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An electrochemical system for efficiently harvesting low-grade heat energy

An electrochemical system for efficiently harvesting low-grade heat energy ARTICLE Received 21 Nov 2013 | Accepted 23 Apr 2014 | Published 21 May 2014 DOI: 10.1038/ncomms4942 An electrochemical system for efficiently harvesting low-grade heat energy 1, 2, 1 2 2 2 1,3 Seok Woo Lee *, Yuan Yang *, Hyun-Wook Lee , Hadi Ghasemi , Daniel Kraemer , Gang Chen & Yi Cui Efficient and low-cost thermal energy-harvesting systems are needed to utilize the tremendous low-grade heat sources. Although thermoelectric devices are attractive, its efficiency is limited by the relatively low figure-of-merit and low-temperature differential. An alternative approach is to explore thermodynamic cycles. Thermogalvanic effect, the dependence of electrode potential on temperature, can construct such cycles. In one cycle, an electrochemical cell is charged at a temperature and then discharged at a different temperature with higher cell voltage, thereby converting heat to electricity. Here we report an 2 þ electrochemical system using a copper hexacyanoferrate cathode and a Cu/Cu anode to convert heat into electricity. The electrode materials have low polarization, high charge capacity, moderate temperature coefficients and low specific heat. These features lead to a high heat-to-electricity energy conversion efficiency of 5.7% when cycled between 10 and 60 C, opening a promising way to utilize low-grade heat. 1 2 Department of Materials Science and Engineering, Stanford University, Stanford, California 94305, USA. Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA. Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory, 2575 Sand Hill Road, Menlo Park, California 94025, USA. * These authors contributed equally to this work. Correspondence and requests for materials should be addressed to G.C. (email: [email protected]) or to Y.C. (email: [email protected]). NATURE COMMUNICATIONS | 5:3942 | DOI: 10.1038/ncomms4942 | www.nature.com/naturecommunications 1 & 2014 Macmillan Publishers Limited. All rights reserved. Step 3: cooling ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/ncomms4942 ow-grade heat sources (o100 C) are ubiquitous, generated This cycle is also plotted on a temperature–entropy (T–S) 1,2 in energy conversion and utilization processes . Among the diagram to clarify the thermodynamics (Fig. 1b). In process 1, Lmethods for converting this energy to electricity, the cell is in the discharged state and heated from T to T L H thermoelectric (TE) materials and devices have been studied (low to high temperature) at open circuit. Since CuHCF 3–9 2 þ extensively for several decades . Despite recent progress, has a negative a and Cu/Cu has a positive a, the OCV of the however, the figure of merit (ZT) of thermoelectrics is limited full cell decreases during this process. The cell is then charged 10,11 to 2 at high temperatures and 1.5 below 100 C . Seebeck at a low voltage at T in process 2, and the entropy of the effect in electrochemical system is also investigated for thermal cell increases through heat absorption during the electrochemical energy harvesting in similar architectures as a TE device, but the reaction. In process 3, the cell is disconnected and cooled efficiency achieved is usually lower than 0.5% below 100 C since from T to T , and thus the OCV increases. In the final process, H L the thermopower is limited by poor ionic conductivity of the cell is discharged at a higher voltage at T , and the entropy electrolyte, which is more than three orders of magnitude of the cell decreases through the ejection of heat into the smaller than the electronic conductivity in state-of-the-art TE environment. After the cycle, the system returns to the 12–15 materials . An alternative approach of electrochemical system original discharged state at T . Since the charging voltage is lower for thermal energy harvesting is to explore thermo- than the discharging voltage, net work (W) is extracted as the dynamic cycle as in thermomechanical engines. Here we report difference between charging and discharging energy. This is the an efficient thermally regenerative electrochemical cycle (TREC) opposite of the consumption of energy due to electrochemical based on the thermogalvanic effect, temperature dependence hysteresis during a typical charge/discharge cycle of a battery, of electrode potential. For a half-cell reaction, A þne -B, the since the charging energy here is partially provided by heat temperature coefficient is defined as (Supplementary Fig. 1). Such a conversion process of thermal energy into electrochemical energy requires that the electro- @V DS A;B a ¼ ¼ ð1Þ chemical voltage hysteresis during charge/discharge at a fixed @T nF temperature is much smaller than the voltage difference caused where V is the electrode potential, T is temperature, n is the by temperature change, calling for the highly reversible electro- number of electrons transferred in the reaction, F is Faraday’s chemical electrodes. constant and DS is the partial molar entropy change for the A,B half-cell reaction in isothermal condition (see Supplementary Note 1). This effect indicates that the voltage of a battery depends on temperature; thus a thermodynamic cycle can be constructed by discharging the battery at T and charging back at T .If 1 2 (−) (+) the charging voltage at T is lower than the discharging voltage at Step 2 T , net energy is produced by the voltage difference, originating >0 <0 charging from heat absorbed at the higher temperature, similar to a thermomechanical engine with the Carnot efficiency as the upper limit. In practice, instead of transport property limited in TE devices, the efficiency of TREC is limited by the heat capacity of materials and effectiveness of heat exchangers . The concept of TREC was developed a few decades ago for high-temperature Step 4 applications (500–1,500 C) and showed efficiency of 40–50% of the Carnot limit. But, low-temperature TREC did not received as discharging much attention since electrode materials with low polarization and high charge capacity at low temperature were limited . Hammond and William tested an aqueous redox couple for low-temperature solar-thermal applications, but the precipitation of reactants, large internal resistance and poor solubility of active Step 2: charging redox species causing large heat capacity of the system prevented them from reporting device operational characteristics and ΔG =ΔH –T ΔS measuring the device efficiency, although a high efficiency was H H H H theoretically projected based on the measured open-circuit voltage OCV and 100% heat recuperation assumption. The W =|ΔG –ΔG | recent development of highly reversible electrode materials with H L very low polarization loss during the research of rechargeable batteries has now made it possible for us to exploit the TREC ΔG =ΔH –T ΔS concept in a new way. L L L L Here we present a high-efficiency TREC for harvesting low- Step 4: discharging grade heat energy by employing solid copper hexacyanoferrate 2 þ (CuHCF) as a positive electrode and Cu/Cu as a negative electrode in an aqueous electrolyte. The fast kinetics, high charge Entropy, S capacity, high-temperature coefficient (a) and low heat capacity of these materials allow the system to operate with excellent Figure 1 | Working principle of TREC for thermal energy harvesting. efficiency. (a) Schematic view of thermal cycling: process 1, heating up the cell; process 2, charging at high temperature; process 3, cooling down the cell; Results process 4, discharging at low temperature. (b) Temperature–entropy Working principle of TREC. To harvest thermal energy, the (T–S) diagram of thermal cycling assuming a temperature range between entire device undergoes a thermal cycle containing four processes: T and T . The theoretical energy gained over one cycle is the area L H heating up, charging, cooling down and discharging (Fig. 1a). of the loop determined by the temperature difference and entropy change. 2 NATURE COMMUNICATIONS | 5:3942 | DOI: 10.1038/ncomms4942 | www.nature.com/naturecommunications & 2014 Macmillan Publishers Limited. All rights reserved. Step 1: heating Step 3: cooling Temperature, T Step 1: heating NATURE COMMUNICATIONS | DOI: 10.1038/ncomms4942 ARTICLE The efficiency of the system (Z) is calculated as the net work to 70 C. Figure 2a shows the OCV change of the CuHCF 2 þ (W) divided by the thermal energy input. If the enthalpy change electrode (50% state of charge), the Cu/Cu (3 M) electrode and DH and the entropy change DS are the same at T and T , which the full cell for each 10-C increment when the voltage is set at 0 V H L is a good approximation when DT ¼ (T  T ) is small, the at 10 C. The potentials of both electrodes exhibit a linear H L maximum W is DTDS (Fig. 1b). The energy input to complete the dependence on temperature, indicating a constant a in the cycle includes two parts: the heat absorbed at T (Q ¼ T DS) temperature window tested. The measured temperature H H H 2 þ and the external heat required to raise the temperature of the coefficients of CuHCF, Cu/Cu and the full cell are  0.36, system (Q ). As part of heat rejected from the cooling process 0.83 and  1.20 mV K , respectively. These experimental values HX can be used for the heating process through heat recuperation, match with the expected ones. Figure 2b shows the voltage versus Q can be expressed as Q ¼ (1  Z )C DT, where C is the time plot of the full cell over one thermal cycle between 10 and HX HX HX p p total heat capacity of the electrochemical cell and Z is the 60 C when the specific current density is 7.2 mA g with respect HX efficiency of the heat recuperation (See Supplementary Fig. 2 and to active materials (All current, energy and power densities are Supplementary Note 2). Consequently Z can be expressed as: based on the mass of active materials, including CuHCF, þ 2 þ electrolyte for Na , copper and water for Cu in this paper.). W DTDS  E loss In process 1, the OVC of the cell decreases from 0.406 to 0.337 V Z ¼ ¼ ð2Þ Q þ Q T DSþð1  Z ÞC DT H HX H p HX as the temperature increases from 10 to 60 C. Then the cell is charged for 250 min at 60 C in process 2 and the voltage where E is the energy loss due to the cell electrical resistance. loss gradually increases. In process 3, the OCV of the cell increases Note that DTDS ¼ aQ DT, where Q is the charge capacity of the c c from 0.613 to 0.679 V as the temperature decreases back to 10 C. battery and a is the temperature coefficient of the electrochemical The cell is discharged in process 4 at 10 C until the voltage cell. The efficiency can be written as reaches the initial voltage of the discharged state at the beginning 1  IðR þ R Þ=jj a DT of process 1. The corresponding plot of voltage against specific H L Z ¼ Z ð3Þ charge capacity based on the mass of CuHCF is shown in Fig. 2c. 1 þ Z ð1  Z Þ=jj Y c HX The average charging voltage is 59.0 mV lower than the average- where I is the current used in discharging and charging. R and H discharging voltage and thus electrical energy is generated with a R are the internal resistance at T and T , respectively. Y ¼ aQ / L H L c net energy density of 5.2 J g . The voltage spikes at the beginning C , is a dimensionless parameter to describe the requirements of p of each process are electrochemical in nature and are due to the system for high efficiency. A thorough derivation of efficiency overpotential and internal resistance. At the end of process 4, is presented in Supplementary Notes 3 and 4. If only the the discharging curve forms nearly perfect closed loop with contributions of the electrode materials are considered, and it is only tiny loss of electric charges. The Coulombic efficiency assumed that both electrodes have the same properties except (ratio of the amount of charge extracted during discharging to opposite signs of the temperature coefficient, Y ¼ aq /c and it is c p that of adding in during charging) for this cycle is adequately defined as the figure of merit of an electrode material for high B98.6%. TREC, but not thermocells. Here, q is the specific charge capacity and c is the specific heat of an electrode. Consequently, it is clear that a higher temperature coefficient (a), a higher specific Efficiency of TREC. The efficiency of the cycle is estimated based charge capacity (q ) and a smaller specific heat (c ) lead to higher c p on equation (2). Effects of internal resistance and Coulombic efficiency for heat-to-electricity conversion. In addition, low- efficiency are both taken into account. Details of calculations are voltage polarization and effective heat recuperation can shown in Supplementary Note 4 and Supplementary Fig. 3. also improve the efficiency. The value of Y for individual Figure 3a plots the cycle efficiency versus the efficiency of heat materials can be negative or positive, depending on the sign of the recuperation when cycled between 10 and 60 C. The current temperature coefficient, although efficiency expression takes its density is 7.2 mA g . When heat recuperation is not used, the absolute value. cycle efficiency is 3.7%. The final system efficiency could be much higher when heat recuperation is used, depending on the effi- Electrochemical system for harvesting thermal energy. ciency of the heat recuperation system (Z ). We have designed HX Considering these requirements, we have selected solid CuHCF as and tested two heat recuperation schemes using dummy cells and the positive electrode for the TREC because of its negative commercial battery cells, since the current laboratory cell is too temperature coefficient (  0.36 mV K ), high specific charge small to match the heat exchanger size. The test combined with capacity (60 mAh g ) compared with redox couples in solution, thermal modelling shows that heat recuperation efficiency (Z ) HX 1  1 relatively low specific heat (1.07 JK g ), and ultra-low voltage between 45–80% can be achieved (details are shown in 19–21 hysteresis . The corresponding figure of merit Y is as high as Supplementary Note 6). In the following, we will assume 50% 0.073. For the negative electrode, a copper metal immersed in heat recuperation efficiency to discuss the cycle efficiency, which 3 M Cu(NO ) aqueous solution is selected because of the high we believe is a conservative number. With 50% heat recuperation 3 2 1 2 þ positive temperature coefficient (0.83 mV K ) of Cu/Cu and efficiency, the corresponding cycle efficiency increases to 5.7%. its large specific charge capacity (825 mAh g Cu). Although the Figure 3b shows the efficiency at various cycling conditions with corresponding Y for Cu alone is as high as 6.55, the electrolyte is T varying between 40 and 70 C and T fixed at 10 C. At a H L an active component in the full cell and its contribution to heat current density of 7.2 mA g and Z ¼ 50%, the cycle effi- HX capacity is considerable. Including the electrolytes, the ciencies are 2.9% for T ¼ 40 C, 4.8% for 50 C, 5.7% for 60 C corresponding Y are  0.031 and 0.125 for CuHCF/6 M NaNO and 5.5% for 70 C. The efficiency becomes higher as T increases 3 H 2 þ and Cu/3 M Cu , respectively. Y for the full cell reaches  0.068 because of larger voltage difference between the charging and with both electrolyte and electrode considered (see Supplementary discharging curves and faster kinetics at higher temperature. Table 1 and Supplementary Note 5). The relevant redox reactions However, this tendency changes between a T of 60 and 70 C, III þ at each electrode are Na Cu[Fe (CN) ] þ a(Na þ e ) ¼ since the Coulombic efficiency of CuHCF starts to decrease at 0.71 6 0.72 III II 2 þ Na Cu[Fe (CN) ] [Fe (CN) ] and Cu þ these temperatures. When the temperature is higher than 80 C, 0.71 þ a 6 0.72  a 6 0.72 þ a 2e ¼ Cu. The temperature coefficient of each electrode was significant decrease of Coulombic efficiency leads to rapid drop of tested by measuring the OCV while varying temperature from 10 the cycle efficiency (see Supplementary Fig. 4). When the current NATURE COMMUNICATIONS | 5:3942 | DOI: 10.1038/ncomms4942 | www.nature.com/naturecommunications 3 & 2014 Macmillan Publishers Limited. All rights reserved. –1 –1.20 mV K –1 –0.36 mV K ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/ncomms4942 0.7 CuHCF Cu Full cell Step 1 Step 2 Step 3 Step 4 60 0.7 40 0.6 Step3 0.6 60 0.5 0.5 –20 Step1 0.4 –40 0.4 –60 0.3 –80 0.3 10 20 30 40 50 60 70 02468 10 12 0 10 20 30 40 50 60 –1 Temperature (°C) Time (h) Specific capacity (mAh g ) 2 þ Figure 2 | The electrochemical system for harvesting thermal energy with CuHCF and Cu/Cu electrodes. (a) Voltage change of the CuHCF electrode, the Cu electrode and the full cell compared with the initial voltage at 10 C when the temperature varies from 10 to 70 C. The slopes of the fitting lines (grey) represent the temperature coefficients of electrodes and the full cell. (b) Voltage plot of the cell during one cycle of thermal energy harvesting when the temperature is varied between 10 and 60 C and the current density is 7.2 mA g . The temperature of each process is shown by the grey-dotted line, which is artificially superimposed for clarity. (c) A voltage plot of the cell versus the specific charge capacity of CuHCF during one cycle with the same conditions as in b. The red line represents heating (process 1) and charging (process 2) of the cell at 60 C, and the blue line represents cooling (process 3) and discharging (process 4) of the cell at 10 C. overpotential. The efficiency is much higher than previous reports Carnot limit on thermogalvanic cells (Supplementary Table 2). Long-term cycling. The cycling performance of the thermal energy-harvesting system is shown in Fig. 4a. T and T are set to H L 50 C and 20 C to represent widely accessible temperatures of waste heat and room temperature, respectively. The current 1  1 density is 17.9 mA g . The energy density reaches 1.26 J g in the initial cycle with an efficiency of 1.8%. The average efficiency is 1.7% (Z ¼ 50%). Figure 4b compares the full-cell voltage 4 HX versus specific capacity of CuHCF for the 1st and 40th cycle. A slight shift of the loop is observed, but there is no significant change in the overall shape. In addition, the cycling performance 020 40 60 80 100 of CuHCF at higher temperature is confirmed by long-term Heat recuperation efficiency (%) galvanostatic cycling of a CuHCF electrode at 70 C. At this temperature, the capacity decay is only 9.1% over 500 cycles –1 (Supplementary Fig. 5). This result signifies that this TREC for 7.2 mA g –1 thermal energy harvesting is expected to have stable cycling with 17.9 mA g further optimization. Discussion Since TE devices are major candidates for waste heat recovery, it is useful to point out the differences between TE devices and TREC. The ZT of TE materials are determined by transport properties, while the thermogalvanic figure of merit Y is determined by thermodynamic properties. TE devices can have high-power density, provided that one can manage heat flow on both hot and the cold sides to create the needed temperature 30 40 50 60 70 80 difference, while TREC has relatively low-power density. Its Temperature (°C) power density depends on applied current density and voltage Figure 3 | Efficiency of TREC. (a) Efficiency of the cell cycle versus heat gap between charging and discharging of a cycle. We have recuperation efficiency to be potentially included in the system when the estimated a power density of 1.2 mW g for cell operating temperature range is between 10 and 60 C and the current density is between 10–80 C at current density of 58.5 mA g with a 7.2 mA g . Grey-dotted line represents the theoretical Carnot efficiency. 1-hour cycling time, based on the mass of all active materials and (b) Efficiency of the cell for various high temperatures (T )from 40 to electrolytes (see Supplementary Fig. 6). Further improvement in 70 C and two current densities, 7.2 and 17.9 mA g , when the low power density can be realized by optimizing device configuration, temperature (T ) is fixed at 10 C and 50% heat recuperation efficiency is utilizing porous copper electrode, and exploring new system included in the calculation. with fast kinetics and large temperature coefficient (see Supplementary Note 7). On the other hand, due to its constant temperature operation, thermal management challenges, which density increases to 17.9 mA g for higher power output, the are crucial for low-grade waste heat utilization, can be easier, as cycle efficiencies are still as high as 1.9% for T ¼ 40 C, 3.2% for we have demonstrated in the heat recuperation testing 50 C, 5.0% for 60 C and 5.4% for 70 C despite the larger (Supplementary Figs 7–13 and Supplementary Table 3). With 4 NATURE COMMUNICATIONS | 5:3942 | DOI: 10.1038/ncomms4942 | www.nature.com/naturecommunications & 2014 Macmillan Publishers Limited. All rights reserved. –1 0.83 mV K Step4: discharging (10°C) –1 5.2 J g Step2: charging (60°C) Voltage change (mV) Cycle efficiency (%) Cycle efficiency (%) Voltage (V) Temperature (°C) Voltage (V) NATURE COMMUNICATIONS | DOI: 10.1038/ncomms4942 ARTICLE output while maintaining high efficiency of thermal energy harvesting. Our work points to the great potential of TREC for utilizing ubiquitous low-temperature heat sources. Methods Material synthesis and electrode preparation. CuHCF was synthesized by 2 0 a simple co-precipitation method. In total, 40 mM of Cu(NO ) and 20 mM of 3 2 K Fe(CN) (Sigma Aldrich) were prepared in 120 ml of distilled water, then both 3 6 solutions were simultaneously added in drops into 60 ml of deionized-water under vigorous stirring. A yellowish green precipitate formed during the precipitation. –2 Then, the solid precipitate was filtered and washed several times with deionized- water. Afterward, the precipitate was dried in vacuum oven at 40 C for 12 h. The diameter of as-formed particles is typically below 100 nm (Supplementary Fig. 14) To prepare electrodes, a mixture of 70% wt/wt CuHCF, 20% wt/wt amorphous 010 20 30 40 carbon (Timcal Super P Li) and 10% wt/wt polyvinylidene fluoride (Kynar HSV Cycles 900) was grounded by hand. 1-methyl-2-pyrrolidinone was added in the mixture to form slurry, which was spread on carbon cloth current collector (Fuel Cell Earth). The mass loading of CuCHF was between 2 and 3 mg on area of about 0.25 cm . th 0.7 50 °C/Charge 20 °C/Discharge Electrochemical characterizations. TREC is demonstrated as form of a flooded 0.6 st beaker cell as shown in Supplementary Fig. 3B. CuHCF on carbon cloth 2 2 (B0.25 cm ) is connected to working electrode. Cu foil (B4cm ) is connected to counter electrode. In total, 6 M NaNO and 3 M Cu(NO ) electrolytes are used for 3 3 2 CuHCF and Cu electrodes, respectively. These electrolytes are separated by three 0.5 anion exchange membranes (Selemion DSV, AGC engineering, LTD, Japan). Ag/AgCl in saturated KCl solution is located between the membranes as a reference electrode. Electrochemical test of the cell is performed by a potentiostat with 50 mV resolution (VM3, BioLogic). During the measurement, recording voltage was 0.4 fluctuating 0.2 mV due to noise. The temperature measurement uncertainty is estimated to be 0.2 C as we wait until equilibrium in an environment chamber (BTU-133, ESPEC North America, INC.), while the precision of the thermometer is 0.3 0.1 C.’ The overall relative uncertainty in efficiency is estimated to be less than 0 102030405060 3%, which corresponds to less than 0.2% in the absolute conversion efficiency. –1 Specific capacity (mAh g ) Figure 4 | Cycling performance of the thermally regenerative Specific heat measurement. The specific heat (c ) of the CuHCF was measured 2 þ electrochemical system with CuHCF and Cu/Cu electrodes. by differential scanning calorimetry test after drying the sample at 40B50 C for more than 24 h. The measurements were carried out by differential scanning (a) Measured energy density and corresponding efficiency when 50% heat calorimetry Q100 (TA instrument). The measurement range was 20–70 C with the recuperation efficiency is included in the calculations. The cell is cycled ramping rate of 5 Cmin . The heat flow curve is shown in Supplementary between 20 and 50 C and the current density is 17.9 mA g . The  1  1 Fig. 15. The calculated c of CuHCF is 1.07 J g K . asterisk denotes changing of the electrolyte because of drying after the 24th cycle. (b) Voltage plot of the cell versus specific charge capacity of Efficiency calculation. The thermal-to-electricity efficiency is based on experi- CuHCF during the 1st (dotted line) and 40th (solid line) cycles under mental charge/discharge curves of TREC cells. The specific heat is calculated based the same conditions as in a. The red and blue lines represent charging at on experimental measurements. More details can be found in Supplementary 50 C and discharging at 20 C, respectively. Notes 3 and 4. References such an understanding first, we can now convert the efficiency 1. Chu, S. & Majumdar, A. Opportunities and challenges for a sustainable energy achieved in TREC into familiar ZT in TE materials. The estimated future. Nature 488, 294–303 (2012). ZT is 3.5 for the efficiency of 5.7% when temperature is varied 2. Rattner, A. S. & Garimella, S. Energy harvesting, reuse and upgrade to reduce from 10 to 60 C, current density is 7.2 mA g and Z ¼ 50% is primary energy usage in the USA. Energy 36, 6172–6183 (2011). HX 3. Rosi, F. D. 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Commun. 2, 550–554 S.W.L., Y.Y., G.C. and Y.C. conceived the idea, designed experiments, analysed data and (2011). wrote the paper. S.W.L., Y.Y., H.-W.L. and H.G. carried out experiments. D.K. provided 20. Pasta, M., Wessells, C. D., Huggins, R. A. & Cui, Y. A high-rate and long cycle helpful suggestions and discussions. All the authors read the paper and made comments. life aqueous electrolyte battery for grid-scale energy storage. Nat. Commun. 3, G.C. and Y.C. directed the collaborative research. 1149–1155 (2012). 21. Wessells, C. D., Peddada, S. V., McDowell, M. T., Huggins, R. A. & Cui, Y. The effect of insertion species on nanostructured open framework hexacyanoferrate Additional information battery electrodes. J. Electrochem. Soc. 159, A98–A103 (2012). Supplementary Information accompanies this paper at http://www.nature.com/ 22. Bejan, A. & Kraus, A. D. Heat Transfer Handbook (Wiley-Interscience, 2003). naturecommunications 23. Serth, R. W. Process Heat Transfer: Principles and Applications (Academic, 2007). Competing financial interests: The authors declare no competing financial interests. Reprints and permission information is available online at http://npg.nature.com/ Acknowledgements reprintsandpermissions/ Y.C. acknowledges the support by the U.S. Department of Energy, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering under Contract No. DE-AC02- How to cite this article: Lee, S. W. et al. An electrochemical system for efficiently 76SF00515 through the SLAC National Accelerator Laboratory LDRD project. H.-W.L. harvesting low-grade heat energy. Nat. Commun. 5:3942 doi: 10.1038/ncomms4942 acknowledges the support from Basic Science Research Program through the National (2014). 6 NATURE COMMUNICATIONS | 5:3942 | DOI: 10.1038/ncomms4942 | www.nature.com/naturecommunications & 2014 Macmillan Publishers Limited. 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An electrochemical system for efficiently harvesting low-grade heat energy

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Abstract

ARTICLE Received 21 Nov 2013 | Accepted 23 Apr 2014 | Published 21 May 2014 DOI: 10.1038/ncomms4942 An electrochemical system for efficiently harvesting low-grade heat energy 1, 2, 1 2 2 2 1,3 Seok Woo Lee *, Yuan Yang *, Hyun-Wook Lee , Hadi Ghasemi , Daniel Kraemer , Gang Chen & Yi Cui Efficient and low-cost thermal energy-harvesting systems are needed to utilize the tremendous low-grade heat sources. Although thermoelectric devices are attractive, its efficiency is limited by the relatively low figure-of-merit and low-temperature differential. An alternative approach is to explore thermodynamic cycles. Thermogalvanic effect, the dependence of electrode potential on temperature, can construct such cycles. In one cycle, an electrochemical cell is charged at a temperature and then discharged at a different temperature with higher cell voltage, thereby converting heat to electricity. Here we report an 2 þ electrochemical system using a copper hexacyanoferrate cathode and a Cu/Cu anode to convert heat into electricity. The electrode materials have low polarization, high charge capacity, moderate temperature coefficients and low specific heat. These features lead to a high heat-to-electricity energy conversion efficiency of 5.7% when cycled between 10 and 60 C, opening a promising way to utilize low-grade heat. 1 2 Department of Materials Science and Engineering, Stanford University, Stanford, California 94305, USA. Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA. Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory, 2575 Sand Hill Road, Menlo Park, California 94025, USA. * These authors contributed equally to this work. Correspondence and requests for materials should be addressed to G.C. (email: [email protected]) or to Y.C. (email: [email protected]). NATURE COMMUNICATIONS | 5:3942 | DOI: 10.1038/ncomms4942 | www.nature.com/naturecommunications 1 & 2014 Macmillan Publishers Limited. All rights reserved. Step 3: cooling ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/ncomms4942 ow-grade heat sources (o100 C) are ubiquitous, generated This cycle is also plotted on a temperature–entropy (T–S) 1,2 in energy conversion and utilization processes . Among the diagram to clarify the thermodynamics (Fig. 1b). In process 1, Lmethods for converting this energy to electricity, the cell is in the discharged state and heated from T to T L H thermoelectric (TE) materials and devices have been studied (low to high temperature) at open circuit. Since CuHCF 3–9 2 þ extensively for several decades . Despite recent progress, has a negative a and Cu/Cu has a positive a, the OCV of the however, the figure of merit (ZT) of thermoelectrics is limited full cell decreases during this process. The cell is then charged 10,11 to 2 at high temperatures and 1.5 below 100 C . Seebeck at a low voltage at T in process 2, and the entropy of the effect in electrochemical system is also investigated for thermal cell increases through heat absorption during the electrochemical energy harvesting in similar architectures as a TE device, but the reaction. In process 3, the cell is disconnected and cooled efficiency achieved is usually lower than 0.5% below 100 C since from T to T , and thus the OCV increases. In the final process, H L the thermopower is limited by poor ionic conductivity of the cell is discharged at a higher voltage at T , and the entropy electrolyte, which is more than three orders of magnitude of the cell decreases through the ejection of heat into the smaller than the electronic conductivity in state-of-the-art TE environment. After the cycle, the system returns to the 12–15 materials . An alternative approach of electrochemical system original discharged state at T . Since the charging voltage is lower for thermal energy harvesting is to explore thermo- than the discharging voltage, net work (W) is extracted as the dynamic cycle as in thermomechanical engines. Here we report difference between charging and discharging energy. This is the an efficient thermally regenerative electrochemical cycle (TREC) opposite of the consumption of energy due to electrochemical based on the thermogalvanic effect, temperature dependence hysteresis during a typical charge/discharge cycle of a battery, of electrode potential. For a half-cell reaction, A þne -B, the since the charging energy here is partially provided by heat temperature coefficient is defined as (Supplementary Fig. 1). Such a conversion process of thermal energy into electrochemical energy requires that the electro- @V DS A;B a ¼ ¼ ð1Þ chemical voltage hysteresis during charge/discharge at a fixed @T nF temperature is much smaller than the voltage difference caused where V is the electrode potential, T is temperature, n is the by temperature change, calling for the highly reversible electro- number of electrons transferred in the reaction, F is Faraday’s chemical electrodes. constant and DS is the partial molar entropy change for the A,B half-cell reaction in isothermal condition (see Supplementary Note 1). This effect indicates that the voltage of a battery depends on temperature; thus a thermodynamic cycle can be constructed by discharging the battery at T and charging back at T .If 1 2 (−) (+) the charging voltage at T is lower than the discharging voltage at Step 2 T , net energy is produced by the voltage difference, originating >0 <0 charging from heat absorbed at the higher temperature, similar to a thermomechanical engine with the Carnot efficiency as the upper limit. In practice, instead of transport property limited in TE devices, the efficiency of TREC is limited by the heat capacity of materials and effectiveness of heat exchangers . The concept of TREC was developed a few decades ago for high-temperature Step 4 applications (500–1,500 C) and showed efficiency of 40–50% of the Carnot limit. But, low-temperature TREC did not received as discharging much attention since electrode materials with low polarization and high charge capacity at low temperature were limited . Hammond and William tested an aqueous redox couple for low-temperature solar-thermal applications, but the precipitation of reactants, large internal resistance and poor solubility of active Step 2: charging redox species causing large heat capacity of the system prevented them from reporting device operational characteristics and ΔG =ΔH –T ΔS measuring the device efficiency, although a high efficiency was H H H H theoretically projected based on the measured open-circuit voltage OCV and 100% heat recuperation assumption. The W =|ΔG –ΔG | recent development of highly reversible electrode materials with H L very low polarization loss during the research of rechargeable batteries has now made it possible for us to exploit the TREC ΔG =ΔH –T ΔS concept in a new way. L L L L Here we present a high-efficiency TREC for harvesting low- Step 4: discharging grade heat energy by employing solid copper hexacyanoferrate 2 þ (CuHCF) as a positive electrode and Cu/Cu as a negative electrode in an aqueous electrolyte. The fast kinetics, high charge Entropy, S capacity, high-temperature coefficient (a) and low heat capacity of these materials allow the system to operate with excellent Figure 1 | Working principle of TREC for thermal energy harvesting. efficiency. (a) Schematic view of thermal cycling: process 1, heating up the cell; process 2, charging at high temperature; process 3, cooling down the cell; Results process 4, discharging at low temperature. (b) Temperature–entropy Working principle of TREC. To harvest thermal energy, the (T–S) diagram of thermal cycling assuming a temperature range between entire device undergoes a thermal cycle containing four processes: T and T . The theoretical energy gained over one cycle is the area L H heating up, charging, cooling down and discharging (Fig. 1a). of the loop determined by the temperature difference and entropy change. 2 NATURE COMMUNICATIONS | 5:3942 | DOI: 10.1038/ncomms4942 | www.nature.com/naturecommunications & 2014 Macmillan Publishers Limited. All rights reserved. Step 1: heating Step 3: cooling Temperature, T Step 1: heating NATURE COMMUNICATIONS | DOI: 10.1038/ncomms4942 ARTICLE The efficiency of the system (Z) is calculated as the net work to 70 C. Figure 2a shows the OCV change of the CuHCF 2 þ (W) divided by the thermal energy input. If the enthalpy change electrode (50% state of charge), the Cu/Cu (3 M) electrode and DH and the entropy change DS are the same at T and T , which the full cell for each 10-C increment when the voltage is set at 0 V H L is a good approximation when DT ¼ (T  T ) is small, the at 10 C. The potentials of both electrodes exhibit a linear H L maximum W is DTDS (Fig. 1b). The energy input to complete the dependence on temperature, indicating a constant a in the cycle includes two parts: the heat absorbed at T (Q ¼ T DS) temperature window tested. The measured temperature H H H 2 þ and the external heat required to raise the temperature of the coefficients of CuHCF, Cu/Cu and the full cell are  0.36, system (Q ). As part of heat rejected from the cooling process 0.83 and  1.20 mV K , respectively. These experimental values HX can be used for the heating process through heat recuperation, match with the expected ones. Figure 2b shows the voltage versus Q can be expressed as Q ¼ (1  Z )C DT, where C is the time plot of the full cell over one thermal cycle between 10 and HX HX HX p p total heat capacity of the electrochemical cell and Z is the 60 C when the specific current density is 7.2 mA g with respect HX efficiency of the heat recuperation (See Supplementary Fig. 2 and to active materials (All current, energy and power densities are Supplementary Note 2). Consequently Z can be expressed as: based on the mass of active materials, including CuHCF, þ 2 þ electrolyte for Na , copper and water for Cu in this paper.). W DTDS  E loss In process 1, the OVC of the cell decreases from 0.406 to 0.337 V Z ¼ ¼ ð2Þ Q þ Q T DSþð1  Z ÞC DT H HX H p HX as the temperature increases from 10 to 60 C. Then the cell is charged for 250 min at 60 C in process 2 and the voltage where E is the energy loss due to the cell electrical resistance. loss gradually increases. In process 3, the OCV of the cell increases Note that DTDS ¼ aQ DT, where Q is the charge capacity of the c c from 0.613 to 0.679 V as the temperature decreases back to 10 C. battery and a is the temperature coefficient of the electrochemical The cell is discharged in process 4 at 10 C until the voltage cell. The efficiency can be written as reaches the initial voltage of the discharged state at the beginning 1  IðR þ R Þ=jj a DT of process 1. The corresponding plot of voltage against specific H L Z ¼ Z ð3Þ charge capacity based on the mass of CuHCF is shown in Fig. 2c. 1 þ Z ð1  Z Þ=jj Y c HX The average charging voltage is 59.0 mV lower than the average- where I is the current used in discharging and charging. R and H discharging voltage and thus electrical energy is generated with a R are the internal resistance at T and T , respectively. Y ¼ aQ / L H L c net energy density of 5.2 J g . The voltage spikes at the beginning C , is a dimensionless parameter to describe the requirements of p of each process are electrochemical in nature and are due to the system for high efficiency. A thorough derivation of efficiency overpotential and internal resistance. At the end of process 4, is presented in Supplementary Notes 3 and 4. If only the the discharging curve forms nearly perfect closed loop with contributions of the electrode materials are considered, and it is only tiny loss of electric charges. The Coulombic efficiency assumed that both electrodes have the same properties except (ratio of the amount of charge extracted during discharging to opposite signs of the temperature coefficient, Y ¼ aq /c and it is c p that of adding in during charging) for this cycle is adequately defined as the figure of merit of an electrode material for high B98.6%. TREC, but not thermocells. Here, q is the specific charge capacity and c is the specific heat of an electrode. Consequently, it is clear that a higher temperature coefficient (a), a higher specific Efficiency of TREC. The efficiency of the cycle is estimated based charge capacity (q ) and a smaller specific heat (c ) lead to higher c p on equation (2). Effects of internal resistance and Coulombic efficiency for heat-to-electricity conversion. In addition, low- efficiency are both taken into account. Details of calculations are voltage polarization and effective heat recuperation can shown in Supplementary Note 4 and Supplementary Fig. 3. also improve the efficiency. The value of Y for individual Figure 3a plots the cycle efficiency versus the efficiency of heat materials can be negative or positive, depending on the sign of the recuperation when cycled between 10 and 60 C. The current temperature coefficient, although efficiency expression takes its density is 7.2 mA g . When heat recuperation is not used, the absolute value. cycle efficiency is 3.7%. The final system efficiency could be much higher when heat recuperation is used, depending on the effi- Electrochemical system for harvesting thermal energy. ciency of the heat recuperation system (Z ). We have designed HX Considering these requirements, we have selected solid CuHCF as and tested two heat recuperation schemes using dummy cells and the positive electrode for the TREC because of its negative commercial battery cells, since the current laboratory cell is too temperature coefficient (  0.36 mV K ), high specific charge small to match the heat exchanger size. The test combined with capacity (60 mAh g ) compared with redox couples in solution, thermal modelling shows that heat recuperation efficiency (Z ) HX 1  1 relatively low specific heat (1.07 JK g ), and ultra-low voltage between 45–80% can be achieved (details are shown in 19–21 hysteresis . The corresponding figure of merit Y is as high as Supplementary Note 6). In the following, we will assume 50% 0.073. For the negative electrode, a copper metal immersed in heat recuperation efficiency to discuss the cycle efficiency, which 3 M Cu(NO ) aqueous solution is selected because of the high we believe is a conservative number. With 50% heat recuperation 3 2 1 2 þ positive temperature coefficient (0.83 mV K ) of Cu/Cu and efficiency, the corresponding cycle efficiency increases to 5.7%. its large specific charge capacity (825 mAh g Cu). Although the Figure 3b shows the efficiency at various cycling conditions with corresponding Y for Cu alone is as high as 6.55, the electrolyte is T varying between 40 and 70 C and T fixed at 10 C. At a H L an active component in the full cell and its contribution to heat current density of 7.2 mA g and Z ¼ 50%, the cycle effi- HX capacity is considerable. Including the electrolytes, the ciencies are 2.9% for T ¼ 40 C, 4.8% for 50 C, 5.7% for 60 C corresponding Y are  0.031 and 0.125 for CuHCF/6 M NaNO and 5.5% for 70 C. The efficiency becomes higher as T increases 3 H 2 þ and Cu/3 M Cu , respectively. Y for the full cell reaches  0.068 because of larger voltage difference between the charging and with both electrolyte and electrode considered (see Supplementary discharging curves and faster kinetics at higher temperature. Table 1 and Supplementary Note 5). The relevant redox reactions However, this tendency changes between a T of 60 and 70 C, III þ at each electrode are Na Cu[Fe (CN) ] þ a(Na þ e ) ¼ since the Coulombic efficiency of CuHCF starts to decrease at 0.71 6 0.72 III II 2 þ Na Cu[Fe (CN) ] [Fe (CN) ] and Cu þ these temperatures. When the temperature is higher than 80 C, 0.71 þ a 6 0.72  a 6 0.72 þ a 2e ¼ Cu. The temperature coefficient of each electrode was significant decrease of Coulombic efficiency leads to rapid drop of tested by measuring the OCV while varying temperature from 10 the cycle efficiency (see Supplementary Fig. 4). When the current NATURE COMMUNICATIONS | 5:3942 | DOI: 10.1038/ncomms4942 | www.nature.com/naturecommunications 3 & 2014 Macmillan Publishers Limited. All rights reserved. –1 –1.20 mV K –1 –0.36 mV K ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/ncomms4942 0.7 CuHCF Cu Full cell Step 1 Step 2 Step 3 Step 4 60 0.7 40 0.6 Step3 0.6 60 0.5 0.5 –20 Step1 0.4 –40 0.4 –60 0.3 –80 0.3 10 20 30 40 50 60 70 02468 10 12 0 10 20 30 40 50 60 –1 Temperature (°C) Time (h) Specific capacity (mAh g ) 2 þ Figure 2 | The electrochemical system for harvesting thermal energy with CuHCF and Cu/Cu electrodes. (a) Voltage change of the CuHCF electrode, the Cu electrode and the full cell compared with the initial voltage at 10 C when the temperature varies from 10 to 70 C. The slopes of the fitting lines (grey) represent the temperature coefficients of electrodes and the full cell. (b) Voltage plot of the cell during one cycle of thermal energy harvesting when the temperature is varied between 10 and 60 C and the current density is 7.2 mA g . The temperature of each process is shown by the grey-dotted line, which is artificially superimposed for clarity. (c) A voltage plot of the cell versus the specific charge capacity of CuHCF during one cycle with the same conditions as in b. The red line represents heating (process 1) and charging (process 2) of the cell at 60 C, and the blue line represents cooling (process 3) and discharging (process 4) of the cell at 10 C. overpotential. The efficiency is much higher than previous reports Carnot limit on thermogalvanic cells (Supplementary Table 2). Long-term cycling. The cycling performance of the thermal energy-harvesting system is shown in Fig. 4a. T and T are set to H L 50 C and 20 C to represent widely accessible temperatures of waste heat and room temperature, respectively. The current 1  1 density is 17.9 mA g . The energy density reaches 1.26 J g in the initial cycle with an efficiency of 1.8%. The average efficiency is 1.7% (Z ¼ 50%). Figure 4b compares the full-cell voltage 4 HX versus specific capacity of CuHCF for the 1st and 40th cycle. A slight shift of the loop is observed, but there is no significant change in the overall shape. In addition, the cycling performance 020 40 60 80 100 of CuHCF at higher temperature is confirmed by long-term Heat recuperation efficiency (%) galvanostatic cycling of a CuHCF electrode at 70 C. At this temperature, the capacity decay is only 9.1% over 500 cycles –1 (Supplementary Fig. 5). This result signifies that this TREC for 7.2 mA g –1 thermal energy harvesting is expected to have stable cycling with 17.9 mA g further optimization. Discussion Since TE devices are major candidates for waste heat recovery, it is useful to point out the differences between TE devices and TREC. The ZT of TE materials are determined by transport properties, while the thermogalvanic figure of merit Y is determined by thermodynamic properties. TE devices can have high-power density, provided that one can manage heat flow on both hot and the cold sides to create the needed temperature 30 40 50 60 70 80 difference, while TREC has relatively low-power density. Its Temperature (°C) power density depends on applied current density and voltage Figure 3 | Efficiency of TREC. (a) Efficiency of the cell cycle versus heat gap between charging and discharging of a cycle. We have recuperation efficiency to be potentially included in the system when the estimated a power density of 1.2 mW g for cell operating temperature range is between 10 and 60 C and the current density is between 10–80 C at current density of 58.5 mA g with a 7.2 mA g . Grey-dotted line represents the theoretical Carnot efficiency. 1-hour cycling time, based on the mass of all active materials and (b) Efficiency of the cell for various high temperatures (T )from 40 to electrolytes (see Supplementary Fig. 6). Further improvement in 70 C and two current densities, 7.2 and 17.9 mA g , when the low power density can be realized by optimizing device configuration, temperature (T ) is fixed at 10 C and 50% heat recuperation efficiency is utilizing porous copper electrode, and exploring new system included in the calculation. with fast kinetics and large temperature coefficient (see Supplementary Note 7). On the other hand, due to its constant temperature operation, thermal management challenges, which density increases to 17.9 mA g for higher power output, the are crucial for low-grade waste heat utilization, can be easier, as cycle efficiencies are still as high as 1.9% for T ¼ 40 C, 3.2% for we have demonstrated in the heat recuperation testing 50 C, 5.0% for 60 C and 5.4% for 70 C despite the larger (Supplementary Figs 7–13 and Supplementary Table 3). With 4 NATURE COMMUNICATIONS | 5:3942 | DOI: 10.1038/ncomms4942 | www.nature.com/naturecommunications & 2014 Macmillan Publishers Limited. All rights reserved. –1 0.83 mV K Step4: discharging (10°C) –1 5.2 J g Step2: charging (60°C) Voltage change (mV) Cycle efficiency (%) Cycle efficiency (%) Voltage (V) Temperature (°C) Voltage (V) NATURE COMMUNICATIONS | DOI: 10.1038/ncomms4942 ARTICLE output while maintaining high efficiency of thermal energy harvesting. Our work points to the great potential of TREC for utilizing ubiquitous low-temperature heat sources. Methods Material synthesis and electrode preparation. CuHCF was synthesized by 2 0 a simple co-precipitation method. In total, 40 mM of Cu(NO ) and 20 mM of 3 2 K Fe(CN) (Sigma Aldrich) were prepared in 120 ml of distilled water, then both 3 6 solutions were simultaneously added in drops into 60 ml of deionized-water under vigorous stirring. A yellowish green precipitate formed during the precipitation. –2 Then, the solid precipitate was filtered and washed several times with deionized- water. Afterward, the precipitate was dried in vacuum oven at 40 C for 12 h. The diameter of as-formed particles is typically below 100 nm (Supplementary Fig. 14) To prepare electrodes, a mixture of 70% wt/wt CuHCF, 20% wt/wt amorphous 010 20 30 40 carbon (Timcal Super P Li) and 10% wt/wt polyvinylidene fluoride (Kynar HSV Cycles 900) was grounded by hand. 1-methyl-2-pyrrolidinone was added in the mixture to form slurry, which was spread on carbon cloth current collector (Fuel Cell Earth). The mass loading of CuCHF was between 2 and 3 mg on area of about 0.25 cm . th 0.7 50 °C/Charge 20 °C/Discharge Electrochemical characterizations. TREC is demonstrated as form of a flooded 0.6 st beaker cell as shown in Supplementary Fig. 3B. CuHCF on carbon cloth 2 2 (B0.25 cm ) is connected to working electrode. Cu foil (B4cm ) is connected to counter electrode. In total, 6 M NaNO and 3 M Cu(NO ) electrolytes are used for 3 3 2 CuHCF and Cu electrodes, respectively. These electrolytes are separated by three 0.5 anion exchange membranes (Selemion DSV, AGC engineering, LTD, Japan). Ag/AgCl in saturated KCl solution is located between the membranes as a reference electrode. Electrochemical test of the cell is performed by a potentiostat with 50 mV resolution (VM3, BioLogic). During the measurement, recording voltage was 0.4 fluctuating 0.2 mV due to noise. The temperature measurement uncertainty is estimated to be 0.2 C as we wait until equilibrium in an environment chamber (BTU-133, ESPEC North America, INC.), while the precision of the thermometer is 0.3 0.1 C.’ The overall relative uncertainty in efficiency is estimated to be less than 0 102030405060 3%, which corresponds to less than 0.2% in the absolute conversion efficiency. –1 Specific capacity (mAh g ) Figure 4 | Cycling performance of the thermally regenerative Specific heat measurement. The specific heat (c ) of the CuHCF was measured 2 þ electrochemical system with CuHCF and Cu/Cu electrodes. by differential scanning calorimetry test after drying the sample at 40B50 C for more than 24 h. The measurements were carried out by differential scanning (a) Measured energy density and corresponding efficiency when 50% heat calorimetry Q100 (TA instrument). The measurement range was 20–70 C with the recuperation efficiency is included in the calculations. The cell is cycled ramping rate of 5 Cmin . The heat flow curve is shown in Supplementary between 20 and 50 C and the current density is 17.9 mA g . The  1  1 Fig. 15. The calculated c of CuHCF is 1.07 J g K . asterisk denotes changing of the electrolyte because of drying after the 24th cycle. (b) Voltage plot of the cell versus specific charge capacity of Efficiency calculation. The thermal-to-electricity efficiency is based on experi- CuHCF during the 1st (dotted line) and 40th (solid line) cycles under mental charge/discharge curves of TREC cells. The specific heat is calculated based the same conditions as in a. The red and blue lines represent charging at on experimental measurements. More details can be found in Supplementary 50 C and discharging at 20 C, respectively. Notes 3 and 4. References such an understanding first, we can now convert the efficiency 1. Chu, S. & Majumdar, A. Opportunities and challenges for a sustainable energy achieved in TREC into familiar ZT in TE materials. The estimated future. Nature 488, 294–303 (2012). ZT is 3.5 for the efficiency of 5.7% when temperature is varied 2. Rattner, A. S. & Garimella, S. Energy harvesting, reuse and upgrade to reduce from 10 to 60 C, current density is 7.2 mA g and Z ¼ 50% is primary energy usage in the USA. Energy 36, 6172–6183 (2011). HX 3. Rosi, F. D. 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Process Heat Transfer: Principles and Applications (Academic, 2007). Competing financial interests: The authors declare no competing financial interests. Reprints and permission information is available online at http://npg.nature.com/ Acknowledgements reprintsandpermissions/ Y.C. acknowledges the support by the U.S. Department of Energy, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering under Contract No. DE-AC02- How to cite this article: Lee, S. W. et al. An electrochemical system for efficiently 76SF00515 through the SLAC National Accelerator Laboratory LDRD project. H.-W.L. harvesting low-grade heat energy. Nat. Commun. 5:3942 doi: 10.1038/ncomms4942 acknowledges the support from Basic Science Research Program through the National (2014). 6 NATURE COMMUNICATIONS | 5:3942 | DOI: 10.1038/ncomms4942 | www.nature.com/naturecommunications & 2014 Macmillan Publishers Limited. All rights reserved.

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Published: May 21, 2014

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