Advertisement

Ionics

, Volume 21, Issue 2, pp 459–469 | Cite as

Maxwell displacement current and nature of Jonsher’s “universal” dynamic response in nanoionics

  • Alexandr Despotuli
  • Alexandra Andreeva
Original Paper

Abstract

A new notion—Maxwell displacement current on a potential barrier—is introduced in the structure-dynamic approach of nanoionics for the description of a collective phenomenon: coupled ion transport and dielectric-polarization processes occurring during the ionic space charge formation and relaxation in a nonuniform potential landscape. We simulate the processes: (i) in an electronic conductor (EC)/advanced superionic conductor (AdSIC) ideally polarizable coherent heterojunction, (ii) in a few strained monolayers of a solid electrolyte (SE) located between two AdSICs forming coherent interfaces with SE. We prove that the sum of ionic current over any barrier and Maxwell displacement current through the same barrier is equal to the current of the current generator. A “universal” dynamic response, Reσ*(ω) ∝ ω n (n < ≈1), was found for the frequency-dependent complex conductivity σ*(ω) for case (ii) with an exponential distribution of potential barrier heights in SE. The nature of the phenomenon is revealed. The amplitudes of nonequilibrium ion concentrations (and induced voltages) in the space charge region of SE change approximately as ∝ ω −1. These amplitudes made a main linear contribution to Reσ*(ω). The main deviation from linearity is provided by the cosine of phase shift φ between current and voltage in SE-space charge region but the cosφ depends relatively slightly on ω (near constant loss effect) for coupled ion transport and dielectric-polarization processes.

Keywords

Nanoionics Maxwell displacement current Universal dynamic response Computer modeling 

References

  1. 1.
    Mehrer H (2007) Diffusion in solids. Springer, Berlin-Heidelberg-New YorkCrossRefGoogle Scholar
  2. 2.
    Dyre JC, Maass P, Roling B, Sidebottom DL (2009) Fundamental questions relating to ion conduction in disordered solids. Rep Prog Phys 72(4):046501. doi: 10.1088/0034-4885/72/4/046501 CrossRefGoogle Scholar
  3. 3.
    Sidebottom DL (2009) Colloquium: understanding ion motion in disordered solids from impedance spectroscopy scaling. Rev Mod Phys 81:999–1014. doi: 10.1103/RevModPhys.81.999 CrossRefGoogle Scholar
  4. 4.
    Macdonald JR (2010) Addendum to “Fundamental questions relating to ion conduction in disordered solids. J Appl Phys 107(10):101101. doi: 10.1063/1.3359703 CrossRefGoogle Scholar
  5. 5.
    Bindi L, Evain M, Pradel A, Albert S, Ribes M, Menchetti S (2006) Fast ion conduction character and ionic phase-transitions in disordered crystals: the complex case of the minerals of the pearceite–polybasite group. Phys Chem Miner 33:677–690. doi: 10.1007/s00269-006-0117-7 CrossRefGoogle Scholar
  6. 6.
    Fong DD, Stephenson GB, Streiffer SK, Eastman JA, Auciello O, Fuoss PH, Thompson C (2004) Ferroelectricity in ultrathin perovskite films. Science 304(5677):1650–1653. doi: 10.1126/science.1098252 CrossRefGoogle Scholar
  7. 7.
    Boulant A, Emery J, Jounanneaux A, Buzare JY, Bardeau JF (2011) From micro- to nanostructured fast ionic conductor Li0.30La0.56 0.13Ti O3: size effects on NMR properties. J Phys Chem C 115(31):15575–15585. doi: 10.1021/jp2048794
  8. 8.
    Despotuli AL, Andreeva AV, Rambabu B (2005) Nanoionics of advanced superionic conductors. Ionics 11(3–4):306–314. doi: 10.1007/BF02430394 CrossRefGoogle Scholar
  9. 9.
    Despotuli AL, Andreeva AV (2009) A short review on deep-sub-voltage nanoelectronics and related technologies. Int J Nanosci 8(4–5):389–402. doi: 10.1142/S0219581X09006328 CrossRefGoogle Scholar
  10. 10.
    Despotuli AL, Andreeva AV (2010) Nanoionics: new materials and supercapacitors. Nanotechnol Russ 5(7–8):506–520. doi: 10.1134/S1995078010070116 CrossRefGoogle Scholar
  11. 11.
    Liu SH (1980) Lattice gas model for the metal-electrolyte interface. Surf Sci 101(1–3): 49–56. doi:  10.1016/0039-6028(80)90598-1, doi:  10.1016/0039-6028(80)90598-1#doilink
  12. 12.
    Macdonald JR (1982) Layered lattice gas model for the metal-electrode interface. Surf Sci 116(1):135–147. doi: 10.1016/0039-6028(82)90683-5 CrossRefGoogle Scholar
  13. 13.
    Macdonald JR, Liu SH (1983) An iterated three-layer model of the double layer with permanent dipoles. Surf Sci 125(3):653–678. doi: 10.1016/S0039-6028(83)80053-3 CrossRefGoogle Scholar
  14. 14.
    Kilic MS, Bazant MZ, Ajdary A (2007) Steric effects in the dynamics of electrolytes at large applied voltages: I. Double-layer charging. Phys Rev E 75(2):021502CrossRefGoogle Scholar
  15. 15.
    Bazant MZ, Storey BD, Kornyshev AA (2011) Double layer in ionic liquids: overscreening versus crowding. Phys Rev Lett 106(4):046102. doi: 10.1103/PhysRevLett.106.046102 CrossRefGoogle Scholar
  16. 16.
    Kislenko SA, Amirov RN, Samoylov IS (2013) Molecular dynamic simulation of the electrical double layer in ionic liquids. J Phys Conf Ser 418:012021. doi: 10.1088/1742-6596/418/1/012021 CrossRefGoogle Scholar
  17. 17.
    Borukhov I, Andelman D, Orland H (1997) Steric effects in electrolytes: a modified Poisson-Boltzmann equation. Phys Rev Lett 79(3):435–438. doi: 10.1103/PhysRevLett.79.435 CrossRefGoogle Scholar
  18. 18.
    Singh MB, Kant R (2011) Theory of electric layer dynamics at blocking electrode. arXiv:1103.0681v1 [cond-mat.mtrl-sci]Google Scholar
  19. 19.
    Soestbergen M, Biesheuvel PM, Bazant MZ (2010) Diffuse-charge effects on the transient response of electrochemical cells. Phys Rev E 81(2):021503. doi: 10.1103/PhysRevE.81.021503 CrossRefGoogle Scholar
  20. 20.
    Despotuli AL, Andreeva AV (2012) Model, method and formalism of new approach to ion transport processes description for the solid electrolyte/electronic conductor blocking heterojunctions. Nano and Microsystem Technique (Russian) 9:16–21. http://www.nanometer.ru/2013/08/22/nanoionika_333471.html
  21. 21.
    Despotuli AL, Andreeva AV (2012) Computer modeling on sub-nanometer scale the ion-transport characteristics of the solid electrolyte/electronic conductor blocking heterojunctions. Nano and Microsystem Technique (Russian) 11:15–23. http://www.nanometer.ru/2013/08/22/nanoionika_333471.html
  22. 22.
    Despotuli AL, Andreeva AV (2013) Maxwell displacement current in nanoionics and intrinsic ion-transport properties of model nanostructures. Nano and Microsystem Technique (Russian) 8:2–9. http://www.nanometer.ru/2013/08/22/nanoionika_333471.html
  23. 23.
    Despotuli AL, Andreeva AV (2013) Modeling on sub-nanometer scale of fast ionic transport processes on blocking heterojunctions of solid electrolyte/ electronic conductor. Electronic Journal: Phase transformations, ordering states and new materials (Russian). 2:7–12. http://ptosnm.ru/ru/issue/2013/2/83/publication/776
  24. 24.
    Despotuli AL, Andreeva AV (2013) Maxwell displacement current in nanoionics. Modeling of processes of space charge relaxation on blocking heterojunctions of solid electrolyte/ electronic conductor. Electronic Journal: Phase transformations, ordering states and new materials (Russian). 10: 26–40. http://ptosnm.ru/ru/issue/2013/10/91/publication/856
  25. 25.
    Despotuli AL, Andreeva AV (2012) Structure-dynamic approach in nanoionics. Modeling of ion transport on blocking electrode. arXiv:1311.3480 [cond-mat.mtrl-sci]Google Scholar
  26. 26.
    Despotuli AL, Nikolaichik VI (1993) A step towards nanoionics. Solid State Ionics 60(4):275–278. doi: 10.1016/0167-2738(93)90005-N CrossRefGoogle Scholar
  27. 27.
    Andreeva AV, Despotuli AL (2005) Interface design in nanosystems of advanced superionic conductors. Ionics 11(1–2):152–160. doi: 10.1007/BF02430415 CrossRefGoogle Scholar
  28. 28.
    Flygare WH, Huggins RA (1973) Theory of ionic transport in crystallographic tunnels. J Phys Chem Solids 34(7):1199–1204. doi: 10.1016/S0022-3697(73)80209-4 CrossRefGoogle Scholar
  29. 29.
    Ardell AJ (2012) Gradient energy, interfacial energy and interface width. Scripta Mater 66(7):423–426. doi:  10.1016/j.scriptamat.2011.11.043, doi:  10.1016/j.scriptamat.2011.11.043#doilink
  30. 30.
    Lee KR, Ahn K, Chung YC, Lee J, Yoo HI (2012) Lattice distortion effect on electrical properties of GDC thin films: experimental evidence and computational simulation. Solid State Ionics 229(12):45–53. doi:  10.1016/j.ssi.2012.10.007, doi:  10.1016/j.ssi.2012.10.007#doilink
  31. 31.
    Despotuli AL, Andreeva AV (2003) Creation of new types of thin-film solid electrolyte supercapacitors for microsystems technology and micro (nano)electronics. MicrosystTechn (Russ) 11:2–10Google Scholar
  32. 32.
    Ukshe EA, Bukun NG (1990) Development of the model of adsorptive double-layer relaxation in superionic conductors. Sov Electrochem 26(11):1221–1229Google Scholar
  33. 33.
    Bukun NG, Ukshe AE (2009) Impedance of solid electrolyte systems. Russ Electrochem 45(1):11–24. doi: 10.1134/S1023193509010030 CrossRefGoogle Scholar
  34. 34.
    Jonscher AK (1977) The ‘universal’ dielectric response. Nature 267(6):673–679. doi: 10.1038/267673a0 CrossRefGoogle Scholar
  35. 35.
    Funke K (2013) Solid state ionics: from Michael Faraday to green energy—the European dimension. Sci Technol Adv Mater 14(4):043502. doi: 10.1088/1468-6996/14/4/043502 CrossRefGoogle Scholar
  36. 36.
    Wojnarowska Z, Swiety-Pospiech A, Grzybowska K, Hawelek L, Paluch M, Ngai KL (2012) Fundamentals of ionic conductivity relaxation gained from study of procaine hydrochloride and procainamide hydrochloride at ambient and elevated pressure. J Chem Phys 136(16):164507. doi: 10.1063/1.4705274 CrossRefGoogle Scholar
  37. 37.
    Popov II, Nigmatullin RR, Khamzin AA, Lounev IV (2012) Conductivity in disordered structures: verification of the generalized Jonscher’s law on experimental data. J Appl Phys 112(9):094107. doi: 10.1063/1.4764343 CrossRefGoogle Scholar
  38. 38.
    Sibik J, Shalaev EY, Zeitler JA (2013) Glassy dynamics of sorbitol solutions at terahertz frequencies. Phys Chem Chem Phys 15(5):11931–11942. doi: 10.1039/c3cp51936h CrossRefGoogle Scholar
  39. 39.
    Dyre JC (2013) Aging of CKN: modulus versus conductivity analysis. Phys Rev Lett 110(24):245901. doi: 10.1103/PhysRevLett.110.245901 CrossRefGoogle Scholar
  40. 40.
    Rim YH, Kim M, Kim JE, Yang YS (2013) Ionic transport in mixed-alkali glasses: hop through the distinctly different conduction pathways of low dimensionality. New J Phys 15(2):023005. doi: 10.1088/1367-2630/15/2/023005 CrossRefGoogle Scholar
  41. 41.
    Mattner C, Roling B, Heuer A (2013 ) The frequency-dependence of nonlinear conductivity in disordered systems: an analytically solvable model. arXiv:1302.3258v1[cond-mat.dis-nn]Google Scholar
  42. 42.
    Banhatti RD, Laughman D, Badr L, Funke K (2011) Nearly constant loss effect in sodium borate and silver meta-phosphate glasses: new insights. Solid State Ionics 192(1):70–75. doi: 10.1016/j.ssi.2010.04.032 CrossRefGoogle Scholar
  43. 43.
    Ke S, Lin P, Huang H, Fan H, Zeng X (2013) Mean-field approach to dielectric relaxation in giant dielectric constant perovskite ceramic. J Ceram, Article ID 795827. doi:  10.1155/2013/795827
  44. 44.
    Kumar TV, Chary AS, Bhardwaj S, Awasthi AM, Reddy SN (2013) Dielectric relaxation, ionic conduction and complex impedance studies on NaNO3 fast ion conductor. Int J Mater Sci Appl 2(6):173–178. doi:  10.11648/j.ijmsa.20130206.12, doi:  10.11648/j.ijmsa.20130206.12#_blank
  45. 45.
    Parida BN, Das PR, Padhee R, Choudhary RN (2013) Structural, dielectric and electrical properties of Li2Pb2La2W2Ti4Nb4O30 ceramic. Bull Mater Sci 36(5):883–892. doi: 10.1007/s12034-013-0543-3 CrossRefGoogle Scholar
  46. 46.
    Kader MM, Kabbany FE, Naguib HM, Gamal WM (2013) Charge transport mechanism and low temperature phase transitions in KIO3. J Phys Conf Ser 423:012036. doi: 10.1088/1742-6596/423/1/012036 CrossRefGoogle Scholar
  47. 47.
    Kriaa A, Saad KB, Hamzaoui AH (2012) Synthesis and characterization of cancrinite-type zeolite, and its ionic conductivity study by AC impedance analysis. Russ J Phys Chem A 86(3):2024–2032. doi: 10.1134/S0036024412130158 CrossRefGoogle Scholar
  48. 48.
    Šantić A, Moguš-Milanković A (2012) Charge carrier dynamics in materials with disordered structures: a case study of iron phosphate glasses. Croat Chem Acta 85(3):245–254. doi: 10.5562/cca1989 CrossRefGoogle Scholar
  49. 49.
    Chaari M, Matoussi A (2012) Electrical conduction and dielectric studies of ZnO pellets. Phys B 407(9):3441–3447. doi: 10.1016/j.physb.2012.04.056 CrossRefGoogle Scholar
  50. 50.
    Peng-Fei C, Sheng-Tao L, Jian-Ying L, Can D, Yan Y (2012) Physical meaning of conductivity spectra for ZnO ceramics. Chin Phys B 21(9):097201. doi: 10.1088/1674-1056/21/9/097201 CrossRefGoogle Scholar
  51. 51.
    Sorokin NI, Sobolev BP (2008) Frequency response of the low-temperature ionic conductivity of single crystals R1-y My F3-y (R = La-Er; M = Ca, Sc, Ba, Cd). Phys Solid State 50(3):402–407. doi: 10.1134/S1063783408030037 CrossRefGoogle Scholar
  52. 52.
    Regonini D, Adamaki V, Bowen CR, Pennock SR, Taylor J, Dent AC (2012) AC electrical properties of TiO2 and Magnéli phases, TinO2n – 1. Solid State Ionics 229:38–44. doi: 10.1016/j.ssi.2012.10.003 CrossRefGoogle Scholar
  53. 53.
    Singh DP, Shahi K, Kar KK (2013) Scaling behavior and nearly constant loss effect in AgI–LiPO3 composite glasses. Solid State Ionics 231:102–108. doi: 10.1016/j.ssi.2012.10.025 CrossRefGoogle Scholar
  54. 54.
    Bowen CR, Almond DP (2006) Modelling the ‘universal’ dielectric response in heterogeneous materials using microstructural electrical networks. Mater Sci Technol 22(6):719–724. doi: 10.1179/174328406X101328 CrossRefGoogle Scholar
  55. 55.
    Henn F, Devautour-Vinot S, Giuntini JG, Bisquert J, Garcia-Belmonte G, Platon C, Varsamis E, Kamitsos E (2010) Analysis of AC permittivity response measured in an ionic glass: a comparison between iso and non-iso thermal conditions. IEEE Trans Dielectr Electr Insul 17(4):1164–1171. doi: 10.1109/TDEI.2010.5539686 CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Institute of Microelectronics Technology and High Purity MaterialsRussian Academy of ScienceChernogolovkaRussia

Personalised recommendations