Dielectric Modulus: Experiment, Application, and Interpretation
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- Βασίλης Τιτάνος Λαιμός
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1 Delecrc odulu: Expermen, Applcaon, and Inerpreaon Hory Bac Propere Expermenal Approach Applcaon Ranko Rcher Tuoral on "Broadband Delecrc Specrocopy and Applcaon" Llle, July 5
2 From hear modulu o elecrcal modulu N. G. ccrum, B. E. Read, G. Wllam, Anelac and Delecrc Effec n Polymerc Sold (Wley, London, 967) ECHANICAL DIELECTRIC (cg) re σ ran γ hear complance J γ J σ hear modulu G σ G γ G J elecrc feld E dplacemen D permvy D E elecrc modulu E D? (Dover, New York, 99)
3 Conan Feld v. Conan Charge: The odulu H. Fröhlch, Theory of Delecrc, Clarendon, Oxford, 958 S.R. Ello, J. Non-Cry. Sold, 7 (994) 97
4 Elecrcal relaxaon N. G. ccrum, B. E. Read, G. Wllam, Anelac and Delecrc Effec n Polymerc Sold (Wley, London, 967) P.B. acedo, C.T. oynhan, R. Boe, Phy. Chem. Glae 3 (97) 7. Hodge, K. L. Nga, C. T. oynhan, J. Non-Cry. Sold 35 (5) 4 F. S. Howell, R. A. Boe, P. B. acedo, C. T. oynhan, J. Phy. Chem. 78 (974) 639
5 BASIC PROPERTIES
6 Delecrc Relaxaon and Reardaon delecrc dplacemen D Q A U d E elecrc feld D E E D D Reardaon ( ) * ( ) Y * Y * ( ) Y I * U* ( ) ( ) / Relaxaon ( ) * ( ) Z * Z * U* I * ( ) Z ( ) ( )
7 defnon of delecrc and elecrc quane V volage I curren Q charge D dplacemen E elecrc feld P polarzaon delecrc funcon elecrc modulu χ ucepbly j curren deny σ conducvy ρ revy permvy of vacuum pf m A V - m S cm - eady ae relaon D E E D ( ) E E P D E χ χ j σ E jσ j jσ Q D A V E d ˆ ˆ /ˆ D& j I A ˆ ˆ ρ ˆ / E ρ j j D& Q I ( ) d ˆ σ ˆ ˆ σ σ σ ˆ ρ / ˆ σ ˆ ρ ρ ρ conan feld ep E() E θ() σ σ P () () ( ) D E jσ j E () σ & () dc j σ D& E ( ) j E & ( ) ( ) D( ) E E [ ( ) ] E χ () conan charge ep D() D θ() P () E D ( ) ( ) D E( ) D [ ( ) ] σ E
8 Relaon for me/frequency, eplon/modulu, and probably dene probably deny g ()d complex elecrc modulu *() reardaon funcon () relaxaon funcon () probably deny g ()d complex delecrc funcon *() ( ) ( ) ( ) ( ) ( ) θ ( ) ( ) () ( ) π d e d e ( ) ( ) () ( ) π d e d e () ( ) ( )( ) d e g () ( ) ( ) d e g ( ) ( ) () d g ( ) ( ) () d g ( ) ( ) * * Kramer-Krong relaon ( ) ( ) ( ) ( ) [ ] ( ) π π π d dx x x dx x x x ln ln
9 me-cale relaon: () - () for he Debye cae ( ) ( ) ˆ ˆ ( ) ( ) ( ) ( ) ( ) wh ˆ ˆ ˆ ame funcon a (), bu dfferen parameer
10 me-cale relaon: () - () for he non-debye cae ( ) ( ) ˆ ˆ Kohlrauch-Wllam- Wa (KWW) Cole-Cole (CC) ( ) ( ) ( ) α ˆ Cole-Davdon (CD) ( ) ( ) [ ] γ ˆ β α γ () ( ) β exp R. Rcher, Phyca A 87 () 6 N. Io, R. Rcher, J. Chem. Phy.
11 odel calculaon for Debye proce dc-conducvy ˆ ( ) ( ) ˆ ( ) ˆ ( ) ' () 3 σ dc ' () '' () - '' () '' () ' ().. ' () '' () - - σ log () log ()
12 Relaxaon veru Reardaon (), ', '', anδ '' ' anδ ' '' () () (), ', '' log (/ - ) log (/) ee: N. G. ccrum, B. E. Read, G. Wllam, Anelac and Delecrc Effec n Polymerc Sold (Dover, New York, 99)
13 Idencal Informaon Dfferen Empha '' 4 3 n-propanol (99 K - K).8 '' log (f/hz) log (f/hz)
14 Dfferen Technque - Idencal Informaon () Tme doman: () / () ( )[ e ] ( / ) () ( ) e β [ ] Kohlrauch-Wllam-Wa log(/) Frequency doman: *() ''() * ( ) * ( ) [ ( ) ] α γ log() '() Havrlak-Negam
15 DIELECTRIC ODULUS TECHNIQUE
16 Real Delecrc Relaxaon: The Elecrc odulu R C ref C geo U U() * ( ) * ( ) U ( ) E( ) P ( ) ( ) con. charge H. Wagner, R. Rcher, Polymer 38 (997) 55
17 Comparng () wh *().3 creolphhalendmehyleher T 35 K Selje - [g ()] *() daa (#) *() daa (#3) 5 ().. 5 '(), ''(). () daa (#) Laplace[g ()] - - / - - / - H. Wagner, Deraon, 999, anz R. Rcher, J. Non-Cry. Sold 35 () 9
18 Delecrc odulu of Poly(vnyl aceae) () / PVAc 33 K 9 K log (/) () ( ) exp KWW β KWW σ dc exp o [ () - ] / [ - ] K PVAc 9 K () log (/) exp KWW β KWW H. Wagner, R. Rcher, Polymer 38 (997) 55
19 Dynamc of Poly(vnyl aceae) acro 6 Decade n Tme log ( del KWW / ) poly(vnylaceae) T: 88.5 K o K : 3 n o. y Vogel- Fulcher- Tammann vcoy 3n relaxaon me andard T g relaxaon me over year relaxaon me 3 K / T H. Wagner, R. Rcher, Polymer 38 (997) 55 H. Wagner, R. Rcher, Polymer 38 (997) 58 R. Rcher, Phyca A 87 () 6
20 Same Dynamc Above and Below ' - T g ' 3 -log (<>/) -3-6 PVAc T g purely knec / 4 8 T g,cal 3 K all dpole reman acve β KWW T / K me emperaure uperpoon (TTS) H. Wagner, R. Rcher, Polymer 38 (997) 55
21 Nozak, ahmo: poly(vnyl aceae) n he frequency range -6-6 Hz dfferen dynamc above and below T g? Delecrc relaxaon meauremen of poly(vnyl aceae) n glay ae n he frequency range -6-6 Hz R. Nozak, S. ahmo, J. Chem. Phy. 87 (987) 7
22 I Ulra-Long Relaxaon Tme Daa Ueful? Temperaure dependence of relaxaon me and he lengh cale of cooperave moon for gla-formng lqud B.. Erwn, R. H. Colby, J. Non-Cry. Sold 37-3 () 5 Temperaure and volume effec on local egmenal relaxaon n poly(vnyl aceae) C.. Roland, R. Caaln, acromol. 36 (3) 36
23 I Ulra-Long Relaxaon Tme Daa Ueful? Daa analy wh he Vogel-Fulcher- Tammann-Hee equaon J. F. ano, E. Perera, J. Phy. Chem. A 8 (4) 84 Unveral calng, dynamc fragly, egmenal relaxaon, and vrfcaon n polymer mel E. J. Salzman, K. S. Schwezer, J. Chem. Phy. (4)
24 Thermally Smulaed odulu Relaxaon. 33 T() PVAc.8 (T,)/ T / K 3 mk / (T,) /.6.4. PVAc (T,)/ T α 7 3 / 3 ρ (T,) / T -log (/) HN (mulaed) HN VFT f (ohermal) T / K T / K advanage: ample cooled a zero feld H. Wagner, R. Rcher, Polymer 38 (997) 58
25 Elecrc odulu of Ionc Glae ()/..8.6 CKN 335 K - 4 K me/.4 Ca(NO 3 ).6 KNO 3 E 9 V d 66 µm σ n σ KWW ( ) n KWW Γ β o ( n / β ) KWW Γ( n) KWW - e d[ () / ] / dln() / KWW me / β KWW d d Φ( ) ( ln) ( ) dφ d ln KWW KWW β e KWW H. Wagner, R. Rcher, J. Appl. Phy. 85 (999) 75
26 Elecrc odulu of Ionc Glae 7 6 CKN ρ() / Ω cm ρ() / ρ () ( ) d 4 K - 33 K me / ˆ σ ˆ ˆ σ σ σ ˆ /ˆ ˆ ˆ ˆ ρ / ˆ ρ / ˆ σ ˆ ˆ ρ ρ ρ H. Wagner, R. Rcher, J. Appl. Phy. 85 (999) 75
27 DIELECTRIC HOLE-BURNING EXPERIENTS
28 Homogeneou veru heerogeneou dynamc HOOGENEOUS HETEROGENEOUS D Smuaon: Bnary 8: Lennard-Jone Lqud ENSEBLE AVERAGE log φ me log φ me dark: 5 % lea moble parcle lgh: 5 % mo moble parcle R. Rcher, Chem. Phy. Le. 6 (993) 3 S.C. Glozer, C. Dona, J. Phy.: Conden. aer (999) A85
29 Specrally elecve delecrc expermen g KWW (ln).3 β KWW.5.. heang log ( / KWW ) g KWW (ln).3. β KWW.5 anhole pecrally elecve 'heang' 3 b. hole log ( / KWW ) E ( ) Eb n( b) π ( ) Q b E b B. Schener, R. Böhmer, A. Lodl, R.V. Chamberln, Scence 74 (996) 75
30 Delecrc hole-burnng echnque: Wha do we look for? φ(), φ*()..5 elecve heang φ*() plan heang φ*() orgnal repone φ() φ () () 3() 8() 9 () ( ) ( ) ( ) ( ) φ * 3 ( ) 4 () 5() 6() 7 () ( ) ( ) ( ) ( ) log (/)
31 '() Delecrc relaxaon and reardaon n vcou glycerol log ( / - ) *() veru *() '(), ''() ''() ample hckne: 6.4 µm '() ''() frequency doman daa *(,T) T 9.8 K '() ''() log ( / - ) T 83.5 K T 87.3 K T 9.8 K T 95.8 K T.5 K '(), ''() K. Duvvur, R. Rcher, J. Chem. Phy. 8 (3) 356
32 Explong () for hgh frequency hole-burnng n () n () T 83.5 K T 87.3 K T 9.8 K T 95.8 K T.5 K /..8 n () T.5 K varable : ung parallel capacance par par n (), n ().6.4. b n (), C par 5 nf n (), C par / K. Duvvur, R. Rcher, J. Chem. Phy. 8 (3) 356
33 DHB reul for glycerol: Vercal and horzonal dfference 3 () () H() T 87.3 K 3 vercal & horzonal gnal a: n 6 w f b. Hz V b 9 V E b 4 kv/cm T 87.3 K H() - - / K. Duvvur, R. Rcher, J. Chem. Phy. 8 (3) 356
34 DHB reul for glycerol: Burn-frequency dependence log ( max / ) - - T 83.5 K T 87.3 K T 9.8 K T 95.8 K T.5 K poon of vercal hole veru burn frequency - - log ( b / ) ''() amplude of horzonal hole veru relave burn frequency ''() H max log ( HN ). H max () E ref / Eb K. Duvvur, R. Rcher, J. Chem. Phy. 8 (3) 356
35 DHB reul for glycerol: Wang-me dependence max ( w ) / max () T 87.3 K w / f b. Hz f b.6 Hz f b. Hz f b.6 Hz f b. Hz f b 6. Hz log ( mod / ) - pump - wa - probe w max max mod b ( ) ( ) w exp w mod T 87.3 K T 9.8 K T 95.8 K T.5 K - - log ( b / ) K. Duvvur, R. Rcher, J. Chem. Phy. 8 (3) 356
36 DIELECTRIC HOLE-BURNING ODEL
37 Orgnal obervaon and 'box-model' T T T 3 T 4... T N N γ γ γ γ... γ phonon bah T B. Schener, R. Böhmer, A. Lodl, R. V. Chamberln, Scence 74 (996) 75 B. Schener, R. V. Chamberln, G. Dezemann, R. Böhmer, J. Chem. Phy. 7 (997) 7746 R. V. Chamberln, B. Schener, R. Böhmer, a. Re. Soc. Symp. Proc. 455 (997) 7
38 Calculaon of energy lo (heang) for RC nework R R R 3 R 4... R N C C C C3 C4 CN g(ln) RC... dvc d P p ˆ () ( ) V ( ) V ( ) ( < ) X C, VC RC Q A () V ( ) C () V () I () R R C A VR R ( ) polarzaon power N ( ) C C Cgeo RC R. Rcher, Phyca A 3 (3) 43
39 Calculaon of heang p() for RC nework amplude π π 3π 4π..5 p() V x () P() / E () x prevou eady ae cae: q eq π υe E n ( ) ( ), b nπ nπ b b b, oherwe nπ b > nπ b p () E υ ( ) [ ( ) ( ) ( )] b b n b co b exp b b [ exp( nπ )] exp( ) b,, nπ > nπ b b R. Rcher, Phyca A 3 (3) 43
40 Delecrc and hermal relaxaon me n glycerol REAL IAG LOG N. O. Brge, S. R. Nagel, Phy. Rev. Le. 54 (985) 674 R R R 3 R 4... R N c p... c p c p 3 c p 4 c p N C C C C3 C4 CN N... phonon bah c p g(ln) β KWW.64 β KWW.65 g(ln) K. Schröer and E. Donh, J. Chem. Phy. 3 () 9
41 Only one ep furher: Tau' are locally correlaed c p... c p c p 3 c p 4 c p N c p.5 JK cm 3 3 phonon bah 4... c p N E eff A ln 4 ( T ) K R R R 3 R 4... R N C C C C3 C4 CN , 75.7 α HN.95, γ HN.58, HN 85 g(ln) odel: locally correlaed rucural and hermal relaxaon me heerogeney K.R. Jeffrey, R. Rcher, K. Duvvur, J. Chem. Phy. 9 (3) 65
42 DHB n glycerol: Calculaed v. meaured reul 3 () () H() 3 H() vercal & horzonal gnal a n 6 w f b. Hz V b 9 V E b 4 kv/cm - - / log ( max / ) log ( b / ) K.R. Jeffrey, R. Rcher, K. Duvvur, J. Chem. Phy. 9 (3) 65
43 DHB n glycerol: Calculaed v. meaured reul max ( w ) / max () log ( mod / ). - - w / - max v. b - - log ( b / ) K.R. Jeffrey, R. Rcher, K. Duvvur, J. Chem. Phy. 9 (3) 65
44 Summary andard mpedance: *() from -3 Hz o 7 Hz yeld dynamc wh hgh reoluon modulu hf me by a facor of x ( ) delecrc modulu a drecly meaurable quany: me conan of > y are acceble hermally mulaed () ue low feld only how knec naure of T g, advanageou for dcrmnang varou model of relaxaon Hermann Wagner Franz Sckel Deuche Forchunggemenchaf Sonderforchungberech 6 (anz) Kalyan Duvvur Suan Wenen ASU-CLAS ar-up NSF - CHE-465 ACS/PRF AC7
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