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PCCP Paper 22 B. E. Conway, Electrochemical Supercapacitors, New York, Kluwer Academic/Plenum Publishers, 1993. 23 For recent theoretical work on this subject, in the specific context of the lithium-ion battery, see, e.g., J. Lu ̈ck and A. Latz, Modeling of the electrochemical double layer and its impact on intercalation reactions, Phys. Chem. Chem. Phys., 2018, 20, 27804. 24 This has caused confusion in the pedagogical literature, especially because the spontaneous generation of the dou- ble layer meets Volta’s original definition of the emf as a mechanism that causes and maintains the separation of opposite charges. See, e.g., D. Roberts, How batteries work: A gravitational analog, Am. J. Phys., 1983, 51, 829. Our point here is that both supercapacitors and batteries develop double layers, but only the battery can drive a closed circulation of current. 25 P. Horowitz and W. Hill, The Art of Electronics, 3rd edn Cambridge, Cambridge U. P., 2015, p. 71. 26 P. Le Corbeiller, The non-linear theory of the maintenance of oscillations, J. Inst. Electr. Engrs., 1936, 79, 361. 27 P. Le Corbeiller, Theory of prime movers, in Non-Linear Mechanics, ed. K. O. Friedrichs, P. Le Corbeiller, N. Levinson and J. J. Stoker, Providence, Brown U., 1943, pp. 2.1–2.18. 28 A. A. Andronov, A. A. Vitt and S. E`. Khakin, in Theory of Oscillators, ed. W. Fishwick, Mineola, NY, Dover, 1987 [1966], p. 200. 29 L. Y. Gorelik, A. Isacsson, M. V. Voinova, B. Kasemo, R. I. Shekhter and M. Jonson, Shuttle Mechanism for Charge Transfer in Coulomb Blockade, Phys. Rev. Lett., 1998, 80, 4526 [arXiv:cond-mat/9711196]. 30 C. W. W ̈achtler, P. Strasberg, S. H. L. Klapp, G. Schaller and C. Jarzynski, Stochastic thermodynamics of self-oscillations: the electron shuttle, New J. Phys., 2019, 21, 073009 [arXiv:1902.08174 [cond-mat.stat-mech]]. 31 C. W. W ̈achtler, P. Strasberg and G. Schaller, Proposal of a Realistic Stochastic Rotor Engine Based on Electron Shut- tling, Phys. Rev. Appl., 2019, 12, 024001 [arXiv:1903.07500 [cond-mat.stat-mech]]. 32 C. H. Hamann, A. Hamnett and W. Vielstich, Electrochemistry, 2nd edn, Weinheim, Wiley-VCH, 2007, sec. 5.2.2. 33 E. von Hauff, Impedance Spectroscopy for Emerging Photo- voltaics, J. Phys. Chem. C, 2019, 123, 11329. 34 S. L. Carnie and G. M. Torrie, The Statistical Mechanics of the Electrical Double Layer, Adv. Chem. Phys., 1984, 56, 141. 35 C. W. Monroe, Mechanics of the Ideal Double-Layer Capa- citor, J. Electrochem. Soc., 2020, 167, 013550. 36 M. Favaro, B. Jeong, P. N. Ross, J. Yano, Z. Hussain, Z. Liu and E. J. Crumlin, Unravelling the electrochemical double layer by direct probing of the solid/liquid interface, Nat. Commun., 2016, 7, 12695. 37 See, e.g., S. H. Strogatz, Nonlinear Dynamics and Chaos, 2nd edn, Boulder, Westview Press, 2014, sec. 8.2. 38 R. Alicki, D. Gelbwaser-Klimovsky and A. Jenkins, A thermo- dynamic cycle for the solar cell, Ann. Phys. (N. Y., NY, U. S.), 2017, 378, 71 [arXiv:1606.03819 [cond-mat.stat-mech]]. 39 For such a treatment, in the particular case of the Li-ion battery, see K. E. Thomas, J. Newman and R. M. Darling, 3 For a modern historical survey of this extremely long- running debate, see H. Kragh, Confusion and Controversy: Nineteenth-Century Theories of the Voltaic Pile, in Nuova Voltiana: Studies in Volta and His Times, vol. I, ed. F. Bevilacqua and L. Fragonese, Milan, Hoepli, 2000, pp. 133–167. 4 H. Chang, How Historical Experiments Can Improve Scien- tific Knowledge and Science Education: The Cases of Boil- ing Water and Electrochemistry, Sci. Educ., 2011, 20, 317. 5 H. Chang, Who cares about the history of science?, Notes Rec., 2017, 71, 91. 6 E. Purcell and D. J. Morin, Electricity and Magnetism, 3rd edn, Cambridge, UK, Cambridge U. P., 2013, p. 127. 7 W. M. Saslow, Voltaic cells for physicists: Two surface pumps and an internal resistance, Am. J. Phys., 1999, 67, 574. 8 R. Baierlein, The elusive chemical potential, Am. J. Phys., 2001, 69, 423. 9 A. Singer, Z. Schuss, B. Nadler and R. S. Eisenberg, Memory- less control of boundary concentrations of diffusing parti- cles, Phys. Rev. E: Stat., Nonlinear, Soft Matter Phys., 2004, 70, 061106. 10 The term elastic capacitor was first used, in a biophysical context, in J. M. Crowley, Electrical Breakdown of Bimolecular Lipid Membranes as an Electromechanical Instability, Biophys. J., 1973, 13, 711. 11 M. B. Partenskii and P. C. Jordan, Squishy capacitor’ model for electrical double layers and the stability of charged interfaces, Phys. Rev. E: Stat., Nonlinear, Soft Matter Phys., 2009, 80, 011112. 12 M. B. Partenskii and P. C. Jordan, Relaxing gap capacitor models of electrified interfaces, Am. J. Phys., 2011, 79, 103. 13 R. Alicki, D. Gelbwaser-Klimovsky and A. Jenkins, The leaking elastic capacitor as a model for active matter, arXiv:2010.05534 [physics.class-ph], submitted to Phys. Rev. E: Stat., Nonlinear, Soft Matter Phys. 14 C. E. Brennen, Hydrodynamics of Pumps, Cambridge, Cam- bridge U. P., 2011, ch. 2. 15 M. T. M. Koper, Non-linear phenomena in electrochemical systems, J. Chem. Soc., Faraday Trans., 1998, 94, 1369. 16 D. Li, Y. Sun, Z. Yang, L. Gu, Y. Chen and H. Zhou, Electrochemical oscillation in Li-ion batteries, Joule, 2018, 2, 1265. 17 R. Imbihl and G. Ertl, Oscillatory kinetics in heterogeneous catalysis, Chem. Rev., 1995, 95, 667. 18 M. V. F. Delmonde, L. F. Sallum, N. Perini, E. R. Gonzalez, R. Schlo ̈gl and H. Varela, Electrocatalytic Efficiency of the Oxidation of Small Organic Molecules under Oscillatory Regime, J. Phys. Chem. C, 2016, 120, 22365. 19 M. H. Braga, J. E. Oliveira, A. J. Murchison and J. B. Goodenough, Performance of a ferroelectric glass electrolyte in a self-charging electrochemical cell with negative capacitance and resistance, Appl. Phys. Rev., 2020, 7, 011406. 20 A. Isakova and K. Novakovic, Oscillatory chemical reactions in the quest for rhythmic motion of smart materials, Eur. Polym. J., 2017, 95, 430. 21 See Ref. [14], ch. 8. View Article Online 9438 | Phys. Chem. Chem. Phys., 2021, 23, 9428–9439 This journal is © the Owner Societies 2021 Open Access Article. Published on 23 March 2021. Downloaded on 6/26/2022 1:50:45 PM. This article is licensed under a Creative Commons Attribution-NonCommercial 3.0 Unported Licence.PDF Image | Dynamic theory battery electromotive force
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