DIELECTRIC SPECTROSCOPY. & Comparison With Other Techniques

Transcription

1 DIELECTRIC SPECTROSCOPY & Comparison With Other Techniques

2 DIELECTRIC SPECTROSCOPY measures the dielectric and electric properties of a medium as a function of frequency (time) is based on the interaction of an external electric field with the electric dipole moment and charges of the medium

3 Dielectric properties Complex dielectric permittivity relative to vacuum ε * (ω)=ε (ω)-iε (ω) Complex conductivity σ * (ω)=σ (ω)+iσ (ω) Complex electric modulus Μ * (ω)=μ (ω)+iμ (ω) as a function of temperature

4 Medium in an external electric field Electric Field D=ε E+P P=ε χ s E ε s = χ s +1 D=ε ε s E

5 Medium in an external electric field Relation between macroscopic and microscopic quantities P= 1 V i p i Dipole moments can have an induced or a permanent character Permanent dipole moments, µ Induced polarization, P P 1 N = µ i + P = µ + P V V i µ Is determined by: The interaction between the dipoles The local electric field at the location of the dipole

6 Medium in an external electric field Relation between macroscopic and microscopic quantities No interaction between dipoles and local electric field equal to the outer applied field thermal energy interaction energy between the dipole and the electric field µ = 2 µ 3kT E ε ε = s 2 1 µ 3ε kt N V Langevin equation Interactions between molecules, effect of polarization of environment ε ε = s ε F = µ Fg 3ε kt s( ε + ) ( 2ε + ε ) 2 s N V Onsager-Kirkwood-Froehlich equation 2 2 Internal field Onsager factor µ int g = = 1+ z cosψ Dipole interactions Kirkwood-Froehlich factor 2 µ

7 Dielectric dispersion in time domain Perturbation Electric Field E(t) ε(t) Response Electric Displacement D(t) E(t) D(t) ε t E ε ε s E ( ) ( ) D ε t =ε ( t) = ε + ( ε s ε ) ϕ( t) E ε oo ε E ϕ ( ) = ϕ( ) = 1 t t ( t) = ϕ( t) Φ 1

8 Dielectric dispersion in frequency domain Perturbation Electric Field E(ω) ε * (ω) Response Electric Displacement D * (ω) E(t)=E sin(ϖt) D(t)=D sin(ϖt-δ) δ ϖt ( ω) = D ( ω) + id ( ω) * D ( ω) cosδ( ω) D = D ( ω) sinδ( ω) D = ε D D ε E ( ω) = cosδ( ω) ε D ε E ( ω) = sinδ( ω)

9 Time-frequency domain Time dependent dielectric function ε(t) Complex dielectric function ε * (ω) dε( t) dt 1 = 2π * ( ε ( ω) ε ) exp[ iωt] dω ( t) * dε ε ( ω) = ε dt exp[ iωt]dt Relation between dielectric function and correlation function ( ε )[ ( )] ε( t) ε = s ε Φ t * ε ( ω) ε = 1 ( ε ε ) s dφ dt ( t) exp[ iωt]dt Φ( t) = µ ( ) µ ( t) + 2 µ ( ) µ ( t) i i i i i< j i µ i 2 i j Φ( ) = 1 Φ( t ) =

10 Dielectric dispersion in frequency domain Debye relaxation t Φ ( t) = exp τd 4 3 ε' ε ( t) ε t = ε 1 exp τ D 2 1 ε'' ε *( ω) ε = ε + 1+ iωτ D f(hz)

11 Dielectric dispersion in frequency domain Kolhrauch-Williams-Watts KWW relaxation t Φ ( t) = exp τ ε ( t) ε KWW β KWW t = ε 1 exp τ KWW β KWW ε' Havrilliak-Negami relaxation 1 Φ ( ω) = * HN ε *( ω) = ε + 1 [ 1+ ( iωτ ) α ] γ HN ε [ + ( iωτ ) α ] γ HN 1 ε'' f(hz) KWW γ = 1.812( 1 α) β αγ

12 Dielectric dispersion in frequency domain

13 Dipole moments in polymers

14 Molecular motions accommodate dipole reorientation in polymers Decreasing frequency of external field

15 Dielectric dispersion in frequency domain - 6 C - 4 C 3x x1-1 dielectric loss, ε'' C C frequency [Hz]

16 Glassy state (localized motions) I, relaxations Depends on chemical structure and local molecular environment Motion of groups present in side chain around the main chain or bonds of the side chain Motion of groups in the main chain The relaxation of Johari-Goldstein type Thermally activated motion between two potential wells separated by a potential barrier

17 Glassy state (localized motions) II Characteristics of dielectric dispersion Temperature dependence of relaxation rate (time) is Arrhenius f β E = f exp β kt Dielectric strength,, increases with increasing T, more dipoles contribute act ε µ g kt F Onsager 2 N V Broad (4-6 decades) symmetric dielectric dispersion, becomes narrower with increasing T as a result of molecular environment homogenization

18 Glassy state (localized motions) II 7 6 Glassy State logf max Liquid/Rubbery State /T[K -1 ]

19 Rubbery/liquid state (segmental motions) I relaxation (dynamic glass transition) relaxation time reflects the time involved in the structural rearrangement (glass transition) of the molecules τ changes by many orders of magnitude from the liquid to the glass The α-relaxation in polymers involves cooperative micro-brownian segmental motions of the chains Segmental motions are associated with conformational transitions taking place about the skeletal bonds

20 Rubbery/liquid state (segmental motions) II Characteristics of dielectric dispersion Temperature dependence of relaxation rate (time) described by VTF equation = B fα f exp α T T Dielectric strength,, decreases with increasing T more strongly than predicted by ε µ g kt F Onsager 2 Asymmetric dielectric dispersion High f side slope, n: local chain dynamics (n increases as T increases) Low f side slope, m: cooperative dynamics of environment (m increases as T increases) N V

21 Rubbery/liquid state (global motions) I 7 6 Glassy State logf max Liquid/Rubbery State /T[K -1 ]

22 Rubbery/liquid state (global motions) I Normal mode relaxation (nm) Observed in polymers containing dipoles type A and AB Motions of the whole chain Observed at frequencies lower than the α relaxation The relaxation time of the process is strongly dependent of the molecular weight

23 Rubbery/liquid state (global motions) II Characteristics of dielectric dispersion T dependence of relaxation rate (time) same as this of relaxation Dielectric strength proportional to the mean end-to-end vector of chain 4πN ε = nm A µ 2 p F 3kTM Onsager r /T[K -1 ] m=1 and n=.7 predicted by theory, in practice n considerably smaller logf max Liquid/Rubbery State Glassy State

24 Rubbery/liquid state (charge motions) Conductivity Motion of charge carriers * σ ( 1) * ( ω) = σ ( ω) + iσ ( ω) = iωε ε ( ω) ( ω) = ωε ε ( ω) σ ( ω) = ωε ( ε ( ) ) σ ω 1 is not affected increases with decreasing f (slope of log vs logf equal to -1) independent of f equal to dc conductivity, dc T dependence of dc Arrhenius, VTF or other gives information on the conductivity mechanism

25 Separation of charges at interfaces Maxwell-Wagner-Sillars relaxation (MWS) Blocking of charges at interfaces inside inhomogeneous materials Existence of regions with different characteristics (, ) Relaxation rate (time) depends on: volume fraction, shape, and values of regions Electrode Polarization Blocking of charges at sample/electrode interfaces Observed as a steep increase of Magnitude and frequency position of the process depend on the conductivity of the sample (high values of shift polarization to high f) Time of the process depends on the sample thickness (increase of thickness results in an increase of time of process)

26 Comparison with other techniques Understanding the correlation between parameters of the molecular and supermolecular structures and macroscopic properties. Contribution to open questions regarding the relaxation by covering the widest possible time/frequency scale range by different experimental techniques

27 Comparison with Mechanical measurements Material testing method & tool for studying dynamics in polymers Material in an external mechanical field insulator elastic solid, conductor viscous liquid Viscoelastic response is analogous to dielectric dispersion Modulus representation is used In order dielectric dispersion be compared to mechanical one electric modulus has to be used for data representation M * 1 ( ω ) = * ε ( ω)

28 Comparison with Mechanical measurements Extension in broad f range by constructing master plots

29 Comparison with Mechanical measurements Comparison of relaxation time temperature dependence

30 Comparison with Mechanical measurements Selectivity of dielectric spectroscopy (block copolymers)

31 Comparison with Quasielastic Neutron Scattering Observation of the dynamics on a microscopic length and time scale ( s) S(Q, ) contains not only temporal information but also spatial information of the particle correlation function

32 Comparison with Quasielastic Neutron Scattering Different T Different T

33 Comparison with Quasielastic Neutron Scattering S 1 ω ( ) * ( Q, ω) = ImΦ ( ω) ( Q, T) ( T) τ( Q) τ =α τ ( ) Q = 1A 1, T Comparable to τ diel ( T)

34 References A. Broadband dielectric spectroscopy, F. Kremer and A. Schoenhals eds. Chapter 1 Theory of Dielectric Relaxation A. Schoenhals and F. Kremer Chapter 7 Molecular dynamics in polymer model systems, A. Schoenhals Chapter 16 Dielectric and Mechanical Spectroscopy a Comparison, T. Pakula Chapter 18 Polymer dynamics by dielectric spectroscopy and neutron scattering-a comparison, A. Arbe, J. Colmenero and D. Richter B. Electrical Properties of Polymers, E. Riande and R. Diaz-Calleja C. Dielectric Spectroscopy of Polymeric materials, J. Runt and J. Fitzgerald