CET Volume 86 DOI: 10.3303/CET2186084 Paper Received: 4 September 2020; Revised: 21 February 2021; Accepted: 16 April 2021 Please cite this article as: Leal Silva J.F., Doubek G., Maciel Filho R., 2021, Impact of the Catalytic Activity of Carbon Nanotubes in the Performance of Li-O2 Batteries, Chemical Engineering Transactions, 86, 499-504 DOI:10.3303/CET2186084 CHEMICAL ENGINEERING TRANSACTIONS VOL. 86, 2021 A publication of The Italian Association of Chemical Engineering Online at www.cetjournal.it Guest Editors: Sauro Pierucci, Jiří Jaromír Klemeš Copyright © 2021, AIDIC Servizi S.r.l. ISBN 978-88-95608-84-6; ISSN 2283-9216 Impact of the Catalytic Activity of Carbon Nanotubes in the Performance of Li-O2 Batteries Jean Felipe Leal Silva, Gustavo Doubek, Rubens Maciel Filho Advanced Energy Storage Division – Center for Innovation on New Energies (AES/CINE), School of Chemical Engineering, University of Campinas (UNICAMP). Rua Michel Debrun, s/n, Campinas, SP, Brazil, ZIP code 13083-841. jefelipe@outlook.com; jefelipe@feq.unicamp.br The demand for new energy storage technologies has been rising in recent years with the increased adoption of electric vehicles and intermittent renewable electricity sources such as wind and solar power. Among the new energy storage technologies under development, the Li-O2 battery chemistry represents an option with a very high energy density potential. One of the key components of Li-O2 batteries is the O2 electrode in which the discharge product (Li2O2) is deposited. Among the possible materials to be used in the manufacture of these electrodes, carbon nanotubes represent one of the best options: besides high conductivity and the possibility to tailor structures with high porosity, carbon nanotubes present catalytic activity and can be used as support for other catalysts focused on specific electrochemical reactions. This work presents a model of a Li-O2 battery developed to evaluate the impact of catalytic activity on the capacity of the cell. The model considers a generic catalytic activity, which is varied in a range, combined with different current densities to evaluate the impact of power density and reaction rate in the distribution of discharge products in the electrode. Results suggest a strong compromise between power density and energy density because high power density leads to low energy density and vice versa. The relationship between catalytic activity and properties of carbon nanotubes is also discussed considering the use of this material in the manufacturing of electrodes. 1. Introduction Wind and solar power are expected to increase their market share in the coming years because of their decreasing installation costs. Therefore, owing to their intermittent nature, energy storage solutions must be developed accordingly (Lu et al., 2017). Among energy storage options, batteries represent a versatile solution because they can be installed in modules in almost any location, different from the currently most used energy storage grid-scale technology, which is pumped hydropower (Bragard et al., 2010). However, installation costs for many battery technologies still represent a barrier for their wide adoption, and one of the main factors affecting cost is energy density (Li et al., 2017). In this context, Li-O2 batteries represent an attractive option because of their potentially high energy density (Tan et al., 2017a). Interest in Li-O2 batteries has been increasing in the last years mainly with experimental works considering different combinations of electrolytes and O2 electrodes (Kwak et al., 2020). The O2 electrode needs to be an inexpensive material with catalytic properties to ensure high energy efficiency and an adequate lifetime. Many materials have been being considered as potential candidates for the final design of Li-O2 batteries because of factors such as manufacturing process, catalytic nature, or porosity (Tan et al., 2017b). However, these assessments of candidate materials, one by one, are not enough to compare their performance in the final design of the battery for commercialization because they are generally normalized by the weight of catalyst and they are not similar in properties. Moreover, the catalytic activity of the O2 electrode needs to be compatible with the electrolyte capacity to transport Li+ and O2 to the reaction site (Wang et al., 2020). Therefore, this work presents a model of a Li-O2 battery that evaluates the impact of the catalytic activity on the specific capacity after deep discharge. The model consisted of a Li-O2 cell using carbon nanotubes as the O2 electrode because of the possibility to adjust their reactivity by several methods that create defects in their structure (Tan et al., 2012) and because of the electrical properties and potentially low cost of this electrode 499 material (Kim et al., 2018). Results can be used to determine minimum performance requirements for catalysts in general based on the limitations imposed by mass transfer of reacting species in Li-O2 batteries. 2. Methodology 2.1 Battery model The Li-O2 battery model consists of a 1D representation of a battery, as shown in Figure 1. The following conditions were assumed in the model (Sahapatsombut et al., 2013; Tan et al., 2017a): isothermal operation; discharge product is Li2O2 (Eq. 1 and 2); electrolyte behaves according to the concentrated solution theory; the pores of the O2 electrode (Figure 1) are filled with a binary lithium salt in a non-aqueous electrolyte solution; O2 transport inside the cell occurs exclusively via molecular diffusion in liquid (no gas phase inside the O2 electrode and no convection). Figure 1: Schematic representation of a Li-O2 battery and the derived simplified 1D model used in this study → + ( = 0.00 ) (1) 2 + + 2 → ( = 2.96 ) (2) The battery is modeled based on the Newman model, which considers solid (discharge products, electrode, etc) and electrolyte solution as a superimposed continuum. The material balance for species is given by Eq. (3) ( )⁄ = −∇ ∙ + (3) in which is the concentration, is the volume fraction of electrolyte, is the molar flux, and is the production rate. In the absence of convection, the mass transfer for Li+ and O2 is given by Eq. (4) and Eq. (5), respectively: = − , ∇ + ⁄ (4) = − , ∇ (5) in which , and , are the effective diffusion coefficients for Li+ and O2, is the transference number of Li+, is Faraday’s constant, and is the current density in the liquid solution, given by Eq. (6) for a binary electrolyte in a Li-O2 cell: = − ∇ − 2 ⁄ ( − 1) + (1 + ln( ) ln( )⁄ )∇ ln( ) (6) in which is the effective ionic conductivity, is the electrolyte potential, is the universal gas constant, is the temperature, and is the activity coefficient of the Li salt. The term ln( ) ln( )⁄ , which is the activity dependence, was fixed at -1.03 (Sahapatsombut et al., 2013). The current density in the O2 electrode is: = − ∇ (7) in which is the effective conductivity in the electrode. These effective parameters depend on the tortuosity and geometry of the system, and they can be obtained via the porosity of the material using the Bruggeman correlation. In the case of particles with a cylindrical shape, such as carbon nanotubes, these corrections are as follows (Tjaden et al., 2016; Yuan et al., 2015): , = (8) , = (9) 500 = (10) = (1 − ) (11) in which is the diffusion coefficient of Li+ in the electrolyte, is the diffusion coefficient of O2 in the electrolyte, is the conductivity of the electrolyte, and is the conductivity of the O2 electrode. In the continuum model, charges are conserved between phases, which can be expressed as: ∇ ∙ + ∇ ∙ = 0 (12) ∇ ∙ = (13) in which is the specific surface area of pores per unit volume of the electrode and is the average transfer current density. In this system, Li2O2 is the only discharge product. Therefore, the rate at which Li2O2 is produced, based on stoichiometry and number of transferred electrons in Eq. (1) and (2), is: = − , ℎ ℎ = −2, = 2 (14) in which is the stoichiometric coefficient for Li+ in Eq. (1), i.e., -2, and is the number of transferred electrons (2). For the electrochemical reaction at the O2 electrode, the Butler-Volmer model is used: = , exp ( ) − ( ) exp (15) = − − ∆ − (16) ∆ = (17) in which is the concentration of a species , is the anodic rate constant, is the cathodic rate constant, is the symmetry factor (0.5), is the overpotential of the surface at the O2 electrode, ∆ is the voltage drop across the Li2O2 film, is the resistivity across the Li2O2 film, is the equilibrium potential (Eq. 2), and is the volume fraction of the discharge product (Li2O2). At the Li electrode, Eq. (18) is used: = exp ( ) − exp ( ) (18) in which and are the exchange current density and the surface overpotential, both at the Li electrode. Initially, the discharge product is formed as a solubilized species. Therefore, up to the solubility limit ( , ), the change in concentration of Li2O2 is given by Eq. (19), and beyond that, it is given by Eq. (20): = − , < , (19) , = , ≥ , (20) in which is the concentration of Li2O2 in the electrolyte, and , is the concentration of solid Li2O2 (which deposits inside the pores of the O2 electrode). As a result of the formation of the discharge product, the volume fraction of the discharge product ( ) and the active surface area of the O2 electrode ( ) change: = , , , (21) = 1 − / (22) in which , , is the initial concentration of the solid product, is the molecular weight of the Li2O2, is the density of the discharge product, is the initial surface area, is the initial electrode void fraction, and the exponent is an empirical value: low values indicate high blockage of the surface area (plate-like structures), whereas high values model the formation of coarser structures. A value of = 0.5 has been used, but this value can be adjusted based on experimental validation. The initial surface area can be calculated based on the initial porosity and the average particle radius : = 2 / (23) 501 In Eq. (23), the coefficient 2 is used for nanotubes. At boundary 2 (Figure 1), oxygen is available at a partial pressure of . The concentration of oxygen at the boundary can be estimated using the ideal gas law (Eq. 24), and the saturated concentration of oxygen inside the electrolyte at the boundary can be estimated using a solubility factor , as described by Eq. (25): , = / (24) = , (25) 2.2 Simulation and analysis The battery model was implemented in COMSOL Multiphysics 5.6 (2020, COMSOL Inc., Sweden). The simulations were run on a 64-bit Windows 10 Pro with 32 GB of RAM and an Intel Core i5-9600KF. The Li electrode, represented as boundary 1 in the model (Figure 1), was set to a potential of 0 V, and the desired current density was applied at boundary 2 (Figure 1). The cell potential was also read at boundary 2. The simulation of the galvanostatic discharge process ran indefinitely until a cell potential of 2.5 V was reached. The mesh was physics-controlled with extremely fine elements. To evaluate the impact of catalytic activity, was varied in a range of 1×10-18 to 1×10-15 m7 s-1 mol-2 (Sahapatsombut et al., 2013). Three different current densities ( ) were applied in the study (0.5, 2.0, and 3.5 A m-2) to force different situations of mass transport. Table 1: Parameters used in the simulation of the Li-O2 cell (Fiates et al., 2020; Gittleson et al., 2017; Laurent et al., 2010; Sahapatsombut et al., 2013) Variable Value Variable Value Variable Value , 1000 mol m-3 0.965 A m-2 0.21 bar , 0.09 mol m-3 1.1×10-15 m s-1 50 Ω m2 2.50×10 -10 m2 s-1 1.5 S m -1 1500 kg m -3 1.24×10 -9 m2 s-1 100 S m -1 30 nm 2.96 V 250 µm 0.4 0.9 50 µm 300 K 0.5 45.881 g mol -1 0.45 3. Results and Discussion 3.1 Impact of catalytic activity on cell capacity Figure 2 shows the discharge curve for the Li-O2 cell for four different cathodic rate constants and three different discharge current densities. For lower current densities, the specific capacity of the cell is not affected by the kinetics: at 0.5 A m-2, all cases reported a capacity of about 12000 mAh g-1. Nevertheless, a higher cathodic rate constant yields a discharge plateau at a higher voltage. Therefore, an increase in the cathodic rate constant increases the voltage efficiency and decreases the energy that would be lost because of overpotential. Similar findings were reported in the literature in the comparison of electrodes based on Ketjenblack carbon using CuFe as the catalyst for the oxygen reduction reaction (Ren et al., 2011). Figure 2: Discharge curve for the Li-O2 cell under different values of kc and iapp Experimental evaluation of the effect of the catalytic activity on the specific capacity at deep discharge requires reproducibility in electrode manufacturing, which is still challenging (Ren et al., 2011). Nevertheless, 502 according to this battery model, this effect becomes more evident at larger current densities, though the difference is small. At a current density of 3.5 A m-2, a of 1×10-18 m7 s-1 mol-2 yields a specific capacity of 4616 mAh g-1, whereas a of 1×10-15 m7 s-1 mol-2 yields a capacity of 5347 mAh g-1 (an increase of 16%). However, at this current density, the voltage drops too fast and compromises cell efficiency. Therefore, the main benefit of increasing the cathodic rate constant is the decrease in cell overpotential. 3.2 Impact of catalytic activity on the distribution of discharge product Figure 3 presents the combined effect of the cathodic rate constant and applied current density on the porosity (void fraction) of the electrode as a function of the dimensionless length of the electrode. As the discharge progresses, at a low current density, the discharge product becomes well distributed throughout the O2 electrode independently of the cathodic rate constant. On the other hand, at a high current density (3.5 A m-2), because of the sluggish O2 mass transport, the O2 supply decreases, thus increasing the cell overpotential. In this case, a higher cathodic rate constant decreases the cell overpotential, which allows the discharge process to go further, thus leading to an increased cell capacity. In this case, a major part of the discharge product accumulates at the end of the electrode facing the O2 feed side because of limitations in O2 mass transport. Figure 3: Evolution of porosity as a function of the dimensionless length (0%: separator side, 100%: O2 feed side) of the O2 electrode with time for different values of kc and iapp Increased cell capacity at high current density as a consequence of increased catalytic activity has been shown previously (Hou et al., 2020), and it was connected to the achieved decrease in cell overpotential as well. Based on these findings, adjusting the catalytic activity is fundamental to efficiently use the void volume fraction of the O2 electrode, thus increasing the capacity of Li-O2 cells. Previous literature had indicated the possibility of increasing the cell capacity by using a non-uniform catalyst distribution (Andrei et al., 2010). Such an arrangement is only possible by using layered materials of small dimensions, such as carbon nanotubes. The catalytic activity of carbon nanotubes is adjustable by several treatments, and they can be used as support for other more noble catalysts as well. Therefore, carbon nanotubes represent a very suitable candidate to produce Li-O2 batteries with higher energy efficiency. 4. Conclusion The development of Li-O2 batteries still requires many improvements in terms of catalysis, and an interesting approach is to evaluate the impact of catalytic activity to better understand its impact on battery performance. Results of the simulation of a Li-O2 cell indicate that an increased cathodic rate constant decreases the cell overpotential. At a small current density, this has little impact on the specific capacity of the cell. Nevertheless, at higher current densities, the decreased cell overpotential allowed by the faster kinetics compensates for the low O2 concentration caused by the combined effect of faster discharge and slow O2 mass transport. Overall, 503 the results indicate that the cathodic rate constant has little impact on the specific capacity of the Li-O2 cell but a great impact on cell overpotential. Therefore, higher energy density and efficiency can be achieved by using materials with increased catalytic activity. This result highlights the importance of using versatile materials such as carbon nanotubes because of the possibility to adjust their catalytic activity. 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