Dielectric spectra dominated by charge transport processes, as examplified for Ionic Liquids. F.Kremer

Transcription

1 Dielectric spectra dominated by charge transport processes, as examplified for Ionic Liquids F.Kremer

2 Content 1. Reminder concerning Broadband Dielectric Spectroscopy (BDS).. What are Ionic Liquids (IL)? 3. Basic equations controlling the relation between glassy dynamics and charge transport; are they fulfilled in Ionic Liquids (IL)?

3 1. Reminder concerning Broadband Dielectric Spectroscopy (BDS).

4 E Dielectric spectroscopy electric field E Debye relaxation * ε ε s ε = ε + (1 + iωτ ) ε'=ε s P P S P 0 polarization P P D ( ) 0 complex dielectric function t t ε'' ε' ε'=ε Δε=ε s -ε ε'' max ω max ω [rad s -1 ] ε s ε ε ( ω) = ε + 1+ ( ω τ ) = + ε s ε ε ( ω) ω τ 1 ( ωτ)

5 The linear interaction of electromagnetic fields with matter is described by Maxwell s equations D curl H = j + t D = ε ε E j σ E 0 = (Ohm s law) Current-density and the time derivative of D are equivalent = ( ) = + i ε ω ε ε ( ) i σ ω σ σ σ = iωε ε 0 6/14/01 5

6 Analysis of the dielectric spectra propylene glycol K 0 K 10 4 ε ε K frequency [Hz] K frequency [Hz]

7 . What are Ionic Liquids (IL)?

8 Example for ion-conducting glassy materials: Ionic Liquids (ILs) Ionic liquids are salts between organic cations and simple anions: BMIM BF4 BMIM SCN 1-butyl-3-methylimidazolium tetrafluoroborate 1-n-butyl-3-methylimidazolium thiocyanate Properties of ILs: Low glass transition temperatures High conductivity at room temperature Low viscosity even at low temperature (00 K) Novel solvents Applications of ILs: Medium in fuel cells, super-capacitors, batteries and solar cells Catalysis, extraction and separation processes Lubricants and fuels

9 Structures of some of the ILs studied: HMIM Cl EMIM BF4 HMIM PF6 MOIM BF4 HMIM BF4 BMIM BF4 HEMIM BF4 MMIM MePO4 MMIM EtPO4 3-MEP EtSO3

10 Summary concerning Ionic Liquids (IL) 1.: IL are molten salts between large organic cations and small anions..: IL have a low calorimetric glass transition temperature (0K) and hence a low viscosity even below room temperature. 3.: IL have a high electrical conductivity at room temperature. 4.: IL are novel solvents. 5.: Typical applications of ILs are: Medium in fuel cells, supercapacitors, batteries and solar cells; catalysers in extraction and separation processes; lubricants.

11 3. Basic equations controlling the relation between glassy dynamics and charge transport; are they fulfilled in Ionic Liquids (IL)?

12 Basic relations between rotational and translational diffusion Stokes-Einstein relation: D = kt ζ Maxwell s relation: η =τ η G Einstein-Smoluchowski relation: D λ ω c = D: diffusion coefficient, ζ (=6π η a) : frictional coefficient,t: temperature, k: Boltzmann constant, a: radius of molecule, η: viscosity G : instantaneous shear modulus (~ Pa) η: viscosity,τ η : structural relaxation time λ : characteristic (diffusion) length ω c : characteristic (diffusion) rate Basic electrodynamics and Einstein relation: qd 0 0 c σ = qn μ = n σ ω kt σ 0 : : dc conductivity, μ: mobility ; q: elementary charge, n: effective number density of charge carriers

13 Predictions to be checked experimentally: 1.:.: 3.: 4.: ωc = P ωη kt P = π G λ as D λ ω c = σ0 ~ ωc ωc: characteristic (diffusion) rate ωη: structural relaxation rate G : instantaneous shear modulus (~ 10 8 Pa for ILs), a s : Stokes hydrodynamic radius ~λ, k: Boltzmann constant, λ: characteristic diffusion length ~. nm D : molecular diffusion coefficient (Barton-Nakajima-Namikawa (BNN) relation) Measurement techniques required: Broadband Dielectric Spectroscopy (BDS); Pulsed Field Gradient (PFG)-NMR; viscosity measurements;

14 Dielectric spectra of MMIM MePO4 ionic liquid log ε ' log σ' [S/cm] K 58 K 48 K 38 K 8 K 18 K 08 K log f [Hz] log ε'' log σ'' [S/cm] Strong temperature dependence of the charge transport processes and electrode polarisation

15 Broadband conductivity spectra of an ionic liquid log (σ' /S cm -1 ) K 60 K 40 K 0 K 10 K 00 K 190 K ω c σ 0 OMIM NTf log (σ'/σ 0 ) log (ω/s -1 ) log (ω/ω c ) Lines represent fits by RBM iωτ ( ) c σω= σ0 ln( 1 iωτ ) + c J.C. Dyre, J. App. Phys. 1988, 64, 5 J. R. Sangoro et al. Soft Matter (011) J. R. Sangoro et al. JCP(008) 18, C. Krause et al. J Phys. Chem. B (010), The random barrier model (RBM) quantitatively describes the measured dielectric spectra

16 Random Barrier Model (Jeppe Dyre et al.) Hopping conduction in a spatially randomly varying energy landscape Analytic solution obtained within Continuous-Time-Random Walk (CTRW) approximation The largest energy barrier determines Dc conduction The complex conductivity is described by: iωτ ( ) e σω= σ0 ln( 1 iωτ ) + e τ e is the characteristic time related to attempt frequency to overcome the largest barrier determining the Dc conductivity

17 Correlation between the mechanical relaxation rate ω η and the hopping rate ω c ω c (s -1 ), ω η (s -1 ) ω c ω η BMIM BF 4 HMIM PF 6 HMIM BF 4 Measured G inf BMIM BF4 (0.07 GPa) HMIM PF6 (0.07 GPa) G HMIM BF4 (0.04 GPa) 3,6 4,0 4,4 4,8 5, 5,6 1000/T (K -1 ) Stokes-Einstein, Einstein- Smoluchowski and Maxwell relations: P ω c = P ω kt = G π G λ a η s 1 Typically: G 0.1 GPa; λ. nm; a s.1 nm; J. R. Sangoro et al.(009) Phys. Chem. Chem. Phys.

18 log ω c (s -1 ) Correlation between the mechanical relaxation rate ωη and the hopping rate ω log ω η (s -1 ) Stokes-Einstein, Einstein- Smoluchowski and Maxwell relations: ω P c = P ω kt = G π G λ a η s c 1 Typically: G 0.1 GPa; λ. nm; a s.1 nm; J. R. Sangoro et al.phys. Chem. Chem. Phys, DOI: /b816106b,(009).

19 Temperature dependence of dc conductivity of ILs -4-4 log σ 0 (S/cm) -8-1,5 3,0 3,5 4,0 4,5 5,0 5,5 1000/T (K -1 ) 0,50 0,75 1,00 T g /T Excellent scaling with calorimetric glass transition temperature log σ 0 (S/cm) -8-1 HMIM BF 4 (187 K) HMIM PF 6 (194 K) HMIM I (08 K) HMIM Br (16 K) HMIM Cl (0 K)

20 Temperature dependence of characteristic diffusion rate log 10 ω e (s -1 ) 0 - T g by DSC 4,0 4,4 4,8 5, 5,6 1000/T (K -1 ) 0,85 0,90 0,95 1,00 Characteristic diffusion rate shows a strong dependence on the anion (BF4 < PF6 < I < Br < Cl) log 10 ω e (s -1 ) 0 - HMIM BF 4 HMIM PF 6 HMIM I HMIM Br HMIM Cl T g /T T g by DSC

21 Predictions checked experimentally: 1.:.: ωc = P ωη kt P = 1 G π G λ a s ωc: characteristic (diffusion) rate ωη: structural relaxation rate G : instantaneous shear modulus (~ 10 8 Pa for ILs), a s : Stokes hydrodynamic radius ~λ, k: Boltzmann constant, λ: characteristic diffusion length ~. nm

22 Comparison with Pulsed-Field-Gradient NMR and determination of diffusion coefficients from dielectric spectra From Einstein-Smoluchowski and basic electrodynamic definitions it follows: qd( T) n( T) q λ σ0( T) = nt ( ) qμ( T) = nt ( ) q = ~ ωc kt kt τ ( T ) (n(t): number - density of charge carriers; µ(t): mobility of charge carriers) h log D [m s -1 ] D NMR D E 3,5 4,0 4,5 5,0 1000/T (K -1 ) 1.: Quantitative agreement between PFG-NMR measurements and the dielectric determination of the diffusion coefficients..: The empirical BNN-relation is an immediate consequence. 3.: The separation of n(t) and µ(t) from σ0 (T) is readily possible.

23 Separation of n(t) and µ(t) from σ 0 (T) log D [m s -1 ] MMIM MePO ,5 4,0 4,5 5,0 1000/T [1/K] log N [1/m 3 ] D NMR D E 3,5 4,0 4,5 5,0 1000/T (K -1 ) μ log µ [m V -1 s -1 ] J. Sangoro, et al., Phys. Rev. E 77, 0510 (008) µ(t) shows a VFT temperature dependence n(t) shows Arrhenius-type temperature dependence The σ 0 (T) derives its dependence from µ(t)

24 Universality of charge transport in ionic liquids log σ 0 (S/cm) HMIM Cl HMIM I HMIM Br HMIM BF 4 demo demo demo demo demo demo demo demo demo demo MMIM Me PO 4 demo demo demo demo demo EMIM Et PO 4 demo demo demo demo demo BMIM BF 4 demo demo demo demo demo demo demo demo demo demo HMIM PF 6 DMIM Et PO 4 HEMIM BF 4 MOIM BF 4 3-MEP EtSO 4 3-OMA BTA TBP Br log ω c (s -1 ) Universality despite significant structural variation (imidazolium-, ammonium-, pyridinium and phosphoniumbased ionic liquids) BNN relation holds J. R. Sangoro et al. PCCP DOI: /b816106b,(009). Despite the structural variation, universal response is observed over 11 decades

25 Predictions checked experimentally: 3.: D λ ω c = ωc: characteristic (diffusion) rate λ: characteristic diffusion length ~. nm D : molecular diffusion coefficient σ0 : Dc conductivity Applying the Einstein-Smoluchowski relation enables one to deduce the root mean square diffusion distance λ from the comparison between PFG-NMR and BDS measurements. A value of λ ~. nm is obtained. Assuming λ to be temperature independent delivers from BDS measurements the molecular diffusion coefficient D. Furthermore the numberdensity n(t) and the mobility μ(t) can be separated and the BNN-relation is obtained. 4.: σ0 ~ ωc (Barton-Nishijima-Namikawa (BNN) relation)

26 Predictions checked experimentally: 1.:.: 3.: 4.: ωc = P ωη kt P = 1 G π G λ a D λ ω c = σ0 ~ ωc s ωc: characteristic (diffusion) rate ωη: structural relaxation rate G : instantaneous shear modulus (~ 10 8 Pa for ILs), a s : Stokes hydrodynamic radius ~λ, k: Boltzmann constant, λ: characteristic diffusion length ~. nm D : molecular diffusion coefficient (Barton-Nishijima-Namikawa (BNN) relation)

27 Summary concerning the relation between glassy dynamics and charge transport in IL? 1. Glassy dynamics (rotational diffusion) and charge transport (translational diffusion) are related according to the theory of Brownian dynamics as developed by Einstein, Stokes and Smoluchowski.. The basic equations connecting diffusion and molecular friction are quantitatively fulfilled. 3. The empirical Barton-Nishijima-Namikawa (BNN) relation is an immediate consequence.

28 Homologous sequence Chemical structure of (1)1-alkyl-3-methylimidazolium bis(trifluoromethylsulfonylimides), and () 1-alkyl-3-vinylimidazolium bis(trifluoromethylsulfonylimides.

29 Effect of cation volumes on charge transport in ILs log D (m s -1 ) OMIM NTf OVIM NTf PrVIM NTf BMIM NTf PrMIM NTf PFG NMR BDS /T (K -1 ) λ P (nm) log μ (m V -1 s -1 ) 0,0 0, μ 00 K μ 43 K 0,15 0,0 0,5 0,30 V c (nm 3 ) Quantitative agreement between BDS and PFG NMR Mobility decreases exponentially with cation volume and becomes more pronounced at lower temperatures

30 Separation technique applied to BMIM BF4 BMIM BF4 3,6 4,0 4,4 4,8 5, -10 D BDS -10 log D (m s -1 ) log n (m -3 ) ,6 4,0 4,4 4,8 5, 5,6 1000/T (K -1 ) D NMR µ BDS 3,6 4,0 4,4 4,8 5, 1000/T (K -1 ) log µ (m V -1 s -1 ) Full agreement between the PFG NMR and the dielectrically determined diffusion coefficients J. R. Sangoro,...S. Naumov, J. Kärger,..., J. Chem. Phys. 18, 1509 (008)