J. Inst. Electrostat. Jpn.

, 31, 1 (2007) 2 7ࠞ࡝࠙ࡓࠕࠗࠝࡁࡑ࡯ߩ㕖✢ᒻ⺃㔚ࠬࡍࠢ࠻࡞’િ

ⴕ*,**,1䋬ᒛ⠍**䋬቞

㓶**䋬↰ᧄኪ૫㇢**㧔2006 ᐕ 9 ᦬ 15 ᣣฃઃ; 2006 ᐕ 11 ᦬ 15 ᣣฃℂ㧕

Nonlinear Permittivities in Potassium Salt Ionomers of Ethylene Copolymer
Nobuyuki MAKI*,**, Sho CHO**, Yuu MORIMOTO**, Yoshiro TAJITSU**(Received September 15, 2006; Accepted November 15, 2006)

We report the frequency spectra of complex linear and nonlinear permittivities of potassium ionomer films
prepared from poly (ethylene-co-methacrylic acid) in the frequency range from 1 kHz to 1 MHz, at room
temperature. A characteristic conduction relaxation phenomenon was observed in the spectra, whichsuggested the existence of different ion conduction mechanisms between the high and low-frequency regions.
We also found that the ratio of linear to nonlinear conductivities calculated from nonlinear permittivities wasclosely related to the elementary process of ionic transport. Furthermore, the ratio obtained from nonlinear
measurements allowed an estimate of the important parameters which characterized ionic transport inion-conducting polymers, such as the hopping distance of ion or the size of a connected cluster of the site
capable of the ion hopping, without the need for any additional assumptions in potassium ionomer films.
1䋮䋮3⋧䊝䊂䊦䉕␜䈜䋮ߪߓ߼ߦ䉝䉟䉥䊉䊙䊷䈫䈲䋬⇹᳓ᕈ䈱㜞 ಽሶਥ㎮䈮ዋ㊂䈱䉟䉥䊮⃻࿷䉅䈦䈫䉅ᐢ䈒⹺䉄䉌䉏䈩䈇䉎䉝䉟䉥䊉䊙䊷䈱㜞ᰴ᭴ㅧ䊝ၮ䉕ዉ౉䈚䈢㜞ಽሶ䈱✚⒓䈪䈅䉎䋮䈭䈎䈪䉅䉣䉼䊧䊮䉝䉟䉥䊉䊂䊦䈲䋬1990ᐕ䈮Eisenberg, Hird, Moore䈏ឭ᩺䈚䈢䊝䊂䊦䊙䊷䈲䋬䊖䉴䊃㜞 ಽ ሶ 䈪䈅䉎ૐ ኒ ᐲ 䊘䊥䉣䉼䊧䊮䈱ᕈ ⢻ 䉕଻䋨EHM䊝䊂䊦䋩䈪䈅䉎 2) 䋮EHM䊝䊂䊦䈪䈲䋬䊙䊦䉼䊒䊧䉾䊃䈫⒓ᜬ䈚䈭䈏䉌䋬㊄ዻ䉟䉥䊮᨞ᯅ䈮⿠࿃䈜䉎ൻቇ⊛䊶‛ℂ⊛䈭‛䈘䉏䉎㕒㔚⊛䈮ಝ㓸䈚䈢䉟䉥䊮ಝ㓸૕䈱ᦨዊන૏䈏䋬䈘䉌䈮ᕈ䈏ઃਈ䈘䉏䈩䈍䉍䋬Ꮏᬺ⊛䈮䉅ᐢ䈒೑↪䈘䉏䈩䈇䉎䊒䊤䉴䉼ಝ㓸䈚䈢䋬䉟䉥䊮䉪䊤䉴䉺䊷䈱᭎ᔨ䈏ឭ᩺䈘䉏䈩䈇䉎䋮䊙䊦䉼䉾䉪䈪䈅䉎䋮䊒䊧䉾䊃䈱䉁䉒䉍䈪䈲䋬䉟䉥䊮ಝ㓸ജ䈱ᓇ㗀䈪䋬㜞ಽሶ㎮ㆇേ䉝䉟䉥䊉䊙䊷䈱㜞ᰴ᭴ㅧ䈮㑐䈚䈩䈲䋬⇹᳓ᕈ䈱㜞ಽሶ䊙䈱᧤❈䈘䉏䈢㗔ၞ䈏ሽ࿷䈜䉎䋮䉝䉟䉥䊉䊙䊷ਛ䈱䊙䊦䉼䊒䊧䊃䊥䉾䉪䉴ਛ䈪䋬ⷫ᳓ᕈ䈱㊄ዻ䉟䉥䊮ၮ䈏ಝ㓸䈚䋬૗䉌䈎䈱᭴䉾䊃䈏Ⴧട䈜䉎䈫䋬㓞ធ䈜䉎䊙䊦䉼䊒䊧䉾䊃䈱ㆇേ᧤❈㗔ၞ䈲ㅧ 䉕 ᒻ ᚑ 䈜 䉎 䈖 䈫 䈏 ᒰ ೋ 䉋 䉍 ᜰ ៰ 䈘 䉏 䈩 䈐 䈢 䋮 1968 ᐕ 䈮 䈲㊀䈭䉍䋬䈘䉌䈮ᄢ䈐䈭ㆇേ᧤❈㗔ၞ䉕ᒻᚑ䈜䉎䋮䈖䈱ᄢ䈐䈭ㆇLongworth䈫Vaughan䈏䌘✢࿁᛬䊌䉺䊷䊮䉕ၮ䈮 㽲䊘䊥䉣䉼േ᧤❈㗔ၞ䉕䋬Eisenberg䉌䈲䉟䉥䊮䉪䊤䉴䉺䊷䈫ฬઃ䈔䈢䋮䉟䊧䊮䈱䊤䊜䊤⚿᥏㗔ၞ䋬㽳䊘䊥䉣䉼䊧䊮䈱㕖᥏㗔ၞ䋬෸䈶䋬㽴䉥䊮䉪䊤䉴䉺䊷䈱ሽ ࿷ 䈲䋬䉝䉟䉥䊉䊙䊷䈱ജ ቇ ⊛ ᕈ ⾰ 䈫⺃ 㔚䉟䉥䊮ಝ㓸ㇱ 䈱䋳䈧䈱㗔ၞ䈎䉌䈭䉎䋳⋧ 䊝䊂䊦䉕ឭ᩺䈚䈩䈇⊛ᕈ⾰䈮ᄢ䈐䈭ᓇ㗀䉕ਈ䈋䈩䈇䉎䈫䈘䉏䈩䈍䉍䋬ജቇ⊛᜼േ1)䈮䈧䈇䈩䈲䋬䈖䉏䉁䈪ᄙ䈒䈱ႎ๔䈏䈘䉏䈩䈇䉎 3,4) 䋮䈚䈎䈚䋬䉝䉎 䋮࿑䋱䈮䋬Longworth╬䈱ឭ᩺䈚䈢䉣䉼䊧䊮䉝䉟䉥䊉䊙䊷䈱ࠠ࡯ࡢ࡯࠼㧦㕖✢ᒻ⺃㔚䉴䊕䉪䊃䊦䇮䉦䊥䉡䊛䉝䉟䉥䊉䊙䊷䇮ዉ㔚ᕈ䇮䉟䉥䊮ಝ㓸ㇱ* ਃ੗䊶䊂䊠䊘䊮 䊘䊥䉬䊚䉦䊦ᩣᑼળ␠㩷 䊁䉪䊆䉦䊦䉶䊮䉺䊷 䋨299-0108 ජ⪲⋵ᏒේᏒජ⒳ᶏጯ6䋩Technical Center, DuPont Mitsui Polychemicals Co.,
LTD. 6 Chigusa-kaigan, Ichihara-shi, Chiba-ken
299-0108, JAPAN** 㑐⷏ᄢቇᄢቇ㒮 Ꮏቇ⎇ⓥ⑼ (564-8680㩷 ᄢ㒋ᐭ็↰Ꮢጊᚻ↸㩷 3-3-35)
Graduate School of Engineering, Kansai University,
3-3-35 Yamate, Suita, Osaka 564-8680, Japan
1 makin@mdp.co.jp㪺㫉㫐㫊㫋㪸㫃㫃㫀㫅㪼㩷㫇㪿㪸㫊㪼
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㪸㫄㫆㫉㫇㪿㫆㫌㫊㩷㫇㪿㪸㫊㪼㫧㫧㫀㫆㫅㫀㪺㩷㪸㪾㪾㫉㪼㪾㪸㫋㪼㫊Fig.1 The structure model of ethylene ionomer as proposed
by Longworth et al 1) .

13ࠞ࡝࠙ࡓࠕࠗࠝࡁࡑ࡯ߩ㕖✢ᒻ⺃㔚ࠬࡍࠢ࠻࡞㧔’ િⴕࠄ㧕䉟䉥䊉䊙䊷䈱⺃㔚⊛᜼േ䈲㕖Ᏹ䈮ዊ䈘䈭䉅䈱䈪䈅䉎䈫੍᷹䈘䈱㔚⇇ਅ䈮䈍䈔䉎⷗䈎䈔਄䈱㔚⩄⒖േ䉕␜ໂ䈚䈩䈇䉎䈖䈫䉕5)ႎ๔䈚䈩䈇䉎 11) 䋮䈚䈎䈚䈭䈏䉌䋬↪䈇䈢᷹ቯⵝ⟎䈱ಽ⸃⢻䈏䉏䉎䈖䈫䈎䉌䋬⺃㔚⊛᜼േ䈮㑐䈜䉎ႎ๔䈲଀䈲ዋ䈭䈇 䋮10㱘m䈪䈅䉎䈢䉄䋬䊚䉪䊨䈭㗔ၞ䈪䈱㔚⩄᜼േ䈮㑐䈜䉎ᖱႎ䈫䈖䉐䈪䋬䉣䉼䊧䊮䉝䉟䉥䊉䊙䊷䈱㊄ዻ䉟䉥䊮䈲䋬੝㋦䈅䉎䈇䈲䊅䊃䊥䉡䊛䈏৻⥸⊛䈪䈅䉎䈏䋬䉦䊥䉡䊛䉕㊄ዻ䉟䉥䊮䈫䈜䉎䉁䈪䈲ᓧ䉌䈭䈎䈦䈢䋮䉝䉟䉥䊉䊙䊷(䉦䊥䉡䊛䉝䉟䉥䊉䊙䊷)䈲䋬䉝䉟䉥䊉䊙䊷᮸⢽⥄૕৻ᣇ䋬㜞ಽሶ䈱⎇ⓥ䈪䈲⺃㔚䉴䊕䉪䊃䊨䉴䉮䊏䊷䈱ᚻᴺ䉕6)

䈏ዉ㔚ᕈ䉕␜䈜䈖䈫䈏ႎ๔䈘䉏䈩䈇䉎 䋮䈖䈱․㐳䈮ᵈ⋡䈚䈩䋬㚟૶䈚䈢⎇ⓥ䈏䋬㔚⩄⒖േ䈮㑐䈜䉎᦭⋉䈭ᖱႎ䉕ਈ䈋䈩䈇

䈖䈖10ᐕ⒟䈱㑆䋬䉦䊥䉡䊛䉝䉟䉥䊉䊙䊷䈲Ꮺ㔚㒐ᱛ᧚ᢱ䈫䈚䈩䋬䉎䋮䈚䈎䈚䈭䈏䉌䋬⺃㔚䉴䊕䉪䊃䊨䉴䉮䊏䊷᷹ቯ䈱ᄙ䈒䈲ශട㔚7䋩㔚ሶㇱຠ൮ⵝ╬䈱Ꮏᬺಽ㊁䈮䈍䈇䈩ᐢ䈒೑↪䈘䉏䈩䈇䉎 䋮⇇䈮㔚ᵹ䈏Ყ଀䈜䉎㗔ၞ䋬හ䈤✢ᒻ㗔ၞ䈮㒢䉌䉏䈩䈇䈢䋮ᚒ䇱䈲䋬એ೨䈮䋬䉦䊥䉡䊛䉝䉟䉥䊉䊙䊷䈱㔚⩄᜼േ䈱⋥ធ↰ ኪ 䈲䋬ᓥ ᧪ 䈱✢ ᒻ 㗔 ၞ 䈱ዉ 㔚 䉴䊕䉪䊃䊦䈱⎇ ⓥ 䉕䋬㕖 ✢⊛ 䈭 ᛠ ី 䈏 น ⢻ 䈭 䊌 䊦 䉴 㕒 㔚 ᔕ ജ ᴺ (Pulsedᒻ㗔ၞ䈮䉁䈪᜛ᒛ䈜䉎䈖䈫䈏䋬⺃㔚᜼േ䈱⸃᣿䈮ᄢᄌ᦭ല

Eleotroacoustic Method)

8-10 䋩䈪䈅䉎䈖䈫䉕␜䈚䈩䈐䈢 12) 䋮䉕↪䈇䈢ⓨ㑆㔚⩄ಽᏓ䈱᷹ቯ䉕ⴕ䈦䈩䈇䉎䋮ᓧ䉌䉏䈩䈇䉎ઍ⴫⊛䈭⚿ᨐ䉕䋬࿑2,3䈮␜䈜䋮ᚒ䇱䈲䉦䊥䉡䊛䉝䉟䉥䊉䊙䊷䉕↪䈇䈢✢ᒻ䈱⺃㔚䉴䊕䉪䊃䊦䈖䉏䈲৻⥸⊛䈭⛘✼ᕈ䊒䊤䉴䉼䉾䉪䈪䈅䉎⋥㎮⁁ૐኒᐲ䊘䊥䈱♖ኒ᷹ቯ䉕ⴕ䈇䋬Longworth䋬Eisenberg╬䈮䉋䉍ឭ᩺䈘䉏䉣䉼䊧䊮(LLDPE)䈫䋬ઍ⴫⊛䈭䉦䊥䉡䊛䉝䉟䉥䊉䊙䊷䈱ⓨ㑆㔚䈩䈇䉎㜞 ᰴ ᭴ ㅧ 䊝䊂䊦䈮䉋䉍੍ ᷹ 䈘䉏䈩䈐䈢㔚 ⩄ ᜼ േ 䈮ኻ⩄ಽᏓ䈱᷹ቯ⚿ᨐ䉕␜䈜䋮䈭䈍䋬࿑䈱❑ゲᣇะ䈲㔚⩄ኒᐲᔕ䈜䉎䈫ᕁ䉒䉏䉎⺃㔚✭๺⃻⽎䉕䈲䈛䉄䈩⷗಴䈚䋬ႎ๔䈚䈢ಽ Ꮣ 䉕␜ 䈚䋬ᮮ ゲ ᣇ ะ 䈲⹜ ᢱ 䈱ෘ 䉂ᣇ ะ 䉕␜ 䈜䋮䉁䈢䋬ฝ

13 䋩஥䈏ᱜᭂ஥䋬Ꮐ஥䈲⽶ᭂ஥䈮ኻᔕ䈚䋬਄ᣇ䈱ᮨᑼ࿑䈲䊐䉞✭๺᜼േ䈱䉋䉍⹦⚦䈭ᖱႎ䉕ᓧ䉎䈼䈒ታ㛎䉕ⴕ䈇䋬᦭⋉䈭⚿䊦䊛ᢿ㕙䉕␜䈜䋮࿑ 2䈮␜䈜LLDPE䈱႐ว䋬ᱜᭂ஥䈱ታ㔚ᨐ䉕ᓧ䈢䈱䈪ႎ๔䈜䉎䋮䋮੹࿁䋬ᚒ䇱䈲䋬⺃㔚᷹ቯ䉕㕖✢ᒻ䈮䉁䈪⊒ዷ䈘䈞䋬䈖䈱⩄䋬෸䈶⽶ᭂ஥䈱ታ㔚⩄䈏᷹ⷰ䈘䉏䈢䋮䈭䈍䋬ಽ⸃⢻䈱ᓇ㗀䈪ᱜ䊶⽶㔚ᭂ䈱ㄭற䈮⺃ዉಽᭂ䈲᷹ⷰ䈘䉏䈩䈇䈭䈇䋮䈖䉏2䋮䋮ታ䈮ኻ䈚䋬䉦䊥䉡䊛䉝䉟䉥䊉䊙䊷䈪䈲࿑3䈮␜䈜䉋䈉䈮䋬ᱜᭂ஥䈱

2.1ࠞ࡝࠙ࡓࠕࠗࠝࡁࡑ࡯᮸⢽㛎ታ㔚⩄䈲᷹ⷰ䈘䉏䈢䈏䋬⽶ᭂ஥䈱ታ㔚⩄䈲᷹ⷰ䈘䉏䈝䋬ᱜ䉝䉟䉥䊉䊙䊷䈱⵾ㅧ䊒䊨䉶䉴䈮䈲䋬ṁⲢᴺ䈫Ṣቯᴺ䈏䈅䉎ᭂ஥䈮ᄢ䈐䈭⽶䈱㔚⩄ಽᏓ䈏᷹ⷰ䈘䉏䈢䋮䈖䈱᷹ቯ⚿ᨐ䈲䋬䈏䋬ᧄᬌ⸛䈪䈲᛼಴ᯏ䈮䉋䉎ṁⲢᴺ䉕↪䈇䈢 14) 䋮䉁䈝䋬䊖䉴䊃LLDPE䈱ⓨ㑆㔚⩄ಽᏓ䈫ᄢ䈐䈒⇣䈭䉍䋬䉦䊥䉡䊛䉝䉟䉥䊉䊙䊷㜞 ಽ ሶ 䈫 䈚 䈩 䋬 䉣 䉼 䊧 䊮 85wt% 䈫 䋬 䊜 䉺 䉪 䊥 䊦 ㉄㪌㪅㪇㪜㪂㪈㪈㪅㪌㪜㪂㪉㪂㪈㫂㪭㪧㫆㫋㪸㫊㫊㫀㫌㫄㩷㪠㫆㫅㫆㫄㪼㫉㩷㪝㫀㫃㫄㪣㪣㪛㪧㪜㩷㪝㫀㫃㫄㪚㪿㪸㫉㪾㪼䇭㪛㪼㫅㫊㫀㫋㫐㩿㪚㪆㫄㪊㪀㪚㪿㪸㫉㪾㪼䇭㪛㪼㫅㫊㫀㫋㫐㩿㪚㪆㫄㪊㪀㪂㪈㫂㪭㪇㪅㪇㪜㪂㪇㪺㪸㫋㪿㫆㪻㪼㪇㪅㪇㪜㪂㪇㪸㫅㫆㪻㪼㪺㪸㫋㪿㫆㪻㪼㪸㫅㫆㪻㪼㪄㪌㪅㪇㪜㪂㪈㪄㪈㪅㪌㪜㪂㪉㪫㫀㫄㪼㩿㫄㫊㪅㪀㪫㫀㫄㪼㩿㫄㫊㪅㪀㪝㫀㫃㫄䇭㪫㪿㫀㪺㫂㫅㪼㫊㫊㪝㫀㫃㫄㩷㪫㪿㫀㪺㫂㫅㪼㫊㫊Fig.2 Charge distribution of LLDPE film.

Fig.3 Charge distribution of a potassium ionomer film.

2

43112007ࠞ࡝࠙ࡓࠕࠗࠝࡁࡑ࡯ߩ㕖✢ᒻ⺃㔚ࠬࡍࠢ࠻࡞㧔’ િⴕࠄ㧕

(CH 2 =C(CH 3 )COOH 䋬 ಽ ሶ ㊂ 86.1)15wt% 䉕 䋬 㜞 ࿶ 䊤 䉳 䉦 䊦䉕ශട䋬䈠 䈱ᔕ ╵㔚⩄ 䌄 (t)(ᔕ ╵ 㔚 ᵹI(t))䉕䉼䊞䊷䉳䉝䊮䊒㊀วᴺ䈮䉋䉍㊀ว䈚䋬䉣䉼䊧䊮䍃䊜䉺䉪䊥䊦㉄౒㊀ว૕䋨෸䈶㔚ᵹ䉝䊮䊒૬↪䋩䈪ᬌ಴䈜䉎䋮ᬌ಴䈘䉏䈢D(t)䋨䉁䈢䈲(E-15MAA)䉕ᓧ䈢䋮ᰴ䈮䋬㊄ዻ䉟䉥䊮Ḯ䈫䈚䈩䉦䊥䉡䊛Ⴎ䉕↪

㔚ᵹI(t)䋩 䈫䋬ශട㔚⇇䈱ାภE(t)䈮䉋䉍䋬㕖✢ᒻⶄ⚛⺃㔚ᗧ䈚䋬E-15MAA䈫䉦䊥䉡䊛Ⴎ䉕䋬E-15MAAਛ䈱䊜䉺䉪䊥䊦㉄䈫₸ 㱑 n * 䋨䉁䈢䈲ዉ㔚₸ 㱟 n *䋩H n * H n ' jH n " (n=1,2,3䊶䊶)V n * V n' jV n " (n=1,2,3䊶䊶)䉦䊥䉡䊛(K䋬ේ ሶ ㊂ 39.1)䈏䊝䊦Ყ 䈪䋬40%(E-15MAA-0.4K)䋬
60%(E-15MAA-0.6K)䋬80%(E-15MAA-0.8K)䈫䈭䉎䉋䈉䈮੍(2)(3)

䉄䊑䊧䊮䊄䈚䋬140㷄䈎䉌260㷄䈮⸳ ቯ 䈚䈢᛼ ಴ ᯏ 䉕↪ 䈇䈩䋬䉕᳞䉄䉎䋮ᧄ䉲䉴䊁䊛䈱♖ᐲ䈲䋬࿑5ਛ䈮䈍䈔䉎䋬ାภེ䋬䉝ṁⲢਛ๺෻ᔕ䈮䉋䉍䉦䊥䉡䊛䉝䉟䉥䊉䊙䊷䉕ᓧ䈢䋮࿑ 4䈮䉣䉼䊮䊒䋬S/NᲧ䈱㜞䈇ାภ♽䈏ᡰ䈋䈩䈇䉎䋮䊧䊮䍃䊜䉺䉪䊥䊦㉄౒㊀ว૕䈫䉦䊥䉡䊛䉝䉟䉥䊉䊙䊷䈱ൻቇ᭴ㅧ䉦䊥䉡䊛䉝䉟䉥䊉䊙䊷䊐䉞䊦䊛䈮䈍䈔䉎⺃㔚✭๺⃻⽎䈲䋬ᓥ᧪↰ኪ╬䈏ᛒ䈦䈩䈐䈢⺃㔚✭๺⃻⽎ 16-18) 䉋䉍䋬ା ภ឵▚䈪䉕␜䈜䋮૞ ᚑ 䈚 䈢 E-15MAA 䋬 E-15MAA-0.4K 䋬 E-15MAA-0.6K 䋬1/100⒟ᐲ䈫䈲䉎䈎䈮ዊ䈘䈒 13 䋩 䋬ᓥ᧪䈱㕖✢ᒻ᷹ቯ䈱♖ᐲ䉕

E-15MAA-0.䋸K䉕↪䈇䈩䋬180㷄䈮⸳ቯ䈚䈢䉟䊮䊐䊧䊷䉲䊢䊮⿥䈋䈩䈇䈢䋮䈠䈖䈪䋬੹࿁ᚒ䇱䈲䋬᷹ቯ๟ᵄᢙၞ䉕ᄢ᏷䈮೙䊐䉞䊦䊛ᚑᒻᯏ䈮䉋䉍䋬䈠䉏䈡䉏50㱘mෘ䈱䊐䉞䊦䊛䉕૞ᚑ䈚

㒢䋨25 mHz~10 MHz䋨⚂䋹ᩴ䋩䉕1 kHz~1 MHz(3ᩴ)䋻䉣䉼䊧䈢䋮䊮䉝䉟䉥䊉䊙䊷✭๺䈱ሽ࿷䈜䉎▸࿐䈻೙㒢䋩䋬䉁䈢䉝䊮䊒䈫ାภ⊒↢ེ䈱䉲䉴䊁䊛᭴ᚑㇱ᧚䉕ᄢ䈐䈒ᄌᦝ䈚䋬䈘䉌䈮䉼䊠䊷

2.2䊆䊮䉫䉕๟ᵄᢙ․ൻ䈜䉎䈖䈫䈪䋬᷹ቯ♖ᐲ䉕䈅䈕䈢䋮䈭䈍䋬䉝᷹ቯ⹜ᢱ䊮䊒ಾ䉍ᦧ䈋䈱䉴䉟䉾䉼䊉䉟䉵䈏ᄢ䈐䈇䈖䈫䈎䉌䋬䉝䊮䊒䈲੹࿁૞ᚑ䈚䈢ฦ䉦䊥䉡䊛䉝䉟䉥䊉䊙䊷䊐䉞䊦䊛䈮䋬㔚ᭂ䈫䈚䈩㊄䉕15)䋮䉦䊥䉡䊛䉝䈱᷹ቯၞ䈪䉋䉍♖ᐲ䈅䈕䉎䈖䈫䈏䈪䈐䈢㔚⩄䉝䊮䊒䈱䉂䈫䈚䋬䉟䉥䊉䊙䊷䊐䉞䊦䊛䈲䊋䊦䉪䈱ዉ㔚ᕈ䈏ૐ䈇䈢䉄䋬⴫㕙ᣇะ㔚ᵹ䉝䊮䊒䈲ᄖ䈚䈢䋮ᦝ䈮ⓥᭂ䈱䊉䉟䉵ኻ╷䈫䈚䋬᷷ᐲ೙ᓮ䈮ᵹ䉏䉎㔚ᵹ䈱ᓇ㗀䉕ឃ㒰䈚䈭䈒䈩䈲䈭䉌䈭䈇䋮䈖䈱䈢䉄䋬᷹ㇱ䋨䊍䊷䉺╬䋩䉕ᄖ䈚䋬ᄖੂାภ䉕೥ᷫ䈚䈢䋨䈠䈱䈢䉄䋬੹࿁䈲ቯ⹜ᢱ䈮䈲䉧䊷䊄㔚ᭂ䉕⸳䈔䈢䋮䉁䈢䋬⹜ᢱෘ䉂䈮ኻ䈚䈩ᄢቶ᷷䈱䉂䈱᷹ቯ䈪䈅䉎䋩䋮䈠䈱⚿ᨐ䋬ᓥ᧪ⵝ⟎䉋䉍䋬⫳⌕䈚䈩䋬⺃ 㔚䉴䊕䉪䊃䊦᷹ቯ↪䈱⹜ ᢱ䈫䈚䈢䈐䈭㔚ᭂ㕙Ⓧ䈫䈜䉎䈖䈫䈪䋬㔚⇇䈏ဋ৻䈮⹜ᢱ䈮ශട䈘䉏䉎

1KHz~1MHZ䈱▸࿐ౝ䈪䈅䉏䈳㕖✢ᒻ⺃㔚♖ᐲ䈲70䌤䌂⒟䉋䈉䈮䈚䈢䋮ะ਄䈚䈢䋮

2.33䋮䋮  ⚿  ᨐ㕖✢ᒻ᷹ቯࠪࠬ࠹ࡓߩᡷༀ䉦䊥䉡䊛䉝䉟䉥䊉䊙䊷䊐䉞䊦䊛䈱⺃㔚᷹ቯ䋬ዉ㔚᷹ቯ䈮䈲䋬࿑ 6 䈮ቶ᷷䋨28.5㷄䋩䈮䈍䈔䉎䋬䉦䊥䉡䊛䉟䉥䊮䉕ో䈒฽䉁䈭䈇↰ኪ╬䈏㐿⊒䈚䈩䈐䈢✢ᒻ෸䈶㕖✢ᒻⶄ⚛⺃㔚䊶ዉ㔚᷹ቯ䉣䉼䊧䊮䍃䊜䉺䉪䊥䊦㉄౒㊀ว૕ E-15MAA 䈫䋬䈠䉏䈡䉏䉦䊥䉡䊛ⵝ⟎䉕↪䈇䈢䋮ⵝ⟎䈱⹦⚦䈲ᣢႎ12 䋩䈱ઁ䈪䈅䉎䈱䈪䋬◲න䉟䉥䊮䈪 40mol%(E-15MAA-0.4K)䋬60mol%(E-15MAA-0.6K)䋬

䈮એਅ䈮ේℂ䉕䉁䈫䉄䉎䋮

80mol%(E-15MAA-0.8K)ਛ๺䈚䈢䋬䉦䊥䉡䊛䉝䉟䉥䊉䊙䊷䊐䉞䊦ᧄ䉲䉴䊁䊛䈪䈲䋬⹜ᢱ䈮ᝄ᏷E 0 䈱ᱜᒏᵄ䋬E

E 0 cos Zt䊛 䈱 ✢ ᒻ ⺃ 㔚 ₸ ⯯ ㇱ 㱑 1” 䈱 䉴 䊕 䉪 䊃 䊦 䉕 䉁 䈫 䉄 䈢 䋮(1)E-15MAA-0.4K䋬E-15MAA-0.6K䋬E-15MAA-0.8K ో䈩䈱䉦䊥䉡䉣䉼䊧䊮䊶䊜䉺䉪䊥䊦㉄౒㊀ว૕㪪㪰㪥㪫㪟㪜㪪㪠㪱㪜㪩㪚㪟㪊㪄㩿㪚㪟㪉㪄㪚㪟㪉㪀㫅㪄㩿㪚㪟㪉㪄㪚㪀㫄㪄㪚㪦㪦㪟㪤㪠㪚㪩㪦㩷㪚㪦㪤㪧㪬㪫㪜㪩㪭㪦㪣㪫㪘㪞㪜㩷㪘㪤㪧㪣㪠㪝㪠㪜㪩㪮㪘㪭㪜㩷㪤㪜㪤㪦㪩㪰䉦䊥䉡䊛䉝䉟䉥䊉䊙䊷㪜㩷㩿㫋㪀㪘㪫㪫㪜㪥㪬㪘㪫㪦㪩㪚㪟㪊㪚㪟㪊㪄㩿㪚㪟㪉㪄㪚㪟㪉㪀㫇㪄 㩿㪚㪟㪉㪄㪚㪀㫈㪄 㩿㪚㪟㪉㪄㪚㪀㫉㪄㪄 㪂㪚㪦㪦㩷㪢 㪚㪦㪦㪟㪜㩷㪔㩷㪜㪇㩷㪺㫆㫊㱥㫋㪪㪘㪤㪧㪣㪜

Fig.4 Chemical structure of ethylene methacrylic acidcopolymer and potassium ionomer.

㪛㪛㩷㩿㫋㪀

㪚㪟㪘㪩㪞㪜㩷㪘㪤㪧㪣㪠㪝㪠㪜㪩Fig.5 Schematic diagram of experimental system formeasuring permittivities.12)35ࠞ࡝࠙ࡓࠕࠗࠝࡁࡑ࡯ߩ㕖✢ᒻ⺃㔚ࠬࡍࠢ࠻࡞㧔’ િⴕࠄ㧕䊛䉝䉟䉥䊉䊙䊷䈮䈍䈇䈩䋬10kHz 䈎䉌 100kHz 䈮⺃㔚✭๺䉕␜䈜㜞ಽሶߩ୯㧘଀߃߫㧘ࡐ࡝ࠛ࠴࡟ࡦࠝࠠࠪ࠼♽㜞ಽሶߩ'V3䊏䊷䉪䈏ሽ࿷䈚䈩䈇䉎䋨࿑ 6 ⍫ශㇱಽ䋩䋮䈖䉏䈮ኻ䈚䈩䋬䉦䊥䉡䊛䉟= 8.01x10-17SmV-2ߣᲧߴ㕖Ᏹߦዊߐ޿16)㧚߹ߚ㧘㔚⩄߇Ყ䉥䊮䉕ో䈒฽䉁䈭䈇 E-15MAA 䈪䈲䋬✭๺⃻⽎䉕␜䈜䊏䊷䉪䈏⊒セ⊛᧤❈ߐࠇߡ޿ࠆ㜞ಽሶߢᓧࠄࠇߡ޿ࠆ'V3 = 5.18x10-18⃻䈚䈩䈇䈭䈇䋮䈖䈱᷹ቯ⚿ᨐ䈲䋬⺃㔚✭๺⃻⽎䈱ሽ࿷䈏䋬䉦䊥䉡ࠃࠅ߽ዊߐ޿17,18)㧚හߜ㔚⩄⒖േ߇߆ߥࠅߎߩࠕࠗࠝࡁࡑ࡯䊛䉟䉥䊮䈱ሽ࿷䈮⋥ធ⿠࿃䈚䈩䈇䉎䈖䈫䉕ⵣઃ䈔䈩䈇䉎䋮䉁䈢䋬ߪ᧤❈ࠍฃߌߡ޿ࠆߎߣࠍ␜ໂߔࠆ㧚࿑ਛ䈱 䂾 䈲 㱑 3 '䋬 䃂 䈲䉦䊥䉡䊛䉟䉥䊮Ớᐲ䈏ᷫዋ䈜䉎䈮䈧䉏䈩䋬䊏䊷䉪ᒝᐲ䈏ዊ䈘䈒䈭

㱑 3 "䈱᷹ቯ୯䉕䋬ታ✢䈲(4),(5)ᑼ䈮ၮ䈨䈒⸘▚⚿ᨐ䉕␜䈜䋮
3ᰴ 䈱㕖 ✢ ᒻ ⺃ 㔚 䉴䊕䉪䊃䊦䈮䈍䈇䈩䋬࿑ 䈮␜ 䈜䉋䈉䈮䋬10䈦䈩䈇䉎䈖䈫䈏䉒䈎䉎䋮䈖䉏䈮ኻ䈚䈩䋬3 ᰴ䈱㕖✢ᒻⶄ⚛⺃㔚

kHzએ਄䈪䈲䋬 㱑 3 ’䈫 㱑 3 "䈱䊏䊷䉪䉕฽䉄䋬⦟䈒ౣ⃻䈪䈐䉎䈖䈫䉴䊕䉪䊃䊦䈪䈅䉎 㱑 3 *= 㱑 3 ' - j 㱑 3 "䈲䉋䉍ⶄ㔀䈭ᒻ⁁䉕␜䈚䈢䋮䈏ಽ䈎䉎䋮䈚䈎䈚䈭䈏䉌䋬1 kHz䈎䉌10 kHz䈱▸࿐䈪䈲 㱑 3 "䈱

࿑ 7 䈮 㱑 3 *䈱᷹ቯ⚿ᨐ䉕␜䈜䋮3 ᰴ䈱㕖✢ᒻⶄ⚛⺃㔚₸ታ⸘▚୯䈫᷹ቯ୯䈏ᄢ䈐䈒⇣䈭䈦䈩䈇䉎䋮䈖䉏䈲䋬20 kHzㄭறㇱ 㱑 3 ' 䋬 ⯯ ㇱ 㱑 3 " 䈫 䉅 䋬 䉦 䊥 䉡 䊛 䉟 䉥 䊮 Ớ ᐲ 䈏 80mol% 䈎 䉌䈮䈅䉎✭๺⃻⽎䈮೎䈱⃻⽎䋨࿑6䈱 㱑 䋱 "䈱1 kHzએਅ䈱┙䈤

60mol%䈮ਅ䈏䉎䈫䋬✭๺⃻⽎䉕␜䈜䊏䊷䉪ᒝᐲ䈏ᕆỗ䈮ዊ䈘䈒਄䈏䉍䈮෻ᤋ䈜䉎㔚ᭂಽᭂ䈭䈬䈱ᓇ㗀䋩䈏㊀⇥䈘䉏䈩䈇䉎䈢䈭䈦䈩䈇䉎䋮䉄䈫⠨ 䈋䈩䈇䉎䋮䉁䈢䋬E-15MAA-0.4K䋬E-15MAA-0.6K䈪䋬䈖

↰ኪ䈲䋬᷹ⷰ䈚䈢㜞ಽሶ䈱✢ᒻ෸䈶㕖✢ᒻ䈱ዉ㔚✭๺䉴䈱✭๺䉴䊕䉪䊃䊦䈏ዊ䈘䈒㕖✢ᒻⵝ⟎䈱♖ᐲ䈱㒢⇇䉅䈅䉍䋬䈲䈦䊕䉪䊃䊦䉕⛔৻⊛䈮ౣ⃻䈜䉎✭๺㑐ᢙ 㱟 nrelax 12)

V nrelax

V n*'V njZW n(1  ( jZW n ) En )DnjnZH n*䈐䉍䈞䈝䋬(4),(5)ᑼ䈱ᦛ✢䈅䈩䈲䉄䈲䈪䈐䈭䈎䈦䈢䋮

(4)

4.

⠨

ኤ

䉟䉥䊮ᤃേ䈏᭽䇱䈭hopping䉺䉟䊒䉕␜䈜႐ว䈮䈧䈇䈩ᓧ䉌(n=1,3)䉏䉎㔚ᵹI䈲䋬෩ኒ䈮⸘▚䈘䉏䈩䈇䉎12,19,20䋩䋮․䈮ᦨㄭ䈪䈲ዉ㔚(5)ᕈ㜞ಽሶ䈱㔚 ⩄ ⒖ േ ᯏ᭴䈮䈧䈇䈩䈲䋬dynamic percolation䉕䋬ႎ๔䈚䈩䈇䉎䋮䈖䈖䈪䋬✭๺ᒝᐲ 㰱㱟 n 䋬✭๺ᤨ㑆 㱠 n 䋬✭

theory21,22䋩䈏ಽሶ㎮䈱䉶䉫䊜䊮䊃ㆇേ䉕ၮ䈮䈚䈢dynamics䉕෻ᤋ๺ᤨ 㑆䈱ಽᏓ 䉕⴫䈜ᜰᢙ 㱍 n 䋬 㱎 n 䈪䈅䉎䋮࿑ 8䈮(4),(5)ᑼ䉕䈚䈢䊝䊂䊦䈫䈚䈩ᵈ⋡䉕㓸䉄䈩䈍䉍19 䋩 䋬䊘䊥䉣䉼䊧䊮䉥䉨䉲䊄♽↪䈇䈩䋬E-15MAA-0.8K䈱㕖✢ᒻ⺃㔚䉴䊕䉪䊃䊦䈱䇸ᦛ✢䈅䈩㜞ಽሶ䈮䈧䈇䈩䈲㕖✢ᒻᕈ䉕฽䉄䈩⸃ᨆ䈏ᚑഞ䈚䈩䈇䉎12䋩䋮䈢䈲䉄(fitting)䇹䉕䈚䈢⚿ᨐ䉕␜䈜䋮䈖䈖䈪䋬 D3 = 2.98, E3 = 0.88,

䈣䈚䋬䈠䈱ᛒ䈇䈲ᾘ㔀䉕ᭂ䉄䉎਄䈮䋬⸃ᨆ䈮䈲⹦⚦䈭᭴ㅧ䈱

W3 = 5.03x10-6s, 'V3 = 2.12x10-19SmV-2ߢ޽ࠆ㧚ߎߎߢᓧߚᖱ ႎ 䈏ᔅ ⷐ 䈪䈅䉍䋬䉦䊥䉡䊛䉝䉟䉥䊉䊙䊷䈱䉋䈉䈭䋬ⶄ 㔀 䈭㜞'V3ߩ୯ߪ㧘ࠗࠝࡦ߇㜞ಽሶਛࠍ⥄↱ߦേߌࠆࠗࠝࡦዉ㔚ᕈ

1.00.4

ψ ψ0.1+㪜㪄㪈㪌㪤㪘㪘㪄㪇㪅㪍㪢K (60)

46H H (10-20m2/V2)+
㪜㪄㪈㪌㪤㪘㪘㪄㪇㪅㪏㪢K (80)

0.2+
㪜㪄㪈㪌㪤㪘㪘㪄㪇㪅㪋㪢K (40)+㪜㪄㪈㪌㪤㪘㪘K (0)102K(40)‫ ع‬ǭ3” of E-15MAA-0.6K

0.5

ψ

H1" / H0K(80)K(60)٨ ǭ3” of E-15MAA-0.8K‫ غ‬ǭ3’ of E-15MAA-0.6K
K(60)0.30.0010

٤ ǭ3’ of E-15MAA-0.8K
K(80)

᷷ᐲ30͠
᷹ቯ㪫㪼㫄㫇㪅㪊㪇㷄K(40)ٌ ǭ3’ of E-15MAA-0.4K

ً ǭ3” of E-15MAA-0.4K

0.0-0.5

1010f (Hz)-9-1.0x10

3.0

3.5

4.0

4.5

5.0

5.5

6.0log f (Hz)Fig.7 Frequency spectra of the third-order nonlinear

Fig.6 ǭ 1 "/ ǭ 0 spectrum of potassium ionomer, exhibiting apermittivities in potassium ionomers.

change in potassium ion content.

463112007ࠞ࡝࠙ࡓࠕࠗࠝࡁࡑ࡯ߩ㕖✢ᒻ⺃㔚ࠬࡍࠢ࠻࡞㧔’ િⴕࠄ㧕ᰴ᭴ㅧ䉕ᜬ䈧㜞ಽሶ䈱႐ว䈮䈲㔍䈚䈇 19) 䋮ㅢᏱ䋬᭴ㅧ㕙䈱ᖱႎ䈏ዋ䈭䈇႐ว䋬⸃ᨆ䈮䈲hoppingℂ⺰20)䉥䊮ಝ㓸૕䈱䉰䉟䉵䋩䈮ኻᔕ䈚䈩䈇䉎䈫⠨䈋䈩䈇䉎䋮䉁䈢䋬৻䉕↪䈇䉎䋮䈖䉏⥸䈮䉦䊥䉡䊛䉝䉟䉥䊉䊙䊷䈱ዉ㔚ᕈ䈲䋬㜞Ớᐲ䈮䉦䊥䉡䊛䉟䉥䈲䋬hoppingℂ⺰䈏䋬䉨䊞䊥䉝䊷䈏site㑆䉕hopping䈪⒖േ䈜䉎䊮䈪ਛ๺䈘䉏䈢႐ว䈮䈱䉂⊒⃻䈜䉎䈖䈫䈏⍮䉌䉏䈩䈇䉎(଀䈋䈫䈉ᒻ䈪ዷ㐿䈘䉏䉎䈢䉄䈮䋬᭴ㅧ䈱ᖱႎ䉕䈜䈼䈩site䉇bond䈫䈳䋬E-15MAA䊔䊷䉴䈪䈲⚂80mol%ਛ๺એ ਄䈪䋬ዉ㔚ᕈ䈏䈇䈉ᒻ䈪⟎䈐឵䈋ᓧ䉎䈫䈇䈉೑ὐ䈮䉋䉎䋮ᧄႎ๔䈮䈍䈇䈩䉅䋬ᕆỗ䈮⊒⃻䈜䉎) 6) 䋮䈘䉌䈮䋬䉦䊥䉡䊛䉇䊅䊃䊥䉡䊛䉝䉟䉥䊉䊙䊷

hoppingℂ⺰䉕↪䈇䉎䈏䋬䉋䉍৻⥸⊛䈭⸃ᨆ䈫䈜䉎䈢䉄䈮䋬䉟䈱䉟䉥䊮ಝ㓸૕ᒻᚑ䈲ਛ๺ᐲ60%⒟ᐲ䈪ቢᚑ䈚䋬䈠䉏એ਄䉥䊮䈱hopping䈏ㄭធsite㑆䈱䉂䈮⸵䈘䉏䉎䈫䈇䈉න⚐䊝䊂䊦䈱ਛ๺ᐲ䈪䈲䊚䉪䊨⋧ಽ㔌䈏⿠䈖䉎䈖䈫䈏ႎ๔䈘䉏䈩䈇䉎 27) 䋮䈪䈲䈭䈒䋬䉣䊈䊦䉩䊷⊛䈮ૐ䈇૏⟎䈻䉅hopping䈏⸵䈘䉏䉎䋬䉋䉍৻⥸⊛䈭䊝䊂䊦ᚒ䇱䈲䋬䈖䉏䉌䈱ႎ๔䉕〯䉁䈋䋬㜞Ớᐲ䈮䉦䊥䉡䊛䉟䉥䊮䈪ਛvariable range hopping model๺䈘䉏䈢႐ว䈮䈍䈇䈩䋬䉦䊥䉡䊛䉝䉟䉥䊉䊙䊷䈱䉟䉥䊮ಝ㓸ㇱ

(VRHM) 20) 䉕↪䈇䉎䋮

'UeaE
2eNaP0 exp() sinh()
NT2NTI䈲䋬ᐔဋhopping〒㔌a=52nm䈮ኻᔕ䈜䉎䋬⺃㔚✭๺⃻⽎䈮㑐ਈ䈜䉎⊒㆐䈚䈢䋬䈅䉎⒳䈱䉟䉥䊮䉪䊤䉴䉺䊷᭴ㅧ (એ㒠(6)domain䈫⒓䈜䉎)䉕ᒻᚑ䈜䉎䉅䈱䈫⠨䈋䈩䈇䉎䋮䈖䈖䈪ᐔဋhopping〒㔌a䋬ශട㔚⇇E䋬⛘ኻ᷷ᐲT䋬ᭂ㒢⊛䈭 䈍 䋬 䉦 䊥 䉡 䊛 䉟 䉥 䊮 䈪 40mol%(E-15MAA-0.4K) 䋬䈭 hopping ⏕ ₸ P 0 䋬 ⚛ 㔚 ⩄ e 䋬 䉨 䊞 䊥 䉝 䊷 䈱 ᢙ ኒ ᐲ N 䋬60mol%(E-15MAA-0.6K)ਛ๺䈚䈢䉣䉼䊧䊮䉝䉟䉥䊉䊙䊷䈪䈲䋬

Boltzmannቯᢙ㱖䋬site㑆䈱ᵴᕈൻ䉣䊈䊦䉩䊷㰱U䈪䈅䉎䋮䈖3ᰴ 䈱 㕖 ✢ ᒻ ⶄ ⚛ 䉴 䊕䉪 䊃 䊦᷹ ቯ 䈏 ಴ ᧪ 䈩䈇 䈭䈇 䋮 䈖 䉏䈲䈖䈪䋬I䉕ᒻᑼ⊛䈮E䈪ዷ㐿䈜䉎䈫䋬V 1 E  V 3 E 3  㨯㨯㨯I

V1V3'U
1 2 2
e a P0 N exp()
NT
NT
1'U)
e 4 a 4 P0 N exp(3 3NT
24N Tdomain᭴ㅧ䈏ᒻᚑ䈘䉏䈭䈇䈢䉄䈎䋬᷹ቯ♖ᐲ䈱㒢⇇䈎䈲⃻࿷䈱䈫䈖䉐䈲ਇ᣿䈪䈅䉎䋮

(7)

5䋮䋮 䉁䈫䉄(8)䉦䊥䉡䊛䉝䉟䉥䊉䊙䊷䈱㕖✢ᒻⶄ⚛⺃㔚₸䈱᷹ቯ䈏น⢻䈭ታ㛎䉲䉴䊁䊛䉕᭴▽䈚䋬㕖✢ᒻⶄ⚛⺃㔚₸䈱䉴䊕䉪䊃䊦䉕᷹

(9)䉕ᓧ䉎䋮䈖䈖䈪䋬✢ᒻⶄ⚛⺃㔚䉴䊕䉪䊃䊦䈎䉌䋨8䋩ᑼ䉕↪䈇䈩a1.0䈱fitting䉕⹜䉂䈩䉅䋬ᧂ⍮ቯᢙ䈏ᄙ䈒䋬૗ 䉌䈎䈱઒ ቯ䉕ዉ౉

٤ ǭ3’ of E-15MAA-0.8KK(80)K(80)٨ ǭ3” of E-15MAA-0.8K

䈚䈭䈔䉏䈳ਇน⢻䈪䈅䉎䋮䈫䈖䉐䈏䋬 㱟 1 䈫 㱟 3 䈱Ყ䈲ᰴ䈱ᑼ䈪⴫䈞䉎12 䋩 䋮H H (10-20m2/V2)

䈧䉁䉍䋬 㱟 1 䈫 㱟 3 䈱୯䈏ታ㛎⊛䈮⹏ଔ䈏䈪䈐䉏䈳䋬䋨10䋩ᑼ䉕

V3V1e2a 2
24N 2T 2㧙‫ޓޓޓ‬theorytheory

0.5(10)0.0-0.5↪䈇৻⟵⊛䈮ታ㛎୯䈱䉂䈪䋬ᐔဋhopping〒㔌a䈱୯䉕᳞䉄䉎䈖䈫䈏น⢻䈮䈭䉎䋮䈖䈖䈪䈲䋬䉦䊥䉡䊛䉟䉥䊮䈪80mol%ਛ๺䈚-9-1.0x10䈢䉣䉼䊧䊮䉝䉟䉥䊉䊙䊷(E-15MAA-0.8K)䈱ታ㛎䉋䉍ᓧ䈢㜞๟

3.0

3.5

4.0

4.5

5.0

5.5

6.0log f (Hz)ᵄ ஥ ෸ 䈶ૐ ๟ ᵄ ஥ 䈱ᭂ 㒢 ୯ 䈱 㱟 1 䈫 㱟 3 䉕↪ 䈇䈩a䈱⹏ ଔ䉕ⴕ䈇䋬a=3nm䈫a=52nm䉕ᓧ䈢䋮䈖䉏䉁䈪ዊⷺᢔੂX✢࿁ᨆ䉇䋬㔚ሶ㗼ᓸ㏜ⷰኤ䋬ේሶ㑆

Fig.8 Comparison of observed (circles) and fittedജ 㗼 ᓸ ㏜ ᴺ 䈮䉋䉍ႎ ๔ 䈘䉏䈩䈇䉎 23-26) 䉝䉟䉥䊉䊙䊷䈱䉟䉥䊮(solid lines) frequency spectra of the third-orderಝ 㓸 ૕ 䉰 䉟 䉵 䈲 ᢙ nm 䈪 䈅 䉎 䈖 䈫 䈎 䉌 䋬 ᚒ 䇱 䈱 ᓧ 䈢 ᐔ ဋnonlinear permittivities of E-15MAA-0.8K.

hopping〒㔌a=3nm䈲䉟䉥䊮ಝ㓸૕ౝ䈪䈱㔚⩄⒖േ〒㔌䋨䉟57ࠞ࡝࠙ࡓࠕࠗࠝࡁࡑ࡯ߩ㕖✢ᒻ⺃㔚ࠬࡍࠢ࠻࡞㧔’ િⴕࠄ㧕ቯ䈚䈢䋮᷹ቯ䈚䈢⺃㔚䉴䊕䉪䊃䊦䈲䋬✭๺⃻⽎䉕઻䈇ⶄ㔀䈭10) T. Maeno, K. Fukunaga, IEEE Trans. DEI, 6 (1996) 754

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⊛䈭hopping〒㔌䉕⹏ଔ䈜䉎䈖䈫䈏䈪䈐䈢䋮

13䋩 ’િⴕ䋬ዊᨋବ䋬દᄙᵄஜ䋬㊄ፒ㓷⟵䋬↰ኪ૫㇢䋺㕒㔚᳇䈖䉏䉁䈪䋬䉦䊥䉡䊛䉝䉟䉥䊉䊙䊷䉕฽䉃䉣䉼䊧䊮䉝䉟䉥䊉䊙䊷ቇળ⹹, 31, 134 (2006)䈪ឭ໒䈘䉏䈩䈇䉎䉟䉥䊮ಝ㓸૕䈱ᄢ䈐䈘䈲ᢙ nm䈪䈅䉍䋬䈖䉏14) ⍫㊁િ৻,ᐔᴛᩕ૞✬䋺䉝䉟䉥䊉䊙䊷䍃䉟䉥䊮ᕈ㜞ಽሶ᧚䈲ᧄ ᬌ ⸛ 䈪⏕ ⹺ 䈘䉏䈢䋬ᐔ ဋ hopping〒 㔌 a=3nm䈏␜ 䈜㔚ᢱ,䉲䋭䉣䊛䉲䋭಴

(2004)⩄⒖േ䈱⚛ㆊ⒟(Elementary Process)䈮ኻᔕ䈚䈩䈇䉎䈫⠨䈋

15䋩 N. Maki, S. Nakano, M. Kanasaki, and Y. Tajitsu, The䈩䈇䉎䋮䈖䉏䈮ኻ䈚a=52nm䈱᷹ቯ⚿ᨐ䈲䋬E-15MAA-0.8K䈮

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