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Dielectric properties of acetonitrile confined in carbon nanotubes
Journal Pre-proofs Dielectric Properties of Acetonitrile Confined in Carbon Nanotubes Mehmet Orhan, Alper Kinaci, Tahir Cagin PII: DOI: Reference:
S0301-0104(19)30246-0 https://doi.org/10.1016/j.chemphys.2019.110598 CHEMPH 110598
To appear in:
Chemical Physics
Received Date: Accepted Date:
4 March 2019 11 November 2019
Please cite this article as: M. Orhan, A. Kinaci, T. Cagin, Dielectric Properties of Acetonitrile Confined in Carbon Nanotubes, Chemical Physics (2019), doi: https://doi.org/10.1016/j.chemphys.2019.110598
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© 2019 Published by Elsevier B.V.
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r?2`2 0 bi M/b 7Q` /B2H2+i`B+ +QMbi Mi Q7 p +mmKX A7 i?2 /B2H2+i`B+ T`QT2`iB2b Q7 i?2 bvbi2K `2 bbmK2/ iQ #2 HBM2 ` M/ BbQi`QTB+- i?2 TQH `Bx iBQM- P- Bb T`QTQ`iBQM H iQ i?2 2H2+i`B+ }2H/- E- M/ ;Bp2M #v P(ν) = 0 X (ν)E(ν)
UjV
r?2`2 X (ν) `2T`2b2Mib 7`2[m2M+v /2T2M/2Mi 2H2+i`B+ bmb+2TiB#BHBivX am#biBimiBM;
1[M j BMiQ 1[M k H2 /b iQ
D(ν) = 0 (1 + X (ν))E(ν) = 0 E(ν) = a (ν)E(ν),
(ν) =
a (ν) 0
U9V
U8V
r?2`2 a (ν) M/ (ν) `2 + HH2/ +QKTH2t #bQHmi2 T2`KBiiBpBiv M/ +QKTH2t `2H@ iBp2 T2`KBiiBpBiv Q7 i?2 bvbi2K `2bT2+iBp2HvX h?2 +QKTH2t `2H iBp2 T2`KBiiBpBiv Bb r`Bii2M bBKTHv (ν) = 1 + X (ν)
UeV
r?Qb2 `2 H M/ BK ;BM `v T `ib- (ν) = 0 (ν) − i00 (ν)- +Q``2bTQM/ iQ i?2 `2H iBp2 RRy
T2`KBiiBpBiv M/ i?2 /B2H2+i`B+ HQbb Q7 i?2 bvbi2K `2bT2+iBp2HvX
AM i?Bb bim/v- +QKTH2t T2`KBiiBpBiv ? b #22M 2p Hm i2/ 7Q` irQ HBKBiBM; + b2b2Bi?2` 7Q` +QHH2+iBp2 /vM KB+b KQM; i?2 *L KQH2+mH2b Q` 7Q` p MBb?BM; BMi2`@ +iBQMb KQM; i?2K Ub22 /Bb+mbbBQMb #v J+Zm ``B2 i _27X (ke)- QM T ;2 9d9 M/ T ;2b 9N8@9Nd 7Q` 7m`i?2` /Bb+mbbBQMbVX d
.m2 iQ +QM}M2K2Mi Q7 i?2 *L- QM2 + M 2tT2+i i? i i?2 /B2H2+i`B+ T2`KBi@ iBpBiv /2T2M/b QM i?2 Q`B2Mi iBQM BMbB/2 i?2 im#2X h?2`27Q`2- 2z2+iBp2 /B2H2+i`B+ T2`KBiiBpBiv + M #2 /2}M2/ b /Bb+mbb2/ BM _27X (kd)(ν) = RR8
2r (ν) + z (ν) 3
UdV
r?2`2 r M/ z `2T`2b2Mi ` /B H M/ tB H /B2H2+i`B+ T2`KBiiBpBiv `2bT2+iBp2HvX .2Mb2 bvbi2K TT`Q +?, AM i?2 }`bi + b2- r?2M QM2 +QMbB/2`b i?2 bvbi2K b ;2M2` H + b2 i? i bvbi2K Bb /2Mb2 M/ 2 +? /BTQH2 KQK2Mi Bb +Q``2H i2/ rBi? 2 +? Qi?2`- i?2M i?2 bvbi2K Bb bbmK2/ iQ 2t?B#Bi +QHH2+iBp2 /v@ M KB+b BM r?B+? i?2`2 Bb /BTQH2@/BTQH2 BMi2` +iBQM KQM; i?2 KQH2+mH2bX qBi? TTHB+ iBQM Q7 HBM2 ` `2bTQMb2 i?2Q`v 7Q` 2[mBHB#`BmK- i?2 2H2+i`B+ bmb+2TiB#BHBiv BM j. Bb ;Bp2M #v X (ν) =
1 hM(0) · M(0)i ˙ Liν {−Φ}, kB T V 0
U3V
r?2`2 i?2 QT2` iQ` Liw bi M/b 7Q` 6Qm`B2`@G TH +2 i` Mb7Q`K- BX2X ˙ = Liw {−Φ}
Z∞
−iνt
e
0
dΦ(t) dt − dt
UNV
M/ M(t) Bb p2+iQ`B H bmK Q7 /BTQH2 KQK2Mib Q7 +QMbiBim2Mi KQH2+mH2b i iBK2 iX kB M/ T bi M/ 7Q` "QHixK MM +QMbi Mi M/ i?2`KQ/vM KB+ i2KT2` im`2 `2bT2+iBp2HvX o Bb i?2 pQHmK2 2M+HQb2/ #v *LhbX AM i?Bb + b2i?2 +Q``2H iBQM 7mM+iBQM Bb i`2 i2/ b
Φ(t) = Rky
hM(0) · M(t)i . hM(0) · M(0)i
URyV
AM 1[X Ry- i?2 bvbi2K Bb bbmK2/ iQ #2 /2Mb2 bvbi2K r?2`2 HH BMi2` +@ iBQMb KQM; i?2 KQH2+mH2b ? p2 #22M i F2M ++QmMiX h?mb- 1[X 3 H2 /b iQ bQHmiBQM- +QKTH2t T2`KBiiBpBiv- i? i BMi2` +iBQM Q7 i?2 /BTQH2 KQK2Mi Q7 2 +? KQH2+mH2 Bb +Q``2H i2/ rBi? Qi?2` KQH2+mH2bX .BHmi2 bvbi2K TT`Q +?, AM i?2 b2+QM/ + b2- +`Qbb i2`Kb #2ir22M i?2 /BTQH2 KQK2Mib QM /Bz2`2Mi KQH2+mH2b `2 p MBb?2/ M/ i?2 bvbi2K Bb bbmK2/ 3
iQ #2 /BHmi2 bvbi2K BM r?B+? i?2 /vM KB+b Q7 2 +? /BTQH2 KQK2Mi Bb BM/2T2M/2Mi 7`QK i?2 Qi?2`bX AM bm+? + b2- i?2 +Q``2H iBQM 7mM+iBQM Bb 2tT`2bb2/ BM i2`Kb Q7 Q`B2Mi iBQM Q7 i?2 /BTQH2 KQK2Mi Q7 2 +? KQH2+mH2 bm+? i? i
N m P
i=1 Φ(t) = N m P i=1
ui (0) · ui (t)
, ui (0) · ui (0)
7QHHQr2/ #v i?2 2H2+i`B+ bmb+2TiB#BHBiv N m P ui (0) · ui (0) 1 i=1 ˙ Liν {−Φ}, X (ν) = kB T V 0
URRV
URkV
r?2`2 Nm M/ u `2 i?2 MmK#2` Q7 i?2 KQH2+mH2b BM i?2 bvbi2K M/ i?2 /BTQH2 KQK2Mi Q7 2 +? KQH2+mH2 `2bT2+iBp2HvX
Rk8
AM i?2 7QHHQrBM; b2+iBQM- i?2 mi?Q`b b?Qr ?Qr i?2 BMi2` +iBQM K2+? MBbK KQM; i?2 BM/BpB/m H /BTQH2 KQK2Mib z2+ib i?2 /B2H2+i`B+ #2? pBQ` BM i?2 #mHF M/ +QM}M2/ *LX 9X _2bmHib M/ .Bb+mbbBQMb G TH +2@6Qm`B2` i` Mb7Q`Kb TT2 `2/ BM #Qi? 1[M 3 M/ Rk- /2T2M/BM; QM i?2
Rjy
bbmKTiBQM Q7 BMi2` +iBQM K2+? MBbK- `2 +QKTmi2/ QM i?2 ` r / i bT MMBM; y iQ 8y Tb iQ 2p Hm i2 i?2 `2H t iBQM T?2MQK2MQM BMbB/2 i?2 M MQ im#2bX h?2 iBK2 bi2T ∆t = 5 7bX h?2 2z2+i Q7 im#2 /B K2i2` QM #Qi? r (ν) M/ z (ν) Bb BHHmbi` i2/ BM 6B;m`2b R@9X JQ`2Qp2` r2 BHHmbi` i2/ i?2 2z2+i Q7 KQ/2 7`2[m2M+B2b Rj8
QM i?2 p `B iBQM Q7 /B2H2+i`B+ T2`KBiiBpBiv Q7 *L BMbB/2 *Lh Ujy@jyV BM 6B;m`2 8X M Hvb2b b?Qr i? i i?2 BMi2` +iBM; KQH2+mH2b TT`QtBK iBQM H2 /b iQ `2HB@ #H2 2biBK i2 Q7 tB H i?2 /B2H2+i`B+ +QMbi Mi +QM}M2/ BM *Lh Ujy-jyV +QKT `2/ rBi? 2tT2`BK2Mi H / imK- jeX88- b Q7 _27X (k3) Ub22 h #H2 eV r?BH2 i?2 /B2H2+i`B+
R9y
+QMbi Mi # b2/ QM i?2 /BHmi2 bvbi2K TT`Q +? /Q2bMǶi b?Qr Kmim H +QMbBbi2M+v rBi? i?2 2tT2`BK2Mi H QM2X Ai Bb Q#pBQmb i? i i?2 /2MbBiv Bb K M ;BM; T?vbB+ H N
T ` K2i2` BM i?2 K ;MBim/2 Q7 i?2 tB H /B2H2+i`B+ +QMbi MiX 1bT2+B HHv 7Q` rB/2` im#2b- i?2 HB[mB/ b?Qrb #mHF #2? pBQ` BM i?2 tB H /B`2+iBQMX h?2 /B2H2+i`B+ +QM@ bi Mi +QKTmi2/ 7Q` *L BMbB/2 *Lh Ujy@jyV- jdXRy- Bb +HQb2 i?2 2tT2`BK2Mi H R98
#mHF p Hm2- jeX88X *QMi` `v iQ Q#b2`p iBQM K /2 #v GBM M/ +Q@rQ`F2`b `2@ TQ`i2/ BM (kd)- i?2 im#2b rBi? bK HH /B K2i2`b TQbb2bb HQr2` tB H T2`KBiiBpBivX q2 i?BMF i? i b i?2 /2MbBiv #2+QK2b bK HH2`- i?2 KQH2+mH2b ? p2 KQ`2 bT +2 iQ KQp2 7`22HvX h?2 /BTQH2b `2 MQi 7Q`+2/ iQ HB;M i?2Kb2Hp2b BM i?2 tB H /B`2+@ iBQMX AM ` /B H /B`2+iBQM- /B2H2+i`B+ T2`KBiiBpBiv r2`2 HH /`QTT2/ /` biB+ HHv iQ
R8y
HKQbi p +mK T2`KBiiBpBivX am+? T?2MQK2MQM r b Q#b2`p2/ #v bQK2 mi?Q`bX 6Q` 2t KTH2- *? # M ? b ii`B#mi2/ bK HH p Hm2b Q7 /B2H2+i`B+ +QMbi Mi BM *Lhb mM/2` +QMbB/2` iBQM iQ bBM;H2 }H2 T ii2`M /m2 iQ +QM}M2K2Mi `2H iBp2Hv M ``Qr im#2bX P`B2Mi iBQM Q7 /BTQH2b Bb +`m+B H BM /2i2`KBMBM; ` /B H /B2H2+i`B+ T2`KBi@ iBpBivX 6B;m`2 d b?Qrb ?Qr ;@7 +iQ` p `B2b HQM; i?2 ` /B H /B`2+iBQM Q7 *LhaX
R88
AM ` /B H /B`2+iBQM- MQ T`272``2/ Q`B2Mi iBQM Bb Q#b2`p2/ i 7 ` r v 7`QK i?2 r HH Q7 i?2 *LhbX >Qr2p2`- bm+? Q`B2Mi iBQMb `2 HKQbi +HQb2 iQ 2 +? Qi?2`X h?Bb #2? pBQ` K v H2 / iQ /` biB+ /2+`2 b2 BM ` /B H /B2H2+i`B+ T2`KBiiBpBivX 45 40 35 30 25 20 15 10 5 0 10
0
10
1
10
2
6B;m`2 R, 6`2[m2M+v /2T2M/2Mi /B2H2+i`B+ T2`KBiiBpBiv BM tB H /B`2+iBQM # b2/ QM /BHmi2 bvbi2K TT`Q +?2bX
Ry
40 35 30 25 20 15 10 5 0 10
0
10
1
10
2
6B;m`2 k, 6`2[m2M+v /2T2M/2Mi /B2H2+i`B+ T2`KBiiBpBiv BM tB H /B`2+iBQM # b2/ QM /2Mb2 bvbi2K TT`Q +?2bX
1.5
1
0.5
0 10
0
10
1
10
2
6B;m`2 j, 6`2[m2M+v /2T2M/2Mi /B2H2+i`B+ T2`KBiiBpBiv BM tB H /B`2+iBQM # b2/ QM /BHmi2 bvbi2K TT`Q +?2bX
RR
1.2
1
0.8
0.6
0.4
0.2
0 10
0
10
1
10
2
6B;m`2 9, 6`2[m2M+v /2T2M/2Mi /B2H2+i`B+ T2`KBiiBpBiv BM tB H /B`2+iBQM # b2/ QM /2Mb2 bvbi2K TT`Q +?2bX
40 35 30 25 20 15 10 C-C-N bending mode at 380 cm-1 CH rocking mode at 1061 cm -1
5 0
3
0
500
1000
1500
2000
2500
3000
3500
6B;m`2 8, .B2H2+i`B+ +QMbi Mi M/ HQbb Q7 *L +QM}M2/ BM *LhUjy@jyV b 7mM+iBQM Q7 7`2@ [m2M+vX AM i?Bb ;` T;? i?2 bvbi2K Bb bbmK2/ iQ #2 +QKTQb2 Q7 BMi2` +iBM; KQH2+mH2bX LQiB+2 i? i- i?2 2z2+i Q7 *@*@L #2M/BM; KQ/2 i j3y cm−1 M/ CH3 `Q+FBM; KQ/2 i RyeR cm−1 QM i?2 p `B iBQM Q7 /B2H2+i`B+ +QMbi Mi M/ HQbb `2 2 bBHv B/2MiB}2/X
Rk
h #H2 j, *QKTmi2/ bi iB+ /B2H2+i`B+ +QMbi Mib Q7 i?2 +2iQMBi`BH2 i T = 298 EX G TH +2@ 6Qm`B2` i` Mb7Q`Kb T2`7Q`K2/ QM / i rBi? ∆t = 5 7b M/ MmK#2` Q7 iBK2 bi2Tb r b RyyyyX >2`2- dense M/ dilute bi M/ 7Q` +QKTmi iBQMb # b2/ QM i?2 bbmKTiBQMb Q7 BMi2` +iBM; KQH2+mH2b M/ MQM@BMi2` +iBM; KQH2+mH2b `2bT2+iBp2Hv
.B2H2+i`B+ +QMbi Mi
*LhURy-RyV
*LhUR8-R8V
*LhUky-kyV
*LhUjy-jyV
0r,dense (0)
RXy9Re
RXyd
RXyN8
RXRkR
0z,dense (0)
ReX9yy
kRXyR9
kdXkk
jdXRyy
0dense (0)
eXReR
dXdR3
NX3yj
RjXRR
0r,dilute (0)
RXjyR
RXk3d
RX89N
RXey3
0z,dilute (0)
RdXjRy
kdXjky
jjXkNy
99X89y
0dilute (0)
eXejd
NXNe9
RkXRkN
R8XNR3
50 45 40 35 30 25 20 15 10
15
20
25
30
35
40
45
6B;m`2 e, +H2 ` /2KQMbi` iBQM Q7 ?Qr bi iB+ /B2H2+i`B+ +QMbi Mi BM tB H /B`2+iBQM p `B2b rBi? *LhǶb /B K2i2`X
i i?Bb bi ;2- r2 rQmH/ HBF2 iQ QmiHBM2 /Bb+`2T M+v #2ir22M i?2 #2? pBQ` Q7 r i2` M/ *L +QM}M2/ BM M MQ im#2bX Hi?Qm;? /B2H2+i`B+ +QMbi Mi Q7 i?2 Rey
r i2` BM aq*Lh i2M/b iQ /2+`2 b2 b i?2 /B K2i2` Q7 i?2 im#2 BM+`2 b2b (kd)- Bi /2+`2 b2b +QMbB/2` #Hv BM bT?2`B+ H M MQ + pBiv Q7 #Qmi Rk ³ BM /B K2i2` b `2TQ`i2/ BM `272`2M+2 (kN)X *QMi` `v iQ r i2` BM aq*Lh- i?2 /B2H2+i`B+ +QMbi Mi Q7 i?2 *L BM+`2 b2b rBi? i?2 bBx2 Q7 i?2 im#2 b b?QrM BM 6B;X eX JQ`2Qp2`-
Rj
i?2 /B2H2+i`B+ +QMbi Mi T`2/B+i2/ 7Q` HH + b2b mM/2` +QMbB/2` iBQM Bb biBHH bK HH2` Re8
i? M #mHF QM2 Ui?2 + H+mH i2/ M/ 2tT2`BK2Mi H QM2(jy)VX AM Qi?2` rQ`/b- i?2 2z2+i Q7 +QM}M2K2Mi Bb biBHH TT`2+B i2/ 2p2M 7Q` H `;2 bBx2b Q7 i?2 im#2bX AM Q`/2` iQ K F2 +H2 ` r?v bm+? BM+`2 b2 BM /B2H2+i`B+ +QMbi Mi r b Q#b2`p2/ rBi? BM+`2 bBM; /B K2i2`b Q7 im#2b- EB`FrQQ/ +Q``2H iBQM 7 +iQ`(jR)- ; 7 +iQ`r b BMi`Q/m+2/ c g=
Nm X i=1
URjV
hcos θij i,
r?2`2 θij /2MQi2b i?2 M;H2 #2ir22M i?2 Q`B2Mi iBQMb Q7 i?2 Bth M/ i?2 Dth /BTQH2X h?2 + H+mH i2/ +Q``2H iBQM 7 +iQ` 7Q` BM+`2 bBM; ` /BB BM 2 +? *Lh Bb b?QrM BM 6B;X dX i }`bi ;H M+2- Bi + M #2 Q#b2`p2/ i? i i?2`2 Bb MQ +Q``2H iBQM 1.3
CNT (10,10) CNT (15,15) CNT (20,20) CNT (30,30)
1.2 1.1 1
g factor
0.9 0.8 0.7 0.6 0.5 0.4 0.3
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Non-dimensional radial position, r/r0
6B;m`2 d, _ /B H p `B iBQM Q7 EB`FrQQ/ +Q``2H iBQM 7 +iQ` + H+mH i2/ 7`QK i?2 1[X RjX LQi2 i? i i?2 ` /Bmb Q7 2 +? *Lh Bb b2i iQ mMBivX
Rdy
#2ir22M i?2 Bth KQH2+mH2 M/ i?2 Qi?2`b rBi?BM i?2 }`bi ? H7 Q7 i?2 ` /Bmb Q7 i?2 *Lh URy@RyVX h?Bb Bb /m2 iQ bi`QM; ` `27 +iBQM 2z2+ib Q#b2`p2/ BM i?2 +Q`2 Q7 i?Bb *LhX h?Bb `2;BQM r?2`2BM ` `27 +iBQM 2z2+ib `2 Q#b2`p2/ #2+QK2b bK HH2` rBi? BM+`2 bBM; bBx2b Q7 *LhbX "2vQM/ i?Bb +`BiB+ H ` /Bmb- +Q``2H iBQMb bi `ib iQ /2p2HQT M/ + M #2 `2T`2b2Mi2/ b +QMiBMmQmb 7mM+iBQMbX AM i?2 bK HH2bi im#2-
Rd8
i?2 Q`B2Mi iBQM Q7 KQH2+mH2b /Q2b MQi +? M;2 Km+? BM ? H7 Q7 *LhǶb ` /BmbX 6Q` H `;2` im#2b- KQH2+mH2b Q`B2Mi iBQMb Qb+BHH i2 rBi?BM +2`i BM M;H2 bT MX
R9
h?Bb #2? pBQ` bHQrb /QrM BM i?2 pB+BMBiv Q7 i?2 r HHX Ai Bb +H2 ` i? i i?2 +QmTH2/ /vM KB+b Q7 #Qi? ` `27 +iBQM M/ i?2 +QM}M2K2Mi 2z2+i /2+`2 b2b i?2 /B2H2+i`B+ +QMbi Mi 2MQ`KQmbHvX Hi?Qm;? i?2 +QM}M2K2Mi BM bK HH2` *Lh 2M+Qm` ;2b R3y
b2H7@Q`; MBx2/ M/ /B`2+i2/ /BTQH2b BM i?2 /B`2+iBQM 7`22 iQ KQp2- BM i?2 tB H /B`2+iBQM Q7 M MQ im#2b- /QKBM Mi ` `27 +iBQM 2z2+i i`B2b iQ HB;M ` i?2` HBKBi2/ MmK#2` Q7 KQH2+mH2b QTTQbBi2 iQ i?Qb2 Q7 bm`7 +2 `2;BQMX q2 #2HB2p2 i? i i?2 K BM `2 bQM 7Q` +QMbB/2` #H2 /`QTb BM /B2H2+i`B+ +QMbi Mi Bb BM+`2 bBM; 7` +iBQM H pQHmK2 Q7 ` `27 +iBQM rBi? bK HH2` bBx2b Q7 i?2 *LhbX
R38
aQ 7 `- i?2 `2bmHib Q7 /B2H2+i`B+ `2H t iBQM i?2Q`v M/ Q#i BM2/ 7`2[m2M+v /2T2M/2Mi /B2H2+i`B+ +QMbi Mi 7Q` #Qi? mM/2` i?2 bbmKTiBQMb Q7 /BHmi2 M/ /2Mb2 bvbi2Kb r2`2 BMi`Q/m+2/X AM //BiBQM iQ i?2b2- i?2 /B2H2+i`B+ +QMbi Mi r b 2p Hm i2/ b ν → 0 BM 1[X N BM +QMDmM+iBQM rBi? 1[MX Ry- Ub22 _27X (jk)Vlim
ν→0
Z∞
e−iνt
0
−
dΦ(t) dt = 1. dt
UR9V
h?mb- 1[M e bBKTHB}2b iQ
1 Mz2 =1+ kB T V 0
UR8V
2 Mr 1 . =1+ 2kB T V 0
UReV
0z (0)
0r (0)
>2`2- Mz M/ Mr `2 i?2 iQi H /BTQH2 KQK2Mi BM x M/ ` /B H /B`2+iBQMb Q7 i?2 RNy
bvbi2KX h?2 +QMp2`;2M+2 Q7 i?2 2Mb2K#H2 p2` ;2 Bb FMQrM iQ i F2 TH +2 BM HQM; T2`BQ/ Q7 iBK2X 6Q` i?Bb `2 bQM- BM Qm` bBKmH iBQMb- i?2 p2` ;2b ? p2 #22M i F2M Qp2` 8yy Tb r?B+? b22K iQ #2 bm{+B2Mi #v BMbT2+iBM; bvKTiQiB+ #2? pBQ` Q7 i?2 /B2H2+i`B+ +QMbi Mi rBi? `2bT2+i iQ iBK2 Ub22 i?2 6B;X 3VX ai M/ `/ /2pB iBQMb r2`2 HbQ iQQ bK HH BM Qm` + H+mH iBQMbX
R8
a) Dielectric constant in longitudional direction, 55
z
z
(10,10) (15-15) (20-20) (30-30)
Dielectric constant along the tube axes,
50 45 40 35 30 25 20 15
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
time (s)
5 10
b) Dielectric constant in radial direction,
r
Dielectric constant in radial direction,
r
1.14
-10
1.12 1.1 1.08 1.06 1.04 (10-10) (15-15) (20-20) (30-30)
1.02 1
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
time (s)
5 10
-10
c) Dielectric constant,
18
Dielectric constant,
16 14 12 10 8 6 4
0
0.5
1
1.5
2
2.5
3
time (s)
3.5
4
4.5
5 10-10
6B;m`2 3, .B2H2+i`B+ +QMbi Mib Q#i BM2/ 7`QK i?2 ~m+im iBQM 7Q`KmH b 1[MbX R8 M/ Rec V 7Q` tB H /B`2+iBQM #V 7Q` ` /B H /B`2+iBQM- +V 7Q` BbQi`QTB+ bvbi2KX
Re
h #H2 9, ai iB+ /B2H2+i`B+ +QMbi Mib #v 1[MbX R8 M/ ReX
RN8
h?2 bvbi2K
.2MbBiv Q7 *L UF;fK3 V
r
z
*LhURy-RyVY*L
9eyXeR
*LhUR8-R8VY*L
8d8Xdd
1.04 ± 0.08
17.80 ± 0.14
6.63 ± 0.19
*LhUky-kyVY*L
e9yX89
1.08 ± 0.07
22.29 ± 0.12
8.15 ± 0.15
*LhUjy-jyVY*L
edNXR3
1.09 ± 0.05
27.63 ± 0.11
9.93 ± 0.13
"mHF
dddXyy
1.12 ± 0.05
37.2 ± 0.10
13.08 ± 0.11
@
j3Xyy
h?2 bi iB+ /B2H2+i`B+ +QMbi Mib `2bmHiBM; 7`QK i?2 HBKBiBM; + b2 r2`2 6.63 ±
0.19- 8.15 ± 0.15- 9.93 ± 0.13 M/ 13.08 ± 0.11 7Q` *Lhb URy@RyV- UR8@R8V- Uky@kyV M/ Ujy@jyV `2bT2+iBp2HvX h?2 `2bmHib Q#i BM2/ 7`QK i?2 ~m+im iBQM 7Q`KmH `2 ;QQ/ ;`22K2Mi rBi? i?Qb2 Q7 `2H t iBQM i?2Q`vX
AM Q`/2` iQ 2Hm+B/ i2 i?2 2z2+i Q7 pB#` iBQM bT2+i` QM i?2 p `B iBQM Q7 /B@ kyy
2H2+i`B+ T2`KBiiBpBiv- r2 b?Qr i?2 TQr2` bT2+i` H /2MbBiv Q7 iBK2 /2`Bp iBp2 Q7 iBK2 +Q``2H iBQM 7mM+iBQM + H+mH i2/ 7`QK 1[X RR 7Q` irQ 2ti`2K2 + b2b- *Lh URy@RyV M/ Ujy@jyV Ub22 6B;X NVX h?2`2 Bb bB;MB}+ Mi b?B7i BM i?2 7`2[m2M+v Q7 *R@> #2M/BM; KQ/2 r?B+? H2 /b iQ bi`QM; T2 F QM #Qi? bT2+i` H /2MbBiB2bX *R@> bi`2i+?BM; KQ/2 HbQ b?B7ib QM i?2 b?QmH/2` r?2`2BM TH i2 m Bb 7Q`K2/ i
ky8
?B;? 7`2[m2M+B2bX am+? /BbiBM+iBQM r b MQi Q#b2`p2/ BM i?2 pB#` iBQM bT2+i` b?QrM BM 6B;X RyX AM 7`2[m2M+B2b bK HH2` i? M eyy +K−1 /BbiBM+iBQMb #2ir22M i?2 KQ/2b Q7 #Qi? + b2b `2 MQi /BbiBM;mBb? #H2X h?2 mi?Q`b [m2biBQM r?2i?2` i?2 /B2H2+i`B+ `2H t iBQM Q7 i?2 *L Q#2vb .2#v2 i?2Q`v Q` MQiX h?2 /BTQH2 KQK2Mi +Q``2H iBQM 7mM+iBQM K2 bm`2b i?2 +Q`@ `2H iBQM #2ir22M i?2 M(t) rBi? M(0)X ++Q`/BM; iQ .2#v2- BM bmKK `v- BMBiB H
+Q``2H iBQM M 2 (0) i2M/b iQ /2+`2 b2 2tTQM2MiB HHv iQ x2`Q /m2 iQ KQH2+mH ` BMi2` +iBQMbX L2p2`i?2H2bb- /2+ v Q7 i?2 MQ`K HBx2/ /BTQH2 iBK2 +Q``2H iBQM 7mM+@
iBQMb + H+mH i2/ 7`QK 1[X Ry Bb MQi Q7 bBKTH2 .2#v2 `2H t iBQM 7Q`KX h?2`27Q`2 i?2 MQ`K HBx2/ /BTQH2 iBK2 +Q``2H iBQM 7mM+iBQMb r2`2 }ii2/ iQ #B2tTQM2MiB H
Rd
jeX88 _27X (k3)
6B;m`2 N, SQr2` bT2+i`mK Q7 Q7 iBK2 /2`Bp iBp2 Q7 iBK2 +Q``2H iBQM 7mM+iBQM + H+mH i2/ 7`QK 1[X RRX
−17
1
x 10
Bulk acetonitrile Acetonitrile confined inside CNT (10-10)
0.9
Acetonitrile confined inside CNT (15-15) Acetonitrile confined inside CNT (20-20)
0.8
−18
x 10
Raman intensity
Acetonitrile confined inside CNT (25-25)
Inset view at around 2900 cm−1
4.5
Acetonitrile confined inside CNT (30-30)
0.7
4
0.6 −19
x 10
0.5
15
0.4
10
3.5
Inset view at around 850 cm
−1
2700
2800
2900
3000
3100
3200
5
0.3 600
700
800
900
1000
1100
0.2 0.1 0 0
500
1000
1500
2000
2500
3000
3500
wavelength (cm−1 )
6B;m`2 Ry, o `B iBQM Q7 pB#` iBQM H 7`2[m2M+B2b /2T2M/BM; QM i?2 im#2 /B K2i2`X
R3
h #H2 8, h?2 _2H t iBQM iBK2 bbQ+B i2/ rBi? /BbT2`bBQM M/ `2H t iBQM iBK2b 7Q` i?2 HB[mB/ +2iQMBi`BH2X "B2tTQM2MiB H 7mM+iBQM r b miBHBx2/ 7Q` i?2 }iiBM; i?2 MQ`K HBx2/ /BTQH2 +Q``2H @ iBQM 7mM+iBQMbX
τm UbV
"
τn UbV
h?2 `2H t iBQM iBK2 UbVc hτ i =
2 +Bτ 2 Aτm n Aτm +Bτn
*Lh URy@RyV- (R2 = 0.968)
yXdkk
2.848 × 10−13
yXkd3
5.465 × 10−12
4.847 × 10−12
*Lh UR8@R8V- (R2 = 0.968)
yX393
2.535 × 10−13
yXR8k
4.69 × 10−12
3.659 × 10−12
*Lh Uky@kyV- (R2 = 0.984)
yXd3d
2.290 × 10−13
yXkRj
2.135 × 10−12
1.595 × 10−12
*Lh Ujy@jyV- (R2 = 0.986)
yXeN3
2.645 × 10−13
yXjyk
1.587 × 10−12
1.221 × 10−12
"mHF U+ H+mH i2/V
yXdRy
1.077 × 10−13
yXkNy
2.110 × 10−12
1.900 × 10−12
7mM+iBQMb i? i `2 ;Bp2M #v hM(0) · M(t)i = Ae(−t/τm ) + Be(−t/τn ) hM(0) · M(0)i
URdV
r?2`2 A- B M/ τm - τn `2 /BbT2`bBQM i2`Kb M/ iBK2 T ` K2i2`b iQ #2 /2i2`@ KBM2/ 7`QK }iiBM; T`Q+2/m`2 `2bT2+iBp2HvX h?2 + H+mH i2/ `2H t iBQM iBK2b r2`2 kRy
bmKK `Bx2/ BM h #H2 8X 6`QK h #H2 8- Bi + M #2 `2 HBx2/ i? i i?2 +QKTmi2/ /BTQH2 iBK2 +Q``2H @ iBQM 7mM+iBQM / i MQiB+2 #Hv /2pB i2 7`QK i?2 #mHF .2#v2 `2H t iBQM #2? pBQ`X Hi?Qm;? i?2 7 bi2` +QKTQM2Mi Q7 /B2H2+i`B+ `2H t iBQM τm Bb bK HH2` i? M τn i?2 +Q2{+B2Mi Q7 i?2 7 bi2` +QKTQM2Mi- i?2 +Q2{+B2Mi A- b22Kb iQ K M ;2 `2@
kR8
H t iBQM T?2MQK2M X h?2 + H+mH i2/ iBK2 2pQHmiBQM Q7 i?2 /BTQH2 +Q``2H iBQM 7mM+iBQM b?Qr2/ i? i i?2 /BzmbBp2 M/ bHQr2` `2bTQMb2 Bb KBbb2/ BM i?2 BMBiB H T? b2 Q7 i?2 iBK2 2pQHmiBQMX Hi?Qm;? i?2 K2 M `2H t iBQM iBK2 Bb M Q`/2` Q7 K ;MBim/2 ;`2 i2` i? M i?2 BM2`iB H +QKTQM2Mi- τm - i?2 /vM KB+b Q7 i?2 bvbi2K Bb /QKBM i2/ #v i?2 `Qi iBQM H /BzmbBQM Q7 KQH2+mH2b M/ BM2`iB H 2z2+ib r?B+?
kky
`2 i F2M TH +2 BM b?Q`i iBK2X AM //BiBQM- i?2`2 Bb MQ Kmim H +QMbBbi2M+v #2ir22M i?2 + H+mH i2/ `2H t iBQM iBK2 7Q` #mHF bvbi2K r?B+? Bb H`2 /v RXN Tb M/ i?2 2tT2`BK2Mi H p Hm2- jXj8 Tb- b `2TQ`i2/ BM _27X (jy)X AM i?2 b2+QM/ r v- .2#v2 i?2Q`v Q7 /B2H2+i`B+ bm;;2bi i? i hM(t) · M(0)i
RN
/2+ vb 7`QK Bib BMBiB H p Hm2 2tTQM2MiB HHv bm+? i? i hM(t) · M(0)i = e−|t|/τD hM(0) · M(0)i
UR3V
r?2`2 τD `2T`2b2Mib .2#v2 `2H t iBQM iBK2X am#biBimiBQM Q7 1[MX R3 BMiQ 1[MX N rBi? ++QKT MvBM; 1[MbX 3 M/ e- ;Bp2b /2T2M/2M+v Q7 /B2H2+i`B+ T2`KBiiBpBiv QM 7`2[m2M+vX h?mb .2#v2 `2H t iBQM iBK2 + M #2 bi i2/ BM i2`Kb /B2H2+i`B+ T2`KBiiBpBiv- BX2X
1 0 (ν) − 1 = 2 . 0 (0) − 1 1 + ν 2 τD
URNV
h?2 .2#v2 `2H t iBQM iBK2b Q#i BM2/ 7`QK i?2 M Hvb2b 7Q` *Lhb URy@RyV M/ Ujy@jyV `2 HKQbi 2[m H iQ yXNkd M/ yX8k Tb `2bT2+iBp2HvX h?2 2biBK i2 Q7 .2@ kk8
#v2 i?2Q`v ;Bp2M #v 1[MX R3 + MMQi + Tim`2 i?2 b?Q`i iBK2 `Qi iBQM H #2? pBQ` Q7 KQH2+mH ` /BTQH2b b `2TQ`i2/ BM _27X (jj)X h?Bb Bb i?2 `2 bQM r?v T`2/B+@ iBQM Q7 .2#v2 i?2Q`v +QMi` /B+ib rBi? i?2 BM2`iB H iBK2 +QKTQM2Mi K2MiBQM2/T`2pBQmbHvX AM //BiBQM iQ i?2 `2H t iBQM iBK2- KQH2+mH ` `2Q`B2Mi iBQM /vM KB+b BM +2@
kjy
iQMBi`BH2 r b M Hvx2/ i?`Qm;? i?2 iBK2 +Q``2H iBQM 7mM+iBQM
Cl (t) = hPl (¯ u(0) · u ¯ (t))i
UkyV
r?2`2 Pl `2T`2b2Mib li? G2;2M/`2 TQHvMQKB H M/ u ¯ (t) = u(t)/u(t) Bb i?2 mMBi p2+iQ` Q7 i?2 /BTQH2 KQK2MiX h?2 +Q``2H iBQM 7mM+iBQMb bbQ+B i2/ rBi? i?2 G2;2M/`2 TQHvMQKB Hb `2
C1 (t) = hcos θ(t)i C2 (t) =
1
3 cos2 θ(t) − 1 2
UkRV
UkkV
r?2`2 cos θ(t) = u ¯ (t) · u ¯ (0)X _2Q`B2Mi iBQM iBK2b τl Ul = 1, 2V ? p2 #22M Q#i BM2/
kj8
#v }iiBM; i?2 / i T`Q/m+2/ 7`QK 1[MbX kR M/ kk iQ i`BTH2 2tTQM2MiB H 7mM+iBQMb b Q7 i?2 7Q`K Cl (t) = Ae(−t/τm ) + Be(−t/τn ) + Ce(−t/τo ) . ky
UkjV
h #H2 e, l = 1
hτ1 i =
*Lh URy@RyV
*Lh UR8@R8V
*Lh Uky@kyV
*Lh Ujy@jyV
yXkk3
yXk3j
yX983
yX8kk
τm UbV
5.981 × 10−12
4.730 × 10−12
4.290 × 10−12
3.460 × 10−12
"
yXed3
yX8ek
yXj33
yXj88
τn UbV
6.082 × 10−11
1.327 × 10−11
1.300 × 10−11
1.010 × 10−11
*
@
yXR9N
yXR8y
yXRk8
τo UbV
@
2 +Bτ 2 +Cτ 2 Aτm o n Aτm +Bτn +Cτo
UbV
3.949 × 10
−13
3.890 × 10
−13
2.700 × 10−13
5.906 × 10−11
1.189 × 10−11
1.047 × 10−11
7.828 × 10−12
UR2 = 0.999V
UR2 = 0.999V
UR2 = 1.000V
UR2 = 1.000V
1 CNT (10-10) CNT (15-15) CNT (20-20) CNT (30-30)
0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5 10
-11
6B;m`2 RR, _2Q`B2Mi iBQM +Q``2H iBQM 7mM+iBQMb 7Q` p `vBM; im#2 /B K2i2`b- l = 1X
hBK2 2pQHmiBQM Q7 C1 (t) M/ C2 (t) b b?QrM BM 6B;m`2b RR M/ Rk r2`2 }ii2/ iQ i`BTH2 2tTQM2MiB H 7mM+iBQMb M/ `2bmHiBM; `2@Q`B2Mi iBQM iBK2b r2`2 i #mH i2/ k9y
BM h #H2 e M/ dX h?2 `2bmHib b?Qr i? i `2Q`B2Mi iBQM Q7 KQH2+mH2b +QM}M2/ BM M MQim#2b `2 i F2M TH +2 `2H iBp2Hv HQM; iBK2b +QKT `2/ iQ i?Qb2 Q7 #mHF bi i2 Uτ1 = 3.28 × 10−12 _27X (j9) M/ τ2 = 1.02 × 10−12 _27X (j8)VX LQ Kmim H +QMbBbi2M+v 7Q` `2Q`B2Mi iBQM iBK2b +QKTmi2/ 7Q` *Lh Ujy@jyV +QKT `2/ rBi?
kR
h #H2 d, l = 2
τm UbV
hτ2 i =
*Lh URy@RyV
*Lh UR8@R8V
*Lh Uky@kyV
*Lh Ujy@jyV
yXj9y
yX8y3
yX93d
yX9Ne
5.020 × 10
−12
4.120 × 10
−12
3.320 × 10
−12
2.670 × 10−12
"
yXjN3
yXyNk3
yXyd99
yXy993
τn UbV
6.060 × 10−11
3.200 × 10−11
3.850 × 10−11
4.770 × 10−11
*
yXk89
yXjN
yX9jy
yX98y
τo UbV
2.510 × 10−13
3.400 × 10−13
3.650 × 10−13
3.910 × 10−13
5.678 × 10−11
1.996 × 10−11
2.494 × 10−11
2.901 × 10−11
UR2 = 0.999V
UR2 = 0.999V
UR2 = 0.999V
UR2 = 0.999V
2 +Bτ 2 +Cτ 2 Aτm n o Aτm +Bτn +Cτo
UbV
1 CNT (10-10) CNT (15-15) CNT (20-20) CNT (30-30)
0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5 10
-11
6B;m`2 Rk, _2Q`B2Mi iBQM +Q``2H iBQM 7mM+iBQMb 7Q` p `vBM; im#2 /B K2i2`b- l = 2X
kk
i?2 #mHF bi i2 _2Q`B2Mi iBQM iBK2b /2+`2 b2 rBi? BM+`2 bBM; /B K2i2` Q7 i?2 im#2b k98
b r2HHX h?Bb #2? pBQ` +QMi` /B+ib Qm` 2tT2+i iBQMb #2+ mb2 b i?2 /B K2i2` Q7 i?2 im#2 2MH `;2b i?2 BMi2` +iBQMb KQM; i?2 *L KQH2+mH2b b?QmH/ `2b2K#H2 iQ i? i Q7 #mHF bi i2X am+? +QMi` biBM; `2Q`B2Mi iBQM iBK2b rBi? i?2 #mHF bi i2 K v #2 ii`B#mi2/ iQ H `;2 MmK#2` Q7 *L KQH2+mH2b BMi2` +iBM; rBi? i?2 *Lh iQKb QM i?2 pB+BMBiv Q7 BMi2`7 +2X h?2 MmK#2` Q7 bm+? BMi2` +iBM; KQH2+mH2b
k8y
/2T2M/b QM i?2 /B K2i2` Q7 i?2 im#2 b 2tT2+i2/X aQ 7 `- i?2 mi?Q`b T`2b2Mi i?2 2z2+i Q7 7`2[m2M+v M/ i?2 im#2 /B K2i2` QM i?2 /B2H2+i`B+ T`QT2`iB2b #v /Bz2`2Mi r vbX Pm` K BM +QM+HmbBQMb r2`2 ;Bp2M i?2 T`Q+22/BM; b2+iBQMX >Qr2p2`- r2 i?BMF i? i bim/vBM; rBi? MQM@/BK2MbBQM H ;`QmT Q7 T ` K2i2`b T`2b2Mi2/ BM ?2`2 K v #2 mb27mH 7Q` 7mim`2 T2`bT2+iBp2bX 6Q` i?Bb Tm`TQb2- QM2 + M BMi`Q/m+2 MQM@/BK2MbBQM H T ` K2i2`b ;`QmT i? i /2KQMbi` i2 +QKT2iBM; 2z2+ib #2ir22M i?2 #bQHmi2 /B2H2+i`B+ T2`KBiiBpBiv M/ pBb+Qmb /BzmbBQMX h?2 MQM@/BK2MbBQM H T ` K2i2` ;`QmT + M #2 `2 / b 2 (0)0 DντD kB T , 2 u d
Uk9V
r?2`2 D- ν M/ u bi M/ 7Q` /BzmbBQM +Q2{+B2Mi- FBM2K iB+ pBb+QbBiv M/ i?2 /BTQH2 KQK2Mi Q7 *L 7Q` T ` K2i2`b ;Bp2M BM h #H2 R `2bT2+iBp2HvX EBM2K iB+ pBb+QbBiv- ν = µ/ρ r?2`2 ρ Bb /2MbBiv Q7 *L BM +QM}M2/ pQHmK2- M/ /Bzm@ bBQM +Q2{+B2Mi- D `2 #Q``Qr2/ 7`QK i?2 }`bi T `i Q7 i?Bb bim/v U_27X (je)VX k88
b r2 /Bb+mbb2/ T`2pBQmbHv #bQHmi2 /B2H2+i`B+ T2`KBiiBpBiv Bb BM~m2M+2/ #v i?2 /2+`2 bBM; bBx2 Q7 +QM}MBM; bi`m+im`2 r?2`2 BM Bi T `iB HHv BM+`2 b2b rBi? i?2 /B K2i2`X *QMi` `v iQ /B2H2+i`B+ T2`KBiiBpBiv- pBb+QbBiv i2M/b iQ #2 H `;2 rBi? bK HH2` im#2 /B K2i2`b- HBF2 /BzmbBQM +Q2{+B2MiX am+? +QMi2M/BM; T?vbB+ H T @ ` K2i2`b BM M QM2 MQM@/BK2MbBQM H ;`QmT `2bmHib BM M BKTQ`i Mi p `B iBQM
key
7`QK Bib ?B;?2bi kXd3 iQ i?2 HQr2bi yXykR p Hm2- /2T2M/BM; QM i?2 im#2 /B K2i2`X h?Bb #2? pBQ` 2Hm+B/ i2b ?Qr #bQHmi2 /B2H2+i`B+ T2`KBiiBpBiv Bb bmb+2TiB#H2 BM /2}MBM; /2+HBMBM; i`2M/ Q7 MQM@/BK2MbBQM H ;`QmT Q7 T ` K2i2`bX Ai b?QmH/ #2 +H2 ` i? i i?2 pBb+QbBiv M/ /BzmbBQM +Q2{+B2Mi TH v M 2bb2MiB H `QH2 BM i2`Kb Q7 Bib Q`/2` Q7 K ;MBim/2 +QKT `2/ rBi? i?Qb2 Q7 i?2 Qi?2`bX h?2 p `B iBQM Q7 i?Bb
ke8
MQM@/BK2MbBQM H ;`QmT Q7 T ` K2i2`b + M ;Bp2 bQK2 ?BMib iQ bmT2`+ T +BiQ`b kj
3
2
1.5
0
D B
(0) D 2 k T / (u2d)
2.5
1
0.5
0 1
1.5
2
2.5
3
diameter of nano tubes (m)
3.5
4
4.5 10
-9
6B;m`2 Rj, o `B iBQM Q7 MQM@/BK2MbBQM H ;`QmT Q7 T ` K2i2`b b 7mM+iBQM Q7 im#2 /B K2i2`X .BzmbBQM +Q2{+B2Mi- FBM2K iB+ pBb+QbBiv- M/ Qi?2` T ` K2i2`b `2 2p Hm i2/ i kN3 E
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k9
i?2 /Bbi M+2 #2ir22M i?2 iQK r?Qb2 TQi2MiB H r2HH Bb i?2 K tBKmK KQM; i?2 Qi?2`b M/ * iQKb Q7 i?2 *Lh rBHH #2 bBKTHv δr = rpore −
√
σmax σC ,
Uk8V
r?2`2 σmax Bb BMi2`KQH2+mH ` 2[mBHB#`BmK /Bbi M+2 7Q` M iQK i? i ? b K tB@ KmK TQi2MiB H r2HH KQM; i?2 +QMbiBimiBM; iQKb Q7 i?2 bvbi2K M/ σC Bb i?2 BMi2`KQH2+mH ` 2[mBHB#`BmK /Bbi M+2 Q7 i?2 *LhX AM Qm` + H+mH iBQMb δr Bb 2[m H iQ jXjdj ³ r?B+? Bb HKQbi 2[m H iQ M ? H7 Q7 i?2 ` /Bmb Q7 TQ`2 UBM Qm` + b2 0.50rCN T (10−10) = 3.387³V h?2`27Q`2- r2 T`QTQb2 `2H iBQM- bm+? i? i rmin.
of pore
√ > 2 σσC
UkeV
BM Q`/2` iQ 2HBKBM i2 BM+`2 b2 BM pBb+QbBiv- i?2 pQHmK2 Q7 ` `2}2/ `2;BQM rBi?BM i?2 TQ`2 M/ iQ 2Mbm`2 Q++mT M+v Q7 bQHp2Mi KQH2+mH2b M/ BQMb BM i?2 TQ`2X AM 1[MX ke- rmin. kdy
of pore -
σ M/ σC `272` i?2 KBMBKmK ` /Bmb Q7 i?2 TQ`2 QM i?2
2H2+i`Q/2 bm`7 +2- i?2 G2MM `/@CQM2b 2[mBHB#`BmK /Bbi M+2 Q7 i?2 iQK r?Qb2 TQi2MiB H r2HH Bb i?2 K tBKmK Q7 i?2 iQKb Q7 +QMbiBim2Mi KQH2+mH2bfBQMb M/ G2MM `/@CQM2b 2[mBHB#`BmK /Bbi M+2 Q7 i?2 * iQK Q7 i?2 *Lh `2bT2+iBp2HvX AMp2biB; iBQM Q7 i?2 TQ`2 bBx2 K v #2 #2M2}+B H 7Q` i?2 BM/mbi`v M/ Bb H27i iQ MQi?2` bim/v 7Q` KQ`2 /2i BHbX
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S0301-0104(19)30246-0 https://doi.org/10.1016/j.chemphys.2019.110598 CHEMPH 110598
To appear in:
Chemical Physics
Received Date: Accepted Date:
4 March 2019 11 November 2019
Please cite this article as: M. Orhan, A. Kinaci, T. Cagin, Dielectric Properties of Acetonitrile Confined in Carbon Nanotubes, Chemical Physics (2019), doi: https://doi.org/10.1016/j.chemphys.2019.110598
This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
© 2019 Published by Elsevier B.V.
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RyNX9dR
RyyXy
*R@*k@L
R3yXyyy
88Xy
*@*@* U*LhV
RkyXyyy
RyyXy
hQ`bBQM 7Q` *Lh
ϕ0jk U/2;V
Vjk (F+ H/KQH)
njk
y
kkX8y
k
T `iB H +? `;2b # b2/ QM JSkfe@jRRY: (kj)
(F+ H/KQH)
σ (˚ )
[
*R
yXyN8y
jX98d
@yX88k
*k
yXyN8y
jX98d
yX9d8
>
yXyR8k
kXkR9d
yXRNy
L
yXR9Ny
jXkNk
@yX9Nj
G2MM `/@CQM2b T ` K2i2`b M/
9
rBi? +QMp2`;2M+2 +`Bi2`B Q7 1.0 × 10−8 M/ 1.0 × 10−10 7Q` 2M2`;v M/ 7Q`+2 `2@
bT2+iBp2HvX GQM; ` M;2 2H2+i`Qbi iB+ BMi2` +iBQMb r2`2 + H+mH i2/ #v i?2 S `iB+H2@
ey
S `iB+H2- S `iB+H2 J2b? USSSJV K2i?Q/ (k8) rBi? +mi@Qz Q7 13³ M/ `2H iBp2 2``Q`- 1.0 × 10−5 - BM 7Q`+2 2p Hm iBQMbX h?2 GC +mi@Qz mb2/ BM bBKmH iBQMb r b HbQ 13³X h?2 /B2H2+i`B+ +QMbi Mi ? b #22M b2i iQ mMBiv M/ M2B;?#Q` HBbi ? b #22M mT/ i2/ BM 2p2`v 10 iBK2 bi2TbX aBKmH iBQMb r2`2 T2`7Q`K2/ BM irQ bi ;2bX AM i?2 }`bi bi ;2 Q7 i?2 bBKm@
e8
H iBQMb- `K+? B`b aBM;H2@q HH2/ * `#QM L MQ hm#2b Uaq*LhbV rBi? }p2 /B7@ 72`2Mi /B K2i2`b r2`2 }HH2/ rBi? *LX AM i?2 b2+QM/ bi ;2- bvbi2Kb Q7 *L }HH2/ aq*Lhb r2`2 bBKmH i2/X 1[m iBQMb Q7 KQiBQM BM GJSSa `2 bQHp2/ #v iBK2@`2p2`bB#H2 K2 bm`2@T`2b2`pBM; o2`H2i Q` `_1aS BMi2;` iQ`b /2T2M/BM; QM i?2 2Mb2K#H2 ULoh Q` LShV mb2/X ++Q`/BM; iQ ivT2 Q7 K2MiBQM2/ bi ;2b
dy
i?2 7QHHQrBM; +QKTmi iBQM H bi` i2;B2b r2`2 2KTHQv2/X h?2 7QHHQrBM; b2+iBQM /2b+`B#2b ?Qr i?2 + `#QM M MQim#2b r2`2 }HH2/ rBi? +2iQMBi`BH2X kXRX 6BHHBM; S`Q+2bb PT2M@2M/2/ *Lhb r?Qb2 H2M;i? Bb 9NXRN ³ r2`2 BKK2`b2/ BM bBKmH iBQM 3
#Qt BM bBx2 8yX33×8yX33×RyRXdd ³ r?B+? Bb 7mHH Q7 *L KQH2+mH2b i #mHF d8
/2MbBiv- ddd F;fK3 - i2KT2` im`2- kN3 EX Pp2`H TTBM; KQH2+mH2b Q7 *L rBi? i?2 iQKb Q7 *Lh r2`2 b?B7i2/ T`QT2`Hv #v Qm` ?QK2@K /2 +Q/2 bQ i? i # / +QMi +ib `2 2HBKBM i2/X LSh 2Mb2K#H2 ? b #22M 2KTHQv2/ /m`BM; i?2 }HHBM; T`Q+2bb- M/ i?2 BMi2;` iBQM iBK2 bi2T r b yX8 7bX h?2 bvbi2K r b ?2 i2/ iQ kN3 E bi `iBM; 7`QK Ry E #v TTHvBM; i?2 LQQb2@>QQp2` i?2`KQbi i rBi? k8 7b
3y
+QmTHBM; iBK2X LQb2@>QQp2` # `Qbi i rBi? k8y 7b +QmTHBM; iBK2 r b mb2/ iQ b2i i?2 T`2bbm`2 R iKX 7i2` ey Tb T2`BQ/ Q7 r `KBM; M/ T`2bbm`2 `2;mH iBQM iBK2i?2 bvbi2K r b r2HH 2[mBHB#` i2/ Qp2` jyy Tb T2`BQ/ Q7 iBK2 r?BH2 +2Mi2` Q7 K bb HQ+ iBQM Q7 i?2 *Lh r b }t2/ bT iB HHv BM 2 +? k8 7bX PM+2 }HHBM; T`Q+2bb i F2M TH +2- KQH2+mH2b r?Qb2 +2Mi2` Q7 K bb HQ+ iBQMb `2 QmibB/2 Q7 i?2 *Lh r2`2
38
2t+Hm/2/X h?2M- i?2 *Lh M/ *L KQH2+mH2b r2`2 /Qm#H2/ #v BKBi iBM; i?2 Q`B;BM H bvbi2KX AM i?Bb + b2- i?2 H2M;i? Q7 i?2 *Lhb r b BM+`2 b2/ iQ N3Xj3 ³X
8
h #H2 k, :2QK2i`B2b Q7 bvbi2Kb M/ /2MbBiB2b Q7 +QM}M2/ *L avbi2K
avbi2K /BK2MbBQMb
LmK#2` Q7 *L KQH2+mH2b
.2MbBiv Q7 *L
U³V
BM i?2 bvbi2K
UF;fK3 V
"mHF *L
50.88 × 50.88 × 50.88
R8yy
dddXy
*L Y *Lh URy-RyV
d = 13.55- l = 98.38
Ne
9eyXeR
*L Y *Lh UR8-R8V
d = 20.33- l = 98.38
kdy
8d8Xdd
*L Y *Lh Uky-kyV
d = 27.11- l = 98.38
8j9
e9yX89
*L Y *Lh Ujy-jyV
d = 40.67- l = 98.38
Rkd9
edNXR3
.2i BHb Q7 `2bmHiBM; *L@*Lh bvbi2Kb M/ /2MbBiB2bR r2`2 i #mH i2/ BM kX AM i?2 T`Q+22/BM; b2+iBQM r2 /2b+`B#2 i?2 K2i?Q/ Q7 / i T`Q/m+iBQM bBKmH iBQMb 7Q` M HvxBM; i?2 BMi2` +iBQMb #2ir22M i?2 KQH2+mH2b Q7 +2iQMBi`BH2 M/ + `#QM Ny
M MQim#2bX kXkX aBKmH iBQMb Q7 *L BMbB/2 *Lh *Lhb r2`2 HQ+ i2/ QM `2+i M;mH ` T ` HH2H2TBT2/ #Qt r?2`2 T2`BQ/B+ #QmM/@ `v +QM/BiBQMb r2`2 BKTQb2/ BM 2 +? /B`2+iBQMX h?2 HQM;Bim/BM H H2M;i? Q7 i?2 #Qt r b b2i iQ N3Xj3 ³ bQ i? i BMi2` +iBQMb Q7 *L KQH2+mH2b rBi? bm``QmM/
N8
`2 i F2M TH +2 Dmbi QM 2 +? QT2M 2M/b Q7 *LhbX aBKmH iBQM T`Q+2/m`2 7Q` *L@*Lh +QmTH2 Bb i?2 b K2 b i? i Q7 }HHBM; T`Q+2bb rBi? bQK2 2t+2TiBQMbX avbi2Kb r2`2 r2HH 2[mBHB#` i2/ Qp2` kyy Tb 7i2` i?2 i2KT2` im`2 r b b2i iQ kN3 E rBi?BM Ryy Tb- M/ i?2M / i r2`2 +QHH2+i2/ BM 2p2`v 8 7b M/ Qp2` 8yy Tb 7Q` #Qi? p2HQ+BiB2b M/ TQbBiBQMb Q7 *L KQH2+mH2bX JQH2+mH ` bi` BM ` i2 i2MbQ`b
Ryy
r2`2 `2+Q`/2/ BM 2p2`v yX8 7b Qp2` RX8 Mb r?BH2 +2Mi2` Q7 K bb p2HQ+Biv Q7 *Lh r b `2KQp2/ BM 2p2`v R8y 7bX AM i?2 T`Q+22/BM; b2+iBQMb- r2 rQmH/ HBF2 iQ BMi`Q/m+2 /B2H2+i`B+ T`QT2`iB2b Q7 *L bvbi2K iB+ HHvX R *L
KQH2+mH2b r2`2 bbmK2/ iQ Q++mTv i?2 +QM}M2K2Mi pQHmK2 /` rM #v *Lhb
e
jX .B2H2+i`B+ `2H t iBQM Ry8
AM i?Bb b2+iBQM- i?2 mi?Q`b rBHH /Bb+mbb /B2H2+i`B+ T?2MQK2MQM Q7 i?2 *L mM/2` +QM}M2K2MiX 6Q` i?Bb Tm`TQb2- i?2 bvbi2K Bb bbmK2/ iQ #2 BbQi`QTB+TQH `Bx #H2- ?QKQ;2M2Qmb M/ +QMiBMmQmb K2/B X 6m`i?2`KQ`2- M 2ti2`M H M/ 7`2[m2M+v /2T2M/2Mi 2H2+i`B+ }2H/- E(ν)- Bb +iBM; QM BiX LQr- 2H2+i`B+ /BbTH +2K2Mi p2+iQ` + M #2 r`Bii2M b i?2 bmK Q7 2ti2`M HHv +iBM; 2H2+i`B+ }2H/ M/ TQH `Bx iBQM }2H/ @ BX2XD(ν) = 0 E(ν) + P(ν),
UkV
r?2`2 0 bi M/b 7Q` /B2H2+i`B+ +QMbi Mi Q7 p +mmKX A7 i?2 /B2H2+i`B+ T`QT2`iB2b Q7 i?2 bvbi2K `2 bbmK2/ iQ #2 HBM2 ` M/ BbQi`QTB+- i?2 TQH `Bx iBQM- P- Bb T`QTQ`iBQM H iQ i?2 2H2+i`B+ }2H/- E- M/ ;Bp2M #v P(ν) = 0 X (ν)E(ν)
UjV
r?2`2 X (ν) `2T`2b2Mib 7`2[m2M+v /2T2M/2Mi 2H2+i`B+ bmb+2TiB#BHBivX am#biBimiBM;
1[M j BMiQ 1[M k H2 /b iQ
D(ν) = 0 (1 + X (ν))E(ν) = 0 E(ν) = a (ν)E(ν),
(ν) =
a (ν) 0
U9V
U8V
r?2`2 a (ν) M/ (ν) `2 + HH2/ +QKTH2t #bQHmi2 T2`KBiiBpBiv M/ +QKTH2t `2H@ iBp2 T2`KBiiBpBiv Q7 i?2 bvbi2K `2bT2+iBp2HvX h?2 +QKTH2t `2H iBp2 T2`KBiiBpBiv Bb r`Bii2M bBKTHv (ν) = 1 + X (ν)
UeV
r?Qb2 `2 H M/ BK ;BM `v T `ib- (ν) = 0 (ν) − i00 (ν)- +Q``2bTQM/ iQ i?2 `2H iBp2 RRy
T2`KBiiBpBiv M/ i?2 /B2H2+i`B+ HQbb Q7 i?2 bvbi2K `2bT2+iBp2HvX
AM i?Bb bim/v- +QKTH2t T2`KBiiBpBiv ? b #22M 2p Hm i2/ 7Q` irQ HBKBiBM; + b2b2Bi?2` 7Q` +QHH2+iBp2 /vM KB+b KQM; i?2 *L KQH2+mH2b Q` 7Q` p MBb?BM; BMi2`@ +iBQMb KQM; i?2K Ub22 /Bb+mbbBQMb #v J+Zm ``B2 i _27X (ke)- QM T ;2 9d9 M/ T ;2b 9N8@9Nd 7Q` 7m`i?2` /Bb+mbbBQMbVX d
.m2 iQ +QM}M2K2Mi Q7 i?2 *L- QM2 + M 2tT2+i i? i i?2 /B2H2+i`B+ T2`KBi@ iBpBiv /2T2M/b QM i?2 Q`B2Mi iBQM BMbB/2 i?2 im#2X h?2`27Q`2- 2z2+iBp2 /B2H2+i`B+ T2`KBiiBpBiv + M #2 /2}M2/ b /Bb+mbb2/ BM _27X (kd)(ν) = RR8
2r (ν) + z (ν) 3
UdV
r?2`2 r M/ z `2T`2b2Mi ` /B H M/ tB H /B2H2+i`B+ T2`KBiiBpBiv `2bT2+iBp2HvX .2Mb2 bvbi2K TT`Q +?, AM i?2 }`bi + b2- r?2M QM2 +QMbB/2`b i?2 bvbi2K b ;2M2` H + b2 i? i bvbi2K Bb /2Mb2 M/ 2 +? /BTQH2 KQK2Mi Bb +Q``2H i2/ rBi? 2 +? Qi?2`- i?2M i?2 bvbi2K Bb bbmK2/ iQ 2t?B#Bi +QHH2+iBp2 /v@ M KB+b BM r?B+? i?2`2 Bb /BTQH2@/BTQH2 BMi2` +iBQM KQM; i?2 KQH2+mH2bX qBi? TTHB+ iBQM Q7 HBM2 ` `2bTQMb2 i?2Q`v 7Q` 2[mBHB#`BmK- i?2 2H2+i`B+ bmb+2TiB#BHBiv BM j. Bb ;Bp2M #v X (ν) =
1 hM(0) · M(0)i ˙ Liν {−Φ}, kB T V 0
U3V
r?2`2 i?2 QT2` iQ` Liw bi M/b 7Q` 6Qm`B2`@G TH +2 i` Mb7Q`K- BX2X ˙ = Liw {−Φ}
Z∞
−iνt
e
0
dΦ(t) dt − dt
UNV
M/ M(t) Bb p2+iQ`B H bmK Q7 /BTQH2 KQK2Mib Q7 +QMbiBim2Mi KQH2+mH2b i iBK2 iX kB M/ T bi M/ 7Q` "QHixK MM +QMbi Mi M/ i?2`KQ/vM KB+ i2KT2` im`2 `2bT2+iBp2HvX o Bb i?2 pQHmK2 2M+HQb2/ #v *LhbX AM i?Bb + b2i?2 +Q``2H iBQM 7mM+iBQM Bb i`2 i2/ b
Φ(t) = Rky
hM(0) · M(t)i . hM(0) · M(0)i
URyV
AM 1[X Ry- i?2 bvbi2K Bb bbmK2/ iQ #2 /2Mb2 bvbi2K r?2`2 HH BMi2` +@ iBQMb KQM; i?2 KQH2+mH2b ? p2 #22M i F2M ++QmMiX h?mb- 1[X 3 H2 /b iQ bQHmiBQM- +QKTH2t T2`KBiiBpBiv- i? i BMi2` +iBQM Q7 i?2 /BTQH2 KQK2Mi Q7 2 +? KQH2+mH2 Bb +Q``2H i2/ rBi? Qi?2` KQH2+mH2bX .BHmi2 bvbi2K TT`Q +?, AM i?2 b2+QM/ + b2- +`Qbb i2`Kb #2ir22M i?2 /BTQH2 KQK2Mib QM /Bz2`2Mi KQH2+mH2b `2 p MBb?2/ M/ i?2 bvbi2K Bb bbmK2/ 3
iQ #2 /BHmi2 bvbi2K BM r?B+? i?2 /vM KB+b Q7 2 +? /BTQH2 KQK2Mi Bb BM/2T2M/2Mi 7`QK i?2 Qi?2`bX AM bm+? + b2- i?2 +Q``2H iBQM 7mM+iBQM Bb 2tT`2bb2/ BM i2`Kb Q7 Q`B2Mi iBQM Q7 i?2 /BTQH2 KQK2Mi Q7 2 +? KQH2+mH2 bm+? i? i
N m P
i=1 Φ(t) = N m P i=1
ui (0) · ui (t)
, ui (0) · ui (0)
7QHHQr2/ #v i?2 2H2+i`B+ bmb+2TiB#BHBiv N m P ui (0) · ui (0) 1 i=1 ˙ Liν {−Φ}, X (ν) = kB T V 0
URRV
URkV
r?2`2 Nm M/ u `2 i?2 MmK#2` Q7 i?2 KQH2+mH2b BM i?2 bvbi2K M/ i?2 /BTQH2 KQK2Mi Q7 2 +? KQH2+mH2 `2bT2+iBp2HvX
Rk8
AM i?2 7QHHQrBM; b2+iBQM- i?2 mi?Q`b b?Qr ?Qr i?2 BMi2` +iBQM K2+? MBbK KQM; i?2 BM/BpB/m H /BTQH2 KQK2Mib z2+ib i?2 /B2H2+i`B+ #2? pBQ` BM i?2 #mHF M/ +QM}M2/ *LX 9X _2bmHib M/ .Bb+mbbBQMb G TH +2@6Qm`B2` i` Mb7Q`Kb TT2 `2/ BM #Qi? 1[M 3 M/ Rk- /2T2M/BM; QM i?2
Rjy
bbmKTiBQM Q7 BMi2` +iBQM K2+? MBbK- `2 +QKTmi2/ QM i?2 ` r / i bT MMBM; y iQ 8y Tb iQ 2p Hm i2 i?2 `2H t iBQM T?2MQK2MQM BMbB/2 i?2 M MQ im#2bX h?2 iBK2 bi2T ∆t = 5 7bX h?2 2z2+i Q7 im#2 /B K2i2` QM #Qi? r (ν) M/ z (ν) Bb BHHmbi` i2/ BM 6B;m`2b R@9X JQ`2Qp2` r2 BHHmbi` i2/ i?2 2z2+i Q7 KQ/2 7`2[m2M+B2b Rj8
QM i?2 p `B iBQM Q7 /B2H2+i`B+ T2`KBiiBpBiv Q7 *L BMbB/2 *Lh Ujy@jyV BM 6B;m`2 8X M Hvb2b b?Qr i? i i?2 BMi2` +iBM; KQH2+mH2b TT`QtBK iBQM H2 /b iQ `2HB@ #H2 2biBK i2 Q7 tB H i?2 /B2H2+i`B+ +QMbi Mi +QM}M2/ BM *Lh Ujy-jyV +QKT `2/ rBi? 2tT2`BK2Mi H / imK- jeX88- b Q7 _27X (k3) Ub22 h #H2 eV r?BH2 i?2 /B2H2+i`B+
R9y
+QMbi Mi # b2/ QM i?2 /BHmi2 bvbi2K TT`Q +? /Q2bMǶi b?Qr Kmim H +QMbBbi2M+v rBi? i?2 2tT2`BK2Mi H QM2X Ai Bb Q#pBQmb i? i i?2 /2MbBiv Bb K M ;BM; T?vbB+ H N
T ` K2i2` BM i?2 K ;MBim/2 Q7 i?2 tB H /B2H2+i`B+ +QMbi MiX 1bT2+B HHv 7Q` rB/2` im#2b- i?2 HB[mB/ b?Qrb #mHF #2? pBQ` BM i?2 tB H /B`2+iBQMX h?2 /B2H2+i`B+ +QM@ bi Mi +QKTmi2/ 7Q` *L BMbB/2 *Lh Ujy@jyV- jdXRy- Bb +HQb2 i?2 2tT2`BK2Mi H R98
#mHF p Hm2- jeX88X *QMi` `v iQ Q#b2`p iBQM K /2 #v GBM M/ +Q@rQ`F2`b `2@ TQ`i2/ BM (kd)- i?2 im#2b rBi? bK HH /B K2i2`b TQbb2bb HQr2` tB H T2`KBiiBpBivX q2 i?BMF i? i b i?2 /2MbBiv #2+QK2b bK HH2`- i?2 KQH2+mH2b ? p2 KQ`2 bT +2 iQ KQp2 7`22HvX h?2 /BTQH2b `2 MQi 7Q`+2/ iQ HB;M i?2Kb2Hp2b BM i?2 tB H /B`2+@ iBQMX AM ` /B H /B`2+iBQM- /B2H2+i`B+ T2`KBiiBpBiv r2`2 HH /`QTT2/ /` biB+ HHv iQ
R8y
HKQbi p +mK T2`KBiiBpBivX am+? T?2MQK2MQM r b Q#b2`p2/ #v bQK2 mi?Q`bX 6Q` 2t KTH2- *? # M ? b ii`B#mi2/ bK HH p Hm2b Q7 /B2H2+i`B+ +QMbi Mi BM *Lhb mM/2` +QMbB/2` iBQM iQ bBM;H2 }H2 T ii2`M /m2 iQ +QM}M2K2Mi `2H iBp2Hv M ``Qr im#2bX P`B2Mi iBQM Q7 /BTQH2b Bb +`m+B H BM /2i2`KBMBM; ` /B H /B2H2+i`B+ T2`KBi@ iBpBivX 6B;m`2 d b?Qrb ?Qr ;@7 +iQ` p `B2b HQM; i?2 ` /B H /B`2+iBQM Q7 *LhaX
R88
AM ` /B H /B`2+iBQM- MQ T`272``2/ Q`B2Mi iBQM Bb Q#b2`p2/ i 7 ` r v 7`QK i?2 r HH Q7 i?2 *LhbX >Qr2p2`- bm+? Q`B2Mi iBQMb `2 HKQbi +HQb2 iQ 2 +? Qi?2`X h?Bb #2? pBQ` K v H2 / iQ /` biB+ /2+`2 b2 BM ` /B H /B2H2+i`B+ T2`KBiiBpBivX 45 40 35 30 25 20 15 10 5 0 10
0
10
1
10
2
6B;m`2 R, 6`2[m2M+v /2T2M/2Mi /B2H2+i`B+ T2`KBiiBpBiv BM tB H /B`2+iBQM # b2/ QM /BHmi2 bvbi2K TT`Q +?2bX
Ry
40 35 30 25 20 15 10 5 0 10
0
10
1
10
2
6B;m`2 k, 6`2[m2M+v /2T2M/2Mi /B2H2+i`B+ T2`KBiiBpBiv BM tB H /B`2+iBQM # b2/ QM /2Mb2 bvbi2K TT`Q +?2bX
1.5
1
0.5
0 10
0
10
1
10
2
6B;m`2 j, 6`2[m2M+v /2T2M/2Mi /B2H2+i`B+ T2`KBiiBpBiv BM tB H /B`2+iBQM # b2/ QM /BHmi2 bvbi2K TT`Q +?2bX
RR
1.2
1
0.8
0.6
0.4
0.2
0 10
0
10
1
10
2
6B;m`2 9, 6`2[m2M+v /2T2M/2Mi /B2H2+i`B+ T2`KBiiBpBiv BM tB H /B`2+iBQM # b2/ QM /2Mb2 bvbi2K TT`Q +?2bX
40 35 30 25 20 15 10 C-C-N bending mode at 380 cm-1 CH rocking mode at 1061 cm -1
5 0
3
0
500
1000
1500
2000
2500
3000
3500
6B;m`2 8, .B2H2+i`B+ +QMbi Mi M/ HQbb Q7 *L +QM}M2/ BM *LhUjy@jyV b 7mM+iBQM Q7 7`2@ [m2M+vX AM i?Bb ;` T;? i?2 bvbi2K Bb bbmK2/ iQ #2 +QKTQb2 Q7 BMi2` +iBM; KQH2+mH2bX LQiB+2 i? i- i?2 2z2+i Q7 *@*@L #2M/BM; KQ/2 i j3y cm−1 M/ CH3 `Q+FBM; KQ/2 i RyeR cm−1 QM i?2 p `B iBQM Q7 /B2H2+i`B+ +QMbi Mi M/ HQbb `2 2 bBHv B/2MiB}2/X
Rk
h #H2 j, *QKTmi2/ bi iB+ /B2H2+i`B+ +QMbi Mib Q7 i?2 +2iQMBi`BH2 i T = 298 EX G TH +2@ 6Qm`B2` i` Mb7Q`Kb T2`7Q`K2/ QM / i rBi? ∆t = 5 7b M/ MmK#2` Q7 iBK2 bi2Tb r b RyyyyX >2`2- dense M/ dilute bi M/ 7Q` +QKTmi iBQMb # b2/ QM i?2 bbmKTiBQMb Q7 BMi2` +iBM; KQH2+mH2b M/ MQM@BMi2` +iBM; KQH2+mH2b `2bT2+iBp2Hv
.B2H2+i`B+ +QMbi Mi
*LhURy-RyV
*LhUR8-R8V
*LhUky-kyV
*LhUjy-jyV
0r,dense (0)
RXy9Re
RXyd
RXyN8
RXRkR
0z,dense (0)
ReX9yy
kRXyR9
kdXkk
jdXRyy
0dense (0)
eXReR
dXdR3
NX3yj
RjXRR
0r,dilute (0)
RXjyR
RXk3d
RX89N
RXey3
0z,dilute (0)
RdXjRy
kdXjky
jjXkNy
99X89y
0dilute (0)
eXejd
NXNe9
RkXRkN
R8XNR3
50 45 40 35 30 25 20 15 10
15
20
25
30
35
40
45
6B;m`2 e, +H2 ` /2KQMbi` iBQM Q7 ?Qr bi iB+ /B2H2+i`B+ +QMbi Mi BM tB H /B`2+iBQM p `B2b rBi? *LhǶb /B K2i2`X
i i?Bb bi ;2- r2 rQmH/ HBF2 iQ QmiHBM2 /Bb+`2T M+v #2ir22M i?2 #2? pBQ` Q7 r i2` M/ *L +QM}M2/ BM M MQ im#2bX Hi?Qm;? /B2H2+i`B+ +QMbi Mi Q7 i?2 Rey
r i2` BM aq*Lh i2M/b iQ /2+`2 b2 b i?2 /B K2i2` Q7 i?2 im#2 BM+`2 b2b (kd)- Bi /2+`2 b2b +QMbB/2` #Hv BM bT?2`B+ H M MQ + pBiv Q7 #Qmi Rk ³ BM /B K2i2` b `2TQ`i2/ BM `272`2M+2 (kN)X *QMi` `v iQ r i2` BM aq*Lh- i?2 /B2H2+i`B+ +QMbi Mi Q7 i?2 *L BM+`2 b2b rBi? i?2 bBx2 Q7 i?2 im#2 b b?QrM BM 6B;X eX JQ`2Qp2`-
Rj
i?2 /B2H2+i`B+ +QMbi Mi T`2/B+i2/ 7Q` HH + b2b mM/2` +QMbB/2` iBQM Bb biBHH bK HH2` Re8
i? M #mHF QM2 Ui?2 + H+mH i2/ M/ 2tT2`BK2Mi H QM2(jy)VX AM Qi?2` rQ`/b- i?2 2z2+i Q7 +QM}M2K2Mi Bb biBHH TT`2+B i2/ 2p2M 7Q` H `;2 bBx2b Q7 i?2 im#2bX AM Q`/2` iQ K F2 +H2 ` r?v bm+? BM+`2 b2 BM /B2H2+i`B+ +QMbi Mi r b Q#b2`p2/ rBi? BM+`2 bBM; /B K2i2`b Q7 im#2b- EB`FrQQ/ +Q``2H iBQM 7 +iQ`(jR)- ; 7 +iQ`r b BMi`Q/m+2/ c g=
Nm X i=1
URjV
hcos θij i,
r?2`2 θij /2MQi2b i?2 M;H2 #2ir22M i?2 Q`B2Mi iBQMb Q7 i?2 Bth M/ i?2 Dth /BTQH2X h?2 + H+mH i2/ +Q``2H iBQM 7 +iQ` 7Q` BM+`2 bBM; ` /BB BM 2 +? *Lh Bb b?QrM BM 6B;X dX i }`bi ;H M+2- Bi + M #2 Q#b2`p2/ i? i i?2`2 Bb MQ +Q``2H iBQM 1.3
CNT (10,10) CNT (15,15) CNT (20,20) CNT (30,30)
1.2 1.1 1
g factor
0.9 0.8 0.7 0.6 0.5 0.4 0.3
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Non-dimensional radial position, r/r0
6B;m`2 d, _ /B H p `B iBQM Q7 EB`FrQQ/ +Q``2H iBQM 7 +iQ` + H+mH i2/ 7`QK i?2 1[X RjX LQi2 i? i i?2 ` /Bmb Q7 2 +? *Lh Bb b2i iQ mMBivX
Rdy
#2ir22M i?2 Bth KQH2+mH2 M/ i?2 Qi?2`b rBi?BM i?2 }`bi ? H7 Q7 i?2 ` /Bmb Q7 i?2 *Lh URy@RyVX h?Bb Bb /m2 iQ bi`QM; ` `27 +iBQM 2z2+ib Q#b2`p2/ BM i?2 +Q`2 Q7 i?Bb *LhX h?Bb `2;BQM r?2`2BM ` `27 +iBQM 2z2+ib `2 Q#b2`p2/ #2+QK2b bK HH2` rBi? BM+`2 bBM; bBx2b Q7 *LhbX "2vQM/ i?Bb +`BiB+ H ` /Bmb- +Q``2H iBQMb bi `ib iQ /2p2HQT M/ + M #2 `2T`2b2Mi2/ b +QMiBMmQmb 7mM+iBQMbX AM i?2 bK HH2bi im#2-
Rd8
i?2 Q`B2Mi iBQM Q7 KQH2+mH2b /Q2b MQi +? M;2 Km+? BM ? H7 Q7 *LhǶb ` /BmbX 6Q` H `;2` im#2b- KQH2+mH2b Q`B2Mi iBQMb Qb+BHH i2 rBi?BM +2`i BM M;H2 bT MX
R9
h?Bb #2? pBQ` bHQrb /QrM BM i?2 pB+BMBiv Q7 i?2 r HHX Ai Bb +H2 ` i? i i?2 +QmTH2/ /vM KB+b Q7 #Qi? ` `27 +iBQM M/ i?2 +QM}M2K2Mi 2z2+i /2+`2 b2b i?2 /B2H2+i`B+ +QMbi Mi 2MQ`KQmbHvX Hi?Qm;? i?2 +QM}M2K2Mi BM bK HH2` *Lh 2M+Qm` ;2b R3y
b2H7@Q`; MBx2/ M/ /B`2+i2/ /BTQH2b BM i?2 /B`2+iBQM 7`22 iQ KQp2- BM i?2 tB H /B`2+iBQM Q7 M MQ im#2b- /QKBM Mi ` `27 +iBQM 2z2+i i`B2b iQ HB;M ` i?2` HBKBi2/ MmK#2` Q7 KQH2+mH2b QTTQbBi2 iQ i?Qb2 Q7 bm`7 +2 `2;BQMX q2 #2HB2p2 i? i i?2 K BM `2 bQM 7Q` +QMbB/2` #H2 /`QTb BM /B2H2+i`B+ +QMbi Mi Bb BM+`2 bBM; 7` +iBQM H pQHmK2 Q7 ` `27 +iBQM rBi? bK HH2` bBx2b Q7 i?2 *LhbX
R38
aQ 7 `- i?2 `2bmHib Q7 /B2H2+i`B+ `2H t iBQM i?2Q`v M/ Q#i BM2/ 7`2[m2M+v /2T2M/2Mi /B2H2+i`B+ +QMbi Mi 7Q` #Qi? mM/2` i?2 bbmKTiBQMb Q7 /BHmi2 M/ /2Mb2 bvbi2Kb r2`2 BMi`Q/m+2/X AM //BiBQM iQ i?2b2- i?2 /B2H2+i`B+ +QMbi Mi r b 2p Hm i2/ b ν → 0 BM 1[X N BM +QMDmM+iBQM rBi? 1[MX Ry- Ub22 _27X (jk)Vlim
ν→0
Z∞
e−iνt
0
−
dΦ(t) dt = 1. dt
UR9V
h?mb- 1[M e bBKTHB}2b iQ
1 Mz2 =1+ kB T V 0
UR8V
2 Mr 1 . =1+ 2kB T V 0
UReV
0z (0)
0r (0)
>2`2- Mz M/ Mr `2 i?2 iQi H /BTQH2 KQK2Mi BM x M/ ` /B H /B`2+iBQMb Q7 i?2 RNy
bvbi2KX h?2 +QMp2`;2M+2 Q7 i?2 2Mb2K#H2 p2` ;2 Bb FMQrM iQ i F2 TH +2 BM HQM; T2`BQ/ Q7 iBK2X 6Q` i?Bb `2 bQM- BM Qm` bBKmH iBQMb- i?2 p2` ;2b ? p2 #22M i F2M Qp2` 8yy Tb r?B+? b22K iQ #2 bm{+B2Mi #v BMbT2+iBM; bvKTiQiB+ #2? pBQ` Q7 i?2 /B2H2+i`B+ +QMbi Mi rBi? `2bT2+i iQ iBK2 Ub22 i?2 6B;X 3VX ai M/ `/ /2pB iBQMb r2`2 HbQ iQQ bK HH BM Qm` + H+mH iBQMbX
R8
a) Dielectric constant in longitudional direction, 55
z
z
(10,10) (15-15) (20-20) (30-30)
Dielectric constant along the tube axes,
50 45 40 35 30 25 20 15
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
time (s)
5 10
b) Dielectric constant in radial direction,
r
Dielectric constant in radial direction,
r
1.14
-10
1.12 1.1 1.08 1.06 1.04 (10-10) (15-15) (20-20) (30-30)
1.02 1
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
time (s)
5 10
-10
c) Dielectric constant,
18
Dielectric constant,
16 14 12 10 8 6 4
0
0.5
1
1.5
2
2.5
3
time (s)
3.5
4
4.5
5 10-10
6B;m`2 3, .B2H2+i`B+ +QMbi Mib Q#i BM2/ 7`QK i?2 ~m+im iBQM 7Q`KmH b 1[MbX R8 M/ Rec V 7Q` tB H /B`2+iBQM #V 7Q` ` /B H /B`2+iBQM- +V 7Q` BbQi`QTB+ bvbi2KX
Re
h #H2 9, ai iB+ /B2H2+i`B+ +QMbi Mib #v 1[MbX R8 M/ ReX
RN8
h?2 bvbi2K
.2MbBiv Q7 *L UF;fK3 V
r
z
*LhURy-RyVY*L
9eyXeR
*LhUR8-R8VY*L
8d8Xdd
1.04 ± 0.08
17.80 ± 0.14
6.63 ± 0.19
*LhUky-kyVY*L
e9yX89
1.08 ± 0.07
22.29 ± 0.12
8.15 ± 0.15
*LhUjy-jyVY*L
edNXR3
1.09 ± 0.05
27.63 ± 0.11
9.93 ± 0.13
"mHF
dddXyy
1.12 ± 0.05
37.2 ± 0.10
13.08 ± 0.11
@
j3Xyy
h?2 bi iB+ /B2H2+i`B+ +QMbi Mib `2bmHiBM; 7`QK i?2 HBKBiBM; + b2 r2`2 6.63 ±
0.19- 8.15 ± 0.15- 9.93 ± 0.13 M/ 13.08 ± 0.11 7Q` *Lhb URy@RyV- UR8@R8V- Uky@kyV M/ Ujy@jyV `2bT2+iBp2HvX h?2 `2bmHib Q#i BM2/ 7`QK i?2 ~m+im iBQM 7Q`KmH `2 ;QQ/ ;`22K2Mi rBi? i?Qb2 Q7 `2H t iBQM i?2Q`vX
AM Q`/2` iQ 2Hm+B/ i2 i?2 2z2+i Q7 pB#` iBQM bT2+i` QM i?2 p `B iBQM Q7 /B@ kyy
2H2+i`B+ T2`KBiiBpBiv- r2 b?Qr i?2 TQr2` bT2+i` H /2MbBiv Q7 iBK2 /2`Bp iBp2 Q7 iBK2 +Q``2H iBQM 7mM+iBQM + H+mH i2/ 7`QK 1[X RR 7Q` irQ 2ti`2K2 + b2b- *Lh URy@RyV M/ Ujy@jyV Ub22 6B;X NVX h?2`2 Bb bB;MB}+ Mi b?B7i BM i?2 7`2[m2M+v Q7 *R@> #2M/BM; KQ/2 r?B+? H2 /b iQ bi`QM; T2 F QM #Qi? bT2+i` H /2MbBiB2bX *R@> bi`2i+?BM; KQ/2 HbQ b?B7ib QM i?2 b?QmH/2` r?2`2BM TH i2 m Bb 7Q`K2/ i
ky8
?B;? 7`2[m2M+B2bX am+? /BbiBM+iBQM r b MQi Q#b2`p2/ BM i?2 pB#` iBQM bT2+i` b?QrM BM 6B;X RyX AM 7`2[m2M+B2b bK HH2` i? M eyy +K−1 /BbiBM+iBQMb #2ir22M i?2 KQ/2b Q7 #Qi? + b2b `2 MQi /BbiBM;mBb? #H2X h?2 mi?Q`b [m2biBQM r?2i?2` i?2 /B2H2+i`B+ `2H t iBQM Q7 i?2 *L Q#2vb .2#v2 i?2Q`v Q` MQiX h?2 /BTQH2 KQK2Mi +Q``2H iBQM 7mM+iBQM K2 bm`2b i?2 +Q`@ `2H iBQM #2ir22M i?2 M(t) rBi? M(0)X ++Q`/BM; iQ .2#v2- BM bmKK `v- BMBiB H
+Q``2H iBQM M 2 (0) i2M/b iQ /2+`2 b2 2tTQM2MiB HHv iQ x2`Q /m2 iQ KQH2+mH ` BMi2` +iBQMbX L2p2`i?2H2bb- /2+ v Q7 i?2 MQ`K HBx2/ /BTQH2 iBK2 +Q``2H iBQM 7mM+@
iBQMb + H+mH i2/ 7`QK 1[X Ry Bb MQi Q7 bBKTH2 .2#v2 `2H t iBQM 7Q`KX h?2`27Q`2 i?2 MQ`K HBx2/ /BTQH2 iBK2 +Q``2H iBQM 7mM+iBQMb r2`2 }ii2/ iQ #B2tTQM2MiB H
Rd
jeX88 _27X (k3)
6B;m`2 N, SQr2` bT2+i`mK Q7 Q7 iBK2 /2`Bp iBp2 Q7 iBK2 +Q``2H iBQM 7mM+iBQM + H+mH i2/ 7`QK 1[X RRX
−17
1
x 10
Bulk acetonitrile Acetonitrile confined inside CNT (10-10)
0.9
Acetonitrile confined inside CNT (15-15) Acetonitrile confined inside CNT (20-20)
0.8
−18
x 10
Raman intensity
Acetonitrile confined inside CNT (25-25)
Inset view at around 2900 cm−1
4.5
Acetonitrile confined inside CNT (30-30)
0.7
4
0.6 −19
x 10
0.5
15
0.4
10
3.5
Inset view at around 850 cm
−1
2700
2800
2900
3000
3100
3200
5
0.3 600
700
800
900
1000
1100
0.2 0.1 0 0
500
1000
1500
2000
2500
3000
3500
wavelength (cm−1 )
6B;m`2 Ry, o `B iBQM Q7 pB#` iBQM H 7`2[m2M+B2b /2T2M/BM; QM i?2 im#2 /B K2i2`X
R3
h #H2 8, h?2 _2H t iBQM iBK2 bbQ+B i2/ rBi? /BbT2`bBQM M/ `2H t iBQM iBK2b 7Q` i?2 HB[mB/ +2iQMBi`BH2X "B2tTQM2MiB H 7mM+iBQM r b miBHBx2/ 7Q` i?2 }iiBM; i?2 MQ`K HBx2/ /BTQH2 +Q``2H @ iBQM 7mM+iBQMbX
τm UbV
"
τn UbV
h?2 `2H t iBQM iBK2 UbVc hτ i =
2 +Bτ 2 Aτm n Aτm +Bτn
*Lh URy@RyV- (R2 = 0.968)
yXdkk
2.848 × 10−13
yXkd3
5.465 × 10−12
4.847 × 10−12
*Lh UR8@R8V- (R2 = 0.968)
yX393
2.535 × 10−13
yXR8k
4.69 × 10−12
3.659 × 10−12
*Lh Uky@kyV- (R2 = 0.984)
yXd3d
2.290 × 10−13
yXkRj
2.135 × 10−12
1.595 × 10−12
*Lh Ujy@jyV- (R2 = 0.986)
yXeN3
2.645 × 10−13
yXjyk
1.587 × 10−12
1.221 × 10−12
"mHF U+ H+mH i2/V
yXdRy
1.077 × 10−13
yXkNy
2.110 × 10−12
1.900 × 10−12
7mM+iBQMb i? i `2 ;Bp2M #v hM(0) · M(t)i = Ae(−t/τm ) + Be(−t/τn ) hM(0) · M(0)i
URdV
r?2`2 A- B M/ τm - τn `2 /BbT2`bBQM i2`Kb M/ iBK2 T ` K2i2`b iQ #2 /2i2`@ KBM2/ 7`QK }iiBM; T`Q+2/m`2 `2bT2+iBp2HvX h?2 + H+mH i2/ `2H t iBQM iBK2b r2`2 kRy
bmKK `Bx2/ BM h #H2 8X 6`QK h #H2 8- Bi + M #2 `2 HBx2/ i? i i?2 +QKTmi2/ /BTQH2 iBK2 +Q``2H @ iBQM 7mM+iBQM / i MQiB+2 #Hv /2pB i2 7`QK i?2 #mHF .2#v2 `2H t iBQM #2? pBQ`X Hi?Qm;? i?2 7 bi2` +QKTQM2Mi Q7 /B2H2+i`B+ `2H t iBQM τm Bb bK HH2` i? M τn i?2 +Q2{+B2Mi Q7 i?2 7 bi2` +QKTQM2Mi- i?2 +Q2{+B2Mi A- b22Kb iQ K M ;2 `2@
kR8
H t iBQM T?2MQK2M X h?2 + H+mH i2/ iBK2 2pQHmiBQM Q7 i?2 /BTQH2 +Q``2H iBQM 7mM+iBQM b?Qr2/ i? i i?2 /BzmbBp2 M/ bHQr2` `2bTQMb2 Bb KBbb2/ BM i?2 BMBiB H T? b2 Q7 i?2 iBK2 2pQHmiBQMX Hi?Qm;? i?2 K2 M `2H t iBQM iBK2 Bb M Q`/2` Q7 K ;MBim/2 ;`2 i2` i? M i?2 BM2`iB H +QKTQM2Mi- τm - i?2 /vM KB+b Q7 i?2 bvbi2K Bb /QKBM i2/ #v i?2 `Qi iBQM H /BzmbBQM Q7 KQH2+mH2b M/ BM2`iB H 2z2+ib r?B+?
kky
`2 i F2M TH +2 BM b?Q`i iBK2X AM //BiBQM- i?2`2 Bb MQ Kmim H +QMbBbi2M+v #2ir22M i?2 + H+mH i2/ `2H t iBQM iBK2 7Q` #mHF bvbi2K r?B+? Bb H`2 /v RXN Tb M/ i?2 2tT2`BK2Mi H p Hm2- jXj8 Tb- b `2TQ`i2/ BM _27X (jy)X AM i?2 b2+QM/ r v- .2#v2 i?2Q`v Q7 /B2H2+i`B+ bm;;2bi i? i hM(t) · M(0)i
RN
/2+ vb 7`QK Bib BMBiB H p Hm2 2tTQM2MiB HHv bm+? i? i hM(t) · M(0)i = e−|t|/τD hM(0) · M(0)i
UR3V
r?2`2 τD `2T`2b2Mib .2#v2 `2H t iBQM iBK2X am#biBimiBQM Q7 1[MX R3 BMiQ 1[MX N rBi? ++QKT MvBM; 1[MbX 3 M/ e- ;Bp2b /2T2M/2M+v Q7 /B2H2+i`B+ T2`KBiiBpBiv QM 7`2[m2M+vX h?mb .2#v2 `2H t iBQM iBK2 + M #2 bi i2/ BM i2`Kb /B2H2+i`B+ T2`KBiiBpBiv- BX2X
1 0 (ν) − 1 = 2 . 0 (0) − 1 1 + ν 2 τD
URNV
h?2 .2#v2 `2H t iBQM iBK2b Q#i BM2/ 7`QK i?2 M Hvb2b 7Q` *Lhb URy@RyV M/ Ujy@jyV `2 HKQbi 2[m H iQ yXNkd M/ yX8k Tb `2bT2+iBp2HvX h?2 2biBK i2 Q7 .2@ kk8
#v2 i?2Q`v ;Bp2M #v 1[MX R3 + MMQi + Tim`2 i?2 b?Q`i iBK2 `Qi iBQM H #2? pBQ` Q7 KQH2+mH ` /BTQH2b b `2TQ`i2/ BM _27X (jj)X h?Bb Bb i?2 `2 bQM r?v T`2/B+@ iBQM Q7 .2#v2 i?2Q`v +QMi` /B+ib rBi? i?2 BM2`iB H iBK2 +QKTQM2Mi K2MiBQM2/T`2pBQmbHvX AM //BiBQM iQ i?2 `2H t iBQM iBK2- KQH2+mH ` `2Q`B2Mi iBQM /vM KB+b BM +2@
kjy
iQMBi`BH2 r b M Hvx2/ i?`Qm;? i?2 iBK2 +Q``2H iBQM 7mM+iBQM
Cl (t) = hPl (¯ u(0) · u ¯ (t))i
UkyV
r?2`2 Pl `2T`2b2Mib li? G2;2M/`2 TQHvMQKB H M/ u ¯ (t) = u(t)/u(t) Bb i?2 mMBi p2+iQ` Q7 i?2 /BTQH2 KQK2MiX h?2 +Q``2H iBQM 7mM+iBQMb bbQ+B i2/ rBi? i?2 G2;2M/`2 TQHvMQKB Hb `2
C1 (t) = hcos θ(t)i C2 (t) =
1
3 cos2 θ(t) − 1 2
UkRV
UkkV
r?2`2 cos θ(t) = u ¯ (t) · u ¯ (0)X _2Q`B2Mi iBQM iBK2b τl Ul = 1, 2V ? p2 #22M Q#i BM2/
kj8
#v }iiBM; i?2 / i T`Q/m+2/ 7`QK 1[MbX kR M/ kk iQ i`BTH2 2tTQM2MiB H 7mM+iBQMb b Q7 i?2 7Q`K Cl (t) = Ae(−t/τm ) + Be(−t/τn ) + Ce(−t/τo ) . ky
UkjV
h #H2 e, l = 1
hτ1 i =
*Lh URy@RyV
*Lh UR8@R8V
*Lh Uky@kyV
*Lh Ujy@jyV
yXkk3
yXk3j
yX983
yX8kk
τm UbV
5.981 × 10−12
4.730 × 10−12
4.290 × 10−12
3.460 × 10−12
"
yXed3
yX8ek
yXj33
yXj88
τn UbV
6.082 × 10−11
1.327 × 10−11
1.300 × 10−11
1.010 × 10−11
*
@
yXR9N
yXR8y
yXRk8
τo UbV
@
2 +Bτ 2 +Cτ 2 Aτm o n Aτm +Bτn +Cτo
UbV
3.949 × 10
−13
3.890 × 10
−13
2.700 × 10−13
5.906 × 10−11
1.189 × 10−11
1.047 × 10−11
7.828 × 10−12
UR2 = 0.999V
UR2 = 0.999V
UR2 = 1.000V
UR2 = 1.000V
1 CNT (10-10) CNT (15-15) CNT (20-20) CNT (30-30)
0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5 10
-11
6B;m`2 RR, _2Q`B2Mi iBQM +Q``2H iBQM 7mM+iBQMb 7Q` p `vBM; im#2 /B K2i2`b- l = 1X
hBK2 2pQHmiBQM Q7 C1 (t) M/ C2 (t) b b?QrM BM 6B;m`2b RR M/ Rk r2`2 }ii2/ iQ i`BTH2 2tTQM2MiB H 7mM+iBQMb M/ `2bmHiBM; `2@Q`B2Mi iBQM iBK2b r2`2 i #mH i2/ k9y
BM h #H2 e M/ dX h?2 `2bmHib b?Qr i? i `2Q`B2Mi iBQM Q7 KQH2+mH2b +QM}M2/ BM M MQim#2b `2 i F2M TH +2 `2H iBp2Hv HQM; iBK2b +QKT `2/ iQ i?Qb2 Q7 #mHF bi i2 Uτ1 = 3.28 × 10−12 _27X (j9) M/ τ2 = 1.02 × 10−12 _27X (j8)VX LQ Kmim H +QMbBbi2M+v 7Q` `2Q`B2Mi iBQM iBK2b +QKTmi2/ 7Q` *Lh Ujy@jyV +QKT `2/ rBi?
kR
h #H2 d, l = 2
τm UbV
hτ2 i =
*Lh URy@RyV
*Lh UR8@R8V
*Lh Uky@kyV
*Lh Ujy@jyV
yXj9y
yX8y3
yX93d
yX9Ne
5.020 × 10
−12
4.120 × 10
−12
3.320 × 10
−12
2.670 × 10−12
"
yXjN3
yXyNk3
yXyd99
yXy993
τn UbV
6.060 × 10−11
3.200 × 10−11
3.850 × 10−11
4.770 × 10−11
*
yXk89
yXjN
yX9jy
yX98y
τo UbV
2.510 × 10−13
3.400 × 10−13
3.650 × 10−13
3.910 × 10−13
5.678 × 10−11
1.996 × 10−11
2.494 × 10−11
2.901 × 10−11
UR2 = 0.999V
UR2 = 0.999V
UR2 = 0.999V
UR2 = 0.999V
2 +Bτ 2 +Cτ 2 Aτm n o Aτm +Bτn +Cτo
UbV
1 CNT (10-10) CNT (15-15) CNT (20-20) CNT (30-30)
0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5 10
-11
6B;m`2 Rk, _2Q`B2Mi iBQM +Q``2H iBQM 7mM+iBQMb 7Q` p `vBM; im#2 /B K2i2`b- l = 2X
kk
i?2 #mHF bi i2 _2Q`B2Mi iBQM iBK2b /2+`2 b2 rBi? BM+`2 bBM; /B K2i2` Q7 i?2 im#2b k98
b r2HHX h?Bb #2? pBQ` +QMi` /B+ib Qm` 2tT2+i iBQMb #2+ mb2 b i?2 /B K2i2` Q7 i?2 im#2 2MH `;2b i?2 BMi2` +iBQMb KQM; i?2 *L KQH2+mH2b b?QmH/ `2b2K#H2 iQ i? i Q7 #mHF bi i2X am+? +QMi` biBM; `2Q`B2Mi iBQM iBK2b rBi? i?2 #mHF bi i2 K v #2 ii`B#mi2/ iQ H `;2 MmK#2` Q7 *L KQH2+mH2b BMi2` +iBM; rBi? i?2 *Lh iQKb QM i?2 pB+BMBiv Q7 BMi2`7 +2X h?2 MmK#2` Q7 bm+? BMi2` +iBM; KQH2+mH2b
k8y
/2T2M/b QM i?2 /B K2i2` Q7 i?2 im#2 b 2tT2+i2/X aQ 7 `- i?2 mi?Q`b T`2b2Mi i?2 2z2+i Q7 7`2[m2M+v M/ i?2 im#2 /B K2i2` QM i?2 /B2H2+i`B+ T`QT2`iB2b #v /Bz2`2Mi r vbX Pm` K BM +QM+HmbBQMb r2`2 ;Bp2M i?2 T`Q+22/BM; b2+iBQMX >Qr2p2`- r2 i?BMF i? i bim/vBM; rBi? MQM@/BK2MbBQM H ;`QmT Q7 T ` K2i2`b T`2b2Mi2/ BM ?2`2 K v #2 mb27mH 7Q` 7mim`2 T2`bT2+iBp2bX 6Q` i?Bb Tm`TQb2- QM2 + M BMi`Q/m+2 MQM@/BK2MbBQM H T ` K2i2`b ;`QmT i? i /2KQMbi` i2 +QKT2iBM; 2z2+ib #2ir22M i?2 #bQHmi2 /B2H2+i`B+ T2`KBiiBpBiv M/ pBb+Qmb /BzmbBQMX h?2 MQM@/BK2MbBQM H T ` K2i2` ;`QmT + M #2 `2 / b 2 (0)0 DντD kB T , 2 u d
Uk9V
r?2`2 D- ν M/ u bi M/ 7Q` /BzmbBQM +Q2{+B2Mi- FBM2K iB+ pBb+QbBiv M/ i?2 /BTQH2 KQK2Mi Q7 *L 7Q` T ` K2i2`b ;Bp2M BM h #H2 R `2bT2+iBp2HvX EBM2K iB+ pBb+QbBiv- ν = µ/ρ r?2`2 ρ Bb /2MbBiv Q7 *L BM +QM}M2/ pQHmK2- M/ /Bzm@ bBQM +Q2{+B2Mi- D `2 #Q``Qr2/ 7`QK i?2 }`bi T `i Q7 i?Bb bim/v U_27X (je)VX k88
b r2 /Bb+mbb2/ T`2pBQmbHv #bQHmi2 /B2H2+i`B+ T2`KBiiBpBiv Bb BM~m2M+2/ #v i?2 /2+`2 bBM; bBx2 Q7 +QM}MBM; bi`m+im`2 r?2`2 BM Bi T `iB HHv BM+`2 b2b rBi? i?2 /B K2i2`X *QMi` `v iQ /B2H2+i`B+ T2`KBiiBpBiv- pBb+QbBiv i2M/b iQ #2 H `;2 rBi? bK HH2` im#2 /B K2i2`b- HBF2 /BzmbBQM +Q2{+B2MiX am+? +QMi2M/BM; T?vbB+ H T @ ` K2i2`b BM M QM2 MQM@/BK2MbBQM H ;`QmT `2bmHib BM M BKTQ`i Mi p `B iBQM
key
7`QK Bib ?B;?2bi kXd3 iQ i?2 HQr2bi yXykR p Hm2- /2T2M/BM; QM i?2 im#2 /B K2i2`X h?Bb #2? pBQ` 2Hm+B/ i2b ?Qr #bQHmi2 /B2H2+i`B+ T2`KBiiBpBiv Bb bmb+2TiB#H2 BM /2}MBM; /2+HBMBM; i`2M/ Q7 MQM@/BK2MbBQM H ;`QmT Q7 T ` K2i2`bX Ai b?QmH/ #2 +H2 ` i? i i?2 pBb+QbBiv M/ /BzmbBQM +Q2{+B2Mi TH v M 2bb2MiB H `QH2 BM i2`Kb Q7 Bib Q`/2` Q7 K ;MBim/2 +QKT `2/ rBi? i?Qb2 Q7 i?2 Qi?2`bX h?2 p `B iBQM Q7 i?Bb
ke8
MQM@/BK2MbBQM H ;`QmT Q7 T ` K2i2`b + M ;Bp2 bQK2 ?BMib iQ bmT2`+ T +BiQ`b kj
3
2
1.5
0
D B
(0) D 2 k T / (u2d)
2.5
1
0.5
0 1
1.5
2
2.5
3
diameter of nano tubes (m)
3.5
4
4.5 10
-9
6B;m`2 Rj, o `B iBQM Q7 MQM@/BK2MbBQM H ;`QmT Q7 T ` K2i2`b b 7mM+iBQM Q7 im#2 /B K2i2`X .BzmbBQM +Q2{+B2Mi- FBM2K iB+ pBb+QbBiv- M/ Qi?2` T ` K2i2`b `2 2p Hm i2/ i kN3 E
/2bB;M2`bX *Q iBM; + `#QM M MQim#2b iQ i?2 2H2+i`Q/2 K i2`B Hb Bb i`2M/BM; i2+?MB[m2 iQ BM+`2 b2 bT2+B}+ bm`7 +2 `2 Q7 i?2 2H2+i`Q/2 ++2bbB#H2 iQ 2H2+i`QHvi2 BQMb iQ BM+`2 b2 + T +Bi M+2X h?mb- QM i?2 +Q i2/ bm`7 +2 Q7 i?2 2H2+i`Q/2b- i?2`2 rBHH #2 pQB/b r?B+? `2b2K#H2 iQ BMi2`BQ` pQHmK2 Q7 i?2 + `#QM M MQ im#2bX .m2 iQ BMi2`@ KQH2+mH ` 7Q`+2b KQM; i?2 KQH2+mH2b M/ BQMb i? i +QMbiBimi2 2H2+i`QHvi2 K @ i2`B Hb- i?2`2 rBHH bQK2 pQHmK2 r?2`2 2H2+i`QHvi2 KQH2+mH2bfBQMb +QmH/MǶi `2 +?X AM i?Bb i2ti- r2 /2}M2 bm+? pQHmK2 b EMm/b2M `2;BQM b r2HHX .2+`2 bBM; TQ`2 bBx2- BM M HQ;Qmb iQ M MQim#2Ƕb BMi2`BQ` pQHmK2- `2bmHib BM H2bb 2H2+i`QHvi2 K i2@ `B Hb BMbB/2 TQ`2b- M/ i?Bb H2 /b iQ H2bb + T +Bi M+2 b r2HHX L2p2`i?2H2bb- i?2`2 Bb MQ +QMb2Mbmb #Qmi i?2 QTiBK H p Hm2 Q7 i?2 TQ`2 bBx2X Hi?Qm;?- G `;2Qi 2i HX (jd) TQBMi Qmi i? i QTiBK H p Hm2 Q7 TQ`2 bBx2 bi`B+iHv /2T2M/b mTQM i?2 bBx2 Q7 BQMb- aBKQM M/ :Q;QibB (j3) `2TQ`i M MQK HQmb + T +Bi M+2 BM+`2 b2 BM + `#QM 2H2+i`Q/2b r?2`2 i?2 TQ`2 bBx2 Bb H2bb i? M R MKX AM 7 +i- Qm` M Hv@ b2b 7Q` *Lh URy@RyV rBi? /B K2i2` RXj88 MK `2p2 H mM/2`HvBM; K2+? MBbK Q7 BMi2` +iBQM Q7 i?2 bQHp2Mi iQKb rBi? i?2 * iQKb Q7 i?2 *LhX A7 r2 `2K2K#2` i?2 ` /Bmb Q7 ` `2}2/ `2;BQM r?Qb2 p Hm2 TT`QtBK i2Hv M ? H7 Q7 i?2 ` /Bmb Q7 i?2 *LhURy@RyV Ub22 6B;m`2 d 7Q` /2i BH2/ pB2rV- r2 + M 2p2Mim HHv `2 HBx2 i? i
k9
i?2 /Bbi M+2 #2ir22M i?2 iQK r?Qb2 TQi2MiB H r2HH Bb i?2 K tBKmK KQM; i?2 Qi?2`b M/ * iQKb Q7 i?2 *Lh rBHH #2 bBKTHv δr = rpore −
√
σmax σC ,
Uk8V
r?2`2 σmax Bb BMi2`KQH2+mH ` 2[mBHB#`BmK /Bbi M+2 7Q` M iQK i? i ? b K tB@ KmK TQi2MiB H r2HH KQM; i?2 +QMbiBimiBM; iQKb Q7 i?2 bvbi2K M/ σC Bb i?2 BMi2`KQH2+mH ` 2[mBHB#`BmK /Bbi M+2 Q7 i?2 *LhX AM Qm` + H+mH iBQMb δr Bb 2[m H iQ jXjdj ³ r?B+? Bb HKQbi 2[m H iQ M ? H7 Q7 i?2 ` /Bmb Q7 TQ`2 UBM Qm` + b2 0.50rCN T (10−10) = 3.387³V h?2`27Q`2- r2 T`QTQb2 `2H iBQM- bm+? i? i rmin.
of pore
√ > 2 σσC
UkeV
BM Q`/2` iQ 2HBKBM i2 BM+`2 b2 BM pBb+QbBiv- i?2 pQHmK2 Q7 ` `2}2/ `2;BQM rBi?BM i?2 TQ`2 M/ iQ 2Mbm`2 Q++mT M+v Q7 bQHp2Mi KQH2+mH2b M/ BQMb BM i?2 TQ`2X AM 1[MX ke- rmin. kdy
of pore -
σ M/ σC `272` i?2 KBMBKmK ` /Bmb Q7 i?2 TQ`2 QM i?2
2H2+i`Q/2 bm`7 +2- i?2 G2MM `/@CQM2b 2[mBHB#`BmK /Bbi M+2 Q7 i?2 iQK r?Qb2 TQi2MiB H r2HH Bb i?2 K tBKmK Q7 i?2 iQKb Q7 +QMbiBim2Mi KQH2+mH2bfBQMb M/ G2MM `/@CQM2b 2[mBHB#`BmK /Bbi M+2 Q7 i?2 * iQK Q7 i?2 *Lh `2bT2+iBp2HvX AMp2biB; iBQM Q7 i?2 TQ`2 bBx2 K v #2 #2M2}+B H 7Q` i?2 BM/mbi`v M/ Bb H27i iQ MQi?2` bim/v 7Q` KQ`2 /2i BHbX
k8
kd8
8X *QM+Hm/BM; `2K `Fb h?Bb bim/v T`2/B+ib /B2H2+i`B+ #2? pBQ` Q7 +2iQMBi`BH2 BM aq*Lhb #v b2`B2b Q7 +QKTmi iBQM H 2tT2`BK2MibX q2 ? p2 /Bb+mbb2/ ?Qr i?2 +QM}M2K2Mi 2z2+i +? M;2b i?2 /B2H2+i`B+ T`QT2`iB2b Q7 i?2 +2iQMBi`BH2 i kN3 EX .B2H2+i`B+ T`QT2`iB2b Q7 i?2 *L b22Kb iQ #2 p2`v b2MbBiBp2 #Qi? ` `27 +iBQM
k3y
M/ +QM}M2K2Mi 2z2+ibX h?2 K ;MBim/2 Q7 i?2 /B2H2+i`B+ +QMbi Mi Bb 7mM+@ iBQM Q7 i?2 bBx2 Q7 i?2 /BHmi2 pQHmK2c BX2X- BM+`2 bBM; bBx2 r?B+? /BKBMBb?2b i?2 /B2H2+i`B+ +QMbi Mi +QQT2` iBM; rBi? i?2 +QM}M2K2Mi 2z2+iX "Qi? ` /B H M/ tB H /B2H2+i`B+ +QMbi Mib /2+`2 b2b rBi? /B K2i2` Q7 i?2 im#2bX LQ T`272``2/ Q`B2Mi iBQM Q7 i?2 /BTQH2b HQM; i?2 ` /B H /B`2+iBQM b22Kb iQ #2 i?2 Qi?2` `2 @
k38
bQM 7Q` HQr p Hm2b Q7 i?2 ` /B H /B2H2+i`B+ +QMbi MiX q2 ? p2 mb2/ irQ /Bz2`2Mi K2i?Q/b BM i?2 bBKmH iBQM Q7 /B2H2+i`B+ `2H t iBQMX AM i?2 }`bi QM2- i?2 bvbi2K Bb i`2 i2/ b bvbi2K +QKTQb2/ Q7 BMi2` +iBM; KQH2+mH2bX AM i?2 Qi?2` QM2- i?2 bvbi2K Bb i`2 i2/ b BM/BpB/m H KQH2+mH2b r?B+? /Q MQi z2+i 2 +? Qi?2`X h?2 `2bmHib Q7 #Qi? TT`QtBK iBQMb `2 iQi HHv /Bz2`2MiX Pm` bBKmH iBQMb 7Q` i?2
kNy
#mHF bi i2 b?Qr i? i i?2 bbmKTiBQM Q7 BMi2` +iBM; T `iB+H2b ;Bp2b #2ii2` `2bmHi r?B+? +QMbiBimi2b r2HH rBi? i?2 2tT2`BK2Mi H / i X JQ`2Qp2`- r2 Q#b2`p2/ i? i i?2 `2H t iBQM iBK2 Q7 i?2 +2iQMBi`BH2 BM+`2 b2b +QMbB/2` #Hv +QKT `2/ rBi? 2tT2`BK2MibX h?2 `2H t iBQM T`Q+2bb Bb K BMHv # b2/ QM `Qi iBQM H /BzmbBQMX " b2/ QM Qm` 7m`i?2` /Bb+mbbBQMb- r2 +QM+Hm/2 i? i- 7Q` #2ii2` /BzmbBQM Q7
kN8
i?2 bQHp2Mi KQH2+mH2bfBQMb +`Qbb i?2 TQ`Qmb bm`7 +2 i? i K /2 Q7 *Lhb- i?2 KBMBKmK TQ`2 ` /Bmb b?QmH/ #2 ;`2 i2` i? M irB+2 i?2 /Bbi M+2 #mBHi #2ir22M i?2 iQK r?Qb2 TQi2MiB H r2HH Bb i?2 ?B;?2bi KQM; i?2 +QMbiBim2Mi iQKb Q7 2H2+i`QHvi2 bQHmiBQM M/ i?2 *LhǶb * iQKX eX +FMQrH2/;2K2Mi
jyy
h?2 MmK2`B+ H + H+mH iBQMb `2TQ`i2/ BM i?Bb T T2` r2`2 7mHHv T2`7Q`K2/ i hl"AhE lGE"AJ- >B;? S2`7Q`K M+2 M/ :`B/ *QKTmiBM; *2Mi2` Uh_l" `2bQm`+2bVX S`Q72bbQ` J2?K2i P`? M rBb?2b iQ 2tT`2bb ?Bb ;` iBim/2 7Q` i?2 pBb@
ke
BiBM; b+B2MiBbi b+?QH `b?BT Q7 h?2 *QmM+BH Q7 >B;?2` 1/m+ iBQM Q7 i?2 _2Tm#HB+ Q7 hm`F2vX
jy8
_272`2M+2b (R) hX #/ HH ?- .X G2KQ`/ Mi- "X *H m/2@JQMiB;Mv- `2 `QQK i2KT2` im`2 BQMB+ HB[mB/b #H2 iQ BKT`Qp2 i?2 b 72iv Q7 bmT2`+ T +BiQ`b Q`; MB+ 2H2+@ i`QHvi2b rBi?Qmi /2;` /BM; i?2 T2`7Q`K M+2b\- CQm`M H Q7 SQr2` aQm`+2b kyR UyV UkyRkV j8j Ĝ j8NX /QB,RyXRyRefDXDTQrbQm`XkyRRXRyXRR8X
jRy
l_G
?iiT,ffrrrXb+B2M+2/B`2+iX+QKfb+B2M+2f `iB+H2fTBBf
ayjd3dd8jRRykRdyd (k) PX LX E Hm;BM- oX oX *? # M- oX oX GQbFmiQp- PX oX S`2x?/Q- lMB@ 7Q`K /BzmbBQM Q7 +2iQMBi`BH2 BMbB/2 + `#QM M MQim#2b 7 pQ`b bmT2`@ + T +BiQ` T2`7Q`K M+2- L MQ G2ii2`b 3 U3V Ukyy3V kRkeĜkRjy- TJA., jR8
R3ekdky9X
`sBp,?iiT,ffTm#bX +bXQ`;f/QBfT/7fRyXRykRfMHydkNde;-
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Q` i2 b bmT2`+ T +BiQ` 2H2+i`QHvi2- J22iBM; #bi` +ib JkyRk@yk UeV UkyRkV 8R9X
`sBp,?iiT,ffK X2+b/HXQ`;f+QMi2MifJkyRk@ykfef8R9X
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HB[mB/b- CQm`M H Q7 i?2 "` xBHB M *?2KB+ H aQ+B2iv Rd UkyyeV Ryd9 Ĝ Ry3kX l_G
?iiT,ffrrrXb+B2HQX#`fb+B2HQXT?T\b+`BTi4b+Bn `ii2ti TB/4
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kd
jjy
Ukyy8V Re9Ry9X /QB,RyXRyejfRXRNyejkyX l_G ?iiT,ffHBMFX BTXQ`;fHBMFf\SGf3efRe9Ry9fR (e) aX SBH i?Qii i?BH- EX EX h? bM22K - JX aX h? vvBH- JX SX SBHH B- *X oX LBp2/Bi? - ?B;? pQHi ;2 bmT2`+ T +BiQ` # b2/ QM BQMB+ HB[mB/ rBi? M +iBp i2/ + `#QM 2H2+i`Q/2- J i2`B Hb _2b2 `+? 1tT`2bb 9 UdV UkyRdV yd88yjX
jj8
l_G ?iiT,ffbi +FbXBQTXQ`;fky8j@R8NRf9fB4df 4yd88yj (d) qX@uX hb B- SX@GX h #2`M - SX aBKQM- 1H2+i`Q+?2KB+ H [m `ix +`vbi H KB@ +`Q# H M+2 U2[+KV bim/v Q7 BQM /vM KB+b BM M MQTQ`Qmb + `#QMb- CQm`@ M H Q7 i?2 K2`B+ M *?2KB+ H aQ+B2iv Rje Uk9V UkyR9V 3dkkĜ3dk3- TJA., k93eN3N8X `sBp,?iiTb,ff/QBXQ`;fRyXRykRfD 8yj99Nr- /QB,RyXRykRf
j9y
D 8yj99NrX l_G ?iiTb,ff/QBXQ`;fRyXRykRfD 8yj99Nr (3) _X EQix- JX > ?M- SX _m+?- _X : HH v- *QKT `BbQM Q7 T`2bbm`2 2pQHmiBQM
BM
bmT2`+ T +BiQ`
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T`QiB+
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