Abstract
We consider ionic transport by diffusion and migration through microstructured solid electrolytes. The assumed constitutive relations for the constituent phases follow from convex energy and dissipation potentials which guarantee thermodynamic consistency. The effective response is determined by homogenizing the relevant field equations via the notion ofmulti-scale convergence. The resulting homogenized response involves several effective tensors, but they all require the solution of just one standard conductivity problem over the representative volume element. A multi-scale model for semicrystalline polymer electrolytes with spherulitic morphologies is derived by applying the theory to a specific class of two-dimensional microgeometries for which the effective response can be computed exactly. An enriched model accounting for a random dispersion of filler particles with interphases is also derived. In both cases, explicit expressions for the effective material parameters are provided. The models are used to explore the effect of crystallinity and filler content on the overall response. Predictions support recent experimental observations on doped poly-ethylene-oxide systems which suggest that the anisotropic crystalline phase can actually support faster ion transport than the amorphous phase along certain directions dictated by the morphology of the polymeric chains. Predictions also support the viewpoint that ceramic fillers improve ionic conductivity and cation transport number via interphasial effects.
Similar content being viewed by others
References
Agoras M., Ponte Castañeda P.: Homogenization estimates for multi-scale nonlinear composites. Eur. J. Mech. A/Solids 30, 828–843 (2011)
Allaire G.: Homogenization and two-scale convergence. S.I.A.M. J. Math. Anal. 23, 1482–1518 (1992)
Allaire G., Briane M.: Multiscale convergence and reiterated homogenization. Proc. R. Soc. Edin. 126A, 297–342 (1996)
Berthier C., Gorecki W., Minier M., Armand M.B., Chabagno J.M., Rigaud P.: Microscopic investigation of ionic conductivity in alkali metal salts-poly(ethylene oxide) adducts. Solid State Ion. 11, 91–95 (1983)
Bourbatache K., Millet O., Aït-Mohtar A., Amiri O.: Chloride transfer in cement-based materials. Part 1. Theoretical basis and modelling. Int. J. Numer. Anal. Meth. Geomech. 37, 1614–1627 (2012)
Burba C.M., Woods L., Millar S.Y., Pallie J.: Polymer chain organization in tensile-stretched poly(ethylene oxide)-based polymer electrolytes. Electrochim. Acta 57, 165–171 (2011)
Casado-Díaz J., Gayte I.: The two-scale convergence method applied to generalized Besicovitch spaces. Proc. R. Soc. Lond. A 458, 2925–2946 (2002)
Ciocek M., Sannier L., Siekierski M., Golodnitsky D., Peled E., Scrosati B., Glowinkowski S., Wieczorek W.: Ion transport phenomena in polymeric electrolytes. Electrochim. Acta 53, 1409–1416 (2007)
Coleman R.D., Noll W.: The thermodynamics of elastic materials with heat conduction and viscosity. Arch. Ration. Mech. Anal. 13, 167–178 (1963)
Croce F., Persi L., Scrosati B., Serraino-Fiory F., Plichta E., Hendrickson M.A.: Role of the ceramic fillers in enhancing the transport properties of composite polymer electrolytes. Electrochim. Acta 46, 2457–2461 (2001)
Croce F., Sachetti S.L., Scrosati B.: Advanced, lithium batteries based on high-performance composite polymer electrolytes. J. Power Sour. 162, 685–689 (2006)
Doyle M., Fuller T.F., Newman J.: The importance of the lithium ion transference number in lithium/polymer cells. Electrochim. Acta 39, 2073–2081 (1994)
Fullerton-Shirey S.K., Maranas J.K.: Effect of LiClO4 on the structure and mobility of PEO-based solid polymer electrolytes. Macromolecules 42, 2142–2156 (2009)
Funke K.: Solid State Ionics: from Michael Faraday to green energy the European dimension. Sci. Technol. Adv. Mater. 14, 043502 (2013)
Gitelman L., Israeli M., Averbuch A., Nathan M., Schuss Z., Golodnitsky D.: Polymer geometry and Li+ conduction in poly(ethylene oxide). J. Comp. Phys. 227, 8437–8447 (2008)
Golodnitsky D., Peled E.: Stretching-induced conductivity enhancement of LiI-(PEO)-polymer electrolyte. Electrochim. Acta 45, 1431–1436 (2000)
Golodnitsky D., Livshits E., Ulus A., Barkay Z., Lapides I., Peled E., Chung S.H., Greenbaum S.: Fast ion transport phenomena in oriented semicrystalline LiI-P(EO) n -based polymer electrolytes. J. Phys. Chem. A 105, 10098–10106 (2001)
Gurtin M.E., Fried E., Anand L.: The Mechanics and Thermodynamics of Continua. Cambridge University Press, Cambridge (2010)
Marzantowicz M., Krok F., Dygas J.R., Florjańczyk Z., Zygadlo-Monikowska E.: The influence of phase segregation on properties of semicrystalline PEO:LiTFSI electrolytes. Solid State Ion. 179, 1670–1678 (2008)
Milton G.W.: The Theory of Composites. Cambridge University Press, Cambridge (2002)
Minami T., Tatsumisago M., Wakihara M., Iwakura C., Kohjiya S., Tanaka I.: Solid state ionics for batteries. Springer, Berlin (2005)
Robitaille C.D., Fauteux D.: Phase diagrams and conductivity characterization of some PEO-LiX electrolytes. J. Electrochem. Soc. 133, 315–325 (1986)
Suquet, P.: Elements of homogenization for inelastic solid mechanics. In: Sanchez-Palencia, E., Zaoui, A. (eds.) Homogenization techniques for composite media. Lecture Notes in Physics 272. Springer, Berlin, pp. 193–278 (1987)
Siekierski M., Wieczorek W., Nadara K.: Mesoscale models of conductivity in polymeric electrolytes–A comparative study. Electrochim. Acta 53, 1556–1567 (2007)
Stephan A.M., Nahm K.S.: Review on composite polymer electrolytes for lithium batteries. Polymer 47, 5952–5964 (2006)
Xiao Y., Bhattacharya K.: A continuum theory of deformable, semiconducting ferroelectrics. Arch. Rational Mech. Anal. 189, 59–95 (2008)
Author information
Authors and Affiliations
Corresponding author
Additional information
Communicated by Andreas Öchsner.
Rights and permissions
About this article
Cite this article
Curto Sillamoni, I.J., Idiart, M.I. A model problem concerning ionic transport in microstructured solid electrolytes. Continuum Mech. Thermodyn. 27, 941–957 (2015). https://doi.org/10.1007/s00161-014-0391-4
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00161-014-0391-4