Non-linear Effects in Physics of Dielectrics

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Αιγιδιος Μέλιοι
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1 Non-lnear ffect n Phyc of Delectrc Hgh-Feld Delectrc Repone: DILCTRIC TUTORIAL Madrd, Span 6 September Coulombc tre Langevn effect nergy aborpton Tme-reolved technque Revere othermal calormetry Ranko Rchert

2 ε''(ω) delectrc relaxaton technque D ε ε log(ωτ) ε'(ω) delectrc dplacement D Q A V d electrc feld

3 typcal cae near the gla tranton propylene glycol T 7-98 K (3 K) ε' 3 ε'' - 3 ν [Hz] - 3 ν [Hz] reult uually ndependent of feld ampltude

4 varety of hgh feld technque voltage voltage voltage tme tme tme hgh DC feld low AC feld manly ω hgh AC feld no ba ω + 3ω low AC feld on hgh pule ND(t) Heat va σ dc avod heatng

5 non-lnear uceptblty ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) K K ymmetry 3 3 ymmetry caualty ymmetry: caualty: electret χ χ χ ε χ χ χ χ χ χ ε P P P P P ( ) ( ) [ ] ( ) λε ε ε λ λ ε ε : Pekara factor ln ( ) ( ) ( ) ( ) t t d t dp t P θ θ ϕ θ χε θ uperpoton prncple : ( ) ( ) dt t J J kt V L F L J J L e e e e F F e F F the equlbrum fluctuaton n the conjugate flux auto - correlaton functon of are related to Kubo (95') : lnear tranport coeffcent R. Green, M.S.

6 Coulombc tre

7 Coulombc tre exerce µm top electrode 6 mm Ø bottom electrode 3 mm Ø rng outer: mm Ø rng nner: mm Ø glycerol at 83 kv/cm work F d ε ε A F d lnε d a.7 F F () t () t [ co( ωt )] V Fd 3 N ( QV ) ( CV ) VC V + V C V ε A d 5 Y > GPa (Teflon only) a.67 MPa d lnε d energy Q V ε ε A F ε ε A + ay ay m (Teflon rng, d -6 mm) 6.7 QV V Q

8 delectrc aturaton

9 expected non-lnearty: delectrc aturaton (aka Langevn effect) coθ coθ e e µ µ coθ cotanh kt kt µ Langevn coθ L kt functon µ wth a kt coθ L( a) cotanh( a) a f µ << kt or a << coθ π π a µ 3 3kT µ coθ kt µ coθ kt dθ dθ L(a) coθ a/3 L(a) a/3 coθ. 6 8 a µ / kt

10 aturaton n water at 93 K Pekara ε λε vanvleck ε ε ( ) ε ( ) Nµ 5ε V ( kt ) 3 ε ( ε + ) ( ε + ε ) ( ε + ε ) H. A. Kolodzej, G. Parry Jone, M. Dave, J. Chem. Soc. Faraday Tran. 7 (975) 69 J. H. van Vleck, J. Chem. Phy. 5 (937) 556 A. Pekara, Acta Phy. Polon. 8 (959) 36

11 tme reolved ND experment M. Gorny, J. Zolo, S. J. Rzoka, Rev. Sc. Intrum. 67 (996) 9

12 feld effect (7-83 kv/cm) reult for propylene glycol ln ε' ln ε' 5.6 Hz - Hz propylene glycol coθ ε Nµ 5ε V ( van Vleck) ε' 6 π coθ e π e µ coθ µ coθ kt ( kt ) 3 kt dθ µ 3kT dθ ε ( ε + ) ( ε + ε ) ( ε + ε ) propylene glycol kv/cm 6 8 [ V cm - ] ε'' - 3 ν [Hz] S. Wenten, R. Rchert, Phy. Rev. B 75 (7) 63 S. Wenten, R. Rchert, J. Phy.: Conden. Matter 9 (7) 58

13 energy aborpton

14 delectrc hole-burnng technque: ummary tme ε : polarzaton at contant feld 'burn cycle' (n 3) τ τ τ 3 ω b () t b n( ωbt) πε ε ( ) Q ω b b 'wat' P(t), P*(t)..5 'meaure cycle' electve heatng P*(t) plan heatng P*(t) orgnal repone P(t) log (t/) B. Schener, R. Böhmer, A. Lodl, R. V. Chamberln, Scence 7 (996) 75 B. Schener, R. V. Chamberln, G. Dezemann, R. Böhmer, J. Chem. Phy. 7 (997) 776

15 feature of homogeneou dynamc local behavor enemble average log Φ(t) tme

16 feature of heterogeneou dynamc local behavor enemble average log Φ(t) tme

17 hgh feld mpedance - beyond the lnear regme SI-6 GN PZD-7 C geo 36 pf µm ε' 6 propylene glycol V- V- V n 3 V R Ω ε'' feld up to 5 kv/cm µ up to.8 kt. Hz to 5 khz range - 3 ν [Hz] P ε electret 3 χ caualty ( ) ( ) ( 3) 3 ( ) + χ + 3 χ + 3 χ + 3 χ + 3 χ + K ymmetry uually too mall ymmetry uually way toomall S. Wenten, R. Rchert, Phy. Rev. B 75 (7) 63 S. Wenten, R. Rchert, J. Phy.: Conden. Matter 9 (7) 58

18 analyzer nput protecton AD 59 L R n 5 Ω C n.8 pf I ba fa Ampltude [ + (ωτ) ] -/ τ f -6dB 675 Hz. 3 5 ν / Hz R PROTCT 3 MΩ: protect agant 3 V (no tme lmt) S. Wenten, R. Rchert, Phy. Rev. B 75 (7) 63 S. Wenten, R. Rchert, J. Phy.: Conden. Matter 9 (7) 58

19 addng tme-reoluton capablte to hgh-feld technque DS-35 PZD-7 voltage GN Trg Ch Ch Sgma- V n 3 V R kω V(t) / V I(t) / I - - current feld ampltude 5: 3. to 6 kv/cm S () t V () t or I () t R I ω π ω π π ω π ω n co ( ωt) S( t) dt Aco( ϕ ) ( ωt) S( t) dt An( ϕ ) tme / m A R + I ϕ arctan π tanδ tan ϕ I R L.-M. Wang, R. Rchert, Phy. Rev. Lett. 99 (7) 857 W. Huang, R. Rchert, J. Phy.Chem. B (8) 999

m channel M depth bt @ M/ bt @ M/ Ncolet Sgma

20 ngle / multple frequency technque V(t) / V - Stanford Reearch DS-35 Generator tme / m channel M depth M/ M/ Ncolet Sgma Dgtal Ocllocope W. Huang, R. Rchert, J. Chem. Phy. 3 (9) 959

21 ω veru 3ω data analy low feld repone current hgh feld repone ω approxmaton ε h - ε lo ω +3ω repone A 3ω / A ω tme

22 3ω gnal durng feld change: 3. to 6 kv/cm V 3ω / V ω I 3ω / I ω. % voltage. %. %.6 % current. %. %. % tme / D λ lnε D D ω 3ω ( + λ ) n( ωt) 3 3 () t εε n( ωt) + λεε n( ωt) εε εε + λεε 3 () t λεε n( 3ωt ) A A ω 3ω 3 εε εε lnε ω R π ω I π π ω π ω n co ( 3ωt ) V ( t) ( 3ωt ) V ( t) dt dt A R + I A A 3ω ω lnε W. Huang, R. Rchert, ur. Phy. J. B 66 (8) 7

23 calculated frequency dependence of χ glycerol T 6 K ε''(ω, ) ε'' 5 5 χ 3 (ω) - 3 ν / Hz R. Rchert, J. Non-Cryt. Sold (n pre)

24 hgh feld mpedance of glycerol and propylene carbonate glycerol ( 83 kv/cm) propylene carbonate ( 77 kv/cm) 3. PC T 66 K 5 83 kv/cm ln ε''.. ε'' (a) ε'' 5 5 kv/cm glycerol T 3 K 3 ν / Hz ln ν ln(tan δ) tan δ (c) ν / Hz ε''(b)... ( T cfg T ) / K R. Rchert, S. Wenten, Phy. Rev. Lett. 97 (6) 9573 W. Huang, R. Rchert, J. Chem. Phy. 3 (9) 959

25 re of confguratonal temperature for dfferent frequence.6 ν 5 Hz ν khz ν khz ln(tan δ)... ln(tan δ) MTHF T 96. K % 3% % % % ν t hallmark of heterogenety regardng τ T or c p (ω) 5 5 tme / m W. Huang, R. Rchert, J. Chem. Phy. 3 (9) 959

26 agreement between experment and model ν Hz ln(tan δ) 5 3 PC T 66 K ln(tan δ) I 3ω / I ω 5 3 I 3ω / I ω ω R π ω I π A π ω π ω R n co + I ( nωt) S( t) ( nωt) S( t) I ϕ arctan R π tanδ tan ϕ dt dt tme / A A 3ω ε ω ln W. Huang, R. Rchert, J. Chem. Phy. 3 (9) 959

27 non-teady tate veron of 'box'-model ε'' τ τ τ 5 τ log (ω) τ τ τ ext. feld heat ω τ τ 3 τ τ τ 5 τ eparately for each doman ε εg C D dt dt dt V I ( τ ) dτ g( τ ) ( ) and T ( ) T () t ε () t ε j () t dt τ () t () t j () t τ () t V T () t dt ε ε C τ () t dd p, () t τ ( ) C () t () t T () t () t ntal condton : τ dτ () t T T C () t Aj + A j () t T d p τ T p, C p. ε ε p, C A k BT p, D τ T () t () t C d A ε ε dt for adabatc cae () t p + j () t W. Huang, R. Rchert, J. Chem. Phy. 3 (9) 959

28 non-teady tate veron of 'box'-model () t n( ωt) for each mode '' ε εg C p, C ( τ ) dτ g( τ ) p dτ ε ε C p, C p ntal condton : D ( ) and T ( ) T (equl.) V ( t) ( t) d polarzaton : conf.temp.: adj. tme cont.: dd dt dt dt τ () t ε () () t ε D () t j t τ () t τ () t () t j () t τ () t V T () t T + ε ε C τ () t () t τ ( ) T p, () t T A T kbt I () t Aj + A j () t d() t A ε ε dt + j () t W. Huang, R. Rchert, J. Chem. Phy. 3 (9) 959

29 hgh feld mpedance technque ε'' glycerol T 6 K χ 3 (ω) - 3 ν / Hz ε''(ω, ) ε''(ω,)) ε''(ω, ) ε''(ν ) ε'' τ g(τ) ε''.... ε'' 5 ω / - τ / m T 66 K ν khz.. τ / m ν khz (a) (b) T.3... τ g(τ) Tcfg T R. Rchert, J. Non-Cryt. Sold (n pre) R. Rchert, Thermochm. Acta (ubmtted)

30 tetng the clam: τ T τ D veru τ T τ D /h L.-M. Wang, R. Rchert, Phy. Rev. Lett. () h. h. h. h.7 h.5 PC T 66 K ln(tan δ) tme / + + h t D D D p B A D t D T D p B A D D D T e h h c T k e c T k τ τ ω τ τ ω τ ρ ε ε τ ω τ τ ω τ ρ ε ε τ τ ln ln * ln h T τ D τ 5% : reult ± D τ T τ

31 ummary of relevant non-lnear effect (~ ) ln ε' ln ε'' ln ε' 5.6 Hz - Hz ln ε'' Hz -. khz propylene glycol 6 8 [ V cm - ] Coulombc tre : Fd F () t () t co( ωt ) delectrc aturaton : ε Nµ 5ε V ( van Vleck) ˆ ε ( τ ) ( kt ) energy aborpton : T e QV, Q CV, C εε A ε ε A 3 ε ε ωτ c + ω τ ( ω) ε + ε g( τ ) p ε ε A 3 ε ( ε + ) ( ε + ε ) ( ε + ε ) 3 N d T e dτ + ωτ * ε ε A ωτ + ω τ S. Wenten, R. Rchert, Phy. Rev. B 75 (7) 63

32 revere calormetry

33 bac technque: heat capacty Dfferental Scannng Calormetry T S T R ample ref. heater power W. Kauzmann, Chem. Rev. 3 (98) 9

34 dynamc heat capacty n glycerol N. O. Brge, S. R. Nagel, Phy. Rev. Lett. 5 (985) 67 A. A. Mnakov et al. Thermochm. Acta 3 (3) 89

35 tandard dynamc heat capacty c p c p c p3 c p... c pn τ τ τ 3 τ... τ N c p conventonal heat ource

36 revere dynamc heat capacty (othermal) electrc feld n( t / τ 3 ) c p c p c p3 c p... c pn τ τ τ 3 τ... τ N c p

37 revere dynamc: mcrowave heatng n low moton typcal frequency:.5 GHz

38 what do we learn? nonlnearty from energy aborpton meaure confguratonal C p thermal tme cale thermal heterogenety alcohol / onc lqud phycal agng

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