Introduction

A new thermoelectric technology, that converts waste heat near room temperature and/or human body heat to electric energy at low cost and high efficiency, is required for a “smart” society. A semiconductor-based thermoelectric device, that uses the so-called Seebeck effect, is a promising technology and is.applied for practical use in Peltier cooling and thermal power generation in space vehicles1. However, the current devices must be bulky and heavy to convert the temperature difference between the electrodes into a sufficient voltage, which is an inevitable disadvantage of the device.

Recently, several researchers2,3,4,5 reported that a thermocell that uses the difference in the thermal coefficient (α = dV/dT) of the redox potential (V) between the anode (αanode) and cathode (αcathode) materials can convert the cell temperature (Tcell) into the electric energy. The thermocell can produce electric energy in the thermal cycle between low (TL) and high (TH) temperatures, making in share contract with the semiconductor-based thermoelectric device. Figure 1 shows a schematic of stages of the thermocell thermal cycle: (a) warming from TL to TH, (b) discharge at TH, (c) cooling from TH to TL, and (d) discharge at TL. In the (a) warming process, the redox potentials of the anode and cathode change by αanode and αathode, respectively. We expect a thermally induced change in Vcell as large as ΔT(αcathode − αanode). In other words, electric energy is thermally stored in the thermocell. Some amount of the stored electric energy can be extracted by the (b) discharge process at TH. During the (b) cooling process, the redox potentials of the anode and cathode change by −αanode ΔT and −αcathode ΔT, respectively. The stored electric energy can be extracted by the (d) discharge process at TL. Lee et al.2 fabricated a thermocell with an anode and cathode made of [Fe(CN)6]3+/[Fe(CN)6]4+ 6 and a Prussian blue analogue (PBA) solid and succeeded in extracting electric energy. Yang et al.3. fabricated a thermocell with an anode and cathode made of Cu+/Cu2+ 6 and a PBA solid and succeeded in extracting electric energy. Shibata et al.5 fabricated a thermocell, consisting of two types of PBA solids with different α values. The thermocell produces electric energy with high thermal efficiency (η = 1%) between TH (=295 K) and TH (=323 K). This type of thermocell extends the application range of the battery materials from energy storage to energy conversion.

Figure 1
figure 1

Schematic illustration of thermal cycle vs. voltage (Vcell) and temperature (Tcell) of the thermocell. The cycle consists of four processes. (a) Heating from TL to TH, (b) discharge at TH, (c) cooling from TH to TL, and (d) discharge at TL. Processes (a) and (c) are performed in the open circuit condition. QH and QL are the inflow and outflow of heat, respectively, and WH and WL are the electric works at TH and TL, respectively.

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PBAs with chemical formulae are of LixM[Fe(CN)6]y and NaxM[Fe(CN)6]y (M = transition metal) are promising candidates for cathode materials in lithium-ion and sodium-ion secondary batteries7,8,9,10,11,12,13,14,15,16. Most of the PBA materials have face-centrered cubic (fcc) (Fm \(\bar{3}\) m; Z = 4) or trigonal (R \(\bar{3}\) m; Z = 3) structures17, consisting of a three-dimensional (3D) jungle-gym-type host framework with guest Li+/Na+ ions and H2O molecules, which are accommodated in the nanopores of the framework. The framework contains considerable [Fe(CN)6] vacancies (10–30%). The discharge curves of Co- and Mn-PBAs show characteristic plateaus, the redox reaction of which are well assigned using X-ray absorption spectroscopy18,19. PBAs are also promising materials for thermocells because the magnitude and sign of α can be controlled by the chemical composition20. The α values of NaxCo[Fe(CN)6]0.92,9H2O (NCF90) in the lower-lying plateau and the value of NaxCo[Fe(CN)6]0.713.6H2O (NCF71) are ~1.3 and ~0.7 mV/K, respectively. Interestingly, the α of NaxMn[Fe(CN)6]0.83 3.5H2O (NMF83) in the lower-lying plateau is negative (approximately − 0.3 mV/K).

In our previous work5, we demonstrated that the NCF71/NCF90 thermocell can convert temperature into electric energy with 1% thermal efficiency between TL = 295 K and TH = 323 K. In this work, we systematically investigated the thermal efficiency (η) of the NMF83/NCF90 thermocell against the temperature difference (ΔT) between TL and TH. The η of the NMF83/NCF90 thermocell is expected to be higher than that of the NCF71/NCF90 thermocell because Δα (=αcathode − αanode ~ 1.7 mV/K) is much larger in the former cell. We found that η increases in proportion to ΔT and reaches 3.19% at ΔT = 56 K. The linear increase in η is ascribed to the linear increase in the cell voltage (Vcell) and charge (QNCF90) extracted from NCF90. We further confirmed that the magnitude of QNCF90 is quantitatively reproduced by the slopes of the discharge curves in NMF83 and NCF90.

Discharge curve of a half–cell

Figure 2 shows the discharge curves of the (a) NMF83 and (b) NCF90 films. The curve of NMF83 [(a)] shows two plateaus (plateaus I and II) near 1.1 and 0.6 V vs. Ag/AgCl. Plateau I (<20 mAh/g) near 1.1 V is ascribed to the reaction19: Mn3+0.49Mn2+0.51[Fe3+(CN)6]0.83 + 0.49Na+ + 0.49 e− → Na0.49Mn2+[Fe3+(CN)6]0.83. Plateau II (>20 mAh/g) near 0.6 V is ascribed to the reaction: Na0.49Mn2+[Fe3+(CN)6]0.83 + 0.83Na+ + 0.83 e− → Na1.32Mn2+[Fe2+(CN)6]0.83. In the discharge process, Na+ ions are inserted into the framework, which causes reduction of Mn3+/Fe3+ to maintain the charge neutrality. The curve of NCF90 [(b)] shows two plateaus (plateaus III and VI) near 1.0 and 0.5 V vs. Ag/AgCl. Plateau III (<50 mAh/g) near 1.0 V is ascribed to the reaction:18 Co3+[Fe3+(CN)6]0.6[Fe2+(CN)6]0.3 + 0.6Na+ + 0.6 e− → Na0.6Co3+[Fe2+(CN)6]0.9. Plateau VI (>50 mAh/g) near 0.5 V is ascribed to the reaction: Na0.6Co3+[Fe2+(CN)6]0.9 + Na+ + e− → Na1.6Co2+[Fe2+(CN)6]0.9.

Figure 2
figure 2

Discharge curves of (a) NaxMn[Fe(CN)6]0.83 3.5H2O (NMF83) and (b) NaxCo[Fe(CN)6]0.92.9H2O (NCF90) films measured at 0.5 C. For convenience of explanation, we defined plateaus I, II, III, and IV.

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The difference (Δα = αcathode − αanode) in α is a crucial parameter for a thermocell, because Vcell increases in proportion to Δα. Fukuzumi et al.20 systematically investigated the α values of prototypical PBAs against the Na concentration (x). In NMF83, α gradually decreases from 1.4 to − 0.4 mV/K with increasing in x. At plateau II, α becomes negative (approxmately −0.3 mV/K). In NCF90, α is ~0.4 mV/K and ~1.3 mV/K in plateau III and IV, respectively. Therefore, we can maximize Δα if we chose NMF83 (plateau IV) and NCF90 (plateau II) as the anode and cathode, respectively. As discussed later, the slope of the plateau is another crucial parameter. In this work, we define the discharge curves of NMF83 [Fig. 1(a)] and NCF90 [Fig. 1(b)] as VNMF83(Q) and VNCF90(Q), respectively. The slopes, i.e., dVNMF83/dQ and dVNCF90/dQ, are roughly evaluated as −3.5 and −0.5 mV/(mAh/g) at plateaus II and IV, respectively.

Thermal Cycle Measurement of Thermocell

We fabricated a two-pole beaker-type thermocell; for this thermocell, the anode, cathode and electrolyte are an as-grown NMF83 film, pre-oxidized NCF90 film, and an aqueous solutions containing 17 mol/kg NaClO4, respectively. The as-prepared thermocell was slowly cooled down to TL (=282 K). At TL, the thermocell shows a finite Vcell (~0.1 V), which was discharged to 0 V under the constant current condition. If Tcell is slowly increased by ΔT(=TH − TL) in the open circuit condition, the redox potentials of the anode and cathode change by αanodeΔT and αcathodeΔT, respectively, in the warming process. We expect a thermally induced change in Vcell as larger as ΔT(αcathode − αanode). In other words, the electric energy is thermally stored in the thermocell. The amount of stored electric energy can be evaluated by the discharge process to 0 V under a constant current condition. The sweep area on the voltage-charge diagram corresponds to the stored electric energy. The behaviour of Vcell in the cooling process is opposite to that in the warming process. In this cooling process, the redox potentials of the anode and cathode change by −αanodeΔT and −αcathodeΔT, respectively. We expect a thermally induced change in Vcell as larger as −ΔT(αcathode − αanode). The stored electric energy can be extracted by the discharge process to 0 V under constant current condition. Therefore, our thermocell can convert temperature to electric energy in the thermal cycle between TL and TH.

Figure 3 shows a prototypical example of the thermal cycle of the NMF83/NCF90 thermocell at ΔT = 40 K. Black and red colours represent the data obtained in the first and second cycles, respectively. In the (a) warming process, Vcell linearly increases with the increase in Tcell at a rate of 1.2 mV/K. The rate is comparable to Δα (~1.6 mV/K). At TH, the cell shows a finite voltage (Vcell = 40 mV), i.e., the cell is thermally-charged. In the (b) discharge process at TH, Vcell linearly decreases with the extracted charge. The final extracted charge (QNCF90) from NCF90 is11.3 mAh/g, which is 10.8% of the discharge curve of NCF90 [Fig., 1(b)]. The electric work (WH = 3.29 meV/NCF90) at TH is roughly evaluated by qVcell/2, where q is the final extracted charge per NCF90. In the (c) cooling process, Vcell linearly decreases with the decrease in Tcell at a rate of 1.3 mV/K. At TL, the cell shows a finite voltage (Vcell = −44 mV). In the (d) discharge process, QNCF90 was 8.4 mAh/g. The electric work (WL) at TL is 2.82 meV/NCF90. The data in the second cycle are highly similar to those in the first cycle.

Figure 3
figure 3

Temperature (Tcell) and voltage (Vcell) of the NCF83/NCF90 thermocell in the respective processes of the thermal cycle at ΔT = 40 K. (a) Warming process from TL (=282 K) to TH (=322 K) in the open circuit condition, (b) discharge process at TH at constant current (I = 1.1 μA), (c) cooling process from TH to TL in the open circuit condition, and (d) discharge process at TL at constant current (I = −1.1 μA). Black and red colours represent the data obtained in the first and second cycles, respectively.

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Figure 4 shows another example of the thermal cycle at ΔT = 56 K. In the (a) warming process, Vcell linearly increases with the increase in Tcell at a rate of 1.1 mV/K. At TH (=338 K), the cell shows a finite voltage (Vcell = 60 mV). In the (b) discharge process at TH, Vcell linearly decreases with the extracted charge, where QNCF90 is 28.0 mAh/g, which is 26.7% of the discharge curve of NCF90 [Fig. 1(b)], and WH is 12.80 meV/NCF90. In the (c) cooling process, Vcell linearly decreases with the decrease in Tcell at a rate of 1.2 mV/K. At TL (=282 K), the cell shows a finite voltage (Vcell = −65 mV). In the (d) discharge process, QNCF90 is 20.0 mAh/g and WL is 9.70 meV/NCF90. Figure S1 shows the discharge curves at TH and TL against ΔT.

Figure 4
figure 4

Thermal cycle (ΔT = 56 K) of the NCF83/NCF90 thermocell: (a) Warming process from TL (=282 K) to TH (=338 K) in the open circuit condition, (b) discharge process at TH at constant current (I = 0.6 μA), (c) cooling process from TH to TL in the open circuit condition, and (d) discharge process at TL at constant current (I = −0.6 μA).

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Thermal Efficiency Against ΔT

The thermal efficiency (η) is defined by WH + WL/QH, where QH is the inflow of heat. Table 1 shows WH, WL, QH, and η against ΔT. Furthermore, WH (WL) was roughly evaluated as qVcell/2 at TH (TL), where q is the final extracted charge per NCF90 in the discharge process at TH (TL) and QH was evaluated as (Canode + Ccathode)ΔT, where Canode (Ccathode) is the heat capacity of anode (cathode) material. We neglected the heat capacity of the electrolyte because the amount of electrolyte is minimized in the current thermocell made of redox-capable solids. Using the specific heat (=4.16 meV/K per formula unit) of the ideal Na2Co[Fe(CN)6] in the Dulong-Petit law, QH is expressed as 4.16(1 + n)ΔT per NCF90, where n [=nNMF83/nNCF90. where nNMF83 (nNCF90) is the number of the the NMF83 (NCF90) units] is the molar ratio. Additionally, WH, WL, QH, and η monotonously increases with ΔT, and η reaches 3.19% at ΔT = 56 K, which corresponds to19% of the Carnot efficiency (ηcarnot = 17.0%).

Table 1 Parameters and performance of the NMF83/NCF90 thermocell.
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Comparison with Previous Works

In Table 2, we compare the cell parameters and η in the current thermocell with those in previously reported thermocells. In the thermocells reported in ref.2 and ref.3, ehe electrolyte is different between the anode and cathode and is separated by a membrane. However, the thermocells made of two types of PBA solids (ref.5 and this work) use the same electrolyte in the anode and cathode. As discussed in the following section, η increases linearly with ΔT. We should compare η/ΔT, rather than η, among the thermocells, and the η/ΔT values of the thermocells made of PBA solids are comparable to those of the thermocells reported in ref.2 and ref.3.

Table 2 Comparison of the parameters and thermal efficiency (η) of the thermocell.
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In the thermocells made of PBA solids, η/ΔT (=0.07%/K) in the NMF83/NCF90 thermocell is much higher than that (=0.04%/K) in the NCF71/NCF90 thermocell. The enhancement of η/ΔT is ascribed to the larger Δα in the NMF83/NCF90 thermocell. Specifically, Δα is ~ 1.6 and 0.53 mV/K for the NMF83/NCF90 and NCF71/NCF90 thermocell, respectively.

Discussion

We turn the discussion to the ΔT dependence of Vcell, QNCF90, and η. Figure 5(a) shows the ΔT dependence of Vcell. The open and closed circles represent the data at TH and TL, respectively, and Vcell increases linearly with ΔT, as indicated by the solid line. The coefficient (=1.15 mV/K) is comparable to αNCF90 − αNMF83 (~ 1.6 mV/K). Thus, we experimentally confirm the relationship of Vcell = ΔT(αNCF90 − αNMF83).

Figure 5
figure 5

ΔT dependence of the (a) cell voltage (Vcell), (b) final extracted charge (QNCF90) from NCF90, and (c) thermal efficiency (η). The open and closed circles in (a) and (b) represent the data at TH and TL, respectively. The solid lines in (a) and (c) indicate the results of least-squares fitting. The crosses in (b) are values calculated from the discharge curves of NMF83 and NCF90.

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Figure 5(b) shows the ΔT dependence of QNCF90. The open and closed circles represent the data at TH and TL, respectively. We quantitatively evaluate QNCF90 at TH from the discharge curves, VNMF83(Q) and VNMF83(Q), of NMF83 and NCF90. By applying the Tayloer expansion, Vcell at TH is expressed as Q NCF90dVNCF90/dQ + (−QNNF83dVNMF83/dQ), where Q NCF90 (QNMF83) is the final extracted charges from NCF90 (NMF83). The first and second terms are negative, because dVNCF90/dQ < 0, dVNMF83/dQ < 0, and QNMF83 < 0. The charge neutrality between the anode and cathode imposes a constraint condition of mNMF83QNMF83 = −mNCF90QNCF90, where mNMF83 (mNCF90) is the mass of NMF83 (NCF90). We obtaine QNCF90 = −Vcell/(dVNCF90/dQ + m−1dVNMF83/dQ), where m = mNMF83/mNCF90. We note that m = n (MNMF83/MNCF90), where MNMF83 (=338.5) and MNCF90 (=324.0) are the molecular weights of NMF83 and NCF90, respectively, and dVNMF83/dQ and dVNCF90/dQ are roughly evaluated as −3.5 and −0.5 mV/(mAh/g). In Fig. 5(b), these calculated QNCF90 values at TH are plotted with crosses. The calculated QNCF90 satisfactorily reproduces the experimentally-obtained QNCF90. We further confirmed the strong correlation between the calculated and experimentally-obtained QNCF90 data at TL (Fig. S2), thus, we demonstrating the empirical relationship of QNCF90 = −Vcell/(dVNCF90/dQ + m−1dVNMF83/dQ). These arguments clearly indicate that the slope of the discharge curve is a determining parameter of QNCF90. In other words, the flatter the discharge curve becomes, the higher η becomes.

Figure 5(c) shows the ΔT dependence of η, where η linearly increase with ΔT, as indicated by the solid line., because Vcell [=ΔT(αNCF90 − αNMF83)], QNCF90 [=−Vcell/(dVNCF90/dQ + m−1dVNMF83/dQ)] and QH increases in proportion to ΔT.

Summary

We systematically investigated Vcell, QNCF90, and η of the NMF83/NCF90 thermocell against ΔT. These three quantities increase linearly with ΔT, and η reaches 3.19% at ΔT = 56 K, which corresponds to 19% of the Carnot efficiency (ηcarnot = 17.0%). We further confirmed that the magnitude of QNCF90 is quantitatively reproduced by the slopes of the discharge curves of NMF83 and NCF90. These observations unambiguously illustrate us the strategy for enhancing η of the thermocell, that is, to explore and/or develop materials with a higher |α| and a flatter discharge curve.

Method

Fabrication and characterization of NMF83 and NCF90 films

Thin films of NaxMn[Fe(CN)6]0.83 3.5H2O (NMF83) and NaxCo[Fe(CN)6]0.92,9H2O (NCF90) were synthesized by electrochemical deposition on an indium tin oxide (ITO) transparent electrode. Details of the synthesis conditions are described in literature19,21. The film area was 1.0 cm2. The NMF83 film consists of crystalline particles of a few hundred nm and the colour is white. The NCF90 film also consists of crystalline particles of a few hundred nm and the colour is light green. The film thicknesses were determined by a profilometer (BRUKER Dektak3030). The chemical composition of the film was determined by the inductively coupled plasma (ICP) method and CHN organic elemental analysis.

The synchrotron radiation X-ray powder diffraction (XRD) measurements were performed at BL02B2 beamline22 at the SPring-8. The films were removed from the ITO glass and were filled in 300 μm glass capillaries. The capillary was placed at the Debye Scherrer camera. The XRD patterns were monitored with a one-dimensional semiconductor detector (MYTHEN, Dectries Ltd.). The exposure time was 5 min. The wavelength of the X-rays (=0.69963 Å) was calibrated by the cell parameter of a standard CeO2 powder. Figure S3 shows the magnified diffraction pattern of NMF83 and NCF90. All reflections in NMF83 are assigned to a face-centrered cubic (fcc) structure (Fm \(\bar{3}\) m; Z = 4), whereas those in NCF90 are assigned to a trigonal (hexagonal setting) structure (R \(\bar{3}\) m; Z = 3). The cell parameters were refined using the Rietan-PF program23, and a = 10.5210(2) Å in NMF83, aH = 7.4353(4) Å and cH = 17.4758(11) Å in NCF90.

The charge/discharge curves of the NMF83 and NCF90 films were measured with a potentiostat (HokutoDENKO HJ1001SD8) using a three-pole beaker-type cell. The working, referential, and counter electrodes were the PBA film, a standard Ag/AgCl electrode, and Pt, respectively. The electrolytes consisted of aqueous solutions containing 17 mol/kg NaClO4. The charge/discharge rate was 0.5 C. The cut-off voltage was ranged from 0.20 to 1.15 V vs. Ag/AgCl. The mass of each film was evaluated using thickness, area, and density. We confirmed that the actual densities of the NMF83 and NCF90 films were 0.71 and 0.58 of the ideal density, respectively.

Thermal cycle measurement of thermocell

The thermocell is a two-pole beaker-type cell (Fig. S4). The anode, cathode and electrolyte are the as-grown NMF83 film, pre-oxidized NCF90 film, and aqueous solutions containing 17 mol/kg NaClO4, respectively. Pre-oxidization of the NCF90 film was performed at Vupper = 0.65 V against Ag/AgCl in aqueous solutions containing 17 mol/kg NaClO4. The as-prepared thermocell was slowly cooled to TL (=282 K). At TL, the thermocell show a finite Vcell (~0.1 V), which was discharged to 0 V under a constant current condition (0.1 C). The discharge rate was defined by the inverse of the charging time [hour] of the NCF90 film.

The thermal cycle measurement consists of four processes: (a) warming process from TL to TH, (b) discharge process at TH, (c) cooling process from TH to TL, and (d) discharge process at TL. In the (a) warming process, Tcell was slowly increased from TL to TH in the open circuit condition, and Tcell was monitored by a platinum resistance thermometer in the electrolyte. At (b) TH, the thermally-charged cell was discharged at 0.1 C. In the (c) cooling process, Tcell was slowly decreased from TH to TL in the open circuit condition. At (d) TL, the thermally-charged cell was discharged at 0.1 C. TL was fixed at 282 K and TH was changed from 292 K to 338 K.