-23.3%with varying equivalents from 0.5 to 1.5.
Kinetic studies were investigated using a recirculating batch reactor where the solution was pumped through a vici sample loop connected to a HPLC for online analysis.As described in section 2.4.3.A similar methodology was used to the one above however temperature was varied and concentration, but equivalents were maintained.

Continuous Flow Chemistry:
Reservoir solutions were prepared to the desired concentrations by dissolving the described reagents in solvent with stirring at ambient conditions, except for EDC.HCl, that was heated to 30 °C until dissolution and maintained at this temperature throughout the optimisation.
An example HPLC chromatogram is illustrated in Figure S6: The flow platform was set up according to Figure 2 using a reactor volume of 2.7 mL with PFA tubing and a back pressure of 100 psi.The self-optimisation was conducted with respect to four continuous parameters: residence time, iBA equivalents, EDC.HCl equivalents and temperature.The upper and lower parameter bounds for each are described in Table S3.The initial objective for each optimisation was to maximise yield, then simultaneously maximize reaction mass efficiency and space-time yield.

Route (b) Data and Further Analysis
Kinetic studies were conducted in batch making use of online sampling for reaction monitoring.Clear concentration and temperature trends are identifiable in Figure S7, all studies were conducted at 30 °C with 1.15 equivalents of EDC and 1.1 equivalents of iBA respective to DiEHA.
The increase in by-product formation has not been directly quantified due to complications with the co-elution of N-acylurea with other signals in both HPLC and GC for a range of methods.HPLC traces illustrating the overlap between EDC, EDU and the N-acylurea between 0.4 and 1.5 minutes.Biphenyl and DEHiBA are observable around 2.3 and 4.5-4.8minutes respectively.Despite changes to the HPLC method these peaks were not resolved.Table S4 provides the raw data for the experimental conditions exploited in the optimisation of route (b) and the performance metrics associated.

Batch Chemistry:
No major solubility issues were encountered for iBAnhydride over a range of common organic solvents therefore batch reactions were trialled using tetrahydrofuran, toluene, hexane, ethyl acetate, acetone, acetonitrile, and diethyl ether via the following procedure: DiEHA (0.0845 g, 0.35 mmol) was combined with solvent in a 5 mL volumetric flask, similarly iBAnhydride (0.0554 g, 0.35 mmol) was charged with the same solvent to a 5 mL volumetric flask.These solutions were combined in a 25 mL round bottom flask whereby a large temperature rise (not measured) saw most solutions reach boiling points and condensate formed on glassware.Yields were not recorded for these reactions and the chemistry was transitioned into continuous flow without further batch investigations.

Flow Chemistry
Reservoir solutions were prepared to the desired concentrations by dissolving the reagents in solvent with stirring at ambient conditions.
An example HPLC chromatogram is illustrated in Figure S8: The flow platform was set up according to Figure 2 using a reactor volume of 2.7 mL with PFA tubing and a back pressure of 100 psi.The self-optimisation was conducted with respect to three continuous parameters: residence time, iBAnhydride equivalents, and temperature.The upper and lower parameter bounds for each are described in Table S5.The initial objective for each optimisation was to maximise yield, then simultaneously maximize reaction mass efficiency and space-time yield.

Routes (c-d) Data and Further Analysis
A comparison between the performance metrics, RME and STY demonstrates the improved performance of the reaction in acetonitrile over that of the reaction in hexane although similar trade-off curves are apparent.Reaction Mass Efficiency (%) Space Time Yield (g L-1 h-1)

Figure S15: RME, STY comparison between routes (c) and (d)
Table S6 provides the raw data for the experimental conditions exploited in both optimisations and the performance metrics associated.Reservoir one was prepared by dissolving the biphenyl in Di(2-ethylhexyl)amine with stirring at ambient conditions.
An example HPLC chromatogram is illustrated in Figure S10.The flow platform was set up according to Figure 2 using a reactor volume of 4.0 mL with stainless steel tubing and a back pressure of 100 psi.
The self-optimisation was conducted with respect to three continuous parameters: residence time, iBAnhydride equivalents, and temperature.The upper and lower parameter bounds for each are described in Table S7.The initial objective for each optimisation was to maximise yield, then simultaneously maximize reaction mass efficiency and space-time yield.Reservoir 1: Di(2-ethylhexyl)amine (400 g, 1.66 mol), and biphenyl (8.7588 g, 0.0568 mol).
An example HPLC chromatogram is illustrated in Figure S12 using the HPLC method previously described.S9.The initial objective for each optimisation was to maximise yield and reaction mass efficiency, then simultaneously maximize reaction mass efficiency and space-time yield.A concise dataset (Table S10) demonstrating the trend between conditions and the area ratio for the signals at 0.5 and 1.7 minutes.The signal at 0.5 minutes increases with increasing iBA equivalents predominantly whilst the signal at 1.7 minutes intensifies with both an increase in temperature and residence time.

Figure S1 -
Figure S1 -The self-optimising flow reactor platform and its visual schematic

Figure S5 :
Figure S5: HPLC (top) and GC-FID (bottom) calibration curves for DEHiBA from the commercial supplier, our purified DEHiBA is also in agreement with these plots

FigureFigure S7 :
Figure S6: A typical HPLC chromatogram for route (a)The flow platforms were set up according to Figure2all using a reactor volume of 2.7 mL with PFA tubing and a back pressure of 100 psi.The self-optimisation was conducted with respect to three continuous parameters for setups (i) and (ii): residence time, iBCl equivalents, and temperature.Whilst setup (iii) optimised four continuous

Figure S8 :
Figure S8: Reaction data for route a, setups (i) and (iii), where the dashed lines show the theoretical maxima for their accessible parameter space during each optimisation

Figure S11 :
Figure S11: Kinetic studies for route (b) in batch at 30 °C with online sampling to a HPLC with 1.15 equivalents of EDC and 1.1 equivalents of iBA respective to DiEHAThe proposed reaction pathways that route (b) can take, discounting the inclusion of DMAP from the reaction can be found in Scheme S3.

Figure S13 :
Figure S13: Typical HPLC traces for route (b) where EDC, EDU and the N-acylurea overlap between 0.4 and 1.5 minutes.

Figure S18 :
Figure S18: An example HPLC chromatogram from route (f)The flow platform was set up according to Figure2using a reactor volume of 4.0 mL with stainless steel tubing a back pressure regulator set to 210 bar before the sample loop and a back pressure of 100 psi following the sample loop.The self-optimisation was conducted with respect to three continuous parameters: residence time, iBA equivalents, and temperature.The upper and lower parameter bounds for each are described in TableS9.The initial objective for each optimisation was to maximise yield and reaction mass efficiency, then simultaneously maximize reaction mass efficiency and space-time yield.
GC-MS used to identify the unknown signal that was in fact the thermal degradation product of DEHiBA:

Figure S19 :
Figure S19: GC-MS chromatogram for the degradation product of DEHiBA

Figure
Figure S20: 1 H NMR spectra of DEHiBA from the commercial supplier (top) compared with DEHiBA manufactured and purified in this work

Table S1 :
The reagent costs for the raw materials used in this research as of March 2022

Table S4 :
Reaction conditions and outcomes from the optimisation of setups (i) and(iii)

Table S5 :
The upper and lower bounds for the variables optimised in route(b)

Table S6 :
complete dataset from the optimisation of route(b)

Table S7 :
The upper and lower bounds for the variables optimised in route (c) and (d), top and bottom table respectively

Table S8 :
complete dataset from the optimisation of routes (c) and(d)

Table S9 :
The upper and lower bounds for the variables optimised in route(e)

Table S11 :
The upper and lower bounds for the variables optimised in route(f)

Table S12 :
Area ratios for the signals at 0.5 and 1.7 minute retention times

Table S13 :
complete dataset for the optimisation of route (f)