1 / 43

IMPEDANCE SPECTROSCOPY: DIELECTRIC BEHAVIOUR OF POLYMER ELECTROLYTES

IMPEDANCE SPECTROSCOPY: DIELECTRIC BEHAVIOUR OF POLYMER ELECTROLYTES. By Ri Hanum Yahaya Subban Ph. D Faculty of Applied Sciences/Institute of Science UiTM Shah Alam. OUTLINE. IMPEDANCE SPECTROSCOPY (IS) BACKGROUND IS PRINCIPLE IS TECHNIQUE IS PLOT OF SIMPLE CIRCUITS

jmayberry
Download Presentation

IMPEDANCE SPECTROSCOPY: DIELECTRIC BEHAVIOUR OF POLYMER ELECTROLYTES

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. IMPEDANCE SPECTROSCOPY: DIELECTRIC BEHAVIOUR OF POLYMER ELECTROLYTES By RiHanumYahayaSubban Ph. D Faculty of Applied Sciences/Institute of Science UiTM Shah Alam

  2. OUTLINE • IMPEDANCE SPECTROSCOPY (IS) BACKGROUND • IS PRINCIPLE • IS TECHNIQUE • IS PLOT OF SIMPLE CIRCUITS • IS PLOT OF MODEL SYSTEMS • IS PLOT OF REAL SYSTEMS • CONSTANT PHASE ELEMENT (CPE) • IS PLOT OF REAL SYSTEMS AND CPE • IMPEDANCE RELATED FUNCTIONS • Z, Y AND M PLOTS FOR SIMPLE CIRCUITS • SOME APPLICATION OF IS • SOME PRACTICAL DETAILS FOR IS

  3. IS: BACKGROUND Also known as  AC Impedance Spectroscopy  Complex Impedance Spectroscopy  Electrochemical Impedance Spectroscopy (when applied to electrochemical systems) Popular use of IS:  To determine electrical conductivity of ionic conductors  To identify different processes that contribute to the total conductivity: bulk contribution, grain boundary contribution, diffusion, etc.  Through identifying an equivalent circuit for the impedance plot involved

  4. IS: BACKGROUND L • Resistance of sample R =  L A A  = resistivity of the material L = length of the sample A = area of cross-section of the sample • Conductivity  = 1 = L/A •  R • By measuring R,L and A,  can be calculated

  5. IS: PRINCIPLE PRINCIPLE: IS V(t) i(t) • Sine wave signal V(t) = Vo sin t • of low amplitude is applied to a sample • Vo = maximum voltage •  = 2f, angular frequency • The resulting current i(t) = io (sin t + ) • = phase difference between i(t) and V(t) • (current is ahead of voltage by ) • The impedance Z = V(t) = Vo sin (t) • i(t) io (sin t + ) • Z is a function of frequency and has magnitude Z = Vo = Zo and a phase angle  • io • Both Z and  are frequency dependent quantities : phase shift

  6. IS: PRINCIPLE • Since ac impedances are frequency dependent quantities they are represented by Z() Z() can be considered as a complex quantity with a real component Z’() and imaginary component Z”() Z() = Z’() + j Z”() , j =-1 where real impedance = Z’ = Z cos( ) imaginary impedance = Z”= Z sin( ) with a phase angle  = tan-1 (Z”/ Z’) Magnitude of Z, Z = [(Z’)2 + (Z”)2]1/2 Complex Impedance plane Im. Z Z Z”  Z’ Real Z

  7. IS: TECHNIQUE Small ac signal (V  10 mV) is applied to sample over a wide range of frequency (mHz to MHz) Solid sample Liquid sample Sample holder Electrode Sample Impedance spectrometer: LCR meter/FRA Electrode Computer

  8. IS: TECHNIQUE Measure Z(f) as a function of f(=2f) over a wide range of frequency (mHz to MHz) Plot Z(f) versus f in the form of -Z’’(f) vs Z’(f) for various f (Cole-Cole plot/ Complex impedance plot/Nyquist plot) Useful to evaluate : -electrical parameters such as conductivity of ionic conductors(solid or liquid), mixed conductors - electrode-electrolyte interfacial effects and related phenomena - electrochemical parameters/processes of the system under study Also used for studying dielectric behaviour of materials

  9. Z” R Z’ IS PLOT OF SIMPLE CIRCUITS a. Pure resistance R R Z” Z = R for all values of  or f Z = R and  = 0 Z’ = R and Z” =0 Z’ Impedance plot is a point on the real axis at Z’ = R

  10. Z”  Z’ IS PLOT OF SIMPLE CIRCUITS b. Pure capacitance C C -ve Z” Z = 1 = -j jC C Z’ = 0 and Z” = -1 C Z = Z” varies with frequency As  increases, Z decreases Z points lie along the Z” axis Z’ Impedance plot is a straight line lying on the Z” axis

  11. Z’ IS PLOT OF SIMPLE CIRCUITS c. R and C connected in series C -ve Z” R The total impedance Z = R - j C With Z’ = R and Z” = -1 C R Z’ On complex plane the graph becomes a straight line at Z’ = R, parallel to the Z” axis

  12. IS PLOT OF SIMPLE CIRCUITS d. R and C connected in parallel • = 1 + 1 = 1 + jC • Z R 1/j C R • Z = R • 1 + j C • = R(1 - jRC) = R(1 - jRC) • (1 + jRC) (1 - jRC) 1 + (RC)2 • = R - jR2C • 1 + 2R2C2 1 + 2R2C2 • = Z’ - jZ” with Z” = RC • Z’ • On eliminating  : (Z’- R/2)2 + (Z”)2 = (R/2)2 R C Equation of a circle

  13. IS PLOT OF SIMPLE CIRCUITS d. R and C connected in parallel -ve Z” Impedance plot is a semicircle with centre (R/2, 0) on the Z’ axis Maximum point on the semicircle corresponds to mRC = 1  m = 1 RC m R/2 Z’ R where RC =   Time constant or Relaxation time Note: Z’ and Z” axes must have the same scales to see the semicircle Fromm , C can be calculated for an unknown circuit

  14. IS PLOT OF SIMPLE CIRCUITS e. Combined circuits R2 R1 R1 Rs C1 C1 C2 -ve Z” -ve Z” 2 = R2C2 1 = R1C1 1 = R1C1 R1+ R2 Z’ Rs Rs + R1 Z’ R1 due to internal resistance of electrolyte/electrode interface

  15. IS PLOT OF MODEL SYSTEMS a. Ionic solid with two non-blocking electrodes Eg: Ag/AgI/Ag (Ag+ mobile, I- immobile) No ion accumulation at the electrodes Cell arrangement  R and C connected in parallel (equivalent circuit) (assume no electrode resistance) Electrodes  Rb= bulk resistance Sample Rb Cb (Cg) bulk capacitance Cb Expected impedance plot Cb is related to vacuum capacitance Co; Cb = Co And Co =oA d -ve Z” m A - area of cross section  - dielectric constant d - thickness of sample o – permittivity of free space  Z’ Rb Rb/2

  16. IS PLOT OF MODEL SYSTEMS a. Ionic solid with two non-blocking electrodes: experimental results  Rb Cb Cb(Cg) bulk capacitance • Li6SrLa2Ta2O12 • Li6BaLa2Ta2O12 with Li electrodes  Thangadurai and Weppner Ionics 12 (2006) 81-92 Note: depressed/distorted semicircles

  17. IS PLOT OF MODEL SYSTEMS b. Ionic solid with two blocking electrodes Egs: AgI with Pt electrodes, Ag+ mobile and I- immobile Ions cannot enter the electrodes , get accumulated at the electrodes two double layer of charges at electrode/electrolyte interfaces two double layer capacitances at the interfaces ( C’dl) Expected impedance plot -ve Z” Equivalent circuit m  R/2 + + + - - - - - - + + + + - R R Z’ R C’dl  C’dl Cdl will add a spike to the Impedance plot C Cdl C Cdl= effective double layer capacitance

  18. IS PLOT OF MODEL SYSTEMS b. An ionic solid with two blocking electrodes: experimental results SS/PVC-LiCF3SO3/SS Au/Li6BaLa2Ta2O12/Au Subban and Arof, Journal of New Materials for Electrochemical Systems 6 (2003) 197-203 Thangaduarai and Weppner Ionics 12 ( 2006) 81-92 Note: depressed/distorted semicircles and slanted/curved spikes

  19. IS PLOT OF MODEL SYSTEMS c. Polycrystalline solid with two blocking electrodes Conduction will occur inside the grain (intra grain-bulk conduction) and along the grain boundaries (inter grain conduction) System = crystalline grain + grain boundaries + electrode/electrolyte interface Electrode/electrolyte interface Grain Expected impedance plot  Pt Pt Grain boundary Bulk Thickness of grain boundary is small  large Cgb Rgb is large - larger semicircle for GB The overall σ : is determined by Rb +Rgb -ve Z” Rgb Rb Z’ Cdl Rb+ Rgb Rb Cgb Cb Equivalent circuit

  20. IS PLOT OF MODEL SYSTEMS c. A polycrystalline solid with two blocking electrodes: experimental results R1 R2 High frequency semicircle (small C) bulk conduction Low frequency semicircle (large C)  grain boundary conduction C1 C2 100 Hz 10 kHz From the values of the capacitances different semicircles can be associated with different conduction process in the sample Cdl SS/ Li1+xCrxSn2-xP3-yVyO12/SS Norhaniza, Subban and Mohamed, Journal of Power Sources 244 (2013) 300-305 Note: Slanted/curved spike and depressed/distorted semicircles

  21. IS PLOT OF MODEL SYSTEMS TYPICAL C VALUES In general, a number of processes can contribute to the total conduction and an ideal equivalent circuit (hypothetical ) may be represented by the following simple circuit (various circuits possible) Cdl Different phases or Orientation of crystal planes Double layer capacitance at the electrode Bulk Grain boundary • R and C values ,particularly C values differ for different processes • Each transport process may give a semicircle to the Impedance plot • From the approximate C values different processes may be identified Actual identification of different processes must be based on dependence on temperature, pressure, etc. R1 R2 R3 C2 C3 C1

  22. IS PLOT OF REAL SYSTEMS IS plot of real systems and devices are usually complicated • Deviate from ideal behaviour due to : • Distorted semicircles may arise due to • - Overlap of semicircles with various time constants • Depressed semicircles may arise due to • - Electrolyte is not homogeneous • - Distributed microscopic properties of the electrolyte • Slanted or curved spikes may arise due to • - Unevenness of electrode/electrolyte interfaces • - Charge transfer across the electrode/electrolyte interface, diffusion of • species in the electrolyte or electrode The deviation from ideal behaviour of Impedance plot is explained in terms of a new circuit parameter called Constant Phase Element (CPE)

  23. CONSTANT PHASE ELEMENT (CPE) In general CPE has the properties of R and C (equivalent to a leaky capacitor) Mathematically impedance of a CPE is given by the Complex quantity: ZCPE = 1 = Zo (jω)-n , 0 ≤ n ≤ 1 Y0(jω) n When n = 0, Z is frequency independent and Zo  R, CPE ≅ pure Resistance When n = 1, Z = 1/jωY0 . Hence Yo C, CPE ≅ pure Capacitance

  24. CPE When 0 < n < 1, CPE acts as intermediate between R and C Can show that R and CPE in parallel gives a circular arc in the impedance plane as shown Usually CPE is denoted by the circuit element Q -Z” R • CPE alone gives an inclined straight line (pink) at angle (n=90) • CPE // R gives a tilted semicircle with its centre (C) depressed so that the plot appears as an arc (green) • - The diameter of the semicircle is inclined at (1-n) = 90  -Q- Q R n= 90° Z’ (1-n)= 90° C

  25. IS PLOT OF REAL SYSTEMS AND CPE The general equivalent circuit of a solid electrolyte with non perfect blocking electrodes may take the form R2 R1 R3 CPE4 -Z” Resulting impedance plot will have depressed semicircles and a slanted spike Here processes are assumed to be well separated CPE3 CPE2 CPE1 Z’ R1 R1 + R2 R1 + R2 + R3

  26. IMPEDANCE RELATED FUNCTIONS • There are several other measured or derived quantities related to impedance (Z) which often play important role in IS: • Admittance (Y) • Dieletric/Permittivity (ε) • Modulus (electric) (M) Generally referred to as ‘immitances’ • The four different formalisms give the same information in different ways • However each formalism highlights different features of the system • Thus it may be worthwhile to plot the data in more than one formalism in • order to extract all possible information from the results • Z plot gives prominence to most resistive elements • M plot gives prominence to smallest capacitance • Eg: To study grain boundary effects , Z plot is good • To study bulk effects M plot is good

  27. IMPEDANCE RELATED FUNCTIONS A.C voltage applied to a sample v = Zi Generally impedance Z = R + j X; R = resistance, X = reactance Hence the current , Where

  28. IMPEDANCE RELATED FUNCTIONS Complex Admittance Complex Permittivity Complex Electrical Modulus

  29. Z, Y AND M PLOTS FOR SIMPLE CIRCUITS C R -ve Z” M”   Y” m  R M’ C0/2C Z’ Y’ 1/Rb

  30. Z, Y AND M PLOTS FOR SIMPLE CIRCUITS R Y” C R/2 -ve Z” M” m m    1/R Y’ M’ Z’ R R/2 Co/2C

  31. SOME APPLICATION OF IS DETERMINATION OF DC IONIC CONDUCTIVITY OF IONIC CONDUCTORS : - Z” vs Z’ PVC-NH4CF3SO3-Bu3MeNTf2N In general IS plot consists of a depressed semicircle with a tilted spike and intercept on the real axis corresponds to Rb Rb may be determined graphically by drawing the best semicircle OR by fitting R//C circuit with suitable values of R and C. Here the value R= Rb R -Zi() Note: both Z‘ and Z‘’ axes must have the same scale in order to see the semicircle . If only spike is present , it can be extended to obtain the intercept R • is calculated from R by using • =LA/Rb p2 2 L - thickness of sample A - area of contact p1 2 S.K. Deraman Ph.D thesis UiTM 2014

  32. SOME APPLICATION OF IS DETERMINATION OF DC IONIC CONDUCTIVITY : - Z’’ vs. Z’ plot OF IONIC CONDUCTORS PVA-NH4x (x = Cl, Br, I) Equivalent circuit of PVA-NH4x at low NH4x concentration R1 CPE2 CPE1 A0 A5 Semi-circle disappears Only resistive component prevails at higher frequency as NH4Br/I content increases A5 Equivalent circuit of PVA-NH4x at high NH4x concentration CPE3 A25 A30 Hema et. al J. Non Crystalline Solids 355 (2009) 84-90

  33. SOME APPLICATION OF IS Analysis Of IS Plot: Choosing equivalent circuits Choosing the correct equivalent circuit can be difficult Softwares do not give a unique equivalent circuit (model) for a particular IS plot but may suggest a number of complicated circuits (multiple models) Some possible equivalent circuits A Two time-constant impedance spectrum An example: B -Z” Z’ C R1 R1 + R2 B

  34. SOME APPLICATION OF IS Analysis Of IS Plot: Choosing equivalent circuits The model chosen should not only fit the IS data but also must be verifiable through other experiments, theories and justifiable through other known facts , etc. An example: The circuits below can give 3 distinct semi-circles in the IS plot if their time constants are well separated b a C1 C2 C3 Cg Can be equivalent to CR R1 R2 R3 Rg C2 RR R2 a is more suitable for a polycrystalline sample b is more suitable for a homogeneous material

  35. SOME APPLICATION OF IS DETERMINATION OF DIELECTRIC PARAMETERS OF IONIC CONDUCTORS ’vs log f (permittivity/ dielectric constant, transport processes ) : Low frequency: Static dielectric constant  10 4 • ε’ : • a measure of a material’s polarisation • associated with capacity to store charge and • represents the amount of dipole alignment in • a given volume • related to dielectric relaxation High frequency: Optical dielectric constant at 104Hz  between 3.5 and 5 Compared to pure PVC film = 3 In ionic conductors: Relaxation peaks usually not observed due to large electrode polarisation effects Alternative is M’ /M” or ac conductivity PVC(1-x)LiCF3SO3xLiPF6 Subban and Arof Ionics 9 (2003) 375-381

  36. SOME APPLICATION OF IS DETERMINATION OF DIELECTRIC PARAMETERS OF IONIC CONDUCTORS : ’ vs concentration Same trend: variation with concentration PCL-NH4SCN Woo et. al Materials Chemistry and Physics 134 (2012) 755-761

  37. SOME APPLICATION OF IS DETERMINATION OF DIELECTRIC PARAMETERS OF IONIC CONDUCTORS M”vs log f (relaxation time , transport processes ) : PEO- AgCF3SO3 Relaxation peaks Relaxation peak is responsible for fast segmental motion which reduces the relaxation time and increase the transport properties fmax Relaxation time  =1/2fmax Gondaliya et.al Materials Sciences and Applications 2 (2011) 1639-1643

  38. SOME APPLICATION OF IS DETERMINATION OF DIELECTRIC PARAMETERS OF IONIC CONDUCTORS Tan  vs log f (relaxation time and nature of conductivity relaxation) : Tan  = ”/‘ • Single well defined resonance peak is an indication of long range conductivity relaxation in good ionic conductors • From FWHM value can find out Debye conformation (=1.14) or otherwise. Effect of temperature Effect of concentration MG30-LiCF3SO3 Yap et. al, Physica B 407(20120 2421-2428

  39. SOME APPLICATION OF IS Number density of charge carriers h, mobility , diffusion coefficient D, transference number t ion etc, DETERMINATION OF IONIC TRANSPORT PARAMETERS IN IONIC CONDUCTORS : Chitosan-LiClO4-TiO2-DMC Muhammad et. al, Key Engineerinhg Materials 594-595 (2014) 608-612

  40. SOME APPLICATION OF IS Number density of charge carriers h, mobility , diffusion coefficient D, transference number t ion etc, DETERMINATION OF IONIC TRANSPORT PARAMETERS IN IONIC CONDUCTORS : CMC-NH4Br Eg. For CMC H+ CMC Sample with optimised conductivity Samsudin and Isa, J. of Applied Sciences 12 (2012) 174-179

  41. SOME APPLICATION OF IS DETERMINATION OF IONIC CONDUCTION MODEL log () -  dc vs. log () (exponent s ) : Gradient = s Small Polaron Hopping (SPH ) model Samsudin and Isa, J. of Current Engineering Research 1(2) (2011) 7-11

  42. SOME PRACTICAL DETAILS FOR IS Frequency window limitation: the available equipment have limited frequency range: fl to fh • Only part of IS spectrum is obtained (depends on R and C value) • Changing the temperature may show different parts of the full spectra provided no new conduction processes comes into play at different temperatures • Curve fitting is needed to see full spectrum

More Related