Diffusion and Current Generation in Porous Electrodes for Thermo

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Diffusion and Current Generation in Porous Electrodes for Thermo-Electrochemical Cells Ju Hyeon Kim, and Tae June Kang ACS Appl. Mater. Interfaces, Just Accepted Manuscript • DOI: 10.1021/acsami.9b08381 • Publication Date (Web): 22 Jul 2019 Downloaded from pubs.acs.org on July 23, 2019

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ACS Applied Materials & Interfaces

Diffusion and Current Generation in Porous Electrodes for Thermo-Electrochemical Cells Ju Hyeon Kim and Tae June Kang*

Department of Mechanical Engineering, INHA University, Incheon 22212, South Korea

KEYWORDS: thermocell, porous electrode, iron perchlorate, carbon fiber, Thiele modulus

ABSTRACT

Carbon-based porous electrodes have led to remarkable improvements in the performance of thermochemical cells or thermocells that electrochemically harvest low-grade waste thermal energy. However, the output current from the thermocells is hampered by diffusion effect that leads to depleted ion concentration as the ions

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permeate through the porous electrode. Here, we advance a theoretical basis for quantitative description of the diffusion effect on current generation in such porous electrodes. One single dimensionless parameter of Thiele modulus describes the effect according to the theory adopted from the well-established results in the literature. Experimental results for carbon fiber electrodes are illustrated and quantified by the theory. The theory presented here would provide a basis for the choice and design of porous electrodes for thermocells. The results should also provide a basis for devising electrochemical devices with highly porous electrodes.

INTRODUCTION A huge amount of low-grade heat from solar, geothermal, and various industrial processes is recycled at low efficiency or just discarded to the atmosphere.1-3 Considering that almost two thirds of all the energy produced is discharged as waste heat, an effective utilization of this low-grade heat in the form of electrical energy would be a boon for renewable energy market for industrial or even household use.


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Thermoelectrochemical cell (thermocell or TEC) as a conversion process that utilizes an electrochemical pathway has received much attention in recent years owing to convenient large-scale deployability.4-10 The TEC exploits temperature-dependent redox potential to convert heat directly into useful electrical energy without regenerative processes.11-14 Continuous power generation that involves simple components and low maintenance renders the TECs quite attractive. However, a low power density and correspondingly low conversion efficiency remains an obstacle to the commercialization of TECs in the utilization of waste thermal energy. Early studies on TECs utilized archetypal non-reactive material of platinum as electrodes.15, 16 With the advent of highly porous and conductive carbon electrodes, remarkable advances have been made in the TEC performance.4,

7, 9, 17-19

Porous

carbon materials are desirable as they have a higher specific surface area and a higher exchange current density compared to non-porous electrodes, which contributed to the efficiency improvement. The conversion efficiency relative to the Carnot cycle has been improved to 3.9%,5 which renders TECs commercially viable.



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For a given porous electrode, the exposed surface area, or electrochemical active surface area (ECSA) for the redox reactions, is equivalent to volume. Doubling the volume, for instance, doubles the surface area. A larger electrode volume for a higher power makes it more difficult for ions to diffuse through the thicker porous electrode. As the ions diffuse through the porous electrode, they are consumed through the redox reaction to generate current. Therefore, the ion concentration decreases with increasing distance from the electrode surface, and at some point in the electrode, the ion concentration becomes almost zero if the electrode is thick enough. In this work, we probe the diffusional effect in detail. We utilize a classical formalism available to quantify the effect with highly aligned carbon fiber sheets. One of the favorable factors for choosing the carbon fiber sheet is that it is commercially available and widely used in the electrochemical devices. The other is that the carbon fibers in the sheet are highly aligned in one direction such that the ECSA of the electrode material is quantitatively controllable by laminating the carbon fiber sheets. An aqueous electrolyte of iron (II/III) perchlorate (Fe(ClO4)2/Fe(ClO4)3) is utilized for the experiments.


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EXPERIMENTAL SECTION Materials and electrolyte preparation: Polyacrylonitrile (PAN) based carbon fiber sheet (PyrofilTM, Mitsubishi Chemical) that is non-woven and unidirectional sheet of carbon filament was used as an electrode material in demonstrating power generation of TEC devices. Each filament diameter is 6 μm and has a good thermal conductivity of 20 W/m∙K. It also has good mechanical properties, such as an elastic modulus of 295 GPa and the tensile strength of 4.4 GPa. For the preparation of TEC electrolytes, 0.8 M concentration of iron (II) perchlorate (Iron (II) perchlorate hydrate 98%, Fe(ClO4)2·xH2O, Sigma Aldrich) and iron (III) perchlorate (Iron (III) perchlorate hydrate crystalline, Fe(ClO4)3·xH2O, Sigma Aldrich) electrolyte solution was prepared for evaluating electrolyte performance. This perchlorate electrolyte is quite effective in converting waste heat to electricity using TECs.20 Provided concentrations here and elsewhere are total molar concentrations. All solutions were prepared using water from a high purity deionization system (Ultra 370, YOUNG LIN instruments) and were degassed before use by bath sonication. To avoid the effect of electrolyte degradation, the freshly prepared electrolytes were immediately incorporated for all measurements. 5 ACS Paragon Plus Environment


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Measurement of temperature coefficient of redox potential: The temperature coefficient of redox potential for the iron (II/III) electrolyte was investigated by measuring the temperature dependence of the potential difference using a nonisothermal cells, as described in our previous work.7, 21 Briefly, a U-shaped cell was used that consists of two half cells surrounded by water pockets. The temperature of each compartment was controlled by the circulating cold and hot water stored in thermostatic baths (AD-RC08, AND Korea), providing a ±0.1oC control of the water temperatures. A half-cell has a diameter of 1.0 cm and the distance between half-cells is 8.5 cm long to inhibit the thermal conduction between cell. The sheet of carbon fibers was used as an electrode material to measure a potential difference generated by the temperature difference of half-cells. A thermocouple (K-type, TM-947SD, LT Lutron) was inserted in close proximity to the electrode for each half-cell. An output voltage from the cell was recorded using a multimeter (Keithley 2000, Tektronix). Instrumental: Cyclic voltammetry (CV) measurements were performed to investigate the electrochemical properties of the redox reaction as affected by the number of stacks. Cyclic voltammograms were obtained using the conventional three-electrode


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scheme with carbon fiber sheet working electrode, platinum wire counter electrode and saturated Ag/AgCl reference electrode. The electrolyte solution of 10 mM Fe(ClO4)3 with 1.0 M KCl as the supporting electrolyte was used for all CV measurements. The scan rate was controlled in the range of 100 to 10 mV/sec. The current and voltage output from the cell was measured using a computer controlled voltage–current meter (CS310, Corrtest instruments) with 10 μV potential resolution and 10 pA current sensitivity from -10 to 10 V. Scanning electron microscopy (CX200TM, COXEM) was used to observe the surface morphology of carbon fiber sheet electrode at an acceleration voltage of 10 KeV. RESULT AND DISCUSSION Electrochemical characterization of carbon fiber sheet electrodes Electrochemical reversibility was checked first, prior to evaluation of the TEC performance, for the reaction of iron (II/III) perchlorate electrolyte on the carbon fiber material using cyclic voltammetry (CV) analysis. Using the conventional three electrode configuration, cyclic voltammograms were obtained with Pt electrode for comparison, as shown in Figure 1a. A 10 mM Fe(ClO4)3 solution with 1.0 M KCl as the



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supporting electrolyte was used for this experiment. We applied an initial potential of 0.9 V and the potential was swept negatively to reduce Fe3+ to Fe2+. The CV measurements were performed for a number of cycles and the voltammogram at the third cycle was shown in the figure. As shown in the figure, the ratio of anodic to cathodic peak current is close to unity for both carbon fiber and Pt electrodes. The peak separation between the reduction and oxidation reactions on the carbon fiber electrode was measured to be 146 mV, which is higher than that of Pt electrode (~74 mV). Figure 1b shows the peak current versus the scan rate square-rooted as a function of scan rate from 100 to 10 mV/sec. In electrochemically reversible electron transfer processes involving freely diffusing redox ions, the Randles-Sevcik equation describes that the dependence of the peak current on the square root of the scan rate should be linear.22,23 As shown in the figure, the carbon fiber electrode shows a nearly linear relationship as in the case of the Pt electrode, although it slightly deviates from the linearity. It indicates that the redox reactions on carbon fiber electrode are electrochemically quasi-reversible, not occurred by the surface adsorption of redox ions on the electrodes.23 Therefore, it is


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concluded from the CV analysis that the redox reaction of the iron (II/III) perchlorate electrolyte on carbon fiber electrodes appears to be quasi-reversible and selfregenerative, as with the Pt electrode.



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Figure 1. (a) Cyclic voltammograms of the electrolyte solution of 10 mM Fe(ClO4)3 with 1.0 M KCl as the supporting electrolyte reacting on Pt and carbon fiber electrodes. (b) Peak current versus scan rate square-rooted. 10 ACS Paragon Plus Environment

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Redox reaction of iron (II/III) perchlorate and temperature coefficient of redox potential Figure 2a shows a schematic for the redox reaction of the iron (II/III) perchlorate electrolyte on carbon fiber electrodes, driven by a temperature difference applied to the electrodes at both ends of TEC. At the cold anode, Fe2+ is oxidized to Fe3+ by releasing an electron. The potential difference between the two electrodes causes the electron to flow through an external load and move to the hot cathode. At the hot cathode, Fe3+ is reduced to Fe2+ by receiving the electron, thereby maintaining electrical charge equilibrium in the TEC. Fast transport of ions is one of the most important parameters for continuously generating high output power. To minimize concentration gradients of products and reactants between the electrolyte and the electrodes, the TEC presented here has horizontal parallel electrodes with the cold electrode placed above the hot electrode. This cell orientation homogenizes the electrolyte with convective transport driven by the density gradient of electrolyte.7, 24



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A temperature coefficient of redox potential (α)25-27 relates the output voltage that can be obtained from a cell to the temperature difference applied to the electrodes in the cell, which can be expressed as follows: 𝛥𝑉

𝛼 = 𝛥𝑇

|𝑝

=

∆𝑠0𝑟𝑥

(1)

𝑛𝐹

where ΔV is the full-cell voltage, ΔT is the inter-electrode temperature difference, Δsrx0 is the entropy change for the redox reaction, n is the number of electrons transferred in the reaction, and F is Faraday’s constant. The temperature coefficient of the iron (II/III) perchlorate electrolyte reacting on a carbon fiber sheet was determined by measuring the open-circuit voltage from the cell over a range of temperature difference between 0 and 25°C with an increment of ±5°C (see Experimental Section for more details). As shown in Figure 2b, the α was measured to be +1.70 mV/K, which is higher in absolute magnitude than that of ferric and ferrocyanide redox couple (-1.43 mV/K)4, 7, 19 that has been typically used as an aqueous electrolyte for TECs. The reaction entropy change (Δsrx0) of the redox couple can be calculated from eq 1, which is as high as ~ 164 J/mol∙K. This high temperature coefficient, originating from a high entropy change of the redox reaction, is highly 12 ACS Paragon Plus Environment

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desirable for harvesting low-grade heats, considering that the temperature difference between waste heat source and its surrounding is small.



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Figure 2. (a) Schematic of the redox reaction of the iron (II/III) perchlorate electrolyte on carbon fiber electrodes, driven by a temperature difference applied to the electrodes at both ends of TEC. (b) Measurement of the temperature coefficient for 0.8 M iron (II/III) perchlorate with carbon fiber sheet electrodes.

Effect of diffusion in porous electrodes on TEC performance To investigate the effect of diffusion in porous electrodes on the power generation of TECs, carbon fiber sheets laminated in parallel were utilized as the porous electrode. Detailed preparation process is provided in Supporting Information. The electrode material and its laminated structure allow quantitative control of the ECSA of the electrode without any change in the electrode tortuosity that is another important parameter affecting the current generation. Figure 3a shows the thermocell configuration that was used for the performance evaluation. The TEC electrodes had a cross sectional area of 1.0 cm × 1.0 cm and a spacing of 5 mm between the electrodes. The concentration of the iron (II/III) perchlorate redox couple was 0.8 M. Unidirectional nature of the non-woven carbon 14 ACS Paragon Plus Environment

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fiber sheet is shown in the SEM image of Figure 3b. This original carbon fiber sheet was used without any surface treatment, such as carbon activation28, 29 that is typically used to increase the electrochemical active area of electrodes. Since the main objective was to investigate the diffusion effect on current generation in porous electrodes for thermocells rather than to maximize the power density, a small temperature difference of 31oC was applied between the two electrodes. This difference was calculated using the open-circuit voltage and the observed temperature coefficient (1.7 mV/K) in Figure 2b. Figure 3c gives the power density of the TEC as affected by the number of carbon fiber stacks. The maximum power density increased from 297 mW/m2 to 435 mW/m2 as the number of stacked layers was increased from 1 to 4, approaching a plateau. Electrochemical impedance spectroscopy (EIS) analysis was performed to obtain the changes in exchange current with increasing number of the stacked layers. From the relationship between the charge transfer resistance and the exchange current17,30 (Rct = RT/nFi0, where Rct is the charge transfer resistance, R is the gas constant, T is the temperature in K, i0 is the exchange current), we calculated the exchange current of



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the TECs and plotted them in Figure 3d, in conjunction with the maximum power density of the TECs obtained from Figure 3c. The exchange current increases linearly, indicating that the active electrode area increases linearly with increasing number of layers. In contrast, the saturation behavior of the maximum power density with the number of the stacked layers is quite apparent as shown in the figure. The fact that the power density approaches a plateau even though the active electrode area keeps increasing does indicate that ions are not present in an amount sufficient enough to fully generate the current. In porous electrodes, ions diffuse through the electrode. As they diffuse, their concentration decreases because the ions are consumed along the way into the layer to generate the current, and therefore, the current generation becomes smaller further into the electrode. This diffusion effect on current generation can be quantified in much the same way as in the classical treatment of reactiondiffusion.31-33 Consider for the quantification the redox reaction of the electrolyte involving one electron. The rate of consumption of ions in generating the current is proportional to the ion concentration. Therefore, the intrinsic rate unaffected by diffusion, rc, is given


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by kC where k is the proportionality constant, which is the rate constant, and C is the ion concentration. The actual rate at which the ions are consumed could be affected by diffusion if the electrode is porous and ions diffuse through the porous medium. If we let this actual rate be RG, then ‘effectiveness factor’ η can be defined as follows: η = RG/rc (2) which is the ratio of the actual rate to the intrinsic rate. This effectiveness factor can be derived (see Supporting Information for the derivation) to give31, 32 η = tanh(ϕ)/ϕ (3) where the Thiele modulus ϕ33 is given by ϕ = L(k/De)1/2 (4) Here, L is the thickness of the porous electrode and De is the effective diffusivity of ion in the porous medium. A larger Thiele modulus means a more diffusion-affected reaction or current generation, since a larger modulus means a thicker porous



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electrode, a lower effective diffusivity, or a faster consumption of ions. The hyperbolic tangent function is such that its value is close to its argument, which is the Thiele modulus here, when the argument is less than 0.3, making the effectiveness factor equal to almost unity. When its argument is large, say larger than 3, its value approaches unity. Therefore, if the rate of ion consumption is diffusion-limited such that the Thiele modulus is larger than 3, the effectiveness factor simply becomes 1/ϕ and the actual rate of ion consumption or current generation becomes RG = rc/ϕ

(diffusion-limited)

(5) This result clearly reveals that the actual rate at which the ions are consumed to generate current is reduced by a factor of the Thiele modulus, compared to the rate in the absence of diffusion effect, or the intrinsic rate. Table 1 gives the current density at the maximum power that was taken from Figure 3c as a function of the number of carbon fiber layers or the thickness of the porous electrode, each layer being ~50 μm thick. If the ion concentration were the same throughout the porous electrode of carbon fiber sheet layers, the current would simply


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increase linearly with increasing number of layers. However, the average current density per layer given in the table decreases with increasing number of layers, indicating that the number of ions present in the layers decreases on the average as the number of layers increases. Since the ions are consumed through the redox reaction for the generation of current in the porous electrode, the ion concentration decreases as they permeate through the electrode, the concentration being lower further into the layers. If the rate of ion consumption is diffusion-limited, the concentration should be negligible at some point further into the layers, and the electrode beyond that point is almost devoid of the ions and thus cannot generate current. This reasoning can be confirmed from the quantitative results presented above. The observed or measured total rate in moles per time is RG(AL) = (AL)rc/ϕ for the diffusion-limited rate of ion consumption where A is the electrode cross-sectional area such that (AL) is the total electrode volume, and eq 5 has been used for RG. The total ion consumption rate in moles per time is equivalent to charge/time or the current, and thus the current, I, can be written as follows:



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I = nF(AL)rc/L(k/De)1/2 = nFArc/(k/De)1/2 (6) where eq 6 has been used for the Thiele modulus. Here, nF is the conversion constant from ion concentration to charge. This result states that the current generated becomes independent of the electrode thickness when the thickness becomes larger than a certain value beyond which the ion concentration is negligible. This thickness, according to the first column of Table 1, corresponds to 4 layers of carbon fibers at which the output current gets saturated. The current data in Table 1 can also be used to get an estimate of the intrinsic rate, rc. The estimated intrinsic rate (see Supporting Information for details) in terms of the current density is 14.5 A/m2. This is the current density corresponding to the rate of ion consumption per one layer volume of the electrode, when there is no diffusion effect. The effectiveness factor for the one layer electrode is 0.778 (=11.3/14.5) since the actual measured rate is 11.3 A/m2 (Table 1). A considerable reduction in the achievable current density resulted, a 22.2% reduction, because of the diffusion effect in the porous electrode.


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The diffusion effect becomes severer with addition of more layers, leading to the effectiveness factor of 0.296 for the 4 layer electrode. Successive addition of carbon fiber layer for the electrode does increase the active surface area for ion consumption or ECSA successively, as shown in the increase of exchange current in Figure 3d, but each successive layer added become more diffusion-affected or contains lower ion concentration such that the actual gain in the current density or the power increases only marginally, the gain becoming smaller each time a layer is added. This is the reason why the current density increases from 11.3 A/m2 only to 16.4 A/m2 when 4 layers are used for the electrode, and the power density increases from 297 mW/m2 only to 435 mW/m2 (Figure 3d). The ultimate goal of this study is to predict the performance of TEC utilizing porous electrodes. To this end, we have introduced the Thiele modulus theory and derived the output current of the TEC, whose output is limited by the diffusion of redox ions in the porous electrode. The Thiele modulus here was estimated experimentally by measuring the TEC output currents according to the number of stacked layers. Further



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efforts are needed to formulate Thiele modulus variables, such as k and De in the porous electrode, as electrochemically easy-to-measure variables for TECs.

Table 1. Current density at maximum power as a function of number of carbon fiber layers.

Current density @ Carbon fiber lamination

max. power density (A/m2)

Average current density per layer (A/m2)

Effectiveness factor (η)

1 layer

11.3

11.3

0.778

2 layers

14.6

7.30

0.503

3 layers

16.0

5.33

0.381

4 layers

16.4

4.10

0.296


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Figure 3. (a) TEC configuration used for device performance evaluation. (b) SEM image of the carbon fiber sheet, showing highly aligned strings in one direction. (c) Performance evaluation of the TECs with carbon fiber electrodes as a function of the



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number of stacks. (d) Exchange current and the maximum power density as a function of the number of stacks.

CONCLUSIONS A theoretical basis has been presented for the effect of diffusion on current generation in porous electrode for thermochemical cells. The classical approach wellestablished for the reaction-diffusion taking place in porous media has been adopted for the theory. The theory describes the diffusion effect with one single dimensionless parameter of Thiele modulus, a higher value indicating a more diffusion-affected current generation. The desire to increase the current by increasing the volume of the porous electrode is hampered by more diffusion effect the added volume causes, the ion concentration diminishing as the ions permeate through the porous electrode. These combined effects are quantified and illustrated with a series of experiments involving carbon fiber electrodes. The theory presented here would provide a basis for the choice and design of porous electrode for the purpose of enhancing the 24 ACS Paragon Plus Environment

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performance of the thermochemical cells. The results should also provide a basis for devising electrochemical devices with highly porous nanocarbon electrodes.

ASSOCIATED CONTENT

Supporting Information.

The following files are available free of charge. Fabrication process for carbon fiber electrodes and the TEC using them, Diffusion effect on current generation in porous electrode and estimation of the intrinsic rate. (PDF)

AUTHOR INFORMATION

Corresponding Author *E-mail: [email protected]. Tel: 82-32-860-7304

Notes 25 ACS Paragon Plus Environment


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The authors declare no competing financial interest.

ACKNOWLEDGMENTS This research was supported by the National Research Foundation of Korea (grants No. NRF-2017R1A2B4004022 and NRF-2017M3A9E2063256) and the framework of 2017 international cooperation program (Grant No: NRF-2017K1A4A3013662).

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The output current from the thermocells is hampered by diffusion effect that leads to depleted ion concentration as the ions permeate through the porous electrode. 82x44mm (300 x 300 DPI)

ACS Paragon Plus Environment

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Diffusion and Current Generation in Porous Electrodes for Thermo

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