1. Ion transport and trapping in intercalation materials: EIS parameters interpretation J. Bisquert Universitat Jaume I, Spain Tel-Aviv, sept 7, 2004

2. electroactive materials -Nanoporous semiconductor -Li batteries -Electrochromic metal oxides -Conducting polymers

3. Common features of electroactive materials 3. Characterization by impedance, voltammetry, optical transmission, etc. 1. Variation of composition with potential 2. Control of physical properties (color, conductivity, etc.)

4. Example: nanostructured TiO 2

5. Chemical capacitance Electrostatic capacitance Chemical capacitance J. Bisquert, Phys. Chem. Chem Phys. 5, 5360 (2003).

6. Chemical diffusion coefficient Jump or tracer diffusion coefficient Thermodynamic factor J. Bisquert, V. S. Vikhrenko, J. Phys. Chem. B, 108, 2313-2322 (2004). J. Bisquert, J. Phys. Chem. B, 108, 2323-2332 (2004)

7. Ions in the lattice Random distribution (non-interacting lattice gas)

8. Ions in the lattice Chemical capacitance Jump frequency Thermodynamic factor Chemical diffusion coefficient

9. Diffusion impedance A. Pitarch, G. Garcia-Belmonte, I. Mora-Seró, J. Bisquert Physical Chemistry Chemical Physics, 6, 2983-2988 (2004). The same process over a spatial extension Carrier transfer between two points at different chemical potentials

10. Diffusion impedance

11. Anomalous diffusion Fractional time diffusion J. Bisquert and A. Compte J. Electroanal. Chem. 499, 112-120 (2001).

12. Diffusion and irreversible reaction J. Bisquert Journal of Physical Chemistry B, 106, 325-333 (2002).

13. Diffusion and irreversible reaction J. Bisquert Journal of Physical Chemistry B, 106, 325-333 (2002). Gerischer impedance

14. Diffusion models

15. Ions in the lattice - interactions correlations random

16. lithium intercalation into Li 1− Mn 2 O 4 A rigurous description of ions interactions in the lattice gas model requires to consider the details of the local environment of the diffusing species. Statistically, interactions in the lattice are described by potential energy terms that depend on the occupancies of neighbor sites, next- neighbors, etc. The figure shows local cross-sectional snapshots of the equilibrium configuration of the cubic lattice obtained from the Monte Carlo simulation at (a) lithium content (1− d)=0.2, (b) 0.5 and (c) 0.8. The closed square and the cross-centered square symbols represent lithium ions at the sites of sub- lattices 1 and 2 respectively Sung-Woo Kim and Su-Il Pyun, Electrochim. Acta 46 987-997 (2001)

17. lithium intercalation into Li 1− Mn 2 O 4 Electrode potential E versus lithium content obtained theoretically from the Monte Carlo simulation Sung-Woo Kim and Su-Il Pyun, Electrochim. Acta 46 987-997 (2001)

18. lithium intercalation into Li 1− Mn 2 O 4 Electrode potential E versus lithium content (1− d) curves calculated theoretically from (a) the Monte Carlo simulation, (b) the mean-field approximation, and (c) measured experimentally from the cell Li/1 M LiClO 4 –PC solution/Li 1− Mn 2 O 4 electrode at T=258, 278 and 298 K. Sung-Woo Kim and Su-Il Pyun, Electrochim. Acta 46 987-997 (2001)

19. Mean field approximation obtained by replacing the local interactions by an averaged field (molecular field) which is determined by the distribution of charged particles and which in turn governs the distribution itself Equivalent to a shift of a unique energy level

20. Mean field approximation

21. Two state model-steady states J. Bisquert, V. S. Vikhrenko, Electrochim. Acta, 47, 3977-3988 (2002).

22. Two state model-impedance The lower state represents a reversible chemical reaction in the solid state that immobilizes the ion

23. Two state model-impedance There are two main impedance patterns: Slow trapping, Gerischer impedance (like a reaction) observed at high frequencies and the capacitive line at low frequencies Fast trapping, it is an arc at intermediate frequencies, imposed in the normal diffusion impedance, Warburg at high frequencies

24. Nyquist plots for Mg-ion insertion into the Chevrel phase, covering the whole frequency domain M. D. Levi, H. Gizbar, E. Lancry, Y. Gofer, E. Levi and D. Aurbach J. Electroanal. Chem. 569, 211-223 (2004) Gerischer impedance at intermediate frequencies Mg 2+ and Li + ion insertions into Mo 6 S 8 Two state model-experimental

25. Mg 2+ and Li + ion insertions into Mo 6 S 8 M. D. Levi, D. Aurbach, J. Phys. Chem. B, 109, 2763 (2005) Two state model-experimental General schematic representation of the energy of the available sites for ions insertion into the host matrix according to the single trap model developed by Bisquert et al. (a) Sites A are traps with higher energy barriers and lower bottom energy compared to “shallow” sites B. Ea denotes the activation energy required to liberate the trapped ions, i.e., to transform them into the transition shallow sites. Panel “b” shows the crystal structure of the Chevrel phase which comprises Mo6 octahedra included inside slightly distorted cubes of sulfur anions (filled circles), inner and outer 6 sites rings (for the intercalating ions), which are identified with the trapping sites A and the more shallow sites B. Panel “c” is a simplified view of the crystal structure of panel “b” showing a three- dimensional network of sites A and B only (in order to simplify the view, the Mo6 octahedra and the S8 cubes were removed).

26. Mg 2+ and Li + ion insertions into Mo 6 S 8 M. D. Levi, D. Aurbach, J. Phys. Chem. B, 109, 2763 (2005) Two state model-experimental The change of the barrier heigth as a function of the intercalation level implies a strong change of the kinetics of the traps, which is observed as a strong modification of the intermediate frequency arc. Simulation Experimental

27. Multiple trapping impedance J. Bisquert, G. Garcia-Belmonte, A. Pitarch ChemPhysChem, 4, 287-292 (2003). Formal model of anomalous diffusion

28. Anomalous diffusion impedance J. Bisquert, G. Garcia-Belmonte, A. Pitarch ChemPhysChem, 4, 287-292 (2003). Model of 8 traps following an exponential distribution in energy

29. lithium transport through vanadium pentoxide film The Nyquist plots of the ac- impedance spectra measured on the V 2 O 5 xerogel film electrode in a 1 M LiClO 4 –PC solution at the lithium content,, 0.75, 1.25 and 1.55 which corresponds to the electrode potential, E, 2.8, 2.5 and 2.2 V Li/Li+, respectively. Kyu-Nam Jung, Su-Il Pyun and Jong- Won Lee, Electrochim. Acta 49, 4371- 4378 (2004)

30. lithium transport through vanadium pentoxide film The anodic current transients theoretically calculated for lithium transport by using random walk simulation in consideration of the residence time distribution with =1.3, 1.5 and 1.8. For comparison, the current transient simulated without considering the residence time distribution ( =0) is also presented. Kyu-Nam Jung, Su-Il Pyun and Jong- Won Lee, Electrochim. Acta 49, 4371- 4378 (2004)

31. Lithium intercalation in WO 3 J. Garcia-Cañadas, F. Fabregat-Santiago, I. Porqueras, C. Person, J. Bisquert and G. Garcia-Belmonte, Solid State Ionics, 175, 521-525 (2004). Chemical capacitance Derived from chronopotentiometry The chemical capacitance realices a power law dependence with respect to intercalation level with exponent 0.65.This cannot be explained by a model of gaussian distribution of sites in energy: Elastic interactions effects are important and the chemical potential is described as

32. Lithium intercalation in WO 3 J. Garcia-Cañadas, F. Fabregat-Santiago, I. Porqueras, C. Person, J. Bisquert and G. Garcia-Belmonte, Solid State Ionics, 175, 521-525 (2004). Chemical capacitance The power law dependence with respect to intercalation level with exponent 0.65.This cannot be explained by a model of gaussian distribution of sites in energy Elastic interactions effects are important and the chemical potential is described as

33. Li intercalation in WO 3 J. Garcia-Cañadas, G. Garcia-Belmonte, J. Bisquert, I. Porqueras and C. Person, Solid State Ionics, in press (2005). Chemical capacitance The chemical capacitance depends on film thickness, which supports the interpretation in terms of elastic effects Equilibrium (chemical) film capacitance as a function of the composition (molar fraction) x as derived from chronopotentiometry experiments for film thickness (in nm): (a) 100, (b) 200, (c) 300, and (d) 400. Fine solid lines correspond to fits using

34. Li intercalation in WO 3 The chemical diffusion coefficient is obtained from impedance measurements G. Garcia-Belmonte, V. S. Vikhrenko, J. García-Cañadas, J. Bisquert, Solid State Ionics, 170, 123 (2004).

35. Li intercalation in WO 3 The barrier for ion diffusion is obtained from the jump diffusion coefficient and is seen to vary with intercalation level. This can be explained by first principles calculation of the barrier G. Garcia-Belmonte, V. S. Vikhrenko, J. García-Cañadas, J. Bisquert, Solid State Ionics, 170, 123 (2004) Lourdes Gracia, Jorge García-Cañadas, Germà Garcia-Belmonte, Armando Beltrán, Juan Andrés and Juan Bisquert. Electrochem. Solid St. Letters, in press (2005)

36. Other thermodynamic functions Polarons in conducting polymers J. Bisquert, G. Garcia-Belmonte and J. Garcia-Cañadas. Journal of Chemical Physics, 120, 6726-6733 (2004)

37. Acknowledgments Germà Garcia-Belmonte Francisco Fabregat-Santiago Iván Mora-Seró Jorge García-Cañadas Funding: MCyT, Fundació Caixa Castelló Homepage: www.elp.uji.es/jb.htm E-mail: bisquert@uji.es