Post-Doc description Title: Physical characterization of innovative supercapacitors using equivalent electrical circuit models Research group: Hydrogen and Electrochemical Systems Laboratory: Laboratoire d’Énergie et de Mécanique Théoriques et Appliquées (LEMTA) – UMR 7563 CNRS - Université de Lorraine, Nancy, France Contact: Julia Mainka (julia.mainka@univ-lorraine.fr), Olivier Lottin (Olivier.lottin@univ-lorraine.fr) Period and duration: 12 month starting May 3rd, 2021 Gross salary/month: 2800€ Keywords: electric energy storage, supercapacitors, MXene, modeling, graphene oxide, equivalent electrical circuits, electrochemical impedance spectroscopy, genetic algorithms Description: The Hydrogen and Electrochemical Systems (HSE) team at LEMTA has several years of experience in the characterization and modeling of polymer membrane fuel cells (PEMFC) [1-5]. We are currently applying the same approach to the development of models for the characterization of supercapacitors (SC), useful for example in the context of fuel cell hybridization [6]. This work is carried out in collaboration with North Carolina State University (NCSU, USA) and Deakin University (Australia), which are developing fiber-shaped supercapacitors (FSCs) integrating innovative 2D materials. The work to be carried out in this post-doctoral program aims at developing models in the form of equivalent electrical circuit (EECs) that are as generic as possible so that they can be applied to all kinds of SCs, including those of the NCSU and Deakin University, with a clear consideration of the physico-chemical phenomena at the origin of their electrical behavior. The modeling work will focus primarily on the FSCs from NCSU and Deakin University, which will eventually be used to manufacture tissues capable of storing electricity as shown in Figure 1 [7- 9]. However, it is planned to test the models on more conventional commercial devices, as well as on those of other partners [6].

Figure 1 : Fiber-shaped supercapacitors used for the manufacture of connected textiles capable of storing electricity.

The electrodes of these fiber-shaped supercapacitors are manufactured from innovative 2D materials, including graphene oxides and MXene (a set of transition metal carbides, nitrides and carbonitrides [10]) by wet-spinning as shown in Figure 2 in the example of the NCSU set up [7]. Beyond the applications, which are, after all, quite remote, it is necessary to characterize as well as possible the electrical behavior of these devices to better understand their operation and to improve their performance.

Figure 2 : Principle of the wet-spinning method developed by NCSU for manufacturing the fiber SCs [7].

Indeed, supercapacitors are devices in which energy can be stored in different forms, purely capacitive, electrochemical or in some cases by ion intercalation [11, 12]. This is notably the case for SCs integrating graphene oxides and MXenes [9, 13-15]. The analysis of their electrical behavior can be done in the time domain by measuring the voltage during charge/discharge or in the frequency domain by measuring the complex impedance at a fixed voltage. Its interpretation is then done with electrical models whose elements must - ideally - keep a physical meaning. However, the current models are often non-analytical and above all non-transposable between time and frequency domains [16]. A first objective is the derivation of analytical models that can be used for the characterization of the FSCs in time and frequency domains with a clear consideration of physics at the material scale. The method of choice will be electrochemical impedance spectroscopy (EIS). The usual representation is done in a Nyquist diagram plotting the negative imaginary part of the impedance versus the real part as shown in Figure 3 in the example of a typical spectrum of a FSC manufactured by NCSU.

Figure 3 : Nyquist plot of an impedance spectrum measured on a fiber SC at 0V for frequencies between 1 𝑚𝐻𝑧 and 1𝑀𝐻𝑧.

A specific aspect of SCs integrating 2D materials is the presence of different charge storage mechanisms, electrochemical [9, 14, 17] as suggested by the faradic loop at medium frequencies (above 39 𝐻𝑧 in the above example) and electrostatic [12] corresponding to the inclined slope at low frequencies. The interpretation of the spectra will be done by models in the form of EECs in which the different physical and chemical phenomena are represented by electrical elements such as resistors and capacitors [1, 2, 7, 11, 17-20].

Figure 4 : Example of an EEC developed by our group used for the characterization of the fiber SCs. 𝑅𝑠 is the series

resistance, 𝑅𝑒𝑙 the ionic resistance, the parallel connection of 𝐶𝑃𝐸𝑐𝑡 and 𝑅𝑐𝑡 represents redox reactions and 𝑍𝑊 the impedance related to diffusion inside the electrode. 𝐶𝑃𝐸𝑑𝑙 represents additional electrostatic charge storage.

Figure 4 shows an example of a model developed for the characterization of the SCs at the origin of the spectrum in Figure 3 that is currently being submitted for publication in a scientific journal. A first modeling objective will be the improvement of the existing EEC to be able to distinguish between charge storage by electrical double layer and by ion intercalation which are both currently included in the electrostatic contribution. Ideally, it will then be a question of identifying a single model applicable in time and frequency domains. It will also be necessary to carry out measurements in the laboratory in order to validate the theoretical

results. To do so, the post-doctoral fellow will be able to rely on the team's know-how in the field of fine and instrumented characterization of electrochemical systems such as fuel cells [4, 21-25]. In parallel to the derivation of the electrical model, different numerical resolution algorithms can be tested in order to find the best match between numerical and experimental results. To do so, genetic algorithms will be tested and compared to classical least squares methods. The numerical resolution is usually done with Matlab, but the opening towards other software (Python, C++...) is possible.

Figure 5 : Example of experimental impedance spectra measured on NCSU fiber SCs of different length at 0V for frequencies

between 1 𝑚𝐻𝑧 and 1𝑀𝐻𝑧 and interpolation curves obtained with the EEC of Figure 4.

A second objective will be the application of the best model(s) for the characterization of different fiber-shaped and more classical supercapacities according to their composition, morphology and connection or the characteristics of the wet-spinning manufacturing process. This characterization will support our collaborators in the optimization process of their electrical energy storage devices.

The candidate should ideally have a background in physico-chemistry, electrochemistry

and/or electricity and an experience in mathematical and numerical modeling and should

expect to work mostly under a Matlab environment.

[1] J. Mainka, G. Maranzana, J. Dillet, S. Didierjean et O. Lottin, «Effect of Oxygen depletion along

the air channel of a PEMFC on the Warburg Diffusion Impedance,» J. Electrochem. Soc., vol.

157, n° %111, pp. B1561-B1568, 2010.

[2] S. Touhami, J. Mainka, J. Dillet, S. Ait Hammou Taleb and O. Lottin, "Transmission Line

Impedance Models Considering Oxygen Transport Limitations in Polymer Electrolyte Membrane

Fuel Cells," J. Electrochem. Soc., vol. 166, no. 15, pp. F1209-F1217, 2019.

[3] J. Mainka, G. Maranzana, J. Dillet, S. Didierjean et O. Lottin, « On the estimation of high

frequency parameters of Proton Exchange Membrane Fuel Cells via Electrochemical Impedance

Spectroscopy,» J. Pow. Sources, vol. 253, pp. 381-391, 2014.

[4] G. Maranzana, J. Mainka, O. Lottin, J. Dillet, A. Lamibrac, A. Thomas et S. Didierjean, « A

PEMFC impedance model taking into account convection along the air channel: on the bias

between the low frequency limit of the impedance and the slope of the polarization curve,»

Electrochim. Acta, vol. 83, pp. 13-27, 2012.

[5] J. Mainka, G. Maranzana, A. Thomas, J. Dillet, S. Didierjean et O. Lottin, « One-dimensional

Model of Oxygen Transport Impedance Accounting for Convection Perpendicular to the

Electrode,» Fuel Cells, vol. 12, n° %15, pp. 848-861, 2012.

[6] S. Aït Hammou Taleb, D. Brown, J. Dillet, P. Guillemet, J. Mainka, O. Crosnier, C. Douart, T.

Brousse et O. Lottin, «Direct Hybridization of Polymer Membrane Exchange Membrane Surface

Fuel Cell with Small Aqueous Supercapacitors,» Fuel Cells, vol. 18, n° %13, pp. 299-305, 2018.

[7] N. He, Q. Pan, Y. Liu and W. Gao, "Graphene-Fiber-Based Supercapacitors Favor N-Methyl-2-

pyrrolidone/Ethyl Acetate as the Spinning Solvent/Coagulant Combination," ACS Appl. Mater.

Interfaces, vol. 9, pp. 24568-24576, 2017.

[8] N. He, W. Shan, J. Wang, Q. Pan, J. Qu, G. Wang and W. Gao, "Mordant inspired wet-spinning of

graphene fibers for high performance flexible supercapacitors," J. Mater. Chem. A, vol. 7, pp.

6869-6876, 2019.

[9] J. Zhang, S. Seyedin, S. Qin, Z. Wang, S. Moradi, F. Yang, P. A. Lynch, W. Yang, J. Liu, X. Wang

and J. M. Razal, "Highly Conductive Ti3C2Tx MXene Hybrid Fibers for flexible and elastic Fiber-

Shaped Supercapacitors," Small, vol. 15, p. 1804732, 2019.

[10] M. Naguib, V. Mochalin, M. W. Barsoum and Y. Gogotsi, "MXenes: A New Family of Two-

Dimensional Materials," Adv. Mater., vol. 26, pp. 992-1004, 2014.

[11] L. M. Da Silva, R. Cesar, C. M. Moreira, J. H. Santos, L. G. De Souza, B. Morandi Pires, R.

Vicentini, W. Nunes and H. Zanin, "Reviewing the fundamentals of supercapacitors and the

difficulties involving the analysis of the electrochemical findings obtained for porous electrode

materials," Energy Storage Mater., vol. 27, pp. 555-590, 2020.

[12] B. E. Conway, Electrochemical Supercapacitors: Scientific Fundamentals and Technological

Applications, Springer US, 1999.

[13] C. Zhan, M. Naguib, M. Lukatskaya, P. R. C. Kent, Y. Gogotsi and D. Jiang, "Understanding the

MXene Pseudocapacitance," J. Phys. Chem. Lett., vol. 9, pp. 1223-1228, 2018.

[14] M. Boota, B. Anasori, C. Voigt, M. Q. Zhao, M. W. Barsoum and Y. Gogotsi, "Pseudocapacitive

Electrodes Produced by Oxidant-Free Polymerization of Pyrrole between the Layers of 2D

Titanium Carbide (MXene)," Adv. Mater., vol. 28, pp. 1517-1522, 2016.

[15] X. Mu, D. Wang, F. Du, G. Chen, C. Wang, Y. Wei, Y. Gogotsi, Y. Gao and Y. Dall'Agnese,

"Revealing the Pseudo-Intercalation Charge Storage Mechanism of MXenes in Acidic

Electrolyte," Adv. Funct. Mater., p. 1902953, 2019.

[16] R. German, A. Hammar, R. Lallemand, A. Sari and P. Venet, "Novel experimental identification

method for Supercapacitor Multi-Pore Model in order to monitor the State of Health," IEEE

Transaction on Power Electronics, vol. 31, no. 1, pp. 548-559, 2016.

[17] P. Navalpotro, M. Anderson, R. Marcilla et J. Palma, «Insights into the energy storage

mechanism of hybrid supercapacitors with redox electrolytes be electrochemical Impedance

Spectroscopy,» Electrochim. Acta, vol. 263, pp. 110-117, 2018.

[18] L. Zhang, X. Hu, Z. Wang, F. Sun and D. G. Dorrell, "A review of supercapacitor modeling,

estimation, and applications: A control/management perspective," Renew. Sust. Energ. Rev.,

vol. 81, pp. 1868-1878, 2018.

[19] C. Turpin, D. Van Laethem, B. Morin, O. Rallières, X. Roboam, O. Verdu et V. Chaudron,

«Modelling and analysis of an original direct hybridization of fuel cells and ultracapacitors,»

Math. Comput. Simulat., vol. 131, pp. 76-87, 2017.

[20] A. Lasia, Electrochemical Impedance Spectroscopy and its Applications, New York: Springer New

York, 2014.

[21] A. Lamibrac, G. Maranzana, O. Lottin, J. Dillet, J. Mainka, S. Didierjean, A. Thomas et C. Moyne,

« Experimental characterization of internal currents during the start-up of a proton exchange

membrane fuel cell,» J. Pow. sources, vol. 196, n° %122, pp. 9451-9458, 2011.

[22] S. Touhami, L. Dubau, J. Mainka, J. Dillet, M. Chatenet et O. Lottin, « Anode aging in polymer

electrolyte membrane fuel Cells I: Anode monitoring by ElectroChemical impedance

spectroscopy,» J. Pow. Sources, vol. 471, p. 228908, 2021.

[23] S. Abbou, J. Dillet, G. Maranzana, S. Didierjean et O. Lottin, «Local potential evolutions during

proton exchange membrane fuel cell operation with dead-ended anode–Part I: Impact of water

diffusion and nitrogen crossover,» J. Pow. sources, vol. 340, pp. 337-346, 2017.

[24] S. Abbou, J. Dillet, G. Maranzana, S. Didierjean et O. Lottin, «Local potential evolutions during

proton exchange membrane fuel cell operation with dead-ended anode – Part II: Aging

mitigation strategies based on water management and nitrogen crossover.,» J. Pow. Sources,

vol. 340, pp. 419-427, 2017.

[25] J. Dillet, D. Spernjak, A. Lamibrac, G. Maranzana, R. Mukundan, J. Fairweather, S. Didierjean, R.

I. Borup et O. Lottin, «Impact of flow rates and electrode specifications on degradations during

repeated startups and shutdowns in polymer-electrolyte membrane fuel cells,» J. Pow. Sources,

vol. 250, pp. 68-79, 2014.