DOI: 10.1002/cssc.201403290 Full Papers Enhancing Low-Grade Thermal Energy Recovery in a Thermally Regenerative Ammonia Battery Using Elevated Temperatures Fang Zhang,[a, b] Nicole LaBarge,[a] Wulin Yang,[a] Jia Liu,[a] and Bruce E. Logan*[a] A thermally regenerative ammonia battery (TRAB) is a new approach for converting low-grade thermal energy into electricity by using an ammonia electrolyte and copper electrodes. TRAB operation at 72 8C produced a power density of 236 8 W m¢2, with a linear decrease in power to 95 5 W m¢2 at 23 8C. The improved power at higher temperatures was due to reduced electrode overpotentials and more favorable thermodynamics for the anode reaction (copper oxidation). The energy density varied with temperature and discharge rates, with a maximum of 650 Wh m¢3 at a discharge energy efficiency of 54 % and a temperature of 37 8C. The energy efficiency calculated with chemical process simulation software indicated a Carnot-based efficiency of up to 13 % and an overall thermal energy recovery of 0.5 %. It should be possible to substantially improve these energy recoveries through optimization of electrolyte concentrations and by using improved ion-selective membranes and energy recovery systems such as heat exchangers. Introduction The depletion of fossil fuels and global climate change call for cost-effective utilization of renewable energy that is carbon neutral and sustainable.[1] Low-grade thermal energy from either industrial processes or natural solar or geothermal processes becomes attractive as a possible energy source because of the vast energy potentials.[2] As some of these thermal energy sources may only be intermittently available, energy conversion with technology that also enables energy storage is particularly useful. Liquid-based thermoelectrochemical systems (TESs) represent a promising and inexpensive approach for both the storage and conversion of low-grade thermal energy into electrical power.[3] Most of the previously proposed TESs for low-grade thermal energy conversion rely on the temperature dependence of a redox potential, with the thermal efficiency limited by the Carnot efficiency (h = 1¢TC/TH ; h: Carnot efficiency; TC : absolute temperature of the cold reservoir; TH : absolute temperature of the hot reservoir).[4] The overall thermal energy efficiencies of TESs for low-grade thermal energy harvesting are usually very low and are often reported relative to the Carnot efficiency.[5] In thermogalvanic cells, voltage is produced if there is a temperature gradient across electrodes that have reversible [a] Dr. F. Zhang, N. LaBarge, W. Yang, Dr. J. Liu, Prof. B. E. Logan Department of Civil and Environmental Engineering Penn State University 212 Sackett Building, University Park, PA 16802 (USA) Fax: (+ 1) 814-863-7304 E-mail: blogan@psu.edu [b] Dr. F. Zhang School of Environment and State Key Joint Laboratory of Environment Simulation and Pollution Control Tsinghua University, Beijing 100084 (PR China) Supporting Information for this article is available on the WWW under http://dx.doi.org/10.1002/cssc.201403290. ChemSusChem 2015, 8, 1043 – 1048 redox reactions and the same redox couple.[5, 6] A good relative Carnot efficiency of 1.4 % (0.25 % thermal efficiency) was obtained by using a ferrocyanide/ferricyanide redox couple.[6b] Another recently proposed approach for using thermal energy is a thermally regenerative electrochemical cycle (TREC), in which electrodes discharged at a low temperature can be recharged at a higher temperature.[7] A small prototype TREC (working electrode of 0.25 cm2) achieved a very high thermal efficiency of 5.7 %, which was 33 % of the Carnot efficiency. Salinity gradient energy (SGE) technologies represent an alternative approach for thermal–electric energy conversion, based on using waste heat to create streams of different salinities, so that the thermal energy can be first stored in the electrolyte as chemical energy (salinity gradient energy) and then converted into electrical power.[8] SGE technologies have so far produced power in the range of < 1 to 38 W m¢2.[9] With ammonia–carbon dioxide pressure-retarded osmosis (PRO) for power production, the thermal energy efficiency reached 5– 10 % of the Carnot efficiency, relative to a predicted maximum of 16 %.[8a] To make these SGE technologies economically viable for waste heat recovery, membrane costs must be reduced but the good selectivity and robustness of the membranes must be maintained. A new approach for efficient waste heat conversion to electricity was recently described that combined aspects of thermally regenerative batteries with SGE technologies in what was called a thermally regenerative ammonia battery (TRAB).[10] A maximum power density of 115 1 W m¢2 was produced in a single (first) cycle by using the TRAB, with 60 3 W m¢2 produced over multiple successive cycles with electrolyte regeneration. In a TRAB, power is produced due to the copper ammine complex formed in the anode chamber by adding ammonia to the anolyte, but not the catholyte, because this cre- 1043 Ó 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim Full Papers ates a concentration gradient. Copper reduction occurs at the cathode (Cu2 + + 2 e¢ !Cu), with copper corrosion in the ammonia solution at the anode [Cu + 4 NH3 !Cu(NH3)42 + + 2 e¢ ; Figure S1 in the Supporting Information]. After the discharge of electrical power, ammonia is separated off from the anolyte by conventional distillation, which regenerates that electrolyte. Ammonia is then added to the other electrolyte chamber (which contains electrodeposited copper on the electrode) so that the former anode electrode now functions as the cathode, and copper is redeposited onto the electrode surface. This alternating oxidation/corrosion cycle allows the copper on the electrodes to be maintained in closed-loop cycles because the electrodes are alternately used as the anode and the cathode.[10] The heating and cooling requirements for ammonia regeneration can greatly affect the overall energy efficiency of the process. Previously, the TRAB process was examined only at room temperature, which would require heating and cooling the electrolyte over a wide temperature range relative to the higher temperature of operation. An energy analysis based on distillation of ammonium bicarbonate solutions indicated that solution heating could account for 45 % of the total energy duty over the temperature range of 32–50 8C.[8a] In theory, operation of the TRAB at elevated temperatures should increase the reaction kinetics. Therefore, higher operating temperatures of the TRAB could improve both heat recovery (solution thermodynamics) and reaction kinetics. To examine whether power production and energy recovery could be improved for the TRAB process, we examined the performance of the system at temperatures of up to 72 8C. In order to better understand the extent of the overall energy requirements, we conducted an energy analysis with a commercial process simulation software package and compared the energy recoveries to the Carnot efficiencies for comparison with other TES technologies. Figure 1. Electrode open-circuit potentials at different temperatures (error bars smaller than the symbol size), compared to those estimated by using Nernst equations (lines). ative with temperature and changed from ¢150 mV at a room temperature of 23 8C to ¢197 mV at 72 8C (Figure 1). The more negative open-circuit anode potentials indicated favorable anode reaction thermodynamics at higher temperatures. The open-circuit anode potential was estimated using the Nernst equation to be ¢145 mV at standard conditions (25 8C and 1 atm), which agreed well with the experimental value of ¢150 mV at a room temperature of 23 8C. Due to the lack of tabulated dE0/dT values for the Cu(NH3)42 + /Cu redox couple, we estimated it from the experimental result of ¢1 mV K¢1. The reduction potentials were then adjusted for the term (RT/2F)ln{[a(NH3)]4/a(Cu(NH3)42 + )} using ion activities at the appropriate temperatures, which resulted in values consistent with the experimental results (Figure 1). Power production at various temperatures At room temperature (23 8C), a maximum power density of 95 5 W m¢2 was obtained with the TRAB. An increase in the Results and Discussion Effect of temperature on electrode open-circuit potentials Under open-circuit conditions, the cathode potential slightly decreased with an increase in the temperature, from 305 mV at 23 8C to 287 mV at 72 8C, which indicated a small temperature dependence of ¢0.3 mV K¢1 (Figure 1). The effect of temperature on electrode potentials was estimated using the Nernst equation. For the cathode (Cu2 + + 2 e¢ !Cu), the temperature dependence of the standard reduction potential E0 is 0.011 mV K¢1.[11] With consideration of the Cu2 + -ion activities [based on the term (RT/2F)ln(1/a(Cu2 + )); R: ideal gas constant; F: Faraday constant; a: activity], the estimated temperature dependence is ¢0.2 mV K¢1. The estimated cathode reduction potentials at different temperatures agreed well with the experimental data (Figure 1). The more negative open-circuit cathode potential with the increasing temperature indicated unfavorable cathode reaction thermodynamics at higher temperatures. For the anode with a redox couple Cu(NH3)42 + /Cu, the anode open-circuit potential showed a larger temperature dependence (¢1 mV K¢1) than the cathode. It became more negChemSusChem 2015, 8, 1043 – 1048 www.chemsuschem.org Figure 2. (A) Power densities and (B) electrode potentials of TRABs operated at various temperatures. 1044 Ó 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim Full Papers Power generation over a complete discharge cycle Figure 3. The maximum power production showed a positive relationship with temperature. operating temperature greatly enhanced the power production from 143 6 W m¢2 at 37 8C to 236 8 W m¢2 at 72 8C (Figure 2 A). The maximum power density was directly proportional to the temperature (coefficient of determination R2 = 0.98, calculated probability p = 0.001) with a change of 2.9 0.2 W 8C¢1 (Figure 3). This enhancement in power production was due to the better performance of both electrodes with increasing temperatures (Figure 2 B). Although higher temperatures were not predicted to improve the cathode potentials based on thermodynamics, higher temperatures led to reduced overpotentials for both electrodes, which indicated that the reaction kinetics were improved at higher temperatures. Better copper reduction kinetics at higher temperatures were consistent with a previous study that showed that copper electrodeposition at higher current densities was improved at higher solution temperatures because of reduced electrode overpotentials.[12] Power generation was examined at different temperatures over a complete discharge cycle, at a load that produced the maximum power (2.6 W at 23 and 37 8C, and 1.6 W for 46– 72 8C) or at a low current (20.6 W). The initial power densities always increased with temperature, consistent with polarization results, for both circuit loads. Higher temperatures resulted in reduced cycle lengths owing to both faster electrical discharge and self-discharge (ammonia crossover, as discussed below; Figure 4 A and C). In the low-current tests, the cycle time was greatly reduced at 72 8C, whereas the cycle times were more similar to each other at the lower temperatures. Anode potentials initially slightly increased at the start of the cycle, likely because of accumulation of CuII ions produced by electrode corrosion. After this, the anode potential was relatively stable over the rest of the discharge cycle. The cycle time was primarily limited by the cathode performance, as there were relatively large changes in the cathode potentials (Figure 4 B and D). The overall changes observed in the power density curves were, therefore, mostly due to cathode potentials. The rapid change in cathode potential was, in part, as a result of the faster depletion of Cu2 + ions at higher temperatures with improved kinetics. However, the most important factor was likely faster ammonia crossover at higher temperatures, because it was visually observed that the color of the catholyte changed from a light blue to a darker blue that was similar to the initial color of the anolyte. Total charge transfer and energy densities In tests at circuit loads that produced maximum power densities (2.6 or 1.6 W), the highest recovered total charge of 540 2 C was obtained at 37 8C, and the total charge decreased inversely with the temperature, to 450 20 C at 72 8C (Figure 5 A). In the low-current tests (20.6 W), there was a smaller decrease in the total charge transferred (440 C at 23 8C to 400 C at 56 8C) with increasing temperatures, in comparison with a very large decrease in charge transfer at 72 8C (230 10 C). This decrease was primarily due to a loss of membrane selectivity with increased temperatures, which resulted in greater ammonia crossover from the anolyte to the catholyte chamber. The ammonia that transferred into the catholyte reacted with Cu2 + ions to form Figure 4. Whole batch cycle performance of TRABs that were discharged at the maximum-power condition and Cu(NH3)42 + , which resulted in the low-current condition. (A) Power densities and (B) cathode (open symbols) and anode potentials (filled syma loss of power. A decrease in bols) over a whole batch cycle at the condition that produced the maximum power density. (C) Power densities charge transfer reduced the and D) cathode (open symbols) and anode potentials (filled symbols) over a whole batch cycle discharged at coulombic efficiencies, which a low current. ChemSusChem 2015, 8, 1043 – 1048 www.chemsuschem.org 1045 Ó 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim Full Papers Figure 5. (A) Total charge and corresponding cathodic coulombic efficiency and B) energy density for TRABs that were discharged at the maximum power or at a low current. ranged from 78–93 % for the high power tests, to 40–77 % at the lower current conditions (Figure 5 A). These results indicated that the key to improving power production and charge transfer at higher temperatures will be to maintain membrane selectivity. The energy densities produced by the TRABs were greater in low-current tests than under maximum-power conditions. In low-current tests, the energy densities were nearly constant at 640 Wh m¢3 (range of 620–650 Wh m¢3) for temperatures of 23–56 8C, but there was a large decrease to 330 7 Wh m¢3 at 72 8C (Figure 5 B). When a low resistance was used to maximize power, the energy densities did not significantly change with temperature and averaged 400 Wh m¢3 (range of 390 0.1 Wh m¢3 at 23 8C to 480 3 Wh m¢3 at 37 8C). The higher energy densities under the low-current condition were due to the higher discharge voltage under these conditions (that is, W = QU; W: energy, Q: charge, U: voltage). Figure 6. (A) Discharge energy efficiency (discharge energy versus the stored chemical energy in the TRAB) at the low-current condition and the maximum-power condition. (B) Thermal energy efficiency (discharge energy versus the required thermal energy for regeneration) and that relative to the Carnot efficiency based on the discharge at low current. cause it decreased from 245 kWh m¢3 of anolyte (23 8C) to 230 kWh m¢3 (72 8C). However, the energy needed to increase the solution temperature substantially decreased from 60 to approximately 0 kWh m¢3 of anolyte. As discharging at low current generally produced higher energy densities, we only analyzed the thermal energy efficiency for this condition. The overall thermal energy efficiency was 0.53 0.01 % over the range of 23–56 8C, but it decreased to 0.29 % at 72 8C (Figure 6 B). The Carnot efficiency, estimated with respect to the column reboiler temperature of 70.4 8C, decreased from 14 to 4.2 % because the temperature difference was smaller with the increasing operation temperature. Thus, the efficiency relative to the Carnot efficiency (actual thermal efficiency/Carnot efficiency) increased from 3.8 to 13 % when the anolyte temperature was increased from 23 to 56 8C (Figure 6 B). Comparison of performance with other systems Discharge energy efficiency and thermal energy efficiency The discharge energy efficiency reflected the extraction efficiency of the chemical energy stored in the TRAB. The discharge energy efficiencies generally followed the same trend as the energy densities, with the higher discharge energy efficiency of 50–55 % obtained with low current tests, except for the test at 72 8C during which the efficiency dropped to only 25 % (Figure 6 A). If the cell was discharged at maximum power, the discharge energy efficiencies were lower and averaged 33 % (range of 29 % at 46 8C to 40 % at 37 8C; Figure 6 A). The TRAB thermal energy efficiency was estimated by comparing the electrical energy recovered with the energy required for distillation of the ammonia from the anolyte solution. An increase in the effluent temperature from 23 to 72 8C did not appreciably change the heat duty for distillation beChemSusChem 2015, 8, 1043 – 1048 www.chemsuschem.org The highest energy density obtained herein, under relatively unoptimized conditions (650 Wh m¢3), is only slightly less than the best results obtained to date with PRO by using concentrated seawater brine (860 Wh m¢3),[13] but it is substantially greater than that obtained using reverse electrodialysis (RED) with an ammonium bicarbonate solution (118 Wh m¢3).[8c] Similarly, the discharge energy efficiencies obtained herein (25– 55 %) are comparable to those for PRO (54–56 %) but higher than those obtained with RED (18–38 %).[9] Energy densities produced by a TRAB could easily be improved by using membranes with greater selectivities to reduce ammonia crossover, and thus self-discharge, and by using more concentrated copper solutions. Vanadium flow batteries used for energy storage, which have much higher energy densities of 10– 50 kWh m¢3[14] than the TRABs tested herein, have electrolyte 1046 Ó 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim Full Papers concentrations that are near the solubility limit for vanadium salts (1.7–2.5 m).[15] The Cu2 + -ion concentration used herein was only 0.1 m, which was far below the solubility limit of Cu(NO3)2 (59.2 wt % at 25 8C, 3.5 m).[16] Based on the solubility limit for Cu(NO3)2 of 3.5 m, the theoretical maximum energy density of a TRAB would be 42 kWh m¢3. Therefore, optimization of the electrolyte concentration and minimization of ammonia crossover should allow energy densities of TRABs to approach those of vanadium flow batteries. The advantage of the TRAB, compared with a flow battery, is that the TRAB can be charged using a waste heat source (through ammonia distillation), whereas a flow battery can only be recharged with electrical power. The thermal energy efficiency obtained herein (0.53 0.01 %) was about twice that obtained with a thermogalvanic cell (0.25 %) that was operated at a temperature difference of 60 8C[6a] but was less than that produced by a thermally regenerative electrochemical cycle (5.7 %).[7] However, as noted above, the TRAB thermal energy efficiency could be improved by using a Cu2 + -ion concentration near the solubility limit and better ion-selective membranes at higher temperatures. The Cu2 + /ammonia ratio could also be optimized to improve the thermal energy efficiency. The heat duty was calculated herein for an influent ammonia concentration of 2 m, and therefore, it did not take into account ammonia loss to crossover into the catholyte during the batch cycle operation. This resulted in an overestimation of the energy demand needed for ammonia separation, especially for those cells operated at higher temperatures. However, our analysis did not incorporate any methods for heat recovery, such as the use of heat exchangers to obtain energy recovery by using ammonia condensation in a refrigeration cycle to extract heat.[17] The use of heat exchangers and other methods of heat recovery would save energy and improve the overall thermal energy efficiency of the TRAB process. Conclusions The operation of TRABs at elevated temperatures increased the maximum power production to as much as 236 8 W m¢2 (at 72 8C). The use of these higher temperatures also resulted in lower energy demands for heating electrolytes and distillation of the ammonia used to recharge the battery. However, operation at higher temperatures increased self-discharge as a result of reduced membrane selectivity, which resulted in ammonia transport across the ion-exchange membrane and a decrease in the coulombic efficiency and energy density. Further improvements in performance could be obtained by increasing the Cu2 + -ion and ammonia concentrations, by using membranes with improved ion selectivity at higher temperatures, and by using heat exchangers and other processes to improve heat recovery. Experimental Section The TRAB was constructed as previously described,[10] with anode and cathode chambers separated by an anion-exchange memChemSusChem 2015, 8, 1043 – 1048 www.chemsuschem.org brane (AEM; Selemion AMV, Asashi glass, Japan; effective surface area of 7 cm2 ; Figure S1 in the Supporting Information). The two chambers, each 4 cm long and 3 cm in diameter, were constructed from 4 cm cubes of Lexan with an empty bed volume of 30 mL.[18] Reactors made of high-density polyethylene (HDPE) were tested at elevated temperatures for improved ammonia compatibility. The electrodes were copper mesh (50 Õ 50 mesh; McMaster-Carr, OH; 0.8 Õ 2 cm with a projected surface area of 1.6 cm2 and a mass of 0.2365 0.0004 g), connected by copper wires to an external resistor. Two Ag/AgCl reference electrodes (+ 211 mV versus the standard hydrogen electrode (SHE) at 25 8C; RE-5B; BASi) were inserted into each electrode chamber at the two sides of the copper electrodes, which were 1 cm away from the copper electrode and outside the current path, to monitor electrode potentials (Figure S1 in the Supporting Information). The cathode chamber was stirred with a stirrer bar (6.4 Õ 15.9 mm; VWR; 600 rpm), whereas the anolyte was not mixed. The electrolyte was 0.1 m Cu(NO3)2 and 5 m NH4NO3 (Sigma–Aldrich) dissolved in deionized water. To charge the TRAB, 2 m ammonium hydroxide (Sigma–Aldrich; 5 n solution) was added to the anolyte to form the copper ammonia complex and create the potential difference between the two copper electrodes. For the tests at elevated temperatures, electrolyte solutions were preheated in an oven set at the desired temperature. Polarization tests were performed at set temperatures ranging from room temperature ( 23 8C) to 72 8C, to examine the effect of temperature on electrode performance and power production. Except for tests at room temperature, experiments were performed in a constant-temperature oven. External resistances were switched every 5 min from open circuit to 0.6 W, in decreasing order at the lower temperatures, whereas they were switched in an increasing order for the higher temperatures (56 and 72 8C) because of the relatively fast decay of performance as a result of ammonia crossover at higher temperatures. Both current density (j = U/R A; j: current density, U: voltage, R: external resistance, A: surface area) and power density (P = U2/R A) were normalized to a single-electrode projected surface area (1.6 cm2). Error bars indicate standard deviations for measurements with duplicate reactors. All electrode potentials were recorded versus Ag/AgCl reference electrodes and adjusted for temperature. The effect of temperature on electrode potentials was estimated using the Nernst equation in which ET0 = E0298 + (T¢298.15) ET = ET0¢(RT/nF)ln(ared/aox), 0 (dE /dT) j 298 (ET: electrode potential at absolute temperature T, ET0 : standard electrode potential at temperature T, n: number of electrons) between 0 and 100 8C.[11] The change in the standard reduction potential for the reference electrode as a function of temperature was estimated using the equation developed for a temperature range of 0–95 8C: E0(T in 8C)/V = 0.23695–4.8564 Õ 10¢4 T¢3.4205 Õ 10¢6 T2¢5.869 Õ 10¢9 T3.[19] The potential of the reference electrode was then calculated using the Nernst equation ET = ET0¢(R T/F)ln a(Cl¢) at various temperatures, with the chloride-ion activity estimated using the OLI studio software (Cedar Knolls, NJ). The electrode potentials were converted into standard hydrogen electrode potentials at different temperatures. To evaluate the effect of temperature on the overall batch cycle performance and to compare the discharge performance at various external loads, reactors were allowed to discharge with a fixed external resistance over a complete discharge cycle. The resistance was set at 2.6 W (23 and 37 8C) or 1.6 W (46–72 8C) to examine the discharge performance if the cells produced maximum power density or at 20.6 W to allow the cell to discharge at a lower current. 1047 Ó 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim Full Papers The batch cycle ended when the cell voltage dropped below 20 mV. The total charge over one cycle was calculated by integrating the current–time profile (Q = sI t), and the total energy was calculated by integrating the power–time profile (W = sU I t; U: voltage, I: current, t: time). The energy density was calculated by normalizing the total produced energy in one cycle to the total electrolyte volume (60 mL). Coulombic efficiencies were calculated based on the produced charge in one cycle versus the theoretical charge capacity of 579 C, which was based on catholyte Cu2 + -ion reduction. During electrolyte regeneration, ammonia needed to be separated from the anolyte effluent and redissolved in the catholyte. The thermal energy needed for ammonia separation from the anolyte effluent was estimated based on the energy needed for separation of the copper ammine complex and the distillation energy of ammonia from the anolyte. The simulation results with the OLI software indicated that over 97 % of the free ammonia (78 % of total ammonia) existed in the vapor phase at a temperature of 50 8C and 0.1 atm, so the distillation was modeled as ammonia and water by using Aspen HYSYS software (Cambridge, MA) with a single distillation column (Figure S2 in the Supporting Information). The reboiler temperature as a result of pressure conditions was 70.4 8C, and the condenser temperature was set at 43.3 8C, a limit that can typically be achieved with cooling water. A column pressure drop of 0.15 atm was used,[8a] and a pressure drop of 0.068 atm was used for the partial condenser. Before entry to the column, the solution pressure was decreased to 0.24 atm. In the simulation, the inlet ammonia concentration was set at 2 m with the assumption of no ammonia crossover, which overestimated the energy duty, especially at higher temperatures. The bottom product ammonia concentration was set at 1 ppm. As only the anolyte needed to be heated to distill out the ammonia, the thermal energy duty was reported by normalizing to the anolyte liquid volume, rather than the total electrolyte volume. The energy efficiency was evaluated on the basis of the discharge energy efficiency and the overall thermal energy efficiency. The discharge energy efficiency was based on the ratio between the discharge energy and the stored chemical energy in the battery. The stored chemical energy in the battery was calculated as DG = ¢n F E0, in which E0 was the theoretical open-circuit voltage at various temperatures. The overall thermal energy efficiency was calculated as the discharge energy divided by the total thermal energy estimated for electrolyte regeneration. The Carnot efficiency was estimated from the equation h = 1¢TC/TH, in which TH was the reboiler temperature of 70.4 8C. The thermal efficiency was also reported relative to the Carnot efficiency, by dividing the actual thermal efficiency by the Carnot efficiency. ChemSusChem 2015, 8, 1043 – 1048 www.chemsuschem.org Acknowledgements The authors thank David Jones for help with the analytical measurements. We also thank Dr. Marta Hatzell for useful discussions. 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