マイクロ波領域の誘電緩和で何がわかるか

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みいかさどひら
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2 TDR(time domain reflectometry) Cole-Cole plot Debye Cole-Cole Davidson-Cole Havriliak-Negami KWW

3 Rocard Equation itinerant oscillator model A KWW 42 42

4 /τ ω ω 1.1: Böttcher[1] 3

5 1.1 4 (2.17) 10 1/τ ω 0 ω e τ GHz MHz (H 2 0 MW=18) 25GHz CH 3 OH MW=32 3GHz (C 2 H 5 OH MW=46) 1GHz 0 2.4GHz GHz (CCl 4 ) 1.1

6 1.1 5

7 2 2.1 p 0 (a) ( E = 0) < p 0 >=0 (b) ( E 0) 2.1: 2.1(a) p 0 0 P 2.1(b) P 0 2.1(a) P 2.2 P 6

8 2.2 7 V Q C C = Q V (2.1) C C = εk (2.2) ε ε 0 K C = εk C 0 ε 0 K = ε (2.3) ε 0 ε r = ε ε 0 (2.4) E 1 P P o : 1 (rise transient) (decay transient) [2]

9 2.2 8 P o P 0 P o P o P s P o P o P s dp o = P s P P o (2.5) dt τ 1/τ d(p s P P o ) P s P P o = dt τ (2.6) ln(p s P P o )= t τ + C (2.7) C t =0 P o =0 C = ln(p s P ) { ( P o (t) =(P s P ) 1 exp t )} (2.8) τ P o P s t =0 P P s dp s dt = P s τ ln P o = C t τ (2.9) (2.10) t =0 P o = P s P P o (t) =(P P ) exp ( t ) τ (2.11) dp o (t) = 1 dt τ P o(t) (2.12) ( P o (t) =P o (0) exp t ) τ (2.13) step response function ( Φ or P (t) =exp t ) τ (2.14)

10 2.2 9 τ pulse response function ( φ or P (t) = Φ or P (t) =1 τ exp t ) τ (2.15) ε (ω) =ε +(ε S ε ) 1 τ 0 e iωt φ or P (t)dt (2.16) ε (ω) =ε + ε S ε 1+iωτ (2.17) ε ε S (ω 0) ε = ε S ε (2.17) Debye Debye 4.1 6

11 3 3.1 Hz electric wave microwave Brillouin light visible light Raman scattering IR absorption radiation neutron(inelastic incoherent) NMR TDR LCR meter impedance material analyzer network analyzer photon correlation Fabry-Perot interferometry grating cable waveguide 3.1: LCR TDR 10

12 3.2 TDR(time domain reflectometry) GHz TDR 10 GHz THz THz TDR(time domain reflectometry) TDR (a) Z Z = 3.2(b) Z V 0 Z 0 Time Domain Reflectometry(TDR) TDR ISBN

13 3.2 TDR(time domain reflectometry) 12 (a) S V i Z V r (b) voltage V0 reference plane time (c) 0.45 Voltage (V) R s R x Time (sec.) 40 50x : Time Domain Reflectometry 3.2(b) TDR 3.2(c) TDR ε x (ω) ε s(ω) ε x(ω) = 1+{(cf s)/[jω(γd)ε s(ω)]}ρ f x (3.1) 1+{[jω(γd)ε s(ω)]/(cf s )}ρ f s ρ = V s(ω) V x (ω) V s (ω)+v x (ω) (3.2) f i (z) =z i cot(z i ) z i =(ωd/c)ε(ω) 1/2 d γd V s (ω) R s (t) V x (ω) R x (t) ω c

14 3.2 TDR(time domain reflectometry) 13 R s (t) R x (t) ε s(ω) 3.1 ε x (ω) ε x(ω) γd HP54121T,Hewlett- Packard (HP54120B) (HP54121A) Power Macintosh8100, Apple Computer) GPIB SCSI (MacAdios488s, GW Instruments, Inc.) TDR 200 mv [3][4][5] Hz d=1.0 mm d=2.0 mm Hz d=0.01 mm d

15 (a) (b) 3.3: 3.3 SMAjack-jack 50 Ω mv 200 mv NaCl [6] R s Voltage (V) R s2 R X Time (sec.) x :

16 R S1 R x R S2 NaCl R S2 R x 3.5 3x Voltage (V) x10-9 Time (sec.) 3.5: σ/(iω) (3.2) 3.5 NaCl (3.2) NaCl NaCl TDR TDR TDR

17 3.3 16

18 4 4.1 (2.17) Debye Debye Debye (2.14) Φ or P (t) = ( g k exp t ) (4.1) τ k k (2.15) ( φ or P (t) = g k exp t ) τ k τ k k (4.2) ε (ω) =ε +(ε S ε ) k g k 1+iωτ k (4.3) τ k Debye Debye (4.3) τ k (g k,τ k ) 4.3 τ k Debye 17

19 4.2 Cole-Cole plot Cole-Cole plot Debye Debye ε (ω) =ε + ε S ε 1+iωτ (4.4) 4.1(a) τ ω ε s ε =1 ε =0.1 ωτ = τ ε', ε'' ε" log(f) Hz ε' (a) Debye (b) Debye Cole-Cole plot 4.1: Debye Cole-Cole plot Debye ε (ω) ε (ω) Cole-Cole plot Debye 4.1(b)

20 4.2 Cole-Cole plot Cole-Cole Cole Cole Debye ε Debye [7] ε (ω) =ε + ε S ε 1+(iωτ) β (4.5) β 0 <β 1 β =1 β (4.5) Cole-Cole ε', ε'' β=0.8 β=0.6 β=0.4 β=0.2 β=1.0 ε" β=1.0 β=0.8 β=0.6 β=0.4 β= log(f) Hz ε' (a) Cole-Cole (b) Cole-Cole Cole-Cole plot 4.2: Cole-Cole Debye Cole-Cole Cole-Cole plot Cole-Cole τ Davidson-Cole Davidson Cole [8, 9] ε (ω) =ε + ε S ε (1 + iωτ) α (4.6) α 0 <α 1 α =1 α (4.6) Davidson-Cole

21 4.2 Cole-Cole plot ε', ε'' α=1.0 α=0.8 α=0.6 α=0.4 ε" α=1.0 α=0.8 α=0.6 α= α= α= log(f) Hz ε' (a) Davidson-Cole (b) Davidson-Cole Cole-Cole plot 4.3: Davidson-Cole Havriliak-Negami Havriliak Negami Cole-Cole Davidson-Cole ε (ω) =ε + ε S ε (4.7) (1 + (iωτ) β ) α [10, 11] α 0 <α 1 β 0 <β 1 Havriliak-Negami α β [12] Cole-Cole Davidson-Cole Havriliak-Negami Debye Havriliak-Negami ( ) β(1 α) τ sin βθ G(ln τ) = 1 π { ( τ τ 0 ) 2(1 α) ( τ +2 ) (1 α) cos π(1 α)+1} β 2 (4.8) τ 0 sin π(1 α) θ = arctan τ (4.9) + cos π(1 α) τ 0 [1] α =1 β =1 Cole-Cole Davidson-Cole τ 0

22 4.2 Cole-Cole plot 21 (4.8) α β (4.7) Debye ε S ε τ α β ε', ε'' α,β=1.0 α,β=0.8 α,β=0.6 α,β=0.4 α,β=0.2 ε" α,β=1.0 α,β=0.8 α,β=0.6 α,β=0.4 α,β= log(f) Hz ε' (a) Havriliak-Negami (b) Havriliak-Negami Cole-Cole plot 4.4: Havriliak-Negami ωτ =1 (4.6) (4.8) ω ωτ =1 τ KWW ( ) βkww t Φ or P (t) =exp, 0 <β KWW 1 (4.10) τ 0 (4.10) Kohraush function stretched exponential

23 A KWW ε', ε'' β KWW =1.0 β KWW =0.8 β KWW =0.6 β KWW =0.4 β KWW =0.2 ε" β KWW =1.0 β KWW =0.8 β KWW =0.6 β KWW =0.4 β KWW = log(f) Hz ε' (a) KWW (b) KWW Cole-Cole plot 4.5: KWW β KWW Debye KWW β KWW Ngai 4.10 [13] Cole-Cole Davidson-Cole Havriliak-Negami KWW 4.3 Debye Cole-Cole Davidson-Cole KWW Havriliak-Negami Debye Debye [14] Debye Debye

24 Debye 500kHz 10GHz [15, 16] KHz MHz MHz GHz Debye Cole-Cole Davidson-Cole Havriliak-Negami KWW [17] 4.4 Havriliak Havriliak-Negami α β [12] 4.6

25 HN(α=2.5,β=1) Debye DHO ε', ε'' log(f) Hz 4.6: HN α>1 4.6 Debye Havriliak- Negami α =2.5,β =1 Havriliak-Negami β α β Havriliak-Negami 6 Havriliak-Negami α β Havriliak-Negami Debye Havriliak-Negami 4.6

26 GHz ps ps [18] 4.7

27 : [19] Mashimo TDR [20] Mashimo TDR Havriliak-Negami log(τ) 0.8 α 0.8 Eyring τ τ = h kt exp ( G RT ) (4.11)

28 h k T R G G mix = x G 1 +(1 x) G 2 (4.12) G mix G 1 G 2 x 1 τ mix = h ( ) kt exp Gmix = τ1 x τ (1 x) 2 (4.13) RT log τ mix = x log τ 1 +(1 x) log τ 2 (4.14) Mashimo x =0.83 m m 1 x w G =[x w (m 1)(1 x w )] G w +(1 x w ) G c = m[x w (m 1)/m] G w +(1 x w ) G c (4.15) G G w G c log τ = m[x w (m 1)/m] log τ w +(1 x w ) log τ c (4.16) m =5.9 ± 0.3 (4.16) Sato TDR 300MHz 25GHz 20 C 22.5 C 25 C [21] Davidson-Cole Havriliak-Negami X X >0.4 Cole-Cole Debye 0 <X 4 Cole-Cole

29 Eyring τ τ = h ( ) G kt exp = h RT kt exp ( H RT ) exp ( ) S R (4.17) H S G = H TδS [ ( )] h G = RT ln τ 1 ln (4.18) kt H = ( G/T ) (1/T ) [ ] ln τ1 = R RT (4.19) (1/T ) T S = H G (4.20) G H S X =0.18 H S H S Cole-Cole β X 0.42

30 5 5.1 C 0 ω =2Πf V (t) =V 0 e iωt 90 I(t)=iωC 0 V (t) ω δ δ (a) (b) 5.1: I c = iωcv I l = GV R =1/G I =(iωc + G)V (5.1) ε C = ε C 0 δ tan δ = I l I C = G ωc (5.2) I I =(iωε C 0 + ωε tan δ) V (5.3) 29

31 ε = ε iε tan δ ε ε (5.4) 1 I =(iωε + ωε ) C 0 V = iωε C 0 V (5.5) W W (ω) = 1 2 R(IV )=1 2 ωε (ω)c 0 V 2 0 (5.6) 5.2 (5.6) ωε (ω) ε χ 2 ε ω ω

32 ωε"(ω) ε"(ω) plateau ωε"(ω) ε"(ω) log(f) Hz 5.2: Debye GHz 25GHz 25GHz 5.3 [14, 22] GHz THz

33 Dielectric loss ε" GHz loss peak Barthel Hasted water at room temperature far infrared intermolecular vibration 300 µm 30 µm Absorption coefficient α" (arb. units) water at room temperature micreowave oven far infrared Barthel Hasted Frequency (Hz) Frequency (Hz) (a) (b) 5.3: [14, 22] 5.2 plateau Debye plateau (2.17) ω 1 ωε (ω) 6 ωε (ω) ε (ω)

34 5.3 33

35 Debye [23, 24] dipole moment µ µ u = µ(t)/ µ u d u dt = ω(t) u(t) (6.1) ω(t) ω(t) I d u(t) dt + ζ ω(t) =λ(t)+ µ(t) E(t) (6.2) I zeta ω(t) λ(t) (6.2) λ(t) =0 (6.3) λ i (t)λ j (t ) =2kT ij δ(t t ) (6.4) δ i, j x, y, z I 0 ζ

36 ω(t) = λ(t) ζ + µ(t) E(t) ζ (6.5) (6.5) (6.4) narrowing limit (6.2) (6.5) overdamped limit (THz) (6.5) (6.1) d µ(t) dt = λ(t) ζ + µ(t)+ µ2 E(t) ζ µ[ µ E(t)] ζ (6.6) J d J d = W v (6.7) v = u W (θ, φ, t) dipole moment u u x = sin θ cos φ, u y = sin θ sin φ, u z = cos φ E drift current (6.6) (6.7) E(t) = gradv = V θ e θ 1 V sin θ φ e φ (6.8) = E θ e θ + E φ e φ (6.9) J d = 1 ζ [ V θ e θ + 1 ] V sin θ φ e φ J d J diff W (θ, φ) (6.10) J = J d + J diff J diff = DgradW (6.11)

37 [ W J θ = ζ J φ = ] V θ + D W θ V φ + D sin θ [ W ζ sin θ ] W φ (6.12) (6.13) W t + div J =0 (6.14) divj = 1 [ sin θ θ (J θ sin θ)+ J ] φ φ (6.15) (6.12) (6.15) Fokker-Plank W t [ ( 1 = D sin θw sin θ θ + 1 [ 1 ζ sin θ θ W theta + 1 ( sin θw V θ + 1 sin 2 θ )] 2 W sin 2 θ φ ( 2 W V ))] φ φ (6.16) W t =0 W Maxwell-Boltzmann W 0 = Ae V (θ,φ) k B T (6.17) (6.16) D = k BT ζ Debye relaxation time τ D τ D (6.16) 2τ D W t = + 1 sin θ θ 1 k B T τ D = ( sin θ W θ [ 1 sin θ θ ζ 2k B T ) + 1 sin 2 θ ) ( sin θw V θ 2 W φ sin 2 θ ( W V )] φ φ (6.18) (6.19) (6.20) z V (θ, φ) =V (θ) = µe cos θ (6.20) W(θ, t) = 1 [ ( kb T W(θ, t) sin θ + µe )] t sin θ θ ζ θ ζ sin θw(θ, t) (6.21)

38 6.2 Rocard Equation 37 (6.21) W (θ, t) = a n (t)p n (cos θ), n =1, 2, (6.22) n=0 P n (cos θ) E = E 0 t =0 (after effect solution) W (θ, t) =A(1 + µe 0 g(t) cos θ) (6.23) k B T (6.23) (6.21) ( W (θ, t) =A 1+ µe ) 0 k B T e (2k Bt/ζ)t cos θ dipole moment 2π π 0 0 2π π 0 0 2k B T t ζ µ cos θ = µw cos θ sin θdθdφ W sin θdθdφ = µ2 E 0 e 3k B T (6.24) (6.25) GHz Debye ω 1 ω 3 THz (6.2) 6.2 Rocard Equation t =0 t =0 f(θ, 0) Maxwell-Boltzmann I θ(t)+ζ θ(t)+µe sin θ(t) = λ(t) (t<0) (6.26) I θ(t)+ζ θ(t) = λ(t) (t>0) (6.27)

39 6.2 Rocard Equation 38 λ(t) λ(t)λ(t ) =2kTζδ(t t ) θ(t) Gaussian random variable cos θ(0) cos θ(t) cos 2 θ(0) cos θ(t 1 ) cos θ(t 2 ) = cos θ(t 1 ) cos[θ(t 1 )+ θ] (6.28) θ = θ(t 2 ) θ(t 1 ) cos θ(t 1 ) cos θ(t 2 ) = 1 2 { cos θ + cos [ θ +2θ(t 1)] } = 1 2 R{ exp i θ + exp [i θ +2θ(t 1)] } (6.29) R θ(t 1 ),θ(t 2 ) Gaussian random variable θ Gaussian random variable X { exp ix = exp i X 1 [ X 2 X 2]} (6.30) 2 (6.29) cos θ(t 1 ) cos θ(t 2 ) = 1 { (exp 2 R i θ 1 [ ( θ) 2 θ 2]} 2 { + exp i θ +2θ(t 1 ) 1 }) 2 [ θ +2θ(t 1)] 2 [ θ +2θ(t 1 )] (6.31) θ (6.31) t 2 t 1 cos θ(t 1 ) cos θ(t 2 ) = 1 [ {exp 2 R i θ 1 ( ( θ) 2 θ 2)]} (6.32) 2 θ =0 (6.32) cos θ(t 1 ) cos θ(t 2 ) = 1 2 [ 1 ] 2 ( θ)2 (6.33) mẍ(t) = ζẋ(t)+λ(t) ( x) 2 = 2k ( ) BTm ζ ζ ζ 2 m t 1+e m t ([23], pp ) { [ ( )]} cos θ(0) cos θ(t) kb TI ζt R(t) = = exp cos 2 θ(0) ζ 2 I ζ 1+e I t (6.34) ε[s] ε [0] =1 s 0 e st R(t)dt, s = iω (6.35)

40 6.3 itinerant oscillator model 39 ε[s] ε [0] = 1 s s + γβ [ 1+ γ = k BT Iβ 2,βγ = 1 τ D γ (s/β)+γ +1 + ε [s] ε [0] =1 s β β s + (6.37) ] γ [(s/β)+γ + 1][(s/β)+γ +2] + (6.36) 1 γ 1+ β s + 2γ 2+ β s + 3γ ε[s] ε[0] = 1 1+sτ 3+ β s... ε[s] ε[0] = γβ 2 (s + γβ)(s + β) 1 1+sτ + s 2 τ/β (6.37) (6.38) (6.39) Rocard equation Rocard equation (6.39) CH 3 Cl THz ([25] p.247, [2] p.382) 6.3 itinerant oscillator model itinerant oscillator(io) model dipole µ 1 I 1 dipole µ 2 I 2 cage φ 1,φ 2 cage V (φ 1 φ 2 ) [23] ( I 1 φ1 (t)+ζ 1 φ1 (t) φ ) 1 (t) + V (φ 1 (t) φ 2 (t)) = λ 1 (t) (6.40) ( I 2 φ2 (t)+ζ 1 φ2 (t) φ ) 1 (t) ζ 2 φ2 (t) V (φ 1 (t) φ 2 (t)) = λ 1 (t)+λ 2 (t) (6.41)

41 6.3 itinerant oscillator model 40 1 V (φ 1 φ 2 )=2V 0 sin(φ 1 φ 2 ) (6.42) λ 1 (t),λ 2 (t) λ i (t)λ i (t ) =2k B Tζ i δ ij δ(t t ) (6.43) α [ ] µ 1 (ω) α µ 1 (0) = ωβ2 x y(2ˆαˆγi 1 ˆα2 r ω 2 ) imaginary part x 2 + y 2 α [ ] µ 1 (ω) x(2ˆαˆγi 1 α µ 1 (0) =ˆα2 r ω 2 (6.44) )+ωβ 1 y real part x 2 + y 2 ˆα = ( kt I 1 ) 1 2 (6.45) ˆγ = V 0 I 1 ˆα (6.46) β 1 = ζ 1 /I 1 (6.47) β 2 = ζ 2 /I 2 (6.48) Ω 2 0 = I 1 ω0 2 i 2 (6.49) I r = I 2 /I 1 (6.50) b = β 1 /β 2 (6.51) x 1 = ˆα 2 Ir 1 β 2 (1 + bir 1 ) = K 2 (6.52) x 2 = β 2 (1 + b) (6.53) x 3 = 2ˆαˆγ(1 + Ir 1 )+β2 2 b (6.54) x 4 = 2β 2 ˆαˆγ(1 + bir 1 ) (6.55) x = ω 2 (ω 2 x 3 )+x 1 (x 4 x 2 ω 2 ) (6.56) y = ω [ x 4 + x 1 (x 3 ω 2 ) x 2 ω 2] (6.57) ε (ω) = ε +(ε S ε ) α µ 1 (ω) α µ 1 (0), ε (ω) = (ε S ε ) α µ 1 (ω) α µ 1 (0) (6.58) 1 dipole moment single friction model itinerant oscillator model ([23]pp )

42 6.3 itinerant oscillator model 41 (6.44) I r,b,ˆα, ˆβ, ˆγ [26, 23]

43 A KWW [27] 1 ε = ε (ω) iε (ω) ε (ε) ε ε 0 ε = 0 [ ] dφ (t) exp ( iωt) dt (1.1) dt λ = τ β 0 s = λ 0 + iω λ 0 0 ε (ε) ε ε 0 ε = βλ 0 [exp ( st)] [ exp ( λt β)] t β 1 dt (1.2) ε (ε) ε ε 0 ε = n=1 ( 1) n 1 1 Γ(nβ +1) [ cos nβ π (ωτ) nβ Γ(n +1) 2 i sin nβ π ] 2 (1.3) 0 <β log ωτ <β<1.0 1 log ωτ 0 4 ε (ε) ε = ( 1) n 1 (ωτ 0 ) n 1 ( ) n + β 1 [ Γ cos (n 1) π ε 0 ε Γ(n) β 2 + i sin (n 1) π ] 2 n=1 (1.4) 1.4 t 0 t β 1, (0 <β<1) singularity x = λt β ε (ε) ε ε 0 ε = 0 [exp ( x)] [ exp ( iωτ 0 x 1/β)] (1.5) Macintosh Igor Pro 1 (?) [1] KWW 42

44 [1] C. J. F. Böttcher and P. Bordewijk, Theory of electric polarization, vol. II. Elsevier, second ed., , 20, 42 [2] M. W. Evans, Simulation and symmetry in molecular diffusion and spectroscopy, Adv. Chem. Phys., vol. 81, pp , , 39 [3] Y.-Z. Wei and S. Sridhar, Radiation-corrected open-ended coax line technique for dielectric measurements of liquids up to 20 ghz, IEEE Trans. Microwave Theor. Tech.s, vol. 39, no. 3, pp , [4] T. W. Athey, M. A. Stuchly, and S. S. Stuchly, Measurement of radio frequency permittivity of biological tissues with an open-ended coaxial line: Part i, IEEE Trans. Microwave Theor. Tech.s, vol. MTT-30, no. 1, pp , [5] M. A. Stuchly, T. W. Athey, G. M. Samaras, and G. E. Taylor, Measurement of radio frequency permittivity of biological tissues with an open-ended coaxial line: Part ii-experimental results, IEEE Trans. Microwave Theor. Tech.s, vol. MTT-30, no. 1, pp , [6] S. Mashimo, T. Umehara, S. Kuwabara, and S. Yagihara, Dielectric study on dynamics and structure of water bound to dna using a frequency range hz, J. Phys. Chem., vol. 93, no. 12, pp , [7] K. S. Cole and R. H. Cole, Dispersion and absorption in dielectrics, J. Chem. Phys., vol. 9, pp , [8] D. W. Davidson and R. H. Cole J. Chem. Phys., vol. 18, p. 1417, [9] D. W. Davidson and R. H. Cole J. Chem. Phys., vol. 19, p. 1484, [10] S. Havriliak and S. Negami J. Polymer Sci., vol. C14, p. 99, [11] S. Havriliak and S. Negami Polymer, vol. 8, p. 161, [12] J. Havriliak, Stephen and S. J. Havriliak, Dielectric and mechanical relaxation in materials : analysis, interpretation, and application to polymers. Hanser Publishers, , 23 43

45 44 [13] R. Richert and A. Blumen, Disorder Effects on Relaxational Processes Glasses, Polymers, Proteins. New York: Springer-Verlag, [14] J. BARTHEL, K. BACHHUBER, R. BUCHNER, and H. HETZENAUER, Dielectric spectra of some common solvents in the microwave region. water and lower alcohols, Chem. Phys. Lett., vol. 165, no. 4, pp , , 31, 32 [15] S. Bone and B. Zaba, Bioelectronics. Wiley, [16] N. Miura, N. Asaka, N. Shinyashiki, and S. Mashimo, Microwave dielectric study on bound water of globule proteins in aqueous solution, Biopolymers,vol. 34, pp , [17] N. Shinyashiki, S. Sudo, W. Abe, and S. Yagihara, Shape of dielectric relaxation curve of ethylene glycol oligomer-water mixtures, J. Phys. Chem., vol. 109, no. 22, pp , [18] I. Ohmine, Liquid water dynamics: Collective motions, fluctuation, and relaxation, J. Phys. Chem., vol. 99, pp , [19],., :, [20] S. Mashimo, T. Umehara, and H. Redlin, Structures of water and primary alcohol studied by microwave dielectric analyses, J. Chem. Phys., vol. 95, no. 9, pp , [21] T. Sato, A. Chiba, and R. Nozaki, Dynamical aspects of mixing schemesin ethanolwater mixtures in terms of the excess partial molar activation free energy, enthalpy, and entropy of the dielectric relaxation process, J. Chem. Phys., vol. 110, no. 5, pp , [22] J. B. Hasted, S. K. Husain, F. A. M. Frescura, and J. R. Birch, Far-infrared absorption in liquid water, Chem. Phys. Lett., vol. 118, no. 6, pp , , 32 [23] W. T. Coffey, Y. P. Kalmykov, and J. T. Waldron, The Langevin Equation With Applications in Physics, Chemistry and Electrical Engineering, vol. 10 of World Scientific Seriesin Contemporary Chemical Physics. Singapore: World Scientific, , 38, 39, 40, 41 [24] V. I. Gaiduk, DIELECTRIC RELAXATION AND DYNAMICS OF POLAR MOLECULES, vol. 8 of World Scientific Series in Contemporary Chemical Physics. Singapole: World Scientific,

46 45 [25] J. McConnell, Rotational Brownian Motion and Dielectric Theory. London: Academic Press, [26] M. Evans, G. H. Evans, W. T. Coffey, and P. Grigolini, Molecular Dynamics and Theory of Broad Band Spectroscopy. New York: Wiley, [27] G. Williams and D. C. Watts, Further cosiderations of non symmetrical dielectric relaxation behabiour arising from a simple empirical decay function, Trans. Faraday Soc., vol. 67, pp ,

1 2 2 (Dielecrics) Maxwell ( ) D H

1 2 2 (Dielecrics) Maxwell ( ) D H 2003.02.13 1 2 2 (Dielecrics) 4 2.1... 4 2.2... 5 2.3... 6 2.4... 6 3 Maxwell ( ) 9 3.1... 9 3.2 D H... 11 3.3... 13 4 14 4.1... 14 4.2... 14 4.3... 17 4.4... 19 5 22 6 THz 24 6.1... 24 6.2... 25 7 26