Prediction of Effective Properties of Porous Carbon Electrodes from a Parametric 3D Random Morphological Model
Tóm tắt
Pore structures have a major impact on the transport and electrical properties of electrochemical devices, such as batteries and electric double-layer capacitors (EDLCs). In this work we are concerned with the prediction of the electrical conductivity, ion diffusivity and volumetric capacitance of EDLC electrodes, manufactured from hierarchically porous carbons. To investigate the dependence of the effective properties on the pore structures, we use a structurally resolved parametric model of a random medium. Our approach starts from 3D FIB-SEM imaging, combined with automatic segmentation. Then, a random set model is fitted to the segmented structures and the effective transport properties are predicted using full field simulations by iterations of FFT on 3D pore space images and calculations based on the geometric properties of the structure model. A parameter study of the model is used to investigate the sensitivity of the effective conductivity and diffusivity to changes in the model parameters. Finally, we investigate the volumetric capacitance of the EDLC electrodes with a geometric model, make a comparison with experimental measurements and do a parameter study to suggest improved microstructures.
Tài liệu tham khảo
Balach, J., Miguel, F., Soldera, F., Acevedo, D., Mücklich, F., Barbero, C.: A direct and quantitative image of the internal nanostructure of nonordered porous monolithic carbon using fib nanotomography. J. Microsc. (2012)
Balach, J., Soldera, F., Acevedo, D.F., Mücklich, F., Barbero, C.A.: A direct and quantitative three-dimensional reconstruction of the internal structure of disordered mesoporous carbon with tailored pore size. Microsc. Microanal. 19, 745–750 (2013)
Barsoukov, E., Macdonald, J.: Impedance Spectroscopy: Theory, Experiment, and Applications. Wiley, London (2005)
Bazant, M.Z., Thornton, K., Ajdari, A.: Diffuse-charge dynamics in electrochemical systems. Phys. Rev. E 70(021), 506 (2004)
Beran, M.: Use of the variational approach to determine bounds for the effective permittivity in random media. Il Nuovo Cimento 38(2), 771–782 (1965)
Conway, B.: Electrochemical Supercapacitors: Scientific Fundamentals and Technological Applications. Springer, US (2013)
de Levie, R.: On porous electrodes in electrolyte solutions: I. Capacitance effects. Electrochim. Acta 8(10), 751–780 (1963)
Duffy, D.: Green’s Functions with Applications, Applied Mathematics. CRC Press, Boca Raton (2001)
Eyre, D.J., Milton, G.W.: A fast numerical scheme for computing the response of composites using grid refinement. Eur. Phys. J. Appl. Phys. 6, 41–47 (1999)
Grzhibovskis, R., Heintz, A.: A convolution-thresholding approximation of generalized curvature flows. SIAM J. Numer. Anal. 42(6), 2652–2670 (2005)
Hutzenlaub, T., Becker, J., Zengerle, R., Thiele, S.: How coarsening the 3d reconstruction of a porous material influences diffusivity and conductivity values. ECS Electrochem. Lett. 2(2), F14–F17 (2013)
Jeulin, D., Moreaud, M.: Multi-scale simulation of random spheres aggregates-application to nanocomposites. In: 9th European Congress on Stereology and Image Analysis, Zakopane, Poland, vol. 1, pp 341–348 (2005)
Jeulin, D.: Random structures in physics. In: Bilodeau, M., Meyer, F., Schmitt, M. (eds.) Space, Structure and Randomness. Lecture Notes in Statistics, vol. 183, pp. 183–219. Springer, New York (2005)
Jeulin, D.: Random texture models for material structures. Stat. Comput. 10(2), 121–132 (2000)
Jørgensen, P., Hansen, K., Larsen, R., Bowen, J.: A framework for automatic segmentation in three dimensions of microstructural tomography data. Ultramicroscopy 110(3), 216–228 (2010)
Kanit, T., Forest, S., Galliet, I., Mounoury, V., Jeulin, D.: Determination of the size of the representative volume element for random composites: statistical and numerical approach. Int. J. Solids Struct. 40(13–14), 3647–3679 (2003)
Matheron, G.: Random Sets and Integral Geometry. Wiley series in probability and mathematical statistics, Probability and mathematical statistics. Wiley, London (1975)
Matheron, G.: Elements pour une théorie des milieux poreux. Masson, Paris (1967)
Milton, G.: Bounds on the elastic and transport properties of two-component composites. J. Mech. Phys. Solids 30(3), 177–191 (1982)
Nanjundappa, A., Alavijeh, A.S., Hannach, M.E., Harvey, D., Kjeang, E.: A customized framework for 3-d morphological characterization of microporous layers. Electrochim. Acta 110, 349–357 (2013)
Paasch, G., Micka, K., Gersdorf, P.: Theory of the electrochemical impedance of macrohomogeneous porous electrodes. Electrochim. Acta 38(18), 2653–2662 (1993)
Papanicolau, G., Bensoussan, A., Lions, J.: Asymptotic Analysis for Periodic Structures, Studies in Mathematics and its Applications. Elsevier Science, Amsterdam (1978)
Prill, T., Schladitz, K., Jeulin, D., Faessel, M., Wieser, C.: Morphological segmentation of FIB-SEM data of highly porous media. J. Microsc. 250(2), 77–87 (2013)
Roßberg, K., Paasch, G., Dunsch, L., Ludwig, S.: The influence of porosity and the nature of the charge storage capacitance on the impedance behaviour of electropolymerized polyaniline films. J. Electroanal. Chem. 443(1), 49–62 (1998)
Salzer, M., Spettl, A., Stenzel, O., Smått, J.H., Lindén, M., Manke, I., Schmidt, V.: A two-stage approach to the segmentation of FIB-SEM images of highly porous materials. Mater. Charact. 69, 115–126 (2012)
Sánchez-Palencia, E.: Non-homogeneous Media and Vibration Theory, Lecture Notes in Physics. Springer, London (1980)
Serra, J.: Image Analysis and Mathematical Morphology. Academic Press, London (1982)
Spall, J.C.: Multivariate stochastic approximation using a simultaneous perturbation gradient approximation. IEEE Trans. Autom. Control 37, 332–341 (1992)
Torquato, S., Stell, G.: Bounds on the effective thermal conductivity of a dispersion of fully penetrable spheres. Int. J. Eng. Sci. 23(3), 375–383 (1985)
Wang, H., Pilon, L.: Physical interpretation of cyclic voltammetry for measuring electric double layer capacitances. Electrochim. Acta 64, 130–139 (2012)
Willot, F., Abdallah, B., Pellegrini, Y.P.: Fourier-based schemes with modified green operator for computing the electrical response of heterogeneous media with accurate local fields. Int. J. Numer. Methods Eng. 98(7), 518–533 (2014)