Thermo-Electrochemical Redox Flow Battery for Continuous Conversion of Low-Grade Waste Heat to Power

9 Here we assess the route to convert low grade waste heat (<100 °C) into electricity by leveraging the 10 temperature dependency of redox potentials (Seebeck effect). We use fluid-based redox-active 11 species, which can be easily heated and cooled using heat exchangers. By using a first principles 12 approach, we designed a redox flow battery system with Fe(CN) 63- /Fe(CN) 64- and I - /I 3- chemistry. We 13 evaluate the continuous operation with one flow cell at high temperature and one at low temperature. 14 We show that the most sensitive parameter, the Seebeck coefficient, can be controlled via the redox 15 chemistry, the reaction quotient and solvent additives, and we present the highest Seebeck coefficient 16 for this RFB chemistry. A power density of 0.6 W/m 2 and stable operation for 2 hours are achieved 17 experimentally. We predict high (close to Carnot) heat-to-power efficiencies if challenges in the heat 18 recuperation and Ohmic resistance are overcome, and the Seebeck coefficient is further increased.


Introduction 32
In the quest for reducing CO2 emissions, cutting energy losses has received major attention in the past 33 decade. Despite various efforts to make industrial and power generating processes more efficient, 50 34 to 80% of the primary energy is dissipated as waste heat, where low-grade waste heat (up to 100 °C) 35 forms the largest contribution 1 . Forman et al estimated that in 2012 around 43 PWh (1.6·10 20 J) of low-36 grade waste heat was emitted globally 1 . Although not all waste heat can be converted into power due 37 to the conservation of entropy, the Carnot efficiency (1 − ℎ ) still allows to capture 20% of the low-38 grade waste heat (100 °C) as power, assuming an environment of 25 °C. Converting just this fraction 39 of the low-grade waste heat into electricity could already generate 39% of the world's electricity 40 consumption (22.3 PWh/year, IEA as of 2018 2 ). 41 A major bottleneck for converting low-grade waste heat into power is the low practical efficiency of 42 existing technologies, even compared to the Carnot efficiency. Traditionally, the organic Rankine cycle 43 (ORC) has been used, which converts typically 4-9% of the (100-120 °C) waste heat to power 3 . The 44 relatively low energy efficiency and the corresponding low (environmental and economic) benefits, 45 have limited the practical application of ORC. Newer heat-to-power technologies, e.g. Reverse 46 Electrodialysis 4, 5, 6 , Thermal Regenerable redox-flow Batteries 7, 8 or Pressure Retarded Osmosis 47 combined with membrane distillation 9, 10 , have not shown higher energy efficiencies. Hence, a heat-48 to-power technology with potential for high energy efficiency is demanded. 49 A recent technology with high potential for efficient conversion is the Thermally Regenerative 50 Electrochemical Cycle (TREC) 11 , which makes use of the temperature-dependent battery voltage (i.e., 51 the Seebeck effect). More energy can be obtained upon discharging at a first temperature, compared 52 to the charging at a different temperature, generating net electrical power. Lee et al. has shown 53 experimentally, using a solid Cu/Cu hexacyanoferrate (HCF) battery, that waste heat could be 54 converted into power highly efficiently: even up to 80% of the Carnot efficiency can be reached when 55 heat would be fully recuperated with a heat exchanger. The work by Lee et al. inspired the 56 development of the TREC over the past years 12 , including a membrane free system (NiHCF, Ag/AgCl) 13 , 57 a CoHCF based TREC (CoHFC, Ag/AgCl) 14 and even first applications of a TREC into a combustion 58 engine 15 and the hot roof of a building 16 . 59 However, a practical drawback of the above TRECs is the slow heat transport in solids and stationary 60 fluids. Hence, the use of a battery based on solid redox active species makes the heat recuperation 61 unpractical, leading to long cycle times (several hours for Lee et al.), corresponding to a low power 62 density (1.2 mW/g) 11 . Redox Flow Batteries (RFBs) could leverage the intrinsic facile heating and 63 cooling of liquid redox active species in heat exchangers, which makes them attractive candidates for 64 Here α0 is the Seebeck coefficient at standard concentrations and Q is the reaction quotient of the 93 redox reaction (see SI Note 1 for a derivation and comparison of Seebeck coefficients at different 94 concentrations). 95

Thermo-electrochemical energy 96
The battery's open circuit voltage, OCV (in V), arises from the potential difference between the redox 97 potentials of species 1 and 2, where Q is the reaction quotient of the cell reaction: 98 The Seebeck effect can be leveraged when using two batteries: one battery in which both anolyte and 100 catholyte operate at a high temperature, and a second battery in which both reactions occur at a low 101 temperature. The difference in OCV between the hot battery and the cold battery is: 102 In which Qhot and Qcold indicate the reaction quotient at the operating conditions of the hot and cold 105 battery respectively and αcell is the Seebeck coefficient of the combined electrolytes. The difference in 106 OCV drives an electric current between the hot and the cold battery, which can be used as a power 107 source (Fig. 1a). The maximum power that can be extracted from the difference in battery voltage is 108 given by the Kirchhoff law (eq. 6), which assumes a constant battery resistance, R (in Ω m 2 ) and a 109 constant cell voltage. The maximum power density Pmax (in W/m 2 ) is then given by: 110 eq. 6 111 112 Thermodynamic analysis 113 From a thermodynamic point of view, the battery process can be illustrated in a TS-diagram (Fig. 1b). 114 When the heat from the hot RFB outflow is recuperated via a heat exchanger and no losses are 115 included, the Carnot efficiency can be obtained (see SI Note 2). 116 The expected voltages at the hot and cold RFB are obtained from eq. 4. When including electrical losses 117 (Ohmic resistances, kinetic overpotentials) a V-dQ diagram is established (Fig. 1c&d). The maximum 118 work is obtained when the battery voltage is continuously adapted to the individual battery potentials 119 ( Fig. 1c). This resembles a batch mode operation, or a segmentation of electrodes that can be 120 individually controlled (Fig. S-1). A more practical operation is a continuous, single-stage, battery 121 mode. However, this single charge and discharge voltage, Ehot and Ecold, respectively, compromises the 122 obtainable work (Fig. 1d)  The cyclic voltammetry was performed using a potentiostat (Ivium CompactStat.h10800) with a scan 152 rate of 50 mV/s, cycling between -0.2 and 0.5 V vs Ag/AgCl@20 °C for hexacyanoferrate and 0.2 and 153 0.6 V vs Ag/AgCl@20 °C for polyiodide. The halfway potential (E 1/2 ) was calculated by taking the 154 average of the cathodic and anodic peak positions 21 , which were measured against a Ag/AgCl 155 reference electrode (ProSense B.V.) at 20 °C. The Seebeck coefficient was taken as the slope of the 156 linear fit of E 1/2 versus T data. 157

Single flow cell characterization 158
The cell Seebeck coefficient (i.e., combined with both redox couples) was experimentally assessed 159 using a custom-made PTFE flow cell with graphite sheet electrodes with a geometrical surface area of 160 86.6 cm 2 and FKM gaskets (see and read out with a NI 9213 module. The OCV was measured once the temperature was stable (± 0.5 169 °C for 5 minutes). The temperature of the heating bath was then raised for the next measurement. The  TRECs to date (-2.9 mV/K and -3.0 mV/K respectively) 18, 25 , but do not meet the 3 rd criterion. Hence, 216 despite the predicted high efficiencies, the system suffered from ion crossover causing precipitation 217 of Cu2Fe(CN)6 and a high internal resistance. The V 2+ /V 3+ , Fe(CN)6 3-/Fe(CN)6 4was not tested for 218 stability, but will likely suffer from vanadium crossover as the electrolytes are only separated by a 219 Nafion cation exchange membrane. 220 The sign of the Seebeck coefficient appears to be correlated with the sign of the valence of the redox 221 active species that undergo a simple one-electron transfer reaction. For example redox couples 222 consisting of cations, e.g. Fe 3+ /Fe 2+ , Cu 2+ /Cu + and Co 3+ /Co 2+ , all have positive Seebeck coefficients 20, 26 , 223 while their anion counterparts, e.g. Fe(CN) 3-/Fe(CN) 4and MnO4 -/MnO4 2-, have negative coefficients 11, 224 26 (see SI Note 3 for 54 examples from literature sources). We hypothesize that the change in entropy 225 (and thus the Seebeck coefficient) is dominated by the size of the ion hydration shell, which grows 226 upon increased valence magnitude (Fig. 3a). Unfortunately, this property makes it difficult to satisfy 227 both criterion 1 and 3. 228 To match all three criteria we chose the polyiodide redox couple, as it is not a simple one-electron 229 transfer reaction and deviates from the rule. We ended up a flow cell with I -/I3and Fe(CN)6 3-/4-230 chemistry. The reactions below are written in the discharging (galvanic) form below: 231  I3 -+ 2e - 3 I -232  Fe(CN)6 4- Fe(CN)6 3-+ e -233 The Seebeck coefficients of I -/I3and Fe(CN)6 3-/4were experimentally determined as +1.04 mV/K and -234 1.40 mV/K, respectively (Fig. S-2a). The values agree with reported values in literature, as the Seebeck 235 coefficient of Fe(CN)6 3-/4is well documented to be around -1,4 mV/K 27, 28 and I -/I3agrees with 236 tabulated values when corrected for the concentrations we use here (See SI Note 1). The combination 237 of the two electrolytes predicts a cell-Seebeck coefficient of +2.44 mV/K (Fig. 3b).  (Fig. S-2a). To 241 avoid temperature changes in the Ag/AgCl reference electrode, a long glass salt bridge was used (Fig. S-8b) 27,29 . The polyiodide couple is reported in RFBs well 247 above 1 M 30 and has a stable cycling performance 31, 32 . Also, triiodide electrolytes have been reported 248 well over 80 °C 33 and we therefore assumed the redox couple is stable over a large temperature range. 249 As all active species in the selected redox couples are anions, they are separable by a cation exchange 250 membrane (CEM). The triiodide equilibrium, I3 -↔ I2 + I -, is strongly balanced towards I3 -, which 251 minimizes the potential crossover of I2. Also, Ding et al have shown that a Nafion membrane could be 252 used to separate these two electrolytes for 500 cycles with negligible cross-over effects. Moreover, 253 the combination of these redox couples results in a low cell potential of 0.18 V (at room temperature), 254 which avoids large energy losses due to self-discharge. 255

Single flow cell characterization 256
The OCV of a flow cell exhibits a linear dependence on temperature between 20-40 °C (Fig. 3c), 257 indicating a constant αcell. The obtained Seebeck coefficient is +2.88 mV/K, slightly larger than the 258 individual coefficients that were measured through cyclic voltammetry (+2.44 mV/K). This is likely due 259 to the different ratio of KI to I2 in the electrolyte in the flow cell experiments, causing a different Q in 260 eq. 3 and explaining a change in Seebeck coefficient. The Seebeck coefficient is possibly affected by 261 the change in reaction entropy to other polyiodides (e.g. I5or I7 -) that form at higher iodine 262 concentrations 33 or by the change of reaction towards I2 instead of I3 -, which has a higher Seebeck 263 coefficient 26 . 264 The area resistance of a single flow cell is 7.1 Ω cm 2 at 22 °C and decreases to 3.6 Ω cm 2 at 40 °C. We 265 assume the resistance follows 34 : 266

Comparison with other reported systems 270
We can compare our I -/I3 --Fe(CN)6 3-/4system to other thermo-electrochemical systems, by adopting 271 their dimensionless Figure

eq. 8 275
Here |α| is the absolute Seebeck coefficient of the system, qc is the specific charge capacity and cP the 276 specific heat capacity of the electrodes and electrolyte. Ohmic and Nernstian losses are ignored for all 277 systems (see SI Note 4 for more details). Even though other reported TREC systems use solid redox 278 species and higher concentrated electrolytes, the system we report here has a comparable figure of 279 merit of 0.021 (Table 1), while still having the benefits of liquid handling. A lower Y is expected for all-280 liquid based systems, due to the relatively high heat capacity of water, and poses additional 281 requirements for the heat recuperation. However, the concept of redox flow batteries, allowing liquid-282 liquid heat exchangers, easily improves the heat transfer flux by an order of magnitude compared to 283 stationary with solid redox species, which justifies the 2-3x lower Y for practical TREC systems. 284 Table 1

Proof of concept 293
The heat-to-power performance of the polyiodide/ferrocyanide RFB was evaluated in a continuous 294 flow setup with a cold charging and hot discharging flow cell connected in a loop as per Fig. 1a (more 295 detailed in Fig. S-4b). Fig. 4a shows the power density versus current densities for various temperature 296 differences between the hot and cold cell. We achieved a maximum power density of 0.6 W/m 2 at 13.8 297 A/m 2 and a temperature difference of 34 °C. At this current density, the hot and cold cell are cycling 298 between a state of charge of 50.0% and 51.2%. The maximum power density shifts to higher current 299 densities at higher temperature intervals because both the driving force is larger (larger difference 300 OCVhot -OCVcold) and the Ohmic resistance is lower at higher temperatures. Still, the optimum current 301 density is relatively small compared to commercialized RFBs, limiting also the power densities, due to 302 the high (non-optimized) Ohmic resistance of the system (see Fig. S-3). 303 At the maximum power density in Fig. 4a, 50% of the available energy from the Seebeck effect is 304 converted into electricity. Here 40% of the energy is lost in Ohmic losses and activation overpotential 305 and 10% as concentration overpotential. With perfect heat recovery, the present, non-optimized flow 306 cells would obtain a heat to power efficiency of 5.2% (see SI Note 5 for the derivation). In the present 307 setup, however, with limited glass heat exchangers (Fig. S-5), and poor insulation of the flow cells and 308 tubing, an overall heat-to-power efficiency of 0.004% was obtained. 309 The power density of the system, evaluated for 2 hours (Fig. 4b)

317
Outlook 318 Given the early stage of development and the modest power density/energy efficiency, substantial 319 engineering improvements are necessary to make a RFB based thermo-electrochemical cell feasible 320 for practical operation. The Seebeck coefficient reduced by 0.21 mV/K after 20 hours of cycling ( Fig. S-321 6), likely due to I2 migration across the membrane. We also observed corrosion by iodine and 322 deposition of Prussian blue on the electrodes and membrane (Fig. S-7). Both the membrane and 323 electrodes were not selected for long-term stability in this chemistry. Also, our current experimental 324 design is limited by the high internal resistance and poor insulation. 325 To assess the potential of the reported system we calculated the heat-to-power efficiency of the 326 system while varying the ΔSOC, heat exchanger efficiency, Seebeck coefficient, heat capacity, 327 concentration and Ohmic losses for an optimized system (see SI Note 6). Fig. 5a shows the simulated 328 heat-to-power efficiency vs ΔSOC for various heat exchanger efficiencies for a RFB system in 329 continuous mode. Relying on heat recuperation only, without further improving the Seebeck 330 coefficient or cell operation, will be insufficient to reach substantially high energy efficiency in 331 continuous flow mode. Even at very high heat exchanger efficiencies (99.9%) a large fraction of energy 332 is lost and only a maximum heat to power efficiency of 14% can be obtained. At a more realistic heat 333 exchanger efficiency of 90%, only 3% of the waste heat is recovered as electrical power. The maximum 334 heat-to-power efficiency shifts to higher ΔSOC for lower heat exchanger efficiencies, to reduce the 335 amount of fluid that needs to be heated/cooled in poorer heat exchangers. At a ΔSOC of 0.75, the 336 difference in hot/cold cell voltages becomes 0, due to the hysteresis in the V-dQ curve (Fig. 1d).  Fig. 5b shows the heat-to-power efficiency for a system in batch mode. In batch mode the complete 344 area of the V-dQ curve can be harvested (Fig. 1c), and hence higher efficiencies can be achieved. At a 345 ΔSOC of 1 and a perfect heat exchanger the system will approach the Carnot efficiency. Even with a 346 more realistic heat exchanger efficiency of 90% and ΔSOC = 0.5, more than 6% of the heat can be 347 converted into electricity in batch mode, bettering the current state-of-the-art heat-to-power 348 technologies. Fig. 5c,d show the effect of the Seebeck coefficient on the heat-to-power efficiency for 349 a RFB in continuous and batch mode respectively. As the larger Seebeck coefficient increases the 350 vertical shift of the V-dQ curves, the point of zero work also shifts to higher ΔSOC. The Seebeck 351 coefficient of our system could be increased in practice by the addition a volume fraction of an organic 352 solvent. The Seebeck coefficient ferro/ferricyanide redox couple has been shown to amplify up to -4,2 353 mV K -1 27, 28 with additives. Preliminary experiments have shown that the addition of ethanol to the 354 triiodide electrolyte results in a more positive Seebeck coefficient, resulting in a very large cell Seebeck 355 coefficient ( Fig. S-10). The addition of organic solvents does however reduce conductivity and increase 356 Ohmic losses. Other ways to increase the Seebeck coefficient could be to design a system around 357 polysulfide (-4.08 to -5.33 mV K -1 ) 37 or a redox reaction with a large ΔS due to a phase transition 38, 39 . 358 Finally, the effect of the concentration, heat capacity and Ohmic losses on the heat-to-power efficiency 359 is assessed (Figures S-8 & S-9). Provided that the heat capacity and maximum concentration have 360 intrinsic limits, the Ohmic resistance is the only remaining knob for optimizing the heat-to-power 361 efficiency. A 50 mV Ohmic loss (over the entire two cell circuit) almost halves the heat-to-power 362 efficiency (at current α=2.88 mV/K, ηHX = 90%, 0.3 M active species). A zero-gap flow cell design could 363 be used to minimize the Ohmic resistance and allow for much higher current densities 40 , together with 364 a low resistive membrane. Hence, this proof of concept of a RFB-based system for continuous heat-to-365 power conversion should gain improvement in the realm of higher Seebeck coefficient and low Ohmic 366 resistances to fully unlock its potential for effective conversion of waste heat to power. 367 368 369

Data Availability 370
The data supporting the findings of this study are contained within the paper and its associated 371 Supplementary Information. All other relevant data is available from the corresponding author upon 372 reasonable request and in the Zenodo repository at [to be linked later]. 373 374 375