Journal of Power Sources 585 (2023) 233637 Contents lists available at ScienceDirect Journal of Power Sources journal homepage: www.elsevier.com/locate/jpowsour Interlaboratory study assessing the analysis of supercapacitor electrochemistry data Jamie W. Gittins a, **, 1, Yuan Chen a, b, 1, Stefanie Arnold c, d, Veronica Augustyn e, Andrea Balducci f, Thierry Brousse g, h, Elzbieta Frackowiak i, Pedro Gómez-Romero j, Archana Kanwade k, Lukas Köps f, Plawan Kumar Jha l, Dongxun Lyu a, Michele Meo m, Deepak Pandey n, o, Le Pang p, q, Volker Presser c, d, r, Mario Rapisarda m, Daniel Rueda-García j, Saeed Saeed e, Parasharam M. Shirage k, Adam Ślesiński i, Francesca Soavi s, t, u, Jayan Thomas n, o, v, Maria-Magdalena Titirici w, Hongxia Wang p, q, Zhen Xu a, w, Aiping Yu x, Maiwen Zhang x, Alexander C. Forse a, * a Yusuf Hamied Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge, CB2 1EW, UK b Department of Chemistry, Imperial College London, Exhibition Road, London, SW7 2AZ, UK c INM – Leibniz Institute for New Materials, Campus D2.2, 66123, Saarbrücken, Germany d Department of Materials Science and Engineering, Saarland University, Campus D2.2, 66123, Saarbrücken, Germany e Department of Materials Science and Engineering, North Carolina State University, Raleigh, NC, 27695, United States f Friedrich-Schiller-University Jena, Institute for Technical Chemistry and Environmental Chemistry and Center for Energy and Environmental Chemistry Jena (CEEC Jena), Philosophenweg 7a, 07743, Jena, Germany g Nantes Université, CNRS, Institut des Matériaux de Nantes Jean Rouxel, IMN, F-44000, Nantes, France h Réseau sur le Stockage Electrochimique de l’énergie (RS2E), FR CNRS, 3459, F-80039, Amiens, France i Institute of Chemistry and Technical Electrochemistry, Poznan University of Technology, 60-965, Poznan, Poland j Catalan Institute of Nanoscience and Nanotechnology (ICN2) and The Barcelona Institute of Science and Technology (CSIC-BIST), Campus UAB, Bellaterra, 08193, Barcelona, Spain k Department of Metallurgy Engineering and Materials Science, Indian Institute of Technology Indore, Simrol, 453552, Indore, India l Turku University Centre for Materials and Surfaces (MATSURF), Department of Chemistry, University of Turku, FIN-20500, Turku, Finland m Department of Aeronautics and Astronautics, University of Southampton, Southampton, SO16 7QF, UK n Department of Materials Science and Engineering, University of Central Florida, Orlando, FL, 32816, USA o NanoScience Technology Center, University of Central Florida, Orlando, FL, 32826, USA p School of Chemistry and Physics, Faculty of Science, Queensland University of Technology, Brisbane, Queensland, 4000, Australia q Centre for Materials Science, Queensland University of Technology, Brisbane, Queensland, 4000, Australia r Saarene – Saarland Center for Energy Materials and Sustainability, Campus C4.2, 66123, Saarbrücken, Germany s Department of Chemistry “Giacomo Ciamician”, Università di Bologna, Via Selmi 2, 40126, Bologna, Italy t ENERCube, Centro Ricerche Energia, Ambiente e Mare, Centro Interdipartimentale per la Ricerca Industriale Fonti Rinnovabili, Ambiente, Mare ed Energia (CIRI -FRAME), Università di Bologna, Via Selmi 2, 40126, Bologna, Italy u National Reference Center for Electrochemical Energy Storage (GISEL) - INSTM, Via G. Giusti 9, 50121, Firenze, Italy v CREOL, College of Optics and Photonics, University of Central Florida, Orlando, FL, 32816, USA w Department of Chemical Engineering, Imperial College London, London, SW7 2AZ, UK x Department of Chemical Engineering, University of Waterloo, 200 University Avenue West, Waterloo, Ontario, N2L 3G1, Canada H I G H L I G H T S • Supercapacitor electrochemistry data analysed by 14 different laboratories. • Constant current tests gave lower variability in capacitance than CV tests. • Large variation in capacitance results obtained for ‘non-ideal’ devices. • Capacity should be reported for reliable comparison of device performance. • Researchers must be clear on their definition of ‘specific capacitance’. * Corresponding author. ** Corresponding author. E-mail addresses: jwg37@cam.ac.uk (J.W. Gittins), acf50@cam.ac.uk (A.C. Forse). 1 These authors contributed equally. https://doi.org/10.1016/j.jpowsour.2023.233637 Received 17 May 2023; Received in revised form 31 July 2023; Accepted 12 September 2023 Available online 26 September 2023 0378-7753/© 2023 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). J.W. Gittins et al. Journal of Power Sources 585 (2023) 233637 A R T I C L E I N F O A B S T R A C T Keywords: Supercapacitors are fast-charging energy storage devices of great importance for developing robust and climate- Data analysis friendly energy infrastructures for the future. Research in this field has seen rapid growth in recent years, Electrochemical energy storage therefore consistent reporting practices must be implemented to enable reliable comparison of device Supercapacitors performance. Although several studies have highlighted the best practices for analysing and reporting data from such energy storage devices, there is yet to be an empirical study investigating whether researchers in the field are correctly implementing these recommendations, and which assesses the variation in reporting between different laboratories. Here we address this deficit by carrying out the first interlaboratory study of the analysis of supercapacitor electrochemistry data. We find that the use of incorrect formulae and researchers having different interpretations of key terminologies are major causes of variability in data reporting. Furthermore we highlight the more significant variation in reported results for electrochemical profiles showing non-ideal capacitive behaviour. From the insights gained through this study, we make additional recommendations to the community to help ensure consistent reporting of performance metrics moving forward. 1. Introduction displaying more ideal capacitive behaviour. From these insights, we reinforce correct analysis procedures and make several further recom­ In recent years, interest has risen in fast-charging energy storage de­ mendations to ensure consistent analysis and reporting of performance vices such as supercapacitors, driven by the current climate and energy metrics across researchers. This should significantly benefit the field in crises [1–6]. In the past three years alone, more than 20,000 publications the future. have been published in this area [7], and various approaches have been taken to attempt to improve the energy and power performances of 2. Methods supercapacitors. The performances of existing carbon electrode materials have been improved through heteroatom doping, compositing with 2.1. Experimental pseudocapacitive materials, and by structure optimisation [8–10]. Novel electrode materials with performances on-par with or exceeding carbon All experimental work was carried out by J.W.G. at the University of materials have also been developed, including MXenes, metal-organic Cambridge, one of the study coordinators. Five lab-scale symmetric two- frameworks (MOFs), and transition metal oxides (TMOs) [11–13]. electrode supercapacitor devices, Cells 1–5, were prepared using the Further research has focussed on developing new electrolytes with higher below methods. stable voltage windows and greater ionic conductivities [14–16]. While improving the performance of these devices is crucial, successfully inte­ 2.1.1. Materials grating supercapacitors with other energy conversion and storage tech­ Materials were purchased from Sigma Aldrich (Merck) unless spec­ nologies, including in practical and wearable devices, is also critical for ified below. All materials were used without additional modification many future applications [17,18]. In all these papers, performance met­ unless specified below. rics such as total capacitance, specific capacitance, and internal resis­ Four different electrode materials were used in this study; (i) YP-50F tance are commonly reported by researchers [19–24]. However, with activated carbon, (ii) YP-80F activated carbon, (iii) ammonia- more groups beginning to venture into the field and an increasing number modulated Cu3(HHTP)2 (HHTP = 2,3,6,7,10,11-hexahydroxy­ of reported devices exhibiting non-ideal capacitive behaviour, variation triphenylene), and (iv) DMF-modulated Cu3(HHTP)2 (DMF = dime­ in data analysis can lead to inconsistent and unreliable results being re­ thylformamide). YP-50F and YP-80F were purchased from Kuraray. ported across different laboratories. Ammonia and DMF-modulated Cu3(HHTP)2 were synthesised using It is crucial to have consistent reporting of performance data between existing literature methods [39]. Cu3(HHTP)2 is a porous, layered, different researchers in this field. Many reports have emerged over the electrically conductive metal-organic framework (MOF). past decade discussing the best practices for data analysis and data Three different electrolytes were used in this study; (i) 1 M tetrae­ reporting for energy storage devices [25–38]. These studies have pri­ thylammonium tetrafluoroborate (NEt4BF4) in acetonitrile, (ii) 1 M tet­ marily focused on reporting the correct formulae and methods for data raethylphosphonium tetrafluoroborate (PEt4BF4) in acetonitrile, and (iii) analysis. However, there is yet to be an empirical study investigating undiluted 1-butyl-3-methylimidazolium bis(trifluoromethylsulfonyl) whether researchers in the field are correctly implementing these rec­ imide (BMIM-TFSI) ionic liquid. PEt4BF4 was purchased from TCI ommendations, and assessing the variation in data analysis and Chemicals. BMIM-TFSI was purchased from IoLiTec Ionic Liquids Tech­ reporting between different laboratories. Here, we address this issue by nologies. NEt4BF4 and PEt4BF4 were dried under vacuum at 100 ◦ C for 72 conducting the first interlaboratory study to assess the variation in h before being transferred to a N2 glovebox. Anhydrous acetonitrile reporting of performance metrics from galvanostatic charge-discharge (ACN) was purged with N2 for 3 h before being taken into a glovebox, (GCD) and cyclic voltammetry (CV) datasets for lab-scale fast-charging where it was further dried using activated 3 Å molecular sieves. BMIM- supercapacitor devices, including devices that display both ideal and TFSI was dried at room temperature under a dynamic vacuum for 120 h non-ideal capacitive behaviour. This study does not address variation in before being transferred to a N2 glovebox. experimental supercapacitor assembly, but only the data analysis of Participating groups did not have any information about the elec­ pre-supplied data sets. From this study, we conclude that, while most trode materials and electrolytes used to assemble the supercapacitors groups obtained similar results despite differences in analysis methods, when performing the analysis. misuse of formulae could lead to incorrect values being reported. Furthermore, different interpretations of terminology between labora­ 2.1.2. Electrode film preparation tories can result in different values being reported for a given perfor­ Using an established literature method, freestanding composite mance metric, potentially confusing researchers who are new to the electrode films were prepared [40]. The electroactive material(s) were field. In addition, the variation in results is significantly amplified if the mixed with ethanol (approx. 1.5 mL) and the mixture was sonicated for device shows non-ideal capacitive behaviour, highlighting that calcu­ 5 min to create a loose slurry. This slurry was combined with poly­ lating capacitance for such systems is more challenging than for devices tetrafluoroethylene (PTFE) dispersion (60 wt% in water) in a few drops 2 J.W. Gittins et al. Journal of Power Sources 585 (2023) 233637 of ethanol. The mixture was manually stirred under ambient conditions made with ammonia- and DMF-modulated Cu3(HHTP)2. In these films, until a film was formed. To ensure homogeneity, the film was kneaded the masses of components were calculated so that the final films had a for 20 min and then rolled into a freestanding electrode film using a composition of 85 wt% Cu3(HHTP)2, 10 wt% acetylene black, and 5 wt% homemade aluminium rolling pin. The film was then dried under vac­ PTFE. Films made with YP-50F and YP-80F activated carbons did not uum at 75–100 ◦ C for a minimum of 48 h to remove any remaining require any added conductive additive, and therefore had a final ethanol. To guarantee high rate performance, acetylene black (Thermo composition of 95 wt% activated carbon and 5 wt% PTFE. All films were Fisher Scientific; measured BET area = 62 m2 g− 1) was added to films of uniform thickness, measuring between 250 and 270 μm. Fig. 1. Summary of the data files sent to each of the participating groups, including a graphical depiction of the dataset, key cell parameters, characterisation parameters, and the requested analysis. m1 and m2 (mg) are the masses of the two electrodes in each cell. ν (mV s− 1) is the scan rate used in CV experiments. I (mA) is the constant charge and discharge current used in GCD experiments. 3 J.W. Gittins et al. Journal of Power Sources 585 (2023) 233637 2.1.3. Supercapacitor assembly The participants were asked to calculate a range of electrochemical Coin cells were assembled in Cambridge Energy Solutions CR2032 parameters from the provided datasets including total capacitance (F), SS316 coin cell cases. All cells were two-electrode cells and did not specific capacitance (F g− 1), and total internal resistance (Ω). The utilise a third reference electrode. Electrodes were cut from freestanding analysis requested from each dataset is summarised in Fig. 1. All results composite films using either 3 16 , 1 4 , or 3 8 inch electrode cutters, and / / / received have been anonymised and randomised. A full list of the re­ had areal mass loadings of between 9 and 11 mg cm− 2. The cells were ported results is shown in the Supplementary Information (SI Section 4). assembled in a N2 glovebox (O2 < 0.1 ppm; H2O < 0.1 ppm). It is important to note that not all participating groups supplied data for Cell 1 was assembled with YP-50F electrodes (3.3 mg, 3.1 mg, 0.317 each data file. For Files 1–4, only data from cycle 3 is presented in the cm2) and undiluted BMIM-TFSI electrolyte. Cell 2 was assembled with Results and Discussion section for simplicity. All cycles showed the same ammonia-modulated Cu3(HHTP)2 electrodes (1.9 mg, 2.0 mg, 0.178 trends. cm2) and 1 M PEt4BF4 in ACN electrolyte. Cell 3 was assembled with YP- 80F electrodes (3.2 mg, 3.1 mg, 0.317 cm2) and 1 M NEt4BF4 in ACN 3. Results and discussion electrolyte. Cell 4 was assembled with DMF-modulated Cu3(HHTP)2 electrodes (2.9 mg, 3.1 mg, 0.317 cm2) and 1 M NEt4BF4 in ACN elec­ The scope of this interlaboratory study was limited to assessing trolyte. Finally, Cell 5 was assembled with YP-50F electrodes (6.1 mg, consistency in the analysis and reporting of supercapacitor electro­ 6.6 mg, 0.713 cm2) and 1 M NEt4BF4 in ACN electrolyte. The volume of chemistry data. To achieve this, five electrochemistry datasets (Fig. 1) electrolyte added was kept consistent between cells (approximately 10 were sent to each participating group along with instructions for the drops from a Pasteur pipette). Whatman glass microfiber filters (GF/A) analysis to be performed on each file. Following the independent anal­ were used as separators, and were dried under vacuum at 100 ◦ C for 24 h ysis by the 14 participating groups, the coordinating group performed a before use. Each coin cell contained two stainless steel spacer disks and meta-analysis of the combined results. one stainless steel conical spring to ensure adequate pressure in the cells. The study also aimed to assess differences in the analysis and reporting The coin cells were hermetically sealed at 80 kg cm− 2 for 1 min before of data from cells displaying both “ideal” and “non-ideal” capacitive being removed for testing. performances. Therefore, Files 1 and 3 were from ideal supercapacitor cells, which display approximately linear triangular GCD and rectangular 2.1.4. Electrochemical measurements CV profiles, indicating charge storage is dominated by electric-double All electrochemical measurements were carried out under ambient layer contributions. In contrast, Files 2 and 4 were collected from non- conditions at the University of Cambridge using a BioLogic BCS-800 ideal supercapacitor cells, which display non-linear quasi-triangular Series ultra-precision battery cycler and a Biologic VSP-3e potentio­ GCD and quasi-rectangular CV profiles, indicating that either other stat. Each cell was used to generate one dataset for analysis, producing charge storage mechanisms (e.g. fast redox reactions) contribute to the the corresponding datasets File 1–5. A summary of each dataset, along charge stored, or that the device has a high resistance. The classification with cell assembly parameters, is provided in Fig. 1. of each dataset as ideal or non-ideal is indicated in Fig. 1. Galvanostatic charge-discharge (GCD) experiments were conducted on Cells 1 and 2. Variation in the magntiude of the applied constant 3.1. Galvanostatic charge-discharge (GCD) analysis current during the GCD experiments was negligible. Cyclic voltammetry (CV) experiments were carried out on Cells 3 and 4. A long-term cycling 3.1.1. Total capacitance GCD experiment was carried out on Cell 5. The electrochemical mea­ File 1 is from an ideal supercapacitor and displays a linear GCD surements carried out on each cell are also summarised in Fig. 1. profile, as expected for a device where the charge is solely stored by non-Faradaic ion adsorption in the electric double-layer. As shown in Fig. 2a, most participating groups obtained comparable results when 2.2. Interlaboratory study details calculating the total capacitance from File 1, with over 50% of partici­ pants lying within one sigma of the adjusted mean average. This is 14 research groups participated in the analysis study out of a total of despite differences in analysis methods such as the formulae used and 38 groups who were invited. Web of Science was used to find appro­ differences in determining the discharge slope. See the Supplementary priate research groups to invite. Groups were selected to be invited if Information for detailed information on the analysis methods used by they had published research containing the keyword “supercapacitors” each participating group. However, extreme anomalies were observed, within the past 3 years. No judgement was made on the quality of a accounting for approximately 14% of reported results. These anomalies group’s publications when inviting them to the study. Groups from a were due to incorrect formulae used to calculate the total capacitance, range of different countries were invited to attempt to ensure the di­ with the results being either too small or too large by a factor of two versity of the study. The role of the participating groups was to analyse (SI Section 3). the electrochemistry data provided by the coordinating group inde­ Despite the small size of this study, this striking result reinforces the pendently. Experimental work was carried out for the sole purpose of need to remind the community of the correct formula for calculating obtaining standardised datasets for the participating groups to analyse. total capacitance from linear ideal GCD datasets displaying double-layer The coordinating group (Y.C., J.W.G., D.L., and A.C.F. at the University charge storage to eliminate any potential anomalies in the literature. of Cambridge) did not provide analysis of the electrochemistry data for Having an agreed and established analysis protocol that is accessible to this study. Each participating group was provided with identical data all would help to ensure consistent and replicable results can be files and instructions, specifically the five datasets (File 1–5) as .txt files, generated. The correct general formula for total capacitance, CT, is and an instruction sheet detailing the required analysis. A copy of the shown in Equation (1) [28,30]: data files and the instruction sheet is provided as Supplementary Data. Researchers can check if they are performing the analysis of super­ I CT = ( ΔV ) (1) capacitor data correctly by analysing the data files provided and Δt comparing their results to those given for each data file in the Results and Discussion section below, and in SI Section 4. where I is the constant charging/discharging current (A), and ΔV Δt is the Participating groups submitted their analysis results to the coordi­ gradient of the discharge slope (V s− 1). CT has units of Farads (F). This nating group. The coordinating group then performed meta-analyses of equation assumes that the gradient is constant over the chosen voltage the provided results. See the Supplementary Information for information range of analysis. While most groups used Equation (1), Group 12 on how the results provided were processed (SI Section 1). analysed the dataset using a different approach also seen in the literature 4 J.W. Gittins et al. Journal of Power Sources 585 (2023) 233637 Fig. 2. Total capacitance (F) as reported by participating groups for (a) File 1, from an ideal supercapacitor, and (b) File 2, from a non-ideal supercapacitor. Plots on the left show all data points reported and plots on the right show a zoomed-in view of the enclosed section, highlighting the data distribution about the adjusted mean average where appropriate. This is the mean average obtained after omitting anomalous values that were calculated using incorrect methods. For File 1, anomalous values are excluded from the enclosed section of the plot. σ is the standard deviation in the adjusted mean values. The adjusted mean value for File 1 is 0.172 F. No adjusted mean average value was calculated for File 2 as the use of different equations during the analysis of this file makes the criteria for classification of an anomaly unclear. The highlighted data point in the results of File 2 (blue) is the total capacitance reported by Group 3. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.) [27,30,41]. This method involves calculating the energy stored in the non-ideal devices. If Equation (1) is used to calculate capacitance for a device by integration of the discharge curve and using this value to non-ideal device, researchers should only calculate this over the voltage calculate the capacitance via the energy-capacitance relationship for an range where the capacitance is constant, and should clearly report this ideal supercapacitor (SI Section 3). This approach gives comparable voltage range alongside the capacitance. It must be noted that several results to Equation (1) for ideal double-layer datasets. All groups ana­ groups raised concerns about analysing the non-ideal profile of File 2 lysed the discharge profile to calculate the capacitance. We recommend using ideal capacitive methods. It was suggested by three groups that, that research groups report the voltage range used to calculate the rather than capacitance, capacity is a more suitable electrochemical discharge slope as this can impact the final results. Groups should also property for non-ideal devices due to the variation of capacitance with report whether the Ohmic voltage drop was excluded from the calcu­ cell voltage [42–44]. Indeed, the use of capacity, would be expected to lation of the discharge slope. give identical results for different researchers, and would remove the In contrast to File 1, File 2 is from a non-ideal supercapacitor which ambiguity and confusion seen in Fig. 2b. Furthermore, capacity can be does not display a linear GCD profile, with the discharge slope varying calculated for all energy storage devices displaying a wide range of GCD with voltage (Fig. 1; File 2). 11 out of 14 groups analysed this dataset curves, and thus is an appropriate performance metric to compare the using Equation (1). This gave a larger variation in results compared to File performances of many energy storage devices, some of which may have 1 as the non-linear shape of the GCD amplified differences in analysis, unclear charge storage mechanisms. Therefore, we recommend calcu­ including the voltage range used to determine the discharge slope and lating and reporting capacity for all supercapacitors, especially those whether the Ohmic voltage drop was excluded from the calculation displaying non-linear discharge curves. This is crucial for ensuring (Fig. 2b). As with File 1, two groups used incorrect equations to calculate reliable reporting of performance from non-ideal devices. Capacity can the total capacitance. To attempt to account for the non-linearity of the be calculated using Equation (2) below: data, Groups 3 and 12 used approaches which correspond to calculating Capacity = I • Δt (2) the discharge energy via integration, and then calculating the capacitance from this (SI Section 3). While Group 12 converted the calculated where I is the discharge current (A), and Δt is the discharge time (s). This discharge energy into a capacitance by equating to the energy stored in an equation gives capacity in Coulombs (C), although it is often converted to ideal supercapacitor, the same approach they used for File 1, Group 3 have units of mAh. The discharge energy, calculated via integration, is equated to the energy stored in an ideal battery due to the non-linear also a reliable performance metric to indicate the performance of all nature of the discharge curve. This resulted in a lower reported capaci­ energy storage devices [27,41]. We recommend that this is also reported tance value of 0.012 F (highlighted in Fig. 2b in blue; SI Section 3). for all supercapacitors. Furthermore, this integral approach should be Ultimately, if capacitance is a function of voltage as for File 2, all of used to calculate the energy and power of non-ideal devices, and is also these methods only give a single average capacitance value which does applicable for ideal devices (SI Section 3). Both energy density and power not accurately reflect the complete behaviour of the cell. This may lead density should only be calculated and reported for two-electrode devices. to inflated capacitance values and overreporting of the performance of A previous report on the analysis of supercapacitor data suggested a 5 J.W. Gittins et al. Journal of Power Sources 585 (2023) 233637 different equation for the analysis of non-ideal devices (SI Section 3) capacitances of the positive and negative electrodes are equal. Although [26]. However, we do not believe that this method is correct as it gives a this may not be the case in practice, the value obtained from Equation capacitance value of 0.385 F for File 2, significantly higher than the (4) will still give an indication of the performance of a device and is other methods discussed above. We discourage the use of this equation often quoted in literature, as seen from the fact that 36–37% of the in the future. groups in this study reported Cg,2. We recommend that three-electrode measurements are also performed to independently evaluate the 3.1.2. Specific capacitance capacitance of both the positive and negative electrode independently in As shown in Fig. 3, most of the reported specific capacitance values their respective operating potential windows. Derivations for Equations for both File 1 and File 2 could be split into two distinct groups. In both (3) and (4) are stated in the Supplementary Information (SI Section 2). cases, 54–57% of values fall into the lower group, and 36–37% of values This result demonstrates that different interpretations of specific fall in the upper group, with the values in the upper group being capacitance exist within the community, and these can lead to signifi­ approximately four times larger than those in the lower group. Please cantly different reported values for the same performance metric. This note that most participating groups reported values in the same specific stresses the need for clearer definitions when reporting specific capaci­ capacitance group for both Files 1 and 2 apart from 2 participating tance to eliminate ambiguity in reported results. Therefore, we recom­ groups. There is a greater spread in the reported specific capacitance mend clearly defining how “specific capacitance” is interpreted when values in both the upper and lower groups for the non-ideal dataset File reporting values for this performance parameter in the literature. It is 2, reflecting the larger variation in the reported total capacitance dis­ crucial to indicate if the reported specific capacitance values refer to the cussed above. electrode material in a two-electrode cell, to the electrode material in­ The main reason behind this distinctive difference was how different dependent of device architecture (i.e., a “pseudo” single electrode researchers interpreted the term “specific capacitance”. For participants measurement), or to the overall device including non-active components reporting values within the lower group, specific capacitance was such as current collectors. This would prevent confusion within the interpreted as the specific capacitance of the full cell (i.e. the specific literature and allow for a more straightforward comparison of results. capacitance of the total mass of active electrode material in the two- The use of three-electrode measurements is also recommended to electrode cell assembly) [28]. The general formula used in this case is determine the capacitance of a single electrode. This would remove given in Equation (3): confusion on the terminology for two-electrode devices. CT Cg,1 = (3) 3.1.3. Internal resistance Mcell As shown in Fig. 4, reported total internal resistance values from where CT (F) is the total capacitance as calculated in the previous section both Files 1 and 2 can be divided into two groups, independent of and Mcell (g) is the total mass of the two electrodes in the cell (i.e., Mcell = whether the dataset is classified as ideal or non-ideal. This division is the me,1 + me,2; where me,1 and me,2 are the masses of the two electrodes, result of several groups using the incorrect formula, where the Ohmic respectively). Cg,1 has units of F g− 1. This equation normalises the cell voltage drop at the start of discharging is divided by the current applied capacitance by the total mass of the two electrodes in the cell. In this during the GCD experiment. Instead, the change in current when tran­ study, only the masses of the electrodes in each cell were provided to sitioning from charging to discharging, ΔI, needs to be used for this participating groups. One group recommended that specific capacitance calculation. Assuming the magnitude of the charge and discharge cur­ be calculated using the total mass of the overall cell including the sep­ rents is equal and that no potentiostatic or rest step is applied between arators, current collectors, casings, and other components. charge and discharge, as is the case for these datasets, the current is For participants within the upper group, specific capacitance was changing from +I to − I during this transition. Therefore, ΔI is equal to interpreted as the specific capacitance of the active electrode material in 2I, and the voltage drop should be divided by this value to accurately a single electrode (i.e., independent of device architecture) [25,28,38]. calculate the total internal resistance, as in Equation (5) [28,31,45]: The general formula used in this case is given by Equation (4): ΔVdrop R= (5) 2CT 2I Cg,2 = (4) mave where R is the total internal resistance (Ω), ΔVdrop is the Ohmic voltage drop (V), and I is the charging/discharging current applied (A). Please where mave is the average mass of one electrode in the cell (mave = ½ (me,1 note that ΔVdrop, the Ohmic voltage drop, is distinct from ΔV, the change + me,2)). Cg,1 has units of F g− 1. This interpretation results in a specific in voltage during discharge, given in Equation (1). This result demon­ capacitance value four times greater than the previous interpretation. strates the need to reinforce correct analysis procedures set out in However, it must be noted that Equation (4) assumes that the Fig. 3. Specific capacitance results (F g− 1) as reported by participating laboratories for (a) File 1 (ideal), and (b) File 2 (non-ideal). Two distinct groups of values are seen in both plots (highlighted). The mean value for the upper group in File 1 is 108.0 F g− 1. The mean value for the lower group in File 1 is 26.9 F g− 1. The mean value for the upper group in File 2 is 39.8 F g− 1. The adjusted mean value for the lower group in File 2 is 10.5 F g− 1. 6 J.W. Gittins et al. Journal of Power Sources 585 (2023) 233637 Fig. 4. Total internal resistance (R, Ω) as reported by participating groups for (a) File 1 (ideal), and (b) File 2 (non-ideal), highlighting the mean average and an interval of one standard deviation, σ, either side of this value. Using Equation (5), total internal resistance values of approx. 78.6 Ω and 17.5 Ω are obtained for Files 1 and 2, respectively. previous studies as they are not being strictly followed by the commu­ recommend the agreement and application of a consistent criterion for nity [31,34]. Incorrect calculation of the total internal resistance will measuring the voltage drop from GCD cycles, as outlined in previous also lead to inaccurate reporting of the power, P, of a device (in Watts; work [31,45]. For this study, the internal resistance was calculated at a W), which can be expressed as shown in Equation (6) for an ideal single, fixed applied current. Measuring the voltage drop across a series supercapacitor [31,33]: of GCD experiments with different applied currents would give a more reliable resistance calculation. Vcell 2 P= (6) 4R 3.2. Cyclic voltammetry (CV) analysis This equation is only valid for ideal supercapacitors which display linear GCD plots. See the SI for details on calculating the power of a non- 3.2.1. Total capacitance ideal device (SI Section 2). The reported total capacitance values from CV data, shown in Fig. 5, Further variation within each of the two groups of values is a result of show a similar pattern to those calculated from GCD data shown in differences in determining the voltage drop from the GCD data. Fig. 2. As discussed in Section 1.1, extreme anomalies were observed for Assigning the voltage drop is highly subjective and varies from both Files 3 and 4, accounting for approximately 14–20% of reported researcher to researcher. To eliminate this variation going forwards, we results. These were due to the use of incorrect formulae during analysis. Fig. 5. Total capacitance results (F) collected from participating groups for (a) File 3 from an ideal supercapacitor, and (b) File 4 from a non-ideal device. Plots on the left show all data points reported and plots on the right show the zoomed-in views of the enclosed section, highlighting the adjusted mean average and an interval of one standard deviation, σ , on either side of this value where appropriate. The adjusted mean for File 3 is 0.163 F. No adjusted mean average value is provided for File 4 due to ambiguity over whether capacitance should be calculated for this file. 7 J.W. Gittins et al. Journal of Power Sources 585 (2023) 233637 This highlights the need to remind the community of the correct formula (Fig. 6). For the upper group, the specific capacitance was calculated for calculating total capacitance from CV data to eliminate anomalies in using Equation (4), stated above as Cg,2. For the middle group, the the literature. The correct formula for calculating total capacitance from specific capacitance was calculated using an incorrect formula that CV data for ideal supercapacitors is given in Equation (7): differs from Equation (4) with the factor of two on the numerator ∫ V2 missing. For the lower group, specific capacitance was calculated using CT = V1 I dV (7) Equation (3), stated above as Cg,1. (V2 − V1 ) • v The greater variety of formulae used to calculate specific capacitance for CV datasets compared to GCD datasets was due to additional where (V2 − V1) is the voltage window, and V2 and V1 are the bounds of confusion when using the area of the entire CV cycle during the analysis, the discharge voltage window where capacitive behaviour is observed resulting in the use of an incorrect formula for calculating the specific (V), v is the scan rate (V s− 1), I is the discharge current (A), and dV is the capacitance from CV data. Overall, this data reinforces several points infinitesimal change in cell voltage (V) [28,30]. In this study, 6 of the 14 stated previously. Firstly, one needs to clearly define what “specific participating groups integrated across the entire CV curve (i.e., charge capacitance” means when reporting values for this metric to avoid and discharge) when calculating total capacitance. This requires confusion. Secondly, the community needs to be reminded of the correct dividing by an additional factor of two compared to Equation (7) above formula for calculating specific capacitance from CV data, as 29% of to account for this. However, in future, we recommend that all re­ participants used an incorrect formula in this study. The three groups of searchers use the discharge area only (i.e., negative current voltam­ specific capacitance values are less visible for File 4 as fewer participants metric region) when calculating total capacitance from CV data as this reported values for this dataset due to its non-ideal behaviour. This avoids including contributions from any irreversible Faradaic reactions further illustrates that it may be more suitable to characterise energy that may occur during charging. storage devices with non-ideal charge storage mechanisms with other, Similar to the GCD data discussed in Section 1.1, the CV datasets more appropriate performance metrics. consisted of one from an almost ideal supercapacitor (File 3), which A minor source of variation in the capacitance values calculated from displayed a rectangular CV profile, and another from a non-ideal device CV data was whether a manual or computational method was being used (File 4), which displayed a quasi-rectangular CV profile. As with the to calculate the CV integral. The computational integration calculation non-ideal GCD dataset (File 2), several groups raised concerns regarding is often more accurate than manual analysis, where approximations to calculating capacitance for File 4. As noted previously, capacity may be rectangles are often used. Additionally, analysis methods for addressing a more suitable electrochemical property for non-ideal devices. This pseudocapacitive behaviour, such as selectively analysing the linear echoes previous reports on best practices, and the non-ideal behaviour section of the CV profile, can lead to an overestimation of the integral for resulted in a more significant variation in results when calculating the capacitive region. To eliminate those sources of variation, having an capacitance for File 4 than File 3 [42–44]. established protocol is crucial. This work also finds that the spread of reported total capacitance values calculated from CV datasets is greater than that from GCD datasets. This can be seen by comparing the standard deviations for the 3.3. Long-term cycling analysis reported total capacitance values from File 1 (1.5%) and File 3 (4.0%), a GCD and CV dataset from an ideal device, respectively. This shows that The analysis of long-term GCD cycling data was optional. In this calculating performance metrics from GCD datasets is more reliable than analysis, participating groups were asked to report the capacitance from CV datasets. This is primarily due to the large variation in methods retention after 10,000 cycles (Fig. 7). Only 3 out of 14 groups could analyse for integrating the discharge curve of the CV. This study, therefore, all 10,000 charge-discharge cycles. All of these groups used a computa­ recommends that researchers use GCD datasets to calculate performance tional method to analyse the data. Several groups partially analysed the metrics instead of CV datasets where possible. CV data should primarily long-term cycling data, but did not report capacitance retention values. be used to qualitatively assess the charge storage mechanism of the See the Supplementary Information for more details (SI Section 4.5). supercapacitor. Of the 3 groups who reported capacitance retention values, two chose to define this relative to the capacitance of the 1st cycle. In 3.2.2. Specific capacitance contrast, the other group defined this relative to the maximum capaci­ Unlike the specific capacitance results reported from GCD datasets tance obtained during the long-term cycling. In the future, we recom­ (Section 1.2), the specific capacitance results from CV datasets can be mend that all groups report capacitance retention relative to the divided into 3 distinct groups based on three different formulae used maximum capacitance to account for stabilisation of cycling. This is shown in Equation (8): Fig. 6. Specific capacitance results (F g− 1) collected from participating groups for (a) File 3 (ideal), where three distinctive three groups of reported values are seen, and (b) File 4 (non-ideal), where three groups of values are also present. The mean value for the upper group in File 3 is 104.9 F g− 1. The mean value for the lower group in File 3 is 26.0 F g− 1. The mean value for the upper group in File 4 is 44.7 F g− 1. The adjusted mean value for the lower group in File 4 is 10.8 F g− 1. The mean value for the middle group is not reported as these values have been calculated using incorrect equations. 8 J.W. Gittins et al. Journal of Power Sources 585 (2023) 233637 Fig. 7. (a) Capacitance retention data (%) from long-term GCD cycling data collected from participating groups. (b) A zoomed in view of the data. Cnth cycle Table 1 Capacitance Rentention = × 100% (8) Cmax Recommended formulae for GCD and CV analysis for supercapacitor devices. Performance Galvanostatic charge-discharge Cyclic voltammetry where Cnth cycle is the capacitance calculated for the nth cycle and Cmax is metric (GCD) analysis (CV) the maximum capacitance achieved after stabilisation. This equation Total capacitance I ∫ V2 I dV allows capacitance retention up to the nth cycle to be calculated. To CT = ( ΔV ) CT = V1 (V1 − V2 ) • v allow more groups to obtain an in-depth observation of how perfor­ Δt mance changes over a long period, an accessible and standardised ∫ V2 Capacity Capacity = I • Δt Capacity = I dt V1 analysis program for long-term cycling data is required. Specific Two-electrode cell: Two-electrode cell: capacitance CT CT Cg,1 = Cg,1 = Mcell Mcell 4. Limitations Pseudo single electrode: Pseudo single electrode: 2CT 2CT Cg,2 = Cg,2 = The scope of this study was limited to focus on the analysis of the mave mave most common techniques present in the wider literature and in industry. Internal ΔV N/A R = resistance 2I As a result, there are several limitations to this interlaboratory study. The most relevant ones are listed below: 1. When reporting specific capacitance, one should always make sure to 1. Only two-electrode cell data were provided and analysed in this clarify whether it is the specific capacitance of the electrode material study, even though three-electrode cells are also widely used in in a two-electrode cell, or the specific capacitance of the electrode research for supercapacitor devices to calculate the specific capaci­ material independent of device architecture (i.e., a “pseudo” single tance of electrode materials separately upon positive and negative electrode measurement). This recommendation was suggested by charging [34]. several participating groups in this study. 2. For simplicity, Electrochemical impedance spectroscopy (EIS) data 2. For devices displaying non-ideal behaviour, other performance were not provided for determination of resistance. metrics, such as capacity and discharge energy, need to be calculated 3. The determination of internal resistance was not split into equivalent and reported alongside any average capacitance values [42–44]. series resistance (ESR) and equivalent distribution resistance (EDR) 3. When using GCD datasets to calculate capacitance, the voltage range [31]. used to calculate the discharge slope should be reported, and the 4. As the participating groups were provided with datasets as measured Ohmic voltage drop should be excluded from this calculation. in our laboratory, differences in electrode fabrication, cell assembly, 4. Where possible, GCD datasets should be used to calculate perfor­ and electrochemical measurements between laboratories were not mance metrics instead of CV datasets. assessed. Variations in the manufacturing process, including mass 5. Agreement and application of consistent criteria are necessary for loading, electrode thickness, and pressurisation, can significantly accurate determination of the Ohmic voltage drop in GCD affect device performance [46,47]. experiments. An extension of this study would include the analysis of three- 6. Conclusions electrode and EIS data. A follow-up study to assess how differences in cell assembly also impact reported performance between laboratories In this work, the first interlaboratory study on the analysis of would provide further invaluable recommendations for reducing supercapacitor data was conducted. This study shows that, while most of experimental variation between research groups. the participants reported similar results for different performance met­ rics calculated from GCD and CV datasets, some groups reported 5. Recommendations for ideal and non-ideal supercapacitor incorrect values due to the use of incorrect formulae during analysis. As datasets a result, we remind the community of the correct analysis formulae to ensure more reliable reporting of performance metrics going forwards. Groups must employ correct formulae for electrochemical calcula­ In addition, different valid interpretations of “specific capacitance” be­ tions and follow recommendations for the best practices for analysing tween laboratories resulted in a range of values being reported for this and reporting data from the ideal supercapacitor energy storage devices. performance metric. To avoid confusion going forwards, researchers Here, we reiterate the standard formulae and the key recommendations should clarify their interpretation of “specific capacitance” when as reflected by the current study (Table 1). reporting values. This study also found that the impact of different Additionally, it is important to reinforce the following: practices in data analysis becomes more significant for electrochemical profiles showing less ideal capacitive behaviour. We support previous 9 J.W. Gittins et al. Journal of Power Sources 585 (2023) 233637 recommendations that non-ideal datasets should not be analysed using MUR support under the projects “National Centre for Sustainable formulae for ideal supercapacitors, in which charge is solely stored via Mobility- CNMS-Spoke 13-MOST and “ECOSYSTEM FOR SUSTAINABLE non-Faradaic adsorption of ions in the electric double-layer, to avoid TRANSITION IN EMILIA-ROMAGNA-ECOSISTER” of the National Re­ inaccurate reporting of performances, and capacity should be reported covery and Resilience Plan (NRRP-PNRR). for such devices. In the future, establishing an accessible and stand­ ardised open-access analysis protocol for calculating performance met­ Appendix A. Supplementary data rics of fast-charging energy devices is required to improve the consistency of analysis and reporting. An agreed computational analysis Supplementary data to this article can be found online at https://doi. program could benefit the community by further eliminating variations org/10.1016/j.jpowsour.2023.233637. caused by subjectivity in manual analysis. Further efforts are recom­ mended to consider the key findings of this study when developing, for References example, an optimized machine-learning algorithm that automatically derives the relevant key data from various data files under different [1] Z. Yang, J. Zhang, M.C.W. Kintner-Meyer, X. Lu, D. Choi, J.P. Lemmon, J. Liu, Electrochemical energy storage for green grid, Chem. Rev. 111 (2011) 3577–3613, testing conditions. 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