工学研究所所報第 36 号目次
巻頭

言

工学研究所についての雑感 ·········································· 遠藤
総信行 ····· 1

説
水に濡れない材料 ···················································· 金

仁華 ····· 2

熱・換気回路網モデルによる建築環境工学分野での研究開発 ············ 奥山

博康 ····· 5

高密度バイオマスブリケットの着火燃焼特性～

バイオマスのエネルギー利用に向けて······································ 伊東

弘行、井田

民男、藤田

～

修 ···· 16

次世代機械材料「金属ガラス」の特性と加工 ·························· 寺島
直列型多重暗号の安全性とその応用 ···································· 藤岡

岳史 ···· 22
淳 ···· 32

効率対ムダ世界におけるカメレオン基準とメジアン・コントロール法 ···· 松井

正之 ···· 40

鋼管部材の簡易な疲労損傷評価方法 ······················ 大熊

八紀 ···· 46

武司、安井

共同研究
長方形形状の超伝導ニオブトンネル接合の超伝導電流と有限電圧電流ステップの２次元磁界特性······································ 中山

明芳、阿部

晋、穴田

哲夫 ···· 63

正延、松井正之 ···· 70

持続可能なリーン生産・物流マネジメント···································· 中島

健一、松丸

環境調和型物質変換及び新エネルギープロセス創出の基盤となるナノ構造触媒の開発·························· 引地

史郎、内藤

周弌、吉田

暁弘、中澤

順 ···· 77

空気電池用電極触媒および高分子電解質膜の開発···························· 松本

太、田中

学、南部

典稔、岸岡

真也 ···· 87

カーボンナノチューブ内部の 1 次元的ナノ空間に閉じ込められた水の誘電物性······································ 松田

和之、相澤

啓仁、真庭

豊 ···· 95

クオンテイルと完備べき等左半環の表現定理 ················ 西澤弘毅、古澤仁 ··· 106

総合論文

随

想
神奈川大学 21 年間の触媒研究 ······································· 内藤

周弌 ··· 114

高分子微粒子と 50 年 ··············································· 川口

春馬 ··· 118

年次報告 ············································································ 122
神奈川大学工学研究所所報執筆規定 ···················································· 127
編集後記 ············································································ 133

CONTENTS
Preface
Impression of Research Institute for Engineering············ Nobuyuki ENDOH ····· 1
Review
Super-liquid-repelling Materials ································ Ren-Hua JIN ····· 2
Research and development on the basis of the thermal and air flow network model forbuilding environmental engineering field ················· Hiroyasu

OKUYAMA ····· 5

Ignition and Combustion Characteristics of Highly Densified Biomass Briquette······························· Hiroyuki ITO Tamio IDA Osamu FUJITA ···· 16
Properties and Processing of Metallic Glass ················· Takeshi TERAJIMA ···· 22
Sequential Multiple Encryption: Security and Application ······ Atsushi FUJIOKA ···· 32
A Chameleon’s Criteria and Medium Control in Efficiency vs. Muda World······················································ Masayuki MATSUI ···· 40
Simple Method for Evaluating Fatigue damage of Pipe Members·····································Takeshi OHKUMA Hachinori YASUI ···· 46
Joint ResearchTwo-dimensional Magnetic Field Characteristics
of Superconducting Current and Current Steps at Finite voltage of Niobium junctions····················· Akiyoshi NAKAYAMA Susumu ABE Tetsuo ANADA ···· 63
Lean manufacturing and logistics management for sustainability····· Kenichi NAKASHIMA Masanobu MATSUMARU

Masayuki MATSUI ···· 70

Development of Nano-scale Fine Structure Catalysts for Green Chemistry and Novel Energy
Processes···· Shiro HIKICHI

Shuichi NAITO

Akihiro YOSHIDA Jun NAKAZAWA ···· 77

Development of Electrocatalyst and Polymer Electrolyte Membrane for Air-Battery
Futoshi MATSUMOTO

Manabu TANAKA Noritoshi NANBU

Shin-ya KISHIOKA · 87

Dielectric Properties of Water Confined Inside Pseudo-one-dimensional Nanoscopic Space ofCarbon Nanotubes··· Kazuyuki MATSUDA Hirohito AIZAWA Yutaka MANIWA ···· 95
Comtribution
Representation Theorems for Quantales and Complete Idempotent Left Semirings·································· Koki NISHIZAWA Hitoshi FURUSAWA ··· 106
Essay
Study on the Heterogeneous Catalysis for Twenty-one Years at Kanagawa University···························································· Shuichi NAITO ··· 114
My Life of Research Devoted to Polymeric Micro-Particles ·· Haruma KAWAGUCHI ··· 118
Annual Reports of the Institute ······················································· 122
Manuscript Submission Instruction ··················································· 127
Letters from the Editors ····························································· 133



ᕳ㢌ゝ

ᕤᏛ◊✲ᡤ࡟ࡘ࠸࡚ࡢ㞧ឤ㐲⸨ ಙ⾜㸨Impression of Research Institute for Engineering
Nobuyuki ENDOH㸨௒ᖺ㸪⚄ዉᕝ኱Ꮫࡣ๰❧ 85 ᖺ㸪ᕤᏛ◊✲ᡤࡣ๰タ 38
ᖺࢆ㏄࠼ࡲࡋࡓ㸬᣺ࡾ㏉ࡿ࡜㸪ἲᚊᏛ⛉࡟ጞࡲࡿ኱Ꮫ๰

ᣢࡗ࡚࠸ࡓࡓࡵ㸪ከࡃࡢ⊂๰ⓗ࡞㛤Ⓨ◊✲ࡀ㐙⾜ࡉࢀ㸪ࡑࡢຌ⦼ࡣᕤᏛ◊✲ᡤᡤሗ࡟グ㘓ࡉࢀ࡚࠸ࡲࡍ㸬❧࠿ࡽ 11 ᖺᚋࡢ 1939 ᖺ࡟ᶵᲔᕤ㸪㟁Ẽᕤ㸪⤒Ⴀᕤࡢᕤ࡜ࡇࢁ࡛㸪㏆ᖺ᪥ᮏࡢᕤᏛ⣔㡿ᇦࡢᵝᏊࢆぢ࡚࠾ࡾࡲᏛ⣔ 3 Ꮫ⛉ࢆ㛤タࡋ㸪⥲ྜ኱Ꮫ࡜ࡋ࡚Ṍࡳጞࡵࡲࡋࡓ㸬ࡍ࡜㸪ᮏ◊✲ᡤ㛤タᙜ᫬ࡢࡼ࠺࡞ໃ࠸ࡀ࡞ࡃ࡞ࡗࡓࡼ࠺

ࡉࡽ࡟㸪1967 ᖺ࡟኱Ꮫ㝔ἲᏛ◊✲⛉㸪⤒῭Ꮫ◊✲⛉࡜࡜࡟ᛮࢃࢀࡲࡍ㸬ࡑࡢ୍ᅉࡣ㸪
ⱝᖺேཱྀࡢᛴ⃭࡞ῶᑡ࡛ࡍ㸬ࡶ࡟ᕤᏛ◊✲⛉ࢆタ⨨ࡋ㸪Ꮫ⏕ᩍ⫱ࡔࡅ࡛ࡣ࡞ࡃ◊✲㛤≉࡟ኻࢃࢀࡓ 20 ᖺ࡜ゝࢃࢀ᭱㏆࡛ࡣ㸪⌮ᕤᏛࡢୡ⏺࡟㐍

Ⓨ࡟ᑐࡋ࡚ࡶ኱࠸࡞ࡿດຊࢆഴὀࡍࡿ኱Ꮫ࡜࡞ࡾࡲࡋࡓ㸬ࡶ࠺࡜ࡍࡿⱝேࡢᩘࡀῶࡗ࡚ࡋࡲࡗࡓࡇ࡜࡟࠶ࡿ࡜⪃࠼ᕤᏛ◊✲⛉㛤タࡢ 8 ᖺᚋ࡟ࡣ㸪ᕤᏛ㒊࡞ࡽࡧ࡟኱Ꮫ㝔ᕤࡽࢀࡲࡍ㸬኱Ꮫཷ㦂⪅ᩘࡣ 10 ᩘᖺ㛫࡛ 30 ୓ே௨ୖῶᑡ

Ꮫ◊✲⛉࡜୍⮴༠ຊࡋ࡚᭱ඛ➃ࡢ⛉Ꮫᢏ⾡㛤Ⓨ࡟㈉⊩ࡍࡋ㸪◊✲࣭〇㐀⣔௻ᴗ࡟ᑵ⫋ࡋࡼ࠺ࡍࡿ㟷ᖺࡢ๭ྜࡶῶ

࡭ࡃ㸪ᮏᕤᏛ◊✲ᡤࢆタ⨨ࡋࡲࡋࡓ㸬ᮏ◊✲ᡤࡣ㛤タᙜࡗ࡚ࡋࡲ࠸ࡲࡋࡓ㸬ࡇࡢࡓࡵ㸪⌧ᅾከࡃࡢᕤᏛ⣔኱Ꮫᩍึ࠿ࡽ㸪๰㐀ᛶ࠶ࡩࢀࡿඃ⚽࡞ࣉࣟࢪ࢙ࢡࢺ◊✲࡟ᑐࡋဨࡀࠕࡇࡢࡲࡲ࡛ 10 ᖺᚋࡢ᪥ᮏࡣ኱୔ኵ࠿㸽ࠖ࡜࠸࠺␲࡚ࡣ◊✲㈨㔠ࢆ᥼ຓࡍࡿ࡜࠸࠺ඛ㐍ⓗ࡞ാࡁࢆࡍࡿ⤌⧊ᛕࢆᣢࡗ࡚ࡋࡲ࠺≧ែ࡛ࡍ㸬ࡉࡽ࡟㸪⏘ᴗᵓ㐀ࡢኚ㠉ࡸ࡛ࡋࡓ㸬ᙜ᫬ࠊࡇࡢࡼ࠺࡞⤌⧊ࡣᅜ❧኱Ꮫ࡛ࡣᩓぢ࡛ࡁ࢚ࢿࣝࢠ࣮࣭⎔ቃၥ㢟࡬ࡢᑐᛂ➼㸪ᚑ᮶ࡢᏛ⾡࣭ᢏ⾡࡟ࡲࡋࡓࡀ㸪⚾❧኱Ꮫ࡟࠾࠸࡚ࡣࡑࢀ࡯࡝ከࡃ࡞࠿ࡗࡓ࡜ᇶ࡙ࡃ▱ぢࡸᡭἲࢆ࣮࣋ࢫ࡟ࡋࡓᩍ⫱࣭◊✲ࡔࡅ࡛ࡣゎᛮ࠸ࡲࡍ㸬ࡇࡢࡼ࠺࡟ᮏ◊✲ᡤࡣ㸪⚄ዉᕝ኱Ꮫࡢ㺀㉁ᐇ๛

Ỵ࡛ࡁ࡞࠸ㅖၥ㢟࡟ࡶ┤㠃ࡋ࡚࠸ࡲࡍ㸬೺࣭✚ᴟ㐍ྲྀ㺁ࡢᘓᏛࡢ⢭⚄ࢆࡶࡘከᩘࡢඃ⚽࡞Ꮫ㒊࣭኱ᕤᏛ◊✲㡿ᇦࡣ㸪ࡑࡢ◊✲ᢏ⾡㛤Ⓨࡸ㛤Ⓨࡉࢀࡓ〇ရᏛ㝔ಟ஢⏕࡜㸪⊂๰ⓗ࡞⪃࠼ࢆᣢࡗࡓᩍဨ࣭◊✲ဨ࡟ࡼࡀᅜᐙࡢᏑᅾࢆᕥྑࡍࡿ㔜せ࡞ᇶ┙ศ㔝࡛࠶ࡾ㸪ᖖ࡟㐍ࡿ๰㐀ⓗ◊✲㛤Ⓨࡢࢧ࣏࣮ࢺࢆࡍࡿ◊✲ᡤ࡜ࡋ࡚㈉⊩ࡋṌࡋ࡞ࡅࢀࡤ࡞ࡾࡲࡏࢇ㸬ࡑࡇ࡛㸪Sustainability ࢆ⥔ᣢ࡚ࡲ࠸ࡾࡲࡋࡓ㸬ࡑࡢ⤖ᯝ⚄ዉᕝ኱Ꮫࡣ㸪ᩥ㒊⛉Ꮫ┬ࡢࡋ㸪㧗࠸ Quality of Life ࢆᐇ⌧ࡍࡿࡓࡵ࡟ࡣ㸪ከࡃࡢ⪽᫂⚾❧኱ᏛᏛ⾡◊✲㧗ᗘ໬᥎㐍஦ᴗࡢᨭ᥼࡟ࡼࡿᏛ⾡ࣇ࡛ࣟ⬟ືⓗ࡞ⱝ࠸◊✲⪅ࢆ⫱࡚㸪࠿ࡘ㸪๰㐀ⓗ࡛㠉᪂ⓗ࡞ࣥࢸ࢕࢔ࣉࣟࢪ࢙ࢡࢺ㸪ࣁ࢖ࢸࢡ࣭ࣜࢧ࣮ࢳ࣭ࢭࣥࢱ࣮

◊✲ࢆࡍࡿࡇ࡜ࡀᚲせ࡛ࡍ㸬ᮏ◊✲ᡤࡣᏛ㒊࣭኱Ꮫ㝔࡜ࣉࣟࢪ࢙ࢡࢺ➼ࡢᩍ⫱◊✲⿦⨨࣭タഛࡢᩚഛ⿵ຓࢆከᩘ

୍య࡜࡞ࡗ࡚㸪ࡇࡢࡼ࠺࡞㔜せ࡞┠ᶆࢆᐇ⌧ࡍࡿࡓࡵ࡟

⋓ᚓࡍࡿࡇ࡜ࡀ࡛ࡁ㸪ࡇࢀ࡟ࡼࡾᕤᏛ⣔㡿ᇦࡢᇶ┙◊✲኱ࡁ࡞ാࡁࢆࡍࡿࡇ࡜ࡀ࡛ࡁࡿ࡜⪃࠼ࡲࡍ㸬ࡉࡽ࡟᪂ࡋ

ᡤ࡜ࡋ୍࡚ᒙ㔜せᛶࢆቑࡋ࡚ࡁ࡚࠾ࡾࡲࡍ㸬࠸㡿ᇦ㸪౛࠼ࡤ㸪Ỉ⏘㈨※ࡸᾏᗏ㈨※ࡢ୺ᶒⓗᶒ฼ࢆᣢᮏ◊✲ᡤࡀ㛤タࡉࢀࡓ᫬ᮇࡣ㸪᪥ᮏ⤒῭ࡢᏳᐃⓎᒎᮇࡘ EEZ ࡟╔┠ࡍࡿࡼ࠺࡞◊✲ศ㔝࡟ࡶຊࢆධࢀࡿࡇ࡜

࡟ᙜࡓࡾ㸪⛉Ꮫᢏ⾡࡟㈉⊩ࡍࡿᕤᏛ⣔ᩍ⫱࣭◊✲ศ㔝࡬ࡶ⪃࠼ࡽࢀࡲࡍ㸬࢖ࣥࢻࡸ୰ᅜࡼࡾࡶ኱ࡁ࡞㡿ᇦࢆᣢࡗࡢ኱ࡁ࡞ᮇᚅࡀ࠶ࡾࡲࡋࡓ㸬ࡑࡢࡓࡵከࡃࡢඃ⚽࡞Ꮫ⏕࡚࠸ࡿ࡜࠸ࢃࢀࡿᗈ኱࡞ EEZ ࢆ㛤Ⓨ࡛ࡁࢀࡤ㸪⭾኱࡞ኳࡀάẼ࠶ࡩࢀࡿ◊✲άືࢆ⾜ࡗ࡚࠸ࡲࡋࡓ㸬ᮏ◊✲ᡤࡣ↛㈨※ࢆᡭ࡟ධࢀࡿࡇ࡜ࡀྍ⬟࡟࡞ࡾ㸪᪂ࡓ࡞᪥ᮏࢆ෌

ࡇࡢࡼ࠺࡞᫬ᮇ࡟㸪኱Ꮫෆ࡟࠾ࡅࡿඃ⚽࡞ࣉࣟࢪ࢙ࢡࢺ

⏕࡛ࡁࡿྍ⬟ᛶࡀ࠶ࡾࡲࡍ㸬඲ୡ⏺ࡢே㢮ࡢᖾ⚟࡟㈉⊩◊✲ࢆᑂᰝࡋ㸪ࡇࢀ࡟㈨㔠ⓗᨭ᥼ࢆࡍࡿඛ㐍ⓗ࡞ไᗘࢆࡍࡿࡓࡵࡢඛ㐍ⓗ࡞◊✲㛤Ⓨࡢ᥎㐍࡜㸪ᅜ㝿ឤぬ࡟ᐩࢇ*ጤဨ㛗㸪ᕤᏛ◊✲⛉
Dean of Graduate School of Engineeringࡔඃ⚽࡞Ꮫ⏕࣭◊✲⪅ࢆ㏦ࡾฟࡍࡓࡵ࡟㸪⚄ዉᕝ኱Ꮫᕤ
Ꮫ◊✲ᡤ࡛኱ࡁ࡞ᙺ๭ࢆ₇ࡌ࡚࡯ࡋ࠸࡜⪃࠼ࡲࡍ㸬Ỉ࡟⃿ࢀ࡞࠸ᮦᩱ㔠 ோ⳹*㸨

Super-liquid-repelling Materials
Ren-Hua JIN

㸯㸬㉸᧕Ỉ࡜ࡣ

ࡣࢼࣀࢸࢡࣀࣟࢪ࣮ࡢ୍ࡘࡢ㔜せ࡞ㄢ㢟࡜࡞ࡾ㸪ᮦᩱ໬⮬↛⏺࡛ࡢ᳜≀ࡢከࡃࡣ㸪Ỉࢆᙎࡃᶵ⬟ࢆഛ࠼ࡿࡇ࡜

Ꮫࡣࡶࡕࢁࢇ㸪ᛂ⏝≀⌮Ꮫ࡛ࡶ㛵ᚰ஦࡟࡞ࡾ㸪Ḣ⡿࢔ࢪࡀከ࠸㸬ࡼࡃ▱ࡽࢀࡿ⌧㇟࡛࠶ࡿࡀ㸪ⶈࡢⴥࡗࡥࡀࡑࡢ

࢔ㅖᅜ࡛ࡢ⇕࠸ど⥺ࢆ㞟ࡵࡓ㸬ࡋ࠿ࡋ࡞ࡀࡽ㸪Ỉࢆᙎࡃ୍౛࡛࠶ࡿ㸬ⶈࡢⴥࡗࡥࡢୖ࡟㸪Ỉ⁲ࢆⴠ࡜ࡋࡓ࡜ࡋࡼ

⾲㠃࡜࠸࠺ࡢࡣ㸪኱᢬ࡣᦶ⪖ᛶࡀᙅࡃ㸪⾪✺࣭ᦶ⪖ࢆక࠺㸬Ỉ⁲ࡣࡓࡕࡲࡕࡲࡿ࡛ࣅ࣮⋢ࡢࡼ࠺࡟㌿ࡀࡿ㸬࡞ࡐ࠺⏝㏵࡟⤖ࡧࡘࡅࡿࡢࡣᴟࡵ࡚ᅔ㞴࡛࠶ࡿ㸬࡞ࡐ࡞ࡽ㸪࠿࡜࠸࠺࡜㸪Ỉ⁲ࡢ᥋ゐゅࡀ 150rࢆ㉺࠼ࡿ࠿ࡽ࡛࠶ࡿ㸬᳜≀࡛ぢࡽࢀࡿࡼ࠺࡟㸪㉸᧕Ỉ⾲㠃ࡣᚲࡎࢼࣀࢧ࢖ࢬࡢ

࡞ࡐ㸪᥋ゐゅࡀࡇࢀ࡯࡝኱ࡁࡃ࡞ࡿࡢ࠿ࢆ▱ࡿࡢࡀ⫢せࢻ࣓࢖࡛ࣥᵓᡂࡉࢀ㸪ࡑࡇ࡟✵Ẽࡀ⁀ࡵࡽࢀࡿࡢ࡛㸪ࡑ࡛࠶ࡿ㸬ᐇࡣ㸪࢟ࣕ࣋ࢶࡢࡼ࠺࡞ࡳࡎࡳࡎࡋ࠸ⴥࡗࡥ࡛

ࡢࢼࣀᵓ㐀⮬యࡀ㸪ᶵᲔᙉᗘࢆᣢࡘࡢࡀᅔ㞴࡛࠶ࡿ࠿ࡽ

ࡶ㸪ࡑࡢ⾲㠃࡛ࡣỈ⁲ࡀ㌿ࡀࡾࡸࡍ࠸㸬ࣂࣛࡢⰼࡶྠᵝ࡛࠶ࡿ㸬౛࠼࡜ࡍࡿ࡜㸪㕲➽ࡣᙉᗘࡀᙉࡃ࡚ࡶ㸪ྠࡌ㔠࡟㸪኱㞵ࡢᚋ࡛࠶ࢁ࠺࡜ⰼࡧࡽࡢ⾲㠃ࡣ⃿ࢀ࡚ࡣ࡞࠸㸬ᒓࢆ㔪ࡢࡼ࠺࡟⣽ࡃࡋࡓࡽ㸪ࡑࡢ㔠ᒓ㔪ࡣእຊ࡛⡆༢࡟᳜≀ࡣỈࢆዲࡴ⏕≀࡛࠶ࡿࡀ㸪ࡔ࠿ࡽ࡜࠸ࡗ࡚㸪Ỉ࡟⃿᭤ࡆࡽࢀ࡚ࡋࡲ࠺㸬ࢼࣀࢧ࢖ࢬࡢ⾲㠃ᮦᩱࡣ㸪ᮦ㉁ࡀ࡝

ࢀࡿࡇ࡜ࢆዲࡴࢃࡅ࡛ࡣ࡞ࡃ㸪Ỉ࡟ᾐ࠿ࢀ࡞࠸ࡼ࠺࡟㸪࠺࠿ࢆၥࢃࡎ㸪ᇶᮏⓗ࡟ࡑࡢᙉᗘࡣᙅࡃ࡞ࡿ㸬㉸᧕Ỉᮦࡑࡢⴥࡗࡥࡢ⾲㠃࡟ࡣᴟࡵ࡚㧗࠸␯Ỉᛶ㸦㉸␯Ỉᛶ㸧ᵓᩱ࡜࠸࠺ࡢࡣ㸪≀㉁ࡢ⾲㠃࡛ࡢࢼࣀタィ࡛࠶ࡿ௨ୖ㸪ࡑ㐀ࢆഛ࠼࡚࠸ࡿ㸬ࡇࢀࡽ࡟ࡣඹ㏻ࡢ⾲㠃ᵓ㐀ࡀᏑᅾࡍࡿ㸬ࡢ⾲㠃ࡢᦶ⪖࡟ᑐࡍࡿᙅࡉࡣ୙ྍ㑊ⓗࡔ࡜ㄆ㆑ࡋࡓୖ࡛

ࡑࢀࡣ㸪ࢼࣀ࡜࣐࢖ࢡࣟࢧ࢖ࢬࡀ⤌ࡳྜࢃࡉࢀࡓ⾲㠃พࡢ◊✲࡛࡞ࡅࢀࡤ࡞ࡽ࡞࠸㸬༶ࡕ㸪㉸᧕Ỉ࡜࠸࠺⾲㠃タฝᵓ㐀࡛࠶ࡾ㸪ࡑࡢᵓ㐀୰ࡢ㝽㛫࡟✵Ẽࢆࡓࡗ࡫ࡾಖᣢ

ィ࡛ࡣ㸪ࡑࡢඛ㐍ⓗᮦᩱ౯್ࢆ㏣ồࡍࡿ࡟࠶ࡓࡗ࡚㸪ᮦࡍࡿ㸬࠸ࢃࡤ㸪✵Ẽࢆ⾲㠃࡟Ᏻᐃ࡟㈓ࡵࡇࡴࡇ࡜ࡀ㉸᧕ᩱ࡜ࡋ࡚ࡢᚲ↛ⓗḞⅬࡑࡢࡶࡢࢆྰᐃࡏࡎ࡟◊✲ㄢ㢟ࢆỈࡢᇶᮏⓗ࡞௙⤌ࡳ࡛࠶ࡿ㸬ᢳฟࡍࡿᚲせࡀ࠶ࡿ㸬Ỉ㸪ࡇࢀࡣ⏕࿨⥔ᣢࡢᇶᮏせ⣲࡛࠶ࡿ㸬ࡋ࠿ࡋ㸪Ỉࡣࡇࡇ࡛ࡣ㸪㉸᧕Ỉᵓ㐀ࢆ㸪እ㒊࡜඲ࡃᦶ᧿ࡋ࡞࠸ᵓ㐀᫬࡟ࡣ࠾ࡑࢁࡋ࠸ࡶࡢ࡬࡜ኚㇺࡍࡿ㸬ᭀ㞵࣭ὥỈ࡞࡝ᆅ≀㸦౛࠼ࡤ㸪⟶≧ᵓ㐀㸪ᐜჾ㸧ࡢෆቨ࡞࡝࡟タィࡍࡿࡇ⌫Ẽೃࢫࢣ࣮࡛ࣝࡢ⌧㇟ࡣࡲࡉ࡟ࡑࡢ౛࡛࠶ࡿ㸬ࡑࢀࡼ࡜ࢆ⪃᱌ࡋ㸪ࡑࡢ㝿㸪㉸᧕Ỉᛶᶵ⬟ࡀఱࢆࡶࡓࡽࡋࡓ࠿

ࡾࡣࡿ࠿࡟ᑠࡉ࠸ࢫࢣ࣮ࣝࡢᕤᏛᮦᩱࡢୡ⏺࡛ࡶ㸪Ỉࡣ࡟ࡘ࠸᳨࡚ウࡋࡓ஦౛ࢆ⤂௓ࡍࡿ㸬ࡋࡤࡋࡤேࠎࢆᅔࡽࡏࡿ㸬ࡑࢀࡣ㗵㸪࢝ࣅ㸪⤖㟢㸪ị⤖࡞࡝࡛࠶ࡿ㸬ᚑࡗ࡚㸪Ỉ࡜↓⦕࡞ࡶࡢ࡯࡝Ύ₩ࢆ⥔ᣢࡍ㸰㸬ࢼࣀพฝ⾲㠃ᵓ㐀ࡢタィἲࡿỈࡣࡌࡁ⾲㠃ࡀồࡵࡽࢀࡿ㸬Ỉ࡟⃿ࢀ࡞࠸ᵓ㐀ࡣ㸪㗵࣭ࢼࣀพฝࡣࢺࢵࣉࢲ࢘ࣥࡲࡓࡣ࣎ࢺ࣒࢔ࢵࣉࡢ᪉ᘧ࡛

࢝ࣅࢆ㜵ࡄࡇ࡜ࡀ࡛ࡁ㸪ࡲࡓ㸪⾲㠃࡛ࡢỈ࡜ࡢᦶ᧿ຊࢆ

タィ࡛ࡁࡿ㸬࣎ࢺ࣒࢔ࢵࣉἲ࡜ࡋ࡚㸪⤖ᬗᛶࢆ᭷ࡍࡿ࣏

పୗࡉࡏࡿࡇ࡜ࡀ࡛ࡁࡿ
㸦┬࢚ࢿࣝࢠ࣮࡛ࡶ࠶ࡿ㸧㸬ᙜ↛㸪࢚ࣜࢳࣞࣥ࢖࣑ࣥ(sPEI)ࢆ㥑౑ࡋࡓࣉࣟࢭࢫࡀ㛤ⓎࡉࢀỈࢆᙎࡃ⾲㠃࡛ࡣ㸪⤖㟢࣭ị⤖ࢆ㜵ࡄࡇ࡜ࡶ࡛ࡁࡿ㸬࡚࠸ࡿ㸬sPEI ࡣỈ⁐ᛶ࡛࠶ࡿࡀ㸪80Υ௨ୖࡢ⇕Ỉ࡛ࡣ࡞ࡇࡢࡼ࠺࡞ࢥࣥࢭࣉࢺࢆ‶ࡓࡍᢏ⾡ࡀ☜❧࡛ࡁࡓࡽ㸪࠸࡜⁐ゎࡋ࡞࠸㸬ࡑࡢ⇕Ỉ⁐ᾮࢆㄪ〇ࡋ㸪ࡑࢀࢆᐊ ࡲࡑࡢ⏝㏵ࡣ㸪᪥ᖖ࠿ࡽ᭱ඛ➃㡿ᇦࡲ࡛㝈ࡾ࡞ࡃᗈࡀࡿ࡜

࡛࡟෭ࡸࡍ࡜ᚲࡎỈศᏊ࡜Ỉ⣲⤖ྜࡋࡓ sPEI ࡢᚤᑠ⧄ண᝿ࡉࢀࡿ㸬ࡇࡇ 10 ᖺ㸪㉸᧕Ỉ⾲㠃タィ࡟㛵ࡍࡿ◊✲⥔ࡢࢼࣀ⤖ᬗࡀ୚࠼ࡽࢀࡿ㸬୍᪉㸪㹱PEI ࡣ㸪ሷᇶᛶ࡟* ᩍᤵ ≀㉁໬Ꮫ⛉㸨ᩍᤵ ≀㉁໬Ꮫ⛉Professor, Dept.
of Mater& Life&Chemistry
Professor,
Dept.
of Mater
Life ChemistryỈ࡟⃿ࢀ࡞࠸ᮦᩱ

ᐩࢇ࡛㸪ᴟᛶࡶᙉࡃ㸪ᇶᮦ⾲㠃࡟௜╔ࡉࢀࡸࡍ࠸㸬ࡇࡢ
ᛶ㉁ࢆ฼⏝ࡍࡿࡇ࡜࡛㸪sPEI ࡢỈ⁐ᾮࢆ⟶≧ࡢᵓ㐀≀࡟྾࠸㎸ࡳ㸪ࡑࢀࢆྤࡁฟࡍ㸬ࡇࡢ༢⣧సᴗ࡟ࡼࡾ㸪⟶≧ᵓ㐀≀ෆቨ࡟㸪⦓ᐦ࡞ sPEI ࡢ྾╔⭷ࢆᙧᡂࡉࡏࡿ㸬ࡑࡢ྾╔⭷ࡣࡸࡀ࡚ sPEI ࡢࢼࣀ⤖ᬗᒙ࡟ኚ᥮ࡉࢀࡿ㸬ࡇࡇ࡛㸪ࡦ࡜ࡘࡢࢸࣥࣉ࣮ࣞࢺᴫᛕࢆᑟධࡍࡿ㸬ࡑࢀࡣ㸪sPEI ࡢゐ፹ᶵ⬟ࢆ⏕࠿ࡍࡇ࡜࡛࠶ࡿ㸬sPEI ࡣሷᇶᛶ࣏
࣐࣮ࣜࡢࡺ࠼㸪࢔ࣝࢥ࢟ࢩࣜ࢔ࣥࡢࢰࣝࢤࣝ཯ᛂࢆಁ㐍ࡉࡏࡿ᭷ຠ࡞ゐ፹࡛࠶ࡿ㸬ᚑࡗ࡚㸪⟶≧ᵓ㐀≀ࡢෆቨ࡟ᙧᡂࡋࡓ sPEI ⤖ᬗᒙࢆ࢔ࣝࢥ࢟ࢩࣜ࢔ࣥࡢỈ⁐ᾮ୰࡟ᾐₕ㸦᥋ゐ㸧ࡉࡏࡿ࡜㸪ࡑࡢ⤖ᬗᒙ⾲㠃࡟࡚㸪ᅗ㸰࢞ࣛࢫ⟶ෆቨ 1⭷ࡢ 6(0 DF ࡜ 7(0 G ෗┿ᵓ㐀⭷ࢆ N2 ࡜ࡍࡿ㸬ࡉࡽ࡟㸪sPEI ⤖ᬗᒙస〇࡟࠾ࡅࡿ sPEI ྾╔ࡢ᮲௳ࢆኚ᭦ࡉࡏࡿࡇ࡜࡛㸪ᅗ㸲࡛ほᐹࡉࢀࡓࡼ࠺࡞⊂≉࡞ࢼࣀᵓ㐀ⷧ⭷ࡀྜᡂ࡛ࡁࡿ㸬ࡇࡇ࡛ࡣ㸪࣐࢖ࢡࣟࢧ࢖ࢬᖜ࡛
ᩘ༑ࢼࣀ࣓࣮ࢺࣝࡢཌࡳࡢࣇ࣮ࣞࢡ≧ᵓ㐀యࡀᇶᮦ⾲㠃඲య࡟ἢࡗ࡚㸪⦓ᐦ࡟❧ࡕ୪ࡪ㸬ࡑࡢࢩ࣮ࢺ≧ᵓ㐀యࡢᅗ ௵ពᙧ≧ࡢᇶᯈ࡟ࢼࣀࢩࣜ࢝ⷧ⭷స〇ࣉࣟࢭࢫ

㏱㐣ᆺ㟁Ꮚ㢧ᚤ㙾㸦TEM㸧ࡢほᐹ࠿ࡽ㸪ࢩ࣮ࢺࡣᐇࡣእ
ᚄ⣙ 15nm㸪ෆᚄࡀ⣙ 3-4nm ࡜࡞ࡿࢼࣀࢳ࣮ࣗࣈࡀᩘᒙ

࢔ࣝࢥ࢟ࢩࣜ࢔ࣥࡢຍỈศゎ࡜⦰ྜ཯ᛂࡀ㐍⾜ࡋ㸪ࡸࡀ㔜࡞ࡗ࡚࠿ࡽ࡞ࡿ࣐ࢵࢺ࡛࠶ࡿࡇ࡜ࡀุ᫂ࡉࢀࡓ㸬ࡇࡢ࡚ࢩࣜ࢝⭷ࡀᯒฟࡍࡿ㸬ࡇࡢ඲㐣⛬ࢆᅗ㸯࡟♧ࡍ㸬➨୍ᵓ㐀⭷ࢆ N3 ࡜ࡍࡿ㸬ẁ㝵ࡣ㸪sPEI ࡢ྾╔࡜⤖ᬗ໬㐣⛬㸪➨஧ẁ㝵ࡣ sPEI ⤖ᬗᒙ⭷ࢆࢩࣜ࢝ࢯ࣮ࢫ⁐ᾮ࡟ᾐₕࡋ㸪ࢩࣜ࢝⭷ࢆసࡿ㐣⛬࡛࠶ࡿ㸬ࡇࡢ༢⣧సᴗ࡟ࡼࡾ㸪⟶≧ᵓ㐀≀ෆቨ࡟㸪ࢩࣜ࢝࠿ࡽ࡞ࡿࢼࣀᵓ㐀⿕そ⭷ࡀᙧᡂࡍࡿ㸬ᅗ㸯ࡢࣉࣟࢭࢫ࡛ࡣ㸪sPEI ྾╔㝿ࡢ ᗘ᮲௳㸪ࡑࡢ྾╔⭷ࡢ෭ࡸࡍ᮲
௳ࢆከᑡኚ࠼ࡿࡇ࡜࡛㸪᭱⤊ⓗ࡟ᚓࡽࢀࡿࢩࣜ࢝ࢼࣀᵓ
㐀⭷ࢆ኱ࡁࡃኚ࠼ࡿࡇ࡜ࡶ࡛ࡁࡿ㸬ᅗ㸰~ᅗ㸲࡛ࡣ㸪࢞ࣛࢫ⟶ࡢෆቨ࡟స〇ࡋࡓ✀ࠎࡢ␗࡞ࡿ⾲㠃ᵓ㐀ࢆ᭷ࡍࡿࢩࣜ࢝ⷧ⭷ࡢ SEM㸦㉮ᰝᆺ㟁Ꮚ㢧ᚤ㙾㸧࡜ TEM㸦㏱㐣ᆺ㟁Ꮚ㢧ᚤ㙾㸧෗┿ࢆ♧ࡍ㸬ᅗ㸰ࡢ
SEM ࢖࣓࣮ࢪ࠿ࡽ㸪ࢩࣜ࢝ࢼࣀࣜ࣎ࣥࡀࡲࡿ࡛ⲡⴥࡢ

ࡼ࠺࡟❧ࡕ୪ࢇࡔࢼࣀⰪ≧ⷧ⭷ࡀほᐹࡉࢀࡿ㸬ࡇࡇ࡛ࡢᅗ㸱࢞ࣛࢫ⟶ෆቨ 1⭷ࡢ 6(0෗┿ࢼࣀࣜ࣎ࣥࡢᖜࡣ࠾࠾ࡼࡑ 100nm ๓ᚋ㸪ཌࡳࡀ 20nm ⛬



ᗘ࡛࠶ࡿ㸬
ࡇࢀࡽࡣᇶᮦ࡟ᑐࡋ㸪ᇶᮏⓗ࡟ᆶ┤ⓗ࡟୪ࡧ㸪㸱㸬ࢼࣀพฝ⾲㠃ᵓ㐀ࡢ␯Ỉ໬ࢼࣀࣜ࣎ࣥࡢ㛫࡟ࡣࢼࣀ࣭࣐࢖ࢡࣟࡢ㝽㛫ࡀᙧᡂࡍࡿ㸬ࡇࡢࡼ࠺࡞ᵓ㐀⭷ࢆ N1 ࡜ࡍࡿ㸬ୖ࡛ᚓࡓ 3 ✀㢮ࡢࢼࣀᵓ㐀ⷧ⭷ N1~N3 ࢆ࢞ࣛࢫᯈୖ
࡛స〇ࡋ㸪ࡑࡢୖ࡟Ỉ⁲ࢆⴠ࡜ࡍ࡜㸪Ỉࡣ୍▐࡛ᗈࡀࡾᅗ㸱ࡢ SEM ࢖࣓࣮ࢪ࡛ࡣ㸪ࢩࣜ࢝ࡢࢼࣀ࣡࢖ࣖࡀᶓ

ࢆࡳࡏ㸪⭷⾲㠃඲యࡀ᏶඲࡟⃿ࢀ࡚ࡋࡲ࠸㸪Ỉ᥋ゐゅࡣఙࡧ≧ែ࡛✚ᒙࡋࡓᵓ㐀࡛࠶ࡿ㸬ࡑࢀࢆୗᆅ࡟㸪୍ᐃ㛫㸮rࢆ♧ࡍ㸬ࡇࢀࡣ㉸ぶỈᛶ࡛࠶ࡿ㸬⭷ࡣࢩ࡛ࣜ࢝ᵓᡂ

㝸࡛ࢼࣀ࣡࢖ࣖࡢจ㞟࡟ࡼࡾᙧᡂࡋࡓࢥࣈࡀⅬᅾⓗ࡟ᗈࡉࢀࡓࡢ࡛㸪ࡑࡢ⾲㠃ࡢᴟᛶࡀᙉࡃ㸪⾲㠃࢚ࢿࣝࢠ࣮ࡶ

ࡀࡗ࡚࠸ࡿ㸬ࡇࡢ⭷ࢆᵓᡂࡍࡿᇶᮏᵓ㐀య࡛࠶ࡿࢼࣀ࣡

㧗࠸㸬ࡑࢀ࡟พฝࡢẟ⣽⟶ຠᯝࡶຍ࠼㸪Ỉࢆᙎࡃ࡜࠸࠺

࢖ࣖࡢኴࡉࡣ 30nm ௨ୗ࡛࠶ࡿ㸬ᅗ 3 ࡛ぢࡽࢀࡿࢼࣀ

ࡼࡾ㸪Ỉࢆ྾࠸ྲྀࡿ≧ែ࡟࡞ࡿ㸬Ỉ᥋ゐゅࡀ㸮rࡢ㉸ぶ⚄ዉᕝ኱ᏛᕤᏛ◊✲ᡤᡤሗ ➨  ྕỈᛶࡶࡢࡣᐇࡣᐜ᫆࡟ࡑࡢṇ཯ᑐࡢ㉸᧕Ỉ࡟ኚ໬࡛ࡁࡿ㸬ᩘ⁲ⴠ࡜ࡋ㸪ࡑࡢᾮ⁲ࡢὶື≧ែࢆㄪ࡭ࡿ㸦ᅗ㸳㸧㸬⯆࿡࡞ࡐ࡞ࡽ㸪ࡑࢀࡢ⾲㠃ᙇຊࢆపୗࡉࡏࢀࡤ῭ࡴヰࡔ࠿ࡽ῝࠸ࡇ࡜࡟㸪fN1 ⭷࡛ࡣ㸪ᾮ⁲ࡀ㏵୰྾╔≧ែ࡜࡞ࡾ㸪࡛࠶ࡿ㸬ࢩࣜ࢝࡜࠸࠺㧗࠸⾲㠃࢚ࢿࣝࢠ࣮ࡢᮦ㉁⾲㠃࡟ὶࢀࡀṆࡲࡗ࡚ࡋࡲ࠺㸬fN2 ⭷࡛ࡣ㸪ᾮ⁲ࡣὶࢀ࡚ฟࡓ

⮬⏤࢚ࢿࣝࢠ࣮㸦⾲㠃ᙇຊ㸧ࡀప࠸≀㉁ࢆ⤖ྜࡉࡏࡿࡢ

ࡀ㸪⟶ෆࡣṧᾮ࡛ởࢀࡿ㸬ࡑࢀ࡟ẚ࡭࡚㸪f3N ⭷࡛ࡣ㸪ࡣ㸪⮳ࡗ࡚⡆༢࡛࠶ࡿ㸬Ỉ࡟⁐ࡅ࡞࠸≀㉁ࢆศᏊ྾╔ࡉࡍ࡭࡚ࡢᾮ⁲ࡀὶࢀ࡚ฟ࡚㸪⟶ෆࡢቨ㠃࡟ࡣṧᾮࡢẼ㓄ࡏࢀࡤⰋ࠸㸬

ࡍࡽ࡞࠸㸬ࡇࢀࡣ᏶⎍࡞⮬ᕫὙίຊ࡛࠶ࡿ㸬ࡇࡢࡇ࡜࠿

ᐇ㝿㸪ୖグࢼࣀᵓ㐀⭷ࡢ⾲㠃ᙇຊࢆపୗࡉࡏࡿࡓࡵ㸪ࡽ㸪ࢩࣜ࢝ࢼࣀࢳ࣮ࣗࣈ㞟ྜ≧ែࡢ࣐ࢵࢺࡀ⦓ᐦ࡟❧ࡕ

N1~N3 ⭷ࢆ㸪ࣇࢵ⣲ࡀከᩘ⤖ྜࡋࡓ࣏࢚ࣜࢳࣞࣥࢢࣜ

୪ࡪᵓ㐀࠿ࡽ࡞ࡿࢼࣀⷧ⭷ࡀࡶࡗ࡜ࡶඃࢀࡓᾮయࡣࡌࡁ

ࢥ࣮ࣝࡢ⁐ᾮ୰࡟ᾐₕࡉࡏ㸪ࢩࣜ࢝⾲㠃࡟␯Ỉᛶࡢࣇࢵᶵ⬟ࢆ᭷ࡍࡿࡇ࡜ࡀࢃ࠿ࡿ㸬⣲໬ྜ≀ࢆ⤖ྜࡉࡏࡓ⭷ fN1, fN2, fN3 ࡟ኚ࠼ࡓ㸬ࡇࢀ࡟ࡼࡾ㸪ࢼࣀᵓ㐀⭷ࡣ㉸᧕Ỉ⭷࡟ኚ㌟ࡍࡿ㸬ࡇࢀࡽࡢ⭷ᅗ㸲࢞ࣛࢫ⟶ෆቨ 1⭷ࡢ 6(0 DF ࡜ 7(0 G ୖ࡛ࡢ㟼ⓗỈ᥋ゐゅࡣ 180r࡟㏆ࡃ㸪ࡑࡢ⾲㠃࡟Ỉ⁲ࢆ஌ࡏࡿࡇ࡜ࡍࡽ࡛ࡁ࡞࠸㸬Ỉࡢ⾲㠃ᙇຊࡣ 173mN/M 㧗ᅗ㸳ෆቨࡀ I1㹼I1⭷࡛⿕そࡉࢀࡓ࢞ࣛࢫ⟶࠸ࡢ࡛㸪fN1, fN2, fN3 ࡢࡼ࠺࡞ࢼࣀᵓ㐀⭷࡛ࡣ⡆༢࡟ᙎ࠿ࢀࡿ㸬⾲㠃ᙇຊࡀప࠸ᾮయࡢࡣࡌࡁࢆㄪ࡭ࡿࡓࡵ㸪Ỉ㸲㸬⤊ࢃࡾ࡟

࡜࢔ࣝࢥ࣮ࣝࡀ༙ࠎΰࡌࡗࡓΰྜᾮ
㸦⾲㠃ᙇຊ 23mN/M㸧㉸᧕ᾮᮦᩱࡣ㸪Ỉ࡛ࡣ㒔ྜᝏࡃࡍࡿ✀ࠎࡢᐙ㟁〇ရ㸪ࢆㄪ〇ࡋ㸪ࡑࡢᾮ୰࡟⭷ࢆᩘ㐌㛫ᾐࡅࡿ㸬ࡑࢀ࡛ࡶ㸪ࡇ౛࠼ࡤ㸪ࢸࣞࣅ㸪෭ⶶᗜ㸪✵ㄪ㸪ࣃࢯࢥࣥ㸪ࣉࣜࣥࢱ࣮

ࢀࡽ⭷⾲㠃ࡣ඲ࡃ⃿ࢀࡎ㸪஝⇱≧ែࢆ♧ࡍ㸬ከࡃࡢ㉸᧕࡞࡝ࡢෆ㒊ᵓ㐀࡟ᛂ⏝࡛ࡁࡿ㸬ࡑࢀࡔࡅ࡛ࡣ࡞࠸㸬ỈࢆỈᮦᩱࡀỈࢆࡣࡌ࠸࡚ࡶ㸪࢚ࢱࣀ࣮ࣝࢆྵࡴỈ⁐ᾮࢆࡣ፹య࡜ࡍࡿᾮయࡣ㸪యᾮ㸪⾑ᾮ㸪ஙᾮ㸪⸆ᾮࢆࡣࡌࡵ㸪ࡌࡅ࡞࠸ࡇ࡜࡟ẚ࡭ࡿ࡜㸪ࡇࢀࡣᙉⅯ࡞ࡣࡌࡁຠᯝ࡛࠶

୰࡟ࡣⰍࢇ࡞≀㉁ࡀ⁐ゎ࣭ศᩓࡉࢀ࡚࠸ࡿ㸬ࡑࢀࡽࢆᙎ

ࡿ㸬ࡇࡢࡇ࡜ࡣ㸪ὶయࢹࣂ࢖ࢫ࡬ࡢ⏝㏵ࢆ㐃᝿ࡉࡏࡿ㸬ࡃࡇ࡜ࡣ┦஫ởᰁ㸪ឤᰁࢆ㜵ࡄࡇ࡜࡟ࡶ⧅ࡀࡿ㸬་⒪࡟

ᕷ㈍ࡢỈᛶ IJ ࢖ࣥࢡࡢሙྜ㸪⤌ᡂࡣ」㞧࡛㸪୍ᐃ㔞ࡢ㛵ࢃࡿ✀ࠎࡢჾᲔ㸪⣽⬊ᇵ㣴㸪デ᩿⏝࢟ࢵࢺ࡞࡝࡟ࡶ⏝Ỉ௨እ㸪࢔ࣝࢥ࣮ࣝ㢮㸪⏺㠃άᛶ๣㸪㢦ᩱ࣭ᰁᩱ࡞࡝ࢆ

㏵ࡀᗈࡀࡿ࡜⪃࠼ࡽࢀࡿ㸬ⶈࡢⴥࡗࡥࡢၨⓎ࠿ࡽ㛤Ⓨࡉྵࡴ㸬Ỉᛶ IJ ࢖ࣥࢡࢆࡣࡌࡅࡿ㉸᧕ᾮᮦᩱࡣ࡯࡜ࢇ࡝▱ࢀࡿ㉸᧕ᾮᢏ⾡ࡀ㸪࠸ࡘ࠿Ỉ࡜ಀࡿ⾲㠃⛉Ꮫࢆ୍᪂ࡍࡿ

ࡽࢀ࡚࡞࠸㸬ෆቨࡀ fN1, fN2, fN3 ࡢࢼࣀᵓ㐀⭷࡛⿕そࡉ࠿ࡶ▱ࢀ࡞࠸㸬ࢀࡓ࢞ࣛࢫ⟶ࢆ⏝࠸㸪ᩳࡵ࡟ࡋࡓ⟶ෆ࡟Ỉᛶ IJ ࢖ࣥ࢟ࢆ⇕࣭᥮Ẽᅇ㊰⥙ࣔࢹࣝ࡟ࡼࡿ
ᘓ⠏⎔ቃᕤᏛศ㔝࡛ࡢ◊✲㛤Ⓨዟᒣ ༤ᗣ㸨

Research and development on the basis of the thermal and air flow network model forbuilding environmental engineering field
Hiroyasu OKUYAMA㸨㸯㸬ࡣࡌࡵ࡟

⬟࡜ࡍࡿ㦵⤌ࡳ࡛ࡶ࠶ࡿ㸬ࡇࡢ㦵⤌ࡳ࡜ࡣ⇕ὶ཰ᨭ࡟㛵୍⯡࡟◊✲ࡢᚿྥ࡟ࡣศᯒᆺ࡜⤫ྜᆺࡀ࠶ࡿࡢ࡛ࡣ࡞

ࡍࡿ᏶඲㐃⤖ࢩࢫࢸ࣒ࡢ⠇Ⅼ᪉⛬ᘧ࡜ྡ௜ࡅࡓࡶࡢ࡛࠶

࠸ࡔࢁ࠺࠿㸬ศᯒᆺࡣ⌧㇟ࢆศ㢮ࡋᇶᮏせᅉ࡟㑏ඖࡋ࡚ࡾ㸪࡝ࡢᵝ࡞✵㛫ⓗ㞳ᩓ໬ἲ࡟ࡶ㛵ࢃࡽࡎ㸪ࡲࡓィ⟬ᑐ⌮ゎ࡟ດࡵࡿࡀ㸪⤫ྜᆺࡣᵝࠎ࡟␗࡞ࡗ࡚ぢ࠼ࡿ⌧㇟࡟㇟≀ࡢ✵㛫ḟඖࡸᙧែ࡟ࡶࡼࡽࡎ㸪୍⯡ⓗ࡟ᡂ❧ࡍࡿ≉

ඹ㏻ࡋ࡚Ꮡᅾࡍࡿཎ⌮ࢆ㏣ồࡍࡿ㸬୧⪅ࡣ㌴ࡢ୧㍯ࡢዴ㛗ࡀ࠶ࡿ㸬ࡉࡽ࡟ࡑࡢ୍యⓗ࡞ࣔࢹࣝ࡜ࡣ㐃❧ᖖᚤศ᪉ࡃ࡝ࡕࡽࡶ୙ྍḞ࡛࠶ࡿ㸬ᇶᮏせᅉࡢ῝࠸⌮ゎࡀ↓ࡅࢀ⛬ᘧ࡛࠶ࡿࡀ㸪ࢩࢫࢸ࣒⌮ㄽࡢ≧ែ✵㛫᪉⛬ᘧࡢᙧ࡟ࡋ

ࡤせᅉ㛫ࢆ㈏ࡃ୍⯡ཎ⌮ࡣᚓࡽࢀ࡞࠸ࡋ㸪▱ぢࡀ୍⯡໬࡚࠸ࡿࡢ࡛㸪ண ィ⟬ࢆ⾜࠺ࡓࡵࡢᏳᐃ࡛ཝᐦ࡞᫬㛫✚ࡉࢀ⤫ྜ໬ࡉࢀ࡞ࡅࢀࡤయ⣔ࡣ↹㞧࡟࡞ࡾḟ࡬ࡢⓎᒎࡣศἲࢆᑟ࠸ࡓࡾ㸪ࢩࢫࢸ࣒ྠᐃࡸ᭱㐺ไᚚ⌮ㄽ➼ࢆᛂ⏝㞴ࡋࡃ࡞ࡿ㸬ࡇࡇ࡛ࡣᘓ⠏⎔ቃᕤᏛࡢศ㔝࡛⤫ྜᆺࡢࣔࡍࡿ㝿ࡢ࣓ࣜࢵࢺࡶ࠶ࡿ㸬ࢹࣝ࡟ࡼࡿᒎ㛤ࢆヨࡳࡓ౛ࢆ⤂௓ࡋࡓ࠸㸬 ḟ⠇ࡢࠕ2.ᘓ⠏ఏ⇕ィ⟬ࡢ⫼ᬒ࡛ࠖࡣᮏࣔࢹࣝࢆᒎ㛤 ᘓ⠏ࡢ෭ᬮᡣ᥮Ẽ࡟࠾࠸࡚ࡣ㐺ษ࡛೺ᗣⓗ࡞ᘓ⠏⎔ቃࡍࡿືᶵ࡜࡞ࡗࡓᚑ᮶ࡢィ⟬ἲࡢၥ㢟Ⅼ➼ࢆ㏙࡭㸪
ࠕ3.

ࢆ᭱ᑠࡢ⎔ቃ㈇Ⲵ࡜࢚ࢿࣝࢠ࣮࡛ᐇ⌧ࡍࡿࡓࡵ㸪タഛࡔ⇕ᅇ㊰⥙ࣔࢹ࡛ࣝࠖࡣᮏࣔࢹࣝࡢⓎᒎࡢ⤒⦋ࢆ㏙࡭ࡿ㸬ࡅ࡛࡞ࡃᘓ⠏⮬యࡢィ⏬ࡀ㔜せ࡛࠶ࡿ㸬ᘓ⠏ᵓᡂ㒊ᮦࡢࡲࡓ✵Ẽὶືࡢィ⟬࡜ゝ࠼ࡤᩘ್ὶయゎᯒࡀⰋࡃ▱ࡽࢀ⇕ఏᑟ㸪⵳⇕㸪⇕ᨺᑕ➼ࡢ⇕ⓗᛶ㉁ࢆᕦࡳ࡟ά࠿ࡋ㸪ࡲ࡚࠸ࡿࡀ㸪ᘓ⠏ศ㔝࡛ࡣ࣐ࢡࣟࢫࢥࣆࢵࢡ࡞ࡀࡽᕤᏛⓗࡓ ᗘᕪ᥮Ẽࡸ㢼ᅽ᥮Ẽࢆά࠿ࡍ✵㛫ᵓᡂࢆィ⏬ࡍࡿࡇ࡛᭷⏝࡞ࠕ4.᥮Ẽᅇ㊰⥙ࣔࢹࣝࠖࢆ⤂௓ࡍࡿ㸬ࡲࡓண࡜࡛㸪እẼ ‵ᗘኚື㸪⮬↛᥮Ẽ㸪ኴ㝧⇕㸪⵨Ⓨ෭༷ࡸィ⟬࡜ࡣ㏫࡛࠶ࡾ㏫᥈ၥ㢟࡜ࡶ࿧ࡤࢀࡿࡀ㸪ࢩࢫࢸ࣒ྠᆅ୰ᜏ ᛶ࡞࡝ࡢ⮬↛࢚ࢿࣝࢠ࣮ࢆ฼⏝ࡍࡿࡢࡀ⎔ቃඹᐃ⌮ㄽࢆ㸪⇕ᅇ㊰⥙ࣔࢹࣝ࡟ࡘ࠸࡚᭱ᑠ஧஌ἲࢆ⏝࠸࡚⏕ᘓ⠏ࡢᇶᮏ࡛࠶ࡿ㸬ࡇࡢࡼ࠺࡞ᘓ⠏ࢆ᳨ウࡍࡿࡓࡵ࡟

₇⧢ࡋࡓࡢ࡛㸪ࡑࡢᒎ㛤⤒⦋ࢆࠕ5.⇕ᅇ㊰⥙ࡢࢩࢫࢸ࣒

ࡣከᒙ࡛ከᩘᐊࡢᘓ≀඲యⓗ࡛ᚤጁ࡞ᅽຊࣂࣛࣥࢫ࡟ࡼ

ྠᐃ⌮ㄽ࡛ࠖ㏙࡭ࡿ㸬ࡇࢀࡣᵝࠎ࡞ ᐃἲࡢ୙☜࠿ࡉホࡿ✵Ẽὶື࡜⇕⛣ືࢆ⪃៖ࡋ࡞ࡅࢀࡤ࡞ࡽ࡞࠸ࡢ࡛㸪௚౯ࡢᨵⰋ࡟ࡶᙺ❧ࡘࡢ࡛ࠕ6.ࡑࡢ௚ࡢ ᐃࢹ࣮ࢱศᯒᢏ

ศ㔝࡛ࡢศᯒⓗఏ⇕ィ⟬ࣔࢹࣝ࡜ࡣᑡࡋ␗࡞ࡾ㸪⥲ྜⓗ⾡ࠖ࡜ࡋ࡚ࡶ㏙࡭ࡿ㸬୍᪉㸪 ᗘࡔࡅ࡛࡞ࡃ‵ᗘࡶྵࡵ࡛ࢩࢫࢸ࣒ⓗ࡞ࣔࢹࣝࡀᚲせ࡟࡞ࡗ࡚ࡃࡿ㸬ࡇࡇ࡛⤂௓࡚ᣑᙇࡋࡓ⇕࣭‵Ẽᅇ㊰⥙ࣔࢹࣝ࡟ࡘ࠸࡚᭱㐺ไᚚ⌮ㄽࡍࡿࡢࡣࡇ࠺ࡋࡓࣔࢹ࡛ࣝ࠶ࡿ㸬ࢆཧ⪃࡟㸪ࣛࢢࣛࣥࢪ࢙஌ᩘἲࢆ㐺⏝ࡋ㸪᭱㐺ࡢ෭࣭ ࢥࣥࣆ࣮ࣗࢱ฼⏝ࡢఏ⇕ィ⟬ࡣᵝࠎ࡞ศ㔝࡟࠾࠸࡚⾜Ỉࡢຍ⇕࣭෭༷㔞࡜㸪ࡇࡢ᫬ࡢ ࣭‵ᗘࡢ≧ែࢆỴᐃࡍࢃࢀ࡚࠸ࡿࡀ㸪᭷㝈せ⣲ἲࡸ᭷㝈య✚ἲ࠶ࡿ࠸ࡣ᭷㝈ᕪ

ࡿࠕ7.≧ែ࡜࢚ࢿࣝࢠ࣮౪⤥ࡢ᭱㐺໬⌮ㄽࠖࢆᒎ㛤ࡋࡓศἲࡀࡼࡃ⏝࠸ࡽࢀ࡚࠸ࡿ࡜ᛮࢃࢀࡿ㸬ࡇࡇ࡛⤂௓ࡍࡿ⤒⦋࡜⌮ㄽࡢព⩏ࢆ㏙࡭ࡿ㸬௨ୖࡢ⌮ㄽࡢ࠺ࡕண ィ⟬ࣔࢹࣝࡢ୍ࡘࡣ⇕ᅇ㊰⥙࡜࿧ࡪࡀ㸪ࡑࢀࡽࡢࣔࢹࣝࢆ⼥ἲࡢ㛤Ⓨ࡟ࡘ࠸࡚ࡣࠕ8.ࢩ࣑࣮ࣗࣞࢩࣙࣥࣉࣟࢢ࣒ࣛ

ྜࡋ୍యⓗ࡞ࣔࢹࣝ࡟ࡍࡿࡇ࡜࡛ᐇ⏝ⓗ࡞ࣔࢹࣝ໬ࢆྍ

NETSࠖ࡜ࡋ࡚⤂௓ࡍࡿ㸬ࡲࡓࢩࢫࢸ࣒ྠᐃ⌮ㄽࡢᐇ⏝໬࡟ࡘ࠸࡚ࡣ㸪ᚑ᮶ࡢ᥮Ẽ ᐃἲࡀࢩࢫࢸ࣒ྠᐃ࡜࠸࠺

*ᩍᤵ ᘓ⠏Ꮫ⛉
Professor, Dept. of Architecture

ほⅬࡀ↓࠿ࡗࡓࡇ࡜࡛ከࡃࡢၥ㢟ࢆᢪ࠼࡚࠸ࡓࡢ࡛㸪ࡇࢀࡽࢆゎỴࡋࡓࠕ9.ከᩘᐊ᥮Ẽ ᐃࢩࢫࢸ࣒ࠖࢆᐇ᪋౛

6⚄ዉᕝ኱ᏛᕤᏛ◊✲ᡤᡤሗ ➨  ྕ࡜ඹ࡟⤂௓ࡍࡿ㸬࡜ࡋ࡚ᅜෆእ࡛ㄆ㆑ࡉࢀࡿࡀ㸪ࡑࡢព࿡ࡍࡿ࡜ࡇࢁࡣᮍ
ࡔே࡟ࡼࡗ࡚ᵝࠎ࡛࠶ࡿ㸬ࢥࣥࣆ࣮ࣗࢱࡀ༑ศⓎ㐩ࡋ࡚㸰㸬ᘓ⠏ఏ⇕ィ⟬ࡢ⫼ᬒ࠸࡞࠿ࡗࡓ᫬௦࡟㸪ᵝࠎ࡞≀⌮⌧㇟ࢆ㟁Ẽᅇ㊰࡟࢔ࢼࣟ ࢥࣥࣆ࣮ࣗࢱࢆ฼⏝ࡋࡓᘓ⠏ఏ⇕ィ⟬ࡢṔྐࢆᑡࡋ᣺

ࢪ࢕ࡋᐇ㦂ࡋ࡚࠸ࡓ㡭࠿ࡽ⇕ᅇ㊰⥙࡜࠸࠺ゝⴥࡀጞࡲࡗ

ࡾ㏉ࢀࡤ㸪ᮏࣔࢹࣝᒎ㛤ࡢᚲせᛶࡀ⌮ゎࡉࢀࡿ࠿ࡶࡋࢀ

ࡓᵝ࡛࠶ࡿ㸬ࡋ࠿ࡋᩘ್ィ⟬ᶵࡀⓎ㐩ࡋ࡚ࡃࡿ࡜㸪⇕ᅇ࡞࠸㸬ࡑࢀࡣ࢚ࢿࣝࢠ࣮ᾘ㈝㔞ࡢண ࢆ୺┠ⓗ࡜ࡋࡓᖺ㊰⥙ࡢᐃᘧ໬ἲࡣ◊✲⪅࡟ࡼࡗ࡚ࡲࡕࡲࡕ࡞ࡶࡢ࡜࡞ࡗ

㛫ࡢ෭ᬮᡣ㈇Ⲵィ⟬ࡢᚲせᛶ࠿ࡽጞࡲࡗ࡚࠸ࡿ㸬⇕㈇Ⲵ

࡚࠸ࡗࡓ㸬౛࠼ࡤ Clarke J.A.[3]ࡸ Edward F.Sowell[4]࡟ࡼ

࡜ࡣẼ㇟᮲௳➼ࡢኚື࡟ᢠࡋ୍࡚ᐃࡢᐊෆ ‵ᗘࢆ⥔ᣢࡿࡶࡢࡶ࠶ࡿ㸬➹⪅ࡢᐃᘧ໬ἲࡣィ⟬ᑐ㇟≀ࡢᙧ≧ࡸ✵ࡍࡿࡓࡵ࡟ᚲせ࡞ᐊ✵Ẽࡢຍ⇕࣭෭༷㔞ࡢࡇ࡜࡛࠶ࡾ㸪㛫ḟඖ࡟ࡼࡽࡎỗ⏝ⓗ࡟ᡂ❧ࡍࡿ≉ᚩࡀ࠶ࡿ㸬➹⪅ࡢ⇕እቨ➼ࢆ㈏ὶࡍࡿ⇕ὶࡀ୺せᅉ࡜࡞ࡿ㸬ᚑࡗ࡚ቨయἲ⥺ᅇ㊰⥙ࣔࢹࣝࡢ⪃᱌ࡣ኱Ꮫ㝔ࡢ᫬௦࡟ኴ㝧⇕㞟⇕ჾࡢィ

᪉ྥࡢ 1 ḟඖ㠀ᐃᖖఏ⇕ィ⟬ࡀึᮇࡢ◊✲ㄢ㢟࡜ࡉࢀࡓ㸬⟬࠿ࡽጞࡲࡾ㸪ಟኈㄽᩥ࡟ྥࡅ࡚ 1974 ᖺ㡭࡟ጞࡲࡗࡓ㸬ఱ✀㢮࠿ࡢᮦᩱᒙ࠿ࡽᵓᡂࡉࢀࡿከᒙቨయࡢ㠀ᐃᖖఏ⇕ࡇ࠺ࡋࡓఏ⇕⣔࡛ࡣ㸪ఏᑟ㸪⾲㠃ఏ㐩㸪ᑐὶࡸᨺᑕ࡞࡝

ࡣᐇࡣゎᯒⓗ࡞ゎࡀᅔ㞴࡛㸪ఱࡽ࠿ࡢᩘ್ⓗ࡞ゎἲ࡟࡞ᵝࠎ࡞ఏ⇕ᙧែࡀᏑᅾࡍࡿ㸬ࡇࢀࡽ඲࡚ࢆྠࡌࣃ࣓࣮ࣛ

ࡽࡊࡿࢆᚓ࡞࠿ࡗࡓ㸬ࡋ࠿ࡋ⌧ᅾ࡞ࡽࡤቨయࡢ㠀ᐃᖖఏࢱࡢ⇕ࢥࣥࢲࢡࢱࣥࢫ ci,j ࡛⾲⌧ࡋࡓ Wisconsin ኱Ꮫࡢኴ⇕ࣔࢹࣝ࡜ࡋ࡚ᕪศἲࡸ᭷㝈せ⣲ἲࡢ㞳ᩓ໬ࣔࢹࣝࢆ⏝㝧࢚ࢿࣝࢠ࣮◊✲ᡤ࡟ࡼࡿࣔࢹࣝ[5]ࡀ㸪ỗ⏝ⓗ࡞⇕ὶ཰࠸ࡑ࠺࡞࡜ࡇࢁ㸪᫬⣔ิࡢ⇕ὶᛂ⟅ಀᩘἲ࡜࠸࠺ィ⟬ἲᨭࡢ⠇Ⅼ᪉⛬ᘧࢆᕤኵࡍࡿୖ࡛ཧ⪃࡟࡞ࡗࡓࡀ㸪඲యࡢࡀ⡿ᅜᬮᡣ෭෾✵Ẽㄪ࿴ᕤᏛ఍㸦ASHRAE㸧࡟ࡼࡗ࡚㐃❧ᖖᚤศ᪉⛬ᘧࡢᐃᘧ໬ἲ࡜ゎἲ࡟㛵ࡋ࡚ࡣᨵⰋࡀᚲ

1970 ᖺ㡭࡟ᥦ᱌ࡉࢀ㸪᪥ᮏࡶࡇࢀ࡟࡞ࡽ࠸᪁⏺ࡢᶆ‽ⓗせࡔࡗࡓ㸬ᮏ⇕ᅇ㊰⥙ࡢᇶᮏ᪉⛬ᘧࡣ⾲㸯ࡢ(1)ᘧ࡟♧ࡍィ⟬ࣉࣟࢢ࣒ࣛ࡜ࡋ࡚᥇⏝ࡉࢀ㸪௒᪥࡟⮳ࡗ࡚࠸ࡿ㸬ࡇࡼ࠺࡟㸪⠇Ⅼ࡛ࡢ⇕ὶ཰ᨭࢆグ㏙ࡋࡓᖖᚤศ᪉⛬ᘧ࡛࠶ࡢィ⟬ἲࡣቨయࡢእẼഃࡢ⾲㠃 ᗘࡀ୕ゅᙧࣃࣝࢫ≧࡟ࡿࡀ㸪ỗ⏝ⓗ࡟ᡂ❧ࡍࡿ⌮⏤ࡣ㸪๓㏙ࡢᵝࠎ࡞ఏ⇕ᙧែບ㉳ࡉࢀࡓሙྜ࡟㸪ᐊෆഃ࡬ࡢ⇕ὶࡢ᫬⣔ิᛂ⟅ಀᩘࢆࢆ୍✀㢮ࡢ୍⯡໬⇕ࢥࣥࢲࢡࢱࣥࢫ ci,j ࡛⾲ࡋ࡚࠸ࡿࡇ

ணࡵィ⟬ࡋ࡚࠾ࡁ㸪ࡇࢀࢆ⏝࠸࡚௵ពࡢእẼ ᗘኚື࡟࡜࡜㸪ࡑࢀࡒࢀࡢ⠇Ⅼࡣ௚ࡢ඲࡚ࡢ⠇Ⅼ࡜⤖ࡧࡘ࠸࡚࠸

ᑐࡍࡿ⇕ὶࢆ⟬ฟࡍࡿ㸬ቨయࡢ⾲㠃 ᗘ࡜⇕ὶࢆ 4 ➃Ꮚࡿ࡜グ㏙ࡋ࡚࠸ࡿࡇ࡜࡟࠶ࡿ㸬ࡇࢀࡽࡢᐃᘧ໬ἲࡣࢥࣥ

㟁ᴟ࡟┦ఝࡉࡏࡓ Pipes[1]ࡢ⌮ㄽࢆᇶ࡜ࡋ࡚㸪Mitalas ࡜ࣆ࣮ࣗࢱࣉࣟࢢ࣒ࣛࡢ୍⯡ⓗ≉ᛶ࡟ࡶ࣐ࢵࢳࡋ࡚࠸ࡿ㸬Stephenson ࡽࡀ᫬㛫ⓗ࡟㞳ᩓⓗ࡛ィ⟬ྍ⬟࡞᪉ἲ[2]ࢆస

࡞ࡐ࡞ࡽࡤ㸪࠶ࡿ஧ࡘࡢ⠇Ⅼ i ࡜ j ࡢ㛫ࡀᐇ㝿࡟ࡘ࡞ࡀࡗࡓ㸬ࡇ࠺ࡋࡓࣔࢹࣝࡀᑟධࡉࢀࡓ⫼ᬒ࡟ࡣ㸪ࡕࡻ࠺࡝ࡗ࡚࠸ࡿ࡜ࡇࢁࡔࡅ㠀㞽ࡢ ci,j ࢆ㓄ิ࡟᱁⣡ࡍࢀࡤ㸪ఱࡶไᚚ⌮ㄽ࡟࠾ࡅࡿྂ඾ⓗ࡞ఏ㐩㛵ᩘἲࡀ࠶ࡗࡓ࡜ᛮࢃࢀ

௦ධࡉࢀ࡞࠸㓄ิせ⣲ࡢ ci,j ࡣ⮬ືⓗ࡟㞽ࡔ࠿ࡽ࡛࠶ࡿ㸬ࡿ㸬ࡋ࠿ࡋບ᣺࡜ᛂ⟅࡛⌧㇟ࢆࢩ࣑࣮ࣗࣞࢺ࡛ࡁࡿࡓࡵ

ࡇࡢព࿡࡛ࡇࡢᇶᮏ᪉⛬ᘧࢆ᏶඲㐃⤖ࢩࢫࢸ࣒ࡢ⠇Ⅼ᪉࡟ࡣ㸪ᑐ㇟⣔ࡀ⥺ᙧᛶ࡜᫬㛫ⓗ୙ኚᛶࢆᣢࡘ࡜࠸࠺๓ᥦ

⛬ᘧ࡜࿧ࢇ࡛࠸ࡿ㸬ࡀᚲせ࡛࠶ࡿ㸬❆ࡸ㞵ᡞࡢ㛤ࡅ㛢ࡵ࡞࡝ఏ⇕ᵓ㐀ࡢኚ໬ࡀ↓࠸஦ົᡤᘓ⠏࡛࠶ࢀࡤࡇࢀࡽࡢ๓ᥦࡣᡂࡾ❧ࡘࡀ㸪ࡑ࠺࡛࡞࠸ఫᏯࡢሙྜ➼࡟ࡣ኱ࡁ࡞ไ⣙࡜࡞ࡿ㸬ࡲࡓ⇕⾲㸯 ᇶᮏ᪉⛬ᘧ࡜グྕ⾲ὶࡔࡅ࡛ྛ㒊ࡢ ᗘࢆゎ࠿࡞࠸ࡇ࡜࡟ࡼࡿィ⟬ᶵ⬟ୖࡢ⇕ὶ➼䛾཰ᨭᘧ
䠄᏶඲㐃⤖䡸䡹䡿䢍䛾⠇Ⅼ᪉⛬ᘧ䠅୙༑ศࡉࡶ࠶ࡿ㸬ࡇ࠺ࡋࡓၥ㢟ࡶ࠶ࡗ࡚㸪ᕪศἲࡸ᭷㝈⇕ᅇ㊰⥙䛾య✚ἲࡢࣔࢹࣝࡶᗄே࠿ࡢ◊✲⪅࡟ࡼࡗ࡚ഐὶⓗ࡟㛤Ⓨࡉࢀ࡚ࡁࡓࡀ㸪⌧௦ไᚚ⌮ㄽ࡟ศ㢮ࡉࢀࡿ≧ែ✵㛫ἲ࡜ࡇࢀࡽࡢ㡿ᇦᆺࡢࣔࢹࣝ࡜ࢆ㛵㐃௜ࡅࡓᒎ㛤ࡣ࠶ࡲࡾ㐍≧ែ᪉⛬ᘧᑕᙳศゎ䛻䜘䜛
ゎᯒⓗ᫬㛫✚ศ䠄NETS䛻ྵ䜎䜜䜛䠅ᒎࡋ࡞࠿ࡗࡓ㸬ࡲࡓࢩࢫࢸ࣒⌮ㄽ࡟ᇶ࡙ࡃಠ▔ⓗ࡞ࣔࢹ

i, j

j

j 1

ng

i, j

j

i

i, j

j 1

M  x C  x  Co  xo  R  gn¦ P  eD

x(t )

i

i 1

i ( t  t0 )

j

j 1

(2)

t

n

t0

i 1

 x(t0 )  ³ ¦ Pi  eDi ( t W )  f * (W )dW (3)ᅇᖐ᪉⛬ᘧㄗᕪ䛾஧ḟᙧᘧ䛾᫬㛫✚ศࣝ࡟ࡼࢀࡤ㸪ண ィ⟬ࡔࡅ࡛ࡣ࡞ࡃ㸪ࢩࢫࢸ࣒ྠᐃ㸪᭱䝅䝇䝔䝮䝟䝷䝯䞊䝍ྠᐃ䛾䛯䜑䛾ホ౯㛵ᩘ㐺ไᚚ࠶ࡿ࠸ࡣ᭱㐺タィ࡜࠸ࡗࡓၥ㢟ࡶ⤫୍ⓗ࡟ㄆ㆑ࡉ䠄SPID䠅

T³ e  W  e dt

Ji

0

t

(4)

䜢᭱ᑠ䛻䛩䜛䝅䝇䝔䝮䝟䝷䝯䞊䝍䜢ồ䜑䜛(䝅䝇䝔䝮䝟䝷䝯䞊䝍䛸䛿䠈mi,j 䠈ci,j 䠈ri,j䛾୕✀䛾ಀᩘ䜢ព࿡䛩䜛)ࢀࡿࡢ࡛ࡣ࡞࠸࠿࡜ᛮࢃࢀࡿ㸬㸱㸬⇕ᅇ㊰⥙ࣔࢹࣝ᭱㐺ไᚚ䛾䛯䜑䛾
᭱㐺໬䛾ホ౯㛵ᩘ ᮏㄽ࡛せ࡜࡞ࡿ➹⪅ࡢ⇕ᅇ㊰⥙ࣔࢹࣝࡢᒎ㛤ࡢ⤒⦋ࢆ

䠄SOCS䠅

㏙࡭ࡿ㸬ࡇࡢゝⴥ⮬యࡣⱥㄒ࡛ࡣ Thermal Network Modeln  non¦ m  x ¦ c  x x  ¦ r  g (1)≧ែ್䛸ධຊ䝧䜽䝖䝹䛾┠ᶆ䛸䛾೫ᕪ䛾஧ḟᙧᘧ

Jct(x  r )  Wx  (x  r )  t (uc  d)  Wc  (u c  d) (5)䜢᭱ᑠ䛻䛩䜛≧ែ䛸ไᚚධຊ䛾䝧䜽䝖䝹䜢Ỵᐃ䛩䜛⇕࣭᥮Ẽᅇ㊰⥙ࣔࢹࣝ࡟ࡼࡿᘓ⠏⎔ቃᕤᏛศ㔝࡛ࡢ◊✲㛤Ⓨ



グྕ⾲
グྕ⾲
n : ᮍ▱ᩘᢅ࠸⥲⠇Ⅼᩘ
no : ᪤▱ᩘᢅ࠸⥲⠇Ⅼᩘ
ng : ⮬⏤ධຊⓎ⏕※⥲ᩘxi : i␒⠇Ⅼࡢ≧ែ㔞( ᗘ➼)mi , j : i␒⠇Ⅼ࡟㛵ࡍࡿᐜ㔞(⇕ᐜ㔞➼)ci , j : j␒࠿ࡽi␒⠇Ⅼ࡬ࡢࢥࣥࢲࢡࢱࣥࢫ
ri , j : ⮬⏤ධຊⓎ⏕※j࠿ࡽ⠇Ⅼi࡬ࡢධຊಀᩘ
g i : ⮬⏤ධຊⓎ⏕※i࡛ࡢⓎ⏕㔞x t ( x1, x 2,    , xn ) : ≧ែ࣋ࢡࢺࣝ
xo t ( xn1,    , xn  no ) : ᪤▱≧ែධຊ࣋ࢡࢺࣝ
g t ( g 1, g 2,    , gng ) : ⮬⏤ධຊ࣋ࢡࢺࣝ
M : mi,j࡟ࡼࡿᐜ㔞࣐ࢺࣜࢵࢡࢫ
>C, Co@ : ci,j࡟ࡼࡿࢥࣥࢲࢡࢱࣥࢫ࣐ࢺࣜࢵࢡࢫ

R : ri,j࡟ࡼࡿ⮬⏤ධຊ࣐ࢺࣜࢵࢡࢫ

Di : M 1  C ࡢᅛ᭷್Pi : ᅛ᭷್Įi࡟㛵ࡍࡿᑕᙳᏊ
1
f * : M  (Co  xo  R  g ) ࡞ࡿ㥑ື࣋ࢡࢺࣝ㸪ヲࡋࡃࡣ[28]r : ≧ែไᚚࡢ┠ᶆ್㸪ヲࡋࡃࡣ[26]Wx : ≧ែࡢ┠ᶆ್࠿ࡽࡢ೫ᕪࡢ஧ḟᙧᘧ࡬ࡢ㔜ࡳ࣐ࢺࣜࢵࢡࢫ
uc : ไᚚ࣋ࢡࢺࣝ
d : ᧯స㔞ࡢつ‽࡜ࡍࡿཧ↷್(0ࡸእẼ ᗘ)
Wc :᧯స㔞ࡢ஧ḟᙧᘧ࡬ࡢ㔜ࡳ࣐ࢺࣜࢵࢡࢫ
e : e y  Z  a :࡛⾲ࡉࢀࡿᅇᖐᘧㄗᕪ㸪ヲࡋࡃࡣ[18]W : ୍⯡໬᭱ᑠ஧஌ἲࡢ㔜ࡳ࣐ࢺࣜࢵࢡࢫ
T : ᐃᮇ㛫ᙜึࡣࡇࡢ㐃❧ᖖᚤศ᪉⛬ᘧࢆ᫬㛫࡟㛵ࡋ࡚ࡣᚋ㏥ᕪศᅗ㸯 ␗✀㞳ᩓ໬ࣔࢹࣝࡢ⼥ྜఏ⇕䞉ᣑᩓ䞉⛣ື⌧㇟⇕ᅇ㊰⥙䛾ᯟ⤌䜏᳨ᰝయ✚ἲ䝰䝕䝹
䠄᭷㝈య✚ἲ䠅᭷㝈せ⣲ἲ䝰䝕䝹

✵㛫ⓗᕪศἲ䝰䝕䝹࡛ゎ࠸࡚࠸ࡓࡀ㸪ࡇࡢ㏆ఝⓗ᫬㛫✚ศࡀ↓᮲௳Ᏻᐃ࡛ᐇ
⏝ⓗ࡛࠶ࡿ⌮⏤ࡣ㸪᥎⛣࣐ࢺࣜࢵࢡࢫࡢᅛ᭷್ࡀ 0 ࠿ࡽ
1 ࡢ㛫࡟࠶ࡿࡇ࡜࡟ࡼࡾㄝ᫂ࡉࢀࡿࡇ࡜ࡀᚋ࡟࡞ࡗ࡚ศ

ᅗ㸰 ⇕ᅇ㊰⥙ࡢࣉࣛࢵࢺ࣮࣒࣍

࠿ࡗࡓ㸬୍᪉㸪ᘓ⠏タഛࡢศ㔝࡛ࡶ⌧௦ไᚚ⌮ㄽࡢᛂ⏝ࡀ᳨ウࡉࢀጞࡵ࡚࠸ࡓ 1977 ᖺᙜ᫬࡟ Julius T.Tou ࡀⴭࡋ㸲㸬᥮Ẽᅇ㊰⥙ࣔࢹࣝࡓ≧ែ✵㛫ἲࡢゎㄝ᭩[6]ࡀཧ⪃࡟࡞ࡾ㸪≧ែ✵㛫᪉⛬ᘧ ᥮Ẽᅇ㊰⥙࡜࠸࠺ゝⴥ⮬యࡶᩘ್ィ⟬ᶵⓎ㐩௨๓ࡢྂࡢᙧ࡟๎ࡿࡼ࠺࡟ᐃᘧ໬ࢆᨵⰋࡋࡓࡇ࡜࠿ࡽ⌮ㄽⓗ࡞ᒎࡃ࠿ࡽ࠶ࡾ㸪㝽㛫ࡸ㛤ཱྀ➼ࡢὶ㊰ࡢ㏻Ẽ᢬ᢠ࡟┦ఝࡋࡓ㛤ࢆጞࡵࡓ㸬ᩘᏛ⪅ࡢΎỈ㐩㞝ࡸᙜ᫬ྠ൉ࡢΎᕝဴᚿࡢ

㟁Ẽ᢬ᢠ⣲Ꮚࢆ⏝࠸ࡓᅇ㊰⥙࡟ࡼࡾ㸪ᐇ㦂ⓗ࡟ゎࢆồࡵຓゝࡶ࠶ࡗ࡚㸪᫬㛫✚ศࡢᏳᐃᛶ᮲௳➼ࡢ⪃ᐹࡔࡅ࡛࡞

࡚࠸ࡓ᫬௦ࡶ࠶ࡗࡓᵝ࡛࠶ࡿࡀ㸪➹⪅ࡢࡶࡢࡢᒎ㛤ࡢ⤒ࡃ㸪⾲㸯ࡢ(3)ᘧ࡟♧ࡍࢩࢫࢸ࣒ࡢᅛ᭷✵㛫࡟ᑐࡍࡿᑕᙳ

⦋ࢆ㏙࡭ࡿ㸬᥮Ẽᅇ㊰⥙ࡶ⇕ᅇ㊰⥙࡜ྠᵝ࡟ࢥࣥࣆ࣮ࣗ

ศゎ࡟ࡼࡿཝᐦ࡞᫬㛫✚ศࡢᑟฟࡶ࡛ࡁࡓ㸬ࡓࡔࡋᅛ᭷

ࢱ฼⏝࡟ኚࢃࡗ࡚࠿ࡽࡣᵝࠎ࡞ᐃᘧ໬ἲࡸゎἲࡀᑟ࠿ࢀ

್ゎᯒࢆ㎿㏿Ᏻᐃ࡟⾜࠺᪉ἲࡢ◊✲ㄢ㢟ࢆṧࡋ࡚࠸ࡿ㸬ࡓ㸬ࡓࡔࡋ⇕ὶࡣ ᗘᕪ࡟ẚ౛ࡍࡿࡢ࡟ᑐࡋ㸪㢼㔞ࡣᅽ ࡲࡓ᭷㝈せ⣲ἲ➼ࡢᩘᏛⓗ✵㛫㞳ᩓ໬ἲ࡜ࡢ㛵㐃ࢆゎ

ຊᕪࡢ 0.5 ஌࡟ẚ౛ࡍࡿሙྜࡀከ࠸Ⅼࡀ⇕ᅇ㊰⥙࡜␗࡞᫂ࡋ࡚࠸࡞࠿ࡗࡓึᮇࡢ⇕ᅇ㊰⥙ࣔࢹ࡛ࣝࡣ㸪ᕤᏛⓗุࡗ࡚࠸ࡿ㸬ྛᐊ࡛ࡣ㢼㔞཰ᨭࡢᘧࡀᡂ❧ࡍࡿ㸬ᚑࡗ࡚ὶ᩿࡟ࡼࡾ⇕ὶ཰ᨭࢆ௬ᐃࡍࡿ㒊ศ࡟ศ๭ࡍࡿ᭷㝈య✚ἲ㊰ࡢ⥲ᩘࡔࡅࡢ㢼㔞࡜ᐊᩘศࡢᅽຊ㸦ᗋ㠃࡛ࡢ㟼ᅽ㸧ࡀࢆ⏝࠸࡚࠸ࡓ㸬ࡋ࠿ࡋ 1984 ᖺ㡭࡟࡞ࡗ࡚᭷㝈せ⣲ἲ࡟࠾㠀⥺ᆺ㐃❧᪉⛬ᘧࡢゎࡃ࡭ࡁᮍ▱ᩘ࡜࡞ࡿ㸬ࡋ࠿ࡋ㠀⥺ࡅࡿ඲య᪉⛬ᘧࢆ㸪 ᗘቃ⏺࡜⇕ὶቃ⏺ࡢᐃᘧ໬ࡢᨵⰋ

ᙧ㐃❧᪉⛬ᘧࢆゎࡃሙྜ࡟᭷ຠ࡞ࢽ࣮ࣗࢺࣥࣛࣉࢯࣥἲ

ࢆ⾜࠺ࡇ࡜࡛㸪≧ែ✵㛫᪉⛬ᘧ࡟ᑐᛂࡉࡏࡿࡇ࡜ࡀ࡛ࡁ

ࢆ㸪ᅽຊಟṇࡢ཰᮰ィ⟬᪉ἲ࡜ࡋ࡚㐺⏝ࡍࡿ࡜ᚲࡎࡋࡶ

ࡓ[9]㸬ᅗ㸯࡜ᅗ㸰ࡢᵝ࡟୧⪅ࡢࣔࢹࣝࡣ㸪≧ែ✵㛫᪉⛬ṇゎ࡟฿㐩ࡋ࡞࠸ၥ㢟ࡀศ࠿ࡗ࡚ࡁࡓࡢ࡛㸪ᵝࠎ࡞ゎἲᘧ࡜࠸࠺ࣉࣛࢵࢺ࣮࣒࡛࣍㸪࣐ࢺࣜࢵࢡࢫせ⣲グἲ࡜୍ࡀᕤኵࡉࢀࡓ⤒⦋[7]ࡀ࠶ࡿ㸬➹⪅ࡢ᪉ἲࡣ㸪ࡑࡢ᣺ືࡢ

⮴ࡋࡓ୍⯡໬⇕ᐜ㔞 mi,j㸪୍⯡໬⇕ࢥࣥࢲࢡࢱࣥࢫ ci,j ࡑ࣓࢝ࢽࢬ࣒ࡢ⪃ᐹ࡟ࡼࡾ㸪ᮏ᮶ࡢࢽ࣮ࣗࢺࣥࣛࣉࢯࣥἲ

ࡋ࡚⮬⏤ධຊಀᩘ ri,j ࢆ௓ࡋ࡚஫᥮ᛶ࡜⼥ྜᛶࢆᣢࡘࡼ

࡟ࡼࡿಟṇ㔞ࢆ༙ศ࡟ࡋ࡚᪋ࡍಟṇࢽ࣮ࣗࢺࣥࣛࣉࢯࣥ

࠺࡟ࡋࡓ㸬ἲ࡜࿧ࡪ᪉ἲࢆ⏝࠸࡚࠸ࡿ㸬ὶࢀࡢィ⟬᪉ἲ࡟ࡣ㸪࣑ࢡࣟࢫࢥࣆࢵࢡ࡞ᩘ್ὶయゎᯒ࡜㸪ࡇ࠺ࡋࡓ᥮Ẽᅇ㊰⥙ࡢࡼ࠺࡞࣐ࢡࣟࢫࢥࣆࢵࢡ࡞᪉ἲࡀ࠶ࡿ㸬᥮Ẽᅇ㊰⥙ࡣ㸪ከᒙከᩘᐊⓗ࡞ᘓ≀඲యࡢ✵Ẽὶືࢆィ⟬ࡍࡿࡢ࡟㐺ࡋ

8⚄ዉᕝ኱ᏛᕤᏛ◊✲ᡤᡤሗ ➨  ྕ࡚࠸ࡿࡀ㸪ᅽຊᦆኻಀᩘࡢྲྀࡾ᪉➼࡟ၥ㢟ࢆṧࡋ㸪୍᪉≀ࡢ᥮Ẽᛶ⬟ࢆ᳨ウࡍࡿሙྜ࡟㸪ྛᐊ࡛ࡣ✵Ẽởᰁ≀㉁ᩘ್ὶయゎᯒࡣ㸪ࡑ࠺ࡋࡓᕤᏛⓗ࡛ᐇ㦂ⓗಀᩘࢆ࠶ࡲࡾ

➼ࡀ༑ศΰྜࡋ࡚࠸ࡿ Multi-chamber ࣔࢹ࡛ࣝᢅ࠺㸬ᚲせ࡜ࡋ࡞࠸཯㠃㸪ᘓ≀඲యⓗ㐺⏝࡟ࡣၥ㢟ࡀ࠶ࡿ㸬ᚑFrank W. Sinden ࡟ࡼࡿ Multi-chamber theory[10]ࡣ㸪ࢩࢫࢸࡗ࡚ᑗ᮶ⓗ࡟ࡣࡇࢀࡽࡢ࣐ࢡࣟ࡜࣑ࢡࣟࡢࣔࢹࣝࢆ⼥ྜ࣒ྠᐃࡢほⅬࡲ࡛㐩ࡋ࡚࠸࡞࠿ࡗࡓࡀ㸪ࢺ࣮ࣞࢧ࢞ࢫࢆ

ࡋࡓࣔࢹࣝࡢ◊✲㛤Ⓨࡀᮃࡲࢀࡿ㸬ࡇࡢ⼥ྜࣔࢹࣝ࡜ࡋ

⏝࠸ࡿ᥮Ẽ ᐃἲࢆ᳨ウࡋࡓࡶࡢ࡛㸪ᣑᩓ⣔ࡢᅛ᭷್ࡢ

࡚ࡣ㸪඲ᅽ࠶ࡿ࠸ࡣ㟼ᅽࢆ⠇Ⅼࡢ≧ែ್࡜ࡋ࡚ᣢࡘᅽຊ

⪃ᐹࡶྵࡳ㸪♧၀࡟ᐩࡴࡶࡢ࡛࠶ࡗࡓ㸬ᮏࢩࢫࢸ࣒ྠᐃ

⠇Ⅼ⣔ࢆಟṇࢽ࣮ࣗࢺࣥࣛࣉࢯࣥἲ࡟ࡼࡗ࡚ᙉࡃ㐃ᡂࡋ⌮ㄽࡢ᭱ึࡢᐇ㐺⏝ࡣከᩘᐊ᥮Ẽ ᐃࢩࢫࢸ࣒࡛࠶ࡗࡓ㸬࡚ゎࡃࣔࢹࣝࡀ㸪ィ⟬Ᏻᐃᛶ࡜ᐇ⏝ᛶ࠿ࡽⰋ࠸ࡢ࡛ࡣ࡞

ࡇࢀࡣ 1979 ᖺ⡿ᅜࡢࢫ࣮࣐ࣜ࢖ࣝᓥཎⓎࡢ஦ᨾࡀዎᶵ

࠸࠿࡜⪃࠼࡚࠸ࡿ㸬࡟࡞ࡗࡓ㸬ࡉࡽ࡟᥮Ẽ࠾ࡼࡧ㝽㛫㢼ࡢᢕᥱࡣ㸪┬࢚ࢿ࡜ࢩࢵࢡࣁ࢘ࢫࡸ⤖㟢ၥ㢟➼ࡢほⅬ࡛ࡶ㔜せ࡛࠶ࡿ㸬➹⪅㸳㸬⇕ᅇ㊰⥙ࡢࢩࢫࢸ࣒ྠᐃ⌮ㄽ

ࡣ 1987 ᖺ࠿ࡽ 1988 ᖺ࡟࠿ࡅ࡚ࢫ࢙࣮࢘ࢹࣥ⋤❧ᕤ⛉኱ ➹⪅ࡢࢩࢫࢸ࣒ྠᐃ⌮ㄽࡢᒎ㛤࡟ࡣ㸪D.V.Pryor ࡜Ꮫࡢ Tor-Göran Malmström ᩍᤵ࠿ࡽᣍ࠿ࢀ࡚㸪ᙜ᫬ࡢᅜ

C.Byron Winn ࡟ࡼࡿᘓ⠏ⓗኴ㝧⇕฼⏝ఫᏯ㸦ࣃࢵࢩࣈࢯ

❧ᘓ⠏◊✲ᡤࡢ Mats Sandberg ᩍᤵࡢ᥮Ẽᐇ㦂᪋タ[11]࡛

࣮࣮ࣛࣁ࢘ࢫ㸧ࡢ⌧ሙ ᐃ࡟ࡼࡿ⇕ⓗᛶ⬟ホ౯᪉ἲࡢヨࡑࡢከᩘᐊ᥮Ẽ ᐃࢩࢫࢸ࣒ࡢ᳨ドᐇ㦂[12]ࢆ⾜ࡗࡓ㸬ࡳ[8]ࡀཧ⪃࡟࡞ࡗࡓ㸬ࡑࡇ࡛ࡣ Sequential filter estimationࡑࡋ࡚ྠᅜ⁫ᅾ୰࡟ゼၥࡋࡓࣝࣥࢻ኱Ꮫࡢ Lars Jensen ᩍ࡜࿧ࡤࢀࡿ᪉ἲࡀ⏝࠸ࡽࢀ࡚࠸ࡓࡀ㸪᭱ᑠ஧஌ἲࡢᮏ㉁ᤵ࠿ࡽ㸪ᬑ㏻ࡢ᭱ᑠ஧஌ἲ࡛ࡣ ᐃㄗᕪ➼ࡀ኱ࡁ࡞ሙྜ

ࢆ෌⪃ࡍࡿཧ⪃࡟࡞ࡗࡓ㸬ࡑࡋ࡚⇕ᅇ㊰⥙ࡢ≧ែ✵㛫᪉࡟㸪୙ྜ⌮࡞㈇ࡢ㢼㔞➼ࡀྠᐃࡉࢀࡿࡢ࡛ࡣ࡞࠸࠿࡜࠸

⛬ᘧࣔࢹࣝࢆ㸪ࡑࡢࢩࢫࢸ࣒࣭ࣃ࣓࣮ࣛࢱࡢ୍⯡໬⇕ᐜ࠺ᣦ᦬ࢆཷࡅࡓ㸬ᙼࡣ⥺ᙧィ⏬࡟ࡼࡿ᪉ἲ[13]ࢆ◊✲ࡋ㔞 mi,j ୍⯡໬⇕ࢥࣥࢲࢡࢱࣥࢫ ci,j ࡑࡋ࡚⮬⏤ධຊಀᩘ ri,j࡚࠸ࡓ㸬ࡑࡢᣦ᦬࡟ࡼࡾ㸪㠀㈇᭱ᑠ஧஌ἲ[14]ࢆ㏣ຍⓗ࡟㛵ࡍࡿᅇᖐᘧ࡟ኚᙧࡋ࡚㸪᭱ᑠ஧஌ἲࢆ⮬ศ࡞ࡾ࡟₇࡟ᑟධࡍࡿࡇ࡜࡟ࡋ㸪ྠᐃ⢭ᗘࢆྥୖࡉࡏࡿࡇ࡜ࡀ࡛ࡁ

⧢ࡋ┤ࡋ㸪⾲㸯ࡢ(4)ᘧ࡟♧ࡍࡼ࠺࡞ᅇᖐᘧㄗᕪࡢホ౯㛵ࡓ㸬ࡉࡽ࡟ 1989 ᖺ࡟ࡣ➨஧ୡ௦ࡢࢥࣥࣃࢡࢺ࡞ ᐃࢩࢫᩘ࠿ࡽ㸪㏲ḟྠᐃ࡜࿧ࡪ᪉ἲ࡜୍ᣓྠᐃ࡜࿧ࡪ஧ࡘࡢ᪉

ࢸ࣒࡟ᨵⰋ[15]ࡋ㸪ᘓ⠏◊✲ᡤࡢ⃝ᆅᏕ⏨༤ኈ࡟ࡼࡿࢩ

ἲࢆᑟ࠸ࡓ㸬๓⪅ࡣ๓㏙ࡢ Sequential filter estimation ࡟┦ࣜࣥࢲ࣮ࣁ࢘ࢫ࡜࿧ࡤࢀࡿ㝽㛫㢼ࢆṇ☜࡟ᢕᥱ࡛ࡁࡿ≉ᙜࡋ㸪ᚋ⪅ࡣ᥎ᐃࡍ࡭ࡁࣃ࣓࣮ࣛࢱ⥲ᩘศࡢࢧ࢖ࢬࡢᡤ

Ṧ࡞ᐇ㦂タഛ[16]᳨࡛ドᐇ㦂ࢆ⾜ࡗࡓ㸬࡞࠾⇕ᅇ㊰⥙ࣔㅝṇつ᪉⛬ᘧࡢ㐃❧᪉⛬ᘧࢆゎࡃ᪉ἲ࡟┦ᙜࡍࡿ㸬୍ᣓࢹࣝࡢࢩࢫࢸ࣒ྠᐃィ⟬ࣉࣟࢢ࣒ࣛࡣ SPID(Systemྠᐃ࡛ࡣ㸪࠶ࡿ⛬ᗘࡢᮇ㛫㛗ࡉࡢ㞳ᩓ᫬㛫ⓗ ᐃࢹ࣮ࢱParameter IDentification)࡜࿧ࢇ࡛࠸ࡿ㸬2001 ᖺ࡟࡞ࡗ࡚ࡼ

඲య࡟㛵ࡋ୍࡚ᗘ࡟ࣃ࣓࣮ࣛࢱࢆ᥎ᐃࡍࡿ㸬ࡇࢀ࡟ᑐࡋ

࠺ࡸࡃࡇࡢ kernel ࡟ᑐࡍࡿධฟຊฎ⌮ࣉࣟࢢ࣒ࣛࢆ㛤Ⓨ

࡚㏲ḟྠᐃ࡛ࡣ㞳ᩓ᫬㛫ⓗ ᐃࢹ࣮ࢱࡢ 1 ࢫࢸࢵࣉẖ࡟ࡍࡿᶵ఍ࡀᚓࡽࢀࡓ㸬᥎ᐃ⤖ᯝࢆᚓ࡚࠸ࡃ₞໬ᘧࢆ⏝࠸ࡿ㸬୧⪅ࡢࢩࢫࢸ࣒ྠ ࡇࡢ⇕ᅇ㊰⥙ࣔࢹࣝࡢࢩࢫࢸ࣒ྠᐃ⌮ㄽࢆ㸪ከᩘᐊ᥮ᐃἲࡢ኱ࡁ࡞㐪࠸ࡣ㸪㏫⾜ิィ⟬ࡢࢧ࢖ࢬ࡜ึᮇ್ࡢᚲẼ ᐃ࡛ࡣ࡞ࡃ㸪ᮏ᮶ࡢᘓ⠏ఏ⇕⣔࡛ ᐃἲ࡜ࡋ࡚౑࠼

せᛶࡢ᭷↓࡛࠶ࡿ㸬㏲ḟྠᐃࡢሙྜ࡟ࡣ≧ែ✵㛫᪉⛬ᘧࡿᵝ࡟ࡍࡿ࡟ࡣ㸪ᐇࡣ኱ࡁ࡞ၥ㢟ࡀᗄࡘ࠿ṧࡉࢀ࡚࠸ࡓ㸬ࡢࢧ࢖ࢬࡢ㏫⾜ิィ⟬࡛ࡍࡴ㸬ᚑࡗ࡚௬࡟㸯ḟ࡛࠶ࢀࡤከᩘᐊ᥮Ẽ ᐃࡢࢺ࣮ࣞࢧ࢞ࢫᣑᩓ⣔࡛ࡣྛᐊࡢᑠࡉ࡞

㏫⾜ิィ⟬ࡣ༢࡞ࡿ㏫ᩘࡢィ⟬࡟ᖐ╔ࡍࡿ㸬ࡇࢀࡣࣇ࢓࡛ࣥ࢞ࢫࢆᨩᢾࡍࡿࡢ࡛㸪ࣔࢹࣝࡢྛᐊ࢞ࢫ⃰ᗘࡢ

Matrix inversion lemma㸦㏫⾜ิ⿵ຓᐃ⌮㸧ࢆ㐺⏝ࡋ࡚࠸

⠇Ⅼࡣ 1 ಶ࡛㛫࡟ྜ࠺㸬ࡋ࠿ࡋᘓ⠏ఏ⇕⣔࡛ࡣ㸪ᐊ✵Ẽࡿ࠿ࡽ࡛࠶ࡿ㸬ィ⟬ࡣ㍍࠸ࡶࡢ࡟࡞ࡿ཯㠃㸪₞໬ᘧࡢึࡼࡾࡶቨయ➼ࡢ㌣యࡢ⇕ᐜ㔞ࡀ኱ࡁ࠸ࡢ࡛㸪㏻ᖖࡢᐊ

ᮇ್ࡢ௬ᐃࢆᚲせ࡜ࡍࡿࡢ࡛⢭ᗘࡀᝏ࠸ୖ࡟㸪 ᐃ್㞧ኚ໬ண ィ⟬ࡢࣔࢹࣝ࡟ࡣ㸪㞳ᩓ໬ࡋࡓ㌣యࢆཷࡅᣢࡘ

㡢ࡢᝏᙳ㡪ࢆཷࡅࡸࡍࡃ㸪ᐇ⏝࡟ࡣ㞴ࡀ࠶ࡿࡇ࡜ࡣ➹⪅⠇Ⅼࡶᚲせ࡟࡞ࡿ㸬ࡋ࠿ࡋࡇࡢẚ㍑ⓗ࡟ከࡃࡢ⠇Ⅼࢆᣢࡢᗄࡘ࠿ࡢᩘ್ᐇ㦂[9]࡟࠾࠸࡚☜࠿ࡵࡽࢀ࡚࠸ࡿ㸬₞໬ࡘ⣽࠿࠸ண ィ⟬ࣔࢹࣝࡣࢩࢫࢸ࣒ྠᐃ࡟ࡣ㐺ࡋ࡚࠸࡞ᘧࡢᩘᘧⓗᑟฟ㐣⛬ࡣ୍ぢ␗࡞ࡿࡶࡢࡢ㸪࠾ࡑࡽࡃ࢝ࣝ

࠸㸬࡞ࡐ࡞ࡽ㌣య୰ࡢ⠇Ⅼ࡟ᑐᛂࡍࡿ㒊ศࢆ㸪⌮᝿ⓗ࡞࣐ࣥࣇ࢕ࣝࢱ࣮ࡶᮏ㉁ⓗ࡟ᮏ㏲ḟྠᐃ࡜ྠࡌ࡜ᛮࢃࢀࡿ

ࣔࢹࣝ࡜ྠࡌ≧ἣ࡛ຍ⇕ࡋ࡚ ᗘࢆ ᐃࡍࡿࡇ࡜ࡣᅔ㞴ࡀ㸪ヲࡋ࠸ẚ㍑᳨ウࡣࡋ࡚࠸࡞࠸㸬ࡇࡢⅬ࡛ࡣ㸪୍ᣓྠࡔ࠿ࡽ࡛࠶ࡿ㸬ᐃࢆ⾜࠺ ᐃᮇ㛫ࢆ⛣ືᖹᆒⓗ࡞ព࿡࡛㸯ࢫࢸࢵࣉࡎࡘ ࡑࡇ࡛ 2004 ᖺ㡭࡟⪃࠼ࡓࡢࡣ㸪ຍ⇕ࡢບ᣺࡜ ᐃࡀᅔࡎࡽࡋ࡚⾜ࡃ᪉ἲࡢ᪉ࡀඃࢀ࡚࠸ࡿ࡜ᛮࢃࢀࡿ㸬ࡇࡢ⇕㞴࡞㌣య୰ࡢ⠇Ⅼࡢኚᩘࡣ㸪ບ᣺࡜ ᐃࡀྍ⬟࡞ᐊ✵Ẽᅇ㊰⥙ࣔࢹࣝࡣ㸪୍⯡ⓗ࡞ᣑᩓ⣔ࡢ㞳ᩓ໬ࣔࢹࣝ࡞ࡢ࡛

ࡢ⠇Ⅼࡢኚᩘࡢ㸰㝵௨ୖࡢ᫬㛫ᚤศኚᩘ࡟ࡼࡾ⨨ࡁ᥮࠼ᗘࡢᣑᩓ⣔ࡔࡅ࡛࡞ࡃ࢞ࢫࡢὶື⣔ࡶ⾲ࡋ࡚࠸ࡿ㸬ᘓࡓᅇᖐᘧࢆᑟࡁྠᐃࡍࡿ᪉ἲ[17]࡛࠶ࡿ㸬୍⯡࡟ඖࡢ≧⇕࣭᥮Ẽᅇ㊰⥙ࣔࢹࣝ࡟ࡼࡿᘓ⠏⎔ቃᕤᏛศ㔝࡛ࡢ◊✲㛤Ⓨែ✵㛫᪉⛬ᘧࡀn ಶࡢ⠇Ⅼ࡟ࡼࡿ㧗ḟ࡞n ḟ࡛࠶ࡗ࡚ࡶ㸪ᐃࡉࢀࡓࣃ࣓࣮ࣛࢱࡢ୙☜࠿ࡉศᩓࡣ㸪ᅇᖐᘧṧᕪ࠿ࡽ

1 ࡘࡢᐊ ኚᩘࡢ n 㝵᫬㛫ᚤศ࡟ࡼࡿ n ಶࡢኚᩘࢆᑟධ

ࡢࡶࡢ࡜㸪 ᐃ୙☜࠿ࡉศᩓ࠿ࡽࡢࡶࡢ࡜஧㏻ࡾィ⟬ࡉࡍࡿࡇ࡜࡛㸪୍ᮏࡢᅇᖐᘧ࡟ᖐ╔ࡍࡿࡇ࡜ࡶ⌮᝿ⓗ࡟ࡣࢀࡿࡇ࡜ࡣศ࠿ࡗ࡚࠸ࡓ㸬ࡑࡇ࡛ࡇࢀࡽࢆ฼⏝ࡋ࡚๓⪅ྍ⬟࡛࠶ࡿ㸬ࡓࡔࡋᅇᖐ࡟᭷ຠ࡞ n 㝵ᚤศ್࡟ࡍࡿࡓࡵ

ࡢᚋ⪅࡟ᑐࡍࡿẚ⋡࡟ࡼࡾ㸪ࢩࢫࢸ࣒ྠᐃ๓ᥦࡢ୙㐺ྜ࡟ࡣ㸪ᑡ࡞ࡃ࡜ࡶ n ✀㢮ࡢ࿘ᮇ࡜఩┦ࡢṇᘻἼ࠿ࡽᡂࡿ

⋡࡜࿧ࡪಙ㢗ᛶホ౯ᣦᶆࢆᐃ⩏ࡋࡓ㸬ᐇ㝿ࡢ ᐃ࡛ࡣ㸪」ྜບ᣺Ἴᙧࡀᚲせ࡜ᛮࢃࢀࡿ㸬ࡋ࠿ࡋᐇ㝿ୖࡢㅖࠎࡢ

ࢩࢫࢸ࣒ྠᐃࡀ๓ᥦ࡜ࡍࡿࣔࢹࣝࡢ⥺ᙧᛶ㸪᫬㛫ⓗ୙ኚᐃㄗᕪ࡜እ஘࡜ᑐ㇟⣔⮬యࡢ᫬㛫ኚ໬ࡶ⪃࠼ࢀࡤ㸪᭷ᛶ㸪✵㛫ⓗ୍ᵝᛶ➼ࡀ༑ศ࡟ᡂࡾ❧ࡓ࡞࠸ࡇ࡜࡟ࡼࡾ⏕ຠ࡞᫬㛫ᚤศ㝵ᩘ࡟ࡣ㝈⏺ࡀ࠶ࡿ㸬ࡲࡓࡇࡢ᪉ἲࡣ୍⯡ࡌࡿྠᐃㄗᕪࡀ኱ࡁ࠸ࡢ࡛࠶ࡿࡀ㸪ࡇࡢホ౯ࡀྍ⬟࡜࡞ᘧ࡟ࡍࡿࡢࡀᅔ㞴࡛࠶ࡗࡓ㸬ࡿ㸬

2008 ᖺ㡭࠿ࡽࢩࢫࢸ࣒ྠᐃࣔࢹࣝࡣᐊ ࡢ⠇Ⅼࡔࡅ௒ᚋ㸪๓㏙ࡢᨵⰋࢩࢫࢸ࣒ྠᐃ⌮ㄽ࡟ࡼࡾ㸪ᘓ⠏ఏ⇕ࡢ⢒ࡃ࡚༢⣧࡞ࣔࢹࣝࢆ⏝࠸ࡿ᪉ྥ࡛ィ⟬ᶵᐇ㦂࡟ࡼࡾ⣔࡟㛵ࡍࡿ ᐃࢩࢫࢸ࣒ࢆヨసࡋ࡚㸪ᐇドⓗ◊✲ࡀᚲせᶍ⣴ࡋጞࡵࡓ㸬㌣యࡢ⇕ᐜ㔞ࡢᙳ㡪ࡣ㸪ᐊ✵Ẽࡢ┦ᙜ⇕࡜⪃࠼࡚࠸ࡿ㸬ᐜ㔞ࢆቑࡸࡍࡇ࡜࡛⪃៖ࡍࡿࡇ࡜࡟ࡋࡓࢃࡅ࡛࠶ࡿ㸬ࡇࡢࡓࡵ࡟ຍ⇕ࡢບ᣺Ἴᙧ࡜ ᐃࢹ࣮ࢱࡢࣇ࢕ࣝࢱࣜࣥࢢ

㸴㸬ࡑࡢ௚ࡢ ᐃࢹ࣮ࢱศᯒᢏ⾡࡟ࡣᕤኵࡀᚲせ࡛࠶ࡗࡓ㸬 ᮏࢩࢫࢸ࣒ྠᐃ⌮ㄽࡢせ࡜࡞ࡿ᭱ᑠ஧஌ἲ࠾ࡼࡧ୙☜ᙜึࡣ▴ᙧἼࡢບ᣺࡟ࡼࡿ 1 ศ⛬ᗘࡢ㛫㝸ẖࡢࢹ࣮ࢱ࠿ࡉホ౯᪉ἲࡣᅇᖐᘧࡀ␗࡞ࡗ࡚ࡶ᭷ຠ࡛࠶ࡿ㸬ࢆ⏝࠸࡚࠸ࡓ㸬 ᐃࢹ࣮ࢱࢆ㸯᫬㛫⛬ᗘࡢ⛣ືᖹᆒᮇ㛫౛࠼ࡤ⡆᫆ⓗ࡞᥮Ẽ ᐃἲ࡜ࡋ࡚ perfluorocarbon tracer࡛ᖹ⁥໬ࡍࢀࡤ㸪ྠᐃ⤖ᯝࡣᨵၿࡉࢀࡓࡀ㸪ࡇࢀࡣ ᐃgas(PFT)ࢆ⏝࠸ࡿ᪉ἲࡀ◊✲ࡉࢀ࡚࠸ࡿ㸬ࡇࢀࡣᐊෆ࡟

ㄗᕪࡣࢠࢨࢠࢨࡢᵝ┦ࢆ࿊ࡋ㸪ࡇࡢᝏᙳ㡪ࡀῶᑡࡍࡿ࠿

⨨࠿ࢀࡿࢻ࣮ࢨ࣮࡜࿧ࡤࢀࡿᑠ⎼࡟ධࡗࡓ≀㉁࠿ࡽࡑࡢ

ࡽ࡛࠶ࡿ㸬ࡲࡓ▴ᙧἼࡼࡾࡶ㸪ࡺࡗࡃࡾ⁥ࡽ࠿࡟ኚ໬ࡍ

᥹Ⓨᛶ࢞ࢫࢆᩘ᪥㛫࠿ࡽᩘࣨ᭶࡟ࢃࡓࡾᨺᩓࡋ㸪ྠ᫬୪ࡿṇᘻἼࡀⰋ࠸ྠᐃ⤖ᯝࢆ୚࠼ࡿࡇ࡜ࡶศ࠿ࡗࡓ㸬⠇Ⅼ⾜ࡋ࡚ᐊෆ࡟⨨ࡃࢧࣥࣉ࣮ࣛ࡜࿧ࡤࢀࡿᑠ⎼࡟ධࡗࡓ྾

ᩘࡢᑡ࡞࠸⢒࠸ࣔࢹ࡛ࣝᐇ⌧㇟ࢆ㏣㝶࡛ࡁࡿࡢࡣບ᣺ࡀ╔≀㉁࡟࢞ࢫࢆ྾╔ࡉࡏ㸪 ᐃᮇ㛫⤊஢ᚋ࡟ᨺᩓ㔞࡜྾ẚ㍑ⓗ࡟㛗࿘ᮇࡢṇᘻἼࡢሙྜ࡛࠶ࡿ㸬▴ᙧἼࡣࣇ࣮ࣜ

╔㔞ࢆศᯒࡋ㸪ᮇ㛫ᖹᆒࡢᨺᩓὶ㔞࡜⃰ᗘࢆồࡵ㸪ᮇ㛫࢚⣭ᩘᒎ㛤ࡍࢀࡤ㧗࿘Ἴᡂศࢆᣢࡘࡇ࡜ࡀศ࠿ࡿࡀ㸪ࡇᖹᆒࡢ᥮Ẽ㔞ࢆ᥎ᐃࡋࡼ࠺࡜ࡍࡿࡶࡢ࡛࠶ࡿ㸬ࡇࡢሙྜࢀࡽࡀ⢒࠸ࣔࢹࣝࡢࢩࢫࢸ࣒ྠᐃ࡟ࡣ㐺ࡉ࡞࠸࡜⪃࠼ࡽ࡟࢞ࢫ཰ᨭᘧࡣᐃᖖ≧ែࡢࡶࡢࢆ⏝࠸ࡿ㸬ࡋ࠿ࡋᐇ㝿࡟ࢀࡓ㸬ࡣ᥮Ẽ㔞ኚ໬࡟ࡼࡗ࡚⃰ᗘኚືࡀ㉳ࡇࡿࡢ࡛㸪᥎ᐃࡉࢀᚑࡗ࡚⛣ືᖹᆒࡣ㸪༢࡞ࡿ ᐃㄗᕪࡢᝏᙳ㡪㍍ῶࡢࡓ

ࡿࡢࡣᮇ㛫ᖹᆒ᥮Ẽ㔞࡜ࡣᑡࡋ␗࡞ࡿ⃰ᗘ㔜ࡳ௜ࡁᖹᆒ

ࡵࡢ᪉ἲ࡜ࡋ࡚ࡔࡅ࡛ࡣ࡞ࡃ㸪⠇Ⅼᩘࡢᑡ࡞࠸⢒࠸ࣔࢹ᥮Ẽ㔞࡛࠶ࡿ[19]㸬ࡲࡓ᝿ᐃࡋࡓࢰ࣮ࣥศࡅࡢኵࠎ࡛ࣇ

ࣝ࡟㐺ࡋࡓప࿘Ἴᩘ୺యࡢ ᐃࢹ࣮ࢱ࡟ࡍࡿࡓࡵࡢ᪉ἲ

࢓ࣥᨩᢾ➼ࡶ⾜ࢃ࡞࠸ࡋ㸪࢞ࢫ⃰ᗘࡀ୍ᵝ࡛࠶ࡿ࠿ࡶ୙

࡜ࡋ࡚ࡶᚲせ࡛࠶ࡿ㸬ࡘࡲࡾ⛣ືᖹᆒࡣ㸪࣮ࣟࣃࢫ࣭ࣇ

☜࠿࡛㸪ᐊ ኚ໬࡟ᙳ㡪ࡉࢀ࡚࢞ࢫⓎ⏕ࡀ୍ᐃ࡛࠶ࡿ࠿

࢕ࣝࢱ࡜ࡋ࡚ࡶ㸪 ᐃࢹ࣮ࢱ࡟ᚲせ࡞๓ฎ⌮࡛࠶ࡿࡇ࡜

ࡶ୙☜࠿࡛࠶ࡿ㸬ࡘࡲࡾᩘᘧࣔࢹࣝࡢ๓ᥦࡀ༑ศ࡟ᡂࡾ

ࡀศ࠿ࡗࡓ㸬❧ࡘ࠿ಖドࡀ↓࠸᪉ἲ࡛࠶ࡿ㸬 ึᮇࡢࢩࢫࢸ࣒ྠᐃ⌮ㄽࡣ௚ࡢᗄࡘ࠿ࡢⅬ࡛ࡶᮍࡔ୙

ࡓࡔࡋᐜ᫆࡟᥎ᐹ࡛ࡁࡿᵝ࡟㸪ᐊᩘศࡢ✀㢮ࡢ࢞ࢫࢆ༑ศ࡛࠶ࡗࡓ㸬ࡇࢀࡽࡶྵࡵ኱ᖜ࡟ᨵⰋࡋࡓ⌮ㄽࢆ 2012⏝࠸ࢀࡤ㸪ከᩘᐊ᥮Ẽ ᐃἲ࡟ࡶᣑᙇྍ⬟࡛࠶ࡿ㸬ᖺฟ∧ࡢㄽᩥ[18]࡟㏙࡭ࡓ㸬ึᮇࡢ⌮ㄽ࡛ࡣ㢼㔞཰ᨭࡸ ➹⪅ࡣ㸪ࢰ࣮ࣥᩘ௨ୖࡢ࡞ࡿ࡭ࡃἑᒣࡢࢧࣥࣉ࣮ࣛ࡜

⇕ࢥࣥࢲࢡࢱࣥࢫࡢᑐ⛠ᛶ➼ࡢᣊ᮰᮲௳ࢆᅇᖐᘧ࡟⪃៖ࢻ࣮ࢨ࣮ࢆタ⨨ࡍࡿࡇ࡜࡛㸪୙☜࠿ࡉࡢホ౯ࢆࡼࡾṇ☜ࡍࡿࡓࡵ࡟ᇙࡵ㎸ࡳ᪉ᘧࢆ࡜ࡗ࡚࠸ࡓࡢ࡛⼥㏻ᛶࡀ༑ศ

࡟ࡍࡿࡔࡅ࡛࡞ࡃ㸪㢼㔞ࡢ᥎ᐃ⢭ᗘࡶྥୖࡍࡿ᪉ἲࢆ⪃࡛ࡣ࡞࠿ࡗࡓୖ࡟㸪ྠᐃࡍࡿࣃ࣓࣮ࣛࢱࡢ㠀㈇ᛶࢆ⪃៖᱌ࡋࡓ[19]㸬ࡘࡲࡾࡑࢀࡲ࡛ࡣᮍ▱ᩘࡢ㢼㔞ࡢಶᩘ࡟➼ࡍࡿࡓࡵࡢ㠀㈇᭱ᑠ஧஌ἲࡀ༑ศ࡟㐺⏝࡛ࡁ࡞࠿ࡗࡓ㸬ࡋ࠸࢞ࢫ཰ᨭᘧࢆᚓ࡚Ỵᐃㄽⓗ࡟㢼㔞ࢆồࡵ࡚࠸ࡓࡢ࡟

ࡑࡇ࡛ᨵⰋ⌮ㄽ࡛ࡣ㸪㐃❧ᅇᖐᘧࡢ⾜᪉ྥ࡟ᣊ᮰᮲௳ᘧ

ᑐࡋ㸪ࡼࡾከࡃࡢ࢞ࢫ཰ᨭᘧࢆᅇᖐᘧ࡜ࡋ࡚ᚓ࡚᭱ᑠ஧

ࢆ㏣ຍࡍࡿᙧࡢᐃᘧ໬࡟ᨵࡵࡓ㸬ࡇࢀ࡟ࡼࡾᣑᙇᛶࡶⰋ

஌ἲ࡛᥎ᐃࡍࡿ࡜࡜ࡶ࡟㸪ࡑࡢṧᕪࢆ฼⏝ࡋ࡚୙☜࠿ࡉࡃ࡞ࡾ㸪」ᩘࡢ⇕ࢥࣥࢲࢡࢱࣥࢫ࠿ࡽ⇕ఏᑟ⋡➼ࡢᇶᮏホ౯ࢆ⾜࠺᪉ἲࢆ⪃࠼ࡓ㸬ⓗ࡞ࣃ࣓࣮ࣛࢱ࡬ࡢᅇᖐࡶᐜ᫆࡟࡞ࡿ㸬୍᪉㸪ᘓ≀ࡢẼᐦᛶ ᐃἲࡢ JIS[20]ࡸ ISO[21]ࡢࢹ࣮

 ࡲࡓึᮇࡢ⌮ㄽ࡛ࡶ୙☜࠿ࡉホ౯ࡢ᰿ᖿࡣ᪤࡟㐀ࡗ࡚ࢱศᯒἲࡶᨵⰋ࡛ࡁࡿ[22]㸬ᚑ᮶ࡢ᪉ἲ࡛ࡣ᥎ᐃࣃ࣓ࣛ

࠶ࡗࡓࡀ㸪ᐇ㝿ࡢィ⟬࡟ࡼࡿ᳨ウࡀ୙༑ศ࡛࠶ࡗࡓ㸬᥎࣮ࢱࡢಙ㢗༊㛫ࡀẚ㍑ⓗ࡟ᗈࡃ࡚ホ౯⢭ᗘࡀⰋࡃ࡞࠿ࡗ

10⚄ዉᕝ኱ᏛᕤᏛ◊✲ᡤᡤሗ ➨  ྕࡓࡀ㸪ᅇᖐᘧࡢṧᕪࢆ฼⏝ࡍࡿ୙☜࠿ࡉศᯒἲ࡟ࡍࡿࡇ

ࡑࡋ࡚᭷ຠ࢚ࢿࣝࢠ࣮ࡢ┬࢚ࢿᛶࢆ⾲ࡍ୕㡯࠿ࡽᡂ❧ࡉ࡜࡛୙☜࠿ࡉホ౯ࡀࡼࡾṇ☜࡟࡞ࡗࡓ㸬ࡲࡓ➹⪅ࡀ⪃᱌ࡏ࡚࠸ࡿ㸬ࡇࢀࡽࡢ㡯ࡢᩘ㔞ⓗᐃ⩏ࡣ㸪 ෭ឤ୰❧ᛶࡀࡋࡓࢩࢫࢸ࣒ྠᐃ๓ᥦࡢ୙㐺ྜ⋡ࡣ㸪 ᐃ୰ࡢእ஘➼ࡢ⇕ⓗ୰❧≧ែ࡟࠶ࡿேయࡢ㌣ᖿ ᗘ࡜ 36.8Υࡢ೫ᕪࡢ஧

ᝏᙳ㡪ࡶྵࡵ㸪෌ ᐃࡀᚲせ࠿ྰ࠿ࡢุ᩿࡟ᙺ❧ࡘ㸬஌࡛࠶ࡾ㸪┬࢚ࢿᛶࡀ౪⤥࢚ࢿࣝࢠ࣮࡜ࢮࣟࡢ೫ᕪࡢ஧

ࡲࡓ༢ᐊࣔࢹࣝࡢ᥮Ẽᅇᩘࢆࢺ࣮ࣞࢧ࢞ࢫࡢ⃰ᗘῶ⾶࡟஌࡛࠶ࡾ㸪ࡲࡓ᭷ຠ࢚ࢿࣝࢠ࣮ࡢ┬࢚ࢿᛶ࡜ࡣ⇕஺᥮ჾࡼࡾ ᐃࡍࡿ ISO ࡢ᪉ἲ[23]ࡶᨵⰋ࡛ࡁࡿ[24]㸬᥮Ẽᅇᩘ࡟ὶࡍ෭Ỉ/ Ỉ࡜እẼ ᗘࡢ೫ᕪࡢ஧஌࡛࠶ࡿ㸬ࡇࢀࡽࡢ᥎ᐃ୙☜࠿ࡉࢆ᭱ᑠ࡟ࡍࡿ᭱㐺ῶ⾶ᮇ㛫ࡢỴᐃἲࡣ㸪ࡢ୕ࡘࡢ೫ᕪࡢ஧஌࡟ࡣ㸪࠾ࡼࡑᑐ➼ࡢ኱ࡁࡉ࡟࡞ࡿᵝᚑ᮶ࡣ⤒㦂ⓗ࡛࠶ࡗࡓࡀ㸪⌮ㄽⓗ᰿ᣐࢆᣢࡕᩘᏛⓗ࡟ồ࡟㔜ࡳಀᩘࢆ஌ࡌࡓୖ࡛㸪᭱ᑠ໬ࡍ࡭ࡁホ౯㛵ᩘࢆᙧᡂࡵࡿ᪉ἲࢆ₇⧢ࡋ㸪ࡇࢀ࡟ࡼࡿ᭱㐺ῶ⾶ᮇ㛫ࡢ㑅ᐃᩘ⾲ࡋ࡚࠸ࡿ㸬⌧≧ࡢ෭ᬮᡣࢩࢫࢸ࣒タィࡣ✵Ẽ ᗘ೫㔜࡛ࢆ୚࠼ࡓ㸬ࡲࡓ᥮Ẽᅇᩘࡢ୙☜࠿ࡉホ౯ࡢ⢭ᗘࡶྥୖࡉ

࠶ࡿࡇ࡜ࡣྰࡵ࡞࠸㸬ே㛫ࡢ ෭ឤࡣ✵Ẽ ᗘࡔࡅ࡛࡞

ࡏࡓ㸬ࡃ࿘ᅖࡢ⇕ᨺᑕ⎔ቃ࡟ࡶ኱ࡁࡃᕥྑࡉࢀࡿ㸬⇕ᨺᑕ⎔ቃࡉࡽ࡟ᮏࢩࢫࢸ࣒ྠᐃ⌮ㄽࡢ༢ᐊ∧࡜ࡶゝ࠼ࡿࡀ㸪ࢺࢆ⪃៖ࡋࡓ෭ᬮᡣ࡜ࡣ㸪ఱࡶࣃࢿࣝࣄ࣮ࢱ࣮ࡸᗋᬮᡣࡔ

࣮ࣞࢧ࢞ࢫࢆṇᘻἼ࡛ᨺฟࡍࡿࡇ࡜࡟ࡼࡾ㸪᭷ຠΰྜᐜ

ࡅࢆព࿡ࡍࡿࡢ࡛ࡣ࡞ࡃ㸪ቨ࣭ᗋ࣭ᒇ᰿ࡢᵝ࡞㌣య⮬య✚࡜᥮Ẽ㢼㔞࡟ศࡅ࡚ ᐃࡍࡿ᪉ἲࡢྍ⬟ᛶࡶ᫂ࡽ࠿࡟

ࡢ㐺ษ࡞᩿⇕ࡶ኱࠸࡟㛵ಀࡍࡿ㸬ࡑࢀࡣᐊෆ⾲㠃 ᗘࡀࡋࡓ[24]㸬

ᨵၿࡉࢀࡿ࠿ࡽ࡛࠶ࡿ㸬ࡉࡽ࡟⌧≧ࡢ෭ᬮᡣࢩࢫࢸ࣒タ࡞࠾௚ࡢศ㔝࡛ࡶᵝࠎ࡞ ᐃἲ࡜ࢹ࣮ࢱศᯒἲࡀ࠶ࡿ

ィࡣ㸪࢚ࢿࣝࢠ࣮ࡢ㉁ࢆ༑ศ⪃៖ࡏࡎ㸪㔞ࡢホ౯࡟೫ࡗࡀ㸪ఱࡽ࠿ࡢᅇᖐᘧ࡜ᣊ᮰᮲௳ᘧࢆ๓ᥦ࡟ࡋࡓ᭱ᑠ஧஌

࡚࠸ࡿ㸬ࡠࡿ࠸෭ Ỉ࡛㛫࡟ྜ࠺ࢩࢫࢸ࣒࡞ࡽࡤ㸪⇕※ἲ࡜ぢ࡞ࡏࡿࡶࡢࡀከ࠸ᵝ࡛࠶ࡿ㸬ᚑࡗ࡚ᮏㄽ࡛ࡢ୙☜ᶵჾࡣ㧗ຠ⋡࡛౑࠼ࡿࡋ㸪ᗫ⇕ࡸኴ㝧⇕➼ࡶ᭷ຠ࡟฼⏝࠿ࡉศᯒἲ࡟ࡼࡾᨵⰋ࠶ࡿ࠸ࡣಟṇࡀ࡛ࡁࡿࡇ࡜ࡀᮇᚅ

࡛ࡁࡿ㸬ࡇ࠺ࡋࡓ᭱㐺໬ࡢࣔࢹࣝ࡜ゎἲ࡟ࡼࢀࡤ㸪ࡼࡾ࡛ࡁࡿ㸬┬࢚ࢿ࡛┬㈨※࡞ࢩࢫࢸ࣒ࡢタィࡀ㐺ษ࡟⾜࠼ࡿ࡜⪃࠼㸪
ᅗ 3 ࡟♧ࡍᵝ࡞ィ⟬ᶵᐇ㦂ࣔࢹࣝࢆ᝿ᐃࡋ࡚⌮ㄽࡢ᳨ド㸵㸬≧ែ࡜࢚ࢿࣝࢠ࣮౪⤥ࡢ᭱㐺໬⌮ㄽ࡞࡝ࡶ⾜ࡗࡓ[26]㸬ࡋ࠿ࡋᮍࡔᮏ⌮ㄽࡣ᭱㐺ไᚚ⌮ㄽࡢ ➹⪅ࡢ⇕ᅇ㊰⥙ࡢ⌮ㄽⓗᒎ㛤࡟ࡣࢩࢫࢸ࣒⌮ㄽࡀ኱࠸ᇦࢆฟ࡚࠸࡞࠸㸬ࢩࢫࢸ࣒࡬ࡢ᭱㐺ධຊࢆỴᐃࡍࡿࡔࡅ

࡟ཧ⪃࡟࡞ࡗࡓࡀ㸪ࡑࡢ≧ែ✵㛫ἲ࡛ᒎ㛤ࡉࢀ࡚࠸ࡿ᭱

ࡔ࠿ࡽ࡛࠶ࡿ㸬ᮏ᱁ⓗ࡞᭱㐺タィ⌮ㄽ࡟࠾࠸࡚ࡣ㸪ࢩࢫ㐺ไᚚ⌮ㄽࡑࡢࡶࡢࡢᛂ⏝ࡀ࡛ࡁࡓࡢࡣ኱ศᚋ࡟࡞ࡗ࡚

ࢸ࣒ࡢࣃ࣓࣮ࣛࢱࡶ᭱㐺໬࡛ࡁ࡞ࡅࢀࡤ࡞ࡽ࡞࠸㸬ࡑࡢ࠿ࡽ࡛࠶ࡿ㸬᭱㐺ไᚚἲࡢゎᘧࡣ㐃⥆ⓗ࡞✚ศ᪉⛬ᘧࡢࡓࡵ࡟ࡣ㠀⥺ᙧࡢ᭱㐺໬ၥ㢟ࢆゎ࠿࡞ࡅࢀࡤ࡞ࡽ࡞࠸ࡔ

ᙧ࡟࡞ࡗ࡚࠸ࡿࡇ࡜ࡀከ࠸ࡢ࡛㸪ᐇ㝿ࡢィ⟬ࢆ⾜࠺ࡓࡵࢁ࠺㸬࡞࠾๓㏙ࡋࡓ≧ែ࡜࢚ࢿࣝࢠ࣮౪⤥ࡢ᭱㐺໬ィ⟬࡟ࡣ㸪ࡲࡎ≧ែ✵㛫᪉⛬ᘧࢆලయⓗ࠿ࡘỗ⏝ⓗ࢔ࣝࢦࣜࣉࣟࢢ࣒ࣛࡣ SOCS(Systematic Optimum Control Strategy)ࢬ࣒࡛ᵓᡂࡍࡿၥ㢟࡜㸪ḟ࡟㞳ᩓ᫬㛫ⓗ࡞ゎᘧ࡟ᨵⰋࡍ

࡜࿧ࢇ࡛࠸ࡿࡀ㸪ᮍࡔධฟຊࡢ࣮ࣘࢨ࣮࣭࢖ࣥࢱ࣮ࣇ࢙

ࡿၥ㢟ࡀ࠶ࡗࡓ㸬๓⪅ࡢၥ㢟ࡣ᪤࡟ゎỴࡉࢀ࡚࠸ࡓࡀ㸪࢖ࢫࡣ㛤Ⓨࡋ࡚࠸࡞࠸㸬ᚋ⪅ࡢၥ㢟ゎỴ࡟ᖺ᭶ࢆせࡋࡓ㸬ࡲࡎࡼࡃ▱ࡽࢀ࡚࠸ࡿ
᭱㐺ࣞࢠ࣮ࣗࣞࢱไᚚၥ㢟࡟ྲྀࡾ⤌ࢇࡔ㸬ࡇࡢ᫬࡟㸪㞳ᩓ᫬㛫ࢩࢫࢸ࣒࡟㛵ࡋ࡚㸪㝶క≧ែࣛࢢࣛࣥࢪ࢙஌ᩘἲ
ࢆ᭱ᑠ஧஌ἲ࡛ゎࡃ᪉ἲ[25]ࡀ᭷⏝࡛࠶ࡿ஦ࡀศ࠿ࡗࡓ㸬ホ౯㛵ᩘ䠙ᙜึࡣ㠀ᐃᖖࣔࢹ࡛ࣝ◊✲ࡋ࡚࠸ࡓ㸬ࡋ࠿ࡋ෭ᬮᡣ᥮Ẽ䠇⇕ⓗᛌ㐺ᛶ
䠄⇕ⓗ୰❧䛻㏆䛔䛣䛸䠅ศ㔝࡟࠾࠸࡚᭱㐺ࣞࢠ࣮ࣗࣞࢱࢆ㐺⏝ࡍࡿ฼Ⅼࡣ࠶ࡲࡾ↓࠿ࡗࡓ㸬ࡑࢀࡣᣑᩓ⣔ࡢ≧ែ✵㛫᪉⛬ᘧࣔࢹࣝࡢᅛ᭷
್ࡣᐇ㈇࡛࠶ࡿࡇ࡜ࡀド᫂[28]࡛ࡁࡿࡼ࠺࡟㸪ᮏ᮶Ᏻᐃ࡞⣔ࡔ࠿ࡽ࡛ࡶ࠶ࡿ㸬ࡑࡇ࡛᭱㐺ไᚚ࡛ࡣ࡞ࡃ㸪᭱㐺タィ⌮ㄽ࡬ࡢᛂ⏝ࡀど㔝࡟ධࡗ࡚ࡁࡓ㸬ᘓ≀ࡔࡅ࡛࡞ࡃ⇕

඲⇕஺᥮ჾ

Ỉ䝁䜲䝹
ຍ‵ჾ

䠇┬䜶䝛䝹䜼䞊ᛶ䠄ᾘ㈝⇕㔞䛜᭱ᑠ䛷䛒䜛䛣䛸䠅䠇ప㉁䜶䝛䝹䜼䞊ᛶ䠄䛼䜛䛔෭ Ỉ䛷㛫䛻ྜ䛖䛣䛸䠅䝟䝛䝹䝠䞊䝍䛣䛾ホ౯㛵ᩘ䜢᭱ᑠ䛻䛩䜛⇕౪⤥䛸 ᗘ≧ែ䜢ゎ䛟ᗋᬮᡣ஺᥮ჾ࡜ேయࡢࣔࢹࣝࡶྵࡵ㸪ࡉࡽ࡟ᢅ࠺≧ែࡶ ᗘࡔࡅ࡛࡞ࡃ‵ᗘࡶྵࡵࡓ≧ែ࣋ࢡࢺࣝࢆᣢࡘᣑ኱ࡋࡓ⣔ࡢ⇕࣭‵ᗘᅇ㊰⥙ࣔࢹࣝ࡟㛵ࡋ࡚㸪⾲㸯ࡢ(5)ᘧ࡟♧ࡍࡼ࠺࡞ホ౯㛵ᩘ࠿ࡽฟⓎࡋ㸪ᐃᖖ≧ែࡢ᭱㐺ゎ[26]ࢆᑟ࠸ࡓ㸬ࡇࡢホ౯㛵ᩘࡢ୰㌟ࡣ㸪࠸ࢃࡤ ෭ឤ୰❧ᛶ㸪
┬࢚ࢿᛶ㸪

䛼䜛䛔෭

Ỉ䛷㛫䛻ྜ䛘䜀ప㉁䛾⮬↛䜶䝛䝹䜼䞊䛜᭷ຠ฼⏝䛷䛝䜛ᅗ㸱 ≧ែ࡜࢚ࢿࣝࢠ࣮౪⤥ࡢ᭱㐺໬ࡢィ⟬ᐇ㦂ࣔࢹࣝ⇕࣭᥮Ẽᅇ㊰⥙ࣔࢹࣝ࡟ࡼࡿᘓ⠏⎔ቃᕤᏛศ㔝࡛ࡢ◊✲㛤Ⓨ㸶㸬ࢩ࣑࣮ࣗࣞࢩࣙࣥࣉࣟࢢ࣒ࣛ 1(76㒊ศࡣ㒊ရ࡜ࡋ࡚ࣛ࢖ࣈࣛࣜ࢕Ⓩ㘓ࡋࣔࢹࣝసᡂసᴗຠ

 NETS(NETwork model Simulation)࡜࿧ࢇ࡛࠸ࡿ

⋡ࢆ㧗ࡵࡿࡇ࡜ࡶ࡛ࡁࡿ㸬ቨయ➼ࡣ୍ḟඖ᭷㝈せ⣲ἲ࡛⇕࣭᥮Ẽᅇ㊰⥙ࣔࢹࣝ࡟ࡼࡿࢩ࣑࣮ࣗࣞࢩࣙࣥࣉࣟࢢࣛ

సᡂࡋ㒊ရ໬ࡋ࡚࠾ࡃࡇ࡜ࡀ࡛ࡁࡿ㸬஧ḟඖ᭷㝈せ⣲ἲ࣒ࡢ㛤Ⓨ⤒⦋࡟ࡘ࠸࡚㏙࡭ࡿ㸬➹⪅ࡣࡇࡢ Kernel ⓗࣉࣔࢹࣝࡶ㒊ရ࡜ࡋ࡚඲యࣔࢹࣝࡢ୰࡟⼥ྜࡍࡿࡇ࡜ࡀ࡛

ࣟࢢ࣒ࣛࢆసᡂࡋ࡚ࡁࡓ㸬ࡋ࠿ࡋᅗᙧⓗ࡞ධฟຊฎ⌮ࣉࡁࡿ㸬ࡲࡓᩘᏛⓗ࡟⠇Ⅼᩘࢆῶࡽࡋ࡚⤒῭ⓗ࡞㏆ఝࣔࢹࣟࢢ࣒ࣛ༶ࡕ࣮ࣘࢨ࣮࣭࢖ࣥࢱ࣮ࣇ࢙࢖ࢫࡀ↓࠸࡜౑࠸ࣝࢆసࡿࡇ࡜ࡶ࡛ࡁࡿ㸬ࡇࢀࡣ≧ែ✵㛫᪉⛬ᘧࡢ⃰⦰࡜㞴࠸㸬ᖾ࠸ 2000 ᖺᗘࡲ࡛ 6 ᖺ㛫⥆࠸ࡓ⤒῭⏘ᴗ┬ࡢఫࡶ࿧ࢇ࡛࠸ࡿࡀ㸪᣺ືゎᯒࡢศ㔝࡛ࡢᢏ⾡ࢆᛂ⏝ࡋࡓࡶᏯ㛤Ⓨࣉࣟࢪ࢙ࢡࢺ࡛࠶ࡿࣁ࢘ࢫࢪࣕࣃࣥࡢᶵ఍ࢆᚓ࡚㸪ࡢ࡛࠶ࡿ㸬⇕࣭᥮Ẽᅇ㊰⥙ࡢࣔࢹࣝᵓ㐀ࢆᥥ࠸ࡓᚋ࡛㸪ࡑࡢᅗᙧⓗ๓ᚋฎ⌮ࣉࣟࢢ࣒ࣛࡢ㛤Ⓨ[27]ࢆࡍࡿࡇ࡜ࡀ

⠇Ⅼ㸪୍⯡໬⇕ࢥࣥࢲࢡࢱࣥࢫ㸪ࢰ࣮ࣥࡸὶ㊰ࡢࣔࢹ࡛ࣝࡁࡓ㸬ࡇࡢ㛤Ⓨࡢ᪉ྥᛶࡣ⤖ᯝⓗ࡟௚ࡢከࡃࡢᢏ⾡ィせ⣲ࢆࢡࣜࢵࢡࡋ࡚ࢲ࢖࢔ࣟࢢࢆ㛤ࡁ㸪ෆ㒊ࣃ࣓࣮ࣛࢱ

⟬ࣉࣟࢢ࣒ࣛ࡜ࡣ㏫࡟࡞ࡗࡓ㸬୍⯡ᘓ⠏ᢏ⾡⪅ྥࡅࡼࡾࡢᐃ⩏ࢆ⾜࠺㸬ࣔࢹࣝࡢᵓ㐀ⓗ࠶ࡿ࠸ࡣࣃ࣓࣮ࣛࢱⓗ࡞ࡶᘓ⠏⎔ቃᕤᏛࡢᑓ㛛ᢏ⾡⪅ྥࡅ࡟ࡋ㸪㐺⏝ඛࢆ≉໬ࡍኚ໬ࢆ࣮ࣔࢻኚ໬࡜࿧ࡪ᪉ἲ࡛ᢅ࠼ࡿࡇ࡜ࡶ≉ᚩ࡛࠶ࡿ㸬ࡿࡼࡾࡶỗ⏝࡟ࡋ㸪ィ⟬ෆᐜࡣࣈࣛࢵࢡ࣎ࢵࢡࢫ໬ࡍࡿ

ࡉࡽ࡟⇕㸪᥮Ẽ㸪࢞ࢫὶືᅇ㊰⥙ࣔࢹࣝ┦஫ࡢᑐᛂ௜ࡅ

ࡼࡾࡶ࣍࣡࢖ࢺ࣎ࢵࢡࢫ໬ࡋࡓ㸬ඖ᮶㸪⇕࣭᥮Ẽᅇ㊰⥙ࡣ㸪ࡇࢀࡽࡢ࠺ࡕࡢ஧⪅ࢆẚ㍑ࡋ࡚ぢࡽࢀࡿ⏬㠃࡟࠾࠸ࡢࣔࢹࣝᅗ⮬యࡀ㐃❧᪉⛬ᘧࡢᵓ㐀ࢆ᫂♧ࡋ࡚࠸ࡿ㸬୍࡚┤ឤⓗ࡟⾜࠼ࡿ㸬ࡲࡓᵝࠎ࡞≧ែ㔞ࢆឤ▱ࡋ࡚ᵝࠎ࡞⯡ࡢே࡟ࡣศ࠿ࡾ㞴࠸࠿ࡶࡋࢀ࡞࠸ࡀ㸪ᑓ㛛ᐙ࡟ࡣィ⟬㔞ࢆ᧯సࡍࡿࣇ࢕࣮ࢻࣂࢵࢡไᚚ๎ࢆ⤌ࡴࡇ࡜ࡀ࡛ࡁࡿ㸬ෆᐜࡀᢕᥱ࡛ࡁࡿ㸬ࡶࡕࢁࢇ㐺⏝ၥ㢟ࢆ≉໬ࡋ࡚㝈ᐃࡍNETSOUT ࡢィ⟬⤖ᯝ⾲♧ࡣ኱ูࡋ࡚㸪 ᗘ㸪࢞ࢫ⃰ᗘ㸪ࢀࡤࣔࢹࣝసᡂࡣ⡆༢࡟࡛ࡁࡿࡀ㸪᪂つᛶࡢ࠶ࡿ◊✲ⓗᐊෆᅽ㸪㢼㔞㸪 ෭ឤண ⏦࿌್ PMV ࡸ⇕㈇Ⲵ➼ࡢ≧ၥ㢟᳨ウ࡟ࡣᑐᛂ࡛ࡁ࡞ࡃ࡞ࡿ㸬NETS ࡣᅗ 4 ࡟♧ࡍࡼែ್࡟㛵ࡍࡿ✵㛫ศᕸ⾲♧࡜㸪ࡇࢀࡽࡢ≧ែ್ࡢ᫬⣔ิ࠺࡟㸪ᚑ᮶ࡢᅛᐃⓗ࡞ィ⟬ࣔࢹ࡛ࣝࡣᅔ㞴࡞᪂つࡢᘓ⠏⾲♧࡟ศࡅࡽࢀࡿ㸬ࡲࡓ࣮ࣔࢻኚ໬ࡸࣇ࢕࣮ࢻࣂࢵࢡไ

ⓗᕤኵࢆ᳨ウࡍࡿࡓࡵ࡟㐺ࡋ࡚࠸ࡿ㸬⌧ᅾࡢ࡜ࡇࢁࡣᘓ

ᚚࡢᐇ⾜≧ἣࡶ☜ㄆ࡛ࡁࡿࡼ࠺࡟࡞ࡗ࡚࠸ࡿ㸬ࡉࡽ࡟ᕷ⠏ⓗ┬࢚ࢿᡭἲࡢ᳨ウ㸪 ⇕⎔ቃࡢ᳨ウ㸪ཷືⓗ࡞෭ᬮ㈍ࡢ⾲ィ⟬ࢯࣇࢺ࡛ࡢศᯒࢆྍ⬟࡜ࡍࡿࡓࡵ࡟ CSV ฟᡣ⿦⨨ࡸ⇕※⿦⨨ࡢ᳨ウ㸪✵Ẽ㉁࡜ࡑࡢᨵၿ᪉ἲࡢ᳨ウ㸪

ຊࡶ⾜࠺ࡇ࡜ࡀ࡛ࡁࡿ㸬NETS ࡣᘓ⠏ศ㔝ࡢၥ㢟᳨ウ࡟᥮Ẽࢩࢫࢸ࣒ࡢ᳨ウ㸪⤖㟢ࡢ᳨ウ➼࡟⏝࠸ࡽࢀ࡚࠸ࡿ㸬㝈ࡽࡎ㸪௚ศ㔝࡛ࡶ౑࠼ࡿࡶࡢ࡜ᮇᚅࡋ࡚࠸ࡿ㸬≉࡟᭷ධຊฎ⌮ࣉࣟࢢ࣒ࣛࢆ NETSGEN㸪ฟຊฎ⌮ࣉࣟࢢࣛ㝈య✚ἲ࡟ࡼࡾᗙᶆ⣔࡟⦡ࡽࢀࡎ㸪ᕤᏛⓗุ᩿࡛㏆ఝ໬

࣒ࢆ NETSOUT ࡜࿧ࡧࡑࢀࡒࢀᅗ 5 ࡜ᅗ 6 ࡟♧ࡍ㸬ࡋࡓᐇ⏝ࣔࢹࣝࢆసࡿࡇ࡜࡟ࡼࡾ㸪ᡭ᪩ࡃィ⟬ࡋ᳨࡚ウ

NETSGEN ࡛ࡣᗄࡘ࠿ࡢࣔࢹࣝせ⣲ࢆࡘ࡞ࡂྜࢃࡏ࡚

ࡋࡓ࠸ሙྜ࡟ࡣ᭷⏝࡜ᛮࢃࢀࡿ㸬ࡲࡓ᫬㛫✚ศ࡞࡝ࡢゎࣔࢹࣝᅗࢆᥥ࠸࡚࠸ࡃ㸬ࡲࡓ㢖⦾࡟⏝࠸ࡽࢀࡿ㢮ᆺⓗ࡞ἲࡶ↓᮲௳Ᏻᐃ࡛࠶ࡾᐇ⏝ⓗ࡛ࡶ࠶ࡿ㸬⎔ቃඹ⏕ⓗ䛺ᵝ䚻䛺┬䜶䝛ᡭἲ䛾᳨ウ䛻㐺䛧䛶䛔䜛䠊
ᒇୖ⥳໬
ኴ㝧⇕฼⏝

⵨Ⓨ෭༷

ቨయࡢ㏻Ẽᒙ࡛⇕࡜‵Ẽࡢไᚚኳ஭ᨺᑕ෭ᡣ

䜽䞊䝹䝏䝳䞊䝤ᗋᬮᡣᆅ┙⇕฼⏝⮬↛᥮Ẽ฼⏝
ኪ㛫እẼ෭ᡣ

᫬ኚᛶ䠈㠀⥺ᙧᛶ䠈⇕ὶ䛾ከḟඖᛶ䛜䛒䜚䠈䝅䝇䝔䝮ⓗ䛺ၥ㢟᳨ウ䛻㐺䛩䜛䠊ᅗ㸲 ࢚࢟ࢫࣃ࣮ࢺ⏝ࢶ࣮ࣝ 㻺㻱㼀㻿 ࡢ㐺⏝ၥ㢟12⚄ዉᕝ኱ᏛᕤᏛ◊✲ᡤᡤሗ ➨  ྕ๪ฎ⌮⇕ᅇ㊰⥙䝰䝕䝹

䡡ᅽᦆಀᩘ䞉ᣦᩘ䚸㢼ᅽಀᩘ䡡䡲䢚䡹ఏᑟ⋡䚸✵㝽⋡ᗘᕪࡸእ㒊㢼ࡀཎᅉ࡜࡞ࡿ㝽㛫㢼ࡸ⮬↛᥮Ẽ࡟ࡶ኱ࡁࡃ

䡲䢚䡹ὶືᅇ㊰⥙䢏䡿䢚䢕᥮Ẽᅇ㊰⥙䝰䝕䝹

୍⯡໬⇕䡶䢙䡼䢚䡴䡼䢙䡹
ᮍ▱⠇Ⅼ
᪤▱⠇Ⅼ
䝌䞊䞁
䠄⇕ᐜ㔞᭷䜚䠅
ᮍ▱⠇Ⅼ䠄⇕ᐜ㔞↓䛧䠅

䝰䝕䝹せ⣲

䝷䜲䝤䝷䝸
≀ᛶ್≉ᛶ್

䡡⇕ఏᑟ⋡䚸ẚ⇕䚸
ᐦᗘ

ὶ㊰

୍⯡໬
䡶䢙䡼䢚䡴䡼䢙䡹
ᮍ▱⠇Ⅼ䠄ᐜ㔞᭷䜚䠅

᪤▱⠇Ⅼᮍ▱⠇Ⅼ䠄ᐜ㔞↓䛧䠅

㏦㢼ᶵᙳ㡪ࡉࢀࡿ㸬஧㝵ᘓ࡚ఫᏯࢆ౛࡟࡜ࢀࡤ㸪෤Ꮨᬮᡣᖖែ
࡛ࡣ↮✺ຠᯝ࡛እẼࡀ୍㝵࡟ධࡾ஧㝵࠿ࡽᢤࡅ࡚࠸ࡃ㸬

䝷䜲䝤䝷䝸
㒊ศ䝰䝕䝹

✵㛫ⓗ㞳ᩓ໬
≧ែ✵㛫᪉⛬ᘧ䛾⃰⦰⌮ㄽ᭷㝈せ⣲ἲ䛻䜘䜛

୍㝵࡛ởࡉࢀࡓ✵Ẽࡀ஧㝵࡟ὶࢀࡿࡢ࡛஧㝵ࡢ✵Ẽ㉁ࡀ
䠄౛䠅ྥὶᆺ⇕஺᥮ჾ(౛䠅ከᒙᘓ≀୍ᒙศᝏࡃ࡞ࡿྍ⬟ᛶࡀ࠶ࡿ㸬ᚑࡗ࡚ᐊ㛫ࡢ✵Ẽὶືࡢᐇែࢆ

(౛䠅ቨ䝃䝤䝅䝇䝔䝮඲య䝰䝕䝹⇕䞉᥮Ẽ䡡䜺䝇䛾

ᢕᥱࡍࡿࡇ࡜ࡣ㔜せ࡛࠶ࡿ㸬ࡓࡔࡋࡇ࠺ࡋࡓᚤ㢼㏿ࡢ✵䡡䢏䡬䢀䢚ኚ໬ᐃ⩏䡡⥺ᙧ䢈䡤䡬䢀䢚䢆䢚䡫䡴ไᚚ
䡡PID䢈䡤䡬䢀䢚䢆䢚䡫䡴ไᚚ䡡䢏䡬䢀䢚䠈䡸䡹䡿䢍䢆䢛䢓䢎䡬䡼䠈
ேⅭ୚᮲௳䠈䢈䡤䡬䢀䢚䢆䢚䡫䡴ไᚚ䛾᪥䢆䢛䡼䡬䢙䡡᪥䢆䢛䡼䡬䢙䛾ᮇ㛫ෆ࿘ᮇࢺ࣮ࣞࢧ࢞ࢫࢆ⏝࠸ࡓ᥮Ẽ ᐃἲࡀᚲせ࡛࠶ࡿ㸬ᚑ᮶ࡢ᥮Ẽ ᐃἲࡣ༢ᐊᢅ࠸࡛࠶ࡾ㸪ከᩘᐊࣔࢹ࡛ࣝ✵Ẽὶື⇕䞉᥮Ẽ䡡䜺䝇䛾㐃ᡂ඲య䝰䝕䝹㥑ື᮲௳Ẽὶືࢆ㢼㏿ ᐃ࠿ࡽ┤᥋ⓗ࡟ ᐃࡍࡿࡇ࡜ࡣ㞴ࡋࡃ㸪⤒㊰ࢆ ᐃࡍࡿ᪉ἲࡣ◊✲㛤Ⓨẁ㝵࡟࠶ࡿ㸬ࡲࡓᐊ࡛ࡢ
࢞ࢫࡢΰྜᐜ✚ࡣᗄఱⓗᐜ✚࡟➼ࡋ࠸࡜௬ᐃࡍࡿࡇ࡜ࡀ㻝㻢㻞 㻢㻥㻝㻢㻝 㻢㻤
㻝㻟
㻝㻡
㻝㻠
㻝㻝㻣

⾜ࢃࢀ࡚࠸ࡓࡢ࡛㸪⁫ὶᇦ➼ࡀ࠶ࡗࡓሙྜ࡟ㄗᕪࢆ⏕ࡌ㻟ࡿ㸬ࡘࡲࡾᮏ᮶᥎ᐃࡍ࡭ࡁࣃ࣓࣮ࣛࢱࡣ㸪᥮Ẽ㢼㔞ࡔࡅ

⠇Ⅼ䛹䛖䛧䛾ᑐᛂ௜䛡࡛࡞ࡃ᭷ຠΰྜᐜ✚࡞࡝」ᩘ࠶ࡿ㸬ࡇࢀ࡟ᑐࡋ࡚ᮏࢩࢫ

ᅗ㸳 ධຊฎ⌮ࣉࣟࢢ࣒ࣛ 㻺㻱㼀㻿㻳㻱㻺ࢸ࣒ྠᐃ⌮ㄽࡣᚑ᮶ࡢ ᐃἲࡀᣢࡘࡇࢀࡽࡢၥ㢟ࢆゎỴ࡛ࡁࡿ㸬඲య䝰䝕䝹䛾㐠㌿≧ἣ
ྛ㒊ศ
䛾䝰䞊䝗
≧ែ

㒊ศ␒ྕ
࣮ࣔࢻ␒ྕ




ไᚚ๎
䛾ᐇ⾜
≧ែ

ไᚚ๎␒ྕ
212))


2))











2))


21








21


2))

⇕ᅇ㊰⥙䝰䝕䝹

࠿ࡘ࡚㛤Ⓨࡋࡓ ᐃࢩࢫࢸ࣒ࡣᅗ 7 ࡟♧ࡍ㸬⿦⨨㢮ࡣ㒊ศ࡜ࡣ✵㛫ⓗ࡞ព࿡ࡔࡅ࡛ࡣ࡞ࡃ㸪୍⯡࡟ࣔࢹࣝᵓᡂせ⣲ࡢ඲య㞟ྜ࡟ᑐࡍࡿ㒊ศ㞟ྜࡶព࿡ࡍࡿ㸬





2))


21

ࢹ࣐࣮ࣥࢡ〇ࡢ᪤〇ရࢆ฼⏝ࡋࡓ㸬ࢥࣥࣆ࣮ࣗࢱไᚚ࡟

ไᚚ๎࡜ࡣ㸪௵ពࡢឤ▱㔞࡟ࡼࡿ௵ព
ࡢ᧯స㔞ࡲ࡛ࡢ₇⟬ᡭ⥆ࡁࢆព࿡ࡋ㸪࣮ࣔࢻ␒ྕࡶ᧯స㔞ࡢ୍✀࡜࡞ࡿ㸬᥮Ẽᅇ㊰⥙䝰䝕䝹

ࡼࡾྛᐊ࡟᩿⥆ⓗ࡟ SF6㸦භࣇࢵ໬◲㯤㸧ࢆὀධࡋ࢞ࢫ

䡲䢚䡹ὶືᅇ㊰⥙䢏䡿䢚䢕⃰ᗘኚ໬ࢆసࡾฟࡋࡓ㸬ࡇࡢኚືࡍࡿ࢞ࢫὀධὶ㔞࡜࢞ࢫ⃰ᗘ࠿ࡽ SPID ࡟ࡼࡾ㸪እẼࡶྵࡴࢰ࣮ࣥ㛫ࡢ㢼㔞㸪

≧
ែ
್
叏
✵
㛫
ศ
ᕸ

᭷ຠΰྜᐜ✚㸪࢞ࢫὀධẚ⋡➼ࡢ୕✀ࡢᣑᩓ⣔ࡢࣃ࣓ࣛ
ᗘࡸPMVࡢศᕸ

㢼㔞ࡢศᕸ࡜ࢰ࣮ࣥ㟼ᅽ࣮ࢱࢆ᥎ᐃࡋࡓ㸬 ᐃ஦౛ࢆ⤂௓ࡍࡿ㸬ࢩࢵࢡࣁ࢘ࢫࡢ

㢼㔞䛸ྥ䛝䝌䞊䞁ᗏ㠃㟼ᅽ
➼ ⥺

≧
ែ
್
ࡢ
᫬
㛫
ኚ
໬

࢞ࢫ⃰ᗘࡢศᕸ

≧
ែ
್

ᕪᅽィ

➼⃰ᗘ⥺

㐠㌿Ⅼ

ࢢࡢᩜᆅ࡟ᘓタࡉࢀࡓ஧㝵ᘓ࡚ᮌ㐀ఫᏯ࡛ 2001 ᖺ 11 ᭶࡟⾜ࡗࡓ ᐃ౛࡛࠶ࡿ㸬ᮏ ᐃ᫬࡟ࡣ➨୕✀ᶵᲔ᥮Ẽ≧

≧
ែ
್

≧
ែ
್

᫬㛫
ᗘኚ໬
PMVኚ໬
⇕㈇Ⲵኚ໬
Ⓨ⇕㔞ኚ໬

᥮Ẽᑐ⟇ᢏ⾡㛤Ⓨ㛵㐃࡛㸪ࡘࡃࡤࡢ㸦㈈㸧࣋ࢱ࣮ࣜࣅࣥ

㏦㢼ᶵែ㸦⤥Ẽࣇ࢓ࣥࡀ↓ࡃ᤼Ẽࣇ࢓ࣥࡔࡅ㸧࡛࠶ࡗࡓ㸬࢞ࢫ᫬㛫࢞ࢫ⃰ᗘኚ໬
࢞ࢫ㝖ཤ㔞ኚ໬
࢞ࢫⓎ⏕㔞ኚ໬᫬㛫㢼㔞ኚ໬ࢰ࣮ࣥ㟼ᅽኚ໬
㏦㢼ᶵ㢼㔞ኚ໬
ᕪᅽ䛾ኚ໬⃰ᗘኚ໬ࡢ⏕ᡂ࡜ ᐃࡣ 11 ᭶ 6 ᪥ᮅ࠿ࡽ 11 ᭶ 12 ᪥ᮅࡲ࡛⾜ࡗࡓࡀ㸪ࡇࡢ୰࡛ 11 ᭶ 6 ᪥ 18 ᫬࠿ࡽ 7 ᪥ࡢ 6 ᫬ᅗ㸴 ฟຊฎ⌮ࣉࣟࢢ࣒ࣛ 㻺㻱㼀㻿㻻㼁㼀

ࡲ࡛ 12 ᫬㛫ศࡢᅗ 8 ࡢ ᐃࢹ࣮ࢱ࡟ࡘ࠸࡚ࢩࢫࢸ࣒ྠ
ᐃࢆ⾜ࡗࡓ⤖ᯝࢆᅗ 9 ࡟♧ࡍ㸬ࡇࡢ 44 ಶ⛬ᗘࡢ㢼㔞࡛
࠶ࢀࡤ 3 ᫬㛫ࡄࡽ࠸࡛ࢩࢫࢸ࣒ྠᐃࡍࡿࡇ࡜ࡀከ࠸ࡢ࡛ ⇕ᅇ㊰⥙ࡢ⌮ㄽⓗᒎ㛤ࡢ୰࡛ᑟ࠿ࢀࡓࢩࢫࢸ࣒ྠᐃ⌮࠶ࡿࡀ㸪᭷ຠΰྜᐜ✚࡜࿧ࢇ࡛࠸ࡿᐇ㉁ⓗ࡞ᐊࡢᐜ✚ 11ㄽࡢᛂ⏝࡜ࡋ࡚㛤Ⓨࡋࡓከᩘᐊ᥮Ẽ ᐃࢩࢫࢸ࣒࡟㛵ࡋಶࡢྠᐃࡶྵࡵ㸪ྠᐃࡍ࡭ࡁᮍ▱ᩘࡀከ࠸ࡇ࡜࠿ࡽ㛗ࡵ࡚⤂௓ࡍࡿ㸬ᘓ⠏᥮Ẽࡣ㸪ᶵᲔ᥮Ẽࡔࡅ࡛࡞ࡃ㸪ෆእ

ࡢ 12 ᫬㛫࡜ࡋࡓ㸬ไᚚከⅬ䡲䢚䡹ὀධ䞉✵Ẽ྾ᘬ⿦⨨









]RQH













⃰ᗘ PJP

㺢㺸㺎㺙㺎㺔㺼㺛ὀධὀධὶ㔞 PJVHF

㸷㸬ከᩘᐊ᥮Ẽ ᐃࢩࢫࢸ࣒

㺔㺼㺛ὀධὶ㔞࡜⃰ᗘࡢ ᐃ䢀䢖䡬䡷䡬䡲䢚䡹䢊䢚䢙䢉䢚ィ⟬ᣑᩓ⣔䛾䡸䡹䡿䢍䢆䢛䢓䢎䡬䡼ྠᐃ⌮ㄽ䛸ィ⟬䝥䝻䜾䝷䝮SPID
System ParameterIDentificationᅗ㸵 ࢩࢫࢸ࣒ྠᐃ⌮ㄽࡢᛂ⏝ࡢከᩘᐊ᥮Ẽ ᐃࢩࢫࢸ࣒

㢼㔞ࡢྠᐃ⇕࣭᥮Ẽᅇ㊰⥙ࣔࢹࣝ࡟ࡼࡿᘓ⠏⎔ቃᕤᏛศ㔝࡛ࡢ◊✲㛤Ⓨ࢞ࢫᨺฟ࡜࢞ࢫ⃰ᗘࡢᐃ⿦⨨ࢆྛᐊ࡟ศᩓ㓄⨨

ձ㹊㹂㹉



ὀධὶ㔞
࢞ࢫ⃰ᗘ



















6)⃰ᗘ㸦PJPὀධ㔞㸦PJVHF㸧




























ᅗ㸶 ᐊ 㻸㻰㻷 ࡛ࡢ࢞ࢫὀධὶ㔞࡜⃰ᗘࡢኚ໬ᅗ  ከᩘᐊ᥮Ẽ ᐃࢩࢫࢸ࣒ࡢᨵⰋ
   ջ )࣮࣍ࣝ
ոὒᐊ& ໭ᮾ㸧ջ)࣮࣍ࣝ չࢺ࢖ࣞ






 ն⣡ᡞ 









ռእẼ

ճὙ㠃࣭ᾎᐊ
   յ⋞㛵࣮࣭࣍ࣝ㝵ẁᐊ

᥮Ẽᅇᩘ
ᅇK

 
ղ࿴ᐊ 㢼㔞m3/h㸦᭷ຠΰྜᐜ✚P㸧





࠶ࡿ࡜ゝ࠼ࡿࡔࢁ࠺㸬ᚑࡗ࡚ᘓ⠏⎔ቃᕤᏛࡢィ⟬ࣔࢹࣝ➼ࡶ㸪ཎ⌮ⓗ࡞⌧㇟ࢆゎ᫂ࡍࡿศᯒⓗ࡞ࣔࢹࣝࡔࡅ࡛࡞

ձ/'.



ࡃ㸪ᘓ≀࡜タഛࡢ඲యⓗ࡛ࢩࢫࢸ࣒ⓗ࡞ᣲືࢆ᳨ウ࡛ࡁ




ࢀࡽࡢ᭱㐺࡞⤌ࡳྜࢃࡏࢆ⪃࠼ࡿᘓ⠏ィ⏬࡜タィࡢⰋࡋ࡛࠶ࡿ㸬ᘓタᕤᏛࡢ୍ࡘࡢᏑᅾព⩏ࡶ᭱㐺⥲ྜ໬ᢏ⾡࡟ࡿከඖ㐃❧᪉⛬ᘧⓗ࡞ࣔࢹࣝࡀ㔜せ࡛ࡣ࡞࠸࠿࡜ᛮ࠺㸬ࡇࡢᚿྥࡢࣔࢹࣝࡢ୍ࡘ࡜ࡋ࡚⇕࣭᥮Ẽᅇ㊰⥙ࣔࢹࣝࡢᴫᛕ࡟ࡼࡿ≧ែ✵㛫᪉⛬ᘧࣔࢹࣝࡀୖࡆࡽࢀࡿ࡜ᛮ࠺㸬⌮ㄽయ⣔ࡣᅗ 11 ࡟♧ࡍࡈ࡜ࡃ࡛࠶ࡿࡀ㸪ṧࡉࢀࡓ⌮ㄽࡀ࠶ࡿ㸬ࡋ࠿ࡋⰋ࠸ᘓ≀࡜タഛࢩࢫࢸ࣒ࡣᚲࡎࡋࡶⰋ࠸

ᝏࡋ࡟࠿࠿ࡗ࡚࠸ࡿ㸬ࡘࡲࡾ᭱㐺࡞⥲ྜ໬ࡢ௙᪉ࡀ㔜せ)ᖹ㠃ᅗ

 
մࢺ࢖ࣞ


ᘓタᕤᏛࢆศゎࡍࢀࡤ㸪ࡼࡾᇶ♏ⓗ࡞௚ࡢᕤᏛࡢᐤࡏ
㞟ࡵ࡛࠶ࡾ㸪ᘓタᕤᏛ⊂⮬ࡢࡶࡢࡣ↓࠸࡜ゝࢃࢀࡿࡇ࡜
ᮦᩱࡸ㒊ရࡸタഛᶵჾࢆ౑࠼ࡤ࡛ࡁࡿࡶࡢ࡛ࡣ࡞ࡃ㸪ࡇշὒᐊ$ ༡す㸧  


պὒᐊ% ༡ᮾ㸧 
յ⋞㛵࣮࣭࣍ࣝ㝵ẁᐊ㸯㸮㸬࠾ࢃࡾ࡟)ᖹ㠃ᅗ

ᅗ㸷 㢼㔞࡜᭷ຠΰྜᐜ✚ࡢࢩࢫࢸ࣒ྠᐃ⤖ᯝㄢ㢟࡜㛤Ⓨⓗ࡞ㄢ㢟ࡣከ࠸㸬ఏ⇕ࡸ᥮Ẽࡣᵝࠎ࡞ᕤᏛศ
㔝࡟ඹ㏻ࡍࡿၥ㢟࡛࠶ࡿࡀ㸪➹⪅ࡢ⤂௓ࡍࡿࣔࢹࣝࡀ௚
ࡢศ㔝࡛ࡶఱ࠿ࡢཧ⪃࡟࡞ࢀࡤᖾ࠸࡛࠶ࡿ㸬࡞࠾௚ศ㔝ᮏከᩘᐊ᥮Ẽ ᐃἲࡣࣁ࣮ࢻ࢙࢘࢔࡟㛵ࡋ࡚㛤Ⓨㄢ㢟ࡀṧࡉࢀ࡚࠸ࡿ㸬⌧≧࡛ࡣ࢞ࢫ⃰ᗘศᯒィࡀ 1 ಶ࡛ከᩘࡢ᪉࡟ࡶ࡞ࡿ࡭ࡃศ࠿ࡾ᫆ࡃ㏙࡭ࡓࡘࡶࡾ࡛࠶ࡿࡀ㸪⣬ᖜࡢ㛵ಀ࡛୙༑ศ࠿ࡶࡋࢀࡎ㸪࠾チࡋ㢪࠸ࡓ࠸㸬ᐊࡢࢺ࣮ࣞࢧ࢞ࢫ⃰ᗘࢆィࡿࡓࡵ࡟㸪ྛᐊ࠿ࡽከⅬ✵Ẽ᥇ྲྀษ᭰ჾࡲ࡛ࢳ࣮ࣗࣈࢆ㓄⨨ࡋ࡚࠾ࡁ㸪1 ศẖ࡟྾ᘬࡍࡿ
≧ែ✵㛫ἲᐊࢆษࡾ᭰࠼ࡿ㸬ᚑࡗ࡚ఫᏯつᶍ࡛ࡶᩘ༑࣓࣮ࢺࣝ࡟࡞ࡿ⇕ᅇ㊰⥙䝰䝕䝹

ࢳ࣮ࣗࣈࢆ㓄⨨ࡍࡿᡭ㛫ࡀᐇ⏝ᛶࢆᦆࡡࡿୖ࡟㸪ᮏ᮶ࡣ඲ᐊࡢྠ᫬ⓗ࡛㐃⥆ⓗ࡞࢞ࢫ⃰ᗘࡀᚲせ࡞࡜ࡇࢁࢆ㸪
ఱศ࠿

タィᢏ⾡

࠾ࡁࡢ ᐃ್࡛┤⥺⿵㛫㏆ఝࡍࡿࡇ࡜࡟ࡼࡿㄗᕪ࡞࡝ࡢ

䝅䝭䝳䝺䞊䝅䝵䞁
1(76ḞⅬࡀ࠶ࡿ㸬ࡑࡇ࡛ᅗ 10 ࡟♧ࡍᵝ࡟㸪࢞ࢫᨺฟჾ࡜ศᯒ
ჾࢆ 1 ࡘࡢ⟽࡟ࢥࣥࣃࢡࢺ࡟ࡲ࡜ࡵࡓࡶࡢࢆᐊᩘศ⏝ពࡋྛᐊ࡟ศᩓࡋ࡚⨨ࡃศᩓᆺࡢࢩࢫࢸ࣒࡟ᨵⰋࡋࡓ࠸࡜

᭱㐺໬⌮ㄽ

ᐃᢏ⾡

ไᚚᢏ⾡

䝅䝇䝔䝮ྠᐃ⌮ㄽ᭱㐺ไᚚ⌮ㄽ

63,'

62&6⪃࠼࡚࠸ࡿ㸬ᅗ  ⌮ㄽయ⣔

14⚄ዉᕝ኱ᏛᕤᏛ◊✲ᡤᡤሗ ➨  ྕ

<ㅰ㎡>

1990

 ࡇࡢ⇕࣭᥮Ẽᅇ㊰⥙ࣔࢹࣝ࡟ᇶ࡙࠸ࡓ㸪ࡉࡽ࡞ࡿ◊✲[13] Lars Jensen,"Determination of Flows and Volumes in Multiple Cell࡜ᒎ㛤ࡢሙࢆ୚࠼࡚㡬࠸ࡓ⚄ዉᕝ኱Ꮫ࡟ឤㅰࡍࡿ㸬ࡲࡓ

Systems",Paper to ROOMVENT-87,Report BKL 1987:3(E),Lundᙜึ◊✲ࡢⓎ᝿ࢆ୚࠼࡚㡬࠸ࡓ᪩✄⏣኱Ꮫ࡜㸪㛤Ⓨࡢሙ

Institute of Technologyࢆ୚࠼࡚㡬࠸ࡓΎỈᘓタ㸪ࡑࡋ࡚ጤク◊✲➼࡛㛤Ⓨࡢ㈨[14] Charles L. Lawson, Richard J. Hanson," Solving Least Squares※ࢆ୚࠼࡚ୗࡉࡗࡓᪧ㏻⏘┬ࡢࣁ࢘ࢫࢪࣕࣃ࣭ࣥࣉࣟࢪ

Problems", Prentice-Hall, Inc., Englewood Cliffs, New Jersey, 1974,࢙ࢡࢺ࡜ከࡃࡢ௻ᴗ㸪◊✲ୖࡢᚚᩍ♧࡜㆟ㄽࢆ㡬࠸ࡓᏛ

ISBN 0 89871 356 0 (pbk.)

఍ࡸጤဨ఍࡛ࡢ᪉ࠎ㸪ࡉࡽ࡟ࡇࡢ⤒⦋࡛࠾ୡヰ࡟࡞ࡗࡓ㸪[15] Hiroyasu Okuyama,"Recent Progress on the Multi-Chamberᮏᩥ࡜ཧ⪃ᩥ⊩࡛ࡣ㏙࡭ᑾࡃࡏ࡞࠿ࡗࡓከࡃࡢ᪉ࠎ࡟ࡶ

Airflow Measurement System",ISRACVE(International Symposium onឤㅰࡍࡿ㸬Room Air Convection and Ventilation Effectiveness),July 1992,
Tokyo,Japan,pp.351-356

ཧ⪃ᩥ⊩[16] Takao Sawachi, Haruki Osawa, Hironao Seto, Yoshinori Taniguchi[1] Pipes,L.A."Matrix Analysis of Heat Transfer Problems",Journal ofand Shigeki Onishi: "A New Experimental Approach for the Evaluation

Franklin Institute, Mar.1957

of Domestic Ventilation Systems, Part 1 - Description of experimental[2] Mitalas,G.P. and Stepenson,D.G."Room Thermal Response

Facilities

Factors",ASHRAE Transaction Vol.73,Part 1,1967

Buoyancy-Driven[3] Clarke J A ," Prospects for Truly Integrated Building Performance

Transactions, 1998 Part 1, pp570-584

Simulation", Sixth International IBPSA Conference(BS99), Kyoto, Japan,[17] ዟᒣ༤ᗣ,⇕ᅇ㊰⥙ࡢཎ㧗ḟ≧ែ᪉⛬ᘧࣔࢹࣝࡢࢩࢫࢸ࣒ࣃ

September 1999, Vol.3,pp1147-1154

࣓࣮ࣛࢱྠᐃࢆ≧ែኚᩘࡢ㧗㝵ᚤศ࡟ࡼࡿపḟ໬᪉⛬ᘧࢩࢫࢸ

and

Their

Application

Airflow

in

to

the

Two-Story

QuantificationofHouses",ASHRAE[4] Edward F. Sowell, Philip Haves, "Numerical Performance of The࣒ࡢほ ࠿ࡽ⾜࠺⌮ㄽ࡬ࡢᒎ㛤,✵Ẽㄪ࿴㺃⾨⏕ᕤᏛ఍Ꮫ⾡ㅮ₇఍

Spark Graph-Theoretic Simulation Program", Sixth International IBPSA

ㅮ₇ㄽᩥ㞟,F-9,2004 ᖺ 9 ᭶,pp437-440

Conference(BS99), Kyoto, Japan, September 1999, Vol.1,pp53-60[18] Hiroyasu Okuyama, et al., “System parameter identification theory[5]

Wisconsin,

and uncertainty analysis methods for multi-zone building heat transfer

Madison:"Modeling of Solar Heating and Air Conditioning",

and infiltration”, Building and Environment, Elsevier, Volume 54,

NSF/RANN/SE/GI/34029/PR/72/4,1972.

August 2012, Pages 39–52[6] Julius T. Tou, (⩻ヂ) ୰ᮧ჆ᖹ, ఀ⸨ṇ⨾, ᯇᑿຮ, "⌧௦ไᚚ⌮[19] Hiroyasu Okuyama, Yoshinori Onishi, Shin-ichi Tanabe, Seiichi

ㄽ" ࢥࣟࢼ♫, 1969, ➨㸱∧

Kashihara, Statistical data analysis method for multi-zonal airflow[7] Helmut E.Feustel,Juergen Dieris,"A Survey of Air Flow Models formeasurement using multiple kinds of perfluorocarbon tracer gas,

Multi-zone Structures",Indoor Environment Program Applied Science

Building and Environment, Vol.44, 2009, pp546–557

Division,Lawrence[20] JIS A2201. Test method for performance of building airtightness by

Solar

EnergyLaboratory,

University

BerkeleyofLaboratory,Berkeley,CA

94720,USA,Mar.1991,LBL-30288,UC-350

fan pressurization,Annex 3 (informative). Calculation of a, n and the[8] D.V.Pryor and C.Byron Winn:"A Sequential filter used for parameter

confidence intervals. 1st ed; 2003-4-1

estimation in a passive solar system",Solar Energy Vol.28, No.1, 1982,[21] ISO 9972. Thermal performance of buildings - determination of air

pp65-73

permeability of buildings - fan pressurization method, Annex C[9] ዟᒣ༤ᗣ,"୍⯡ᣑᩓࢩࢫࢸ࣒ࡢᅇ㊰⥙࡟ࡼࡿ≧ែ✵㛫᪉⛬ᘧ(informative). Recommended procedure for estimating uncertainty in࡜ࡑࡢࢩࢫࢸ࣒ࣃ࣓࣮ࣛࢱࡢྠᐃ⌮ㄽ㸦ࡑࡢ㸰:᭷㝈せ⣲ἲ࡟ࡼࡿ

derived quantities. 2nd ed;2006-05-01.

ࢩࢫࢸ࣒ࣃ࣓࣮ࣛࢱࡢ㏫᥈ၥ㢟࡬ࡢ㐺⏝㸧",᪥ᮏᘓ⠏Ꮫ఍኱఍Ꮫ

[22] Hiroyasu Okuyama, et al. ,“Reconsideration of parameter estimation⾡ㅮ₇᱾ᴫ㞟,1984 ᖺ 10 ᭶,pp.657-658

and reliability evaluation methods for building airtightness measurement[10] Frank W. Sinden: "Multi-Chamber Theory of Air Infiltration",using fan pressurization”, Building and Environment, Elsevier, Volume

Building and Environment, Vol.13, Pergamon Press 1978, pp21-29

47, January 2012, Pages 373–384[11] David Etheridge, Mats Sandberg,"Building Ventilation: Theory and[23] ISO 12569. Thermal performance of buildings - determination of air

Measurement",John Wiley & Sons Ltd, 1996

change in buildings - tracer gas dilution method, 6.1 calculation of air[12]) Hiroyasu Okuyama,"System Identification Theory of the Thermalchange rate, p8, Annex C (informative). Confidence intervals, pp14-15,

Network Model and an Application for Multi-chamber Airflow

annex D (informative).1st ed.; November 2000. Propagation of error

Measurement",Building and Environment, Vol.25, No.4, pp349-363,

analysis, pp. 16-17.

⇕࣭᥮Ẽᅇ㊰⥙ࣔࢹࣝ࡟ࡼࡿᘓ⠏⎔ቃᕤᏛศ㔝࡛ࡢ◊✲㛤Ⓨ

Investigation",Proceedings[24] Hiroyasu Okuyama, et al., “Uncertainty analysis and optimum

Numerical

concentration decay term for air exchange rate measurements:

Conference on Indoor Air Quality and Climate, volume (2), 1996,

of

the

7th

International

Estimation methods for effective volume and infiltration rate”, Building

pp485-490

and Environment, Elsevier, Volume 49, March 2012, Pages 182–192.

[27] Hiroyasu Okuyama, "Thermal and Airflow Network Simulation[25] D.H.Owens, "Multivariable and Optimal Systems",Academic Press,

Program NETS" Proceedings of the 6th International IBPSA Conference

1981, ISBN 0 12 531720 4(Building Simulation '99), Kyoto, September 1999, pp1237-1244[26] Hiroyasu Okuyama,"Optimization Theory for State and Energy[28] ዟᒣ༤ᗣ,"ᘓ⠏≀ࡢ⇕ᅇ㊰⥙ࣔࢹࣝ࡟㛵ࡍࡿ⌮ㄽⓗ◊✲",༤Supply Based on a Heat and Moisture Transfer Network Model andኈྕᏛ఩ㄽᩥ,᪩✄⏣኱Ꮫ,1987 ᖺ 12 ᭶㧗ᐦᗘࣂ࢖࣐࢜ࢫࣈࣜࢣࢵࢺࡢ╔ⅆ⇞↝≉ᛶ㹼 ࣂ࢖࣐࢜ࢫࡢ࢚ࢿࣝࢠ࣮฼⏝࡟ྥࡅ࡚ 㹼ఀᮾ ᘯ⾜㸨㸪஭⏣Ẹ⏨㸨㸨㸪⸨⏣ಟ㸨㸨㸨

Ignition and Combustion Characteristics of Highly Densified Biomass Briquette
Hiroyuki ITO㸨, Tamio IDA㸨㸨, Osamu FUJITA㸨㸨㸨ࡢ◊✲ㄽᩥ࡜ࡋ࡚☜ㄆ࡛ࡁࡿࡶࡢࡣᑡ࡞࠸ࡢࡀ⌧≧࡛࠶㸯㸬⥴ゝᆅ⌫ ᬮ໬࠾ࡼࡧ໬▼⇞ᩱ㈨※ᯤῬࡢၥ㢟࠿ࡽ㸪㏆ᖺࡿ㸬〇㐀ࡋࡓࣂ࢖࣐࢜ࢫ⇞ᩱࢆ⇞↝ࡋ࡚࢚ࢿࣝࢠ࣮ࢆྲྀ

෌⏕ྍ⬟࢚ࢿࣝࢠ࣮ࡀὀ┠ࡉࢀ࡚࠸ࡿ㸬࣮࢝࣎ࣥࢽ࣮ࣗ

ࡾฟࡍୖ࡛㸪⇞ᩱࡢ⇞↝≉ᛶࢆ⌮ゎࡍࡿࡇ࡜ࡣ㸪ຠ⋡ࡢࢺࣛࣝࡢ⪃࠼᪉ࢆ⫼ᬒ࡜ࡍࡿ᳜≀⏤᮶ࣂ࢖࣐࢜ࢫࡢ⇞ᩱࡼ࠸᭱㐺࡞⇞↝ᶵჾࡢタィ࡜࠸࠺ほⅬ࠿ࡽ㠀ᖖ࡟㔜せ࡛໬ࡶࡑࡢࡦ࡜ࡘ࡛࠶ࡿ㸬࣮࢝࣎ࣥࢽ࣮ࣗࢺࣛࣝ࡜ࡣ㸪᳜࠶ࡿ㸬≀ࡀ኱Ẽ୰࠿ࡽ྾཰ࡍࡿ஧㓟໬Ⅳ⣲㔞࡜㸪ࡑࡢ᳜≀ࢆࣂᮏ◊✲࡛ࡣ㸪㧗ᐦᗘᅛయࣂ࢖࣐࢜ࢫࣈࣜࢣࢵࢺ࡛࠶ࡿ

࢖࣐࢜ࢫ⇞ᩱ࡜ࡋ࡚⇞↝ࡋࡓ㝿࡟ᨺฟࡉࢀࡿ஧㓟໬Ⅳ⣲ࣂ࢖࢜ࢥ࣮ࢡࢫ(Bio-coke㸸௨ୗ BIC ࡜⾲グ)(8)ࢆ㸪⇞↝⅔

㔞ࢆᆒ⾮ࡉࡏࡿ㸪ࡍ࡞ࢃࡕ኱Ẽ୰ࡢ஧㓟໬Ⅳ⣲㔞ࢆேⅭ࡛ຍ⇕ࡋࡓ㝿ࡢ⇕ศゎ࣭╔ⅆ࣭⇞↝≉ᛶࢆㄪ࡭ࡓ㸬BICⓗάື࡟ࡼࡗ࡚ቑ኱ࡉࡏ࡞࠸࡜࠸࠺ᴫᛕ࡛࠶ࡿ㸬ࣂ࢖࢜ࡣ㸪㕲⁐ゎ⅔ࡢ▼Ⅳࢥ࣮ࢡࢫ௦᭰⇞ᩱ࡜ࡋ࡚㛤Ⓨࡉࢀࡓ࣐ࢫࡢ⇞ᩱ฼⏝ࡣྂࡃ࠿ࡽ⾜ࢃࢀ࡚࠾ࡾ㸪⌧ᅾ࡛ࡶⓎᒎ㧗ᐦᗘ࣭㧗◳ᗘࡢࣂ࢖࣐࢜ࢫࣈࣜࢣࢵࢺࡢ࿧⛠࡛࠶ࡾ㸪

㏵ୖᅜࢆ୰ᚰ࡜ࡋ࡚ࣂ࢖࣐࢜ࢫᅛయࢆ┤᥋⇞↝ࡍࡿࡇ࡜

ᮌ㉁ᮦࡣ໚ㄽࡢࡇ࡜ᗫᲠ≀➼࠶ࡽࡺࡿ᳜≀⏤᮶ࡢࣂ࢖࢜

࡟ࡼࡾᗈࡃ฼⏝ࡉࢀ࡚࠸ࡿ(1)㸬ᅛయࣂ࢖࣐࢜ࢫ⇞ᩱࡢ฼࣐ࢫᮦ࠿ࡽ〇㐀࡛ࡁࡿࡇ࡜࠿ࡽ㸪ཎᮦᩱ㈨※ㄪ㐩ࡀẚ㍑⏝ᙧែ࡜ࡋ࡚ࡣ㸪ࣂ࢖࣐࢜ࢫᮦࢆࢳࢵࣉ≧ࡸᚤ⢊≧࡟⢊ⓗᐜ᫆࠿ࡘపࢥࢫࢺ࡜࠸࠺≉㛗ࡀ࠶ࡾ㸪௒ᚋ㸪BIC ⇞ᩱ○ࡋ࡚౑⏝ࡍࡿࡶࡢ㸪࣌ࣞࢵࢺࡸࣈࣜࢣࢵࢺ࡟ 1 ḟຍᕤࡢ฼ά⏝ࡀᮇᚅࡉࢀ࡚࠸ࡿ㸬ࡋ࠿ࡋ࡞ࡀࡽ㸪BIC ࡢ⇞↝ࡋ࡚౑⏝ࡍࡿࡶࡢ㸪ࡲࡓⅣ໬࣭࢞ࢫ໬ࡢ๪⏕≀࡜ࡋ࡚ᚓ≉ᛶ࡟㛵ࡋ࡚ࡶ௚ࡢᅛయࣂ࢖࣐࢜ࢫ⇞ᩱ࡜ྠᵝ࡟ᇶ♏◊ࡽࢀࡿࢳ࣮ࣕࢆ฼⏝ࡍࡿࡶࡢࡀ࠶ࡿ㸬ࣂ࢖࣐࢜ࢫᮦࢆᅽ

✲ࡀᑡ࡞ࡃ㸪BIC ࡢᇶ♏⇞↝≉ᛶ㸪࡜ࡃ࡟࣎࢖࣮ࣛ⇞↝⦰ᡂᙧࡋ࡚࣌ࣞࢵࢺࡸࣈࣜࢣࢵࢺ໬ࡍࡿࡇ࡜࡛㸪࢚ࢿࣝ

⅔➼ࢆ᝿ᐃࡋࡓ⇞↝≉ᛶ࡟㛵ࡋ࡚ࡣ➹⪅ࡽࡢ◊✲(9-11)ࢆ

ࢠ࣮ᐦᗘࢆ኱ࡁࡃฟ᮶ࡿࡇ࡜࠿ࡽ㈓ⶶࡸ㍺㏦ࢥࢫࢺࢆ๐

㝖࠸࡚࡯࡜ࢇ࡝ぢࡽࢀ࡞࠸㸬௒ᚋ㸪BIC ࡢ฼⏝⠊ᅖᣑ኱ῶ࡛ࡁࡿ࡯࠿㸪⇞ᩱࡢᆒ㉁ᛶࢆ㧗ࡵࡽࢀࡿࡇ࡜࠿ࡽ⇞ᩱ࠾ࡼࡧ᭱㐺࡞⇞↝ᙧែ㸪⇞↝ჾᙧ≧ࡸ㐠㌿᮲௳ࢆỴᐃࡍࡢ⇞↝ไᚚࢆ⾜࠺ୖ࡛᭷฼࡜࡞ࡿ㸬ࡿ࡟ࡣ㸪BIC ࡢᇶᮏⓗ࡞⇞↝≉ᛶࢆᢕᥱࡍࡿᚲせࡀ࠶ࡿ㸬ᅛయࣂ࢖࣐࢜ࢫࡢ⇞ᩱ໬࡟㛵ࡋ࡚㸪⇞ᩱ〇㐀࣭ᙉᗘホ(2-6)ᮏ✏࡛ࡣ㸪ᖹᡂ 20 ᖺᗘ࡟໭ᾏ㐨ୗᕝ⏫࡛⾜ࢃࢀࡓࠕప

㸬୍᪉㸪ỌⅣ⣲♫఍࡟ྥࡅࡓᢏ⾡ࢩ࣮ࢬⓎ᥀࣭♫఍ࢩࢫࢸ࣒ᐇド஦

ᶫࡽ(7)ࡀᣦ᦬ࡋ࡚࠸ࡿࡼ࠺࡟㸪⇞↝≉ᛶ࡟㛵ࡋ࡚ࡣ㸪ಶࠎᴗ࡛ࠖྲྀࡾୖࡆࡽࢀࡓࢱࢹ⛉ࡢከᖺⲡ࡛࠶ࡿ࢖ࢱࢻࣜࢆ

౯➼ࡢほⅬ࠿ࡽከࡃࡢ◊✲ࡀ⾜ࢃࢀ࡚࠸ࡿ

ཎᩱ࡜ࡍࡿ BIC ࡟↔Ⅼࢆᙜ࡚㸪ࡇࡢ⇞↝⌧㇟࡟㛵ࢃࡿᇶ*෸ᩍᤵ ᶵᲔᕤᏛ⛉
Associate Professor, Dept. of Mechanical Engineering*෸ᩍᤵ ㏆␥኱Ꮫ⌮ᕤᏛ㒊 ᶵᲔᕤᏛ⛉
Associate Professor, Dept. of Mechanical Engineering, Kinki
University*ᩍᤵ ໭ᾏ㐨኱Ꮫ኱Ꮫ㝔ᕤᏛ◊✲㝔 ᶵᲔᏱᐂᕤᏛ㒊㛛
Professor, Div. of Space and Mechanical Engineering,
Hokkaido University

ᮏⓗ࡞ᛶ㉁㸪⇕ศゎ࠾ࡼࡧ⇞↝≉ᛶࢆ⤂௓ࡍࡿ㸬㸰㸬࢖ࢱࢻࣜ BIC ࡢᇶᮏⓗ࡞ᛶ㉁2.1 ࢖ࢱࢻࣜ BIC ࡢ〇㐀࠾ࡼࡧ≀⌮ⓗᛶ㉁ ໭ᾏ㐨ୗᕝ⏫ෆ࡟⮬⏕ࡋ⏝㏵ࡢᑡ࡞࠸ከᖺⲡࡢ࢖ࢱࢻ
ࣜࢆ BIC ཎᮦᩱ࡜ࡋ࡚౑⏝ࡋࡓ㸬ࡇࢀࡣୗᕝ⏫ෆ࡟࠶ࡿ㧗ᐦᗘࣂ࢖࣐࢜ࢫࣈࣜࢣࢵࢺࡢ╔ⅆ⇞↝≉ᛶࣅࢽࣝࣁ࢘ࢫࡢᬮᡣ⏝⇞ᩱ࡬ࡢ౑⏝ࢆ᝿ᐃࡋࡓࡶࡢ࡛㸪ࡧ 13wt%⛬ᗘ࡛࠶ࡿࡇ࡜ࡀࢃ࠿ࡿࠋࡲࡓ㸪Ỉศࡢ⵨Ⓨࡣᾘ㈝ᆅ࡟࡚Ᏻ౯࡟ㄪ㐩ฟ᮶ࡿ฼Ⅼࡀ࠶ࡿ㸬཰㞟᫬ࡢ࢖ࢱ

400K ௨ୗ㸪᥹Ⓨศࡢᨺฟࡣ⣙ 450K ௨ୖ࡛ぢࡽࢀࡿ㸬ࢻࣜࡢእほ෗┿ࢆᅗ 1 ࡟♧ࡍ㸬཰㞟ࡉࢀࡓ࢖ࢱࢻࣜࡣ⮬↛஝⇱ࡢᚋ㸪⢊○ჾ࡛◚○ᚋ㸪㔠ᆺ࡟඘ሸࡋ࡚ຍ⇕ᅽ⦰ᡂᆺࡍࡿ㸬BIC ࡣ౑⏝ࡍࡿ㔠ᆺࡢᙧ≧㸪ᑍἲ࡟ࡼࡾ௵ព
࡟ᡂᆺ࡛ࡁࡿࡀ㸪ࡇࡇ࡛ࡣȭ48mm85mm ࡢ෇⟄ᙧ≧࡜ࡋࡓ㸬᳜≀⏤᮶ࡢࣂ࢖࣐࢜ࢫヨᩱࡣ୺࡟㸪ࢭ࣮ࣝࣟࢫ㸪࡬࣑ࢭ࣮ࣝࣟࢫ࠾ࡼࡧࣜࢢࢽࣥ࠿ࡽᵓᡂࡉࢀࡿࡇ࡜ࡀ▱ࡽࢀ࡚࠸ࡿ㸬඘ሸヨᩱࢆⅣ໬㛤ጞ௨ୗࡢ ᗘ࡟ຍ⇕ࡋ࡞ࡀࡽຍᅽಖᣢࡍࡿࡇ࡜࡛㸪ヨᩱ୰ࡢࣜࢢࢽࣥ࠾ࡼࡧ࡬࣑ᅗ ࢖ࢱࢻࣜ %,& ࡢ⇕㔜㔞ศᯒ⤖ᯝࢭ࣮ࣝࣟࢫࡀ㌾໬࠶ࡿ࠸ࡣ⁐ゎࡋ࡚⤖ྜ๣࡜ࡋ࡚స⏝ࡋ㸪㧗ᐦᗘ࠿ࡘ㧗◳ᗘࡢ BIC ࡀᙧᡂࡉࢀࡿ㸬ᅗ 2 ࡟࢖ࢱࢻࣜ ⇕㔜㔞ศᯒ⤖ᯝ(ᅗ 3)࠿ࡽ㸪❅⣲㞺ᅖẼ୰ࡢỈศ࠾ࡼࡧ

BIC ࡢእほ෗┿ࢆ♧ࡍ㸬᥹Ⓨศࡢᨺฟ࡟ࡼࡿ㉁㔞ῶᑡ࡟ࡘ࠸࡚㸪ࡑࢀࡒࢀ࢔ࣞࢽ
࢘ࢫ๎࠿ࡽᑟ࠿ࢀࡿᘧ(1)ࢆ㐺⏝ࡋ㸪ᅗ 4 ࡟♧ࡋࡓ㸬

§ 1 dm ·ln¨¸© m dt ¹

ln A 

E
RT(1)

ࡇࡇ࡛㸪m : Ỉศ࠶ࡿ࠸ࡣ᥹Ⓨศࡢṧ␃㉁㔞㸪t : ᫬㛫㸪ᅗ ࢖ࢱࢻࣜእほA : 㢖ᗘᅉᏊ㸪E : άᛶ໬࢚ࢿࣝࢠ㸪R : Ẽయᐃᩘ㸪T :ᅗ ࢖ࢱࢻࣜ %,& እほᗘࢆ♧ࡍ㸬⾲ 1 ࡟㸪࢖ࢱࢻࣜ㸪ᮌ㉁࣌ࣞࢵࢺ(ᩘ✀ࡢᖹᆒ್)(12)࠾ࡼ

-5

ࡧ℡㟷Ⅳ(13)ࡢඖ⣲ศᯒ⤖ᯝࢆ♧ࡍ㸬࢖ࢱࢻࣜࡣ㸪ᮌ㉁࣌
㏆࠸್ࢆ♧ࡋ࡚࠸ࡿࡇ࡜ࡀࢃ࠿ࡿ㸬ࡇࡢ࢖ࢱࢻࣜࢆ BIC
࡟ຍᕤࡍࡿࡇ࡜࡛ᐦᗘࡣ 1300kg/m3 ⛬ᗘ࡜࡞ࡿࡀ㸪ࡇࢀ
3

ࡣ㏻ᖖࡢᮌ㉁࣌ࣞࢵࢺࡢᐦᗘ600kg/m ࡢ࠾ࡼࡑ2 ಸᙉ࡛࠶ࡾ㸪࢚ࢿࣝࢠ࣮ᐦᗘࡣ࢖ࢱࢻࣜ BIC ࡢ᪉ࡀ኱ࡁ࠸㸬ln(1/m·dm/dt)

ࣞࢵࢺࡼࡾࡶⅣ⣲๭ྜ㸪Ⓨ⇕㔞࡜ࡶ࡟ⱝᖸᑠࡉ࠸ࡀᴫࡡ

Volatile

-6
-7
-8
-9
-10
0.001

Water vapor
0.002

0.003

0.004

1/T

⾲  ࢖ࢱࢻࣜࡢඖ⣲ศᯒ⤖ᯝᅗ Ỉศ࠾ࡼࡧ᥹Ⓨศࡢ࢔ࣞࢽ࢘ࢫࣉࣟࢵࢺ

࢖ࢱࢻࣜ

ᮌ㉁࣌ࣞࢵࢺ(12)℡㟷Ⅳ(13)

17890

20300

32020

C [wt%]

47.72

50.3

77.22

H [wt%]

5.95

5.7

5.60

N [wt%]

0.47

0.22

1.31

Water [wt%]

6.11

7.7

-

GCVa
[kJ/kg]Experimental result
Volatile matter
Water vapora : Gross Calorific Value
2.2 ࢖ࢱࢻࣜ BIC ࡢ⇕ศゎ≉ᛶ ࢖ࢱࢻࣜ BIC ࡢ⇕㔜㔞ศᯒ⤖ᯝࡢ౛ࢆᅗ 3 ࡟♧ࡍ㸬⇕㔜㔞ศᯒ࡟ࡣ㸪♧ᕪ⇕ኳ⛗㸦┿✵⌮ᕤ TGD-5000RH ᆺ㸧ࢆ⏝࠸㸪ヨᩱ㉁㔞 20mg㸪᪼ ㏿ᗘ 5K/min ࡛㸪✵Ẽ୰࠾ࡼࡧ❅⣲㞺ᅖẼ୰࡟࡚ᐇ᪋ࡋࡓ㸬ᅗ 3 ࡢ⤖ᯝࡼࡾ㸪Ỉศ㸪᥹Ⓨศ࠾ࡼࡧᅛᐃⅣ⣲ศࡣ㸪ࡑࢀࡒࢀ 10wt%, 70wt%࠾ࡼᅗ Ỉศ࠾ࡼࡧ᥹Ⓨศᨺฟ≉ᛶ ❅⣲㞺ᅖẼ୰ ࢔ࣞࢽ࢘ࢫᘧ⟬ฟ್࡜ᐇ㦂್ࡢẚ㍑ 

ᅗ 4 ࡼࡾ㸪Ỉศ⵨Ⓨ࡜᥹Ⓨศᨺฟࡢάᛶ໬࢚ࢿࣝࢠ࣮(E)࠾ࡼࡧ㢖ᗘᅉᏊ(A)ࡣࡑࢀࡒࢀ㸪Ỉศ࡟ᑐࡋ A=1.759
1014 [1/s], E=107.7 [kJ/mol], ᥹Ⓨศ࡟ᑐࡋ A=3.372103[1/s] , E=73.40 [kJ/mol]ࢆᚓࡿ㸬ࡇࢀࡽࡢ್ࢆ⏝࠸ࡓ⇕㔜㔞⚄ዉᕝ኱ᏛᕤᏛ◊✲ᡤᡤሗ ➨  ྕศᯒ࡟࠾ࡅࡿ㉁㔞ῶᑡࡢண ್࡜㸪ᐇ㦂⤖ᯝࢆẚ㍑ࡋࡓ
⤖ᯝࢆᅗ 5 ࡟♧ࡍ㸬ᅗࡼࡾ㸪❅⣲㞺ᅖẼ୰ࡢ㉁㔞ῶᑡࡣ㸪ࣆ࣮ࢡ್࡟ⱝᖸࡢ㐪࠸ࡣぢࡽࢀࡿࡶࡢࡢ㸪Ỉศ࠾ࡼࡧ᥹
Ⓨศࡢᨺฟ࡟࢔ࣞࢽ࢘ࢫᘧࢆ㐺⏝ࡍࡿࡇ࡜࡛ẚ㍑ⓗⰋࡃ⾲⌧࡛ࡁࡿࡇ࡜ࡀࢃ࠿ࡿ㸬㸱㸬࢖ࢱࢻࣜ BIC ࡢᇶ♏⇞↝≉ᛶD ⾲㠃⇞↝     E ᭷⅖⇞↝

3.1 ⇞↝ᐇ㦂⿦⨨ᅗ %,& ࡢ⇞↝ᙧែ ࣎࢖࣮ࣛ⇞↝⅔ෆ࡟࠾ࡅࡿ⇞↝≧ែࢆ᝿ᐃࡋ㸪኱Ẽᅽୗ࡛㧗 ✵Ẽὶ୰࡟⨨࠿ࢀࡓ࢖ࢱࢻࣜBIC ࡢ╔ⅆ࠾ࡼࡧ㻝㻚㻜㻌⇞↝ᣲືࢆㄪ࡭ࡓ㸬ᅗ 6 ࡟㸪౑⏝ࡋࡓᇶ♏⇞↝ᐇ㦂⿦⨨㻜㻚㻤㻌ࡋ㸪BIC ୗ➃㠃࡟ᡤᐃࡢ ᗘ(473㹼873K)࡟ண⇕ࡉࢀࡓ✵Ẽࢆ྿ࡁ௜ࡅࡿ㸬✵Ẽὶ㔞ࡣ 550NL/min.࡟タᐃࡋࡓ㸬౪⤥ࡍࡿண⇕✵Ẽ᮲௳ࡀᏳᐃࡋࡓᚋ࡟BIC ࢆ⇞↝⅔ෆ࡟ᢞ
ධࡋ㸪BIC ࡢ㉁㔞ῶᑡ㸪ୗ➃㠃 ᗘ(IR ࣓࢝ࣛィ )㸪࠾ࡼࡧ BIC ㏆ഐ࢞ࢫ ᗘ(T/C ィ )ࢆィ ࡋࡓ㸬㼁㼚㼎㼡㼞㼚㼠㻌㼒㼞㼍㼏㼠㼕㼛㼚㻌㻌㻌㻙ᴫ␎ࢆ♧ࡍ㸬BIC ࢆෆᚄ 100mm ࡢ⇞↝⅔ෆ୰ኸ࡟ྞࡿ

㻠㻣㻟㻷
㻡㻠㻤㻷
㻡㻞㻟㻷

㻡㻣㻟㻷

㻜㻚㻢㻌

㻡㻥㻤㻷
㻢㻞㻟㻷

㻜㻚㻠㻌
㻤㻣㻟㻷

㻜㻚㻞㻌
㻣㻣㻟㻷

㻢㻣㻟㻷

㻜㻚㻜㻌
㻜

㻝㻜

㻞㻜

㻟㻜

㻠㻜

㻡㻜

㻢㻜

㻱㼘㼍㼜㼟㼑㼐㻌㼠㼕㼙㼑㻌㻌㻌㼙㼕㼚DV
cameraPC

IRcameraZn-Se glass
BlowerSolid surface ignition

Window(quartz glass)

T/C(heater control)
Electric
heater
Flow
meter

1
0.8
0.6

1800

Gas-phase ignition
Unburnt fraction

1600

BIC bottom
surfacetemperature

1400
1200
1000

0.4

800
0.2

600

Gas temperature0ᅗ %,& ᇶ♏⇞↝ᐇ㦂⿦⨨ᴫ␎

400
0

10

Elapsed time min ࢖ࢱࢻࣜ BIC ࢆண⇕✵Ẽ୰࡟࠾࠸ࡓሙྜ㸪BIC ୗ➃㠃
10.8

 BIC ࡢ㉁㔞ῶᑡ࡬ࡢண⇕✵Ẽ ᗘࡢᙳ㡪ࢆㄪ࡭ࡓ⤖ᯝ
࠾࠸࡚ BIC ࡢ⇞↝ࡀほᐹࡉࢀ࡚࠸ࡿ㸬✵Ẽ ᗘ 473K ࡛ࡣᅗ 3 ࡢ⇕ศゎ㛤ጞ ᗘ 450K ࡼࡾ㧗࠸✵Ẽ ᗘ᮲௳࡛࠶ࡿࡀ㸪60min.௨ෆ࡟╔ⅆࡣぢࡽࢀ࡞࠿ࡗࡓ㸬✵Ẽ ᗘ
ࡀ 523K-573K ࡢሙྜ㸪᭷⅖⇞↝ࡢࡳࡀほᐹࡉࢀ㸪㉁㔞ῶᑡࡢ໙㓄ኚ໬ࡣ୍ẁ࡛࠶ࡗࡓ㸬ࡇࢀ࡟ᑐࡋ㸪✵Ẽ ᗘࡀ

Unburnt fraction -ࡀ㉥⇕ࡋ࡚⇞↝ࡍࡿ⾲㠃⇞↝(ᅗ 7 (a))㸪࠾ࡼࡧ BIC ඲యࡀⅆ⅖࡟ໟࡲࢀ࡚⇞↝ࡍࡿ᭷⅖⇞↝(ᅗ 7 (b))㸪ࡢ 2 ࡘࡢࢆᅗ 8 ࡟♧ࡍ㸬ᅗ୰㸪ᛴ⃭࡞㉁㔞ῶᑡࡀぢࡽࢀࡿ㒊఩࡟2030

ᅗ ✵Ẽ ᗘࡀ㧗࠸ . ሙྜࡢ╔ⅆᣲື

3.2 ࢖ࢱࢻࣜ BIC ࡢ╔ⅆᣲື⇞↝ᙧែࡀほᐹࡉࢀࡿ㸬Temperature K

T/CMechanicalscale

Unburnt fraction -Counterweightᅗ %,& ㉁㔞ῶᑡ࡬ࡢ✵Ẽ ᗘࡢᙳ㡪

Gas-phase ignition and
Solid surface ignition
1800
1600

Unburnt fraction

1400
BIC bottom
surfacetemperature

0.6
0.4

1200
1000
800

Gas
temperature

0.2

Temperature K

Bio-cokesampleFulcrum

600

0

400
0

10

20
30
40
Elapsed time min50ᅗ ✵Ẽ ᗘࡀప࠸ . ሙྜࡢ╔ⅆᣲື

598K-873K ࡢሙྜ࡟ࡣ㸪᭱ึ࡟⾲㠃⇞↝㸪ࡑࡢᚋ࡟᭷⅖
⇞↝࡜㉁㔞ῶᑡࡢ໙㓄ኚ໬ࡀ஧ẁ࠶ࡿࡇ࡜ࡀ☜ㄆࡉࢀ㸪 ✵Ẽ ᗘࡀ㧗࠸(Ӎ598K)ሙྜ㸪ᅗ 9 ࡟ぢࡽࢀࡿࡼ࠺࡟㸪౪⤥✵Ẽ ᗘ࡟ࡼࡾ㉁㔞ῶᑡࡢ᫬㛫ᒚṔࡀ␗࡞ࡿࡇ࡜ࡀ

⾲㠃╔ⅆ(⣙ 9min.᫬)ࡀẼ┦╔ⅆ(⣙ 17min.᫬)࡟ඛ⾜ࡋ࡚ࢃ࠿ࡿ㸬⏕ࡌࡓ㸬୍᪉㸪✵Ẽ ᗘࡀప࠸(ӌ573K)ሙྜ㸪ᅗ 10 ࡟ぢ㧗ᐦᗘࣂ࢖࣐࢜ࢫࣈࣜࢣࢵࢺࡢ╔ⅆ⇞↝≉ᛶࡽࢀࡿࡼ࠺࡟㸪㛗࠸ຍ⇕᫬㛫ࢆ⤒ࡓᚋ㸪⾲㠃╔ⅆ࡜Ẽ┦⅖⇞↝㛤ጞ┤ᚋ࡟࠾࠸࡚㢧ⴭ࡛࠶ࡿ㸬ࡇࢀࡽࡣ㸪✵Ẽ╔ⅆࡀ࡯ࡰྠ᫬(⣙ 38min.᫬)࡟Ⓨ⏕ࡍࡿࡢࡀほᐹࡉࢀࡓ㸬ᗘࡀప࠸᪉ࡀ᭷⅖⇞↝᫬㸪࡜ࡃ࡟᭷⅖⇞↝㛤ጞ┤ᚋ࡟࠾ ࡇࡢࡼ࠺࡟౪⤥✵Ẽ ᗘ࡟ࡼࡾ╔ⅆᙧែࡀ␗࡞ࡿࡢࡣ㸪࠸࡚⇕ศゎ࢞ࢫᨺฟ㏿ᗘࡀ኱ࡁ࠸ࡇ࡜ࢆព࿡ࡋ࡚࠾ࡾ㸪

BIC ⾲㠃㓟໬཯ᛂ࡟ࡼࡿ⾲㠃 ᗘୖ᪼ࡀ㛤ጞࡉࢀࡿࡲ࡛

ୖ㏙ࡢ╔ⅆᙧែࡀ✵Ẽ ᗘ࡟ࡼࡾ␗࡞ࡿせᅉ࡜ࡶྜ⮴ࡍ

࡟㸪BIC ෆ㒊࡟࡝ࢀࡔࡅࡢ㡿ᇦࡢண⇕ᒙࡀᙧᡂࡉࢀࡿ࠿

ࡿ㸬ࡍ࡞ࢃࡕ㸪᭷⅖⇞↝㛤ጞ๓ࡢண⇕㡿ᇦࡢᗈࡉࡀ᭷⅖

࡟ࡼࡿ࡜⪃࠼ࡽࢀ࡚࠸ࡿ(10-11)㸬✵Ẽ ᗘࡀ㧗࠸ሙྜ࡟ࡣ㸪⇞↝᫬ࡢ⇕ศゎ࢞ࢫᨺฟ㏿ᗘ㸪ࡦ࠸࡚ࡣ㉁㔞ῶᑡ㏿ᗘ࡟኱ࡁ࡞⇕ὶ㏿࡟ࡼࡾ BIC ⾲㠃 ᗘࡀୖ᪼ࡋࡸࡍ࠸ࡀ㸪ᙳ㡪ࢆ୚࠼ࡿࡶࡢ࡜⪃࠼ࡽࢀࡿ㸬

BIC ෆ㒊࡟ࡣ⾲㠃㏆ഐࡢ⊃࠸ண⇕㡿ᇦࡋ࠿ᙧᡂࡉࢀ࡞࠸㸬 ⇕ⓗ࡟ཌ࠸ࣂ࢖࣐࢜ࢫ⇞ᩱࡢ⇞↝࡟㛵ࡋ࡚㸪ᚑ᮶ᗄࡘࡇࢀ࡟ࡼࡾ㸪ຍ⇕㛤ጞᚋࡢ᪩࠸᫬ᮇ࡟⾲㠃╔ⅆࡀ⏕ࡌࡿ࠿ࡢ◊✲ࡀ࡞ࡉࢀ࡚࠸ࡿ(14-15)ࡀ㸪ண⇕㐣⛬ࡢ㐪࠸࡟ࡼࡿ

ࡀ㸪BIC ෆ㒊 ᗘୖ᪼ࡀ㐜ࢀࡿࡇ࡜࠿ࡽẼ┦╔ⅆࢆ⏕ࡌ⇞ᩱෆ㒊 ᗘศᕸࡢᙳ㡪࡟㛵ࡋ࡚⪃៖ࡉࢀ࡚࠸ࡿࡶࡢࡣ

ࡿࡢ࡟༑ศ࡞⇕ศゎ࢞ࢫࡀᨺฟࡉࢀࡎ㸪Ẽ┦╔ⅆ࡟⮳ࡽぢࡽࢀ࡞࠸㸬ୖ࡛㏙࡭ࡓࡼ࠺࡟㸪㧗ᐦᗘ㸪኱ࡁ࡞ᑍἲ࡞

࡞࠸ࠋ୍᪉㸪✵Ẽ ᗘࡀప࠸ሙྜ࡟ࡣ㸪BIC ⾲㠃㓟໬࠾࡝⇕ⓗ࡟ཌ࠸ࣂ࢖࣐࢜ࢫ⇞ᩱࡢ╔ⅆ࠾ࡼࡧ⇞↝㐣⛬࡟ணࡼࡧ⾲㠃 ᗘୖ᪼࡟᫬㛫ࡀ࠿࠿ࡿࡇ࡜࠿ࡽ㸪㛗࠸᫬㛫ࢆ⇕ᒚṔࡀᑡ࡞࠿ࡽࡎᙳ㡪ࢆ୚࠼ࡿࡓࡵ㸪ࡇࡢᙳ㡪࡟ࡘ࠸

࠿ࡅ࡚ BIC ෆ㒊ࡢᗈ࠸㡿ᇦࡀண⇕ࡉࢀࡿ㸬ࡑࡋ࡚㸪ࡦ࡜࡚༑ศ࡟⪃៖ࡍࡿᚲせࡢ࠶ࡿࡇ࡜ࡀࢃ࠿ࡿ㸬ࡓࡧ⾲㠃㓟໬཯ᛂࡀ㛤ጞࡉࢀࡿ࡜BIC ෆ㒊ࡢᗈ࠸⠊ᅖࡀ⇕ศゎ ᗘࢆ㉸࠼㸪Ẽ┦╔ⅆࡀ⏕ࡌࡿࡢ࡟༑ศ࡞㔞ࡢ⇕㸲㸬࢖ࢱࢻࣜ BIC ࡢ⇕ศゎ࢞ࢫᨺฟ≉ᛶศゎ࢞ࢫࡀᨺฟࡉࢀࡿ㸬ࡇࡢ⤖ᯝ࠿ࡽ㸪✵Ẽ ᗘࡀప࠸BIC ⇕ศゎ࢞ࢫ୰ࡢỈศ࠾ࡼࡧ᥹Ⓨศ๭ྜࡣẼ┦╔ⅆሙྜ࡟ࡣ⾲㠃╔ⅆ࡜Ẽ┦╔ⅆࡀ࡯ࡰྠ᫬࡟⏕ࡌࡿ㸬ࡇࢀࡢࡋ᫆ࡉࡸ⇞↝㏿ᗘ➼࡟ᙳ㡪ࢆ୚࠼ࡿࡇ࡜࠿ࡽ㸪Ỉศ࡜ࡽຍ⇕࡟ᑐࡍࡿBIC ෆ㒊 ᗘศᕸࡢᙧᡂ㐣⛬࡟BIC ࡢ⇕᥹Ⓨศࡑࢀࡒࢀࡢᨺฟ㏿ᗘࢆูࠎ࡟ぢ✚ࡶࡿࡇ࡜ࡣ BIC

ᣑᩓ⋡ (Ș = Ȣ/ȨC, Ȣ: ⇕ఏᑟ⋡㸪Ȩ: ᐦᗘ㸪C: ẚ⇕)ࡢ╔ⅆ࠾ࡼࡧ⇞↝≉ᛶࢆᢕᥱࡍࡿୖ࡛ព⩏῝࠸㸬BIC ຍࡀᐤ୚ࡋ࡚࠾ࡾ㸪ࡉࡽ࡟ࡇࢀ࡟ࡣ BIC ࡢᣢࡘ㧗ᐦᗘ࡜࠸⇕࡟࡜ࡶ࡞࠺Ỉศ࡜᥹Ⓨศࡑࢀࡒࢀࡢᨺฟ≉ᛶࢆ⢭ᗘࡼ࠺≉ᛶࡀᙳ㡪ࡋ࡚࠸ࡿࡶࡢ࡜⪃࠼ࡽࢀࡿ㸬ࡃ⾲⌧ฟ᮶ࡿࣔࢹࣝᵓ⠏ࢆヨࡳ㸪ࡉࡽ࡟ࡑࡢࣔࢹࣝࢆ⏝࠸࡚BIC ྵỈ⋡ࡢỈศ࡜᥹Ⓨศࡑࢀࡒࢀࡢᨺฟ≉ᛶ࡬ࡢ

3.3࢖ࢱࢻࣜ BIC ᭷⅖⇞↝᫬ࡢ㉁㔞ῶᑡ㏿ᗘᙳ㡪ࢆㄪ࡭ࡓ㸬 Ẽ┦╔ⅆ࡟⥆࠸࡚ぢࡽࢀࡿ㸪᭷⅖⇞↝᫬ࡢ BIC ㉁㔞ῶ

4.1 ᑠᆺ UFA(Universal Flammability Apparatus)ᐇ㦂⿦⨨

ᑡ㏿ᗘ࡬ࡢ౪⤥✵Ẽ ᗘࡢᙳ㡪ࢆㄪ࡭ࡓ㸬᭷⅖⇞↝᫬ࡢ

BIC ヨᩱࢆ❅⣲㞺ᅖẼ୰࡟࠾࠸࡚⇕ὶ᮰୍ᐃ࡟࡚ຍ⇕BIC ㉁㔞ῶᑡ㏿ᗘࡣ㸪BIC ࠿ࡽࡢ⇕ศゎ࢞ࢫᨺฟ㏿ᗘ࡜ࡋࡓሙྜࡢ㉁㔞ῶᑡࢆㄪ࡭ࡿࡓࡵ㸪ᑠᆺ UFA(16)ᐇ㦂⿦⨨ᐦ᥋࡟㛵㐃ࡋ࡚࠸ࡿ࡜⪃࠼ࡽࢀࡿ㸬ᅗ 11 ࡟㸪᭷⅖⇞↝᫬ࢆ⏝࠸࡚ຍ⇕ᐇ㦂ࢆᐇ᪋ࡋࡓ㸦ᅗ 12㸧
㸬BIC ୗ➃㠃࠿ࡽࡢ㉁㔞ῶᑡ㏿ᗘࡢኚ໬ࢆ♧ࡍ㸬᥇ྲྀࡋࡓヨᩱ㸦ȭ20mm10mm㸧ࢆእᚄ 35mm㸪ෆᚄ33mm ࡢࢫࢸࣥࣞࢫ〇ṇ᪉ᙧヨᩱ࣍ࣝࢲ࣮୰ኸ࡟㸪᩿⇕

40
35
30

Mass loss rate

g/min

573K
25

673K

ᮦࢆ௓ࡋ࡚ᅛᐃࡋࡓ㸬ヨᩱୖ㒊࡟タ⨨ࡉࢀࡓࢱࣥࢢࢫࢸ

873K
773K
673K
573K
523K

ࣥࣛࣥࣉࣄ࣮ࢱ࡟࡚ BIC ヨᩱ⾲㠃ࢆຍ⇕ࡋ㸪㟁Ꮚኳ⛗࡟ࡼࡾヨᩱࡢ㉁㔞ῶᑡࢆ ᐃࡋࡓ㸬ணࡵ Gardon ᆺ⇕ὶ᮰ィࢆ⏝࠸࡚ຍ⇕㠃࡟ධᑕࡍࡿ⇕ὶ᮰ࢆ᳨㔞ࡋࡓ㸬ࢧࣥࣉࣝ

523K

773K

20

࣍ࣝࢲ࣮࿘ᅖࢆ▼ⱥ⟶࡛そ࠸㸪ヨᩱୗ᪉ࡼࡾ❅⣲࢞ࢫ
873K

15

㸦50NL/min.㸧ࢆ౪⤥ࡍࡿࡇ࡜࡛ BIC ヨᩱࡢእẼ࡟ࡼࡿ㓟໬ࢆ㜵࠸ࡔ㸬

10

Radiant
heater5
Sample

0
1.0

0.8

0.6

0.4

0.2

Unburnt mass fraction of the fuel0.0

Sample

MUF

Quartz tube

ᅗ ᭷⅖⇞↝᫬ࡢ㉁㔞ῶᑡ㏿ᗘ࡬ࡢ✵Ẽ ᗘࡢᙳ㡪✵Ẽὶ㔞 /PLQ 
Nitrogenᅗ 11 ࡼࡾ㸪᭷⅖⇞↝᫬ࡢ㉁㔞ῶᑡ㏿ᗘࡣ㸪౪⤥✵Ẽᗘࡀప࠸࡯࡝኱ࡁ࠸ࡇ࡜ࡀࢃ࠿ࡿ㸬ࡇࡢഴྥࡣ࡜ࡃ࡟᭷

Insulator

SampleholderMechanicalscaleᅗ ᑠᆺ 8)$ ᐇ㦂⿦⨨ᴫ␎⚄ዉᕝ኱ᏛᕤᏛ◊✲ᡤᡤሗ ➨  ྕ
4.2 ⇕ศゎ࢞ࢫᨺฟ≉ᛶࡢゎᯒࣔࢹࣝᅗ 14 ࡟♧ࡍ㸬ᮏ◊✲࡛౑⏝ࡋࡓ BIC ヨᩱࡣ᭷㝈ࡢ㛗ࡉ ෇ᰕ BIC ヨᩱࡢ∦ഃ➃㠃ࢆ㍽ᑕຍ⇕ࡋࡓ㝿ࡢ㸪ヨᩱ࠿

㸦10 mm㸧ࢆᣢࡕ㸪࠿ࡘỈศࢆ⣙ 10 wt%⛬ᗘྵ᭷ࡍࡿ㸬ࡽࡢỈศ࠾ࡼࡧ᥹Ⓨศᨺฟࢆぢ✚ࡶࡿ୍ḟඖゎᯒࣔࢹࣝỈศࡢ⵨Ⓨࡍࡿ ᗘ 373 K ఩⨨ࡢ᫬㛫᥎⛣ࢆぢࡿ࡜㸪ヨࢆసᡂࡋ㸪ᑠᆺ UFA ᐇ㦂ࢆᶍᨃࡍࡿᩘ್ィ⟬ࢆ⾜ࡗࡓ㸬ᩱ඲యࡀ 373 K ௨ୖ࡟ຍ⇕ࡉࢀࡿࡲ࡛ࡢ᫬㛫ࡍ࡞ࢃࡕヨ࿘ᅖࢆ᩿⇕ࡉࢀࡓヨᩱࡢ∦ഃ➃㠃㸦Ȯ= 0 mm㸧ࢆ୍ᐃࡢᩱ୰ࡢỈศࡀ⵨Ⓨࡍࡿࡲ࡛ࡢ᫬㛫ࡣ࠾ࡼࡑ 4.7 min.࡛࠶⇕ὶ᮰࡛ຍ⇕ࡋ㸪BIC ヨᩱෆ㒊 ᗘୖ᪼㸪Ỉศ࠾ࡼࡧ᥹

ࡿࡇ࡜ࡀࢃ࠿ࡿ㸬ࡲࡓ 4.7 min.⤒㐣ᚋ࡟ࡣᛴ⃭࡞ヨᩱ ᗘⓎศᨺฟࢆぢ✚ࡶࡗࡓ㸬ヨᩱࢧ࢖ࢬࡣ UFA ᐇ㦂࡜ྠᵝȭୖ᪼ࡀぢࡽࢀࡿ㸬ࡇࡢࡇ࡜࠿ࡽ㸪᭷㝈㛗ࡉࡢ BIC ヨᩱࢆ

20mm10mm ࡢ෇ᰕᙧ≧㸪BIC ึᮇᐦᗘȨ = 1300 kg/m3㸪ຍ⇕ࡍࡿሙྜ㸪ヨᩱ୰࡟Ỉศࡀṧࡗ࡚࠸ࡿ㛫ࡣヨᩱෆ㒊

BIC ึᮇྵỈ⋡ MC = 11.1 %࡜ࡋࡓ㸬ゎᯒ࡟ࡣ௨ୗ࡟♧ࡢ ᗘୖ᪼ࡀ⦆ࡸ࠿࡛࠶ࡿࡀ㸪Ỉศࡀᢤࡅࡁࡗࡓᚋ࡟ᛴ

ࡍ௬ᐃࢆ⏝࠸ࡓ㸬(a) ࣔࢹࣝࡣ୍ḟඖ࡜ࡋ࡚ᢅ࠸㸪༙ᚄ⃭࡞ ᗘୖ᪼ࡀぢࡽࢀࡿࡼ࠺࡟࡞ࡿࡇ࡜ࡀศ࠿ࡿ㸬௬࡟᪉ྥ࡬ࡢ ᗘศᕸࡣ⏕ࡌ࡞࠸㸬(b) ヨᩱ࿘ᅖ㸦࡜ࡃ࡟ຍ

BIC ヨᩱࡀ↓㝈㛗ࡉࢆ᭷ࡋ࡚࠸ࡿሙྜ࡟ࡣ㸪⦆ࡸ࠿࡞ෆ

⇕㠃㸧ࡢ࿘ᅖ࢞ࢫὶࢀࡢᙳ㡪ࡣ↓どࡍࡿ㸬(c) Ỉศࡢ⵨㒊 ᗘୖ᪼ࡀ⥆ࡁᨺฟ࢞ࢫ㔞ࡣ୍ᐃࡢ್ࢆ⥔ᣢࡍࡿࡶࡢ

Ⓨ₯⇕ࡣ⪃៖ࡍࡿࡀ㸪⇞ᩱࡢ⇕ศゎ࠾ࡼࡧ㓟໬࡟࡜ࡶ࡞

࡜ண᝿ࡉࢀࡿ㸬BIC ヨᩱࡢỈศᨺฟ᏶஢ᚋࡢᛴ⃭࡞࢞ࢫ࠺཯ᛂ⇕ࡣ⪃៖ࡋ࡞࠸㸬(d) Ỉศ࠾ࡼࡧ᥹Ⓨศࡢᨺฟ㏿

ᨺฟ㏿ᗘࡢቑ኱ࡣヨᩱ㛗ࡉࡀ᭷㝈࡛࠶ࡿࡇ࡜࡟㉳ᅉࡋ࡚ᗘ㸦⇕ศゎࣃ࣓࣮ࣛࢱ㸧ࡣࡑࢀࡒࢀ࢔ࣞࢽ࢘ࢫࡢᘧ࡛୚

࠸ࡿ࡜⪃࠼ࡽࢀࡿࡓࡵ㸪௨㝆ࡢ㆟ㄽ࡛ࡣࡇࡢᛴ⃭࡞࢞ࢫ࠼㸪ྛࠎ࢞ࢫ໬ࡍࡿ࡜┤ࡕ࡟ BIC ຍ⇕㠃࠿ࡽᨺฟࡉࢀࡿ

ᨺฟ㏿ᗘቑ኱ࡀࡳࡽࢀࡿ௨๓ࡢ᫬㛫࡟ࡘ࠸࡚ᢅ࠺㸬㸦ణࡋᨺฟ࢞ࢫࡣධᑕ⇕ὶ᮰࡟ࡣᙳ㡪ࢆ୚࠼࡞࠸㸧㸬(e)Calculation result⇕ศゎ࢞ࢫᨺฟ࡟ࡼࡾヨᩱ㉁㔞ࡣῶᑡࡍࡿࡀ㸪య✚ࡣ୙ኚ࡜ࡍࡿ㸦ᐦᗘࡀῶᑡࡍࡿ㸧
㸬(f) ヨᩱࡢ⇕≀ᛶ್ࡢ ᗘ

Experimental
result౫Ꮡᛶࡣ⪃៖ࡋ࡞࠸㸬(g) ヨᩱຍ⇕㠃⾲㠃࡟ࡣ⅊Ⰽయ㏆ఝࢆ㐺⏝ࡍࡿ㸬ヨᩱෆ㒊ࡢ࢚ࢿࣝࢠ࣮ಖᏑᘧ㸪Ỉศ࡜᥹Ⓨศ࡟㛵ࡍࡿ㉁㔞ಖᏑᘧࢆ⪃៖ࡋ㸪㝧ゎἲࢆ⏝࠸࡚ᘧࢆ㞳ᩓ໬ࡋィ⟬ࢆ⾜ࡗࡓ㸬ቃ⏺᮲௳ࡣຍ⇕㠃ഃ࡛ࡣ㍽ᑕධ⇕࡜ᨺᑕ⇕ᦆኻࢆ⪃៖ࡋ㸦Ȣ㸹⇕ఏᑟ⋡㸪T㸹 ᗘ㸪Ȝ㸹ᅗ ᐇ㦂⤖ᯝ࡜ィ⟬⤖ᯝࡢẚ㍑

BIC ヨᩱ⾲㠃ࡢᨺᑕ⋡(0.95 ࡜௬ᐃ)㸪q㸹ຍ⇕⇕ὶ㏿㸪Ȫ㸹࣎ࣝࢶ࣐ࣥᐃᩘ㸪Ts㸹BIC ヨᩱຍ⇕㠃 ᗘ㸧㸪௚➃㠃ഃ࡛
ࡣ᩿⇕࡜ࡋࡓ㸬  ᮏ◊✲࡛౑⏝ࡋࡓ࢖ࢱࢻࣜ BIC ࡢ⇕ఏᑟ⋡(Ȣ)࠾ࡼ
ࡧẚ⇕(C)ࡣᮍ▱࡛࠶ࡿࡀ㸪ḟ࡟♧ࡍ UFA ᐇ㦂⤖ᯝ࡜ᮏゎᯒࣔࢹࣝࢆ⏝࠸ࡓィ⟬⤖ᯝࡢ⇕ศゎ࢞ࢫᨺฟࡢࣆ࣮ࢡ
᫬㛫ࡀ୍⮴ࡍࡿࡼ࠺୚࠼ࡓ㸬ࡇࡢ㝿㸪ࡇࢀࡽࡢ≀ᛶ್ࡣ㸪(17)ᮌᮦ࡟ᑐࡋ࡚▱ࡽࢀ࡚࠸ࡿ್ ࡢ⠊ᅖ࡟⣡ࡲࡿࡼ࠺࡟୚
࠼㸪Ȣ=2.20010-4 W/mmK㸪C=1300 J/kgK ࡜ࡋࡓ㸬

Distance from heated face mm

10ヨᩱෆ㒊ࡢỈศࡀ⵨Ⓨࡋࡁࡿࡲ࡛ࡢ᫬㛫 (§ 4.7 min.)

9
8
7
6
5
4
3
2
923 K

1
0
0

5

10

Time min.

4.3 ⇕ศゎ࢞ࢫᨺฟ㏿ᗘࡢ᫬㛫ኚ໬ᅗ %,& ヨᩱෆ㒊 ᗘኚ໬ N:P

ᑠᆺ UFA ࢆ⏝࠸ࡓຍ⇕ᐇ㦂⤖ᯝ࡜㸪ᮏ◊✲࡛⏝࠸ࡓゎ ᅗ 15 ࡟㸪BIC ヨᩱ࠿ࡽࡢ᥹Ⓨศ࠾ࡼࡧỈศᨺฟ㏿ᗘࡢᯒࣔࢹࣝ࡟ࡼࡿィ⟬⤖ᯝࡢẚ㍑ࢆ⾜ࡗࡓ㸬ᅗ 13 ࡟㸪ຍ⇕ィ⟬⤖ᯝࢆ♧ࡍ㸬ຍ⇕㛤ጞᚋࡍࡄ࡟Ỉศࡢᨺฟࡀጞࡲࡾ㸪⇕ὶ᮰ 50 kW/m2 ࡢሙྜࡢẚ㍑ࢆ♧ࡍ㸬ィ⟬࡟ࡼࡾᚓࡽࢀ

ࡑࡢᚋ⦆ࡸ࠿࡟ᨺฟ㔞ࡣῶᑡࡋ࡚࠸ࡿ㸬᥹ⓎศᨺฟࡣỈ

ࡓ㉁㔞ῶᑡࡣ㸪ᑠᆺ UFA ᐇ㦂⤖ᯝ࡜ẚ㍑ࡋ࡚ᨺฟࡢ㛤ጞศࡢᨺฟ࡟ࢃࡎ࠿࡟㐜ࢀ࡚㛤ጞࡋ㸪᪩࠸᫬ᮇ㸦1.8 min.

᫬ᮇ࠾ࡼࡧᨺฟࣆ࣮ࢡ࡟ⱝᖸࡢᕪ␗ࡣぢࡽࢀࡿࡶࡢࡢ㸪⛬ᗘ㸧࡟ᑠࡉ࡞ࣆ࣮ࢡࢆ♧ࡋࡓᚋ࡟⦆ࡸ࠿࡟ῶᑡࡋ࡚࠸

ẚ㍑ⓗഴྥࢆ⾲⌧ฟ᮶࡚࠸ࡿࡇ࡜ࡀࢃ࠿ࡿ㸬BIC ヨᩱ࠿ࡿ㸬᥹Ⓨศ㸭Ỉศࡢᨺฟ㏿ᗘẚࢆྠ᫬࡟♧ࡋࡓࡀ㸪ຍ⇕ࡽᨺฟࡉࢀࡿ࢞ࢫ㸦Ỉศ㸩᥹Ⓨศ㸧㔞ࡣ㸪ຍ⇕㛤ጞ࠿ࡽ㛤ጞᚋ 1.8 min.࠿ࡽ 4 min.ࡢ㛫࡟⥲࢞ࢫᨺฟ㏿ᗘࡣ⦆ࡸ࠶ࡿᮇ㛫ࡣẚ㍑ⓗ୍ᐃ࡟㏆࠸್ࢆ♧ࡍࡀ㸪ࡑࡢᚋ㸦ᅗ 13㸪࠿࡟ῶᑡࡋ࡚࠸ࡿ୍᪉࡛᥹Ⓨศ㸭Ỉศẚࡣ࡯ࡰ୍ᐃ࡛࠶

4.7 min.㸦ィ⟬್㸧⤒㐣ᚋ㸧ᛴ⃭࡟ቑຍࡋࣆ࣮ࢡࢆ♧ࡍ㸬ࡿࡇ࡜㸪ࡍ࡞ࢃࡕᨺฟ࢞ࢫ୰ࡢỈศ๭ྜࡣ࡯ࡰ୍ᐃ࡛࠶

ྠ᮲௳࡟࠾ࡅࡿ BIC ヨᩱෆ㒊 ᗘࡢኚ໬㸦ィ⟬⤖ᯝ㸧ࢆࡿࡇ࡜ࡀࢃ࠿ࡿ㸬

14

14

12

12

10

10

8

8

Volatile

6

6

Total
4

4

Volatile / Water ratio2࢞ࢫࡣ㸪BIC ᮏ᮶ࡢ᥹Ⓨศ㸭Ỉศ๭ྜ࠿ࡽண᝿ࡉࢀࡿࡼ
ࡾࡶ╔ⅆ㸪⇞↝ࡋ㞴࠸⤌ᡂ࡛࠶ࡿ࡜⪃࠼ࡽࢀࡿ㸬㸳㸬⤖ゝ

2

 ࢖ࢱࢻࣜࢆཎᩱ࡜ࡍࡿ㧗ᐦᗘᅛయࣂ࢖࣐࢜ࢫࣈࣜࢣࢵ

Water
0

0
0

2

4

6

8

10

ࢺ(BIC)ࡢ⇕ศゎ㸪╔ⅆ࠾ࡼࡧ⇞↝≉ᛶࢆㄪ࡭ࡓ㸬ࡑࡢ⤖Time min.

ᅗ  ᨺฟ࢞ࢫ୰ࡢ᥹Ⓨศ࠾ࡼࡧỈศ N:P 

12Volatile / Water ratio

10

10

8

8
6

6

Volatile

4

Total

2

4

ࡧ⇞↝≉ᛶ࡟኱ࡁࡃᙳ㡪ࡍࡿࡇ࡜ࡀࢃ࠿ࡗࡓ㸬௒ᚋ BIC

Volatile / Water ratio

Mass loss rate mg/s

12ࡢ฼ά⏝ࢆ㐍ࡵࡿୖ࡛㸪ࡇࢀࡽ⇕≉ᛶ࡜ BIC 〇㐀ୖࡢ≉ᛶ࠿ࡽ㸪᭱㐺࡞〇㐀࣭⇞↝ᙧែࢆㄪᰝࡍࡿᚲせࡀ࠶ࢁ࠺㸬

2

Water

0

ཧ⪃ᩥ⊩

0
0

2

4

6

8

10

12

14

16

ᯝ㸪╔ⅆ๓ࡢຍ⇕ᒚṔ(ຍ⇕㏿ᗘ)ࡀ BIC ෆ㒊 ᗘศᕸ㸪ᨺฟ࢞ࢫᡂศ(᥹Ⓨศ㸭Ỉศ๭ྜ)ࡦ࠸࡚ࡣ╔ⅆᙧែ࠾ࡼ

14

14



࠸ࡇ࡜࠿ࡽ㸪ᮏ◊✲ࡢ⠊ᅖ࡛ࡣࡇࡢᮇ㛫࡟ᚓࡽࢀࡿᨺฟ
Volatile / Water ratio

Mass loss rate

mg/s㧗ᐦᗘࣂ࢖࣐࢜ࢫࣈࣜࢣࢵࢺࡢ╔ⅆ⇞↝≉ᛶ(1) C.Wang, F.Wang, Q.Yang, R.Liang,”Biomass and Bioenergy” 33,

18Time min.


18

18

16

16

Volatile/Water ratio

14

14

12

12

Volatile

10

10

8

8

6

6

Total

4
2

4

28-3 (2009), pp.427-434.
(3) T.Honjo, T.Ida, M.Fuchihata, H.Sano,”Journal of the Japan Instituteof Energy” 84 (2005), pp.142-148.
(4) P.Gilbert, C.Ryu, V.Sharifi, J.Swithenbank,”Fuel” 88 (2009), pp.
1491-1497.

2

Water

0

0
0

1

2

3

4

5

6

7

(2009), pp. 50-56.
(2) S.Sadaka, S.Negi,”Environmental Progress and Sustainable Energy”

Volatile / Water ratio

Mass loss rate mg/s

ᅗ ᨺฟ࢞ࢫ୰ࡢ᥹Ⓨศ࠾ࡼࡧỈศ N:P (5) O.C.Chin, K.M.Siddiqui,”Biomass and Bioenergy” 18 (2000), pp.

8

Time min.

ᅗ ᨺฟ࢞ࢫ୰ࡢ᥹Ⓨศ࠾ࡼࡧỈศ N:P 

4.4 ⇕ศゎ࢞ࢫᨺฟ㏿ᗘ࡬ࡢຍ⇕⇕ὶ᮰ࡢᙳ㡪

223-228.
(6) D.Singh,”Agricultural wastes” 13 (1985), pp.189-196.
(7) Ọᶫ㸪ᮧୖ㸪㞧㈡㸪”᪥ᮏ⇞↝Ꮫ఍ㄅ (in Japanese)” 51 (158)ᅗ 16㸪17 ࡟ 25 kW/m2 ࠾ࡼࡧ 100 kW/m2 ࡢィ⟬⤖ᯝࢆ
2(2009), pp.310-317.

ࡑࢀࡒࢀ♧ࡍ㸬ຍ⇕⇕ὶ᮰ࡀᑠࡉ࠸ᅗ 16㸦25 kW/m 㸧࡛(8) T.Ida, A.Nakanishi, Osaka TLO, Patent No. 4088933 (2006) Japan.

ࡣᅗ 15㸦50 kW/m2㸧࡜ࡣ␗࡞ࡾ᥹Ⓨศᨺฟࡀ⦆ࡸ࠿࡟㛤(9) ఀᮾ㸪㓇஭㸪஭⏣㸪⸨⏣㸪”᪥ᮏ⇞↝Ꮫ఍ㄅ” ➨ 53 ᕳ 164 ྕጞࡉࢀ᪩࠸᫬ᮇࡢ᥹Ⓨศᨺฟ㏿ᗘࡢࣆ࣮ࢡࡣぢࡽࢀ࡞࠸㸬(2009), pp.1-6.

2

ࡇࢀࡣ 25 kW/m ࡢሙྜ࡟ࡣຍ⇕⇕ὶ᮰ࡀᑠࡉࡃ㸪BIC ຍ(10) H.Ito, Y.Sakai, T.Ida, Y.Nakamura, O.Fujita,“Proc. ASME/JSME 8th⇕㠃௜㏆ࡢ ᗘୖ᪼ࡀ㐜ࢀࡿࡇ࡜࡟ࡼࡾ᥹Ⓨศ࢞ࢫᨺฟ

Thermal Engineering Joint Conference” (2011),AJTEC2011-44145.

ࡶ㐜ࢀࡿࡓࡵ࡜⪃࠼ࡽࢀࡿ㸬ࡇࡢ⤖ᯝ㸪ᨺฟ࢞ࢫ୰ࡢ᥹

(11) H.Ito, Y.Sakai, T.Ida, Y.Nakamura, O.Fujita, “J. Thermal Sci. Tech.”Ⓨศ㸭Ỉศẚࡣ᭱ึᑠࡉࡃ㸪ࡑࡢᚋᚎࠎ࡟ୖ᪼ࡍࡿࡇ࡜

Vol.6, No.1 (2011), pp.111-122.

࡟࡞ࡿ㸬୍᪉㸪ຍ⇕⇕ὶ᮰ࡀ኱ࡁ࠸ᅗ 17 ࡛ࡣ㸪ຍ⇕㛤ጞ(12) I.Obernberger, G.Thek, “Biomass and Bioenergy” 27 (2004),ᚋࡢ᪩࠸᫬ᮇ࡟᥹Ⓨศ࢞ࢫᨺฟࡢ኱ࡁ࡞ࣆ࣮ࢡࡀ⌧ࢀ㸪

pp.653-669.

⥲࢞ࢫᨺฟ㏿ᗘࡶ኱ࡁࡃ࡞ࡿ㸬ࡇࡢ᫬㸪᥹Ⓨศ࢞ࢫᨺฟ

(13) E.Kharbat, K.Annamalai, C.Gopalakrishnan, “Combust. Flame”㛤ጞᚋࡢ᥹Ⓨศ㸭Ỉศẚࡀ᫬㛫࡟ࡼࡽࡎ࡯ࡰ୍ᐃࡢ್࡛

100 (1995), pp.413-421.

᥎⛣ࡍࡿ㸪ࡍ࡞ࢃࡕᨺฟ࢞ࢫ୰ࡢỈศ๭ྜࡣ኱ࡁࡃኚ໬

(14) M.J.Hagge, K.M.Bryden, “Chem. Eng. Science” 57 (2002),ࡋ࡚࠸࡞࠸㸬ࡇࡢ࡜ࡁࡢ᥹Ⓨศ㸭Ỉศẚࡣ 3.7 ⛬ᗘ࡛࠶

pp.2811- 2823.

ࡾ㸪BIC ᮏ᮶ࡢ್㸦7.0 ⛬ᗘ㸧࡟ẚ࡭࡚ᑠࡉࡃ㸪Ỉศࡀ᥹(15) A.Ouedraogo, J.C.Mulligan, J.G.Cleland, “Comb. Flame” 114Ⓨศ࡟ඛ⾜ࡋ࡚ᨺฟࡉࢀ࡚࠸ࡿࡇ࡜ࡀ❚࠼ࡿ㸬ࡇࡢせᅉ(1998), pp.1-12.

࡜ࡋ࡚㸪BIC ࡢ⇕ᣑᩓ⋡ࡀ༑ศ኱ࡁࡃヨᩱຍ⇕㠃ഃࡀ᥹(16) ᑠᙇ, ௚, “᪥ᮏⅆ⅏Ꮫ఍◊✲Ⓨ⾲఍ᴫせ㞟” (2010), p.386.

Ⓨศᨺฟ ᗘ࡟㐩ࡍࡿࡼࡾࡶヨᩱෆ㒊ࡀỈศ⵨Ⓨ ᗘ࡟(17) ᪥ᮏᶵᲔᏛ఍㸪”ఏ⇕ᕤᏛヨᩱ ᨵゞ➨ 4 ∧”㸪p.322.

㐩ࡋ᫆࠸ࡇ࡜ࡀᣲࡆࡽࢀࡿ㸬Ỉศࡀඛ⾜ࡋ࡚ᨺฟࡉࢀ᫆ḟୡ௦ᶵᲔᮦᩱࠕ㔠ᒓ࢞ࣛࢫࠖࡢ≉ᛶ࡜ຍᕤᑎᓥ ᓅྐ*Properties and Processing of Metallic Glass
Takeshi TERAJIMA㸯㸬⥴ゝࡢ Au-Si ⣔࢔ࣔࣝࣇ࢓ࢫྜ㔠ࡢ Rc ࡣᩘ୓ K/s ௨ୖ࡛࠶ࡿ 㔠ᒓ࢞ࣛࢫࡣ࢔ࣔࣝࣇ࢓ࢫྜ㔠ࡢ୰࡛ࡶ≉࡟࢞ࣛࢫᙧ

ࡢ࡟ᑐࡋ, Fe ᇶ㔠ᒓ࢞ࣛࢫࡢRc ࡣ⣙1000K/s, Zr ᇶ㔠ᒓ࢞ᡂ⬟ࡀ㧗ࡃ, ᫂░࡞㐣෭༷≧ែࢆ♧ࡍྜ㔠ࡢ⥲⛠࡛࠶ࡿ.

ࣛࢫࡢ Rc ࡣ 1-100K/s, Pd ᇶ㔠ᒓ࢞ࣛࢫࡢ Rc ࡣ 0.1K/s ࡛㔠ᒓ࢞ࣛࢫࡣ୕ࡘࡢ⤒㦂๎࡟ᙜ࡚ࡣࡲࡿ≉ᐃࡢྜ㔠⤌ᡂ

࠶ࡿ. ᚑ᮶ࡢ࢔ࣔࣝࣇ࢓ࢫྜ㔠ࡣ Rc ࡀ㧗࠸ࡓࡵཌࡉ

࡟࠾࠸࡚ከࡃぢ࠸ࡔࡉࢀ࡚࠸ࡿ(1, 2).

50ȝm ௨ୗࡢ⟩ᖏࡸ┤ᚄ 100ȝm ௨ୗࡢ⥺ᮦࡋ࠿ᚓࡽࢀ࡞

(1) 3 ᡂศ௨ୖࡢከඖ⣔࡛࠶ࡿ࠿ࡗࡓࡀ, 㔠ᒓ࢞ࣛࢫࡣẚ㍑ⓗ㐜࠸෭༷㏿ᗘ࡛ࡶ࢔ࣔࣝ

(2) ᵓᡂཎᏊࡢཎᏊ༙ᚄࡀ஫࠸࡟⣙ 12%௨ୖ␗࡞ࡿ

ࣇ࢓ࢫࢆᙧᡂࡍࡿࡓࡵྜ㔠✀࡟ࡼࡗ࡚ࡣࢭࣥࢳ࣓࣮ࢺࣝ

(3) ᵓᡂඖ⣲ྠኈࡀ㈇ࡢΰྜ⇕ࢆࡶࡕ, ໬ྜ≀ࡀ࢚ࢿ⣭ࡢ኱ࡁࡉࢆᣢࡘࣂࣝࢡ࢔ࣔࣝࣇ࢓ࢫయࡢస〇ࡀྍ⬟࡛ࣝࢠ࣮ⓗ࡟Ᏻᐃ࡛࠶ࡿ

࠶ࡿ. ࣂࣝࢡ㔠ᒓ࢞ࣛࢫࡢฟ⌧ࡣ࢔ࣔࣝࣇ࢓ࢫྜ㔠ࡢ⏘⌧ᅾࡲ࡛࡟ Mg ᇶ(3), Zr ᇶ(4, 5), Fe ᇶ(6, 7), Pd ᇶ(8), Ni ᇶ(9)ࢆࡣࡌࡵ࡜ࡋࡓከᩘࡢ㔠ᒓ࢞ࣛࢫࡀ㛤Ⓨࡉࢀ࡚࠸ࡿ.

ᴗᛂ⏝ࢆᣑ኱ࡍࡿࡔࡅ࡛࡞ࡃ, ᥋ྜࡸຍᕤࢆྍ⬟࡟ࡋࡓⅬ࡛㔜せ࡞ព࿡ࢆᣢࡘ.

୍⯡ⓗ࡟ࣂࣝࢡ㔠ᒓ࢞ࣛࢫࡣᾮ┦ࡢ↓⛛ᗎ࡞ཎᏊ㓄ิࢆ෾⤖ࡍࡿࡓࡵ࡟ྜ㔠⁐‫ࢆ‮‬ᛴ෭จᅛࡋ࡚స〇ࡍࡿ. 㔠㸰㸬㔠ᒓ࢞ࣛࢫ

ᒓ࢞ࣛࢫࡣ⼥Ⅼ×0.6 ⛬ᗘࡢ ᗘ㡿ᇦ࡟࠾࠸࡚‽Ᏻᐃ࡞㐣 ⇕ⓗᣲື෭༷≧ែࡀᏑᅾࡍࡿࡓࡵᚑ᮶ࡢ࢔ࣔࣝࣇ࢓ࢫྜ㔠࡜ẚ㍑

 ᅗ 1 ࡟㔠ᒓ࢞ࣛࢫࡢ඾ᆺⓗ࡞⇕ⓗᣲືࢆ♧ࡋࡓ. 㔠ᒓࡋ࡚࢔ࣔࣝࣇ࢓ࢫࢆᙧᡂ㸦࢞ࣛࢫ໬㸧ࡋࡸࡍ࠸. ኱ᑠࡢ࢞ࣛࢫࡣ㠀ᖹ⾮ᮦᩱ࡛࠶ࡿࡓࡵྠࡌ ᗘ࡛ࡶᾮ┦࠿ࡽᛴཎᏊ༙ᚄࢆᣢࡘᵓᡂඖ⣲ࡀΰᅾࡋ࡚, ඖ⣲㛫࡟㈇ࡢ┦஫෭ࡋࡓሙྜ࡜, ᐊ ࠿ࡽຍ⇕ࡋࡓሙྜ࡛ࡣ┦ኚែࡢᵝ┦స⏝ࡀാ࠸࡚࠸ࡿᾮయ࡛ࡣ↓⛛ᗎ඘ሸࡀ㧗ࡲࡿ࡜ඹ࡟ࡑ

ࡀ␗࡞ࡿ. ࡘࡲࡾᾮ┦࠿ࡽᛴ෭ࡍࡿ࡜‽Ᏻᐃ࡞㐣෭༷≧ࡢᒁᡤᵓ㐀ࡀᖹ⾮≧ែࡢ⤖ᬗ┦࡜ࡣ␗࡞ࡿ㛗⠊ᅖ┦஫సែࢆ⤒࡚࢔ࣔࣝࣇ࢓ࢫࡢࡲࡲ㠀ᖹ⾮จᅛࡍࡿ. ୍᪉࡛㔠⏝ࢆᣢࡗࡓࡶࡢ࡟࡞ࡿࡇ࡜ࡀ␗ᖖᩓ஘㹖⥺ᅇᢡἲ࡞࡝ࢆ

ᒓ࢞ࣛࢫࢆᐊ ࠿ࡽᚎࠎ࡟ຍ⇕ࡋ࡚࠸ࡃ࡜࢞ࣛࢫ㌿఩

(10-12). ࡑࡢ⤖ᗘ Tg ௜㏆࡟࠾࠸࡚྾⇕ࡋ࡚㐣෭༷≧ែ࡟⛣⾜ࡍࡿ. ᭦࡟ᯝ, ᅛ㸭ᾮ⏺㠃࢚ࢿࣝࢠ࣮ࡀቑ኱ࡋ࡚⤖ᬗࡢ᰾⏕ᡂࡀᢚ᪼ ࡋ࡚⤖ᬗ໬ ᗘ Tx ࡟㐩ࡍࡿ࡜┤ࡕ࡟⤖ᬗ໬ࡋ࡚ཎ

ไࡉࢀࡿ. ࡲࡓᣑᩓ⬟ࡀపୗࡋ࡚⢓ᛶࡀቑ኱ࡍࡿ. ⤖ᬗᏊ෌㓄ิ࡟ࡼࡿవ๫࢚ࢿࣝࢠ࣮ࢆᨺฟࡋ࡞ࡀࡽ⇕ຊᏛⓗ⏝࠸ࡓᵓ㐀ゎᯒ࡟ࡼࡾ᫂ࡽ࠿࡟ࡉࢀ࡚࠸ࡿ

໬ࢆ㉳ࡇࡍࡓࡵ࡟ࡣ㛗࿘ᮇࡢཎᏊ෌㓄ิࡀᚲせ࡛࠶ࡿࡀᣑᩓ⬟ࡀపୗࡋ࡚࠸ࡿ㐣෭༷≧ែ࡛ࡣࡑࡢ෌㓄ิࡀᅔ㞴࡛࠶ࡿࡓࡵ㔠ᒓ࢞ࣛࢫࡣ࢔ࣔࣝࣇ࢓ࢫࢆᙧᡂࡋ᫆࠸.
࢞ࣛࢫᙧᡂ⬟ࡢᑻᗘ࡜ࡋ࡚ࡋࡤࡋࡤ࢞ࣛࢫ໬⮫⏺෭༷㏿ᗘ Rc ࡀ⏝࠸ࡽࢀࡿ. ⾲ 1 ࡟௦⾲ⓗ࡞㔠ᒓ࢞ࣛࢫࡢస
〇ྍ⬟࡞᭱኱ࡢཌࡳ࡜, ⮫⏺෭༷㏿ᗘ Rc ࢆ♧ࡋࡓ. ᚑ᮶*෸ᩍᤵ ᶵᲔᕤᏛ⛉
Associate Professor, Dept. of Mechanical Engineering⾲ 㔠ᒓ࢞ࣛࢫࡢ᭱኱࢞ࣛࢫ໬┤ᚄ࡜⮫⏺෭༷㏿ᗘḟୡ௦ᶵᲔᮦᩱࠕ㔠ᒓ࢞ࣛࢫࠖࡢ≉ᛶ࡜ຍᕤ㝈⏺㸦ᅗ 2 ࡢሬࡾࡘࡪࡋ㒊ศ㸧ࡀ㧗ࡃ, ࢫࣉࣜࣥࢢ࡞࡝

Rapidly quenchingࡢ㧗཯Ⓨᮦᩱ࡜ࡋ࡚ᐇ⏝໬ࡉࢀ࡚࠸ࡿ(13).
Amorphous䠄Solid䠅Supercooled
liquidCrystalline
䠄Solid䠅Liquid㽢
R.T.

Glass transition
temp. Tg

Crystalline
temp. Txࡲࡓ㔠ᒓ࢞ࣛࢫ࡟ࡣ⤖ᬗ⢏⏺ࡀᏑᅾࡋ࡞࠸ࡇ࡜࠿ࡽᆒ㉁࡞㓟໬⿕⭷ࢆᙧᡂࡍࡿ. ࡑࡢࡓࡵࡓࡵZr, Ti, Cr, Al࡞࡝ࢆྵࡴ㔠ᒓ࢞ࣛࢫࡣ⪏㣗ᛶ࡟ᴟࡵ࡚ඃࢀࡿ. ᪤࡟

Liquidus
temp. Tm

Fe43Cr16Mo16C15B10 㔠ᒓ࢞ࣛࢫࡣ, ᕤሙࡢࡣࢇࡔᾎᵴࡢ⪏㣗ෆቨ࡜ࡋ࡚ᐇ⏝໬ࡋ࡚࠸ࡿ. ࡋ࠿ࡋ࡞ࡀࡽ⪏㣗ᛶ࡟ඃᅗ  㔠ᒓ࢞ࣛࢫࡢ⇕ⓗᣲືࢀࡿࡇ࡜ࡣ, ⿬ࢆ㏉ࡏࡤ཯ᛂᛶ࡟ஈࡋ࠸ࡇ࡜࡛ࡶ࠶ࡾ,࡟ᖹ⾮࡞㔠ᒓ㛫໬ྜ≀ࢆ⏕ᡂࡍࡿ. ᚑ᮶ࡢ࢔ࣔࣝࣇ࢓ࢫ

ࡣࢇࡔ᥋ྜࡀᅔ㞴࡞஦ࢆព࿡ࡋ࡚࠸ࡿ. ࡣࢇࡔ᥋ྜࢆྍ

ྜ㔠ࡀ࢔ࣔࣝࣇ࢓ࢫ┦࠿ࡽ┤᥋⤖ᬗ┦࡟㌿⛣ࡍࡿࡢ࡟ᑐ

⬟࡟ࡍࡿ㔠ᒓ࢞ࣛࢫࡢ⾲㠃ᨵ㉁࡟ࡘ࠸࡚ࡣᚋ㏙ࡍࡿ.

ࡋ, 㔠ᒓ࢞ࣛࢫࡣ㐣෭༷≧ែࢆ⤒࡚࠿ࡽ⤖ᬗ໬ࡍࡿⅬ࡛ࡑࡢ௚࡟ࡶ㔠ᒓ࢞ࣛࢫࡣỈ⣲྾ⶶᛶ(14), Ỉ⣲㏱㐣ᛶ(14),ᵝ┦ࡀ␗࡞ࡿ. 㐣෭༷≧ែ࡛ࡣ ᗘ࡟ࡶࡼࡿࡀࢳ࣮ࣗ࢖

㌾☢Ẽ≉ᛶ(15)࡞࡝ࢆ♧ࡍ. ࡑࡢࡓࡵᵓ㐀ᮦᩱ, ᚤᑠᶵᲔ࣒ࣥ࢞⛬ᗘࡢὶືᛶࢆ♧ࡍࡓࡵ, ⼥Ⅼࡼࡾࡶప࠸ ᗘ࡛㒊ရ(MEMS), ⇞ᩱ㟁ụࢭࣃ࣮ࣞࢱ, 㧗⣧ᗘỈ⣲ศ㞳⭷,㉸ረᛶຍᕤࡸ᥋ྜ࡞࡝ࡀྍ⬟࡛࠶ࡿ. 㐣෭༷≧ែࡣ⤖ᬗ☢Ẽ࣊ࢵࢻ, ⏕యᮦᩱ࡞࡝ࡢᖜᗈ࠸ศ㔝࡛⏘ᴗᛂ⏝(16)ࡀ

㔠ᒓ࡟ࡣᏑᅾࡋ࡞࠸ࡓࡵ, ඲ࡃ᪂ࡋ࠸ຍᕤࣉࣟࢭࢫࡢ๰

ᮇᚅࡉࢀ࡚࠸ࡿ.

ᡂࡀᮇᚅ࡛ࡁࡿ. 㔠ᒓ࢞ࣛࢫࡢ࢔ࣔࣝࣇ࢓ࢫ┦࡜㐣෭༷ࡇࡢࡼ࠺࡟㔠ᒓ࢞ࣛࢫࡣᵝࠎ࡞ඃࢀࡓ≉ᛶࢆᣢࡘࡀ,≧ែࡣྍ㏫ⓗ࡟㌿⛣ࡍࡿࡀ, ୍ᗘ⤖ᬗ໬ࡍࡿ࡜෌ᗘᾮ┦᥋ྜࢆጞࡵ࡜ࡍࡿᐇ⿦ᢏ⾡ࡀ☜❧ࡋ࡚࠸࡞࠸ࡓࡵᐇ⏝໬࠿ࡽ⮫⏺෭༷㏿ᗘ Rc ௨ୖ࡛ᛴ෭ࡋ࡞࠸㝈ࡾ࢔ࣔࣝࣇ࢓

ࡀ㐜ࢀ࡚࠸ࡓ. ࡇࡢၥ㢟࡟ᑐࡋ⌧ᅾࡲ࡛࡟࣮ࣞࢨ⁐᥋(17,ࢫ┦࡟ࡣᡠࡽ࡞࠸. ࡇࢀࡀ㔠ᒓ࢞ࣛࢫࡢ᥋ྜ, ຍᕤࢆ㞴18)ࡋࡃࡋ࡚࠸ࡿ.

㉸㡢Ἴ᥋ྜ(24), ࣃࣝࢫ㏻㟁ᅽ᥋(25)࡞࡝࡟ࡼࡿ㔠ᒓ࢞ࣛࢫ, 㟁Ꮚࣅ࣮࣒⁐᥋(19), ᦶ᧿ᅽ᥋(20, 21), ᦶ᧿ᨩᢾ᥋ྜ(22, 23),ࡢ᥋ྜࡀヨࡳࡽࢀ, ྜ㔠ࡢ✀㢮࡜኱ࡁࡉ࡟ไ㝈ࡣ᭷ࡿࡀ⁐᥋࡟ᡂຌࡋ࡚࠸ࡿ.

 ≉ᚩ
ᅗ 2 ࡟㔠ᒓ࢞ࣛࢫ࡜⤖ᬗ㔠ᒓࡢ඾ᆺⓗ࡞ᛂຊ㸫ṍࡳ᭤⥺ࢆ♧ࡋࡓ. 㔠ᒓ࢞ࣛࢫࡣཎᏊ㓄ิࡀ୙つ๎ᛶ࡛≉ᐃࡢ 㔠ᒓ࢞ࣛࢫࡢ᥋ྜ

ࡍ࡭ࡾ㠃ࡀᏑᅾࡋ࡞࠸ࡓࡵ㢮ఝࡍࡿ⤖ᬗྜ㔠ࡼࡾࡶ㧗ᙉ㔠ᒓ࢞ࣛࢫࢆ⤖ᬗ໬ࡉࡏࡿࡇ࡜↓ࡃ⁐᥋ࡍࡿࡓࡵ࡟ࡣ,ᗘ࡛⪏⑂ປ≉ᛶ࡟ඃࢀ, ṍࡳ࡟ᑐࡋ࡚◚᩿ࡲ࡛ᙎᛶⓗ࡟⥅ᡭࡢ⁐⼥㒊ࢆ⮫⏺෭༷㏿ᗘ Rc ௨ୖ࡛ᛴ෭ࡍࡿᚲせࡀ

ኚᙧࡍࡿ. ࡲࡓᙎᛶ⋡ࡣ㢮ఝࡍࡿ⤖ᬗྜ㔠࡜ẚ㍑ࡋ࡚ᴫ

࠶ࡿ. ࡶࡋ Rc ࡼࡾࡶ㐜࠸࡜┤ࡕ࡟⤖ᬗ໬ࡋ࡚⬤࠸㔠ᒓ㛫

ࡡ 1㸭3 ࡛࠶ࡿࡀᘬᙇᙉᗘࡣ 3 ಸࢆ᭷ࡍࡿ. ౛࠼ࡤ Mg ྜ໬ྜ≀ࢆ⏕ᡂࡍࡿ. 㔠ᒓ㛫໬ྜ≀ࡢ⏕ᡂࡣ⥅ᡭࢆ⬤ᙅ໬㔠ࡢᙉᗘࡀ 300MPa ࡛࠶ࡿࡢ࡟ᑐࡋ Mg ᇶ㔠ᒓ࢞ࣛࢫࡢ

ࡍࡿࡓࡵ㏻ᖖࡣᮃࡲࢀ࡞࠸. ࡑࡇ࡛ࡇࢀࡲ࡛࡟㔠ᒓ࢞ࣛ

ᙉᗘࡣ 800MPa ࡛࠶ࡾ, SUS304 ࢫࢸࣥࣞࢫ㗰ࡀ 1400MPaࢫࡢ⁐᥋ἲࡀᗄࡘ࠿᳨ウࡉࢀ࡚ࡁࡓ. ᥋ྜἲࡣ ᗘ࡟ࡼ࡞ࡢ࡟ᑐࡋ FeCoBSiNb 㔠ᒓ࢞ࣛࢫࡣ 4400MPa ࡛࠶ࡿ.

ࡗ࡚ᾮ┦᥋ྜ, 㐣෭༷ᾮయ᥋ྜ, ప ᥋ྜ࡟኱ูࡉࢀࡿ.

㔠ᒓ࢞ࣛࢫࡣᙎᛶ㝈⏺ࡀ㧗࠸ࡓࡵṍࡳ࢚ࢿࣝࢠ࣮ࡢ⵳✚ᅗ 3 ࡟㔠ᒓ࢞ࣛࢫࡢ୍⯡ⓗ࡞ CCT㸦㐃⥆෭༷┦ኚែ᭤⥺㸧᭤⥺ࢆ♧ࡋࡓ. 㔠ᒓ࢞ࣛࢫࡣᾮ┦࠿ࡽ෭༷ࡍࡿ㝿࡟ᗘᒚṔࡀ CCT ᭤⥺ࡼࡾࡶᕥഃࢆ㏻ࢀࡤ࢔ࣔࣝࣇ࢓ࢫ
ࢆᙧᡂࡋ, ஺ᕪࡲࡓࡣྑഃࢆ㏻ࢀࡤ⤖ᬗ໬ࢆ㉳ࡇࡍ. ࡘࡲࡾᾮ┦᥋ྜ࡟࠾࠸࡚ CCT ᭤⥺ࡢඛ➃(ࣀ࣮ࢬ)࡟஺ᕪࡋ
࡞࠸ࡼ࠺࡞෭༷㏿ᗘ࡛ᛴ෭ࡍࢀࡤ⥅ᡭࡢ⤖ᬗ໬ࢆ㜵ࡄࡇ࡜ࡀ࡛ࡁࡿ. ࡋ࠿ࡋ࡞ࡀࡽ⁐⼥㒊ࡢ࿘ࡾ࡟ࡣᚲࡎ⇕ᙳ㡪㒊(HAZ)ࡀᏑᅾࡋ, ౛࠼⁐⼥ࡋ࡞ࡃ࡚ࡶ ᗘᒚṔࡀ CCT᭤⥺࡟஺ᕪࡍࢀࡤ⤖ᬗ໬ࡍࡿ. ⁐⼥㒊ࡣ⁐⼥࡟ࡼࡗ࡚ᵓ
㐀⦆࿴ࡢᒚṔࡀึᮇ໬ࡉࢀࡿࡀ, ⇕ᙳ㡪㒊ࡣᵓ㐀⦆࿴ࡀ㐍⾜ࡋ⥆ࡅ࡚࠸ࡿࡢ࡛⤖ᬗ໬ࡢὀពࡀᚲせ࡛࠶ࡿ.

ᅗ 㔠ᒓ࢞ࣛࢫ࡜⤖ᬗ㔠ᒓࡢ୍⯡ⓗ࡞ᛂຊࡦࡎࡳ᭤⥺ᾮ┦᥋ྜࡢ౛࡜ࡋ࡚ࡣ࣮ࣞࢨ⁐᥋ࡸ, 㟁Ꮚࣅ࣮࣒⁐᥋࡞࡝ࡀᣲࡆࡽࢀ, ⌧ᅾࡲ࡛࡟ᯈᮦࡸ⟩ᖏࡢࣅ࣮ࢻ࢜ࣥࣉ
࣮ࣞࢺ⁐᥋ࡀྍ⬟࡛࠶ࡿ. ࡇࢀࡽࡣ㧗㏿࡟⁐᥋ࡍࡿࡇ࡜

⚄ዉᕝ኱ᏛᕤᏛ◊✲ᡤᡤሗ ➨  ྕ᭦࡟ᛂ⏝ࢆᗈࡆࡿࡓࡵ࡟ࡣ㔠ᒓ࢞ࣛࢫࢆ㐺ᮦ㐺ᡤ࡛᥋ྜࡋ࡚」ྜⓗ࡟⏝࠸ࡿࡢࡀ᭷ຠ࡛࠶ࡿ࡜⪃࠼࡚࠸ࡿ. ࡑࡢࡓࡵ࡟ࡣ㔠ᒓ࢞ࣛࢫࢆຍᕤ㸦᥋ྜ, ษ๐, ᡂᙧࢆྵࡴ㸧࡛ࡁ࡞ࡅࢀࡤ┿౯ࢆⓎ᥹ࡍࡿࡇ࡜ࡣ࡛ࡁ࡞࠸. ḟࡢ❶࡛ࡣ㔠ᒓ࢞ࣛࢫຍᕤࡢ୍➃࡜ࡋ࡚㔠ᒓ࢞ࣛࢫࡢ⁐ᑕࢥ࣮ࢸ࢕
ࣥࢢ, ཬࡧ㔠ᒓ࢞ࣛࢫ⾲㠃ࡢ Cu ࣓ࢱࣛ࢖ࢬࢆ⤂௓ࡍࡿ.
㸱㸬㔠ᒓ࢞ࣛࢫࡢ⁐ᑕࢥ࣮ࢸ࢕ࣥࢢ
㧗㏿ࣇ࣮࣒ࣞ⁐ᑕ +92) ࡟ࡼࡿ」ྜ㔠ᒓ࢞ࣛࢫ⓶⭷ࡢస〇ᅗ 㔠ᒓ࢞ࣛࢫࡢ㐃⥆෭༷ኚែ᭤⥺㸦&&7 ᭤⥺㸧࡜ྛ✀᥋ྜἲࡢ ᗘᒚṔࡀྍ⬟࡛࠶ࡿࡀ, ୍᪉࡛࣮ࣞࢨࣅ࣮࣒ࡀ㈏㏻ࡍࡿⷧᯈࡸ

ᐃࡢࡍ࡭ࡾ㠃ࡀ↓࠸ࡓࡵ◚᩿ࡲ࡛ᙎᛶኚᙧࢆࡋ࡚㧗ᙉᗘ
࡛࠶ࡿ. ࡲࡓ⤖ᬗ⢏⏺ࡀ↓࠸ࡓࡵ⢏⏺⭉㣗ࡀ㉳ࡇࡾ࡟ࡃࡃ⪏⭉㣗ᛶ࡟ඃࢀࡿ. ࡇࡢࡼ࠺࡞ඃࢀࡓ≉ᛶࢆᣢࡘ㔠ᒓ⟩ᖏ࡟ࡋ࠿㐺⏝࡛ࡁ࡞࠸.
㐣෭༷≧ែ࡛ࡶ ᗘᒚṔࡀ CCT ᭤⥺ࡼࡾࡶᕥ࡟఩⨨ࡍࢀࡤ㐣෭༷≧ែࢆಖࡘࡇ࡜ࡀ࡛ࡁࡿ. ྜ㔠ࡢ✀㢮࡟ࡼࡗ࡚ࡣᩘศࡢ₯అᮇ㛫ࡀ࠶ࡿࡀᵓ㐀⦆࿴ࡢ㐍ࡳලྜ࡟ࡼ
ࡗ࡚ࡣᴟ➃࡟▷ࡃ࡞ࡿ.

 㔠ᒓ࢞ࣛࢫࡢཎᏊ㓄ิࡣ㛗࿘ᮇⓗ࡞つ๎ᛶࢆᣢࡓࡎ≉ᗘࡀ Tg ௨ୗ࡟࡞ࡿ࡜ᛴ㏿࡟⢓ᛶࡀపୗࡋ, Tx ௨ୖ࡟࡞ࡿ࡜┤ࡕ࡟⤖ᬗ໬ࡍࡿ. ࡑࡢࡓࡵ㐣෭༷≧ែ᥋ྜࡣ⥅ᡭࡢ ᗘࢆ Tg ࠿ࡽ Tx ࡢ⠊ᅖ࡟ไᚚࡍࡿᚲせࡀ࠶ࡿ. 㐣෭༷ᾮయ᥋ྜࡢ౛࡜ࡋ࡚ࡣᦶ᧿ᅽ
᥋, ᦶ᧿ᨩᢾ᥋ྜ, ㉸㡢Ἴ᥋ྜࡀᣲࡆࡽࢀࡿ. ᦶ᧿ᅽ᥋ࡣ✺ྜࡏࡓヨ㦂∦ࢆ┦ᑐⓗ࡟ᅇ㌿ࡉࡏ࡚Ⓨ⏕ࡋࡓᦶ᧿⇕࢞ࣛࢫࢆྛ✀ᮦᩱ⾲㠃࡟ࢥ࣮ࢸ࢕ࣥࢢࡍࢀࡤẕᮦࡢ≉ᛶࢆ⥔ᣢࡋ࡞ࡀࡽ⾲㠃࡟ᙉᗘ࡜⪏㣗ᛶࢆ௜୚ࡍࡿࡇ࡜ࡀ࡛
ࡁࡿ.
㧗㏿ࣇ࣮࣒ࣞ⁐ᑕ HVOF㸦High Velocity Oxygen Fuel
Spraying㸧ࡣ⦓ᐦ࡞ཌ⭷ࢆ㧗㏿࡟ᚓࡽࢀࡿࡇ࡜࠿ࡽ⏘ᴗ⏺࡛ὀ┠ࡉࢀ࡚࠸ࡿ. HVOF ࡣⅉἜ࡞࡝ࡢ⇞ᩱࢆ⇞↝ࡉࡏࡓࣇ࣮࣒ࣞ࡟ྛ✀ཎᩱ⢊ᮎࢆΰྜࡋ࡚ຍ⇕࡜ຍ㏿ࢆ⾜࠸, ᇶᯈୖ࡟྿ࡁ௜ࡅ࡚⓶⭷ࢆᚓࡿ⁐ᑕἲ࡛࠶ࡿ. ࣉࣛࢬ࣐⁐ᑕࡼࡾࡶ┦ᑐⓗ࡟ࣇ࣮࣒ࣞ ᗘࡀప࠸ࡇ࡜࡟≉ᚩ࡛᥋ྜࡍࡿ᥋ྜἲ࡛࠶ࡿ. ᦶ᧿࡟ࡼࡾᦾື㠃ࡣⓎ⇕ࡍࡿࡀ࠶ࡿ(30). ᮏ◊✲ࡣ HVOF ࢆ⏝࠸ࡓ Fe43Cr16Mo16C15B10 㔠ࡀ, ୍᪉࡛࢞ࣛࢫ㌿఩ ᗘ࡟㐩ࡍࡿ࡜㐣෭༷≧ែ࡟㌿⛣ᒓ࢞ࣛࢫ⁐ᑕ⓶⭷ࡢస〇, ཬࡧ WC/12Co ࢧ࣮࣓ࢵࢺࢆ

ࡋ࡚⢓ᛶ⋡ࡀపୗࡍࡿࡓࡵᦶ᧿ຊࡀῶᑡࡍࡿ. ⤖ᯝⓗ࡟ࡇࢀࡽࡢࣂࣛࣥࢫࡀ㔮ࡾྜ࠸, ⥅ᡭࡣ࢞ࣛࢫ㌿఩ ᗘ௜」ྜ໬ࡋ࡚ࡑࡢᦶ᧿ಀᩘࡢపῶ࡜⪏ᦶ⪖ᛶࡢྥୖࢆ⾜࠺ࡇ࡜ࢆ┠ⓗ࡜ࡋ࡚࠸ࡿ.

㏆࡟⮬Ⓨⓗ࡟ಖࡓࢀࡿ࡜ࡉࢀ࡚࠸ࡿ. 㐣෭༷≧ែࡢ⢓ᛶὶືࢆ฼⏝ࡋ࡚᥋ྜࢆ⾜࠸, 㐣෭༷ࡢ₯అ᫬㛫ෆ࡟ᦾືࢆṆࡵࢀࡤᛴ෭ࡍࡿࡇ࡜࡞ࡃ࢔ࣔࣝࣇ࢓ࢫࡢ⥅ᡭࢆᚓࡿࡇ࡜ࡀ࡛ࡁࡿ.
ప ᥋ྜࡢ౛࡜ࡋ࡚ࡣࡣࢇࡔ᥋ྜࡀᣲࡆࡽࢀࡿ. ࡣࢇࡔ᥋ྜ㸦౛࠼ࡤ SnAgCu ࡣࢇࡔࡢ᥋ྜ ᗘࡣ⣙ 573K㸧ࡣ㔠ᒓ࢞ࣛࢫࡢ Tg (Zr ᇶ㔠ᒓ࢞ࣛࢫࡢ Tg ࡣ⣙ 680K)ᮍ‶࡛ᐇ᪋ࡉࢀࡿࡢ࡛㔠ᒓ࢞ࣛࢫࢆ⇕ⓗ࡟⤖ᬗ໬ࡉࡏࡿࡇ࡜࡞
ࡃ᥋ྜࡀྍ⬟࡛࠶ࡿ. ࡲࡓ㔠ᒓ࢞ࣛࢫࢆኚᙧࡉࡏࡎ࡟᥋

᪉ἲ
 WC/12Co ࢧ࣮࣓ࢵࢺ⢊ᮎ(ĳ5-25ȝm)ࡣ↝⤖ࣂࣝࢡ࠿ࡽ
㐀⢏ࡋࡓ. Fe43Cr16Mo16C15B10 㔠ᒓ࢞ࣛࢫ⢊ᮎ(ĳ10-25ȝm)ࡣ࢔࣮ࢡ⁐ゎ࡛ྜ㔠໬ࡋࡓẕྜ㔠࠿ࡽ࢞ࢫ࢔ࢺ࣐࢖ࢬἲ࡛స〇ࡋࡓ. ♧ᕪ㉮ᰝ⇕㔞ᐃ㸦DSC)࡛

Fe43Cr16Mo16C15B10 㔠ᒓ࢞ࣛࢫࡢ Tg, Tx ࡣࡑࢀࡒࢀ 875K ,941K ࡛࠶ࡗࡓ. ᮏᐇ㦂࡛⏝࠸ࡓ㧗㏿ࣇ࣮࣒ࣞ⁐ᑕ⿦⨨ࡢᴫᙧࢆᅗ 4 ࡟♧ࡍ. ΰྜࡋࡓཎᩱ⢊ᮎࢆⅉἜ㸭㓟⣲ࣇྜ࡛ࡁࡿ၏୍ࡢ᥋ྜἲ࡛࠶ࡿ.
᪤࡟㏙࡭ࡓࡼ࠺࡟㔠ᒓ࢞ࣛࢫࡣᶵᲔⓗᛶ㉁, ໬Ꮫⓗᛶ㉁, ☢Ẽⓗᛶ㉁, 㐣෭༷≧ែࡢ⢓ᛶὶືᛶ࡞࡝࡟࠾࠸࡚
ᚑ᮶ࡢ⤖ᬗ㔠ᒓ࡟ࡣぢࡽࢀ࡞࠸≉␗࡞ᛶ㉁ࢆ᭷ࡋ࡚࠸ࡿ.
ࡇࢀࡽࡢ≉ᛶࢆ฼⏝ࡋ࡚ࢳ࣮ࣙࢡࢥ࢔(26), ࢦࣝࣇࢡࣛࣈ
࣊ࢵࢻ(27), ࢸࢽࢫࣛࢣࢵࢺ, ᦠᖏ㟁ヰ⏝⟂య(27), ගࣇ࢓࢖ࣂ࣮᥋⥆➃Ꮚ(28), ගᏛ࣑࣮ࣛ(29)࡞࡝࡟ᛂ⏝ࡉࢀ࡚࠸ࡿ.
ࡇࢀࡽࡢከࡃࡣ㔠ᒓ࢞ࣛࢫ༢యࢆ฼⏝ࡋࡓࡶࡢ࡛࠶ࡿࡀ,ᐃࡋࡓᅗ 㧗㏿ࣇ࣮࣒ࣞ⁐ᑕ㸦+92)㸧ḟୡ௦ᶵᲔᮦᩱࠕ㔠ᒓ࢞ࣛࢫࠖࡢ≉ᛶ࡜ຍᕤ࣮࣒ࣞ࡟ᑟධࡋ࡚ຍ⇕ࡍࡿ࡜ྠ᫬࡟㉸㡢㏿ࡲ࡛ຍ㏿ࡋ࡚ᇶᯈ࡟⾪✺ࡉࡏࡿࡇ࡜࡛⓶⭷ࢆᙧᡂࡍࡿ. ᇶᯈࡣ⾲㠃ࢆࣈࣛࢫࢺຍᕤࡋࡓࢫࢸࣥࣞࢫ㗰 SUS304㸦ཌࡳ 5 mm㸧ࢆ⏝࠸ࡓ. స〇ࡋࡓ」ྜ⁐ᑕ⓶⭷ࡢ⤌⧊ࡣ㉮ᰝᆺ㟁Ꮚ㢧ᚤ㙾, ගᏛ㢧ᚤ㙾, X ⥺ᅇᢡ(XRD)࡛ホ౯ࡋࡓ. ◳ࡉࡣࣅࢵ࣮࢝ࢬ◳ࡉヨ㦂ᶵ࡛⾜ࡗࡓ. ᦶ᧿ಀᩘ ᐃ࡜ᦶ⪖㔞 ᐃࡣ, ࣮࣎ࣝ࢜ࣥࢹ࢕ࢫࢡᦶ⪖ヨ㦂ᶵ࡜ ᚟ᦾືヨ㦂ᶵ࡛
⾜ࡗࡓ.

(a)

」ྜ⁐ᑕ⓶⭷࡜ᦶ⪖≉ᛶ ཎᩱ⢊ᮎ࡟ WC/12Co ࢆ 0, 5, 10, 20㸣ࡢẚ⋡࡛ΰྜࡋ࡚
ᡂ⭷ࡍࡿ࡜, ࡑࢀࡒࢀ 0, 2, 4, 8㸣ࡢ WC/12Co ࡀ⓶⭷࡟ෆ
ໟࡉࢀࡓ. ࠾࠾ࡼࡑཎᩱ⢊ᮎࡢ WC/12Co ྵ᭷⋡ࡢ 40㸣ࡀ⓶⭷࡟ྲྀࡾ㎸ࡲࢀࡿ. ⓶⭷୰ࡢ WC/12Co ࡢྵ᭷㔞ࡣࣇ࣮࣒ࣞࡢ⇞↝ ᗘࢆୖࡆࡿ࡟ᚑ࠸ቑຍࡍࡿࡀ, ࢔ࣔࣝ(b)ࣇ࢓ࢫࡢFe43Cr16Mo16C15B10 ⓶⭷ࡀᚓࡽࢀࡿ ᗘ᮲௳ࢆඃ
ඛࡉࡏࡿ࡜ࣇ࣮࣒ࣞ ᗘࡢୖ㝈ࢆపࡃタᐃࡍࡿᚲせࡀ࠶ࡾ WC/12Co ࡢ཰⋡ࢆ࠶ࡿ⛬ᗘపୗࡉࡏࡿࡇ࡜ࡣ㑊ࡅࡽᅗ  D :&&R)H&U0R&% ཬࡧ E 
:&&R)H&U0R&% 」ྜ໬⓶⭷ࡢ᩿㠃
6(0 ീ  ࢀ࡞࠸.
ᅗ 5 ࡟ WC/12Co ࢆ 10%ྵࡴཎᩱ⢊ᮎ࡜ᚓࡽࢀࡓ⁐ᑕ࡜ࡀ࡛ࡁࡿ. 㐣෭༷ᾮయ᥋ྜ࡛ࡣᛴ෭ࡢᚲせ࡞࠸ࡢ࡛ᆒ

⓶⭷ࡢ XRD ࡢ⤖ᯝࢆ♧ࡋࡓ. ᅇᢡゅ 35o ࠿ࡽ 50o ࡟࢔ࣔ㉁࡞࢔ࣔࣝࣇ࢓ࢫࡢ⓶⭷ࢆẚ㍑ⓗ࡟ᐜ᫆࡟ᚓࡿࡇ࡜ࡀ࡛

ࣝࣇ࢓ࢫ≉᭷ࡢࣁ࣮࣮ࣟࣃࢱ࣮ࣥࡀほᐹࡉࢀࡿ. ࡇࢀࡣ

ࡁࡿ. ࡇࢀࡣ㔠ᒓ࢞ࣛࢫ≉᭷ࡢᛶ㉁ࢆᕦጁ࡟฼⏝ࡋࡓࣉཎᩱࡢFe43Cr16Mo16C15B10 㔠ᒓ࢞ࣛࢫ⢊ᮎࡀ࢔ࣔࣝࣇ࢓ࢫ

ࣟࢭࢫ࡛࠶ࡿ.

ࢆ⥔ᣢࡋࡓࡲࡲ⓶⭷ࢆᙧᡂࡋ࡚࠸ࡿࡇ࡜ࢆព࿡ࡋ࡚࠸ࡿ.

ᅗ 6 ࡟ WC/12Co ࢆ(a)0%-, ཬࡧ(b)8%ྵࡴ WC/12Co–

HVOF ἲ࡛ࡣ኱㒊ศࡢ㔠ᒓ࢞ࣛࢫ⢊ᮎࡀ⼥Ⅼ࡟㐩ࡋ࡚

Fe43Cr16Mo16C15B10 㔠ᒓ࢞ࣛࢫ」ྜ⁐ᑕ⭷ࡢ᩿㠃෗┿ࢆ♧࠾ࡽࡎ, 㐣෭༷ᾮయ≧ែᇦ㸦ǻT=Tx-Tg=66K㸧࡛㣕⾜ࡋ࡞

ࡋࡓ. WC/12Co ࡀ 0㸣࡛ࡣ࣓ࣛࣛ≧ࡢ Fe43Cr16Mo16C15B10

ࡀࡽᇶᮦ࡟㉸㡢㏿࡛⾪✺, ೫ᖹ໬ࡋ࡚࢞ࣛࢫ┦ࡢ⓶⭷ࡀ㔠ᒓ࢞ࣛࢫᒙࡀࢺࣛࣂ࣮ࢫࡈ࡜࡟✚ࡳ㔜࡞ࡗࡓ⤌⧊ࢆᙧᚓࡽࢀࡿ(30). ⁐ᑕ⓶⭷ࡢᙧᡂࢆཎᩱ⢊ᮎྠኈࡢᚤどⓗ࡞ᡂࡋ, ᒙ㛫࡟ࡣẚ㍑ⓗከࡃࡢ✵㝽ࡀほᐹࡉࢀࡓ. ୍᪉࡛᥋ྜ࡜⪃࠼ࢀࡤ, 㐣෭༷≧ែ࡛⢓ᛶὶືᛶࢆᣢࡗࡓ㔠ᒓ

WC/12Co ࢆ 8%ྵࡴ⓶⭷ࡣ⦓ᐦ໬ࡋ࡚࠸ࡿ. 㧗࠸㐠ື㔞࢞ࣛࢫࡀ⾪ᧁ࡛㉸ረᛶኚᙧࡋ࡞ࡀࡽ᥋ྜࡋࡓ࡜ᤊ࠼ࡿࡇ

ࢆᣢࡘ WC/12Co ࡀ Fe43Cr16Mo16C15B10 㔠ᒓ࢞ࣛࢫ࡜ࡢ⾪ᅗ :&&R)H&U0R&% 」ྜ⁐ᑕ⓶⭷ࡢ ; ⥺ᅇᢡࣃࢱ࣮ࣥ  ᅗ :&&R)H&U0R&%」ྜ⁐ᑕ⓶⭷ࡢ᩿㠃ࡢ 9LFNHUV ◳ࡉ  ⚄ዉᕝ኱ᏛᕤᏛ◊✲ᡤᡤሗ ➨  ྕFe43Cr16Mo16C15B10 㔠ᒓ࢞ࣛࢫ」ྜ⓶⭷ࡢᦶᦶ⪖⑞ࢆ♧ࡋ
ࡓ. Fe43Cr16Mo16C15B10 㔠ᒓ࢞ࣛࢫࡢᦶ⪖⑞࡟ࡣ୍㒊࡟ᓥ≧ࡢ௜╔≀ࡀほᐹࡉࢀࡓ. ᦶ⪖࡟ࡼࡿᒁᡤⲴ㔜࡜⇕࡟ࡼࡾ㐣෭༷≧ែ࡟⛣⾜ࡋࡓ㔠ᒓ࢞ࣛࢫࡀจ╔ࡋࡓࡓࡵ࡜᥎
ࡋ࡚࠸ࡿ. ୍᪉࡛ WC/12Co- Fe43Cr16Mo16C15B10 㔠ᒓ࢞ࣛࢫ」ྜ⓶⭷ࡣ㔠ᒓ࢞ࣛࢫ༢యࡼࡾࡶ῝࠸ᦶ⪖യࡀᦾື᪉ྥ࡜ᖹ⾜࡟ほᐹࡉࢀ࡚࠸ࡿࡇ࡜࠿ࡽ WC/12Co ࡢ୍㒊ࡀ⬺ⴠࡋ࡚ᦶ⪖࡟㛵୚ࡋ࡚࠸ࡿ࡜⪃࠼ࡽࢀࡿ.
㔠ᒓ࢞ࣛࢫ≉᭷ࡢ㐣෭༷≧ែࢆ㐺ᙜ࡟฼⏝ࡍࢀࡤⰋ㉁ᅗ ᦶ᧿ಀᩘ࡜ẚᦶ⪖㔞࡞࢔ࣔࣝࣇ࢓ࢫࡢ⓶⭷ࢆẚ㍑ⓗ⡆༢࡟ᚓࡿࡇ࡜ࡀ࡛ࡁࡿ.
ࡲࡓࢧ࣮࣓ࢵࢺ⢊ᮎࢆ」ྜ໬ࡍࢀࡤ㔠ᒓ࢞ࣛࢫ⓶⭷࡟⪏✺ࡍࡿࡇ࡜࡟ࡼࡾ㧗ᐦᗘ໬ࢆಁࡀࡋ࡚࠸ࡿ. ࡑࢀ࡟ᚑ࠸

ᦶ⪖ᛶ, ◳ࡉ, ᦶ᧿ಀᩘࡢపῶ࡞࡝ࡢ≉ᛶࢆ㏣ຍࡍࡿࡇ

ぢ࠿ࡅࡢ Vickers ◳ࡉࡶྥୖࡋ࡚, WC/12Co ࡢྵ᭷㔞ࢆ 0࡜ࡀྍ⬟࡛࠶ࡿ.

࠿ࡽ 8㸣࡟ቑຍࡍࡿ࡜⓶⭷⾲㠃ࡢ Vickers ◳ࡉࡣ 660HV
࠿ࡽ 870HV ࡟ୖ᪼ࡋࡓ(ᅗ 7). ୍᪉࡛᩿㠃ࡢぢ࠿ࡅ◳ࡉࡣ, WC/12Co 㔞࡟㛵ࢃࡽࡎ660HV ๓ᚋ࡛ኚ໬ࡢᖜࡣ࡯࡜

㸲㸬㔠ᒓ࢞ࣛࢫ⾲㠃ࡢ &X ࣓ࢱࣛ࢖ࢬ

ࢇ࡝↓࠿ࡗࡓ. ࡇࢀࡽࡢ␗᪉ᛶࡣ WC/12Co ࡀ೫ᖹ໬ࡋ

㔠ᒓ࢞ࣛࢫࡢప ᥋ྜ࡚⓶⭷ࢆᙧᡂࡋ࡚࠸ࡿࡇ࡜࡟㉳ᅉࡋ࡚࠸ࡿ.
ᅗ 8 ࡟ẚᦶ⪖㔞࡜ᦶ᧿ಀᩘࢆ♧ࡋࡓ. ẚᦶ⪖㔞ࡣ
WC/12Co ࢆ 0 ࠿ࡽ 8㸣࡟ቑຍࡍࡿ࡜ 0.8×10-4mm3Nm ࠿ࡽ-43㔠ᒓ࢞ࣛࢫࡢỗ⏝ⓗ᥋ྜἲ࡜ࡋ࡚ࡣࢇࡔ᥋ྜࡀ࠶ࡿ.
ࡣࢇࡔ᥋ྜࡀ᭷฼࡞Ⅼࡣప ᥋ྜࡀྍ⬟࡞ࡇ࡜࡛࠶ࡿ.
౛࠼ࡤ㖄ࣇ࣮ࣜࡣࢇࡔ Sn-3Ag-0.5Cu ࡣ⣙ 573K ࡛᥋ྜࡀ0.1×10 mm Nm ࡟పῶࡍࡿ. ᦶ᧿ಀᩘࡶ 0.65 ࠿ࡽ 0.5 ࡟ྍ⬟࡛, ࡇࢀࡣከࡃࡢ㔠ᒓ࢞ࣛࢫࡢ࢞ࣛࢫ㌿఩ ᗘࡼࡾపῶࡉࢀ WC/12Co ༢యࡢᦶ᧿ಀᩘ࡛࠶ࡿ 0.42 ࡟㏆᥋ࡋࡶప࠸ࡓࡵ⇕ⓗ࡞⤖ᬗ໬ࢆ㉳ࡇࡍࡇ࡜࡞ࡃ᥋ྜࡍࡿࡇ࡜࡚ ࠸ ࡃ ࡇ ࡜ ࡀ ศ ࠿ ࡗ ࡓ . ᅗ 9(a) ࡟ ᦶ ⪖ ヨ 㦂 ᚋ ࡢࡀ࡛ࡁࡿ. ࡋ࠿ࡋၥ㢟Ⅼࡣ Cu-Zr ⣔㔠ᒓ࢞ࣛࢫ㸦౛࠼ࡤ

Fe43Cr16Mo16C15B10 㔠ᒓ࢞ࣛࢫࡢᦶ⪖⑞ࢆ, (b)࡟WC/12Co-

Cu36Zr48Al8Ag8㸧ࡢ⾲㠃ࡣᙉᅛ࡞㓟໬⿕⭷࡛そࢃࢀ࡚࠸ࡿ
ࡓࡵࡣࢇࡔࡀ඲ࡃࡠࢀ࡞࠸ࡇ࡜࡛࠶ࡿ.
㔠ᒓ࢞ࣛࢫࡢ㓟໬⿕⭷࡜ࡣࢇࡔ࡟ࡼࡿࡠࢀᛶࡢ㛵ಀ࡟ࡘ ࠸ ࡚ࡣ ᪤ ࡟ᗄ ࡘ ࠿ࡢ ሗ ࿌ࡀ ࠶ ࡿ . A. Imai ࡽ ࡣ
Cu60Zr30Ti10 㔠ᒓ࢞ࣛࢫ࡟ᑐࡋ࡚㉸㧗┿✵ୗ࡛ Ar ࢖࢜ࣥࣅ࣮࣒ࢫࣃࢵࢱࣜࣥࢢࢆ⾜࠸⾲㠃ࡢ㓟໬⿕⭷ࡢ㝖ཤࢆ⾜ࡗࡓ. ࡑࡇ࡟ Ag ⷧ⭷ࢆᩘ nm ሁ✚ࡉࡏࡿ࡜኱Ẽ࡟᭚ࡋࡓᚋࡶࡣࢇࡔ࡟ࡼࡿࡠࢀࡀⰋዲ࡟ಖࡓࢀࡿࡇ࡜ࢆ᫂ࡽ࠿࡟

(a)ࡋࡓ(32). H. Nishikawa ࡽࡣ㖄ࣈ࣮ࣜࡣࢇࡔ࡟ࡼࡿྛ✀㔠ᒓ࢞ࣛࢫࡢࡠࢀᛶ࡟ࡘ࠸࡚ㄪᰝࢆ⾜࠸, Pd ᇶ௨እࡢ Zr ᇶ㔠ᒓ࢞ࣛࢫ࡞࡝ࡣ㓟໬⿕⭷ࡀᙉᅛ࡞ࡓࡵ඲ࡃࡠࢀ࡞࠸ࡇ
࡜ࢆሗ࿌ࡋ࡚࠸ࡿ. ࡑࡋ࡚㓟໬⿕⭷ࡢ㝖ཤࢆ┠ⓗ࡜ࡋ࡚ྛ✀ࣇࣛࢵࢡࢫࡢే⏝࡞࡝ࡶヨࡳ࡚࠸ࡿࡀࡠࢀᛶࢆᨵၿ
ࡍࡿࡲ࡛࡟ࡣ⮳ࡗ࡚࠸࡞࠸(33). H. Abe ࡽࡣ Cu-Zr-Ti ⣔㔠ᒓ࢞ࣛࢫࢆࣇࢵ㓟࡟ᾐₕࡋ࡚, ࢖࢜ࣥ໬ഴྥࡢ㐪࠸࠿ࡽ(b)

Zr ࡜ Ti ࢆ㑅ᢥ⁐ゎࡋ࡚⾲㠃࡟ Cu ⷧ⭷ࢆᯒฟࡉࡏࡿ஦࡟
ᡂຌࡋ࡚࠸ࡿ(34). ࡓࡔࡋᚓࡽࢀࡓ Cu ⷧ⭷ࡣከᏍ㉁࡛࠶
ࡾ, ᑦୟࡘ㔠ᒓ࢞ࣛࢫࡢ㓟໬⿕⭷ୖ࡟ሁ✚ࡋ࡚࠸ࡓࡓࡵ,ᅗ ᦶ⪖ヨ㦂⑞ D )H&U0R&% E :&&R)H&U0R&% 」ྜ⁐ᑕ⓶⭷Cu ⷧ⭷ࡀࡣࢇࡔ࡟⁐ゎࡍࡿ࡜㓟໬⿕⭷ࡀ㟢ฟࡋ࡚ࡠࢀ
ࡀᴟ➃࡟ᝏ໬ࡍࡿၥ㢟ࡀ࠶ࡗࡓ. S. Tamura ࡽࡣ, ࡣࢇࡔᾎᵴ࡟ᾐࡋࡓ Zr ᇶ㔠ᒓ࢞ࣛࢫ࡟ᑐࡋ㉸㡢Ἴࢆ୚࠼࡚࢟
ࣕࣅࢸ࣮ࢩࣙࣥຠᯝ࡟ࡼࡾ≀⌮ⓗ࡟㓟໬⿕⭷ࢆ㝖ཤࡍࡿḟୡ௦ᶵᲔᮦᩱࠕ㔠ᒓ࢞ࣛࢫࠖࡢ≉ᛶ࡜ຍᕤᐇ㦂ࢆ⾜ࡗࡓ(35). ࡑࡢ⤖ᯝࡣࢇࡔࢆࡠࡽࡍࡇ࡜࡟ࡣᡂຌCu ⟩ࡢ⁐╔ࣉࣟࢭࢫࡣ┿✵ᐜჾෆ࡛ᐇ᪋ࡉࢀࡑࡢᴫ␎

ࡋࡓࡀ㉸㡢Ἴ࣮࣍ࣥࡢᴟ㏆ഐࡢࡳࡋ࠿⿕⭷㝖ཤຠᯝࡀ࡞

ࢆᅗ 10 ࡟♧ࡋࡓ. (a)༑ศ࡞኱ࡁࡉࢆᣢࡘ Cu 㗪ᆺࡢഃ㠃࠸࡞࡝ᐇ⏝㠃࡛ࡢㄢ㢟ࡣከ࠸. ࡇࢀࡽ࡟ඹ㏻ࡍࡿၥ㢟Ⅼ㸦⭷ཌ2ȝm㸧࡟ w30×l25×t2mmࡢพࡳࢆษ๐ຍᕤࡍࡿ. Cu⟩ࡣ, 㔠ᒓ࢞ࣛࢫࡀ኱Ẽ࡜᥋ゐࡋ୍࡚ᗘ㓟໬⿕⭷ࡀᙧᡂࡍ

ࢆᆒ୍࡟㈞ࡾྜࢃࡏࡓࢱࣥࢢࢫࢸࣥᨭᣢᯈ
㸦ᯈཌ100ȝm㸧ࡿ࡜㝖ཤࡣ┦ᙜᅔ㞴࡞஦࡛࠶ࡿ. ࡑࡇ࡛ᡃࠎࡣ㓟໬⿕⭷࡛ࡑࡢพࡳࢆሰ࠸࡛ᅛᐃࡍࡿ. ࡑࡢᚋ Cu36Zr48Al8Ag8 ẕࡀᙧᡂࡍࡿ๓ࡢ⁐‫ࡢ‮‬ẁ㝵࡛ Cu ⟩ࢆ⁐╔ࡍࡿࡇ࡜࡛㓟ྜ㔠ࢆ▼ⱥ⟶ࣀࢬࣝෆ࡛ㄏᑟຍ⇕⁐ゎࡋ࡚, ⁐‫ࡀ‮‬໬⿕⭷ࡢᙧᡂࢆᢚṆࡍࡿ࢔࢖ࢹ࢕࢔ࢆ╔᝿ࡋࡓ. ᮏ❶࡛1473K ࡟࡞ࡗࡓ᫬Ⅼ࡛ Cu 㗪ᆺࡢพࡳ࡜ Cu ⟩࡜ࡢ㛫㝽࡟ࡣ Cu36Zr48Al8Ag8 㔠ᒓ࢞ࣛࢫ࡟ᑐࡍࡿ Cu ⟩ࡢ⁐╔, ᚤ⣽ᑕฟ㗪㐀ࡍࡿ. (b)Cu ⟩(⼥Ⅼ 1356K)ࡣ⁐‫ࡢ‮‬వ⇕࡛▐᫬⤌⧊,࡟༙⁐⼥ࡋ࡚㔠ᒓ࢞ࣛࢫ⁐‫ࡿࡍ╔⁐࡜‮‬. ୍᪉࡛⁐‫ࡣ‮‬ᗘᒚṔࢩ࣑࣮ࣗࣞࢩࣙࣥ࡟ࡘ࠸࡚ㄽࡌࡿ.

Cu 㗪ᆺ࡟ᢤ⇕ࡉࢀ࡚ᛴ෭จᅛࡍࡿ. (c)⤖ᯝⓗ࡟ Cu ⟩ࡢヨᩱస〇᪉ἲCu36Zr48Al8Ag8 (atom%)ẕྜ㔠ࡣ⣧ᗘ 99.9%௨ୖࡢཎᩱ
㔠ᒓࢆ࢔࣮ࢡ⁐ゎࡋ࡚స〇ࡋࡓ. ♧ᕪ㉮ᰝ⇕㔞 ᐃ DSC⁐╔࡜ Cu36Zr48Al8Ag8 ྜ㔠ࡢ࢞ࣛࢫ໬ࢆྠ᫬࡟㐍⾜ࡉࡏࡿࡇ࡜ࡀ࡛ࡁࡿ. W ⷧᯈࡣ⼥Ⅼࡀ㧗࠸ࡓࡵ⁐╔࡟ࡣ┤᥋㛵୚ࡏࡎ, ᚋ࡛⡆༢࡟ྲྀࡾእࡍࡇ࡜ࡀ࡛ࡁࡿ.

࡛ணࡵ ᐃࡋࡓ Cu36Zr48Al8Ag8 㔠ᒓ࢞ࣛࢫࡢ⇕≀ᛶ್ࡣCu ⟩࡜ Cu36Zr48Al8Ag8 㔠ᒓ࢞ࣛࢫࡢ⁐╔⏺㠃ࡢᚤ⣽ᵓ࢞ࣛࢫ㌿఩ ᗘ Tg=682K, ⤖ᬗ໬ ᗘ Tx=787K, ᖹ⾮┦㐀ࡣ㏱㐣ᆺ㟁Ꮚ㢧ᚤ㙾 TEM (JEOL, JEM-4000EX), ㉮ᰝࡢᾮ┦Ⅼ ᗘ Tm=1143K ࡛࠶ࡿ.

ᆺ㟁Ꮚ㢧ᚤ㙾 SEM㸦HITACHI, SU-70㸧ࢆ⏝࠸࡚ศᯒࡋࡓ.
ࡲࡓ Cu ⁐╔⭷࡟ࡼࡿ㓟໬⿕⭷ᙧᡂࡢᢚṆຠᯝࢆ᳨ドࡍࡿࡓࡵ࡟࣮࢜ࢪ࢙㟁Ꮚศග AES(ULVAC PHI, PHI680S)ࢆ
⏝࠸࡚㓟⣲⃰ᗘࡢ⾲㠃῝ࡉࣉࣟࣇ࢓࢖ࣝࢆ ᐃࡋࡓ. ࡠ
ࢀᛶࡣ Cu36Zr48Al8Ag8 㔠ᒓ࢞ࣛࢫୖ࡟ Su-3Ag-0.5Cu ࡣࢇࡔࢆ 543K ࡛ 1 ศ㛫࡟ࡠࡽࡋࡓᚋ࡟ࡠࢀᗈࡀࡾࢆほᐹࡋ࡚ホ౯ࡋࡓ.
 ᗘᒚṔࡢィ⟬᪉ἲ(a)Cu ⟩࠾ࡼࡧ Cu36Zr48Al8Ag8 㔠ᒓ࢞ࣛࢫࡀ⁐╔㐣⛬࡛⤒ࡓ ᗘᒚṔࢆ᫂ࡽ࠿࡟ࡍࡿࡓࡵ࡟୍ḟඖ㠀ᐃᖖ⇕ఏᑟィ⟬ࢆ⾜ࡗࡓ. 㔠ᒓ࢞ࣛࢫヨ㦂∦ࡣᖹ㠃ᑍἲ㸦w30×l25mm㸧
࡟ᑐࡋ࡚ཌࡳ㸦t2mm㸧ࡀᑠࡉ࠸ࡓࡵ, ཌࡳ᪉ྥࢆ㍈࡜ࡋࡓ୍ḟඖࣔࢹࣝ࡜ぢ࡞ࡋࡓ. ᮦᩱ༊ศ࡜タᐃ್ࡣࡑࢀࡒ(b)ᅗ ⁐‫‮‬௜㏆ࡢィ⟬ࣔࢹࣝ⾲ ᮦᩱࢹ࣮ࢱ(c)ᅗ &X ࣓ࢱࣛ࢖ࢬ &X=U$O$J㔠ᒓ࢞ࣛࢫࡢ D
స〇᪉ἲ E ࢡࣛࢵࢻ㐣⛬ࡢᴫᛕᅗ F ᏶஢⚄ዉᕝ኱ᏛᕤᏛ◊✲ᡤᡤሗ ➨  ྕࢀᅗ 11 ࡜⾲ 2 ࡟ࡲ࡜ࡵࡓ. ༊ศࡣ㡰࡟ Cu 㗪ᆺ㸦ཌࡳ㸸
50mm㸧㸭Cu36Zr48Al8Ag8 㔠ᒓ࢞ࣛࢫ㸦2mm㸧㸭Cu ⟩㸦2ȝm㸧㸭W ⷧᯈ㸦100ȝm㸧࡜ࡋࡓ. ࡑࢀࡒࢀࡢ༊ศ࡟タᐃࡋࡓ࣓ࢵࢩࣗ࡟ࣇ࣮࢚ࣜࡢᘧ㸦1㸧ࢆ㐺⏝ࡋ࡚ᕪศἲ࡟ࡼࡾ
ᗘࡢ᫬㛫ኚ໬ࢆィ⟬ࡋࡓ.

wT
wt

a

w 2T
 q 㸦㸯㸧
wx 2

ࡇࡇ࡛ T, t, x, q, a ࡣࡑࢀࡒࢀ ᗘ, ⤒㐣᫬㛫, ఩⨨, ෆ㒊Ⓨ⇕, ⇕ᣑᩓ⋡࡛࠶ࡿ. ⁐╔ࣉࣟࢭࢫࡣ┿✵ᐜჾෆ࡛⾜ࢃࢀࡿࡓࡵ Cu 㗪ᆺ࡜ W ⷧᯈࡢእቨࡣ᩿⇕ቃ⏺࡜ࡋࡓ.
㔠ᒓ࢞ࣛࢫ⁐‫ࢆ‮‬㗪㎸ࢇࡔ▐㛫ࢆ t㸻0s ࡜ࡋ࡚, ⁐‫ࡢ‮‬ึᮇ ᗘࡣ 1473K ࡜ࡋࡓ. Cu 㗪ᆺ, Cu ⟩, W ⷧᯈࡣ 300K
࡜ࡋࡓ. Cu36Zr48Al8Ag8 㔠ᒓ࢞ࣛࢫࡢ⇕ᣑᩓ⋡㸦300K㹼
1450K㸧ࡣ㢮ఝࡋࡓ≉ᛶࢆᣢࡘ Cu30Zr55Al10Ni5 㔠ᒓ࢞ࣛࢫࡢ್ࢆᘬ⏝ࡋࡓ(36). Cu ࡢ⇕ᣑᩓ⋡ࡣᅛ┦࠿ࡽᾮ┦ࡲ࡛ࡢ㐃⥆ࡋࡓ ᗘᇦ(300K-1505K)࡛ࡑࡢẚ⇕࡜⇕ఏᑟ⋡ࡢ✚࠿ࡽ⟬ฟࡋࡓ(37, 38). W ࡢ⇕ᣑᩓ⋡ࡶྠᵝ࡟⟬ฟࡋࡓ
(300K-1400K) (38). 㠀ᖹ⾮จᅛ࡛ࡣཎᏊ㓄ิࡢᵓ㐀⦆࿴ࡀ㐍ࡴ๓࡟෾⤖ࡉࢀࡿࡓࡵ⤖ᬗ໬࡟క࠺⇕ᨺฟ㸦DSC ࡛ᐃࡋࡓ⤖ᬗ໬࢚ࣥࢱࣝࣆ࣮ࡣ ǻH=3.6 kJ/mol(39㸧㸧ࡣ↓ࡃ,ࡲࡓ෭༷㏿ᗘࡀᴟ➃࡟㏿࠸ࡢ࡛₯⇕ࡣຍ࿡ࡋ࡚࠸࡞࠸.
 ⁐╔⏺㠃ࡢᚤ⣽⤌⧊స〇ࡋࡓヨ㦂∦ࡢ⁐╔㠃ࡣ㖡ගἑࢆ♧ࡋ, ࡯ࡰ඲㠃ࡀ⁐╔ࡋࡓ. ᅗ12 ࡣCu ⟩⁐╔Cu36Zr48Al8Ag8 㔠ᒓ࢞ࣛࢫࡢ
᩿㠃 SEM ീ࡛࠶ࡿ. ୰ኸࡢ㯮Ⰽ㒊ศࡀ Cu ⟩࡛, ୗ༙ศࡢ⅊Ⰽ㒊ศࡀ Cu36Zr48Al8Ag8 㔠ᒓ࢞ࣛࢫ࡛࠶ࡿ. Cu ⟩࡜
Cu36Zr48Al8Ag8 㔠ᒓ࢞ࣛࢫࡣᗈ࠸⠊ᅖ࡛࣎࢖ࢻࡀほ ࡉࢀࡎ㔠ᒓ⤌⧊ⓗ࡟㐃⥆ⓗ࡟᥋ྜࡋ࡚࠸ࡿ. Cu ⟩ࡣ᏶඲࡟ྜ㔠໬ࡍࡿࡇ࡜࡞ࡃ⁐╔ࡋ࡚࠸ࡿࡇ࡜࠿ࡽ, ⤌ᡂࡢ┦஫ᣑᩓࡀ㐍ࡴ๓࡟⁐╔ࡀ᏶஢ࡋࡓ࡜᥎ ࡉࢀࡿ. ୍⯡࡟ࢫᅗ  D &X ࣓ࢱࣛ࢖ࢬ &X=U$O$J㔠ᒓ࢞ࣛࢫࡢ 7(0 ᫂ど㔝ീ E  F  G ࡣࡑࢀࡒࢀ㔠ᒓ࢞ࣛࢫ཯ᛂᒙ
&X ⟩ᒙࡢ㟁Ꮚᅇᢡ  ࣃࢵࢱࣜࣥࢢࡸ࣓ࢵ࢟࡟ࡼࡿ Cu ࢥ࣮ࢸ࢕ࣥࢢࡢᐦ╔ࡣศᏊ㛫ຊ࡟ࡼࡿࡶࡢ࡛࠶ࡿࡀ, ᮏ◊✲࡛ᐇ᪋ࡋࡓ⁐╔ࡢཎ ື ຊ ࡣ 㔠 ᒓ ⤖ ྜ ࡛ ࠶ ࡿ . ࡑ ࡢ ࡓ ࡵ Cu ⟩ ࡜
Cu36Zr48Al8Ag8 㔠ᒓ࢞ࣛࢫࡢᐦ╔ࡣᙉᅛ࡛࠶ࡾ, ࡲࡓ኱Ẽࡀ⁐╔⏺㠃࡟ධࡾ㎸ࡴ㝽㛫ࡶᏑᅾࡋ࡞࠸.
ᅗ 13(a)ࡣ Cu ⟩࡜ Cu36Zr48Al8Ag8 㔠ᒓ࢞ࣛࢫࡢ⏺㠃ࢆ῝ࡉ᪉ྥ࡟࣐࢖ࢡࣟࢧࣥࣉࣜࣥࢢࡋࡓᴟⷧヨᩱࡢ TEM
᫂ど㔝ീ࡛࠶ࡿ. 2Pm ࡢ Cu ⟩ࡢୗ࡟ 4Pm ࡢࢹࣥࢻࣛ࢖
ࢺࡢ཯ᛂᒙࡀᙧᡂࡋ, ᭦࡟ 2Pm ࡢ⤖ᬗ㸭࢔ࣔࣝࣇ࢓ࢫΰ
ྜᒙ, Cu36Zr48Al8Ag8 㔠ᒓ࢞ࣛࢫ࡬࡜⥆ࡃ㐃⥆࡞⤌⧊ࡀほᐹࡉࢀࡓ. ᅗ13(b), (d)ࡣCu36Zr48Al8Ag8 㔠ᒓ࢞ࣛࢫ࠾ࡼࡧ
Cu ⟩㒊ศࡢ㟁Ꮚ⥺ᅇᢡ࡛࠶ࡾࡑࢀࡒࢀ࢔ࣔࣝࣇ࢓ࢫ࠾
ࡼࡧ cubic-Cu ࡛࠶ࡿࡇ࡜ࡀ☜ㄆࡉࢀࡓ. ᅗ 13(c)ࡣ཯ᛂᒙ
ࡢ㟁Ꮚ⥺ᅇᢡ࡛࠶ࡿ. 4 ඖ⣔ྜ㔠ࡢ㠀ᖹ⾮⤌⧊ࡢࡓࡵṇ☜࡞┦ྠᐃࡣ㞴ࡋ࠸ࡀᚤ⤖ᬗ࡛ᵓᡂࡉࢀ࡚࠸ࡿ.
ᅗ 14(a)࡟ Cu ⟩⁐╔ Cu36Zr48Al8Ag8 㔠ᒓ࢞ࣛࢫࡢ AESศᯒ⤖ᯝࢆ♧ࡍ. ⁐╔ࡋࡓ┤ᚋࡢヨᩱ⾲㠃࠿ࡽࡣ
Cu-LMM, C-KLL, O-KLL ࡀ᳨ฟࡉࢀࡓ. C ࡣ௜╔ࡋࡓ᭷ᶵ≀ࡢ⏤᮶࡛࠶ࡿ. Cu ⁐╔ᒙࢆࢫࣃࢵࢱࣜࣥࢢ࡛ྲྀࡾ㝖ࡃ࡜ Cu-LMM, Zr-MNN, Ag-MNN ࡀ᳨ฟࡉࢀࡓ. ᅗ 14(b)࡟⾲㠃ࢆࢫࣃࢵࢱࣜࣥࢢࡋ࡞ࡀࡽ ᐃࡋࡓ AES ῝ࡉࣉࣟࣇ࢓࢖ࣝࢆ♧ࡍ. ᭱⾲㠃࡟ Cu ࡢ㓟໬⿕⭷ࡀほᐹࡉࢀࡿࡀࡑࢀ௨㝆ࡣ㓟⣲ࡢ⃰໬ᒙࡣほᐹࡉࢀ࡞࠿ࡗࡓ.
Cu36Zr48Al8Ag8 㔠ᒓ࢞ࣛࢫࡣ㓟໬⿕⭷ࢆᙧᡂࡍࡿ๓ࡢ⁐‫ࡢ‮‬ẁ㝵࡛ Cu ⟩࡜⁐╔ࡋ, ࡑࡢᚋ Cu ⟩ࡣ㓟໬⿕⭷ࡢᙧᡂࢆᢚṆࡍࡿᙺ๭ࢆᯝࡓࡋࡓ࡜⪃࠼ࡽࢀࡿ.
᳨ฟࡉࢀࡓ Cu ࡣࢫࣃࢵࢱࣜࣥࢢ᫬㛫 0-50min㸦Cu ⟩ᒙ㸧ᅗ &X ࣓ࢱࣛ࢖ࢬ &X=U$O$J㔠ᒓ࢞ࣛࢫࡢ᩿㠃 6(0 ീ  ࡛ࡣ୍ᐃ್ࢆ♧ࡋ, ࢫࣃࢵࢱࣜࣥࢢ᫬㛫 50-140min㸦཯ᛂᒙ㸧࡛ࡣ㐃⥆ⓗ࡟ῶᑡࡉࡏ࡞ࡀࡽ᭱⤊ⓗ࡟ Cu36Zr48Al8Ag8㔠ᒓ࢞ࣛࢫࡢ⤌ᡂ࡟཰᮰ࡍࡿ. ㏫࡟ Zr ࡣ Cu ⟩ᒙ࡛ࡣ᳨ḟୡ௦ᶵᲔᮦᩱࠕ㔠ᒓ࢞ࣛࢫࠖࡢ≉ᛶ࡜ຍᕤ



(a)

ᅗ 6Q$J ࡣࢇࡔࡢࡠࢀ D DVFDVW
&X=U$O$J㔠ᒓ࢞ࣛࢫ E &X ࣓ࢱࣛ࢖ࢬ &X=U$O$J㔠ᒓ࢞ࣛࢫ  ⁐╔㐣⛬ࡢ ᗘᒚṔᗘᒚṔィ⟬ࡢ⤖ᯝࢆᅗ 16 ࡟♧ࡍ. ༊ศࡣᕥ࠿ࡽ Cu

㗪ᆺ(Cu mold)㸭Cu36Zr48Al8Ag8 ྜ㔠㸭Cu ⟩(Cu film)㸭W
ⷧᯈ(W plate)࡜ࡋࡓ. Cu36Zr48Al8Ag8 ⁐‫ ࢆ‮‬Cu 㗪ᆺ࡟ὀධ(b)ࡋࡓ┤ᚋࢆ 0s ࡜ࡋ࡚ึᮇ ᗘࡣ 1473K ࡜ࡋࡓ.
⤒㐣᫬㛫ࡀ 75ms ࡲ࡛ࡣ Cu36Zr48Al8Ag8 ⁐‫࡟ୖࡣ‮‬ฝࡢᗘศᕸࢆ♧ࡍ. ࡇࢀࡣ Cu36Zr48Al8Ag8 ⁐‫ࡢ‮‬వ⇕ࡢ୍㒊ᅗ  D &X ࣓ࢱࣛ࢖ࢬ &X=U$O$J㔠ᒓ࢞ࣛࢫࡢ
$(6 ࢫ࣌ࢡࢺࣝ E $(6 ῝ࡉࣉࣟࣇ࢓࢖ࣝ  

ࡀ Cu ⟩࡟ఏ⇕ࡋ࡚࠸ࡿࡇ࡜ࢆ♧ࡋ࡚࠸ࡿ. Cu ⟩࡜ W ⷧᯈࡢཌࡳࡣ Cu36Zr48Al8Ag8 ⁐‫࡜‮‬ẚ㍑ࡋ࡚⣙ 20 ศࡢ 1 ࡛
࠶ࡾ, ᭦࡟እቨࡣ᩿⇕ቃ⏺࡛࠶ࡿࡓࡵ Cu ⟩ࡣᛴ㏿࡟᪼ฟࡉࢀ࡞࠸ࡀ, ཯ᛂᒙ࡛ࡣ㐃⥆ⓗ࡟⤌ᡂࢆቑຍࡋ࡚᭱⤊ࡍࡿ. 100ms ௨㝆ࡣ Cu36Zr48Al8Ag8 ⁐‫ ࡟୺ࡣ‮‬Cu 㗪ᆺⓗ࡟ Cu36Zr48Al8Ag8 㔠ᒓ࢞ࣛࢫࡢ⤌ᡂ࡟཰᮰ࡍࡿ. ࡇࡇ࡟ࡼࡗ࡚ᢤ⇕ࡉࢀࡿࡓࡵᕥ⫪ୗࡀࡾࡢ ᗘศᕸࢆ♧ࡋ࡞࡛ Cu ⟩ᒙ㸦⭷ཌ 2ȝm㸧ࡢࢫࣃࢵࢱࣜࣥࢢ࡟ 50min ࠿࠿ࡀࡽ෭༷ࡉࢀࡿ.

ࡿ࡜ࡍࡿ࡞ࡽࡤࢫࣃࢵࢱࣜࣥࢢ㏿ᗘࡣ 0.04ȝm/min ࡜ぢᅗ 17 ࡣ Cu ⟩ࡢ༊ศෆ࡛᭱ࡶ Cu36Zr48Al8Ag8 ⁐‫‮‬㸭Cu✚ࡶࡿࡇ࡜ࡀ࡛ࡁ, ཯ᛂᒙࡢࢫࣃࢵࢱࣜࣥࢢ࡟ 90min ࠿⟩⏺㠃࡟㏆᥋ࡍࡿ࣓ࢵࢩࣗࡢ

࠿ࡿࡇ࡜࠿ࡽࡑࡢཌࡳࡣ 3.6ȝm ࡜ᴫ⟬࡛ࡁࡿ. ࡇࡢཌࡳCu36Zr48Al8Ag8 ⁐‫▐ࡣ‮‬᫬࡟ 1370K ࡲ࡛࡟᪼ ࡋ࡚ 50ms

ᗘᒚṔ࡛࠶ࡿ.

ࡣᅗ 13(a)ࡢ TEM ᫂ど㔝ീ࠿ࡽㄞࡳྲྀࡗࡓࢹࣥࢻࣛ࢖ࢺ
཯ᛂᒙࡢཌࡳ࡟࡯ࡰ୍⮴ࡋ, ⤌ᡂኚື࡜཯ᛂᒙࡢᙧᡂࡢ
㛵ಀࡀ♧၀ࡉࢀࡿ. Cu-Zr ⣔㔠ᒓ࢞ࣛࢫࡣ᭱㐺࡞⤌ᡂ࠿ࡽ⤌ᡂࡀࡎࢀࡿ࡜࢞ࣛࢫᙧᡂ⬟ࡀᴟ➃࡟పୗࡍࡿࡇ࡜ࡀ
▱ࡽࢀ࡚࠾ࡾ, ⏺㠃㏆ഐࡢ Cu ࡢᣑᩓ࡟ࡼࡗ࡚࢞ࣛࢫᙧ
ᡂ⬟ࡀపୗࡋࡓ㒊ศࡀඃඛⓗ࡟⤖ᬗ໬ࡋࡓ࡜⪃࠼ࡽࢀࡿ.
ᅗ 15(a), (b) ࡣ Sn-3Ag-0.5Cu ࡣ ࢇ ࡔ ࡟ ࡼ ࡿ
Cu36Zr48Al8Ag8 㔠ᒓ࢞ࣛࢫ༢య, ࠾ࡼࡧ Cu ⟩⁐╔Cu36Zr48Al8Ag8 㔠 ᒓ ࢞ ࣛ ࢫ ࡢ ࡠ ࢀ ࢆ ♧ ࡋ ࡚ ࠸ ࡿ .
Cu36Zr48Al8Ag8 㔠ᒓ࢞ࣛࢫ༢య࡟ᑐࡋ࡚ࡣࡠࢀࢆ඲ࡃ♧ࡉ࡞࠸ࡀ, Cu ⟩⁐╔ Cu36Zr48Al8Ag8 㔠ᒓ࢞ࣛࢫ࡟ᑐࡋ࡚
ࡣࡠࢀ᥋ゐゅࡀ 20°ࡲ࡛ྥୖࡋࡓ. Cu ⟩ࡢ⁐╔࡟ࡼࡾࡠࢀᛶࡀ኱ᖜ࡟ᨵၿࡉࢀࡿࡇ࡜ࡀド᫂ࡉࢀࡓ.

ᅗ &X 㗪ᆺ&X=U$O$J㔠ᒓ࢞ࣛࢫ&X ⟩: ⷧᯈࡢ ᗘศᕸ㸦ィ⟬್㸧  ⚄ዉᕝ኱ᏛᕤᏛ◊✲ᡤᡤሗ ➨  ྕJIM., 31(1990) 177-183.
(5)

A. Peker and W. L. Johnson: Appl. Phys. Lett., 63(1993) 2342-2344.

(6)

A. Inoue and J. S. Gook: Mater. Trans. JIM., 36 (1995)
1180-1183.

(7)

A. Inoue, T. Zhang, T. Itoi, and A. Takeuchi: Mater.
Trans. JIM., 38 (1997) 359-362.

(8)

A. Inoue, N. Nishiyama, and T. Matsuda: Mater. Trans.
JIM., 37 (1996) 181-184.

(9)

H. S. Chen: Rep. Prog. PHys., 43 (1980) 353-432.

(10)E. Matsubara, T. Tamura, Y. Waseda, A. Inoue, M.

ᅗ &X ⟩ࡢ෭༷ ᗘᒚṔ㸦ィ⟬್㸧 ⛬ᗘಖᣢࡉࢀࡿ. Cu ࡢ⼥Ⅼࡣ 1356K ࡛࠶ࡿࡇ࡜࠿ࡽࡇࡢ
▷᫬㛫࡟ Cu ࡣ⁐⼥ࡋ࡚⁐╔ࡀ᏶஢ࡍࡿ. ࡑࡢᚋ t=200ms

Kohinata, T. masumoto: Mater. Trans. JIM, 31 (1990)
228-231.
(11)

T. Masumoto: J. Non Cryst. Solids, 150 (1992)

࡛Cu36Zr48Al8Ag8 㔠ᒓ࢞ࣛࢫ⁐‫⼥ࡢ‮‬ⅬTm(BMG)ࡲ࡛෭
༷ࡉࢀ, t=650ms ࡛࢞ࣛࢫ㌿఩ ᗘ Tg(BMG)࡟฿㐩ࡍࡿ.
Tm(BMG) ࠿ ࡽ Tg(BMG) ࡲ ࡛ ࡢ ෭ ༷ ㏿ ᗘ ࢆ(Tm(BMG)-Tg(BMG))/(650-200)࡜ᐃ⩏ࡍࡿ࡞ࡽࡤ, Cu ⟩ࡢ෭༷㏿ᗘࡣ⣙ 1200K/s ࡜ィ⟬ࡉࢀ, Cu36Zr48Al8Ag8 ྜ㔠ࡢ࢞ࣛࢫ໬⮫⏺෭༷㏿ᗘ 6.4K/s(11)ࢆ኱ࡁࡃୖᅇࡿ㏿ᗘ࡛ᛴ෭ࡉࢀ࡚࠸ࡿࡇ࡜ࡀศ࠿ࡿ. ࡇࢀࡽࡢࢩ࣑࣮ࣗࣞࢩࣙ
ࣥࡢ⤖ᯝ࠿ࡽ Cu ⟩ࡢ⁐╔࡜, Cu36Zr48Al8Ag8 ྜ㔠ࡢ࢔ࣔࣝࣇ࢓ࢫᙧᡂࡀ▷᫬㛫ࡢ࠺ࡕ࡟ྠ᫬㐍⾜ࡋ࡚࠸ࡿࡇ࡜ࡀ
⌮ゎ࡛ࡁࡿ.

E. Matsubara, T. Tamura, Y. Waseda, T. Zhang, A. Inoue,380-385.

(12)

E. Matsubara, T. Tamura, Y. Waseda, A. Inoue, T. Zhang,
T. Masumoto: Mater. Trans. JIM, 33 (1992) 873-878.

(13)

኱㈏ṇ⚽, ᒣཱྀဴ⏨, ༡ཱྀ἞⩏, ᒾ⏣ᖾ୍, ஭ୖ᫂ஂ: ࡲ࡚ࡾ࠶, 38 (1999) 215-253.

(14)ᒣᾆ┿୍, ᮌᮧஂ㐨, ஭ୖ᫂ஂ: 㔠ᒓ, 75 (2005)
48-53.

(15)∾㔝ᙲᏹ, ᑿ⸨㍤ኵ: 㔠ᒓ, 75 (2005) 95-100.

(16)

஭ୖ᫂ஂ, すᒣಙ⾜: 㔠ᒓ, 75 (2005) 125-132.

(17)

Y. Kawahito, T. Terajima, H. Kimura, T. Kuroda, K.
Nakata, S. Katayama, A. Inoue: Mater. Sci. Eng. B, 148㸳㸬⤖ㄽḟୡ௦ᶵᲔᮦᩱ࡜ࡋ࡚ᮇᚅࡉࢀࡿࠕ㔠ᒓ࢞ࣛࢫࠖࡢᇶ

(2008) 105-109.
(18)ᮏⓗ࡞≉ᛶ, ⁐ᑕࢥ࣮ࢸ࢕ࣥࢢ, ⾲㠃ᨵ㉁࡟ࡘ࠸࡚⥲ㄝ
ࡋࡓ. 㔠ᒓ࢞ࣛࢫࡣ≉࡟ඃࢀࡓ≉ᛶࢆᣢࡘࡢ࡛༢⊂࡛౑⏝ࡍࡿࡢࡶⰋ࠸ࡀ, ␗✀ᮦᩱ࡜᥋ྜࡋ࡚ࡇࡑࡑࡢ≉ᛶࡀ⏕࠿ࡏࡿ. 㔠ᒓ࢞ࣛࢫ࠸࠿࡟ࡋ࡚ຍᕤࡍࡿ࠿ࡀ⏘ᴗᛂ⏝Trans, 51 (2010) 1433-1436.
(19)

J. Kim, Y. Kawamura: Scr. Mater., 56 (2007) 709-712.

(20)

Y. Kawamura, Y. Ohno: Scr. Mater., 45 (2001) 279-285.

(21)

C. H. Wong, C. H. Shek: Scr. Mater., 49 (2003)ࡢ㘽࡛࠶ࡿ.

393-397.
(22)

ᘬ⏝ᩥ⊩
(1)

A. Inoue: “Bulk Amorphous Alloys, Preparation andFundamental Characteristics” ed.by A. Inoue, Trans
Tech Publications, 1998, 1-116.

(2)

A. Inoue: “Bulk Amorphous Alloys, Practical
Characteristics and Application” ed.by A. Inoue, Trans
Tech Publications, 1999, 1-148.

(3)

A. Inoue, K. Ohtera, K. Kita, and T. Masumoto: Jpn. J.
Appl. Phys., 27 (1988) L2248-L2251.

(4)

A. Inoue, T. Zhang, and T. Masumoto: Mater. Trans.

Y. Kawahito, Y. Niwa, T. Terajima, S. Katayama: Mater.

Y. F. Sun, Y. S. Ji, H. Fujii, K. Nakata, K. Nogi: Mater.
Sci. Eng. A, 527 (2010) 3427-3432.

(23)

D. Wang, B. L. Xiao, Z. Y. Ma, H. F. Zhang: Scr. Mater.,
60 (2009) 112-115.

(24)

M. Maeda, Y. Takahashi, M. Fukuhara, X. Wang, A.
Inoue: Mater. Sci. Eng. B, 148 (2008) 141-144.

(25)

Y. Kawamura, Y. Ohno: Scr. Mater., 45 (2001) 127-132.

(26)

NEC Tokin <http://www.nec-tokin.com>(27)

LiquidMetal

Technologies<http://www.liwuidmetal.com>(28)

M. Ishida, T. Uehara, T. Arai, H. Takeda, Y. Yamaguchi,
T. Taniguci, M. Kobayashi, H. Ofune: Intermatallics, 10ḟୡ௦ᶵᲔᮦᩱࠕ㔠ᒓ࢞ࣛࢫࠖࡢ≉ᛶ࡜ຍᕤ(29)(2002) 1259-1263.

10)S. Tamura, Y. Tsunekawa, M. Okumiya and M.

S. Hata, N. Yamada, Y. Saotome, A. Inoue, A.

Hatakeyama, J. Mater Proc. Technol. 206 (2008)

Shimokohbe: Proc. China-JPN. Biomaterial Symp. On

322-327.

Advanced Manufact. Eng., (1998) 81.
(30)

(35)

Hatakeyama: J. Mater. Proc. Technol., 206 (2008)

ḟ, ୰ᓥᾈ஧, ஬༑ᔒ㈗ᩍ: ⁐᥋Ꮫ఍ㄽᩥ㞟, 26

322-327.
(36)

Symp. On Advanced Processing of Metals andNakashima, T. Igarashi: J. Alloys Compd., 504S (2010)Materials, edited by F. Kongoli and R.G. Reddy, TMS,
1(2006)649-658.

A. Imai, M. Katayama, S. Maruyama, H. Nishikawa, T.

(37)

wada, H. kimura, M. Fukuhara, T. Takemoto, A. inoue
and Y. Matsumoto,: J. Mater. Res., 24 (2009)(38)

Fukuhara,

A.

Inoue:

Mater.

(39)

Trans.,

50(2009)1326-1329.
(34)

G. K. White and M. L. Minges: Int. J. Thermophys., 18(1997) 1269-1327.

H. Nishikawa, K. Wongpiromsar, H. Abe, T. Takemoto,M.

Y. Waseda, H. Ohta and H. Shibata: NPL Report
CBTLM, S30 (2000).

2931-2934.
(33)

Y. Waseda, H. Shibata and H. Ohta: Proc. Sohn Int.

T. Terajima, F. Takeuchi, K. Nakata, S. Sdachi, K.
S288-S219.

(32)

S. Tamura, Y. Tsunekawa, M. Okumiya and M.

⚟ᮏᫀᏹ, ኱᱓ຬᶞ, ᒣ⏣ᇶᏹ, Ᏻ஭฼᫂, ᮏỤඞ(2008) 74-79.

(31)



H. Abe, K. Sato, H. Nishikawa, T. Takemoto, M.
Fukuhara, A. Inoue: Mater. Trans., 50(2009)1255-1258.

Y. Zhang, H. Hahn: J. Non-Cryst. Solids, (2010), doi:
10.1016/j.jnoncrysol.2010.09.028.

(40)

ᑎᓥᓅྐ, ᮌᮧஂ㐨, ஭ୖ᫂ஂ: 㧗
37(2011)153-158.

Ꮫ఍ㄅ,



┤ิᆺከ㔜ᬯྕࡢᏳ඲ᛶ࡜ࡑࡢᛂ⏝⸨ᒸ ῟

Sequential Multiple Encryption: Security and Application
Atsushi FUJIOKA㸨㸯㸬ࡣࡌࡵ࡟
1970 ᖺ௦࡟බ㛤㘽ᬯྕࡢᴫᛕࡀᥦ♧ࡉࢀࡓࡇ࡜ࢆዎ

ࡢồゎࡀᅔ㞴࡛࠶ࡿ࡜௬ᐃࡍࡿࡇ࡜࡛㸪ࡑࢀ࡟ᇶ࡙ࡃᬯ
ྕᢏ⾡ࡢᏳ඲ᛶࢆド᫂ࡋࡼ࠺࡜࠸࠺ヨࡳ࡛࠶ࡿ㸬ᶵ࡟⌧௦ᬯྕ⌮ㄽࡣⓎᒎࡋ࡚ࡁࡓ㸬ࡑࡢ୰࡛㸪ྛ✀ᬯྕከ㔜ᬯྕ(ME: Multiple Encryption) [1, 2]࡜ࡣ㸪ࡇࡢබ㛤ᢏ⾡࡟ᑐࡋ࡚Ᏻ඲ᛶᐃ⩏ࢆཝᐦ࡟⾜࠸㸪ࡲࡓ㸪ࡑࡢᏳ඲㘽ᬯྕ᪉ᘧࢆከ㔜࡟⏝࠸࡚Ᏻ඲ᛶࢆྥୖࡉࡏࡿヨࡳ࡛࠶ᛶࢆ࡞ࢇࡽ࠿ࡢᩘᏛⓗ࡞ၥ㢟࡟ᖐ╔ࡉࡏࡿド᫂ྍ⬟Ᏻ඲ࡾ㸪኱ࡁࡃศࡅ࡚஧✀㢮ࡢ᪉ᘧ࡟ศ㢮ࡉࢀࡿ1: ┤ิᆺᛶࡀᩚഛࡉࢀࡘࡘ࠶ࡿ㸬(sequential type)࡜୪ิᆺ(parallel type)㸬

ᶵᐦᛶࡢ࠶ࡿ᝟ሗࢆពᅗࡋࡓ┦ᡭ࡟ࡢࡳఏ㐩ࡍࡿࡓࡵ࡟㸪ᬯྕᢏ⾡ࢆ⏝࠸ࡿࡇ࡜ࡣࡼࡃ▱ࡽࢀ࡚࠸ࡿ㸬ࡑࡢ㝿㸪
㏦ಙ⪅࡜ཷಙ⪅ࡢ㛫࡛⛎ᐦ⿹࡟ඹ᭷ࡉࢀ࡚࠸ࡿ᝟ሗࢆ㘽࡜ࡋ࡚ᬯྕ໬ࢆ⾜࡞࠺ࡶࡢࡀඹ㏻㘽ᬯྕ࡛࠶ࡿࡀ㸪ࡇࡢᅗ ┤ิᆺከ㔜ᬯྕᡭἲࢆ⏝࠸ࡓሙྜ㸪ᬯྕ໬ࡸ᚟ྕ࡟⏝࠸ࡿ㘽ࢆ࡝࠺ࡸࡗ
࡚ඹ᭷ࡍࡿ࠿࡜࠸࠺㸪࠸ࢃࡺࡿ㸪㘽㓄㏦ࡢၥ㢟ࡀᏑᅾࡍࡿ㸬୍᪉㸪㏦ಙ⪅࡜ཷಙ⪅ࡀಖᣢࡋ࡚࠸ࡿ㘽ࡀ␗࡞ࡗ࡚࠸
ࡿࡶࡢࡀබ㛤㘽ᬯྕ࡛࠶ࡿ㸬බ㛤㘽ᬯྕ࡛ࡣ㸪࠶ࡿ࣮ࣘࢨࡀබ㛤㘽࡜⛎ᐦ㘽ࡢ࣌࢔ࢆ⏕ᡂࡋ㸪බ㛤㘽ࢆබ㛤ࡋ㸪௚ࡢ࣮ࣘࢨࡀ㸪ࡑࡢ࣮ࣘࢨ࡟࣓ࢵࢭ࣮ࢪࢆ㏦ಙࡋࡓ࠸ሙ
ྜ࡟ࡣ㸪ࡇࡢබ㛤㘽ᬯྕࢆ⏝࠸࡚ᬯྕ໬ࢆ⾜࠸㸪࣮ࣘࢨ┤ิᆺ࡜ࡣ㸪ᖹᩥࢆ࠶ࡿබ㛤㘽ᬯྕ᪉ᘧࡢᬯྕ໬࢔ࣝ
ࢦࣜࢬ࣒( i)࡛ᬯྕ໬ࡋ㸪ࡑࡢฟຊࢆḟࡢබ㛤㘽ᬯྕ᪉ᘧࡢᬯྕ໬࢔ࣝࢦࣜࢬ࣒࡬ࡢධຊ࡜ࡋ࡚ฎ⌮ࢆ⾜࠺ࡶࡢ(ᅗ 1)࡛࠶ࡾ㸪୍᪉㸪୪ิᆺ࡜ࡣ㸪ᖹᩥࢆ࠸ࡃࡘ࠿ࡢࣆ࣮
ࢫ࡟ศ๭ࡋ࡚ࡑࢀࡒࢀࡢࣆ࣮ࢫࢆᖹᩥ࡜ࡋ࡚」ᩘࡢබ㛤㘽ᬯྕ᪉ᘧࡢᬯྕ໬࢔ࣝࢦࣜࢬ࣒࡛ᬯྕ໬ࡍࡿࡶࡢ(ᅗ2)࡛࠶ࡿ㸬

ࡣ⮬㌟ࡋ࠿▱ࡽ࡞࠸⛎ᐦ㘽ࢆ⏝࠸࡚ཷಙࡋࡓᬯྕᩥࢆ᚟
ྕࡍࡿ࡜࠸࠺ࡶࡢ࡛࠶ࡿ㸬ࡇࢀ࡟ࡼࡾ㘽㓄㏦ࡢၥ㢟ࢆゎỴࡍࡿࡇ࡜ࡀ࡛ࡁࡿ㸬බ㛤㘽ᬯྕᢏ⾡࡟࠾࠸࡚㸪ࡑࡢᴫᛕࡢᥦ♧௨㝆ࡋࡤࡽࡃࡣ㸪ලయⓗ࡞᪉ᘧࡀᥦ᱌ࡉࢀ࡚ࡣ㸪ࡑࡢᏳ඲ᛶࡢ୙ഛ
ࡀᣦ᦬ࡉࢀࡿ࡜࠸ࡗࡓ஦౛ࡀ⧞ࡾ㏉ࡉࢀ࡚࠸ࡓ㸬ࡋ࠿ࡋ㸪⌧ᅾ࡛ࡣ㸪ࡑࡢ᪉ᘧࡀ◚ࡽࢀࡓሙྜ࡟㸪࡞ࢇࡽ࠿ࡢᩘᏛ
ⓗ࡞ၥ㢟ࡢゎࡀồࡲࡿࡇ࡜ࢆ♧ࡍࡇ࡜࡛ᬯྕᢏ⾡ࡢᏳ඲ᛶࢆド᫂ࡋࡼ࠺࡜ࡍࡿ㸪࠸ࢃࡺࡿ㸪ド᫂ྍ⬟Ᏻ඲ᛶࡢ⪃࠼᪉ࡀ୺ὶ࡜࡞ࡗ࡚࠸ࡿ㸬ࡍ࡞ࢃࡕ㸪࠶ࡿᩘᏛⓗ࡞ၥ㢟ᅗ ୪ิᆺከ㔜ᬯྕᚑ᮶㸪⣲ᮔ࡞ࡸࡾ᪉ࡢከ㔜ᬯྕ᪉ᘧࡣᏳ඲࡛࡞࠸ࡇ࡜
*ᩍᤵ ᝟ሗࢩࢫࢸ࣒๰ᡂᏛ⛉Professor, Department of Information Systems Creationࡀᣦ᦬ࡉࢀ࡚࠾ࡾ㸪≉࡟㸪┤ิᆺከ㔜ᬯྕ࡛ࡣ㸪஦๓࡟
1 ࡇࢀࡽࢆ⤌ࡳྜࢃࡏࡓ」ྜᆺ(hybrid type)ࡶᏑᅾࡍࡿ

┤ิᆺከ㔜ᬯྕࡢᏳ඲ᛶ࡜ࡑࡢᛂ⏝஘ᩘࢆᣦᐃࡋࡓ᪉ᘧࡢࡳࡀከ㔜ᬯྕࡢᏳ඲ᛶࢆಶࠎࡢබ

࡟㛵ࡍࡿㄆドࡀᚲせ࡜࡞ࡿ㸬࠶ࡿ୙ṇ⪅ࡀ⏕ᡂࡋࡓබ㛤㛤㘽ᬯྕࡢᏳ඲ᛶ࡟ᖐ╔࡛ࡁࡿࡇ࡜ࡀド᫂ࡉࢀ࡚࠸ࡓ

㘽ࢆ௚ேࡢ ID ࡜ࣜࣥࢡࡉࡏࡿࡇ࡜ࡀ࡛ࡁࢀࡤ㸪ࡑࡢ ID[1]㸬

ᐄࡢᬯྕᩥࢆ⮬⏤࡟᚟ྕࡍࡿࡇ࡜ࡀ࡛ࡁ࡚ࡋࡲ࠺࠿ࡽ࡛

ࡇࡢከ㔜ᬯྕࡢᛂ⏝࡟ࡣᵝࠎ࡞ࡶࡢࡀ࠶ࡾ㸪ࡑࡢ୰࡟࠶ࡿ㸬ࡑࡇ࡛㸪ID ᝟ሗ࡟ᇶ࡙ࡃᬯྕࡀ⪃᱌ࡉࢀࡓ㸬᫬㝈බ㛤㘽ᬯྕ[3] ࡀ࠶ࡿ㸬බ㛤㘽ᬯྕ࡛ࡣ㸪ཷಙ⪅ࡣ⮬ID ᝟ሗ࡟ᇶ࡙ࡃᬯྕ(IBE: Identity-Based Encryption) ࡜㌟ࡢ⛎ᐦ㘽࡛ཷಙࡋࡓᬯྕᩥࢆ┤ࡕ࡟᚟ྕࡍࡿࡇ࡜ࡀ࡛

ࡣ㸪㘽⏕ᡂᒁࡀ㸪බ㛤᝟ሗ params ࡜࣐ࢫࢱ࣮⛎ᐦ㘽 mskࡁࡓࡀ㸪᫬㝈බ㛤㘽ᬯྕ࡛ࡣ㸪࠶ࡿ᫬㛫ࢆᣦᐃࡋࡓᙧ࡛

ࡢ࣌࢔ࢆ⏕ᡂࡋ㸪params ࢆබ㛤ࡋ㸪࣮ࣘࢨ 㻵㻰 ࡟ᑐࡋ࡚ᬯྕᩥࡀ⏕ᡂࡉࢀ㸪ཷಙ⪅ࡣ⛎ᐦ㘽࡜ᣦᐃࡉࢀࡓ᫬㛫࡟⛎ᐦ㘽 sk㻵㻰 ࢆ୚࠼㸪௚ࡢ࣮ࣘࢨࡀ㸪ࡑࡢ࣮ࣘࢨ࡟ᖹᩥ m㛵㐃ࡍࡿ᝟ሗࡀ࡞࠸࡜ᬯྕᩥࢆ㛤ࡅ࡞࠸㸪ࡍ࡞ࢃࡕ㸪ᣦ

ࢆ㏦ಙࡋࡓ࠸ሙྜ࡟ࡣ㸪㻵㻰㻌(࡜ params)ࢆ⏝࠸࡚ᬯྕ໬ࢆ

ᐃࡉࢀࡓ᫬้ࡲ࡛᚟ྕࡀ⾜࡞࠼࡞࠸࡜࠸࠺ࡶࡢ࡛࠶ࡿ㸬⾜࠸㸪࣮ࣘࢨࡣ⮬㌟ࡋ࠿▱ࡽ࡞࠸ sk㻵㻰 (࡜ params)ࢆ⏝࠸ࡇࡢ᫬㝈බ㛤㘽ᬯྕࡢᵓᡂἲࡣ஧ࡘ࡟ศࡅࡽࢀ㸪࠶ࡿᩘᏛⓗ࡞ၥ㢟࡟ᇶ࡙࠸࡚ලయⓗ࡞᪉ᘧࢆᥦ᱌ࡍࡿලయⓗ࡚ཷಙࡋࡓᬯྕᩥ c ࢆ᚟ྕࡍࡿ࡜࠸࠺ࡶࡢ࡛࠶ࡿ㸬ࡇࢀ࡟ࡼࡾබ㛤㘽ㄆドࡢၥ㢟ࢆゎỴࡍࡿࡇ࡜ࡀ࡛ࡁࡿ㸬ID ᝟ሗ࡟ᇶ࡙ࡃᬯྕ᪉ᘧ   ࡣ㸪௨ୗࡢᅄࡘࡢከ

ᵓᡂἲ࡜බ㛤㘽ᬯྕ࡞࡝ࡢ୍⯡ⓗ࡞ᬯྕᢏ⾡ࢆ⤌ࡳྜࢃࡏ࡚᫬㝈බ㛤㘽ᬯྕࢆᵓᡂࡍࡿ୍⯡ⓗᵓᡂἲࡀᏑᅾࡍࡿ㸬ᮏ✏ࡣ㸪ࡼࡾ⣲ᮔ࡞ࡸࡾ᪉࡟㏆࠸┤ิᆺከ㔜ᬯྕ᪉ᘧ㡯ᘧ᫬㛫࢔ࣝࢦࣜࢬ࣒࠿ࡽ࡞ࡿ㸬タᐃ: (params; msk) Ћ 㻵㻮㻱㻚㻌㻿㼑㼠㼡㼜(1k)㸬ࡇࡇ࡛㸪ධຊࡣ 1k(k ࡣࢭ࢟ࣗࣜࢸ࢕ࣃ࣓࣮ࣛࢱ).

ࡢᵓᡂἲ[4]࡜ࡑࢀ࡟ᇶ࡙ࡃ᫬㝈බ㛤㘽ᬯྕࡢ୍⯡ⓗᵓᡂἲ[5]ࢆࡲ࡜ࡵࡓࡶࡢ࡛࠶ࡿ㸬฼⏝⪅㘽⏕ᡂ: sk㻵㻰 Ћ 㻵㻮㻱㻚㻌㻱㼤㼠㼞㼍㼏㼠(params, msk, 㻵㻰)㸬ࡇࡇ࡛㸪ධຊࡣබ㛤᝟ሗ params㸪࣐ࢫࢱ࣮⛎ᐦ㘽 msk㸪ID ᝟ሗ 㻵㻰䠊㸰㸬᪤Ꮡ◊✲ᬯྕ໬: c Ћ 㻵㻮㻱㻚㻌㻱㼚㼏(params, 㻵㻰, m)㸬ࡇࡇ࡛㸪ධຊࡣྛ✀ᬯྕᢏ⾡බ㛤㘽ᬯྕ(PKE: public-key encryption)࡜ࡣ㸪࠶ࡿ࣮ࣘࢨࡀබ㛤㘽 pk ࡜⛎ᐦ㘽 sk ࡢ࣌࢔ࢆ⏕ᡂࡋ㸪pk ࢆ⮬㌟ࡢබ㛤᝟ሗ params㸪ID ᝟ሗ 㻵㻰㸪ᖹᩥ m㸬
᚟ྕ: m͛
= 㻵㻮㻱㻚㻌㻰㼑㼏(params; sk㻵㻰; c)㸬ࡇࡇ࡛㸪ධຊࡣබ㛤᝟ಶே㆑ู᝟ሗ(௨ୗ㸪ID ᝟ሗ࡜グࡍ)࡜࡜ࡶ࡟බ㛤ࡋ㸪௚ሗ params㸪⛎ᐦ㘽 sk㻵㻰㸪ᬯྕᩥ c㸬ࡢ࣮ࣘࢨࡀ㸪ࡑࡢ࣮ࣘࢨ࡟࣓ࢵࢭ࣮ࢪ(ᖹᩥ) m ࢆ㏦ಙࡋ᚟ྕࡉࢀࡓ࣓ࢵࢭ࣮ࢪࡣ m࡛͛࠶ࡿ㸬ࡓ࠸ሙྜ࡟ࡣ㸪pk ࢆ⏝࠸࡚ᬯྕ໬ࢆ⾜࠸㸪࣮ࣘࢨࡣ⮬㌟

ࡋ࠿▱ࡽ࡞࠸sk ࢆ⏝࠸࡚ཷಙࡋࡓᬯྕᩥc ࢆ᚟ྕࡍࡿ࡜

ᬯྕࡢᏳ඲ᛶ

࠸࠺ࡶࡢ࡛࠶ࡿ㸬බ㛤㘽ᬯྕ᪉ᘧ

ᬯྕࡢᏳ඲ᛶࡣᵝࠎ࡟ᐃ⩏ࡉࢀ࡚࠸ࡿࡀ㸪⌧ᅾ㸪୺ὶࡣ㸪௨ୗࡢ୕ࡘࡢ࢔ࣝࢦࣜࢬ࣒

࡜࡞ࡗ࡚࠸ࡿᐃ⩏ࡣ㆑ู୙ྍ⬟ᛶ࡟ᇶ࡙ࡃࡶࡢ࡛࠶ࡿ㸬࠿ࡽ࡞ࡿ㸬㆑ู୙ྍ⬟ᛶ࡜ࡣ㸪࠶ࡿᏳ඲ᛶ࡟㛵ࡍࡿࢤ࣮࣒࡟࠾࠸࡚

㘽⏕ᡂ: (pk, sk) Ћ 㻼㻷㻱㻚㻌㻷㻳㼑㼚(1k)㸬ࡇࡇ࡛㸪ධຊࡣࢭ࢟ࣗ

ᨷᧁ⪅(㻭㼐㼢)ࡀ஧ࡘࡢᖹᩥ x0, x1 ࡟ᑐࡍࡿ࡝ࡕࡽ࠿ࡢᬯྕ

ࣜࢸ࢕ࣃ࣓࣮ࣛࢱࢆ k ࡜ࡋࡓ࡜ࡁ࡟ 1 ࢆ k ಶ୪࡭ࡓᩥ c* (ᣮᡓᬯྕᩥ࡜࿧ࡤࢀࡿ)ࡀ୚࠼ࡽࢀࡓ࡜ࡁ㸪ࡑࡢᬯࡶࡢ(1k ࡜⾲⌧ࡍࡿ)㸬

ྕᩥࡀ࡝ࡕࡽࡢᖹᩥࡢࡶࡢ࠿ࢆᙜ࡚ࡿࡇ࡜ࡀ࡛ࡁ࡞࠸ࡇ

ᬯྕ໬: c Ћ 㻼㻷㻱㻚㻌㻱㼚㼏(pk, m)㸬ࡇࡇ࡛㸪ධຊࡣබ㛤㘽 pk㸪ᖹᩥ m㸬
᚟ྕ: m͛
= 㻼㻷㻱㻚㻌㻰㼑㼏(sk, c)㸬ࡇࡇ࡛㸪ධຊࡣ⛎ᐦ㘽 sk㸪ᬯྕᩥ c㸬᚟ྕࡉࢀࡓ࣓ࢵࢭ࣮ࢪࡣ m࡛͛࠶ࡿ㸬࡜ࢆ࠸࠺㸬ࡇࡢ࡜ࡁ㸪ᨷᧁ⪅࡟ᑐࡋ࡚㸪௜ຍⓗ࡞᝟ሗࢆ୚࠼࡞࠸
ࡶࡢࢆ㑅ᢥᖹᩥᨷᧁ(CPA: Chosen Plaintext Attack)㸪ᨷᧁ⪅࠿ࡽၥࢃࢀࡓ(ᣮᡓᬯྕᩥ௨እࡢ)ᬯྕᩥ࡟ᑐࡍࡿᖹᩥ
ࢆ⟅࠼ࡿࡇ࡜ࢆチࡍ㑅ᢥᬯྕᩥᨷᧁ(CCA: Chosenࡇࡇ࡛㸪ࡇࢀࡽ୕ࡘࡢ࢔ࣝࢦࣜࢬ࣒ࡣධຊ㛗࡟㛵ࡍࡿCiphertext Attack)ࡀᏑᅾࡍࡿ(ࡇࡇ࡛㸪ᨷᧁ⪅࠿ࡽၥࢃࢀ

ከ㡯ᘧ᫬㛫࢔ࣝࢦࣜࢬ࣒࡛࠶ࡾ㸪⤖ᯝ㸪k ࡟㛵ࡍࡿከ㡯ࡓᬯྕᩥ࡟ᑐࡍࡿᖹᩥࢆ⟅࠼ࡿ㒊ศࢆ᚟ྕ࢜ࣛࢡࣝ࡜࿧

ᘧ᫬㛫࢔ࣝࢦࣜࢬ࣒࡜࡞ࡿ㸬 b Ћ A(a)ࡣ㸪A ࡀධຊࢆࡪ)㸬≉࡟㸪ᬯྕᩥࢆ㐺ᛂⓗ࡟㑅ࡪࡇ࡜ࡀ࡛ࡁࡿࡶࡢࢆ㐺a ࡜ࡋ࡚ b ࢆฟຊࡍࡿ☜⋡ⓗ࢔ࣝࢦࣜࢬ࣒࡛࠶ࡿࡇ࡜ࢆ

ᛂⓗ㑅ᢥᬯྕᩥᨷᧁ(ACCA: Adaptively ChosenCiphertext

ព࿡ࡋ㸪b = A(a) ࡣ㸪A ࡀ☜ᐃⓗ࢔ࣝࢦࣜࢬ࣒࡛࠶ࡿࡇ

Attack)࡜ࡼࡧ㸪㻯㻯㻭㻞 ࡜グࡍࡿࡇ࡜ࡶ࠶ࡿࡀ㸪ࡑ࠺࡛࡞࡜ࢆ♧ࡋ࡚࠸ࡿ㸬☜⋡ⓗ࢔ࣝࢦࣜࢬ࣒ࢆ㸪ࣛࣥࢲ࣒ᩥᏐ

࠸ࡶࡢ࡜ΰ஘ࡍࡿࡇ࡜ࡀ࡞࠸ሙྜ࡟ࡣ㸪༢࡟ 㻯㻯㻭 ࡜᭩ิ r ࢆ⏝࠸࡚ b = A(a; r)࡜᭩ࡃࡇ࡜ࡶ࠶ࡿ㸬ࡃࡇ࡜ࡶ࠶ࡿ㸬ࡋ࠿ࡋ㸪බ㛤㘽ᬯྕ࡛ࡣ㸪⛎ᐦ㘽ᡤ᭷⪅ࡢID ࡜බ㛤㘽௨ୖࡼࡾ㸪බ㛤㘽ᬯྕ࡟࠾࠸࡚㸪஧ࡘࡢᖹᩥࢆ༊ู࡛

⚄ዉᕝ኱ᏛᕤᏛ◊✲ᡤᡤሗ ➨  ྕࡁ࡞࠸࡜ࡁ 㻵㻺㻰㻙㻯㻼㻭 Ᏻ඲࡜࠸࠸㸪ᨷᧁ⪅࡟᚟ྕ࢜ࣛࢡ
ࣝࢆ୚࠼࡚ࡶ༊ู࡛ࡁ࡞࠸࡜ࡁ㻵㻺㻰㻙㻯㻯㻭 Ᏻ඲࡜࠸࠺(ᅗ3)㸬

ࡲࡎ㸪ᅗ 1 ࡟࠾࠸࡚㸪ࡑࢀࡒࢀࡢᬯྕ໬ࡀ⊂❧࡟⾜ࢃࢀ࡚࠸ࡓሙྜࢆ⪃࠼ࡿ㸬ࡇࡇ࡛㸪᭱⤊ẁࡢᬯྕྠᵝ࡟㸪ID ᝟ሗ࡟ᇶ࡙ࡃᬯྕ࡟࠾࠸࡚ࡶ㸪㻵㻺㻰㻙㻵㻰㻙㻯㻼㻭Ᏻ඲ࡢࡼ࠺࡟࠸࠺㸬n ࡟ᑐࡍࡿ⛎ᐦ㘽 skn ࢆධᡭࡋࡓ(ࡑࢀ௨እࡢ⛎ᐦ㘽ࡣ▱ࡽ࡞࠸) ᨷᧁ⪅ࢆ᝿ᐃࡍࡿ㸬ࡇࡢᨷᧁ⪅ࡣ⮬㌟࡛ࡣ㸪ᣮᡓᬯྕᩥࢆᖹᩥࡲ࡛᚟ྕࡍࡿ
ࡇ࡜ࡣ࡛ࡁ࡞࠸࠿ࡶࡋࢀ࡞࠸ࡀ㸪᭱⤊ẁn ࡟㛵ࡋ࡚ࡣ

᚟ྕࡀྍ⬟࡛࠶ࡿ㸬ࡑࡇ࡛㸪ᣮᡓᬯྕᩥ࡟ᑐࡋ࡚㸪skn ࢆ⏝࠸࡚᚟ྕࡋ㸪ࡑࢀࢆ෌ᗘn ࡟㛵ࡋ࡚ᬯྕ໬ࡋࡓሙྜ㸪ࡇࡢᬯྕࡀᑡ࡞ࡃ࡜ࡶ 㻵㻺㻰㻙㻯㻼㻭 Ᏻ඲࡛࠶ࡿ࡞ࡽࡤ㸪ࢭ㸻࢟ࣗࣜࢸ࢕ࣃ࣓࣮ࣛࢱ k ࡟㛵ࡋ࡚↓ど࡛ࡁࡿ኱ࡁࡉࡢ


Ț-୍ᵝᛶࢆᣢࡘࡢ࡛㸪⤖ᯝ㸪ᚓࡽࢀࡓᬯྕᩥࡣ㧗࠸☜⋡࡛ᣮᡓᬯྕᩥ࡜ࡣ␗࡞ࡿࡇ࡜࡟࡞ࡿ㸬ࡑࡇ࡛㸪ࡇࡢᬯྕᅗ 㻵㻺㻰㻙㻯㻯㻭 ࢤ࣮࣒ᩥࢆ᚟ྕ࢜ࣛࢡࣝ࡟ᑜࡡࡿࡇ࡜࡛ᖹᩥࢆධᡭࡍࡿࡇ࡜ࡀ
බ㛤㘽ᬯྕࡸ ID ᝟ሗ࡟ᇶ࡙ࡃᬯྕ࡟࠾࠸࡚ 㻵㻺㻰㻙㻯㻼㻭Ᏻ඲࡞᪉ᘧ࠿ࡽ 㻵㻺㻰㻙㻯㻯㻭 Ᏻ඲࡞᪉ᘧࢆᵓᡂࡍࡿࡇ࡜ࡣ㸪࡛ࡁ㸪᭱⤊ⓗ࡟㸪ከ㔜ᬯྕ࡟ᑐࡍࡿ㆑ู୙ྍ⬟ᛶࢆ◚ࡿࡇ࡜ࡀ࡛ࡁࡿ㸬୍⯡ⓗ࡟ࡣ㞴ࡋ࠸ࡀ㸪ࣛࣥࢲ࣒࢜ࣛࢡࣝࣔࢹࣝ[6]࡜࠸࠺

ࡇࡢࡼ࠺࡞ᨷᧁࢆ෌ᬯྕ໬ᨷᧁ࡜࠸࠸㸪⣲ᮔ࡞┤ิᆺᏳ඲ᛶド᫂ࣔࢹࣝࢆ⏝࠸ࡿ࡜㸪ẚ㍑ⓗᐜ᫆࡟ᐇ⌧࡛ࡁࡿከ㔜ᬯྕ᪉ᘧࡣࡇࡢᨷᧁ࡟ᑐࡋ࡚⬤ᙅ࡛࠶ࡾ㸪ࡑࡢࡓࡵࡇ࡜ࡀ▱ࡽࢀ࡚࠸ࡿ㸬ࡇࡇ࡛㸪ࣛࣥࢲ࣒࢜ࣛࢡࣝࣔࢹࣝ

࡟㸪࡞ࢇࡽ࠿ࡢᕤኵࡀᚲせ࡜࡞ࡿ㸬࡜ࡣ㸪࠶ࡿ㛵ᩘࡢฟຊࢆᨷᧁ⪅ࡣ⮬㌟࡛ィ⟬࡛ࡁࡎ㸪እ㒊࠿ࡽࡑࡢィ⟬್ࢆࡶࡽࢃ࡞ࡅࢀࡤ࡞ࡽ࡞࠸࡜࠸࠺Ᏻ඲

ከ㔜ᬯྕࡢᐃ⩏ᛶド᫂ࣔࢹ࡛ࣝ㸪౛࠼ࡤ㸪ࣁࢵࢩࣗ㛵ᩘ࡞࡝ࢆࣛࣥࢲ࣒

ከ㔜ᬯྕ᪉ᘧ

࢜ࣛࢡࣝ࡜ࡋ࡚ᢅ࠺ࡇ࡜࡟ࡼࡾᏳ඲ᛶド᫂ࢆ⾜࠺ࡇ࡜ࡀࢦࣜࢬ࣒࠿ࡽ࡞ࡿ㸬ከ࠸㸬㘽⏕ᡂ: (PKn, SKn) Ћ 㻹㻱㻚㻷㻳㼑㼚n(1k)㸬ࡇࡇ࡛㸪ධຊࡣ 1k (kࡇࡇ୍࡛ࡘ㸪ᬯྕࡢᛶ㉁ࢆ⾲ࡍࣃ࣓࣮ࣛࢱࢆᐃ⩏ࡋ࡚࠾ࡃ㸬k ࢆࢭ࢟ࣗࣜࢸ࢕ࣃ࣓࣮ࣛࢱ㸪   = (㻼㻷㻱㻚㻌㻷㻳㼑㼚㻘㻌㻼㻷㻱㻚㻌 㻱㼚㼏㻘㻌 㻼㻷㻱㻚㻌 㻰㼑㼏)ࢆබ㛤㘽ᬯྕ᪉ᘧ࡜ࡍࡿ㸬୚࠼ࡽࢀࡓ x Ѯ{0, 1}*㸪y Ѯ{0, 1}*㸪㻼㻷㻱㻚㻌㻷㻳㼑㼚(1k)࡛⏕ᡂࡉࢀࡓpk ࡟ᑐࡋ࡚㸪Pr[r Ћ{0, 1}rlen(k) : y = 㻼㻷㻱㻚㻌㻱㼚㼏(pk; x; r)] ࢆg(x, y) ࡛グࡍ(ࡇࡇ࡛ rlen(k) ࡣ k ࡟㛵ࡍࡿከ㡯ᘧ࡛࠶ࡾ㸪ࡣ㸪௨ୗࡢ୕ࡘࡢከ㡯ᘧ᫬㛫࢔ࣝࡣࢭ࢟ࣗࣜࢸ࢕ࣃ࣓࣮ࣛࢱ).
ࡇࡇ࡛㸪ධຊࡣබ㛤㘽PKn㸪
ᬯྕ໬: c Ћ 㻹㻱㻚㻱㼚㼏n(PKn, m)㸬
ᖹᩥ m㸬
᚟ྕ: m͛
= 㻹㻱㻚㻰㼑㼏n(SKn, c)㸬ࡇࡇ࡛㸪ධຊࡣ⛎ᐦ㘽 SKn㸪ᬯྕᩥ c㸬
᚟ྕࡉࢀࡓ࣓ࢵࢭ࣮ࢪࡣ m࡛͛࠶ࡿ㸬ᬯྕ໬࡟ᚲせ࡞ࣛࣥࢲ࣒ᩥᏐิࡢ㛗ࡉ࡛࠶ࡿ)㸬ࡇࡢ࡜ࡁ㸪௵ពࡢ x Ѯ{0, 1}*, y Ѯ{0, 1}*, (pk; sk) Ћ 㻷㻳㼑㼚(1k) ࡟ᑐࡋ࡚㸪 g(x, y) ӌ Ț ࡀᡂࡾ❧ࡘ࡞ࡽࡤ㸪ࡣȚ-୍ᵝከ㔜ᬯྕ᪉ᘧ

࡟ᑐࡍࡿᏳ඲ᛶ࡜ࡋ࡚ࡣ㸪ඛ࡟㸪

㏙࡭ࡓࡼ࠺࡟ከ㔜ᬯྕ࡟ᑐࡍࡿ᚟ྕ࢜ࣛࢡࣝࡢࡳࡀ୚࠼
ࡽࢀ࡚࠸ࡿࣔࢹࣝࡀ⪃࠼ࡽࢀࡿ(ᅗ 4)㸬ࡇࡢࣔࢹࣝ࡟ᇶ࡙

ᛶࢆᣢࡘ࡜࠸࠺[10]㸬
kࡇࡢ☜⋡ g(x㸪y) ࡣෆ㒊࡛(pk㸪sk) Ћ 㻷㻳㼑㼚(1 ) ࡟㛵ࡍࡃᏳ඲ᛶࡣ㸪⊂❧࡟ᥦ᱌ࡉࢀ㸪ࡑࢀࡒࢀ㸪㻵㻺㻰㻙㻹㻱㻙㻯㻯㻭 Ᏻࡿ☜⋡ⓗ࡞᣺⯙ࢆ⾜ࡗ࡚࠸ࡿⅬ࡟ὀពࡉࢀࡓ࠸㸬ࡍ࡞ࢃ

඲ᛶ[1]㸪 㼣㻹㻯㻯㻭 Ᏻ඲ᛶ[2]࡜࿧ࡤࢀ࡚࠸ࡿ㸬ࡇࡢᏳ඲ࡕ㸪࠶ࡿබ㛤㘽ᬯྕ᪉ᘧࡀ㸪ࢭ࢟ࣗࣜࢸ࢕ࣃ࣓࣮ࣛࢱ kᛶࡣ㸪┤ิ࣭୪ิ࠸ࡎࢀࡢᆺࡢከ㔜ᬯྕ࡟ࡶ㐺⏝࡛ࡁࡿ㸬࡟㛵ࡋ࡚↓ど࡛ࡁࡿ኱ࡁࡉࡢȚ-୍ᵝᛶࢆᣢࡘ࡜ࡁ㸪ከࡃࡢ pk ࡟ᑐࡋ࡚↓ど࡛ࡁࡿ኱ࡁࡉ࡜࡞ࡿࡢ࡛࠶ࡗ࡚㸪ࡍ࡭࡚ࡢ pk ࡟ᑐࡋ࡚ᡂࡾ❧ࡘᚲせࡣ࡞࠸㸬㸻ከ㔜ᬯྕࡢᏳ඲ᛶ
ከ㔜ᬯྕ࡛㸪ྠᵝ࡟㐺ᛂⓗ㑅ᢥᬯྕᩥᨷᧁࡢඖ࡛ࡢ㆑
ู୙ྍ⬟ᛶࢆ⪃࠼࡚ࡳࡿ㸬ࡍ࡞ࢃࡕ㸪ᨷᧁ⪅࡟ᑐࡋ࡚ከᅗ 㻵㻺㻰㻙㻹㻱㻙㻯㻯㻭 ࢤ࣮࣒㔜ᬯྕ࡟ᑐࡍࡿ᚟ྕ࢜ࣛࢡࣝࡀ୚࠼ࡽࢀ࡚࠸ࡿࡶࡢ࡜ࡍ
ࡿ㸬ḟ࡟㸪୪ิᆺከ㔜ᬯྕ࡟ᑐࡋ࡚ࡢࡳᐃ⩏ྍ⬟࡞Ᏻ඲ᛶ┤ิᆺከ㔜ᬯྕࡢᏳ඲ᛶ࡜ࡑࡢᛂ⏝ࢆ⤂௓ࡍࡿ㸬㼣㻹㻯㻯㻭 Ᏻ඲ᛶ࡛ࡣከ㔜ᬯྕ࡟㛵ࡍࡿᬯྕᬯྕ໬: c Ћ 㼀㻾㻱㻚㻌㻱㼚㼏(tpk, T, upk, m)㸬ࡇࡇ࡛㸪ධຊࡣ᫬ᩥ࡟ᑐࡍࡿ᚟ྕ⤖ᯝࢆධᡭྍ⬟࡛࠶ࡗࡓࡢ࡟ᑐࡋ࡚㸪ሗᒁࡢබ㛤㘽 tpk㸪᫬้᝟ሗ T㸪࣮ࣘࢨࡢබ㛤㘽 upk㸪㻹㻯㻯㻭 Ᏻ඲ᛶ࡛ࡣ㸪᚟ྕ⤖ᯝ(ᖹᩥ)࡛ࡣ࡞ࡃ㸪ࡑࢀࢆศᖹᩥ m㸬๭ࡋࡓࡶࡢ(ಶࠎࡢ㒊ศ᝟ሗ)ࡀධᡭ࡛ࡁ㸪㼟㻹㻯㻯㻭 Ᏻ඲ᛶ࡛ࡣ㸪ከ㔜ᬯྕ࡟㛵ࡍࡿᬯྕᩥ࡟ᑐࡍࡿ᚟ྕ⤖ᯝࡔࡅ࡛࡞ࡃ㸪(ከ㔜ᬯྕࢆᵓᡂࡋ࡚࠸ࡿ) ಶࠎࡢබ㛤㘽ᬯྕ࡟ᑐ᚟ྕ: m͛
= 㼀㻾㻱㻚㻌㻰㼑㼏(tpk, sT , usk, c)㸪ධຊࡣ᫬ሗᒁࡢබ㛤㘽tpk㸪᫬้㘽 sT 㸪࣮ࣘࢨࡢ⛎ᐦ㘽 usk㸪ᬯྕᩥ c㸬᚟ྕࡉࢀࡓ࣓ࢵࢭ࣮ࢪࡣ m࡛͛࠶ࡿ㸬ࡍࡿ᚟ྕ⤖ᯝࡶධᡭ࡛ࡁࡿ࡜࠸࠺ࣔࢹ࡛ࣝ࠶ࡿ[2]㸬
᫬㝈බ㛤㘽ᬯྕ࡟ᑐࡍࡿᏳ඲ᛶ࡜ࡋ࡚ࡣ㸪ඛ࡟㸪㏙࡭

ࡇࢀࡽࡢᏳ඲ᛶࡢ㛵ಀࡣ㸪ࡓࡼ࠺࡟᫬ሗᒁ࡟ᑐࡍࡿࡶࡢ࡜࣮ࣘࢨ࡟ᑐࡍࡿࡶࡢࡢ஧

㼣㻹㻯㻯㻭 (=㻵㻺㻰㻙㻹㻱㻙㻯㻯㻭) ӌ 㻹㻯㻯㻭 ӌ 㼟㻹㻯㻯㻭✀㢮ࢆ⪃࠼ࡿᚲせࡀ࠶ࡿࡀ㸪ࡑࢀࡒࢀ࡟஧ࡘࡢᏳ඲ᛶࡀ

࡜࡞ࡾ㸪ࡇࢀࡽࡢ୰࡛ࡣ㸪㼟㻹㻯㻯㻭 Ᏻ඲ᛶࡀ᭱ࡶᙉ࠸Ᏻ
඲ᛶ࡜࡞ࡿ㸬

ᐃ⩏ࡉࢀ࡚࠸ࡿ㸬㻵㻺㻰㻙㻾㼀㻾㻙㻯㻯㻭㻞 Ᏻ඲ᛶ[7]ࡣ㸪᫬ሗᒁࡢ⛎ᐦ㘽ࢆᣢࡓ࡞࠸ᨷᧁ⪅ࡀ᫬㝈බ㛤㘽ᬯྕࡢ㆑ู୙ྍ⬟ᛶࢆ◚ࢁ࠺࡜ࡍ᫬㝈බ㛤㘽ᬯྕࡿࡶࡢ࡛㸪᚟ྕ࢜ࣛࢡࣝ࡬ࡢၥ࠸ྜࢃࡏ࡟㝿࡟㸪ᬯྕᩥබ㛤㘽ᬯྕ࡟࠾࠸࡚ࡣ㸪ᬯྕᩥࢆཷಙࡋࡓ࣮ࣘࢨࡣ⮬c ࡜ඹ࡟㸪᫬้᝟ሗ T ࡜ࡑࡢᬯྕᩥࡢཷಙ⪅࡟࠾ࡅࡿ⛎

㌟ࡢ⛎ᐦ㘽ࢆ⏝࠸࡚㸪┤ࡕ࡟㸪᚟ྕࢆ⾜࠺ࡇ࡜ࡀ࡛ࡁࡿ㸬ᐦ㘽 usk ࢆ㏦ಙࡍࡿࣔࢹ࡛ࣝ࠶ࡿ㸬୍᪉㸪㻵㻺㻰㻙㻯㼀㻯㻭 Ᏻࡑࡇ࡛㸪ṇつࡢ࣮ࣘࢨ࡛࠶ࡗ࡚ࡶ㸪ᣦᐃࡉࢀࡓ᫬้ࡲ࡛

඲ᛶ[8]ࡣ㸪᚟ྕ࢜ࣛࢡࣝ࡬ࡢၥ࠸ྜࢃࡏ࡟㝿࡟㸪ཷಙ⪅᚟ྕࡀ⾜࠼࡞࠸᫬㝈බ㛤㘽ᬯྕࡀ⪃᱌ࡉࢀࡓ㸬࡟࠾ࡅࡿ⛎ᐦ㘽 usk ࡛ࡣ࡞ࡃ㸪ཷಙ⪅࡟࠾ࡅࡿබ㛤㘽᫬㝈බ㛤㘽ᬯྕ(TRPKE: Timed-Release Public-Key Encription)

upk ࢆ௜ຍࡍࡿࣔࢹ࡛ࣝ࠶ࡿ(ᅗ 5)㸬㻵㻺㻰㻙㻯㼀㻯㻭 Ᏻ඲ᛶ࡛

࡜ࡣ㸪
᫬ሗᒁࡀ㸪
බ㛤㘽 tpk ࡜⛎ᐦ㘽 tsk ࡢ࣌࢔ࢆ⏕ᡂࡋ㸪ࡣ㸪ᨷᧁ⪅ࡣ upk ࡟ᑐࡍࡿ⛎ᐦ㘽ࢆධᡭࡋ࡚࠸࡞ࡃ࡚ࡶ

tpk ࢆබ㛤ࡋ㸪࠶ࡿ࣮ࣘࢨࡀබ㛤㘽 upk ࡜⛎ᐦ㘽 usk ࡢ࣌ࡼࡃ㸪ࡑࡢࡓࡵ㸪 㻵㻺㻰㻙㻯㼀㻯㻭 Ᏻ඲ᛶࡣ 㻵㻺㻰㻙㻾㼀㻾㻙㻯㻯㻭㻞࢔ࢆ⏕ᡂࡋ㸪 upk ࢆ⮬㌟ࡢ ID ࡜ඹ࡟බ㛤ࡋ㸪௚ࡢ࣮ࣘᏳ඲ᛶࡼࡾࡶᙉ࠸Ᏻ඲ᛶࢆಖド࡛ࡁࡿ㸬ࢨࡀ㸪ࡑࡢ࣮ࣘࢨ࡟࣓ࢵࢭ࣮ࢪ(ᖹᩥ) m ࢆ㏦ಙࡋࡓ࠸ሙྜ࡟ࡣ㸪upk, tpk ࡜᫬้᝟ሗ T ࢆ⏝࠸࡚ᬯྕ໬ࢆ⾜࠸㸪᫬้ T ࡟㐩ࡋࡓࡽ㸪᫬ሗᒁࡀ᫬้㘽 sT ࢆⓎ⾜ࡋ㸪࣮ࣘࢨࡣ㸻

⮬㌟ࡋ࠿▱ࡽ࡞࠸ sk ࡜Ⓨ⾜ࡉࢀࡓ sT㸪 බ㛤ࡉࢀ࡚࠸ࡓ
tpk ࢆ⏝࠸࡚ཷಙࡋࡓᬯྕᩥ c ࢆ᚟ྕࡍࡿ࡜࠸࠺ࡶࡢ࡛
࠶ࡿ㸬ࡇࢀ࡟ࡼࡾ᫬้ T ࡀ᮶ࡿࡲ࡛㸪ᣦᐃࡉࢀࡓ࣮ࣘࢨᅗ 㻵㻺㻰㻙㻯㼀㻯㻭 ࢤ࣮࣒࡟ᑐࡋ࡚ࡶ࣓ࢵࢭ࣮ࢪࡢ⛎༏ᛶࢆಖࡘࡇ࡜ࡀ࡛ࡁࡿ㸬ࡇࡢ࡜ࡁ㸪Ᏻ඲ᛶࡣ᫬ሗᒁ࡟ᑐࡍࡿࡶࡢ࡜࣮ࣘࢨ࡟ᑐ
ࡍࡿࡶࡢࡢ஧✀㢮ࢆ⪃࠼ࡿᚲせࡀ࠶ࡿ㸬㻵㻺㻰㻙㻯㻯㻭㻙㼀㻿 Ᏻ඲ᛶ[7, 8]ࡣ㸪୙ṇ࡞᫬ሗᒁࡀṇつࡢ࣮ࣘࢨ࡟㛵ࡍࡿ᫬㝈බ㛤㘽ᬯྕࡢ㆑ู୙ྍ⬟ᛶࢆ◚ࢁ࠺࡜ࡑࢀࡒࢀ࡟ᑐࡋ࡚㸪㐺ᛂⓗ㑅ᢥᬯྕᩥᨷᧁࡢඖ࡛㆑ู

ࡍࡿࡶࡢ࡛㸪᚟ྕ࢜ࣛࢡࣝ࡬ࡢၥ࠸ྜࢃࡏ࡟㝿࡟㸪ᬯྕ୙ྍ⬟ᛶࢆ‶㊊ࡇ࡜ࡀᮃࡲࡋࡃ㸪ࡲࡓ㸪ࡑࡢ㝿㸪᚟ྕ࢜ᩥ c ࡜ඹ࡟㸪᫬้᝟ሗ T ࡜᫬้㘽 sT ࢆ㏦ಙࡍࡿࣔࢹ࡛ࣝ

ࣛࢡࣝ࡟ᑐࡋ࡚㸪ᵝࠎ࡞࣮ࣘࢨࡢබ㛤㘽ࢆ㑅࡭ࡿࡼ࠺࡟

࠶ࡿ2㸬୍᪉㸪㻵㻺㻰㻙㻿㻯㻯㻭㻙㼀㻿 Ᏻ඲ᛶ[9]ࡣ㸪᚟ྕ࢜ࣛࢡࣝ

ࡍࡿࡼࡾᙉ࠸Ᏻ඲ᛶࢆ⪃៖ࡍࡿᚲせࡀ࠶ࡿ㸬࡬ࡢၥ࠸ྜࢃࡏ࡟㝿࡟㸪᫬้㘽 sT ࡛ࡣ࡞ࡃ㸪ཷಙ⪅࡟࠾ࡅࡿබ㛤㘽 upk ࢆ௜ຍࡍࡿࣔࢹ࡛ࣝ࠶ࡿ( ᅗ 6) 㸬᫬㝈බ㛤㘽ᬯྕࡢᐃ⩏㻵㻺㻰㻙㻯㻯㻭㻙㼀㻿 Ᏻ඲ᛶ࡛ࡣ㸪ᨷᧁ⪅ࡣᣦᐃࡉࢀࡓ࣮ࣘࢨ࡟
ࡣ㸪௨ୗࡢ஬ࡘࡢከ

᫬㝈බ㛤㘽ᬯྕ᪉ᘧ
㡯ᘧ᫬㛫࢔ࣝࢦࣜࢬ࣒࠿ࡽ࡞ࡿ㸬k㛵ࡍࡿ㉁ၥࡋ࠿࡛ࡁ࡞࠸ࡓࡵ㸪㻵㻺㻰㻙㻿㻯㻯㻭㻙㼀㻿 Ᏻ඲ᛶࡣ㻵㻺㻰㻙㻯㻯㻭㻙㼀㻿 Ᏻ඲ᛶࡼࡾࡶᙉ࠸Ᏻ඲ᛶࢆಖド࡛ࡁࡿ㸬kタᐃ: (tpk, tsk ) Ћ 㼀㻾㻱㻚㻌㻿㼑㼠㼡㼜(1 )㸬ࡇࡇ࡛㸪ධຊࡣ 1 (k ࡣࢭ࢟ࣗࣜࢸ࢕ࣃ࣓࣮ࣛࢱ).
฼⏝⪅㘽⏕ᡂ: (upk; usk) Ћ 㼀㻾㻱㻚㻌㻷㻳㼑㼚(tpk)㸬ࡇࡇ࡛㸪ධຊࡣ᫬ሗᒁࡢබ㛤㘽 tpk.
ゎ㝖: sT Ћ 㼀㻾㻱㻚㻌㻾㼑㼘㼑㼍㼟㼑(tpk, tsk , T)㸬ࡇࡇ࡛㸪ධຊࡣ᫬ሗ
ᒁࡢබ㛤㘽 tpk㸪᫬ሗᒁࡢ⛎ᐦ㘽 tsk㸪᫬้᝟ሗ T㸬

2 Cathalo ࡟ࡼࡿ 㻵㻺㻰㻙㻯㻯㻭㻙㼀㻿 Ᏻ඲ᛶࡢᐃ⩏[8]࡛ࡣ㸪s ࢆ௜ຍTࡋ࡚࠸ࡿࡢ࡟ᑐࡋ࡚㸪Cheon ࡽ࡟ࡼࡿ 㻵㻺㻰㻙㻯㻯㻭㻙㼀㻿 Ᏻ඲ᛶࡢᐃ
⩏[7]࡛ࡣ㸪sT ࢆ௜ຍࡋ࡚࠸࡞࠸㸬ࡋ࠿ࡋ㸪᫬ሗᒁ࡟ᑐࡍࡿᏳ඲ᛶ
ࢆ⪃៖ࡋ࡚࠸ࡿࡢ࡛㸪sT ࢆ௜ຍࡍࡿᚲせࡣ࡞࠸ࡇ࡜࡟ὀពࡉࢀࡓ
࠸㸬⚄ዉᕝ኱ᏛᕤᏛ◊✲ᡤᡤሗ ➨  ྕᅗ 㻵㻺㻰㻙㻿㻯㻯㻭㻙㼀㻿 ࢤ࣮࣒ᅗ 㻵㻺㻰㻙㼟㻹㻱㻙㻯㻯㻭 ࢤ࣮࣒௨ୖࡼࡾ㸪᫬㝈බ㛤㘽ᬯྕࡢᏳ඲ᛶࡣ௨ୗࡢ㛵ಀ࡜࡞ࡇࡢᏳ඲ᛶ࡜ 㼟㻹㻯㻯㻭 Ᏻ඲ᛶࡢ┦㐪Ⅼࡣ㸪ಶࠎࡢබ㛤ࡿ㸬㻵㻺㻰㻙㻾㼀㻾㻙㻯㻯㻭㻞㻌 䍺㻌 㻵㻺㻰㻙㻯㼀㻯㻭㻌㻵㻺㻰㻙㻯㻯㻭㻙㼀㻿㻌 䍺㻌 㻵㻺㻰㻙㻿㻯㻯㻭㻙㼀㻿㘽ᬯྕ᪉ᘧ࡟㛵ࡍࡿ᚟ྕ࢜ࣛࢡࣝ(㻼㻷㻱㻚㻌 㻰㼑㼏i)࡟ᑐࡍࡿ⚗Ṇ஦㡯࡛࠶ࡿ㸬㼟㻹㻯㻯㻭 Ᏻ඲ᛶ࡛ࡣ㸪ᣮᡓᬯྕᩥ࡟㛵ࡍࡿ㒊ศ᝟ሗࡢᬯྕᩥࡀၥ࠸ྜࢃࡏ୙ྍ࡞ࡢ࡟ᑐࡋ࡚㸪ࡲࡓ㸪ࡑࢀࡒࢀࡢᏳ඲ᛶᐃ⩏ࡢ㐪࠸ࢆ⾲ 1 ࡟ࡲ࡜ࡵ࡚

㻵㻺㻰㻙㼟㻹㻱㻙㻯㻯㻭 Ᏻ඲ᛶ࡛ࡣ㸪ᣮᡓᬯྕᩥࡢ᚟ྕิ(c* Ѝ
c*n-1 Ѝ࣭࣭࣭Ѝc*1 ) ࡟ᒓࡍࡿᬯྕᩥ(c*i ) ࢆၥ࠸ྜࢃࡏࡍ࠾ࡃ㸬⾲ ᫬㝈බ㛤㘽ᬯྕࡢᏳ඲ᛶ

ᐃ⩏㻵㻺㻰㻙㻾㼀㻾㻙㻯㻯㻭㻞㻌㻵㻺㻰㻙㻯㼀㻯㻭㻌㻵㻺㻰㻙㻯㻯㻭㻙㼀㻿㻌㻵㻺㻰㻙㻿㻯㻯㻭㻙㼀㻿㻌

ᨷᧁ⪅
ཷಙ⪅
ཷಙ⪅
᫬ሗᒁ
᫬ሗᒁ

ၥ࠸ྜࢃࡏࡢᙧᘧ
(usk㸪T㸪c)(upk㸪T㸪c)(T㸪sT㸪c)(upk㸪T㸪c)ࡿࡇ࡜ࡣチࡉࢀ࡞࠸㸬஘ᩘᛶᣊ᮰ᵓᡂ
௨ୗ࡟㸪஘ᩘᛶᣊ᮰ᵓᡂ࡜࿧ࡪከ㔜ᬯྕࡢ┤ิᵓᡂࢆグ㏙ࡍࡿ3㸬
i= (㻼㻷㻱㻚㻌㻷㻳㼑㼚i, 㻼㻷㻱㻚㻌㻱㼚㼏i, 㻼㻷㻱㻚㻌㻰㼑㼏i) (1 ӌ i ӌn,㸱㸬┤ิᆺከ㔜ᬯྕࡢ୍ᵓᡂἲ

n Ӎ 2) ࢆබ㛤㘽ᬯྕ᪉ᘧ㸪Hhi (1 ӌ i ӌ n) ࢆ{0, 1}*ᴫせ࠿ࡽ{0, 1}rleni(k) ࡬ࡢࣁࢵࢩࣗ㛵ᩘ࡜ࡍࡿ㸬ࡇࡇ࡛㸪rleni(k),⣲ᮔ࡞┤ิᆺከ㔜ᬯྕ᪉ᘧࡣ෌ᬯྕ໬ᨷᧁ࡟ᑐࡋ࡚⬤ileni(k) ࡣ k ࡟㛵ࡍࡿከ㡯ᘧ㸪ileni(k) ࡣࣁࢵࢩࣗ㛵ᩘࡢᙅ࡛࠶ࡾ㸪ࡇࢀࢆᅇ㑊ࡍࡿࡸࡾ᪉࡜ࡋ࡚㸪┤ิᆺከ㔜ᬯ࢖ࣥࢹࢵࢡࢫࡢ㛗ࡉ㸪
rleni(k) ࡣ 㻼㻷㻱㻚㻱㼚㼏i ࡛⏝࠸ࡽࢀࡿࣛ

ྕ࡟࠾ࡅࡿྛẁࡢᬯྕ໬࡟ᚲせ࡞ࣛࣥࢲ࣒ᩥᏐิࢆ஦๓

ࣥࢲ࣒ᩥᏐิࡢ㛗ࡉࡢୖ㝈㸪hi ࡣࣁࢵࢩࣗ㛵ᩘࡢ࢖ࣥࢹ

࡟ᣦᐃࡍࡿᵓᡂἲࡀᥦ᱌ࡉࢀ࡚࠸ࡓ㸬ࢵࢡࢫ࡛࠶ࡾ{0, 1}ileni(k) ࠿ࡽ㑅ࡤࢀࡿ㸬ᮏ❶࡛ࡣ㸪ࡇࡢᵓᡂἲࡼࡾࡶࡼࡾ⣲ᮔ࡞┤ิᆺከ㔜ᬯࡇࡢ࡜ࡁ㸪ከ㔜ᬯྕ᪉ᘧ= (㻹㻱㻚㻷㻳㼑㼚n, 㻹㻱㻚㻱㼚㼏n,n

ྕ᪉ᘧ࡟㏆ࡃ㸪ᬯྕ໬࡟ᚲせ࡞᝟ሗࡣ┤๓ࡢᬯྕᩥࡔࡅ

㻹㻱㻚㻰㼑㼏 ) ࢆ௨ୗࡢࡼ࠺࡟ᵓᡂࡍࡿ㸬࡛ࡼ࠸᪉ᘧ[4]ࢆ⤂௓ࡋ㸪ࡇࡢ᪉ᘧࡀ 㻵㻺㻰㻙㻹㻱㻙㻯㻯㻭 Ᏻ඲㘽⏕ᡂ 㻹㻱㻚㻷㻳㼑㼚n: ධຊࡣ 1k (k ࡣࢭ࢟ࣗࣜࢸ࢕ࣃ࣓࣮ࣛ

ᛶ࡟ຍ࠼࡚ࡼࡾᙉ࠸Ᏻ඲ᛶࡶ‶㊊ࡍࡿࡇ࡜ࢆ♧ࡍ㸬ࢱ).
Step 1: 㻼㻷㻱㻚㻌㻷㻳㼑㼚i ࡟ 1k ࢆධຊࡋ㸪(pki, ski) ࢆ⏕ᡂ(i =1, . . . , n)㸬

㻵㻺㻰㻙㼟㻹㻱㻙㻯㻯㻭 Ᏻ඲ᛶ୪ิᆺከ㔜ᬯྕ᪉ᘧ࡟ᑐࡋ࡚ࡣ㸪ከ㔜ᬯྕ᪉ᘧ࡟㛵ࡍ

Step 2: ࣁࢵࢩࣗ㛵ᩘࡢ࢖ࣥࢹࢵࢡࢫhiѮ{0, 1}ileni(k)ࢆࣛ
ࣥࢲ࣒࡟㑅ᢥ(i = 1, . . . , n)㸬

ࡿᬯྕᩥ࡟ᑐࡍࡿ᚟ྕ⤖ᯝࡔࡅ࡛࡞ࡃ㸪(ከ㔜ᬯྕ᪉ᘧࢆ
ᵓᡂࡋ࡚࠸ࡿ)ಶࠎࡢබ㛤㘽ᬯྕ᪉ᘧ࡟ᑐࡍࡿ᚟ྕ⤖ᯝ

Step 3: PKi = (pki, hi), SKi = (ski, hi) ࡟タᐃ
(i = 1, . . . , n)㸬

ࡶධᡭ࡛ࡁࡿ࡜࠸࠺ 㼟㻹㻯㻯㻭 Ᏻ඲ᛶࡀᐃ⩏ࡉࢀ࡚࠸ࡓ㸬ࡑࡇ࡛㸪ྠᵝ࡟┤ิᆺከ㔜ᬯྕ᪉ᘧ࡟ᑐࡋ࡚ࡶ㸪㢮ఝ

Step 4: PKn = (PK1, . . . , PKn) ࡟タᐃ㸬ࡢᏳ඲ᛶࢆᐃ⩏ࡍࡿ㸬ࡍ࡞ࢃࡕ㸪ከ㔜ᬯྕ᪉ᘧ࡟㛵ࡍࡿ

Step 5: SKn = (SK1, . . . , SKn) ࡟タᐃ㸬ᬯྕᩥ࡟ᑐࡍࡿ᚟ྕ⤖ᯝࡔࡅ࡛࡞ࡃ㸪(ከ㔜ᬯྕ᪉ᘧࢆᵓ

Step 6: (PKn, SKn) ࢆฟຊ㸬ࡢබ㛤㘽ࡣ PKn㸪ᑐᛂࡍࡿ⛎ᐦ㘽ࡣ SKn ࡛࠶ࡿ㸬ᡂࡋ࡚࠸ࡿ)ಶࠎࡢබ㛤㘽ᬯྕ᪉ᘧ࡟ᑐࡍࡿ᚟ྕ⤖ᯝࡶධᡭ࡛ࡁࡿ࡜ࡍࡿࡶࡢ࡛㸪ࡇࢀࢆ 㻵㻺㻰㻙㼟㻹㻱㻙㻯㻯㻭 Ᏻ඲ᛶ
࡜࠸࠺(ᅗ 7)㸬3

ṇ☜࡟ࡣ㸪ᩥ⊩[4]࡟グ㏙ࡉࢀࡓ஘ᩘᛶᣊ᮰ᵓᡂ࡜⸨ᓮ-ᒸᮏኚ᥮[10]ࢆྜᡂࡋࡓࡶࡢ࡜࡞ࡗ࡚࠸ࡿ㸬ࡇࡢኚ᭦࡟ࡼࡾ㸪ᵓᡂせ⣲ࢆࡍ࡭࡚ 㻵㻺㻰㻙㻯㻼㻭 Ᏻ඲࡞බ㛤㘽ᬯྕ࠿ࡽ 㻵㻺㻰㻙㻹㻱㻙㻯㻯㻭 Ᏻ඲࡞ከ㔜ᬯྕࢆᵓᡂ࡛ࡁࡿࡇ࡜ࡀ[4]࡟࠾࠸࡚ᣦ᦬ࡉࢀ࡚࠸ࡿ㸬┤ิᆺከ㔜ᬯྕࡢᏳ඲ᛶ࡜ࡑࡢᛂ⏝ᬯྕ໬ 㻹㻱㻚㻱㼚㼏n: ධຊࡣබ㛤㘽 PKn㸪࣓ࢵࢭ࣮ࢪ m㸪ࡇࡇ࡛㸪࡝ࡕࡽࡢሙྜࡶ㸪n{0, 1}rlen (k)㸬ࡇࡇ࡛rlenn(k) =rlen1(k)㸬

ࣛࣥࢲ࣒ᩥᏐิriࡀࢭ࢟ࣗࣜࢸ࢕ࣃ

࣓࣮ࣛࢱ k ࡟㛵ࡋ࡚↓ど࡛ࡁࡿ኱ࡁࡉࡢȚ-୍ᵝᛶࢆᣢ

Step 1: PKn ࢆ(PK1, . . . , PKn) ࡟ᒎ㛤㸬ࡘࡇ࡜ࢆド᫂࡟฼⏝ࡋ࡚࠸ࡿࡇ࡜ࢆᣦ᦬ࡋ࡚࠾ࡃ㸬

Step 2: PKi ࢆ(pki, hi) ࡟ᒎ㛤(i = 1, . . . , n)㸬

ᐃ⌮  බ㛤㘽ᬯྕ᪉ᘧ

,...,

1

n

(nӍ2) ࡀࡍStep 3: c0 = m r ࡟タᐃ㸬࡭࡚ 㻵㻺㻰㻙㻯㻯㻭 Ᏻ඲࡛࠶ࡿ࡜ࡍࡿ㸬ࡇࡢ࡜ࡁ㸪ከ㔜ᬯ

Step 4: i = 1 ࠿ࡽ n ࡲ࡛௨ୗࢆ⧞ࡾ㏉ࡍ:ྕ᪉ᘧci = 㻼㻷㻱㻚㻌㻱㼚㼏i(pki, ci-1; Hhi (ci-1)) ࢆᐇ⾜㸬ࡣࣛࣥࢲ࣒࢜ࣛࢡࣝࣔࢹࣝࡢඖ࡛

㻵㻺㻰㻙㼟㻹㻱㻙㻯㻯㻭 Ᏻ඲࡜࡞ࡿ㸬

Step 5: c = cn ࡟タᐃࡋ㸪c ࢆฟຊ㸬ࡇࡢᐃ⌮ࡶ஧ࡘࡢᨷᧁ⪅ࢆᵓᡂࡍࡿࡇ࡜࡛ド࡛᫂ࡁࡿ㸬c ࡀ m ࡢᬯྕᩥ࡛࠶ࡿ㸬ࡍ࡞ࢃࡕ㸪୍ࡘࡣ㸪nn㸬᚟ྕ 㻹㻱㻚㻰㼑㼏 : ධຊࡣ⛎ᐦ㘽 SK 㸪ᬯྕᩥ c͛

ᨷᧁ⪅࠿ࡽ

1

ࡢ 㻵㻺㻰㻙㼟㻹㻱㻙㻯㻯㻭 Ᏻ඲ᛶࢆ◚ࡿࡢ 㻵㻺㻰㻙㻯㻯㻭 Ᏻ඲ᛶࢆ◚ࡿᨷᧁ⪅ࢆᵓ

Step 1: SKn ࢆ(SK1, . . . , SKn) ࡟ᒎ㛤㸬ᡂࡍࡿࡶࡢ࡛㸪ࡶ࠺୍ࡘࡣ㸪

Step 2: SKi ࢆ(ski, hi) ࡟ᒎ㛤(i = 1, . . . , n)㸬

඲ᛶࢆ◚ࡿᨷᧁ⪅࠿ࡽ

Step 3: c͛
n = c͛࡟タᐃ㸬ᛶࢆ◚ࡿᨷᧁ⪅ࢆᵓᡂࡍࡿࡶࡢ࡛࠶ࡿ㸬ࡢ 㻵㻺㻰㻙㼟㻹㻱㻙㻯㻯㻭 Ᏻi (2ӌiӌn)ࡢ 㻵㻺㻰㻙㻯㻯㻭 Ᏻ඲

Step 4: i = n ࠿ࡽ 1 ࡲ࡛௨ୗࢆ⧞ࡾ㏉ࡍ:c͛
= 㻼㻷㻱㻚㻌㻰㼑㼏i(ski, c͛
i-1i) ࢆᐇ⾜㸬㸲㸬᫬㝈බ㛤㘽ᬯྕࡢ୍ᵓᡂἲ

; Hhi (c͛i-1)) ࡢᡂ❧ࢆ☜ㄆ㸬c͛
= 㻼㻷㻱㻚㻌㻱㼚㼏i(pki, c͛
i-1iᴫせ୙ᡂ❧ࡢሙྜࡣ㸪ԋ ࢆฟຊࡋ࡚೵Ṇ㸬ඛ࡟ࡢ࡭ࡓࡼ࠺࡟᫬㝈බ㛤㘽ᬯྕࡢᏳ඲ᛶ࡜ࡋ࡚ᙉ࠸

࡟ᒎ㛤ࡋ㸪m͛ࢆฟຊ㸬
Step 5: c͛
0 ࢆ m͛r͛ᐃ⩏࡜࡞ࡗ࡚࠸ࡿࡢࡣ㸪㻵㻺㻰㻙㻯㼀㻯㻭 Ᏻ඲ᛶ࡜ 㻵㻺㻰㻙㻿㻯㻯㻭㻙㼀㻿᚟ྕࡉࢀࡓ࣓ࢵࢭ࣮ࢪࡣ m࡛͛࠶ࡿ㸬Ᏻ඲ᛶ࡛࠶ࡿ㸬ࡇࡢ୧⪅ࢆ‶ࡓࡍ᪉ᘧ࡜ࡋ࡚㸪࠶ࡿᩘㄽi-1஘ᩘᛶᣊ᮰ᵓᡂ࡟ࡼࡿከ㔜ᬯྕࡢᏳ඲ᛶ

యⓗᵓᡂ࡛࠶ࡗ࡚㸪බ㛤㘽ᬯྕ᪉ᘧ࡜ ID ᝟ሗ࡟ᇶ࡙ࡃ

ୖࡢၥ㢟࡟ᇶ࡙ࡃ᪉ᘧࡀᥦ᱌ࡉࢀ࡚࠸ࡿ[9]ࡀ㸪ࡇࢀࡣල஘ᩘᛶᣊ᮰ᵓᡂ࡟ࡼࡿከ㔜ᬯྕࡢ᚟ྕ㐣⛬࡟࠾࠸࡚ࡣ㸪c͛
; Hhi i-1(c͛)) ࡢᡂ❧ࡀ☜ㄆࡉࢀࡿᚲせc͛
i = 㻼㻷㻱㻱㼚㼏i(pki, i-1㻌ᬯྕ᪉ᘧࢆ⤌ࡳྜࢃࡏ࡚ᵓᡂࡍࡿࡼ࠺࡞୍⯡ⓗᵓᡂ࡛ࡣ࡞࠿ࡗࡓ㸬ࡀ࠶ࡿࡀ㸪ࡇࡢᬯྕ໬ࡣධຊi-1c͛ ࡟㛵ࡋ࡚☜ᐃⓗ࡞᧯సᮏ❶࡛ࡣ㸪஘ᩘᛶᣊ᮰ᵓᡂ࡟ᇶ࡙ࡃ᫬㝈බ㛤㘽ᬯྕࡢ࡜࡞ࡗ࡚࠸ࡿ㸬ࡍ࡞ࢃࡕ㸪ᣮᡓᬯྕᩥࢆ෌ᬯྕ໬ࡋ࡚ࡶ

ᵓᡂἲ࡟ࡘ࠸࡚グ㏙ࡍࡿ㸬ᮏᵓᡂࡣ㸪஧ẁࡢ஘ᩘᛶᣊ᮰

ඖࡢᬯྕᩥ࡟ᡠࡿࡇ࡜࡟࡞ࡾ㸬ࡇࢀࡣ෌ᬯྕ໬ᨷᧁࡀ᭷

ᵓᡂ࡟࠾࠸࡚㸪୍ẁ┠ࢆ ID ᝟ሗ࡟ᇶ࡙ࡃᬯྕ᪉ᘧ㸪஧ຠ࡟ࡣ࡞ࡽ࡞࠸ࡇ࡜ࢆព࿡ࡋ࡚࠸ࡿ㸬ẁ┠ࢆබ㛤㘽ᬯྕ᪉ᘧ࡜ぢ࡞ࡍࡇ࡜ࡀ࡛ࡁࡿ㸬ࡇࡢ㝿㸪ᐇ㝿࡟㸪஘ᩘᛶᣊ᮰ᵓᡂ࡟ࡼࡿከ㔜ᬯྕࡢᏳ඲ᛶࡣ㸪௨ୗࡢ஧ᐃ⌮࡟࡚ド᫂ࡉࢀࡿ㸬஘ᩘᛶᣊ᮰ᵓᡂ࡟࠾࠸࡚ࡣ㸪ࣁࢵࢩࣗ㛵ᩘ࡬ࡢධຊࢆ┤๓ࡢ᝟ሗ(ᬯྕᩥ࡞࠸ࡋࡣᖹᩥ࡜ࣛࣥࢲ࣒ᩥᏐิࢆ㐃⤖

1, . . . ,2) ࡀࡋࡓࡶࡢ)ࡢࡳ࡟㝈ᐃࡋ࡚ᬯྕ໬࡟ᚲせ࡞ࣛࣥࢲ࣒ᩥᏐࡍ࡭࡚ 㻵㻺㻰㻙㻯㻼㻭 Ᏻ඲࡛࠶ࡿ࡜ࡍࡿ㸬ࡇࡢ࡜ࡁ㸪ከ㔜ิࢆ⏕ᡂࡋ࡚࠸ࡓࡀ㸪ࡇࡇ࡛グ㏙ࡍࡿ᫬㝈බ㛤㘽ᬯྕࡢࡣࣛࣥࢲ࣒࢜ࣛࢡࣝࣔࢹࣝࡢඖ࡛

ᵓᡂἲ࡟࠾࠸࡚ࡣ㸪┤๓ࡢ᝟ሗ࡟ຍ࠼࡚㸪ཷಙ⪅ࡢබ㛤ᐃ⌮  බ㛤㘽ᬯྕ᪉ᘧ
ᬯྕ᪉ᘧ

n (n

㻵㻺㻰㻙㻹㻱㻙㻯㻯㻭 Ᏻ඲࡜࡞ࡿ㸬㘽ࡸ᫬้᝟ሗࡶࣁࢵࢩࣗ㛵ᩘ࡬ࡢධຊ࡜ࡋ࡚࠸ࡿ㸬ࡇࡢࡼ࠺࡞ኚ᭦ࢆຍ࠼ࡿࡇ࡜࡟ࡼࡾ 㻵㻺㻰㻙㻯㼀㻯㻭 Ᏻ඲ᛶࡸ஧ࡘࡢᨷᧁ⪅ࢆᵓᡂࡍࡿࡇ࡜࡛ド᫂ࢆ⾜࠺㸬࠿ࡽ1㻵㻺㻰㻙㻿㻯㻯㻭㻙㼀㻿 Ᏻ඲ᛶ࡛ồࡵࡽࢀ࡚࠸ࡓᨷᧁ⪅ࡀ᚟ྕ࢜ࡢ 㻵㻺㻰㻙㻹㻱㻙㻯㻯㻭 Ᏻ඲ᛶࢆ◚ࡿᨷᧁ⪅ࣛࢡࣝ࡟ၥ࠸ྜࢃࡏࡿᬯྕᩥ࡟࠾࠸࡚බ㛤㘽ࡸ᫬้᝟ሗࡢ 㻵㻺㻰㻙㻯㻼㻭 Ᏻ඲ᛶࢆ◚ࡿᨷᧁ⪅ࢆᵓᡂࡍࢆ⮬⏤࡟㑅ࡪࡇ࡜ࡀ࡛ࡁࡿ࡜࠸࠺Ⅼ࡟ᑐᛂࡍࡿࡇ࡜ࡀ࡛

୍ࡘࡣ㸪ࡿࡶࡢ࡛㸪ࡶ࠺୍ࡘࡣ㸪ࢆ◚ࡿᨷᧁ⪅࠿ࡽࡢ 㻵㻺㻰㻙㻹㻱㻙㻯㻯㻭 Ᏻ඲ᛶi (2ӌiӌn) ࡢ 㻵㻺㻰㻙㻯㻼㻭 Ᏻ඲ᛶࢆ◚ࡿᨷᧁ⪅ࢆᵓᡂࡍࡿࡶࡢ࡛࠶ࡿ㸬ࡁࡿ㸬ࡋ࠿ࡋ㸪ࡑࡢࡓࡵ࡟㸪බ㛤㘽ᬯྕࡸ ID ᝟ሗ࡟ᇶ࡙ࡃ
ᬯྕ࡟ồࡵࡽࢀࡿᛶ㉁࡜ࡋ࡚ࡣ㸪ࠕࢭ࢟ࣗࣜࢸ࢕ࣃ࣓ࣛࡀ 㻵㻺㻰㻙㻯㻼㻭࣮ࢱ k ࡟㛵ࡋ࡚↓ど࡛ࡁࡿ኱ࡁࡉࡢȚ-୍ᵝᛶࢆᣢࡘࠖ

ࡢ࡜࠸࠺ࡶࡢࡔࡅ࡛ࡣ୙༑ศ࡜࡞ࡾ㸪ࡇࢀࢆࡼࡾᙉࡃࡋࡓ

㻵㻺㻰㻙㻹㻱㻙㻯㻯㻭Ᏻ඲ᛶࢆ◚ࡿᨷᧁ⪅ࡀᏑᅾࡋ࡞࠸ࡇ࡜ࢆពࠕ↓ど࡛ࡁࡿ኱ࡁࡉࡢȚ-pk-୍ᵝᛶࢆᣢࡘࠖ࡜࠸࠺ᛶ㉁ࡢ 㻵㻺㻰㻙㻹㻱㻙㻯㻯㻭 Ᏻ඲ᛶࡀドࡀᚲせ࡜࡞ࡿ㸬ࡇࡇ࡛㸪Ț-pk-୍ᵝᛶ࡜ࡣ㸪Ț-୍ᵝᛶ࡛ࡇࢀࡽࡀᵓᡂ࡛ࡁࡿ࡜࠸࠺ࡇ࡜ࡣ㸪iᏳ඲࡛࠶ࡿࡇ࡜࡟཯ࡋ㸪ࡼࡗ࡚㸪ࡑࡢࡼ࠺࡞
࿡ࡋ࡚࠸ࡿ㸬⤖ᯝ㸪᫂ࡉࢀࡓࡇ࡜࡟࡞ࡿ㸬ᐃ⩏ࡉࢀࡓ☜⋡ g(x, y)ࡢୖ㝈Țࡀࡍ࡭࡚ࡢ pk ࡟ᑐࡋ࡚ᡂ

⚄ዉᕝ኱ᏛᕤᏛ◊✲ᡤᡤሗ ➨  ྕ᫬้᝟ሗ T ࡟ᑐࡍࡿ᫬้㘽ࡣ sT ࡛࠶ࡿ㸬ࡾ❧ࡘ࡜ࡋࡓࡶࡢ࡜ࡋ࡚ᐃ⩏ࡉࢀࡿ㸬ࡍ࡞ࢃࡕ㸪↓ど࡛ࡁࡿ኱ࡁࡉࡢȚ-୍ᵝᛶࢆᣢࡘබ㛤㘽ᬯྕ᪉ᘧࡢሙྜ㸪↓ᬯྕ໬㼀㻾㻱㻦㻱㼚㼏: ධຊࡣ᫬ሗᒁࡢබ㛤㘽tpk㸪
᫬้᝟ሗT㸪

ど࡛ࡁࡿᩘࡢබ㛤㘽࡟ᑐࡋ࡚ࡣ㸪Țࡀ↓ど࡛ࡁࡿ኱ࡁࡉ

฼⏝⪅ࡢබ㛤㘽 upk (= pk)㸪࣓ࢵࢭ࣮ࢪ m㸪ࣛࣥࢲ࣒ᩥ

ࢆ㉸࠼࡚ࡶࡼ࠸ࡀ㸪↓ど࡛ࡁࡿ኱ࡁࡉࡢȚ-pk-୍ᵝᛶࢆᏐิ r{0, 1}tre. rlen(k)㸬

ᣢࡘබ㛤㘽ᬯྕ᪉ᘧࡢሙྜ㸪ࡍ࡭࡚ࡢබ㛤㘽࠾࠸࡚Țࡀ

Step 1: tpk ࢆ(params, h1㸪h2) ࡟ᒎ㛤㸬↓ど࡛ࡁࡿ኱ࡁࡉ࡜࡞ࡽ࡞ࡅࢀࡤ࡞ࡽ࡞࠸㸬

Step 2: ௨ୗࢆィ⟬:஘ᩘᛶᣊ᮰ᵓᡂࢆ⏝࠸ࡓ᫬㝈බ㛤㘽ᬯྕ

Step 3:= 㻼㻷㻱㻚㻌㻱㼚㼏(pk, ; Hh2 (pk T

Step 4: c =࡟タᐃࡋ㸪c ࢆฟຊ㸬= 㻵㻮㻱㻚㻌㻱㼚㼏(params, T, m r; Hh1 (pk T m r))= (㻼㻷㻱㻷㻳㼑㼚, 㻼㻷㻱㻱㼚㼏, 㻼㻷㻱㻰㼑㼏) ࢆබ㛤㘽ᬯྕ᪉ᘧ= (㻵㻮㻱㻚㻿㼑㼠㼡㼜, 㻵㻮㻱㻚㻱㼤㼠㼞㼍㼏㼠, 㻵㻮㻱㻚㻱㼚㼏, 㻵㻮㻱㻚㻰㼑㼏)ࢆID ᝟ሗ࡟ᇶ࡙ࡃᬯྕ᪉ᘧ㸪Hh1 ࢆ{0, 1}*࠿ࡽ{0, 1} ibe.rlen(k))) ࢆィ⟬㸬c ࡀ m ࡢᬯྕᩥ࡛࠶ࡿ㸬᚟ྕ 㼀㻾㻱䠊㻰㼑㼏: ධຊࡣ᫬ሗᒁࡢබ㛤㘽 tpk㸪᫬้㘽 sT㸪࡬ࡢࣁࢵࢩࣗ㛵ᩘ㸪Hh2 ࡶ{0, 1}*࠿ࡽ{0, 1}pke.rlen(k) ࡬ࡢࣁ฼⏝⪅ࡢ⛎ᐦ㘽 usk㸪ᬯྕᩥ c㸬ࢵࢩࣗ㛵ᩘ࡜ࡍࡿ㸬ࡇࡇ࡛㸪ilen1(k), ilen2(k), ibe.rlen(k),Step 1: tpk ࢆ(params, h1, h2) ࡟ᒎ㛤㸬

pke.rlen(k)ࢆ k ࡟㛵ࡍࡿከ㡯ᘧ㸪ileni(k)ࡣࣁࢵࢩࣗ㛵ᩘࡢ

Step 2: usk ࢆ(pk, sk) ࡟ᒎ㛤㸬࢖ࣥࢹࢵࢡࢫࡢ㛗ࡉ㸪ibe.rleni(k), pke.rleni(k) ࡣ 㻵㻮㻱㻚㻌 㻱㼚㼏,

= c͛
࡟タᐃ㸬
Step 3: ͛㻼㻷㻱㻚㻌 㻱㼚㼏 ࡛⏝࠸ࡽࢀࡿࣛࣥࢲ࣒ᩥᏐิࡢ㛗ࡉࡢୖ㝈㸪hi= 㻼㻷㻱㻚㻌㻰㼑㼏(sk,Step 4: ͛ࡣࣁࢵࢩࣗ㛵ᩘࡢ࢖ࣥࢹࢵࢡࢫ࡛࠶ࡾ{0, 1}ileni(k) ࠿ࡽ㑅

Step 5: ͛= 㻼㻷㻱㻚㻌㻱㼚㼏(pk, ͛; Hh2 (pk T͛) ࢆィ⟬㸬͛)) ࡢᡂ❧ࢆ᳨ドࡋ㸪୙ᡂ❧࡞ࡽ㸪ԋ ࢆฟຊࡋ㸪೵Ṇ㸬ࡤࢀࡿ㸬ࡇࡢ࡜ࡁ㸪ከࡃࡢබ㛤㘽ᬯྕ᪉ᘧ㸪ID ᝟ሗ࡟ᇶ࡙ࡃᬯྕ᪉ᘧࡀࡑ࠺࡛࠶ࡿࡼ࠺࡟㸪pk ࡸ params ࠿ࡽࢭ

Step 6: m͛
= 㻵㻮㻱㻚㻌㻰㼑㼏(params; sT㸪 ͛) ࢆィ⟬㸬

࢟ࣗࣜࢸ࢕ࣃ࣓࣮ࣛࢱ k ࡀᑟฟ࡛ࡁࡿ࡜௬ᐃࡋ࡚࠾ࡃ㸬

Step 7: ͛= 㻵㻮㻱㻚㻌㻱㼚㼏(params; T㸪m͛
;Hh1 (pk T m͛))ࡢᡂࡇࡢ࡜ࡁ㸪᫬㝈බ㛤㘽ᬯྕ᪉ᘧ= (㼀㻾㻱㻚㻌㻿㼑㼠㼡㼜㻘㻌❧ࢆ᳨ドࡋ㸪୙ᡂ❧࡞ࡽ㸪ԋ ࢆฟຊࡋ㸪೵Ṇ㸬㼀㻾㻱㻚㻌㻷㻳㼑㼚㻘㻌㼀㻾㻱㻚㻌㻾㼑㼘㼑㼍㼟㼑㻘㻌㼀㻾㻱㻚㻌㻱㼚㼏㻘㻌㼀㻾㻱㻚㻌㻰㼑㼏) ࢆ௨ୗࡢStep 8: m͛
ࢆ m͜ r͜࡟ᒎ㛤㸬
Step 9: m͜ࢆฟຊ㸬ࡼ࠺࡟ᵓᡂࡍࡿ㸬タᐃ 㼀㻾㻱㻚㻌 㻿㼑㼠㼡㼜: ධຊࡣ 1k (k ࡣࢭ࢟ࣗࣜࢸ࢕ࣃ࣓࣮ࣛ

᚟ྕࡉࢀࡓ࣓ࢵࢭ࣮ࢪࡣ m࡛͜࠶ࡿ㸬ࡇࡢᵓᡂࢆ IBE-PKE ᵓᡂ࡜࿧ࡪ㸬ࢱ)㸬
Step 1: 㻵㻮㻱㻚㻿㼑㼠㼡㼜 ࡟ 1k ࢆධຊࡋ㸪(params, msk) ࢆ⏕ᡂ㸬
Step 2: ࣁࢵࢩࣗ㛵ᩘࡢ࢖ࣥࢹࢵࢡࢫ h1
h2{0, 1}ilen1(k)࡜

㻵㻮㻱㻙㻼㻷㻱ᵓᡂ࡟ࡼࡿ᫬㝈බ㛤㘽ᬯྕࡢᏳ඲ᛶ

ilen2(k){0, 1}

ࢆࣛࣥࢲ࣒࡟㑅ᢥ㸬

IBE-PKE ᵓᡂ࡟ࡼࡿࡣ 㻵㻺㻰㻙㻯㼀㻯㻭 Ᏻ඲ᛶ࡜Step 3: tpk = (params, h1, h2), tsk = msk ࡟タᐃ㸬㻵㻺㻰㻙㻿㻯㻯㻭㻙㼀㻿 Ᏻ඲ᛶࢆ‶㊊ࡍࡿ㸬

Step 4: (tpk, tsk )ࢆฟຊ㸬ᐃ⌮ 㻟 ID ᝟ሗ࡟ᇶ࡙ࡃᬯྕ᪉ᘧ

࡟࠾ࡅࡿ᫬ሗᒁࡢබ㛤㘽ࡣ tpk ࡛࠶ࡾ㸪ᑐ඲㸪බ㛤㘽ᬯྕ᪉ᘧࡀ 㻵㻺㻰㻙㻵㻰㻙㻯㻼㻭 Ᏻࡀ 㻵㻺㻰㻙㻯㻼㻭 Ᏻ඲࡛㸪࠿ࡘ㸪ᛂࡍࡿ⛎ᐦ㘽ࡣ tsk ࡛࠶ࡿ㸬ࢭ࢟ࣗࣜࢸ࢕ࣃ࣓࣮ࣛࢱ k ࡟㛵ࡋ࡚↓ど࡛ࡁࡿ኱ࡁ

฼⏝⪅㘽⏕ᡂ 㼀㻾㻱㻚㻌㻷㻳㼑㼚㻦 ධຊࡣ tpk㸬ࡉࡢȚ-pk-୍ᵝᛶࢆᣢࡘ࡜௬ᐃࡍࡿ㸬ࡇࡢ࡜ࡁ㸪᫬㝈

Step 1: tpk ࢆ(params, h1㸪h2) ࡟ᒎ㛤ࡋ㸪params ࠿ࡽࢭබ㛤㘽ᬯྕ᪉ᘧ

࢟ࣗࣜࢸ࢕ࣃ࣓࣮ࣛࢱ k ࢆᑟฟ㸬
Step 2: 㻼㻷㻱㻚㻌㻷㻳㼑㼚 ࡟ 1k ࢆධຊࡋ㸪(pk, sk) ࢆ⏕ᡂ㸬ࡣࣛࣥࢲ࣒࢜ࣛࢡࣝࣔࢹࣝࡢඖ࡛ 㻵㻺㻰㻙㻯㼀㻯㻭 Ᏻ඲࡜࡞ࡿ㸬ᐃ⌮  ID ᝟ሗ࡟ᇶ࡙ࡃᬯྕ᪉ᘧࡀ 㻵㻺㻰㻙㻵㻰㻙㻯㻼㻭 Ᏻ

Step 3: upk = pk, usk = (pk; sk) ࡟タᐃ㸬඲㸪බ㛤㘽ᬯྕ᪉ᘧ

Step 4: (upk, usk) ࢆฟຊ㸬ࢭ࢟ࣗࣜࢸ࢕ࣃ࣓࣮ࣛࢱ k ࡟㛵ࡋ࡚↓ど࡛ࡁࡿ኱ࡁ

࡟࠾ࡅࡿ฼⏝⪅ࡢබ㛤㘽ࡣ upk ࡛࠶ࡾ㸪ᑐࡀ 㻵㻺㻰㻙㻯㻼㻭 Ᏻ඲࡛㸪࠿ࡘ㸪ࡉࡢȚ-pk-୍ᵝᛶࢆᣢࡘ࡜௬ᐃࡍࡿ㸬ࡇࡢ࡜ࡁ㸪᫬㝈ᛂࡍࡿ⛎ᐦ㘽ࡣ usk ࡛࠶ࡿ㸬බ㛤㘽ᬯྕ᪉ᘧゎ㝖 㼀㻾㻱䠊㻾㼑㼘㼑㼍㼟㼑: ධຊࡣ᫬ሗᒁࡢබ㛤࣭⛎ᐦ㘽(tpk, tsk )ࡢඖ࡛ 㻵㻺㻰㻙㻿㻯㻯㻭㻙㼀㻿 Ᏻ඲࡜࡞ࡿ㸬ࡣࣛࣥࢲ࣒࢜ࣛࢡࣝࣔࢹࣝ

࡜᫬้᝟ሗ T㸬
Step 1: tpk ࢆ(params, h1㸪h2) ࡟ᒎ㛤㸬ࡇࢀࡽࡢᐃ⌮ࡢド᫂ࡣ㸪ᐃ⌮ 1, 2 ࡢド᫂࡜࡯ࡰྠᵝ࡟

Step 2: dT = 㻵㻮㻱㻚㻌㻱㼤㼠㼞㼍㼏㼠(params, tsk, T) ࢆᐇ⾜㸬⾜࠺ࡇ࡜ࡀ࡛ࡁࡿ㸬

Step 3: sT = dT ࡟タᐃࡋ㸪sT ࢆฟຊ㸬┤ิᆺከ㔜ᬯྕࡢᏳ඲ᛶ࡜ࡑࡢᛂ⏝㸳㸬ࡲ࡜ࡵ࡟࠿࠼࡚
஘ᩘᛶᣊ᮰ᵓᡂࢆ⏝࠸ࡓከ㔜ᬯྕࡢᵓᡂ࡜ࡑࢀࢆ฼⏝ࡋࡓ᫬㝈බ㛤㘽ᬯྕࡢᵓᡂ࡟ࡘ࠸࡚㏙࡭ࡓ㸬᫬㝈බ㛤㘽ᬯྕ࡟ࡣ㸪ཷಙ⪅ࡀᣦᐃ᫬้๓࡟᚟ྕࡋࡓ
࠿ࡗࡓሙྜ㸪㏦ಙ⪅ࡀ᫬㛫๓᚟ྕ㘽ࢆཷಙ⪅࡟㏦ಙࡍࡿ
ࡇ࡜࡛᚟ྕࡀྍ⬟࡜࡞ࡿᶵ⬟ࢆᣢࡘ᫬㛫๓㛤ᑒᶵ⬟௜᫬㝈බ㛤㘽ᬯྕ࡜࿧ࡤࢀࡿᣑᙇࡀᏑᅾࡍࡿ㸬Timed Release Public Key Encryption from Bilinear Pairing͇, ICDCS
2005, IEEE, (2005), pp.504-513.
(4) A. Fujioka, Y. Okamoto, and T. Saito,͆Security of Sequential
Multiple Encryption͇
, IEICE Transactions on Fundamentals, E95-A(1), (2012-01), pp.57-69.
(5) A. Fujioka, Y. Okamoto, and T. Saito,͆Generic Construction ofStrongly Secure Timed-Release Public-Key Encryption͇
, IEICEᮏ✏࡛⤂௓ࡋࡓ IBE-PKE ᵓᡂ࡛ࡣ᫬㛫๓㛤ᑒᶵ⬟ࢆTransactions on Fundamentals, E96-A (1), (2013-01), pp.76-91.

ᐇ⌧ࡍࡿࡇ࡜ࡣ㞴ࡋ࠸ࡀ㸪ᬯྕ໬ࡢ㡰␒ࢆධࢀ᥮࠼

(6) M. Bellare and P. Rogaway, ͆Random Oracles are Practical: A

PKE-IBE ᵓᡂ࡜ࡋࡓሙྜ࡟ࡣ㸪᫬㛫๓㛤ᑒᶵ⬟௜᫬㝈බ

Paradigm for Designing Efficient Protocols͇, ACMCCS '93, ACM,

㛤㘽ᬯྕࡀᐇ⌧࡛ࡁࡿࡇ࡜ࡀᩥ⊩[11]࡟ᣦ᦬ࡉࢀ࡚࠸ࡿ㸬(1993) , pp. 62-73.
(7) J.H. Cheon, N. Hopper, Y. Kim, and I. Osipkov, ͆Timed-Release andㅰ㎡ᮏ✏࡛⤂௓ࡋࡓከ㔜ᬯྕ࡜ࡑࡢᛂ⏝࡟㛵ࡍࡿ୍㐃ࡢ◊

Key-Insulated Public Key Encryption͇
, FC 2006 (LNCS 4107),
Springer, (2006), pp.191-205.

✲ࡣᮾி㟁ᶵ኱ᏛᕤᏛ㒊㰺⸨Ὀ୍ᩍᤵ࡜ࡢඹྠ◊✲ࡢᡂ(8) J. Cathalo, B. Libert, and J. J. Quisquater, ͆ Effcient andᯝ࡛࠶ࡿ㸬ᮏሗࢆࡲ࡜ࡵࡿ࡟࠶ࡓࡾ◊✲ᡂᯝࡢ୍㒊ࢆ㌿

Non-Interactive Timed-Release Encryption͇, ICICS 2005 (LNCS㍕ࡍࡿࡇ࡜ࢆᛌㅙ㡬ࡁឤㅰࡍࡿ㸬3783), Springer, (2005), pp.291-303.
(9) S.S.M. Chow and S.-M. Yiu,͆Timed-Release Encryption Revisited͇,ཧ⪃ᩥ⊩

ProvSec 2008 (LNCS 5324), Springer, (2008), pp.38-51.

(1) R. Zhang, G. Hanaoka, J. Shikata, and H. Imai,͆On the Security of(10) E. Fujisaki and T. Okamoto,͆How to Enhance the Security ofMultiple Encryption or CCA-security + CCA-security = CCA-security?͇
,Public-Key Encryption at Minimum Cost͇
, PKC '99 (LNCS 1560),

PKC 2004 (LNCS 2947), Springer, (2004), pp.360-374.

Springer, (1999), pp. 53-68.

(2) Y. Dodis and J. Katz,͆Chosen-Ciphertext Security of Multiple(11) R. Kikuchi, A. Fujioka, Y. Okamoto, and T. Saito,͆Strong Security

Encryption͇
, TCC 2005 (LNCS 3378), Springer, (2005), pp.188-209.

Notions for Timed-Release Public-Key Encryption Revisited͇,(3) A.C-F. Chan and I.F. Blake,͆Scalable, Server-Passive, User-Anonymous

ICISC 2011 (LNCS 7259), Springer, (2012), pp.88-108.

ຠ⋡ᑐ࣒ࢲୡ⏺࡟࠾ࡅࡿ࣓࢝ࣞ࢜ࣥᇶ‽࡜࣓ࢪ࢔࣭ࣥࢥࣥࢺ࣮ࣟࣝἲᯇ஭ ṇஅ㸨A Chameleon’s Criteria and Medium Control in Efficiency vs. Muda World
Masayuki MATSUI㸨㸯㸬ࡣࡌࡵ࡟

ḟ࡟㸪ࡇࡢ࣓࢝ࣞ࢜ࣥᇶ‽ࢆ୚࠼ࡿ᪂⪺኎ࡾᏊࡢࣔࢹࣝ

ࡇࢀࡣ㸪࠸ࢃࡺࡿຠ⋡ᑐ࣒ࢲ(↓㥏)ୡ⏺࡬ࡢ࠶ࡿ⛉Ꮫⓗࡀ㸪ࢺࣛࣇ࢕ࢵࢡ఍ィἲ(T఍ィ) (1)(2)ࡢࣔࢹࣝ࡜㢮ఝࡋ࡚࠸࢔ࣉ࣮ࣟࢳ࡛࠶ࡾ㸪ࢹ࢕ࢫࢡ࣮ࣜࢺ⣔ࡢࢧ࢖ࣂࢿࢸ࢕ࢡࢫ

ࡿࡇ࡜࡟╔┠ࡋ࡚㸪ࡇࡢᇶ‽࡟࠾ࡅࡿ࡮ࢼࣝࢸ࢕ࡢ⟬ᐃἲㄽ࡛ࡶ࠶ࡿ㸬ࡑࡢࡓࡵ࡟㸪๓ⴭ(1)(2)ࡢࡼ࠺࡟㸪ᕤሙ㸪௻ᴗ㸪࡞࡝ࡢᇶ♏ࢆ୚࠼࡚࠸ࡿ㸬ࡲࡓ㸪ࡇࡢ┦ᑐⓗᇶ‽ࡢὶືᩘ⤒῭ࢆ༢࡟3M&I⣔(ከᵝ⣔)࡛ࡣ࡞ࡃ㸪3M&I-Time⣔(ከᵝ㸭ὶື㠃⟶⌮ἲ(࣓ࢪ࢔࣭ࣥࢥࣥࢺ࣮ࣟࣝἲ)(6)࡜㸪ࢿࢵࢺయ)࡜ࡋ࡚⪃࠼࡚࠸ࡿ㸬࣮࣡ࢡ࣭ࣇ࣮ࣟ⾲⌧(7)࡟ࡼࡿ㐠⏝ἲࡀ♧ࡉࢀ࡚࠸ࡿ㸬ࡑࢀ࡟ࡼࡾ㸪ᚑ᮶ࡢከᵝᛶࡢ෕㛗ᗘ(ᣊ᮰)(3)ࡸ࣒ࢲ(ࣟࢫ)࡟ᑐࡍࡿ᪂ࡋ࠸どⅬࡀぢ࠼࡚ࡃࡿ㸬௨๓ࡢ3M&I(ከᵝᛶ)

㸰㸬࣒ࢲၥ㢟࡜⤒῭ⓗᇶ‽⣔࡛ࡣ㸪ከᵝᛶࡢ୙☜࠿ࡉࡢ⛬ᗘ࡜ࡑࡢᵓ㐀(෕㛗ᗘ)ࡀ୺

㸰㸬㸯 ⤒῭ⓗຠ⋡ᑐ࣒ࢲၥ㢟㢟࡜⪃࠼ࡽࢀ࡚࠸ࡓ㸬 ⛉Ꮫⓗ⟶⌮ἲ(8)࡟࠾ࡅࡿ࣒ࢲ࡟ᑐࡍࡿᇶ‽ࡣ㸪ࢸ࢖࣮ࣛ

3M&I-Time⣔࡜ࡋ࡚ࡢከᵝ⣔ࣉࣟࢭࢫ࡟␃ពࡍࡿ࡜㸪ࡑᇶ‽࡛࠶ࡿ㸬ࡇࢀࡣ㸪୍ὶࡢ⫗యసᴗ⪅ࢆᑐ㇟࡜ࡋ࡚᫬㛫

ࡢព࿡ㄽ(౯್ㄽ)ࡀ⏕ࡌ࡚࠸ࡿ㸬ࡇࡢࡼ࠺࡞ᑐ㇟ࢆᢅ࠺ࡓ

ศᯒࡋ࡚࣒ࢲࢆ┬࠸ࡓ㸪၏୍᭱Ⰻࡢ᪉ἲ(෕㛗ᗘࢮࣟ?)࡛࠶

ࡵ࡟ࡣ㸪ᚑ᮶࡟࡞࠸࣒ࢲㄽࡢ᪂ࡋ࠸ྲྀࡾᢅ࠸᪉ࡀᚲせ࡟࡞ࡿ㸬௚᪉㸪ࢸ࢖࣮ࣛࡣ㸪୍᪥ࡢබṇ࡞௙஦㔞ࡢᑟධ࡟࠶ࡓ

ࡿ㸬ࡑࢀࡀ㸪ព࿡ㄽࢆ┤᥋࡟⪃࠼࡞࠸෕㛗ᗘ࡟ᑐࡋ࡚㸪࣒ࡗ࡚㸪ࡇࡢᇶ‽࡟࠶ࡿ✀ࡢ࣒ࢲࢆྵࡲࡏࡓవ⿱(allowance)ࢲㄽࡀព࿡ㄽࢆ⪃࠼ࡿᚲ↛ᛶ࡛࠶ࡿ㸬ࡇࡇ࡛ࡣ㸪ࡇࡢࡼ࠺ࢆ⪃៖ࡍࡿࡇ࡜ࢆチᐜࡋ࡚࠸ࡿ㸬ࡇࡢࢠࣕࢵࣉࡣఱ࠿㸬࡞ၥ㢟࡟ᑐࡋ࡚࣓࢝ࣞ࢜ࣥᇶ‽(Chameleon’s criteria)(4)ࢆᑟ

ࡇࢀࡇࡑࡀ㸪࣏ࢫࢺ࣭ࢸ࢖࣮ࣛᇶ‽࡟ồࡵࡽࢀࡿࡶࡢ࡛

ධࡋ࡚㸪ゎㄝ࡜࡜ࡶ࡟㸪ᒎᮃࢆࡋ࡚࠸ࡿ(ὀ㸯)㸬

࠶ࡿ㸬ࡑࡢࡓࡵ࡟ࡣ㸪⤒῭ⓗព࿡ㄽ(౯್ㄽ)ࡢᑟධࡀᚲせ࡜⪃࠼ࡽࢀࡿ㸬౛࠼ࡤ㸪ᅾᗜࡢ౯್ࡣ༢࡟኱ᑠࡔࡅ࡛ࡣ࡞

ᮏ⥲ㄝ࡛ࡣ㸪⤒ႠᕤᏛศ㔝࠿ࡽࡇࡢၥ㢟ᥦ㉳ࡀࡉࢀ࡚࠸
ࡿ(ὀ2)㸬ࢸ࢖࣮ࣛࡢ⛉Ꮫⓗ⟶⌮ἲ࡟ࡣ㸪⏕⏘ᛶ㸪⤒῭ᛶࡢࡃ㸪ᇶ‽ࡼࡾ኱࠿ᑠ࠿࡟ࡶࡼࡿ㸬኱࡜࡞ࢀࡤ㐣๫ឤ㸪ᑠ࡜࡞ࢀࡤ୙㊊ឤ࡜࠸࠺౯್ほࡀ⏕ࡌࡿ㸬ྥୖ࡬ࡢ㈉⊩ࡢ୍᪉࡛㸪௚᪉࡛ᵝࠎ࡞ᢈุࡀ࠶ࡿ㸬᭱㏆࡛ࡶ㸪ࡇࡢࢸ࢖࣮ࣛࣜࢬ࣒ࡢ100ᖺ࡟ᑐࡋ࡚㸪⌧௦ⓗࣞࣅࣗ⾲ ࣒ࢲࡢᑐ㇟࡜ᡤᅾ౛

࣮(5)ࡀヨࡳࡽࢀ࡚࠸ࡿ㸬࣒ࢲࡢᑐ㇟ࡲࡎ㸪ࡇࡢ࣏ࢫࢺ࣭ࢸ࢖࣮ࣛࣜࢬ࣒࡟ྥࡅ࡚㸪ࢸ࢖࣮ࣛࡢຠ⋡ᑐ࣒ࢲᇶ‽ࡀ⤯ᑐⓗ࡛࠶ࡿ࡜࠸࠺ᣦ᦬࠿ࡽ㸪┦ᑐⓗ࡞࣓࢝ࣞ࢜ࣥᇶ‽ࢆᑟධࡋ࡚㸪⪃ᐹࢆ⾜ࡗࡓ㸬ࡑࡇ࡛ࡣ㸪ពእ࡟ࡶ㸪㝈⏺฼┈MP(฼┈㸩ᅛᐃ㈝)ࡀ࣒ࢲࡢ᭱኱್࡛࠶

ࣄࢺ
ࣔࣀ
࢝ࢿ
(ཎ౯)

ࡿࡇ࡜ࡀᣦ᦬ࡉࢀ࡚࠸ࡿ㸬

࢝ࢿ
(฼┈)

*ᩍᤵ ⤒ႠᕤᏛ⛉
Professor, Dept. of Industrial Engineering and Management᝟ሗຠ⋡ၥ㢟ࡢᡤᅾ

ᚑ᮶ࡢ࢔ࣉ࣮ࣟࢳ

ಶయవ⿱⋡(Ᏻ඲)ಶู᭱㐺໬(ᖹᆒ್ⓗ)ࢩࢫࢸ࣒ࣂࣛࣥࢩࣥࢢ(ㄪᩚ)♫఍ⓗ᭱㐺໬

ᅛᐃ㈝タィ(✵㛫ࢩࢫࢸ࣒)ኚື㈝㐠⏝(᫬㛫ࣉࣟࢭࢫ)ᦆ┈ศᒱⅬศᯒタഛ/ᢞ㈨ࣜࢫࢡ㑅ዲ(ࣜࢱ࣮ࣥ)ᅾᗜ/㈓⵳

ࣂࢵࣇ࢓㑅ዲ(ࢫࢺࢵࢡ)ࣜ࢔࣭ࣝ࢜ࣉࢩࣙࣥ
ࢹ࣮ࢱ/㈨ᩱ

୙☜ᐇᛶ(෕㛗ᛶ)᝟ሗ⣔ࣔࢹࣜࣥࢢ(ᑬᗘ)᝟ሗ⛉Ꮫ

ຠ⋡ᑐ࣒ࢲୡ⏺࡟࠾ࡅࡿ࣓࢝ࣞ࢜ࣥᇶ‽࡜࣓ࢪ࢔࣭ࣥࢥࣥࢺ࣮ࣟࣝἲ

ࡇࡢᇶ‽ࡣࡲࡓ㸪㟂⤥ࢫࣆ࣮ࢻ࡟ࡼࡗ࡚ྍኚࡢࡣࡎ࡛࠶
ࡿ㸬ࡇࡢゎỴ࡟ࡣ㸪౯್ほ(ព࿡ㄽ)࡟ࡼࡗ࡚ᇶ‽ࢆኚ໬ࡉ㸱㸬࣑ࢡࣟ⤒῭࡜ᇶ‽㸱㸬㸯 ᦆ┈ศᒱⅬศᯒࡢሙྜ

ࡏ࡚ࡸࡿࡇ࡜ࢆ⪃࠼ࡿ㸬ࡇࢀࡀ㸪࣓࢝ࣞ࢜ࣥᇶ‽࡛࠶ࡿ㸬⟶⌮఍ィ࡟࠾࠸࡚ࡼࡃ▱ࡽࢀ࡚࠸ࡿᦆ┈ศᒱⅬᅗࡣ㸪ᅗ⾲㸯ࡣ㸪ࢹ࢕ࢫࢡࣜʊࢺ⣔࡟࠾ࡅࡿ㸪✀ࠎࡢ࣒ࢲࡢᑐ㇟࡜

2ࡢࡼ࠺࡟୚࠼ࡽࢀࡿ㸬ࡇࡇ࡛㸪㝈⏺฼┈ࡣᅛᐃ㈝࡜฼┈ຠ⋡ၥ㢟ࡢᡤᅾࢆࡲ࡜ࡵࡓࡶࡢ࡛࠶ࡿ㸬(ᦆ┈)ࡢ࿴࡛࠶ࡿ㸬ࡓࡔࡋ㸪☜⋡Pࡣ኎ୖ㧗Stࡢศᕸ㛵ᩘࢆ⾲ࡋ࡚࠸ࡿ㸬

㸰㸬㸰 ࣓࢝ࣞ࢜ࣥᇶ‽ࡢᑟධ࡜ᇶ‽ࡇࡢሙྜ㸪ᦆ┈ศᒱⅬ(V)ࡣ㸪఍ィᏛ࡛ࡣḟᘧ࡛୚࠼ࡽ

࣓࢝ࣞ࢜ࣥᇶ‽ࡣ㸪⡆༢࡟ゝ࠼ࡤ㸪᪂⪺኎ࡾᏊၥ㢟(ᅗ1)ࡢゎ࡜ࡋ࡚୚࠼ࡽࢀࡿ㸬ᅾᗜၥ㢟࡟࠾࠸࡚ࡣ㸪ࢧ࢖ࢡࣝ

ࢀ࡚࠸ࡿ㸬


࠶ࡓࡾࡢ⥲࣌ࢼࣝࢸ࢕㛵ᩘࡣ㸪tᮇࡢᅾᗜ㔞ࢆLt㸪ᇶ‽ᅾᗜሺሻ ൌ ᅛᐃ㈝ ൊ 㝈⏺฼┈ሺሻ(3)

㔞ࢆNt࡜ࡋ࡚㸪ḟᘧ࡛୚࠼ࡽࢀࡿ(9)㸬
ࡼࡗ࡚㸪ࡇࡢ࡜ࡁᯇ஭ࡢᘧయ⣔(W=ZL) (1)(2)࡜࡞ࡿ㸪௨ୗࡢ                㛵ಀᘧࡀᡂ❧ࡍࡿ㸬
(1)ሺ୲ ሻ ൌ Ⱦଵ ୲ ൅ Ⱦଶ ሺ୲ െ ୲ ሻା ൅ Ⱦଷ ሺ୲ െ ୲ ሻା                              ሺ㔞   ሻ ൈ ሺ㔠   ሻ ൌ ᅛᐃ㈝(W)䛯䛰䛧䠈ሺܽሻା ‫ ؠ‬ሺܽǡ Ͳሻ䛷䛒䜛䠊(4)ࡇࡢ࡜ࡁࡢ᭱㐺࡞ᅾᗜ㔞ࡣ㸪ᚤศཪࡣᕪศ࡟ࡼࡿ᭱ᑠ໬
࡟ࡼࡗ࡚㸪ḟᘧࡢศᕸ㛵ᩘF(N_t)࡛୚࠼ࡽࢀࡿ㸬 ሺ୲ ሻ ൌȾଷ െ Ⱦଵൌ Ⱦത  ሺͲ ൏ Ⱦത ൏ ͳሻȾଶ ൅ Ⱦଷ

(2)

 ࡇࡢ࣓࢝ࣞ࢜ࣥᇶ‽ࡣ㸪3M&I-Time⣔࡛ࡣ㸪㟂⤥ࢠࣕࢵࣉࡢἼື࡟ࡼࡾ㸪㔜ࡳȕ2࡜ȕ3ࡢ኱ᑠࡀ཯㌿ࢆࡃࡾ㏉ࡍ࡜ࡇࢁ࡟≉ᚩࡀ࠶ࡿ㸬V   








㸱㸬㸰 ⤒῭ⓗ฼┈ᑐᅛᐃ㈝

ࡇࡇ࡛ࡣ㸪ຠ⋡࡜ࡋ࡚฼┈㸪࣒ࢲ࡜ࡋ࡚ᅛᐃ㈝ࢆ⪃࠼࡚㸪     ᘧ(4)ࡼࡾ㸪㝈⏺฼┈(㸻ᅛᐃ㈝㸩฼┈)ࢆᑟධࡍࡿ㸬࠸ࡲ㸪࣓࢝ࣞ࢜ࣥᇶ‽(㝈⏺฼┈MP࠿ࡽࡢࢬࣞࢆ᭱ᑠ໬ࡍࡿᇶ
‽㝈⏺฼┈ၥ㢟ࢆ⪃࠼ࡿ㸬ᅗ ᦆ┈ศᒱⅬ࡜㝈⏺฼┈ࡢ㛵ಀᅗ ᪂⪺኎ࡾᏊࡢࣔࢹࣝ࡜㔜ࡳ࣌ࢼࣝࢸ࢕ ઺ܑ࣓࢝ࣞ࢜ࣥᇶ‽ࡣ㸪࣒ࢲࡣ┦ᑐⓗ࡞ࡶࡢ࡛㸪⎔ቃࡸ≧ἣ࡟ࡼࡗ࡚ࡶኚ໬ࡍࡿࡇ࡜ࢆ♧ࡋ࡚࠸ࡿ㸬ࡇࢀࡣ㸪ࡲࡓ㸪ᑐ ࡇࡢ࡜ࡁ㸪t᫬Ⅼ࡛ࡢ኎ୖ㧗ࢆSt࡜ࡍࡿ࡜㸪᪂⪺኎ࡾᏊࣔࢹࣝ࡟࠾ࡅࡿ⥲࣌ࢼࣝࢸ࢕㛵ᩘࡣ㸪ḟᘧࡢࡼ࠺࡟᭩ࡁ⾲ࡏࡿ㸬㇟≀ࡀᇶ‽ࢆୗᅇࡿ࡮ࢼࣝࢸ࢕࡜ୖᅇࡿ࡮ࢼࣝࢸ࢕ࡢࣂ

ሺሻ ൌ Ⱦଵ ሺሻ ൅ Ⱦଶ ሺ െ ୲ ሻା ൅ Ⱦଷ ሺ୲ െ ሻାࣛࣥࢫ࡟ࡼࡾ㸪ࡑࡢᆒ⾮Ⅼ(࣓ࢪ࢔ࣥ)࡟࡞ࡗ࡚࠸ࡿࡇ࡜ࡀ

ࡓࡔࡋ㸪ࡇࡇ࡛ࡢ࣌ࢼࣝࢸ࢕ࡢព࿡ࡣ㸪௨ୗࡢ㏻ࡾ࡛࠶ࡿ㸬≉ᚩ࡛࠶ࡿ㸬(5)⚄ዉᕝ኱ᏛᕤᏛ◊✲ᡤᡤሗ ➨  ྕȾଵ 㸸㝈⏺฼┈ሺሻ࡛࠶ࡿ ൏ ᅛᐃ㈝㸩฼┈ ൫ᦆ┈൯ ൐ ࡬ࡢ࣌ࢼࣝࢸ࢕Ⱦଶ 㸸ࢆୗᅇࡗࡓ࡜ࡁ࡟࠿࠿ࡿ฼┈൫ᦆ┈൯㻌 㻌ᕸ㻌཰ 㻌┈ศᗘᩘ  ࡬ࡢ࣌ࢼࣝࢸ࢕f (ER)Ⱦଷ 㸸ࢆୖᅇࡗࡓ࡜ࡁ࡟࠿࠿ࡿኚື㈝࡬ࡢ  ࣌ࢼࣝࢸ࢕䚷䚷 ȡP

Į 2(ȕ 2)

ᘧ(5)࠿ࡽ㸪⤒῭ⓗຠ⋡ᑐ࣒ࢲ࡟࠾ࡅࡿ᭱㐺࡞࣓࢝ࣞ࢜ࣥ
ᇶ‽(MP)ࡀᚓࡽࢀࡿ㸬ࡇࢀࡣ㸪ᘧ(5)ࡢ᭱ᑠ໬࡛࠶ࡾ㸪ᘧ(2)O䛸ྠᵝ䛻䠈 ሺሻ ൌ ȾതሺͲ ൏ Ⱦത ൏ ͳሻ䛷୚䛘䜙䜜䜛䠊࣮ࣗࢩࣙࣥࢆᚓࡿࡇ࡜ࡀ࡛ࡁࡿ㸬ࡇࡢࢯ࣮ࣜࣗࢩࣙࣥࡣ㸪ᘧ(4)ࡼࡾᦆ┈ศᒱⅬࡢ⤒῭ⓗࢯ࣮ࣜࣗࢩࣙࣥࡶ୚࠼ࡿ㸬Į 3(ȕ 3)EN

Į 2 BEPᅛᐃ㈝ࡇࢀ࡟ࡼࡾ㸪⤒῭ⓗ࡞ຠ⋡(฼┈)ᑐ࣒ࢲ(ᅛᐃ㈝)ࡢࢯࣜ

䚷 1-ȡP

ኚື㈝MP(L)䊻 ER(p)ᅗ ᪂⪺኎ࡾᏊὶࢺࣛࣇ࢕ࢵࢡ఍ィࣔࢹࣝ ȘȘ 

ᘧ(6)࡛㸪Pࡣฎ⌮⋡࡛࠶ࡾ(0<P<1)㸪⁄ࢀᩘࡀࢮ࡛ࣟࡣ ࡇࡢ㝈⏺฼┈ࡣ㸪ࢫ࣮ࣝࣉࢵࢺ఍ィ(10)࡛ࡢࢫ࣮ࣝࣉࢵࢺ

P=1࡜࡞ࡿ㸬ࡶࡋȡ>1ࡢሙྜ࡟ࡣ㸪✌ാ⋡ȡࢆȡ’(= 1/ȡ)࡜⨨࡟┦ᙜࡍࡿ㸬᭱㏆㸪ࢫ࣮ࣝࣉࢵࢺྥୖ࡛ࡢ඲య᭱㐺ࡀὀ┠ࡁ᥮࠼ࢀࡤ㸪௨ୗࡢ㆟ㄽࡣྠᵝ࡛࠶ࡿ㸬ࡇࡢ࡜ࡁ㸪ᖹᆒ⁄ࡉࢀ࡚࠸ࡿ(11)㸬ࡇࢀࡣ㸪ᚑ᮶ࡢࢥࢫࢺ୰ᚰ୺⩏㸪ࢥࢫࢺࢲࢀᩘȘࡣ㸪Ș=ȡ㸫1(ȡ>1)࡜࡞ࡿ㸬࢘ᚿྥࡀ⦰ᑠ໬ࣜࢫࢡࢆࡶࡘࡓࡵ࡛࠶ࡿ㸬ࡇࡢᘧ(6)ࢆኚᙧࡍࡿ࡜㸪✌ാ㈝⏝ಀᩘĮ2࡜㐟ఇ㈝⏝ಀ ᅜࡢ⤒῭࡛ࡣ㸪ࡇࡢࢫ࣮ࣝࣉࢵࢺྥୖࡣ㸪GDP㸦ᅜෆ⥲ᩘĮ3ࡢ኱ᑠ㛵ಀ࠿ࡽ㸪ECࡣ௨ୗࡢࡼ࠺࡟2㏻ࡾࡢ⾲⌧ࢆࡍ⏕⏘㸧ࡢᡂ㛗࡟ࡘ࡞ࡀࡗ࡚ࡃࡿ㸬ࡇࢀࡣ㸪GDPࡀ୍ᐃᮇ㛫ࡿࡇ࡜ࡀ࡛ࡁࡿ㸬ෆ࡟ᅜෆ࡛⏕⏘ࡉࢀࡓ௜ຍ౯್ࡢ⥲㢠࡛࠶ࡾ㸪ࡲࡓ㝈⏺฼┈ࡢ⥲㢠࡟┦ᙜࡍࡿ࠿ࡽ࡛࠶ࡿ㸬㸲㸬࣑ࢡࣟ⤒῭࡜ᇶ‽ᩘ⌮ ൌ Ƚଵ 㸩൛Ƚଶ 㸩൫Ƚଷ 㸫Ƚଶ ൯൫ͳ㸫ɏ൯ൟǡ Ƚଶ 㸺Ƚଷ

(7) ൌ Ƚଵ L㸩{Ƚଷ 㸩(Ƚଶ 㸫Ƚଷ ) ɏP,(8)Ƚଶ 㸼Ƚଷ

㸲㸬㸯 ࢺࣛࣇ࢕ࢵࢡ఍ィ 7఍ィ ἲࡢᑟධ ౽ᐅⓗ࡟㸪ᘧ(7)ࡢ᪉ࢆ〇㐀ࢱ࢖ࣉ㸪ᘧ(8)ࡢ᪉ࢆࢧ࣮ࣅ

ࡇࡢT఍ィࡣ㸪ຠ⋡࡟ࢥࢫࢺ㸪౯᱁ࢆධࢀ࡚⪃࠼࡚࠸࡚㸪ຠ⋡࡜ࡋ࡚ࡣ✌ാ⋡ࢆྲྀࡾୖࡆ࡚࠸ࡿ㸬ᚑ᮶ࡢ఍ィࢩࢫࢸࢫࢱ࢖ࣉ࡜࿧ࢇ࡛࠸ࡿ㸬ࡇࡢ࡜ࡁ㸪ࢧ࢖ࢡࣝ࠶ࡓࡾࡢ฼┈ࢆEN(=ER-EC)࡜ࡍࡿ࡜㸪཰┈ER(Z)ࡣḟᘧ࡛୚࠼ࡽࢀࡿ㸬࣒ࡣ㸪ᬯ㯲ⓗ࡟✌ാ⋡ࢆ100㸣࡜࠿90㸣ࢆ᝿ᐃࡋ࡚࠸ࡿ㸬⌧௦ࡢࡼ࠺࡟㸪⤒Ⴀࢫࣆ࣮ࢻࡀၥ㢟࡜࡞ࡿ࡜ࡁ㸪ࡇࡢ᝿ᐃࡣ⌧ᐇⓗ࡛ࡣ࡞࠸࡜⪃࠼ࡽࢀࡿ㸬ᐇ㝿㸪୍⯡ࢩࢫࢸ࣒࡟ࡣ㸪ࡑࢀࡒࢀ࡟ᅛ᭷࡞᭱㐺✌ാ⋡ࡀᏑᅾࡍࡿࡢ࡛㸪✌ാ⋡࡟‽ᣐࡍࡿ࣐ࢿࢪ࣓ࣥࢺࡶ㔜せ࡛࠶ࡿ㸬✌ാ⋡➼ࡢ᥎ᐃ࡟ࡣ㸪㏻ᖖࡢఏ⤫ⓗIEᡭἲ(✌ാィჾ㸪WS࡞࡝)࡟ࡼࡗ࡚㸪ᐜ᫆࡟ྍ⬟࡛࠶ࡿ㸬ࡕᆺ௻ᴗࣔࢹࣝࢆࡶ࡜࡟ࡍࡿ࡜㸪༢఩᫬㛫ᙜࡓࡾࡢᖹᆒ㐠⏝㈝⏝ECࡣ㸪ḟᘧ࡛୚࠼ࡽࢀࡿ㸬 ൌ  ൫ᚅࡕ㈝⏝൯㸩൫✌ാ㈝⏝൯㸩൫㐟ఇ㈝⏝൯ൌ Ƚଵ 㸩Ƚଶ ɏ㸩Ƚଷ ൫ͳ㸫ɏ൯ǡ  ɏ ൏ ͳ㸲㸬㸰 ࣓࢝ࣞ࢜ࣥᇶ‽ࡢᩘ⌮࡜㐠⏝ᦆ┈ศᒱⅬศᯒࡢሙྜ㸪᪂⪺኎ࡾᏊࣔࢹࣝࢆT఍ィἲ࡟⩻ヂࡋ࡚⪃࠼ࡿ࡜(ᅗ3)㸪
ࢧ࢖ࢡࣝ࠶ࡓࡾࡢ㈝⏝㛵ᩘࡣ௨ୗ࠸ࡲ㸪ࢧ࢖ࢡࣝ࠶ࡓࡾࡢࢥࢫࢺ࣭ࣔࢹࣝ(ᅗ3)࡜ࡋ࡚㸪ᚅ

ER(Z) = EN㸩EC(9)                        (6)ࡢࡼ࠺࡟୚࠼ࡽࢀࡿ㸬ሺሻ ൌ Ⱦଵ 㸩Ⱦଶ ሺȂ ሻା 㸩Ⱦଷ ሺȂ ሻା(10)

ൌ Ƚଵ 㸩Ƚଶ ɏ㸩Ƚଷ ൫ͳ㸫ɏ൯(11)ࡓࡔࡋ㸪ሺሻା ൌ ሺǡ Ͳሻ࡛࠶ࡿ㸬ୖᘧ࡟࠾࠸࡚ࡣ㸪L<
̿>MP(Ⱦത)㸪࠾ࡼࡧȽ୧ <̿>Ⱦ୧ (i=1,2,3)࡜ࡋ࡚࠸ࡿ㸬ࡲࡓ㸪MP = Ƚଶ 㸩EN (Ƚଶ <Ƚଷ )㸪=Ƚଷ 㸩EN (Ƚଶ >Ƚଷ )࡛࠶ࡿ㸬ຠ⋡ᑐ࣒ࢲୡ⏺࡟࠾ࡅࡿ࣓࢝ࣞ࢜ࣥᇶ‽࡜࣓ࢪ࢔࣭ࣥࢥࣥࢺ࣮ࣟࣝἲ



(O)

ࡼࡗ࡚㸪࣓࢝ࣞ࢜ࣥᇶ‽ࡢỴᐃ(⟬ᐃ)ࡣ㸪T఍ィἲ࡟ࡼࡾĮi (i=1,2,3)ࢆ᥎ᐃࡍࡿ࡜㸪ḟᘧ࡛୚࠼ࡽࢀࡿ㸬ሺ ‫ כ‬ሻ ൌȽଷ Ȃ ȽଵȽଶ 㸩Ƚଷൌ ȾതǡͲ ൏ Ⱦത ൏ ͳ

(12)
(D)
<EC>

<EN>

<ER> (Z)

(I)

(MP)

ࡓࡔࡋ㸪F(࣭)ࡣ཰┈ER࡟㛵ࡍࡿศᕸ㛵ᩘ࡛࠶ࡿ㸬ḟ࡟㸪ኚືࡍࡿ࣓࢝ࣞ࢜ࣥᇶ‽(MP)ࡢ㐠⏝⟶⌮࡟࠶ࡓࡗ࡚ࡣ㸪ᦆ┈ศᒱⅬ⟶⌮ࣉࣟࢭࢫ࡬ࡢὶືᩘ⟶⌮ἲ(6)ࡢ㐺⏝ࡓࡔࡋ㸪ER㸻EN㸩EC㸪

<EN>    EC㸻D㸩I(7)ࡀ⪃࠼ࡽࢀࡿ㸬ࡇࡢሙྜࡢᇶᮏᘧࡣ㸪⏕⏘/ᅾᗜࣔࢹࣝ
ࡢሙྜࡢ఍ィ࡬ࡢ⩻ヂ࠿ࡽ㸪௨ୗࡢࡼ࠺࡟࡞ࡿ㸬ᅗ ࢣ࢖ࣥࢬ⤒῭࡜ᡤᚓ 㝈⏺฼┈ 㻹㻼 ḟᮇᢞධ㔞(O)㸻ḟᮇὶฟ㔞(D)㸫⛣ືᇶ‽(13)

ᅾᗜ(MI) 㸩ᙜᮇᅾᗜ㔞(I)᭱㏆㸪࣐ࢡࣟ⤒῭࡟࠾࠸࡚ࡣ㸪ᢞ㈨(ຠ⋡)ᑐᾘ㈝㸦࣒ࢲ㸧э ḟᮇ㐠㌿㈨㔠(O)㸻ḟᮇኚື㈝(D)㸩⛣ືࡢ㓄ศၥ㢟ࡀㄢ㢟࡜ࡉࢀ࡚࠸ࡿ㸬ࡇࡢၥ㢟ࡶ㸪⾲1ࡼࡾ࣓࢝ࣞ࢜ࣥᇶ‽ࡀࢯ࣮ࣜࣗࢩࣙࣥ࡟ᑐᛂࡋ࡚ࡃࡿ࡜⪃࠼ࡽ㝈⏺฼┈(MP) 㸫ᙜᮇᅛᐃ㈝(I)ࡓࡔࡋ㸪MP㸻Z㸫D(14)ࢀ㸪௒ᚋࡢ᳨ウ࡟࡞ࡿ㸬ࡇࡢ࡜ࡁ㸪ᘧ(13)(14)࡟࠾࠸࡚㸪ྂ඾ⓗ୙➼ᘧ࠿ࡽ㸪ḟ⾲ ⤒῭࡜࣓࢝ࣞ࢜ࣥᇶ‽ၥ㢟ࡢ᭱㐺ᛶ᮲௳㸸O㸻I㸻MP㸻D(㸻Z/2)ࡀᚓࡽࢀࡿ㸬ࡲࡓ㸪ᘧ(14)ࡣ㸪ᅗ㸲ࡢࡼ࠺࡟ࢿࢵࢺ࣮࣡ࢡࣇ࣮࡛ࣟ⾲ࢃࡏࡿ㸬኎ୖᡤᚓ

ࡇࡢ⪃࠼᪉ࡣ㸪ὶື㠃(㈨⏘)⟶⌮ἲ(4) (12)࡟ࡼࡿࣜ࢔ࣝࢱ࢖
࣒⤒Ⴀ࡟ࡶ᭷ຠ࡛࠶ࡿ㸬ḟᮇ㐠㌿㈨㔠
(Ot+1)

Ot

⥔ ᣢ ㈝

㝈⏺฼┈௨

㝈⏺฼┈௨

ሺߚଵ ሻ

ୗሺߚଶ ሻ

ୖሺߚଶ ሻ

࣑ࢡࣟ⤒῭

㝈⏺฼┈

฼┈ ᦆ┈ 

ኚື㈝

࣐ࢡࣟ⤒῭

㝈⏺౯್

ᢞ㈨ ㈓⵳ ౑⏝⪅㈝⏝



Ot+2

ὀ 㝈⏺฼┈ሺሻ ൌ ኎ୖ൫౯᱁൯ െ ኚື㈝

ᮇ㛫
t

ᙜᮇᅛᐃ㈝
(It)

ᮇ㛫
t+1

ᮇ㛫
It+1



t+2

㸳㸬㸰 ௻ᴗ㛫ࢿࢵࢺ࣮࣡ࢡ࡜㐠⏝ࢣ࢖ࣥࢬ⤒῭ࡢሙྜࡶ㸪ᦆ┈ศᒱⅬศᯒ࡜ྠᵝ࡟⪃࠼ࡿ⛣ື㝈⏺฼┈
(MPt)
Dt



ḟᮇኚື㈝
(Dt+1)

࡜㸪ᅜẸᡤᚓࡢ⤒῭㛵ᩘࡣᘧ(11)࡛୚࠼ࡽࢀ㸪࣓࢝ࣞ࢜ࣥ

MPt+1

ᇶ‽(12)ࡀᚓࡽࢀࡿ㸬ࡓࡔࡋ㸪Į2ࡣᾘ㈝㸪ENࡣᢞ㈨࡛࠶ࡾ㸪MPࡣᾘ㈝࡜ᢞ㈨ࡢ࿴(㝈⏺౯್)࡛࠶ࡿ㸬

Dt+2



ᅗ ௻ᴗෆࢿࢵࢺ࣮࣡ࢡࣇ୍࣮ࣟ⾲⌧ ఍ィࣇ࣮ࣟ ࡲࡓ㸪࣐ࢡࣟ⤒῭࡛ࡢಶ(ୡᖏࡸ௻ᴗ)ࡢ㐠⏝⟶⌮ࡣ㸪ᘧ(14)࡜ྠᵝ࡟ࡋ࡚㸪௨ୗࡢࡼ࠺࡟୚࠼ࡽࢀࡿ㸬㸳㸬࣐ࢡࣟ⤒῭࡜ᇶ‽ᩘ⌮㸳㸬㸯 ࢣ࢖ࣥࢬ⤒῭࡬ࡢ㐺⏝௚௻ᴗ࡬ࡢ㈍኎(O)㸻౑⏝⪅㈝⏝(D)㸩⛣ື㝈
⏺౯್(MP) 㸫ᾘ㈝(I)      (15)࣐ࢡࣟ⤒῭࡟࠾࠸࡚ࡣ㸪⤒῭࡟࠾ࡅࡿぢ࠼ࡊࡿᡭ࡜ࡋ࡚㸪㟂せ࡜౪⤥࡟࠾ࡅࡿࣂࣛࣥࢫᶵ⬟࡟╔┠ࡋ࡚࠸ࡿ㸬ࢣ࢖ࣥࢬࡢᅜẸᡤᚓࡢㅖᴫᛕࢆ⏘ᴗ㐃㛵⾲࡟ࡑࡃࡋ࡚ᩚ⌮㸪ຍ➹ࡍࢀࡤ㸪ᅗ㸳ࡢ㏻ࡾ࡛࠶ࡿ(12)㸬(࢝ࢵࢥෆࡣຍ➹)ḟ࡟㸪」ᩘࡢ௻ᴗ➼ࡀὶືᩘ(㠃)⟶⌮ἲ࡟ࡼࡿ㐠⏝⟶⌮ࢆ⾜ࡗ࡚࠸ࡿ࡜ࡍࡿ㸬ᅗ㸴ࡣ㸪⏘ᴗ㐃㛵⾲ⓗ࡟㸪ࡑࡢ௻ᴗ➼ࡢࢿࢵࢺ࣮࣡ࢡ(౛࠼ࡤ㸪SC㸪ୡᖏ㸪⏘ᴗ㛫ࡢ㛵㐃)ࣇࣟ
࣮ࢆ⾲ࡋ࡚࠸ࡿ㸬ࡇࡢ⪃࠼᪉ࡣ㸪௻ᴗ➼ࡸᅜẸᡤᚓ(GDP)ࡢࢿࢵࢺ࣮࣡ࢡ࣭࣮࢜࣌ࣞࢩࣙࣥ࡟᭷ຠ࡜⪃࠼ࡽࢀࡿ㸬⚄ዉᕝ኱ᏛᕤᏛ◊✲ᡤᡤሗ ➨  ྕࡲࡓ㸪ᆅᇦࡸᅜ࡟࠾࠸࡚ࡣ㸪ᑐ㇟ࢩࢫࢸ࣒࡟࠾ࡅࡿᏳᐃ
ࡢࡓࡵ࡟㸪ࣂࣛࣥࢩࣥࢢ(ὀ㸲)ࡀ㔜せၥ㢟࡜࡞ࡿ㸬ࡇࢀࡣ㸪(ὀ2㸧ࡍ࡭࡚ࡢࠕ↓㥏ࠖࡀࠕ↓㥏࡛ࠖࡣ࡞࠸?!

ᑐ㇟ෆࡢ㝈⏺౯್(௜ຍ౯್)ࡢ࣓ࢪ࢔࣭ࣥࢥࣥࢺ࣮ࣟࣝ࡟

⤒ႠᕤᏛ࡜࠸࠺ࡢࡣ㸪100ᖺ࡯࡝๓࡟⡿ᅜࡢࢸ࢖࣮ࣛ࡜

ࡼࡗ࡚ྍ⬟࡜⪃࠼ࡽࢀࡿ㸬࠸࠺ேࡀษࡾᣅ࠸ࡓᏛၥ࡛ࡍ㸬ᙼࡣ㸪ࡇࢀࡲ࡛ࡣே㛫ࢆ୰ᚰ࡟⪃࠼ࡽࢀ࡚࠸ࡓࡀ㸪ࡇࢀ࠿ࡽࡣࢩࢫࢸ࣒(⣔)ࢆ୰ᚰ࡟
⪃࠼㸪⤒Ⴀ᪉ἲࡸ⏕⏘⌧ሙࢆྜ⌮ⓗ࡟⟶⌮ࡍࡿࡇ࡜࡛㸪఍௚௻ᴗ䜈䛾㈍኎
(Oi+1)Oi

Oi + 2♫ཬࡧ♫఍ࡢ⏕⏘ຠ⋡ࢆ࠶ࡆࡿ࡭ࡁ࡛࠶ࡿ㸪࡜࠸࠺ࠕ⛉Ꮫⓗ⟶⌮ἲࠖࢆᥦၐࡋ㸪ࡑࢀࡀ⌧ᅾࡢ⤒ႠᕤᏛ࡟ࡘ࡞ࡀࡗ࡚

ᾘ㈝

௻ᴗ

௻ᴗ

（I
(Iii）
)

i

i+1

࠸ࡲࡍ㸬࡝ࢀࡔࡅ↓㥏(࣒ࢲ)ࢆ┬࠸࡚ຠ⋡ࢆ࠶ࡆࡽࢀࡿ࠿

௻ᴗ
Ii+1

࡝࠺࠿࡜࠸࠺ࡇ࡜ࢆ⪃࠼ࡿᏛၥࡔ࡜࠸࠼ࡿ࡛ࡋࡻ࠺㸬i+2ࡓࡔ㸪ࡍ࡭࡚ࡢ࣒ࢲࡀ࣒ࢲ࡛ࡋࡻ࠺࠿㸪෌⪃ࡋࡓ࠸㸬⤒⛣ື㝈⏺౯್
⛣ື㝈⏺ᢞ㈨
（MP
(MPi）
i)

Di



ႠᕤᏛࡣ㺀௙஦/࣒ࢲࡢ௙⤌ࡳࡢタィ㸩㐠⏝㺁࡜⪃࠼㸪ᚲせ

MPi+1

౑⏝⪅㈝⏝
(Di+1)≀ࢆࠕ⌮⣔ࡢ㢌⬻(෕㛗ᗘ)࡜ᩥ⣔ࡢᚰ(෕㛗ᗘ)ࠖ࡜ࡍࡿ࡜(16)࡟‽ᣐ)㸪࣓࢝ࣞ࢜ࣥᇶ‽ࡣ㸪๓⪅ࡢ෕㛗ᗘ(ᅛᐃ㈝)࡜ᚋ⪅

Di+2



ᅗ ௻ᴗ➼ࡢࢿࢵࢺ࣮࣡ࢡࣇ࣮ࣟ ᅜẸᡤᚓ ࡢ෕㛗ᗘ(฼┈)ࡢ࿴࡛࠶ࡿ⤒῭ⓗ෕㛗ᗘ(㝈⏺฼┈)࡟┦ᙜࡍࡿⅬࡀ㸪ὀពࡉࢀࡿ㸬(ὀ3)࣓ࢪ࢔࣭ࣥࢥࣥࢺ࣮ࣟࣝἲࡣ㸪ఏ⤫ⓗ࡞⤫ィⓗ⟶⌮ࢆ౛࡟࡜ࡿ࡜㸪ⓎὀⅬ(Ᏻ඲ᅾᗜ㸧࡜Ⓨὀ㔞ࢆྠ᫬࡟Ỵᐃࡍ㸴㸬ࡲ࡜ࡵ࡜௒ᚋࡢㄢ㢟ᮏ⥲ㄝ࡛ࡣ㸪⤒῭ⓗ࡟ຠ⋡ᑐ࣒ࢲୡ⏺࡟᭷ຠ࡞㸪࣓࢝ࣞࡿ᪉ᘧ࡜ࡋ࡚≉ᚩ࡙ࡅࡽࢀࡿ㸬ࡇࡢ㉳※ࡣ㸪᪥ᮏ࡟࠾ࡅࡿ

࢜ࣥᇶ‽ၥ㢟࡟ࡘ࠸࡚ゎㄝ࡜ᒎᮃࢆࡍࡿ࡜࡜ࡶ࡟㸪࣓ࢪ࢔ྂ඾ⓗὶືᩘ⟶⌮࡜࡜ࡶ࡟㸪᭱㐺ⓎὀⅬἲ࡛࠶ࡿఏ⤫ⓗ࡞࣭ࣥࢥࣥࢺ࣮ࣟࣝἲࡢᴫせࢆ♧ࡍࡇ࡜ࡀ࡛ࡁࡓ㸬≉࡟㸪࢝㸦s, S)ᅾᗜ᪉ᘧ࡟ࡶ㐳ࡿ࠿ࡶ▱ࢀ࡞࠸㸬ࡑࡢព࿡࡛ࡣ㸪᪂࣓ࣞ࢜ࣥᇶ‽ࡢỴࡵ᪉(⟬ᐃ)࡜㐠⏝ἲ࡟ࡘ࠸᳨࡚ウࡋ࡚㸪᪉ἲࡣࡇࡢ⤫ィⓗ᪉ᘧࢆ☜⋡ⓗ࡟ືⓗ໬ࡋࡓࡶࡢ࡬࡜Ⓨࡑࡢྍ⬟ᛶ࡜ไᚚᛶࡢᇶ♏࡟ࡘ࠸࡚♧ࡋࡓ㸬ᒎࡉࡏࡓ࡜⪃࠼ࡽࢀࡿ㸬ࡇࢀ࡟ࡼࡾ㸪࣓࢝ࣞ࢜ࣥᇶ‽ၥ㢟ࡀ㸪༢࡟⤒῭ⓗ࡞ຠ⋡ᑐ࣒ࢲ࠿ࡽ㸪㟂⤥ࡢࣂࣛࣥࢫ(✌ാ⋡)ࡢୡ⏺࡬ᗈࡆࡽࢀࡿ

(ὀ4)ࣂࣛࣥࢩࣥࢢ(balancing)࡜ࡣ㸪ᑐ㇟ࢩࢫࢸ࣒࡟࠾ࡅࡿ

ࡇ࡜ࢆ᫂ࡽ࠿࡟ࡋ࡚࠸ࡿ㸬ࡇࡢၥ㢟ࡣ㸪ࡼࡾ୍⯡ⓗ࡟ࢧ࣮㞟୰໬㸦bottlenecked㸧ᑐศᩓ໬㸦balanced㸧ࡢ㸪㐣Ώⓗ࡞ࣅࢫୡ⏺࡟࠾࠸࡚ࡶ᭷ຠ࡛㸪ࡇࡢຠ⋡ホ౯➼࡜ࡶ㛵ಀࡢ࠶㠀ᆒ⾮໬≧ែ㸦umequilibriuming㸧࠿ࡽࡢᏳᐃ໬ㄪᩚ࡛࠶

ࡿⅬࡀὀ┠ࡉࢀࡿ㸬ࡿ㸬࠶ࡿ㟂せࢫࣆ࣮ࢻ࡜✀ࠎࡢไ⣙ࡢࡶ࡜࡛ࡣ㸪෕㛗ᗘ㸦࣒ࢲ㸧㈨※ࡢࣂࣛࣥࢩࣥࢢㄪᩚ࡟ࡼࡗ࡚㸪ࡑࡢ᮲௳ୗ࡛ࡢᑐ

ᥦ᱌ࡢ࣓ࢪ࢔࣭ࣥࢥࣥࢺ࣮ࣟࣝἲࡣ㸪ࡸࡸⲨ࠸㦵Ꮚࡢᒎ㛤࡛࠶ࡿࡀ㸪௒ᚋࡉࡽ࡟ヲ⣽࡞᳨ウ࡜ࢶ࣮ࣝࡢ㛤Ⓨ
㸦ODICS࡟⥆ࡃ㸧ࡀᮃࡲࢀࡿ㸬௚᪉㸪࣓࢝ࣞ࢜ࣥᇶ‽ࡣ㸪
(13)⤒῭Ꮫ࡟࠾ࡅࡿA.ࢫ࣑ࢫࡢ୺ⴭ ࡛ࡢぢ࠼ࡊࡿᡭ(㟂せࢫࣆ࣮ࢻ)࡟ᑐࡋ࡚㸪ࡶ࠺୍ࡘⴭ᭩ࡢࢱ࢖ࣉࡢぢ࠼ࡊࡿᡭ(14)࡜ぢ࡞ࡍࡇ࡜ࡀ࡛ࡁࡿ࡜⪃࠼ࡽࢀࡿ㸬ࡇࡇ࡛ࡣ㸪ࡇࢀ࡟ࡼࡿ⤒῭Ꮫ(GDP➼)࡬ࡢ࣐ࢿࢪ࣓ࣥࢺ
ࡢⓎᒎᛶࡶ♧ࡋࡓ㸬௒ᚋࡢࢡࣛ࢘ࢻ᫬௦ࡢ⤒Ⴀ㧗ᗘ໬࡟ྥࡅ࡚㸪ᮏ⥲ㄝ࡛ࡣ௻ᴗ㸪ᆅᇦ㸪ᅜ➼ࡢࣜ࢔ࣝࢱ࢖࣒⤒Ⴀ㸪
(15)ࣂࣛࣥࢩࣥࢢ⤒Ⴀ 㸪ࡉࡽ࡟ࡣ෕㛗ᗘ(࣒ࢲ㸧ࢆ⪃៖ࡋࡓ࣐ࢿࢪ࣓ࣥࢺἲ࡟᭷⏝࡛࠶ࡿࡇ࡜࡟╔┠ࡋ࡚࠸ࡿ㸬㇟ࢩࢫࢸ࣒ࡢᏳᐃ໬ࡀࡶࡓࡽࡉࢀࡿ㸬ཧ⪃ᩥ⊩(1)ᯇ஭ṇஅࠕ⏕⏘௻ᴗࡢ࣐ࢿࢪ࣓ࣥࢺʊ฼┈᭱኱໬࡜ᕤሙ⌮Ꮫࠖ㸪ඹ❧ฟ∧㸪2005(2)Matsui, M., Manufacturing and Service Enterprise with Risks : A
Stochastic Management Approach, Springer, 2008(3)Attneave, F., ᑠ㔝௚ヂࠕᚰ⌮Ꮫ࡜᝟ሗ⌮ㄽ㸫ᇶᮏᴫᛕ㸪᪉ἲ㸪⤖ᯝࠖ㸪ࣛࢸ࢕ࢫ(୸ၿ)㸪1968(4)Matsui, M., Development of Progressive Inventory Method toward
Real Time Age, ACMSA2011, Sanya, China, 2011(5)Brogan, J.W., Exonerating Fredrick Taylor, Industrial Engineer,(ὀ1㸧ࡇࡢཎ✏ࡣ㸪2012ᖺᗘ᪥ᮏ⤒ႠᕤᏛ఍᫓Ꮨ኱఍ண✏㸪⛅Ꮨ◊✲኱఍ண✏ࢆࡶ࡜࡟㸪ࡲ࡜ࡵ࡜ຍ➹ࢆ⾜ࡗࡓࡶࡢ࡛
࠶ࡿ㸬

41-44 (2011.11)(6)ᯇ஭ṇஅ࣭ෆᒣᗈᶞ࣭⸨ᕝ⿱᫭㸸࢜ࣥࢹ࣐ࣥࢻSCM࡟࠾ࡅࡿᅾ
ᗜኚືࡢὶືᩘᅗἲ࡟ࡼࡿ⟶⌮ἲ㸪᪥ᮏ⤒ႠᕤᏛ఍ㄽᩥㄅ㸪ຠ⋡ᑐ࣒ࢲୡ⏺࡟࠾ࡅࡿ࣓࢝ࣞ࢜ࣥᇶ‽࡜࣓ࢪ࢔࣭ࣥࢥࣥࢺ࣮ࣟࣝἲ

Vol.56, No. 2, 139-145 (2005)(7)Johnson, L.A., and Montgomery, D.C., Operations Research in
Production Planning , Scheduling and Inventory Control, John
Wiley, 1974ྥୖ࡛඲య᭱㐺㺁㸪᪥หᕤᴗ᪂⪺♫㸪2008(12)Keynes, J.M., ሷ㔝㇂ヂࠕ㞠⏝࣭฼Ꮚ࠾ࡼࡧ㈌ᖯࡢ୍⯡⌮ㄽࠖ㸪ᮾὒ⤒῭᪂ሗ♫㸪1995ᖺ(1936)(13)A.ࢫ࣑ࢫ㸸㺀ᅜ㇏ㄽ㺁㸪ᒾἼᩥᗜ㸪2001ᖺ(1776)(8)Taylor, F.W., ᭷㈡ヂࠕ⛉Ꮫⓗ⟶⌮ἲࠖ㸪ࢲ࢖ࣖࣔࣥࢻ♫㸪2009(14)A.ࢫ࣑ࢫ㸸㺀㐨ᚨឤ᝟ㄽ㺁㸪ᒾἼᩥᗜ㸪2003ᖺ(1759)(9)Weeks, J.K., Optimizing Planned Load Times and Delivery Dates,(15)ᯇ஭ṇஅ㸸ࣜ࢔ࣝࢱ࢖࣒⤒Ⴀ࡜ὶື㠃⟶⌮ἲ㛤Ⓨ㸪➨30ᅇᶓ

21st Annual Conference Proceedings, APICS, pp.177-188 (1979)(10)Goldratt, E. M., ୕ᮌᮏヂ㺀ࢨ࣭ࢦ࣮ࣝ㺁㸪ࢲ࢖ࣖࣔࣥࢻ♫㸪2001(11)ᮏ㛫ᓠ୍㺀ࢥࢫࢺࢲ࢘ࣥࡀ఍♫ࢆࢲ࣓࡟ࡍࡿʊࢫ࣮ࣝࣉࢵࢺ

ᖿᢏ⾡ࣇ࢛࣮࣒ࣛ㸪᪥ᮏᩍ⫱఍㤋㸪2011ᖺ3᭶(16)ᯇᾆ᫓ᶞ㸸⤒ႠᕤᏛࢥ࣮ࢫࡢ≉Ⰽ㸪⚄኱⤒ႠᕤᏛࢥ࣮ࢫ࢞࢖
ࢲࣥࢫ㈨ᩱ(PPT)㸪2011.4

㗰⟶㒊ᮦࡢ⡆᫆࡞⑂ປᦆയホ౯᪉ἲ኱⇃ Ṋྖ㸨   Ᏻ஭ ඵ⣖㸨㸨

Simple Method for Evaluating Fatigue damage of Pipe Members
Takeshi OHKUMA㸨㸯㸬ࡣࡌࡵ࡟

Hachinori YASUI㸨㸨㡯┠ձ࡟ࡘ࠸࡚ࡣ㸪⥅ᡭࡢᙳ㡪ࢆ↓どࡋ㸪➃㒊ࣆࣥ࡜

㏻ಙ㕲ሪ㸪↮✺ࡢᨭᣢ㕲ሪ࠾ࡼࡧ㏦㟁㕲ሪ➼ࡢࢺࣛࢫࡋ࡚㒊ᮦࡢᅛ᭷᣺ືᩘ࠾ࡼࡧ᣺ື࣮ࣔࢻࢆホ౯ࡉࢀࡿሙ

㕲ሪ࡟࠾࠸࡚ࡣ㸪タィ㢼㏿࡟ᑐࡍࡿᏳ඲ᛶࡢ௚㸪⑂ປᦆྜࡀከ࠸㸬ࡲࡓ㸪↷ᰝ㒊఩ࡶ㒊ᮦ୰ኸ࡜ࡋ㸪⥅ᡭࡢᏳ඲യ࡟ᑐࡍࡿᏳ඲ᛶࡶ㔜せ࡞せ௳࡛࠶ࡿ㸬ࡋ࠿ࡋ࡞ࡀࡽ㸪ᛶࡢ᳨ウࡀ↓どࡉࢀࡿሙྜࡀከ࠸㸬ࡋ࠿ࡋ࡞ࡀࡽ㸪⥅ᡭ⌧≧ᚋ⪅࡟ࡘ࠸࡚ࡣ୎ᑀ࠿ࡘ⡆᫆࡞᳨ウ᪉ἲࡀ☜❧ࡉࢀࡢᙳ㡪࡟ࡼࡗ࡚ᅛ᭷᣺ືᩘࡸᅛ᭷᣺ື࣮ࣔࢻࡀ୧➃ࣆ࡚ࣥ࠸ࡿ࡜ࡣゝ࠸㞴ࡃ㸪タィ⪅࡟࠾࠸࡚ࡶࡇࡢၥ㢟࡬ࡢ㛵ࡢሙྜ࡜␗࡞ࡿࡇ࡜㸪ࡉࡽ࡟ࡣ㸪⥅ᡭࡢᏳ඲ᛶࡶ㔜せ࡞ᚰࡀప࠸ࡢࡀᐇ᝟࡛࠶ࡿ㸬↷ᰝ㡯┠࡜࡞ࡿࡇ࡜ࡀ⪃࠼ࡽࢀࡿ㸬ᮏሗ࡛ࡣ㸪㏻ಙ㕲ሪ⑂ປᦆയࡢせᅉ࡜ࡋ࡚ࡣ㸪ᆅ㟈ࡸ㢼࡟ࡼࡿ㕲ሪ඲యࡢ➼࡟ከࡃ᥇⏝ࡉࢀ࡚࠸ࡿCT࡟ࡼࡿ⟶㏻ࡋ⥅ᡭࡢFEM ゎᛂ⟅࡟క࠺ࡶࡢ㸪ಶᮦࡢ㢼᪉ྥࡢ᣺ື࡟క࠺ࡶࡢ㸪ಶᮦᯒ⤖ᯝ࡟ᇶ࡙࠸࡚㸪⥅ᡭࡢᙳ㡪ࢆ⪃៖ࡋࡓ㒊ᮦࡢ᣺ື≉ࡢ㢼┤஺᪉ྥࡢ᣺ື㸪࠸ࢃࡺࡿ ບ᣺࡟ࡼࡿࡶࡢࡀ⪃࠼ᛶࡢ⡆᫆࡞ホ౯ἲ(1),(2)ࢆ♧ࡍ㸬ࡽࢀࡿ㸬≉࡟㸪ᩳᮦ㸪Ỉᖹᮦ࠾ࡼࡧỈᖹࣈ࣮ࣞࢫ㸪ࡉࡽ㡯┠ղ࡟ࡘ࠸࡚ࡣ㸪⌧≧㸪୍⯡ㄽ࡜ࡋ࡚⟬ᐃἲࢆᥦ♧࡟ࡣᛂຊᮦࢆ⿵๛ࡍࡿ⿵๛ᮦࡣ㸪ẚ㍑ⓗ᭤ࡆ๛ᛶࡀప࠸

ࡍࡿࡇ࡜ࡣᅔ㞴࡛࠶ࡿࡓࡵ㸪㡯┠ձ࡛⏝࠸ࡿゎᯒࣔࢹࣝࡓࡵ㸪タィ㢼㏿௨ୗ࡛ࡢ ບ᣺ࡢⓎ⏕ࡶ⪃࠼ࡽࢀࡿ㸬ࡲࡢ୰࠿ࡽ 1 ౛ࢆྲྀࡾୖࡆ㸪࣍ࢵࢺࢫ࣏ࢵࢺᛂຊࡢ⟬ᐃ஦ࡓ㸪኱ᆺࡢ㕲ሪ࡟࠾࠸࡚ࡣ㸪ࡇࢀࡽࡢ㒊ᮦ࡟✀ࠎࡢ⥅ᡭ౛ࢆ♧ࡍ㸬ࢆᣢࡘ㗰⟶㒊ᮦࡀ⏝࠸ࡽࢀࡿሙྜࡀከ࠸㸬㡯┠ճ࡟ࡘ࠸࡚ࡣ㸪ᗄࡘ࠿ࡢ᪉ἲࡀᥦ᱌(3),(4),(5)ࡉࢀ࡚࠸

ᮏሗࡣ㸪㢼࡟ࡼࡿಶᮦ᣺ືࢆ㉳ᅉ࡜ࡍࡿ㗰⟶㒊ᮦࡢ⑂ࡿࡀ㸪㏆ᖺ࡛ࡣ㸪ࡑࡢᭀ㢼ࡢⓎ⏕せᅉࢆྎ㢼࡜㠀ྎ㢼࡟ປᦆയ࡟╔┠ࡋ㸪ࡑࡢ⡆᫆࡞ホ౯ἲ࡟ࡘ࠸࡚ሗ࿌ࡍࡿࡶ༊ศࡋ࡚ホ౯ࡍࡿ᪉ἲࡀࡋࡤࡋࡤ⏝࠸ࡽࢀ࡚࠸ࡿ(6)㸬ᭀࡢ࡛࠶ࡿ㸬㢼࡟ࡘ࠸࡚ࡣ㸪➹⪅➼ࡀ๓ሗ࡟࠾࠸࡚♧ࡋࡓⲴ㔜ᣦ㔪(7)㢼࡟ࡼࡿಶᮦ᣺ືࢆ㉳ᅉ࡜ࡍࡿ⑂ປᦆയࢆホ౯ࡍࡿሙ࠿ࡽᭀ㢼ࡢ⣼✚స⏝᫬㛫ࢆ⡆᫆࡟ホ౯ࡍࡿ᪉ἲ(8)ࢆ⏝࠸ྜ࡟ࡣ㸪ḟࡢࡼ࠺࡞㡯┠ࡀ᫂ࡽ࠿࡟࡞ࡗ࡚࠸ࡿᚲせࡀ࠶ࡿࡇ࡜࡜ࡋ㸪ᮏሗ࡛ࡣヲ⣽࡟ࡘ࠸࡚ࡣゐࢀ࡞࠸㸬ᭀ㢼௨ࡿ㸬እ࡟ࡘ࠸࡚ࡣ㸪㏆㞄ࡢẼ㇟ᐁ⨫ࡢほ ࢹ࣮ࢱࢆ WeibullձĂ ⥅ᡭࢆ⪃៖ࡋࡓ㒊ᮦࡢ᣺ື≉ᛶࡢ⟬ᐃἲศᕸ࡟ᙜ࡚ࡣࡵ㸪ࡑࡢ⤖ᯝ࠿ࡽ⟬ᐃࡍࡿ᪉ἲࢆ⟬ᐃ஦౛ղĂ ࣍ࢵࢺࢫ࣏ࢵࢺᛂຊࡢ⟬ᐃἲ࡟࠾࠸࡚♧ࡍ㸬ճĂ ↷ᰝᮇ㛫࡟࠾ࡅࡿ㢼㏿ࡢ⣼✚స⏝᫬㛫ࡢ⟬ᐃἲ㡯┠մ࡟ࡘ࠸࡚ࡣ㸪ᩥ⊩(7),(9),(10),(11)➼ࢆཧ⪃࡟㸪㡯┠ձ㸪մĂ 㢼Ⲵ㔜࠾ࡼࡧᛂ⟅್ࡢ⟬ᐃἲղࡢ⤖ᯝࢆ⪃៖ࡋ࡚㢼᪉ྥ࠾ࡼࡧ㢼┤஺᪉ྥࡢⲴ㔜㸪ຍյĂ ⑂ປ᭤⥺࠾ࡼࡧ⑂ປᦆയᗘࡢ⟬ᐃἲ࠼࡚㸪࣍ࢵࢺࢫ࣏ࢵࢺᛂຊࡢ⟬ᐃἲࢆ♧ࡍ㸬ᮏሗ࡛ࡣ㸪ࡇࢀࡽࡢ 5 ࡘࡢ㡯┠ࢆ㡰ḟྲྀࡾୖࡆ࡚ࡑࢀ

㡯┠յ࡟ࡘ࠸࡚ࡣ㸪ᩥ⊩(12)࡟‽ࡌ࡚⟬ᐃ᪉ἲࢆ♧ࡍ㸬ࡒࢀࡢ⟬ᐃἲࢆ♧ࡋ㸪᭱ᚋ࡟ලయⓗ࡞ホ౯஦౛ࢆ♧ࡍ㸬㸰㸬⥅ᡭࢆ⪃៖ࡋࡓ㒊ᮦࡢ᣺ືᛶ≧* ྡ㄃ᩍᤵ ᕤᏛ◊✲ᡤᐈဨᩍᤵ
* Professor Emeritus** (ᰴ)Ἠ๰ᘓ࢚ࣥࢪࢽ࢔ࣜࣥࢢ 㒔ᕷ⎔ቃᢏ⾡◊✲ᡤ** Izumi Sohken Engineering Co., Ltd.

➹⪅➼ࡣ㸪㒊ᮦ࠾ࡼࡧ⥅ᡭࡢ᭷㝈せ⣲ࣔࢹࣝ࡟ࡼࡿᅛ
᭷್ゎᯒࢆ⾜࠸㸪ࡑࡢ⤖ᯝ࡟ᇶ࡙࠸࡚ᅛ᭷᣺ືᩘ࠾ࡼࡧ

㗰⟶㒊ᮦࡢ⡆᫆࡞⑂ປᦆയホ౯᪉ἲᅛ᭷᣺ື࣮ࣔࢻࢆ⡆᫆࡟ホ౯ࡍࡿ᪉ἲࢆᥦ᱌ࡋ࡚࠸ࡿ

࠿ࡽ୰ኸഃࡢ 5t ༊㛫࡛ࡣ㗰⟶ᯈཌ t ࡜୍⮴ࡉࡏ㸪ྠᵝ࡟(1),(2)㸬ᮏሗ࡛ࡣ㸪ࡑࡢᴫせࢆ♧ࡍ㸬l w ༊㛫( l w 㸸๭㎸ࡳ⁐᥋༊㛫ࡢ㛗ࡉ㸪ᅗ 2-1 ཧ↷)࡛ࡣ➼ ᭷㝈せ⣲ἲ࡟ࡼࡿᅛ᭷್ゎᯒᯒ⤖ᯝ࠿ࡽ㒊ᮦ㛗ࡢ 1/20 ௨ୗ࡛࠶ࢀࡤ༑ศ࡞⢭ᗘࡀᚓ  ᭷㝈せ⣲ࣔࢹࣝࡽࢀࡿࡇ࡜ࢆ☜ㄆࡋ㸪⣙ 100mm ࡜ࡋࡓ㸬ẚศ๭(10 せ⣲)㸪୰ኸ㒊࡛ࡣ㸪㗰⟶ࡢࡳࡢணഛᅛ᭷್ゎCT ࡢせ⣲㛗ࡉࡣࡑࢀࡒࢀࡢᯈཌ( t w , t f )࡜ྠ⛬ᗘ࡜᳨ウᑐ㇟ࡣ⾲ 2-1 ࠾ࡼࡧᅗ 2-1 ࡟♧ࡍࡼ࠺࡞ 366 ✀㢮ࡢ㗰⟶㒊ᮦ࡜ࡋࡓ㸬ࡇࡇ࡛ࡢ㒊ᮦ㛗 l ࡣ࣎ࣝࢺ㔜ᚰ㛫㊥ࡋࡓ㸬㞳࡜ࡍࡿ㸬᳨ウ㛗ࡉࡢୗ㝈್ l min ࡣ୧➃ࣆࣥ(13)࡜ࡋ࡚Ⲵ

㉁㔞ࡣᐦᗘ࡜ࡋ࡚୚࠼㸪CT ࣇࣛࣥࢪࡢ࣎ࣝࢺᏍࡢእ

(7)㔜ᣦ㔪 ࡟࠾ࡅࡿุᐃᘧࡼࡾᑟ࠿ࢀࡿୗᘧࡼࡾ⟬ᐃࡋࡓ㸬࿘⠇Ⅼ(ྛ 1 ᮏ࡟௜ 8 ⠇Ⅼ)࡟࠾࠸࡚୪㐍ኚ఩ࢆ㸪㒊ᮦ୰᳨ウ㢼㏿ U H ࡢୖ㝈್(90.7m/s)ࡣ㸪Ⲵ㔜ᣦ㔪(7)ࡢ෌⌧ᮇኸ࡛ࡣᑐ⛠᮲௳࡜ࡋ࡚㍈᪉ྥኚ఩࡜඲ᅇ㌿ゅࢆᣊ᮰ࡋࡓ㸬㛫 500 ᖺࡢ㢼㏿࡛᭱ࡶ㧗࠸್(=58m/s)㸪ᆅ⾲㠃⢒ᗘ༊ศe1ࢆ II㸪ᆅୖ࠿ࡽࡢ㧗ࡉࢆ 200m ࡜ࡋ࡚ᐃࡵࡓ㸬᳨ウ㛗ࡉ

p

p

p

e1 e2

lw
๭㎸䜏⁐᥋༊㛫ࡢୖ㝈್ lmax ࡣ㸪୧➃ࣆࣥ࡜ࡋࡓ⣽㛗ẚࡢୖ㝈ࡀᴫࡡn-䃥dg

200 ࡜࡞ࡿࡼ࠺࡟ 10m ࡜ࡋࡓ㸬ᅉࡳ࡟㸪ࡇࡇ࡛ࡢ᳨ウ㒊

CT-H×B×tw×tfᮦ㛗ࡣ㸪ࡏࢇ᩿ኚᙧࢆ↓どࡋ࡚࠸ࡿ Bernoulli-Euler ࡢ᭤ࡆᱱබᘧࡼࡾᚓࡽࢀࡿ᭤ࡆ᣺ືゎ(13)ࡢ㐺⏝⠊ᅖෆ࡛࠶ࡿ㸬
lmin

­§
° S
max ®¨°¨© 2¯

12

EI 0.83 D ·¸
UA U H St ¸¹½°,15 D ¾
°
¿

䃥-D×t

lg

(2.1)

l 㻔 䝪䝹䝖㔜ᚰ㛫 㻕ᅗ  ⟶㏻ࡋ࢞ࢭࢵࢺࣉ࣮ࣞࢺࡢᙧ≧ᑍἲࡇࡇ࡟㸪 U 㸪 E 㸪 D 㸪 A ࠾ࡼࡧ I ࡣ㸪ࡑࢀࡒࢀ㒊ᮦࡢᐦᗘ㸪ࣖࣥࢢ⋡㸪㗰⟶እᚄ㸪᩿㠃✚㸪᩿㠃 2 ḟ࣮࣓ࣔࣥࢺ㸪 St ࡣࢫࢺ࣮ࣟࣁࣝᩘ࡛ 0.2 ࡜ࡋ࡚࠸ࡿ㸬ࡳ๭㎸ゎᯒࣔࢹࣝࡢ୍౛ࢆᅗ 2-2 ࡟♧ࡍ㸬

㛫
༊
⁐᥋

࢞ࢭ

ࢺࣉ
ࢵ

࣮ࢺ
ࣞ

࢙࢘ࣈ
ࣇࣛࣥࢪ

lg

ᮏ◊✲࡛ࡣ㸪MSC.MARC ࡢ 4 ⠇Ⅼཌ⫗ࢩ࢙ࣝせ⣲ࢆ

l/2
l’=

࠺࡞ࡶࡢ࡛࠶ࡿ㸬

lp

Z

⟶
㗰

๭㎸⁐᥋༊㛫࡛ࡢ㍈᪉ྥࡢせ⣲㛗ࡉࡣ㸪➃㒊࠿ࡽ 5t

YX( t 㸸㗰⟶ᯈཌ㸪ᅗ 2-1 ཧ↷)ࡢ⠊ᅖ࡛ࡣ㗰⟶ᯈཌ࡜୍⮴ࡉ

ᚰ

⥅ᡭ

lw

⏝࠸㸪ᯈཌ᪉ྥࡣ 5 ᒙ࡜ࡋࡓ㸬せ⣲ศ๭つ๎ࡣ௨ୗࡢࡼ

࣎
ࣝࢺ
㔜

CL

ࡏ㸪ࡑࢀࡽࡢෆഃ࡟ࡘ࠸࡚ࡣ CT ࣇࣛࣥࢪᯈཌ t f ࡜ྠ⛬ᗘ࡜ࡋࡓ㸬㗰⟶ࡢ෇࿘᪉ྥࡢせ⣲㛗ࡉࡣ㸪㗰⟶ࡢᯈཌ t ࡜ᅗ  ゎᯒࣔࢹࣝࡢ஦౛ &7B ᴫࡡ୍⮴(12)ࡉࡏࡓ㸬㗰⟶㍈᪉ྥࡢせ⣲㛗ࡉࡣ㸪⥅ᡭ➃㒊⾲  ゎᯒࣔࢹ୍ࣝぴ

CTᙧ㗰
(mm)

㗰⟶
(mm)

ྡ⛠䈜

䝪䝹䝖
ᮏᩘ

䝪䝹䝖Ꮝᚄ䞉䝢䝑䝏䞉䝀䞊䝆➼
(mm)

㛗䛥
l (m)

D

t

H

B

tw

tf

n

d

g

p

e1

e2

lw
(mm)

䏓l

l min

l max

165-CTn _l

165.2

4.5

100

200

8

12

4,6,8

26

120

70

50

20

300

0.5

2.0

10.0

139-CTn _l

139.8

4.0

87.5

175

7.5

11

4,6,8

24

105

60

45

20

280

0.5

2.0

10.0

114-CTn _l

114.3

3.5

87.5

175

7.5

11

4,6,8

24

105

60

40

20

160

0.5

1.0

10.0

101-CTn _l

101.6

3.2

75

150

7

10

4,6,8

24

90

60

40

20

140

0.5

1.0

10.0

089-CTn _l

89.1

3.2

75

150

7

10

4,6,8

24

90

60

40

20

100

0.5

1.0

10.0

076-CTn _l

76.3

3.2

75

150

7

10

4,6,8

24

90

60

40

20

100

0.5

1.0

10.0

䈜 ྡ⛠୰䛾 n 䛿䝪䝹䝖ᮏᩘ䠈l 䛿㒊ᮦ䛾㛗䛥䜢♧䛧䠈2.0m䛾ሙྜ䛻䛿020䛸⾲グ⚄ዉᕝ኱ᏛᕤᏛ◊✲ᡤᡤሗ ➨  ྕ  ᙉ < ㍈᪉ྥࡢᅛ᭷᣺ືᩘ࡜᣺ື࣮ࣔࢻ

ࣈࡢ㍈᪉ྥኚ఩࣮ࣔࢻ್ศᕸࢆ♧ࡍ㸬࡞࠾㸪ྠᅗࡣ㒊ᮦ

ᙉ(Y)㍈᪉ྥࡢᅛ᭷୍ḟ᣺ືᩘ࠾ࡼࡧ᣺ື࣮ࣔࢻ࡟ࡘ

୰ኸ࡟࠾ࡅࡿᙅ(Z)㍈᪉ྥኚ఩࣮ࣔࢻ್ࡀ୍⮴ࡍࡿࡼ࠺࠸࡚ FEM ゎᯒ⤖ᯝ࡜ Bernoulli-Euler ࡢ᭤ࡆᱱබᘧࡼࡾᑟ
࠿ࢀࡿ୍ᵝ࡞㒊ᮦࡢ᭤ࡆ᣺ືゎ(13)(௨㝆㸪⌮ㄽゎ࡜࿧ࡪ)࡟つ‽໬ࡋ࡚࠸ࡿ㸬ྠᅗ࠿ࡽ᫂ࡽ࠿࡞ࡼ࠺࡟㸪ᨭᣢ࣎ࣝࢺᮏᩘࡀᑡ࡞࠸⛬㸪CT ࡢ࢙࢘ࣈࡢ࣮ࣔࢻ್ࡀ኱ࡁࡃ㸪࣎ࣝࢺ㔜ᚰࢆ୰ᚰ࡟

ࢆẚ㍑ࡋ࡚ᅗ 2-3 ࡟♧ࡍ㸬ྠᅗ࡟♧ࡍࡼ࠺࡟ᙉ(Y)㍈᪉ྥࡢᅛ᭷᣺ືᩘ࠾ࡼࡧ᣺

཯᫬ィᅇࡾ࡟ᅇ㌿ࡋࡓࡼ࠺࡞ኚ఩࣮ࣔࢻ࡜࡞ࡗ࡚࠸ࡿ㸬ື࣮ࣔࢻࡣ㸪㒊ᮦࡀኚ᩿㠃࡛࠶ࡿࡇ࡜࡟ࡼࡗ࡚᣺ື࣮ࣔ

࢙࢘ࣈࡶᣊ᮰ࡉࢀࡓᅛᐃᨭᣢ࡜ẚ㍑ࡋ࡚⪃࠼ࡿ࡜㸪࣎ࣝࢻࡀ᭤ᢡࡍࡿⅬࢆ㝖ࡅࡤ㸪୧➃ᅛᐃ࡜ࡋࡓሙྜ࡜Ⰻࡃᑐ

ࢺᮏᩘࡀᑡ࡞࠸࡯࡝ᅛᐃᗘࡀᑠࡉࡃ㸪CT ࡢ࢙࢘ࣈࡀ᭷

ᛂࡍࡿ㸬FEM ࡟ࡼࡿᅛ᭷᣺ືᩘ࡞ࡽࡧ࡟᣺ື࣮ࣔࢻࡀࡸ

ຠ࡟ᶵ⬟ࡋ࡚࠸࡞࠸࡜ぢࡿࡇ࡜ࡀ࡛ࡁࡿ㸬ࡸ◳ࡵ࡟࡞ࡗ࡚࠸ࡿࡢࡣ㸪⥅ᡭࡢ㛗ࡉࡀ᭷㝈࡛࠶ࡿࡓࡵ㸪㻲㻱㻹䛻䜘䜛ᅛ᭷᣺ືᩘ(Hz)1000

ᐇ㉁ⓗ࡞㒊ᮦ㛗ࡀ▷ࡃ࡞ࡿࡓࡵ࡛࠶ࡿ㸬௨ୖࡢ⤖ᯝࡣ㸪ᖹ㗰㸪U Ꮠ⥅ᡭ࠾ࡼࡧ⁁ᙧ⥅ᡭࡢᙉ㍈᪉ྥࡸ༑Ꮠ⥅ᡭ࡟࠾࠸࡚ࡶྠᵝ࡞ഴྥࢆ♧ࡍ࡜⪃࠼ࡽࢀࡿ㸬㻲㻱㻹䛻䜘䜛ᅛ᭷᣺ືᩘ(Hz)

1000
100
୧➃ᅛᐃ

୧➃ᅛᐃ

10
୧➃䝢䞁

1
1
10
100
1000
ᅛᐃ䛾ሙྜ䛾ᅛ᭷᣺ືᩘ(Hz)10a)ᅛ᭷୍ḟ᣺ືᩘ
୧➃䝢䞁

1

1
1
10
100
1000
ᅛᐃ䛾ሙྜ䛾ᅛ᭷᣺ືᩘ(Hz)

୧➃䝢䞁

0.8

䃛(x)

a)ᅛ᭷୍ḟ᣺ືᩘ
1
୧➃䝢䞁

0.4

䕿㻌㻌㻌165-CT8_020
䕧 165-CT8_100

0

0.1

0.2 0.3x/l

0.4 0.5b)᣺ື࣮ࣔࢻ

0.2
0

0.4

0

୧➃ᅛᐃ

0.6

0.6 ୧➃ᅛᐃ

0.2

0.8

䃛(x)

100

䕿㻌㻌㻌165-CT8_020
䕧 165-CT8_100

0

0.1

0.2 0.3x/lᅗ  ᙅ = ㍈᪉ྥࡢᅛ᭷᣺ືᩘ࡜᣺ື࣮ࣔࢻ

0.4 0.5b)᣺ື࣮ࣔࢻ
0.1
0ᅗ  ᙉ < ㍈᪉ྥࡢᅛ᭷᣺ືᩘ࡜᣺ື࣮ࣔࢻ

-0.1
-0.2

  ᙅ = ㍈᪉ྥࡢᅛ᭷᣺ືᩘ࡜᣺ື࣮ࣔࢻ

-0.3

ᙉ㍈࡜ྠᵝ࡟ᙅ㍈ࡢᅛ᭷᣺ືᩘ࡜ᅛ᭷᣺ື࣮ࣔࢻࢆ

-0.4

FEM ゎᯒ⤖ᯝ࡜⌮ㄽゎࢆẚ㍑ࡋ࡚ᅗ 2-4 ࡟♧ࡍ㸬ྠᅗ࡟♧ࡍࡼ࠺࡟㸪ᙅ㍈᪉ྥࡢᅛ᭷᣺ືᩘ࠾ࡼࡧ᣺ື䝪䝹䝖㔜ᚰa) 076-CT4_030

-0.5
-0.6

࣮ࣔࢻࡣ㸪
༙ᅛᐃ≧ែࡢ᣺ືᩘ࠾ࡼࡧ᣺ື࣮ࣔࢻ࡜࡞ࡾ㸪㒊ᮦ㛗ࡀ㛗࠸⛬㸪ᅛᐃᗘࡀ㧗࠸㸬  ᙅ = ㍈᪉ྥ࣮ࣔࢻ᫬ࡢᨭᣢ㒊㏆ഐࡢኚ఩ศᕸ

Z
Y X

䝪䝹䝖㔜ᚰ
b) 076-CT6_030

ᅗ 2-5 ࡟㒊ᮦ㛗ࡀ 3m ࡜➼ࡋࡃ㸪ᨭᣢ࣎ࣝࢺᮏᩘࡀࡑᅗ  ᨭᣢ࣎ࣝࢺᮏᩘࡢ㐪࠸࡟ࡼࡿ &7 ࢙࢘ࣈࡢ

ࢀࡒࢀ 4 ᮏ࡜ 6 ᮏࡢሙྜ࡟ࡘ࠸࡚ᨭᣢ㒊㏆ഐࡢ CT ࢙࢘ᨭᣢ㒊㏆ഐ࡟࠾ࡅࡿ㍈ ; ᪉ྥኚ఩࣮ࣔࢻࡢᕪ␗

㗰⟶㒊ᮦࡢ⡆᫆࡞⑂ປᦆയホ౯᪉ἲ᣺ື≉ᛶࡢ⡆᫆ホ౯ἲ  ୍ᵝ࡞㒊ᮦࡢᅛ᭷᣺ືᩘ࡜᣺ື࣮ࣔࢻ

Bernoulli-Euler ࡢ᭤ࡆᱱබᘧࡼࡾᑟ࠿ࢀࡿ୍ᵝ࡞㒊ᮦ(13)ࡢ᭤ࡆ᣺ືࡢ୍⯡ゎࡣ㸪ḟࡢࡼ࠺࡟⾲ࢃࡉࢀࡿ 㸬
Pc x

A1c cos Jx  A2c sin Jx
 A3c cosh Jx  A4c sinh Jx

Z

ck l

ck

Jl

2

A2

1  0.52654 k f  0.26441k 2f  0.1199 k 3f

(2.10)A3

 A1(2.11)

A4

1.206 k f  0.95116 k 2f  0.36565 k 3f

(2.12)(2.2)
ࡲࡓ㸪ᅗ 2-7 ࡟♧ࡍࡼ࠺࡟㸪᣺ື࣮ࣔࢻࢆ♧ࡍ(2.6)ᘧ

EI UA

(2.3)

ࡣ㸪୧➃ࣆࣥࡢኚ఩࣮ࣔࢻ P pin x ࡜୧➃ᅛᐃࡢኚ఩ࣔ
࣮ࢻ P fix x ࡢ୍ḟ⤖ྜ࡟ࡼࡗ࡚ୗᘧࡢࡼ࠺࡟ࡶ㏆ఝ࡛
ࡁࡿ㸬

(2.4)

ࡇࡇ࡟㸪 P c x 㸪 Z ࠾ࡼࡧ J ࡣ᣺ື࣮ࣔࢻ㸪ᅛ᭷෇᣺ືᩘ࠾ࡼࡧἼືఏ᧛ᐃᩘ㸪 Ac1 㹼 Ac4 ࡣ✚ศᐃᩘ࡛࠶ࡿ㸬ࡲࡓ㸪c k ࡣᮦ➃ࡢᅛᐃᗘ࡟ࡼࡗ࡚ᐃࡲࡿಀᩘ࡛㸪1 ḟ᣺ື࡟㝈ᐃࡍࡿ࡜㸪୧➃ࣆࣥ㸪୧➃ᅛᐃࡢሙྜ࡟ࡣ㸪ࡑࢀࡒࢀ㸪 c kP x

1  k f P pin x  k f P fix x

P pin xP fix xS 㸪 c k | 4.73004 ࡛࠶ࡿ㸬ࡇࡇ࡛㸪୧➃㒊

(2.13)

sin Sx l(2.14)

B1 cos J f x  cosh J f x
 B2 sin J f x  sinh J f x(2.15)

ࡢᅛᐃᗘࢆ⾲ࢃࡍಀᩘ k f (ᅛᐃ:1㸪ࣆࣥ:0)ࢆᑟධࡍࡿ࡜㸪

B1 | 0.629665(2.16)

ᅗ 2-6 ࡟♧ࡍࡼ࠺࡟ c k ࡣ(2.5)ᘧ࡛㏆ఝ࡛ࡁࡿ㸬

B2 | 0.618647(2.17)

J f l | 4.73004(2.18)ck^

S  4.73004  S 1  1  k f 1.1145
5`

0.78956(2.5)

14.73004

4
⌮ㄽゎ

3

0.2

0.4

k

0.6

ᘧ(2.13) (kf=0.5)

0.6
0.4

⌮ㄽゎ(kf=0.5)

0.2

S

0

୧➃ࣆࣥ(kf=0)

0.8

䃛㻓(x)

c

k

ᘧ(2.5)

0.8୧➃ᅛᐃ(kf=1)

0
0

1

0.25
x/l

f

ᅗ  k f ࡜ c k ࡢ㛵ಀ0.5

ᅗ  ᣺ື࣮ࣔࢻࡢẚ㍑

ࡇࡇ࡛㸪㒊ᮦ୰ኸࡢኚ఩∦᣺ᖜࢆ 1 ࡜ࡍࡿ࡜㸪ࡑࡢ᣺ື࣮ࣔࢻ㸪᭤ࡆ࣮࣓ࣔࣥࢺ M x ࠾ࡼࡧ༢఩㛗ࡉᙜࡓࡾࡢ㟼ⓗศᕸⲴ㔜 w x ࡣ௨ୗࡢࡼ࠺࡟⾲ࢃࡉࢀࡿ㸬P x

 EIJ 2 A1 cos Jx  A2 sin Jx
 A3 cosh Jx  A4 sinh Jx

wx

EIJ  P x4୍ᵝ࡞㒊ᮦࡢ୰ኸ࡟㞟୰Ⲵ㔜 P ࡀస⏝ࡍࡿሙྜ㸪㒊ᮦ୰ኸኚ఩࡟ᑐࡍࡿᮦ➃࠿ࡽ 1/4 ࡢ఩⨨࡟࠾ࡅࡿኚ఩ࡢẚ

Pc x Pc l 2(2.6)
A1 cos Jx  A2 sin Jx  A3 cosh Jx  A4 sinh Jx

M x  ࢙࢘ࣈࡢᣊ᮰ᗘ

ࡣ㸪୧➃ࣆࣥࡢሙྜ 11/16㸪୧➃ᅛᐃࡢሙྜ࡟ࡣ 1/2 ࡜࡞
ࡿ㸬

(2.7)
(2.8)

l’ (=l/2)lmlgࡇࡇ࡟㸪 A1 㹼 A4 ࡣ㒊ᮦ୰ኸࡢኚ఩∦᣺ᖜࡀ 1 ࡢሙྜࡢ✚ศᐃᩘ࡛㸪௨ୗࡢࡼ࠺࡟㏆ఝ࡛ࡁࡿ㸬(㈨ᩱᮎ⿵㊊ 1
ཧ↷)
A1

q

g

Ige
ug

uq

g

l’ /2

1.2834 k f  1.0817 k 2f  0.43021k 3f

(2.9)

lb

p

Ip
q

P
l’ /2

Ige 䠖 㻳㻼㻸 䛾᭷ຠ᩿㠃஧ḟ䝰䞊䝯䞁䝖
Ip 䠖 㗰⟶䛾᩿㠃஧ḟ䝰䞊䝯䞁䝖ᅗ  ➃㒊ᅛᐃᗘࢆ⡆᫆ホ౯ࡍࡿࡓࡵࡢࣔࢹࣝup
C
L⚄ዉᕝ኱ᏛᕤᏛ◊✲ᡤᡤሗ ➨  ྕ୍᪉㸪ᅗ 2-8 ࡟♧ࡍࡼ࠺࡟㸪๭㎸⁐᥋༊㛫ࡢ๛ᛶቑຍ

1.5

ศࢆ↓どࡋ࡚㒊ᮦࢆ࢞ࢭࢵࢺ࡜㗰⟶࡛ᵓᡂࡉࢀࡓኚ᩿㠃࡜ぢ࡞ࡍ࡜㸪㒊ᮦ୰ኸⅬ p ࡢኚ఩ u p ࠾ࡼࡧⅬ q ࡢኚ఩Oup

12 I p I ge I p l g  I ge l m

uq

Tg

0
0

(2.20)

10

20

30
lm/lg

50

60

ᅗ  ࢙࢘ࣈ✺ฟ㒊ࡢ᭷ຠ⋡ D e (2.21)  ᣺ືᩘ࠾ࡼࡧ᣺ື࣮ࣔࢻࡢ⡆᫆ホ౯ἲࡲࡎ㸪➃㒊࣎ࣝࢺࡢᮏᩘ n ࡟ᇶ࡙࠸࡚ᘧ(2.26)ࡼࡾ࢙࢘
ࣈࡢ᭷ຠ⋡ D e ࢆồࡵ㸪ࡇࢀ࡟ᇶ࡙࠸࡚࢞ࢭࢵࢺࣉ࣮ࣞ

El g  lm l g lm P
2 I p l g  I ge l m E(2.22)

ࢺࡢ᩿㠃 2 ḟ࣮࣓ࣔࣥࢺࢆ⟬ᐃࡍࡿ㸬D e min(n 8 , 1.0)
nt4

(2.26)⥆࠸࡚㸪ᘧ(2.19)㹼(2.23)ࢆ⏝࠸࡚㒊ᮦ୰ኸኚ఩ u p ࡜➃
(2.23)

㒊࠿ࡽ 1/4 ࡢⅬ q ࡢኚ఩ u q ࢆồࡵ㸪ᘧ(2.25)ࢆ᭩ࡁ᥮࠼
࡚ᚓࡽࢀࡿୗᘧࡼࡾᅛᐃᗘ k f ࢆ⟬ᐃࡍࡿ㸬

11  16uq u p 3

kfࡇࡇ࡟㸪CT ࡢ࢙࢘ࣈ✺ฟ㒊ࡢ᭷ຠ⋡ D e ࢆୗᘧࡢࡼ࠺
࡟࢙࢘ࣈ✺ฟ㧗ࡉ H  t f ( H 㸸࢙࢘ࣈ㧗ࡉ㸪 t f 㸸ࣇࣛࡓࡔࡋ㸪 k f ! 1 ࡢሙྜࡣ k fࣥࢪཌ)࡟ᑐࡍࡿ᭷ຠ㧗ࡉ he ࡢẚ࡜ࡋ࡚ᐃ⩏ࡋ㸪 I ge ࡣ

kfࡇࢀ࡟ᑐᛂࡍࡿ࢞ࢭࢵࢺࣉ࣮ࣞࢺࡢ᭷ຠ᩿㠃஧ḟ࣮࣓ࣔ

(2.27)
1 㸪 k f  0 ࡢሙྜࡣ0 ࡜ࡍࡿ㸬

ࡉࡽ࡟㸪ᅛᐃᗘ k f ࢆᘧ(2.5)࡟௦ධࡋ࡚ c k ࢆ㸪c k ࢆᘧ(2.3)࡟௦ධࡋ࡚ᅛ᭷୍ḟ෇᣺ືᩘ Z ࢆ㸪ࡉࡽ࡟ k f ࢆᘧࣥࢺ࡜ࡍࡿ㸬
he40



I p l g2  4 I ge l g l m  3I ge l m2 l g2 P
12 I ge I p l g  I ge l m‫ۍ‬n=8‫ڧ‬n=6‫ۑ‬n=4(2.19)­° § 2l 3 3l 2 · I ½°
gebb
®1  ¨¨ 3  2 ¸¸
¾u g
lg ¹ I p °°̄ © l g¿­° § l 2 2l · I ½°
ge
 lb ®1  ¨ b2  b ¸¾T g
l g ¸¹ I p °°̄ ¨© l g
¿

ug

0.75

0.5

P
E

2 4
I 2p l g4  I gelm  I p I ge l g lm 4l g2  6l g lm  4lm2

O

1

De

u q ࡣࡑࢀࡒࢀ௨ୗࡢࡼ࠺࡟⟬ᐃ࡛ࡁࡿ㸬De H  t f(2.24)

FEM ゎᯒ⤖ᯝ࡜⌮ㄽゎ࠿ࡽ௨ୗࡢࡼ࠺࡞ᡭ㡰࡛࢙࢘ࣈࡢ᭷ຠ⋡ D e ࢆ㏫⟬ࡍࡿ㸬(2.6)㸪(2.9)㹼(2.12)࠶ࡿ࠸ࡣ(2.13)࡟௦ධࡋ࡚᣺ື࣮ࣔࢻ

P x ࢆᚓࡿࡇ࡜ࡀ࡛ࡁࡿ㸬௨ୖࡢᡭ㡰࡛⟬ᐃࡋࡓ⡆᫆ἲ࡜ FEM ࡟ࡼࡿᅛᐃᗘ k f 㸪ᅛ᭷୍ḟ᣺ືᩘ f1 ࢆ඲ࣔࢹࣝ࡟ࡘ࠸࡚㸪᣺ື࣮ࣔࢻ

ࡲࡎ㸪FEM ゎᯒ⤖ᯝࡢ᣺ື࣮ࣔࢻ࡟ᘧ(2.13)ࢆᙜ࡚ࡣ

P x ࡟ࡘ࠸࡚ࡣ௦⾲஦౛ࢆᅗ 2-10 ࡟ẚ㍑ࡋ࡚♧ࡍ㸬ྠࡵ࡚ᅛᐃᗘ k f ࢆ㸪k f ࢆୗᘧ࡟௦ධࡋ࡚ᚓࡽࢀࡿኚ఩ࡢ

ᅗ࠿ࡽ㸪⡆᫆ἲ࡟ࡼࡿᅛᐃᗘ k f ࠾ࡼࡧᅛ᭷୍ḟ᣺ືᩘẚ u q u p ࢆ⟬ᐃࡍࡿ㸬

f1 ࡣᴫࡡ 10%ࡢㄗᕪࡢ⠊ᅖ࡛᥎ᐃ࡛ࡁ㸪᣺ື࣮ࣔࢻ

uq u p11
1
1 k f  k f
16
2(2.25)

ࡇࡢኚ఩ࡢẚ u q u p ࢆ‶㊊ࡍࡿ I ge ࢆᘧ(2.19)㹼(2.23)
ࡼࡾ཰ᩡィ⟬࡟ࡼࡗ࡚⟬ᐃࡋ㸪࢙࢘ࣈࡢ᭷ຠ⋡ D e ࢆồࡵࡿ㸬௨ୖࡢᡭ㡰࡟ࡼࡾ㏫⟬ࡋࡓ࢙࢘ࣈࡢ᭷ຠ⋡ D e ࢆᅗ
2-9 ࡟♧ࡍ㸬ྠᅗ࡟♧ࡍࡼ࠺࡟㸪࣎ࣝࢺࡢᮏᩘ n 4 ࡢሙྜ࡟ࡣᴫࡡ D e

0.5 㸪 n 6 ࡢሙྜ࡟ࡣᴫࡡ D e

n 8 ࡢሙྜ࡟ࡣᴫࡡ D e

0.75 㸪

1 ࡀୗ㝈್࡛࠶ࡿ㸬 D e ࡀ 1ࢆ㉸࠼ࡿࡢࡣ๭㎸⁐᥋༊㛫ࡢ๛ᛶࡢ๭ቑࢆ⪃៖ࡋ࡚࠸࡞
࠸ࡇ࡜ࡀ᭱ࡶ኱ࡁ࡞せᅉ࡛࠶ࡿ㸬P x ࡶᴫࡡⰋ࠸ᑐᛂࢆ♧ࡍ㸬ᮏ᪉ἲࡀ᭷ຠ࡛࠶ࡿࡇ࡜ࡀゎࡿ㸬㗰⟶㒊ᮦࡢ⡆᫆࡞⑂ປᦆയホ౯᪉ἲ1kf(⡆᫆ἲ)FEM ゎᯒ࡛ࡣ 3 ḟඖࡢࢩ࢙ࣝせ⣲ࢆ⏝࠸㸪⁐᥋ࣅ࣮ࢻࡣ

+10%

0.8



ࣔࢹࣝ໬ࡋ࡚࠸࡞࠸㸬ࡲࡓ㸪ྠᣦ㔪࡛ࡣ㸪ࡇࡢࡼ࠺࡞ࢩ࢙ࣝせ⣲ࢆ⏝࠸ࡓሙྜࡢ࣍ࢵࢺࢫ࣏ࢵࢺᛂຊࡢ⟬ᐃ౛࡜

0.6
0.4

-10%

0.2

‫ۍ‬n=8‫ڧ‬n=6‫ۑ‬n=400

0.2 0.4 0.6 0.8
kf(FEM)a) ᅛᐃᗘࡢẚ㍑

ࡋ࡚㸪ᅗ 3-1 ࡟♧ࡍࡼ࠺࡞ᅜ㝿⯪⣭༠఍㐃ྜࡢ஦౛ࢆྲྀ
ࡾୖࡆ࡚࠸ࡿ㸬ᮏሗ࡛ࡣࡇࡢ᪉ἲࢆ᥇⏝ࡍࡿ㸬࣍ࢵࢺࢫ࣏ࢵࢺᛂຊ

1

H

1 G
2 G

f1(Hz, ⡆᫆ἲ)

1000
100

0.5t
ᅗ  ࣍ࢵࢺࢫ࣏ࢵࢺᛂຊࡢồࡵ᪉ࡢ౛  

1
1

䃛(x)

0.8

1.5t

+10%

10

1

-10%

ࡢ✚ศⅬᛂຊᗘ V j ,o ࡜᭱ෆ⦕ᒙࡢ Gauss ࡢ✚ศⅬᛂຊᗘ

076-CT4_010 FEM

V j ,i ࡼࡾ㸪⾲㠃ࡢᛂຊᗘ ࢆୗᘧ࡛⟬ᐃࡍࡿ㸬

076-CT4_010⡆᫆ἲຊᗘ࡛࡞ࡅࢀࡤ࡞ࡽ࡞࠸ࡢ࡛㸪ᯈཌࡢ᭱እ⦕ᒙࡢ GausskV j

k V j ,o  k V j ,o  k V j ,i2n L  2(3.1)

ࡇࡇ࡟㸪 k ࡣせ⣲ࡢ␒ྕ㸪 n L ࡣせ⣲ࡢᯈཌ᪉ྥࡢᒙ
ᩘ㸪 j ࡣ Gauss ࡢ✚ศⅬࡢ␒ྕ࡛㸪ࡇࡇ࡛ࡣ I㸪II㸪III㸪

0.4
076-CT4_100 ⡆᫆ἲ

0.2

076-CT4_100 FEM

0

0.1 0.2 0.3 0.4 0.5x/lc) ᣺ື࣮ࣔࢻࡢẚ㍑(n=4)

1

165-CT8_020 FEM

0.8

䃛(x)

ලయⓗ࡟ࡣ㸪ࡲࡎ㸪࣍ࢵࢺࢫ࣏ࢵࢺᛂຊࡣᯈ⾲㠃ࡢᛂ

10
100
1000
f1(Hz, FEM)b) ᅛ᭷᣺ືᩘࡢẚ㍑

0.6

0

t

165-CT8_020⡆᫆ἲIV ࡜⾲ࢃࡍ㸬ᅗ 3-1 ࡟࠾࠸࡚ࡢ‫ࡢۍ‬ᛂຊᗘࡀ㔜ᚰ఩⨨࡛ࡢᛂຊᗘ
k V G ࡛࠶ࡿࡢ࡛㸪㗰⟶ࡢ෇࿘᪉ྥࡢ඲࡚ࡢせ⣲㛗ࡉࡀ㗰⟶ᯈཌ࡜ᴫࡡ୍⮴ࡍࢀࡤ㸪࣍ࢵࢺࢫ࣏ࢵࢺᛂຊᗘ

V H , A ࡣ௨ୗࡢࡼ࠺࡟⟬ᐃ࡛ࡁࡿ㸬V H ,A
kVG

0.6
0.4

1 V G  1V G  2 V G

2IV¦ kV j 4

(3.2)
(3.3)

j I

165-CT8_100 ⡆᫆ἲ

0.2
0165-CT8_100 FEM

00.1

0.2 0.3 0.4 0.5x/ld) ᣺ື࣮ࣔࢻࡢẚ㍑(n=8)ᅗ  ⡆᫆ἲ࡜ )(0 ࡢẚ㍑㸱㸬࣍ࢵࢺࢫ࣏ࢵࢺᛂຊࡢ⟬ᐃἲ⟬ᐃἲ

࣍ࢵࢺࢫ࣏ࢵࢺᛂຊ⟬ᐃ౛

076_CT4_015( D =76.3mm㸪 n =4㸪 l =1.5m㸪⾲ 2-1 ཧ↷)ࢆ஦౛࡟㸪ᙉ㍈᪉ྥ᣺ື᫬࠾ࡼࡧᙅ㍈᪉ྥ᣺ື᫬࡟࠾
࠸࡚㒊ᮦ୰ኸ࡛ࡢኚ఩∦᣺ᖜࡀ 1m ࡜࡞ࡿሙྜ࡟ࡘ࠸᳨࡚ウࡍࡿ㸬  ᙉ㍈᪉ྥ᣺ື᫬

⟬ᐃ⤖ᯝࢆᅗ 3-2 ࡟♧ࡍ㸬࡞࠾㸪ᅗ୰ࡢ๭㎸ࡳ⁐᥋༊⑂ປタィᣦ㔪(12)࡛ࡣ㸪ࠕFEM ࡟ࡼࡗ࡚࣍ࢵࢺࢫ࣏ࢵࢺ

㛫ࡼࡾ㒊ᮦ୰ኸഃࡢᛂຊᗘࡣ㗰⟶ࡢ⦕ᛂຊ࡟┦ᙜࡍࡿ㸬ᛂຊࢆ⟬ᐃࡍࡿሙྜ࡟ࡣ㸪ࢯࣜࢵࢻせ⣲ࢆ⏝࠸㸪⁐᥋ࣅࡲࡓ㸪 M Z P ࡣ⡆᫆ἲ࡟ࡼࡗ࡚ồࡵࡓ᭤ࡆ࣮࣓ࣔࣥࢺ

࣮ࢻࡶࣔࢹࣝ໬ࡍࡿࡇ࡜ࡀᮃࡲࡋ࠸ࠖ࡜ࡋ࡚࠸ࡿ㸬ࡋ࠿M ࢆ඲༊㛫࡟Ώࡗ࡚㗰⟶ࡢ᩿㠃ಀᩘ Z P ࡛㝖ࡋ࡚ồࡵࡋ࡞ࡀࡽ㸪ࡇࡇ࡛ᑐ㇟࡜ࡍࡿẕᮦࡀⷧ⫗ࡢ㗰⟶࡛ᮦ㍈᪉

ࡓ⦕ᛂຊ࡛࠶ࡿ㸬ྥ࡟㛗ࡃࣔࢹࣝ໬ࡋ࡞ࡅࢀࡤ࡞ࡽ࡞࠸ࡇ࡜࠿ࡽ㸪๓❶ࡢ⚄ዉᕝ኱ᏛᕤᏛ◊✲ᡤᡤሗ ➨  ྕ



5 107

࠶ࡿ㸬ࡇࢀࡣ㸪⡆᫆ἲ࡟ࡼࡿࡇࡢ᪉ྥࡢ᣺ືᩘ࠾ࡼࡧ᣺
ື࣮ࣔࢻࡀࡸࡸᰂࡽ࠿ࡵ࡟ホ౯ࡉࢀࡿࡇ࡜࡟㉳ᅉࡍࡿ㸬๭㎸ࡳ⁐᥋༊㛫ࡢ㒊ᮦ୰ኸഃ➃㒊࡛ࡢᛂຊ㞟୰ࡣ㢧ⴭ࡛㸪ࡇࡢ఩⨨࡟࠾ࡅࡿ࣍ࢵࢺࢫ࣏ࢵࢺᛂຊ

V H ,A8

4.440 u 10 kN/m ࡀ⑂ປ᳨ウ⏝ࡢᛂຊ࡛㸪ᛂຊ2

ᛂຊᗘ(kN/m2)⡆᫆ἲ࡟ࡼࡿ⦕ᛂຊᗘࡣ㸪FEM ゎᯒࡼࡾࡸࡸᑠࡉࡵ࡛

8

3 10

8

1 10

0
8
-1 10 ๭㎸ࡳ⁐᥋༊㛫
0
0.1
0.2

0.3

0.4

0.5

ᛂຊᗘ(kN/m2)

8

3 10

8

VH,A

0.5

M/ZP

-5 107
8

-1 10

VH,A

0.1

0.15

0.2

㸲㸬㢼㏿ࡢ⣼✚స⏝᫬㛫ࡢ⡆᫆ホ౯᪉ἲ➹⪅➼ࡣ㸪ᭀ㢼࡟ࡼࡿ㢼㏿ࡢ⣼✚స⏝᫬㛫ࡢ⡆᫆ホ౯

0
8

0.4

ᅗ  ᙅ㍈᣺ື᫬ࡢᛂຊᗘศᕸࡢ⟬ᐃ౛

8

-1 10

0.3

x/l
b)๭㎸ࡳ⁐᥋༊㛫ࡢ㒊ᮦ୰ኸഃ➃㒊㏆ഐ

2 108
1 10

0.2

8

a) ඲య

4 10

0.1

0

-1.5 10

x/l
5 108

0

5 107

M/ZP

8

VH,A

x/l
a) ඲య

VH,A

2 108

8

-1 10

8

ᛂຊᗘ(kN/m2)

ᛂຊᗘ(kN/m2)

4 10

M/ZP

-5 107-1.5 10㞟୰ಀᩘࡣ 10 ⛬ᗘ࡜኱ࡁ࡞್࡛࠶ࡿ㸬5 108

๭㎸ࡳ⁐᥋༊㛫0᪉ἲࢆ๓ሗ࡟࠾࠸࡚ᥦ᱌ࡋ㸪ࡑࡢጇᙜᛶࢆ♧ࡋ࡚࠸ࡿ(8)㸬

M/ZP
0.2

ࡇࡢ⡆᫆ἲ࡛⏝࠸ࡽࢀ࡚࠸ࡿ⟬ᐃᘧ࡜ࡑࡢᴫせࢆ௨ୗ࡟x/lb)๭㎸ࡳ⁐᥋༊㛫ࡢ㒊ᮦ୰ኸഃ➃㒊㏆ഐ♧ࡍ㸬ࡲࡎ㸪↷ᰝᮇ㛫 N ᖺ࡟࠾࠸࡚ i ␒┠࡟኱ࡁ࡞ᭀ㢼ࡢ᭱ᅗ  ᙉ㍈᣺ື᫬ࡢᛂຊᗘศᕸࡢ⟬ᐃ౛኱㢼㏿ U r ࡣୗᘧ࡛⟬ᐃࡍࡿ㸬

0.1

0.15

Ur

U 0 k rW

(4.1)

  ᙅ㍈᪉ྥ᣺ື᫬

k rW

0.63 OU  1 ln r  2.9OU  3.9(4.2)⟬ᐃ⤖ᯝࢆᅗ 3-3 ࡟♧ࡍ㸬OU

U 500 U 0

(4.3)

ri

N i  0.5ྠᅗ࡟♧ࡍࡼ࠺࡟㒊ᮦ୰ኸഃ࡟࠾࠸࡚ࡣ㸪⡆᫆ἲ࡟ࡼࡾồࡵࡓ⦕ᛂຊ M Z P ࡣ FEM ࡟ࡼࡿゎᯒ⤖ᯝ࡟Ⰻࡃᑐ

i1,  , mN(4.4)

ࡇࡇ࡟㸪 U 0 㸪 U500 ࠾ࡼࡧ k rW ࡣ㸪Ⲵ㔜ᣦ㔪(7)࡟࠾ࡅ

ᛂࡋ࡚࠾ࡾ㸪⡆᫆ἲ࡟ࡼࡗ࡚⟬ᐃࡉࢀࡿ᭤ࡆ࣮࣓ࣔࣥࢺ

ࡿᇶᮏ㢼㏿㸪෌⌧ᮇ㛫 500 ᖺࡢ㢼㏿࠾ࡼࡧ෌⌧ᮇ㛫᥮⟬ࡣࡇࡢ༊㛫࡛ࡣጇᙜ࡟ホ౯ࡉࢀ࡚࠸ࡿࡇ࡜ࡀゎࡿ㸬ಀᩘ࡛㸪ri ࠾ࡼࡧ m ࡣ i ␒┠࡟኱ࡁ࡞ᭀ㢼ࡢ෌⌧ᮇ㛫࠾୍᪉㸪㒊ᮦ➃㒊࠿ࡽ๭㎸ࡳ⁐᥋༊㛫ࡢ⣙ 2 ಸࡢ⠊ᅖ࡛ࡣ㸪࣍ࢵࢺࢫ࣏ࢵࢺᛂຊ࡜⦕ᛂຊ M Z P ࡢᕪ␗ࡣ኱ࡁ

ࡼࡧᖺᖹᆒࡢᭀ㢼ᩘ࡛࠶ࡿ㸬ᅉࡳ࡟㸪ᘧ(4.1)㹼ᘧ(4.3)ࡣ
Ⲵ㔜ᣦ㔪(7)ࢆ㌿⏝ࡋࡓࡶࡢ࡛࠶ࡿ㸬ࡃ㸪≉࡟㸪๭㎸ࡳ⁐᥋༊㛫ࡢ㒊ᮦ୰ኸഃ➃㒊࡛ࡢᛂຊ㞟ࡑࢀࡒࢀࡢᭀ㢼ࡢ᭱኱㢼㏿࡟ᑐࡍࡿ㢼㏿ࡢẚࡢ 24 ᫬

1.140 u 10 8 kN/m2 ࡛㸪㛫࡟Ώࡿ᫬㛫ኚ໬ࡣ㸪ᘧ(4.5)ࡲࡓࡣᘧ(4.6)࡛⟬ᐃࡍࡿ㸬୰ࡣ㢧ⴭ࡛࠶ࡿ㸬ᅉࡳ࡟ V H , Aᛂຊ㞟୰ಀᩘࡣ 7 ⛬ᗘ࡜኱ࡁ࡞್࡛࠶ࡿ㸬࡞࠾㸪ࡇࡢࣔࢹ࡛ࣝ࣍ࢵࢺࢫ࣏ࢵࢺᛂຊࡀ᭱኱࡜࡞ࡿ
ࡢࡣ㸪๭㎸ࡳ⁐᥋༊㛫ࡢ㒊ᮦ୰ኸഃ➃㒊࡟࠾࠸࡚࡛࠶ࡿ
ࡀ㸪㒊ᮦ࡟ࡼࡗ࡚ࡣ㏫ഃ➃㒊ࡢሙྜࡶ࠶ࡿࡢ࡛ὀពࡀᚲ
せ࡛࠶ࡿ㸬

rU t

1  C 1t exp C 2 t 0.70

(4.5)

rU t

1  C 3 t 2.2 exp C 4 t 1.2(4.6)

C 1 min 0.532  0.0192T N ,0.217(4.7)

C 2 min 0.444  0.0210T N ,0.375(4.8)

C 3 min 0.0565  0.00201T N ,0.0199(4.9)

㗰⟶㒊ᮦࡢ⡆᫆࡞⑂ປᦆയホ౯᪉ἲC 4 min 0.196  0.00870 T N ,0.135

(4.10)

ࡢᖹᆒ㏿ᗘᅽ㸪ᖹᆒ㢼㏿㸪஘ࢀᙉࡉ㸪ኚື㢼㏿ࡢࣃ࣮࣡ࡇࡇ࡟㸪t ࡣ᫬㛫(༢఩:hr)࡛ 0㹼24 ࡢ್㸪T N ࡣᑐ㇟ᆅࢫ࣌ࢡࢺࣝᐦᗘ㸪ྠᶆ‽೫ᕪ࠾ࡼࡧ஘ࢀࡢࢫࢣ࣮࡛ࣝ㸪

Ⅼࡢ⦋ᗘ(༢఩㸸r)࡛࠶ࡿ㸬࡞࠾㸪ᘧ(4.5)ࡣᘧ(4.6)࡟ẚ㍑

f ࡣ࿘Ἴᩘ࡛࠶ࡿ㸬ࡲࡓ㸪 k rW ࡣ(4.2)ᘧ࡟♧ࡍ෌⌧ᮇࡋ࡚Ᏻ඲ഃࡢ್ࢆ୚࠼ࡿ㸬㛫᥮⟬ಀᩘ㸪 K D ࡣ㢼ྥಀᩘ࡛ࡇࡇ࡛ࡣ 1 ࡜ࡍࡿ㸬ࡉࡽ௨ୖ࡟ࡼࡗ࡚⟬ᐃࡉࢀࡿ↷ᰝᮇ㛫ࡢᭀ㢼ࡢ㢼㏿ࢆ㢼㏿࡟㸪 E g ࠾ࡼࡧ E gI ࡣᑠᆅᙧ࡟ࡼࡿᖹᆒ㢼㏿࠾ࡼࡧ஘ࢀ

ẖ࡟ᩚ⌮ࡍࡿࡇ࡜࡛㸪ᭀ㢼࡟ࡼࡿ㢼㏿ࡢ⣼✚స⏝᫬㛫ࡣᙉࡉࡢ⿵ṇಀᩘ㸪 D 㸪 Z G ࠾ࡼࡧ Z b ࡣ㢼㏿ࡢ㖄┤ศᕸ⟬ᐃ࡛ࡁࡿ㸬

ࢆᐃࡵࡿࣃ࣓࣮ࣛࢱ࡛࠶ࡾ㸪ヲ⣽ࡣⲴ㔜ᣦ㔪(7)ࢆཧ↷ࡉࢀࡓ࠸㸬୍⯡໬ኚ఩ࡢศᩓ V q2 ࡣୗᘧ࡛⾲ࢃࡉࢀࡿ㸬㸳㸬㢼Ⲵ㔜࠾ࡼࡧᛂ⟅್ࡢ⟬ᐃἲ 㢼᪉ྥࡢ㢼Ⲵ㔜࡜ᛂ⟅್ࡇࡇ࡛ࡣ㸪Ᏻ඲ഃࡢホ౯࡜ࡋ࡚㸪㒊ᮦࡢྛ㒊࡟స⏝ࡍ

V q2ࡿኚື㢼ຊࡀ㒊ᮦ୰ኸ㧗ࡉ Z ࡛ࡢኚື㢼㏿࡟ẚ౛ࡍࡿ2§ q C Dl ·4¨¨ Z ~D ¸¸ I Z2) 2(5.12)© KD ¹ª S Z, f
S f D Su Z , f D º
df 
u «³0f u 2
»
2
49 D
V uZ
V uZ
¬
¼

ࡶࡢ࡜ࡍࡿ㸬ࡍ࡞ࢃࡕ㸪㒊ᮦ࡟స⏝ࡍࡿ㢼ᅽຊࡣ✵㛫ⓗ࡟᏶඲┦㛵࡜ࡍࡿ㸬ࡇࡢሙྜ㸪ᖹᆒ㢼ຊಀᩘࢆ C D 㸪㢼
᪉ྥࡢ 1 ḟ᣺ື࣮ࣔࢻࢆ P D x ࡜ࡍࡿ࡜㸪㢼᪉ྥࡢ୍⯡໬㢼ຊ S F f ࡣ௨ୗࡢࡼ࠺࡟⾲ࢃࡉࢀࡿ㸬ᅉࡳ࡟㸪ᖹᆒ㢼ຊಀᩘࡣⲴ㔜ᣦ㔪(7)࡟‽ࡎࡿ࡜㸪 CD 1.2 ࡜࡛ࡁࡿ㸬S Z, f4 q Z C D Dl 2 I Z2 u 2
)2
SF f
(5.1)

V uZ

1 1

)2

³0 ³0 P D x1c P D x 2c dx1c dx c2

(5.2)

xc

xl

(5.3)

~
KD

qZ

2

(5.4)

UZ

U 0 K D E Z k rW

(5.5)

EZ

Er E g(5.6)

Er­°1.7 Z Z G D®
°̄1.7 Z b Z G D

IZI rZ E gI

I rZ­°0.1 Z Z G D 0.05®
°̄0.1 Z b Z G D 0.05

Su Z , f

Zb  Z d ZG
Z d Zb2
4V uZ
LZ U Z^1  70.8 fL U `Z

LZ­100 Z 30
®
¯100

0.5

Z

2 56

30m  Z d Z G
Z d 30m(5.13)

᣺ື࡟ᑐࡍࡿᅛ᭷᣺ືᩘ㸪ῶ⾶ᐃᩘ㸪୍⯡໬๛ᛶ࠾ࡼࡧ
୍⯡໬㉁㔞࡛࠶ࡿ㸬ࡉࡽ࡟㸪
f Su Z , f
2
V uZ

³0

df

1

(5.14)

࡞ࡢ࡛㸪f D Su Z , f D
F2(5.15)

V uZ

RD

S
49 D

F

(5.16)

࡞ࡿಀᩘࢆᑟධࡍࢀࡤ㸪୍⯡໬ኚ఩ࡢᶆ‽೫ᕪ V q ࡣ௨

(5.7)

(5.8)

Zb  Z d ZG
Z d Zb~2Sf D 2 M D~~ࡇࡇ࡟㸪 f D 㸪 9 D 㸪 K D ࠾ࡼࡧ M D ࡣ㢼᪉ྥࡢ 1 ḟBD

U aU Z2º
1 ªf
S
f DSF f D »~ 2 «³0 S F f df 
4
9
KD ¬
D
¼

ୗࡢࡼ࠺࡟⾲ࢃࡉࢀࡿ㸬Vq§ q C Dl ·2¨ Z ~ D ¸ I Z ) 1  RD
¨ K
¸
D
©
¹

(5.17)

ࡲࡓ㸪ኚືኚ఩ࡢ᭱኱್ࡢ㒊ᮦ㍈᪉ྥศᕸ y D ,max x(5.9)ࡣ㸪ࣆ࣮ࢡࣇ࢓ࢡࢱ࣮ g D ࢆ⪃៖ࡋ࡚ḟࡢࡼ࠺࡟⾲ࢃࡉࢀࡿ㸬

(5.10)

y D,max x

g DV q P D x

gD

2 ln 600Q D 

QD

f D RD 1  RD

(5.11)

ࡇࡇ࡟㸪 U a 㸪U 0 㸪 qZ 㸪U Z 㸪 I Z 㸪 Su Z , f 㸪V uZ
࠾ࡼࡧ L Z ࡣ㸪✵Ẽᐦᗘ㸪ᇶᮏ㢼㏿㸪㒊ᮦ୰ኸ㧗ࡉ Z ࡛(5.18)

0.577
2 ln 600Q D(5.19)(5.20)

࡞࠾㸪Q D ࡣ㢼᪉ྥࡢࣞ࣋ࣝࢡࣟࢵࢩࣥࢢᩘ࡛࠶ࡿ㸬⚄ዉᕝ኱ᏛᕤᏛ◊✲ᡤᡤሗ ➨  ྕࡇࡇ࡛㸪⡆༢ࡢࡓࡵᖹᆒ㢼㏿࡟ᑐࡍࡿᖹᆒኚ఩ࡶ 1 ḟ኱ࡢኚື࣍ࢵࢺࢫ࣏ࢵࢺᛂຊ V̂ HD ࡣ௨ୗࡢࡼ࠺࡟⾲ࢃ᣺ື࣮ࣔࢻ࡟ẚ౛ࡍࡿ࡜௬ᐃࡍࢀࡤ㸪୍⯡໬ᖹᆒ㢼ຊ Fࡉࢀࡿ㸬࠾ࡼࡧᖹᆒኚ఩ࡢ㍈᪉ྥศᕸ YD x ࡣ௨ୗࡢࡼ࠺࡟⾲ࢃwˆ D xq Z C D D  GD  1(5.30)(5.21)Mˆ D x

M D x  GD  1(5.31)(5.22)

Vˆ HD

ࡉࢀࡿ㸬

q Z C D Dl)

F

q Z C D Dl
)P D x
~
KD

YD x
1

³0 P D x c dx c)

(5.23)V HD  GD  1(5.32)

 㢼┤஺᪉ྥࡢ㢼Ⲵ㔜࡜ᛂ⟅್࡞࠾㸪㢼᪉ྥࡢ 1 ḟ᣺ືᩘࢆ f D ࡜ࡍࢀࡤ㸪ࡇࡢ᪉ྥ~ࡢᅛᐃᗘ k f , D ࢆ⪃៖ࡋ࡚㸪1 ḟ᣺ືࡢ୍⯡໬㉁㔞 M Dࡢ㟼ⓗศᕸⲴ㔜 w x ࡣᘧ(2.8)࡛⾲ࢃࡉࢀࡿࡇ࡜ࢆ♧ࡋ࠾ࡼࡧ ) ࡣ௨ୗࡢࡼ࠺࡟㏆ఝ࡛ࡁࡿ㸬(㈨ᩱᮎ⿵㊊ 2 ཧࡓ㸬ࡇࡢᘧ࡟ᘧ(2.3)ࢆ⪃៖ࡍࡿ࡜௨ୗࡢࡼ࠺࡟᭩ࡁ᥮࠼

↷)

ࡽࢀࡿ㸬
­1
¯2
 0.878228 1  k f , D k f , D

~
MD

)

UAl  ® 1  k f , D 2  0.396478k 2f , D`(5.24)

2 ❶࡟࠾࠸࡚㸪㒊ᮦ୰ኸࡢኚ఩∦᣺ᖜࡀ 1 ࡜࡞ࡿሙྜ

Z 2 UA  P x

wx(5.33)

ࡇࡢᘧ࡜Ⲵ㔜ᣦ㔪(7)ࡢ෇ᙧ᩿㠃ࢆࡶࡘ㒊ᮦࡢ ບ᣺࡟

0.636619 1  k f , D  0.523164 k f , D(5.25)

ࡼࡿⲴ㔜ࢆ⪃៖ࡍࡿ࡜㸪㢼┤஺᪉ྥࡢ 1 ḟ᣺ືࡢᅛ᭷᣺

ࡉࡽ࡟㸪ᖹᆒ㢼㏿࡟ᑐࡍࡿᖹᆒኚ఩ࡶ 1 ḟ᣺ື࣮ࣔࢻ

ືᩘࢆ f L 㸪᣺ື࣮ࣔࢻࢆ P L x ࡜ࡍࡿ࡜㸪 ບ᣺࡟ࡼ࡟ẚ౛ࡍࡿ࡜௬ᐃࡋ࡚࠸ࡿࡢ࡛㸪ᖹᆒ᭤ࡆ࣮࣓ࣔࣥࢺࡢ

ࡿ༢఩㛗ࡉᙜࡓࡾࡢ᭱኱㢼Ⲵ㔜 wˆ L x ࡣ௨ୗࡢࡼ࠺࡟

㍈᪉ྥศᕸ M D x ࡣ௨ୗࡢࡼ࠺࡟⾲ࢃࡉࢀࡿ㸬⾲ࢃࡉࢀࡿ㸬

q C DlM D x  EI D J D2 Z ~ D )KD
u A1, D cos J D x  A2, D sin J D x
 A3, D cosh J D x  A4, D sinh J D x

wˆ L x(5.26)

࡞࠾㸪 I D 㸪J D ࠾ࡼࡧ A1, D 㹼 A4, D ࡣ㸪㢼᪉ྥ࡟㛵ࡍ

YLࡿ᩿㠃 2 ḟ࣮࣓ࣔࣥࢺ㸪ᅛᐃᗘ k f , D ࢆ⪃៖ࡋࡓἼືఏ
᧛ᐃᩘ࠾ࡼࡧ✚ศᐃᩘ࡛࠶ࡿ㸬ࡲࡓ㸪㒊ᮦ୰ኸ࡟࠾ࡅࡿኚ఩∦᣺ᖜࡀ 1 ࡛࠶ࡿሙྜࡢ
࣍ࢵࢺࢫ࣏ࢵࢺᛂຊࡀ V H ࡜ࡋ࡚ᚓࡽࢀ࡚࠸ࡿሙྜ࡟
ࡣ㸪ᖹᆒ㢼ຊ࡟ࡼࡿ࣍ࢵࢺࢫ࣏ࢵࢺᛂຊ V HD ࡣ௨ୗࡢq Z C D Dl
) V H~KD(5.27)

1

G

D

53 G
4S9 L MU a D 2l

(5.35)(5.36)(5.37)

ࡢኚ఩㸪㒊ᮦࡢ඲㉁㔞㸪↓ḟඖඹ᣺㢼㏿㸪㉁㔞ῶ⾶ࣃࣛ

y D,max x(5.28)YD xࡉࡽ࡟㸪ࡇࡢⲴ㔜࡟ࡼࡿ᭱኱᭤ࡆ࣮࣓ࣔࣥࢺࡢศᕸˆ
M L x ࠾ࡼࡧ࣍ࢵࢺࢫ࣏ࢵࢺᛂຊ V̂ HL ࡣ௨ୗࡢࡼ࠺࡟
⾲ࢃࡉࢀࡿ㸬

Mˆ L x࡛࠶ࡾ㸪ᘧ(5.18)࠾ࡼࡧᘧ(5.22)ࢆ⪃៖ࡋ࡚௨ୗࡢࡼ࠺࡟
⾲ࢃࡉࢀࡿ㸬

GD

0.75G 1.1  0.36U r*࣓࣮ࢱ࠾ࡼࡧ㢼┤஺᪉ྥࡢ 1 ḟ᣺ືࡢῶ⾶ᐃᩘ࡛࠶ࡿ㸬࢞ࢫࢺᙳ㡪ಀᩘ G D ࡣ௨ୗࡢࡼ࠺࡟ᐃ⩏ࡉࢀࡿࡢ࡛㸪

GD

U r*

0.26U r*(5.34)

ࡇࡇ࡛㸪 YL 㸪 M 㸪 U r* 㸪 G ࠾ࡼࡧ 9 L ࡣ㸪㒊ᮦ୰ኸࡼ࠺࡟⾲ࢃࡉࢀࡿ㸬V HD

2Sf L 2 UA  YL  P L x
M
2Sf L 2
 YL  P L x
L1  2 g D I Z 1  RD

(5.29)

ࡋࡓࡀࡗ࡚㸪༢఩㛗ࡉᙜࡓࡾࡢኚື᭱኱Ⲵ㔜 wˆ D x 㸪ኚື᭱኱᭤ࡆ࣮࣓ࣔࣥࢺࡢ㍈᪉ྥศᕸ Mˆ x ࠾ࡼࡧ᭱
D

Vˆ HL

 EI L J L2YL
u A1, L cos J L x  A2, L sin J L x
 A3, L cosh J L x  A4, L sinh J L x(5.38)YL V H(5.39)

࡞࠾㸪 I L 㸪 J L ࠾ࡼࡧ A1, L 㹼 A4, L ࡣ㸪ࡇࡢ᪉ྥ࡟㛵ࡍࡿ᩿㠃 2 ḟ࣮࣓ࣔࣥࢺ㸪ᅛᐃᗘ k f , L ࢆ⪃៖ࡋࡓἼືఏ
᧛ᐃᩘ࠾ࡼࡧ✚ศᐃᩘ࡛࠶ࡿ㸬㗰⟶㒊ᮦࡢ⡆᫆࡞⑂ປᦆയホ౯᪉ἲ㸴㸬⑂ປᦆയホ౯᪉ἲ෌⌧ᮇ㛫 500 ᖺࡢ㢼㏿ U 500 (7)㸸42m/s

 ᛂ⟅᣺ᖜ࡜⧞㏉ࡋᅇᩘࡢホ౯ᆅ⾲㠃⢒ᗘ༊ศ(7)㸸III ࡢᖹᆠᆅ㢼㏿ U Zk ࡟ᑐࡍࡿ⑂ປ᳨ウ⏝ࡢ࣍ࢵࢺࢫ࣏ࢵࢺᛂຊ
᣺ᖜ 'V k ࡣ୧᣺ᖜ࡞ࡢ࡛㸪௨ୗࡢࡼ࠺࡟⟬ᐃ࡛ࡁࡿ㸬'V k

2Vˆ Hk(6.1)

ᆅୖ࠿ࡽࡢ㧗ࡉ㸸100m㒊ᮦ࣭⥅ᡭ㸸076_CT4_015(⾲ 2-1 ཧ↷)↷ᰝᮇ㛫 N 㸸100 ᖺῶ⾶ᐃᩘ㸸0.5%ࡇࡢᛂ⟅᣺ᖜࡢ⧞㏉ࡋᅇᩘࢆホ౯ࡍࡿୖ࡛㸪Ᏻ඲ഃ࡟ ᅛ᭷್ࡢホ౯௨ୗࡢࡼ࠺࡟௬ᐃࡍࡿ㸬ձĂ 㢼ྥࡣ㒊ᮦ࡟ṇᑐࡍࡿ㸬㒊ᮦ࣭⥅ᡭㅖඖ୪ࡧ࡟⡆᫆ἲ࡟ࡼࡿᅛ᭷್⟬ᐃ⤖ᯝࢆղĂ ྛ㢼㏿࡛ࡢ᭱኱ᛂ⟅ࡀᅛ᭷᣺ືᩘ࡛⣼✚స⏝᫬

⾲ 7-1 ࡟♧ࡍ㸬࡞࠾㸪⾲୰ࡢ V HS ࠾ࡼࡧ V HW ࡣ㸪ྛ᪉ྥࡢኚ఩∦᣺ᖜࡀ 1m ࡢሙྜࡢ࣍ࢵࢺࢫ࣏ࢵࢺᛂຊ࡛࠶

㛫࡟Ώࡗ࡚⧞㏉ࡉࢀࡿ㸬ࡇࢀࡽࡢ௬ᐃ࡟ࡼࡾ㸪㢼᪉ྥࡢሙྜࡢ⧞㏉ࡋᅇᩘ nkࡾ㸪ࡇࡢ㡯┠࡟ࡘ࠸࡚ࡣ FEM ࡟ࡼࡿ್࡛࠶ࡿ㸬ࡣ㸪ࡇࡢ㢼㏿ࡢ⣼✚స⏝᫬㛫 Tk ࡜㢼᪉ྥࡢᅛ᭷᣺ືᩘ

f D ࢆ⪃៖ࡋ࡚௨ୗࡢࡼ࠺࡟⟬ᐃ࡛ࡁࡿ㸬nk

Tk f D⾲  㒊ᮦ࣭⥅ᡭㅖඖ

(6.2)
㒊ᮦ

㗰ᮦ
㛗䛥

ࡲࡓ㸪㢼┤஺᪉ྥ࡟ᑐࡍࡿ෇ᙧ᩿㠃㒊ᮦࡢ ບ᣺࡟ࡘ㗰⟶Ⲵ㔜ᣦ㔪(7)࡛ࡣ㸪 ບ᣺ࡀⓎ⏕ࡍࡿୗ⏺ࡢ㢼㏿ U r min

0.2 ࠾ࡼࡧᏳ඲⋡=1.2 ࢆ⪃៖ࡋ࡚௨ୗࡢࡼ࠺࡟ᐃࡵ࡚࠸ࡿ㸬U Z t U r min 4.2 f L D | f L D 1.2 St

(6.3)

CT

ᮏሗ࡛ࡣୗᘧࡢࡼ࠺࡟㸪 ບ᣺ࡀⓎ⏕ࡍࡿ㢼㏿ᇦࡢୖ⏺ U r max ࡟ᑐࡋ࡚ࡶᏳ඲⋡ 1.2 ࢆ⪃៖ࡍࡿࡇ࡜࡜ࡍࡿ㸬U r min d U Z d U r max(6.4)

U r min4. 2 f L D(6.5)

U r max

6 .0 f L D

1 .2 f L D S t

ᵓᡂ

⥅ᡭ

(6.6)

ࡢᅛ᭷᣺ືᩘ f L ࢆ⪃៖ࡋ࡚௨ୗࡢࡼ࠺࡟⟬ᐃ࡛ࡁࡿ㸬Tr f L(6.7)
ᙉ㍈

 ⣼✚⑂ປᦆയᗘࡢホ౯᪉ἲḟ❶ィ⟬౛࡟࡚♧ࡍ㸬㸵㸬⑂ປᦆയホ౯஦౛ ⟬ᐃ᮲௳ᘓタᆅ࠾ࡼࡧᆅ⾲㠃⢒ᗘ༊ศ㸪ᇶᮏ㢼㏿ U 0 ࠾ࡼࡧ෌⌧ᮇ㛫 500 ᖺࡢ㢼㏿ U 500 㸪㒊ᮦ୰ኸ఩⨨ࡢᆅୖ࠿ࡽࡢ
㧗ࡉ Z 㸪㒊ᮦ࠾ࡼࡧ⥅ᡭ㸪↷ᰝᮇ㛫 N ࢆ௨ୗ࡜ࡋ㸪ࣞ
࣋ࣝ 2 ࡢ㢼㏿ࢆ෌⌧ᮇ㛫 500 ᖺࡢ㢼㏿࡜ࡍࡿ㸬ᘓタᆅ㸸ᮾி(໭⦋ 35.6 ᗘ)ᇶᮏ㢼㏿ U 0 (7)㸸38m/s

t

ᅛᐃᗘ
ཬ䜃
ᅛ᭷್
ᙅ㍈

2.050E+08 kN/m2
7.850 t/m3
1.5 m
0.0763 m

Ap

0.0032 m
7.349E-04 m2

Ip
H

4.918E-07 m4
0.0750 m

B

0.1500 m

twtf

0.0070 m
0.0100 m

he
I ge
n

0.0325 m
1.217E-07 m4Įepࡇࡢ㢼㏿ᇦࡢ⣼✚స⏝᫬㛫ࢆ Tr ࡜ࡍࡿ࡜㸪
㢼┤஺᪉ྥ

nr

ȡ
l
D

࠸࡚ࡣḟࡢࡼ࠺࡟⪃࠼ࡿ㸬ࢆࢫࢺ࣮ࣟࣁࣝᩘ St

E

4 ᮏ
0.500

e1

0.0600 m
0.0400 m

e2lg

0.0200 m
0.0900 m

lm
lb

0.6600 m
0.2850 m

lw
kf

0.1000 m
1.0000ck
ȦS4.73001314.55 rad./sfS

209.22 Hzı HS
u p /(P /E )4.440E+08 kN/m2
1.163E+05 /m

u g /(P /E )
ș g /(P /E )8.544E+03 /m
1.788E+05 /m2

u q /(P /E )u q /u p

6.790E+04 /m
0.5841kf
ck

0.55174.1902

ȦWfW

1031.64 rad./s
164.19 HzıHW

1.140E+08 kN/m2⚄ዉᕝ኱ᏛᕤᏛ◊✲ᡤᡤሗ ➨  ྕ 㢼㏿ࡢ⣼✚స⏝᫬㛫ࡢ⟬ᐃᘧ(4.1)㹼(4.3)࠾ࡼࡧᘧ(5.5)㹼(5.7)࡟ࡼࡾ㡰ḟ⟬ᐃ࡛ࡁࡿ㸬

ᘧ(4.4)࡟♧ࡍࡼ࠺࡟㸪↷ᰝᮇ㛫 N ᖺ࡟࠾ࡅࡿ 1 ␒┠࡟౛࠼ࡤ㸪1 ␒┠࡟኱ࡁ࡞᭱኱㢼㏿ࡣ௨ୗࡢࡼ࠺࡟⟬ᐃ࡛኱ࡁ࡞᭱኱㢼㏿ࡢ⤒㦂ⓗ෌⌧ᮇ㛫ࡣ 2 N ᖺ࡟┦ᙜࡋ㸪ᮏࡁࡿ㸬
r1 N i  0.5

౛㢟ࡢሙྜ࡟ࡣ 200 ᖺ࡜࠸࠺ࡇ࡜࡟࡞ࡿ㸬࠸ࢃࡺࡿࣞ࣋

100 1  0.5

200 ᖺ

ࣝ 2 ࡢ㢼㏿ࡀ෌⌧ᮇ㛫 500 ᖺࡢ㢼㏿࡟ᴫࡡ┦ᙜࡍࡿࠕᴟ

OU

42 38 1.105

ࡵ࡚⛥࡟Ⓨ⏕ࡍࡿᭀ㢼ࠖࡸࠕ㏻ಙ㕲ሪタィせ㡿࣭ྠゎㄝ

k rW

0.63 OU  1 ln ri  2.9OU  3.9 1.046

Ez

1.7 u Z ZG D

U ri

U 0 k rw

38 u 1.046

U Zi

U ri E Z

50.0 m/s(15)ࠖࡢ෌⌧ᮇ㛫 300 ᖺࡢ㢼㏿࡛࠶ࡿሙྜ㸪ࡇࢀࡽࡢ㢼㏿ࡣྵࡲࢀ࡞࠸ࡇ࡜࡟࡞ࡾ㸪ࡇࢀࡽࡢ㢼㏿࡟ᑐࡍࡿᏳ඲ᛶࡢ᳨ド࡜⑂ປᦆയ࡟ᑐࡍࡿᏳ඲ᛶࡢ᳨ド࡟୙ᩚྜࡀ⏕ࡌࡿࡇ࡜࡟࡞ࡿ㸬

1.7 u 100 450 0.2

1.258

39.8 m/sࡋ࠿ࡋ࡞ࡀࡽ㸪タィࡢほⅬ࠿ࡽࡳࡿ࡜ࡇࡢࡼ࠺࡞ሙྜ

⥆࠸࡚㸪ᭀ㢼ࡢ᫬㛫ኚ໬ࢆ⾲ࢃࡍᘧ࡜ࡋ࡚ᘧ(4.5)ࢆ⏝࡛࠶ࡗ࡚ࡶ㸪↷ᰝᮇ㛫࡟Ⓨ⏕ࡍࡿ඲ᭀ㢼࡟ຍ࠼࡚㸪ᑡ࡞࠸ࡿ㸬ᘓタᆅࡢ⦋ᗘ T N (=35.6r)ࡼࡾᭀ㢼ࡢ᭱኱㢼㏿࡟ࡃ࡜ࡶ 1 ࡘࡢࣞ࣋ࣝ 2 ࡢᭀ㢼࡟ࡼࡿ⣼✚⑂ປᦆയᗘ࡟ᑐ

ᑐࡍࡿ㢼㏿ẚࡣ௨ୗࡢࡼ࠺࡟⾲ࢃࡉࢀࡿ㸬඲ᭀ㢼ࡢ᭱኱ࡍࡿᏳ඲ᛶࡀᢸಖࡉࢀ࡞ࡅࢀࡤ࡞ࡽ࡞࠸㸬㢼㏿࠾ࡼࡧ᫬㛫ኚ໬ࡢ⟬ᐃ⤖ᯝࢆ⾲ 7-2 ࡟♧ࡍ㸬
C 1 min 0.532  0.0192T N ,0.217 0.152ࡑࡇ࡛㸪ࡇࡇ࡛ホ౯ࡍࡿ⣼✚స⏝᫬㛫ࡣ㸪↷ᰝᮇ㛫 N

C 2 min 0.444  0.0210T N ,0.375

ᖺ࡟Ⓨ⏕ࡍࡿୖ఩ N ಶࡢᭀ㢼࡟ຍ࠼࡚ 1 ࡘࡢࣞ࣋ࣝ 2ࡢᭀ㢼ࢆຍ࠼ࡓ⣼✚స⏝᫬㛫࡜ࡍࡿ㸬rU t

1  0.152t exp 0.304t 0.70

UZ t

U Zi rU t  ᭀ㢼ࡢ᭱኱㢼㏿ࡢ⟬ᐃ࡜᫬㛫ኚ໬0.304↷ᰝᮇ㛫ᖺ୰ࡢᆅୖ㧗ࡉ Z ࡟࠾ࡅࡿ i ␒┠࡟኱ࡁ࡞ᭀ㢼ࡢ᭱኱㢼㏿ U Zi ࡣ㸪ᘧ(4.4)࠾ࡼࡧⲴ㔜ᣦ㔪(7)࡟ࡼࡿ
⾲  ᭀ㢼ࡢ᭱኱㢼㏿࡜᫬㛫ኚ໬iri(year)

k rW

t (h)

U ri
(m/s)

U Zi
(m/s)

0

0.167

0.333

0.500

0.667

䞉䞉䞉

23.833

U Z (m/s)

U 500

500.0

1.105

42.0

52.9

52.9

49.7

48.2

47.2

46.3

࣭࣭࣭

14.9

1

200.0

1.046

39.8

50.0

50.0

47.0

45.7

44.6

43.8

࣭࣭࣭

14.1

2

66.7

0.973

37.0

46.5

46.5

43.8

42.5

41.5

40.8

࣭࣭࣭

13.1

3
4

40.0

0.939

35.7

44.9
43.9

42.2
41.2

41.0
40.0

40.1
39.1

39.4
38.4

࣭࣭࣭
࣭࣭࣭

12.7
12.4
12.1

28.6

0.917

34.8

44.9
43.9

0.900
0.887

34.2
33.7

43.1

43.1

40.5

39.3

38.4

37.7

࣭࣭࣭

6

22.2
18.2

42.4

42.4

39.9

38.7

37.9

37.2

࣭࣭࣭

12.0

7

15.4

0.876

33.3

41.9

41.9

39.4

38.2

37.4

36.7

࣭࣭࣭

11.8

5

8

13.3

0.867

32.9

41.4

41.4

39.0

37.8

37.0

36.3

࣭࣭࣭

11.7

9
10

11.8

0.858

32.6

10.5

0.851

32.3

41.0
40.7

41.0
40.7

38.6
38.3

37.5
37.1

36.6
36.3

36.0
35.6

࣭࣭࣭
࣭࣭࣭

11.6
11.5

11

0.844
0.838

32.1
31.9

40.4

40.4

38.0

36.8

36.0

35.4

࣭࣭࣭

11.4

12

9.5
8.7

40.1

40.1

37.7

36.6

35.8

35.1

࣭࣭࣭

11.3

13

8.0

0.833

31.6

䠖

䠖

䠖

39.8
㸸

37.4
㸸

36.3
㸸

35.5
㸸

34.9
㸸

࣭࣭࣭

䠖
100

39.8
㸸

㸸

11.2
㸸

1.0

0.695

26.4

33.2

33.2

31.2

30.3

29.7

29.1

࣭࣭࣭

9.4

  ᭀ㢼ࡢ⣼✚స⏝᫬㛫ࡣ㸪 U Zk  0.5 m/s ௨ୖࡢ㢼㏿ࡢಶᩘ࠿ࡽ U Zk  0.5 m/s㢼᪉ྥࡢ⑂ປᦆയホ౯࡛ࡣ㸪㢼㏿ࡢࣅࣥࢆ 1m/s ࡜ࡋ࡚௨ୖࡢ㢼㏿ࡢಶᩘࢆᘬ࠸࡚ 10 ಸࡍࢀࡤ㸪㢼㏿ U Zk ࡟ᑐᭀ㢼ࡢ⣼✚స⏝᫬㛫ࢆ⟬ᐃࡍࡿ㸬㢼㏿ࡢ୰ኸ್ࢆ U Zk ࡜ࡍࡿ⣼✚స⏝᫬㛫ࡀศ༢఩ࡢ್࡜ࡋ࡚ᚓࡽࢀࡿࡇ࡜࡟࡞

ࡍࡿ࡜㸪⣼✚స⏝᫬㛫 TStorm,k ࡣ U Zk  0.5 m/s ௨ୖ࠿ࡘࡿ㸬ᭀ㢼ࡢ⣼✚స⏝᫬㛫ࡢ⟬ᐃ⤖ᯝࢆ⾲ 7-3 ࡟♧ࡍ㸬

U Zk  0.5 m/s ᮍ‶ࡢ㢼㏿࡜࡞ࡿ᫬㛫ࡢྜィ࡜࡞ࡿ㸬౛࠼ࡤ⾲ 7-2 ࡢࡼ࠺࡟ᭀ㢼ࡢ᫬㛫ኚ໬ࡀᚓࡽࢀ࡚࠸ࡿሙྜ࡟

㢼┤஺᪉ྥ࡟ࡘ࠸࡚ࡣ㸪 ບ᣺ࡢⓎ⏕ࡍࡿ㢼㏿㡿ᇦ࡜ࡋ࡚⾲ 7- 4 ࡢࡼ࠺࡟⟬ᐃ࡛ࡁࡿ㸬㗰⟶㒊ᮦࡢ⡆᫆࡞⑂ປᦆയホ౯᪉ἲ⾲  ᭀ㢼ࡢ⣼✚స⏝᫬㛫 㢼᪉ྥ⏝ 
U Zk (m/s)⣼✚స⏝᫬㛫 T Storm, k (min)䝺䝧䝹2ᭀ㢼௨እ䛾ᭀ㢼
0
720
7,390
0
1,050
7,870
0
1,240
8,280
10
1,720
8,860

53
52
51
50

35
34
33
32

17
16
15
14

䝺䝧䝹2ᭀ㢼
10
40
0
40
0
40
10
40

49
48
47
46
45
44
43
42

31
30
29
28
27
26
25
24

13
12
11
10
9
8
7
6

0
10
10
20
10
20
20
30

40
40
50
40
50
50
50
50

0
0
0
0
0
0
0
0

0
0
20
10
20
30
30
60

2,190
2,770
3,280
3,890
4,420
4,870
5,210
5,530

41
40
39
38
37
36

23
22
21
20
19
18

5
4
3
2
1
0

30
30
30
40
30
40

60
50
60
70
60
70

0
0
0
0
0
0

90
120
180
240
380
520

5,800
6,020
6,260
6,470
6,780
7,090

70
80
50
0

10
0
0
20

ྜィ
760
1,090
1,280
1,760

7,460
7,950
8,330
8,860

9,250
9,710
9,290
6,130
200
0
0
0

0
10
30
30
30
50
50
90

2,230
2,810
3,330
3,930
4,470
4,920
5,260
5,580

9,250
9,710
9,290
6,130
200
0
0
0

0
0
0
0
0
0

120
150
210
280
410
560

5,860
6,070
6,320
6,540
6,840
7,160

0
0
0
0
0
0
145,440

ྜィ

T Storm⾲  ᭀ㢼ࡢ⣼✚స⏝᫬㛫 㢼┤஺᪉ྥ⏝ 
fL(Hz)

U r min(m/s)

U r m ax(m/s)

T Storm, r
(min)

ᙉ㍈

209.22

66.5

95.8

0

ᙅ㍈

164.19

52.2

75.2

10

  ᭀ㢼௨እࡢ⣼✚స⏝᫬㛫

k

km

C

§ Z GIV · IV § H · III¨¨¸¸ ¨¨¸¸ C m© H m ¹ © Z GIII ¹ᮾி⟶༊Ẽ㇟ྎ(ᆅ⾲㠃⢒ᗘ༊ศ IV㸪ほ 㧗ࡉ H m 㸻
35.1m)࡟࠾ࡅࡿ 2008 ᖺ 1 ᭶㹼2012 ᖺ 12 ᭶ࡲ࡛ࡢẖ 10

ศࡢほ ࢹ࣮ࢱ(16)࠿ࡽ௨ୗࡢᡭ㡰࡟ࡼࡾᭀ㢼௨እࡢ㢼㏿ࡢస⏝᫬㛫ࢆ⟬ᐃࡍࡿ㸬࡞࠾㸪ほ ࢹ࣮ࢱ࡟ࡣ๓㏙ࡢᭀ㢼࡟┦ᙜࡍࡿ㢼㏿ࡶྵࡲࢀ࡚࠸ࡿࡀ㸪ࡑࡢᙳ㡪ࡣᑠࡉ࠸࡜⪃࠼ࡽࢀࡿࡓࡵ㸪ほ ࢹ࣮ࢱ࠿ࡽᭀ㢼ࡢࢹ࣮ࢱࢆྲྀࡾ

(7.3)
D

D

1.556C m(7.4)௨ୖ࡟ࡼࡗ࡚ồࡵࡓ Weibull ಀᩘࡣ௨ୗࡢࡼ࠺࡞್࡛
࠶ࡿ㸬
k 1.94 㸪 C

(7.5)

3.73

↷ᰝᮇ㛫 N (=100 ᖺ)㸪ᭀ㢼ࡢ⣼✚స⏝᫬㛫࡟࠾࠸࡚⟬㝖ࡃ➼ࡢ≉ู࡞ฎ⌮ࡣ⾜ࢃ࡞࠸㸬ࡲࡎ㸪ほ ࢹ࣮ࢱࢆࡑࡢࡲࡲ⏝࠸࡚ Weibull ㏆ఝࢆ⾜ᐃ ࡋ ࡓ 㢼 ᪉ ྥ ⏝ ࡢ ⣼ ✚ స ⏝ ᫬ 㛫 ࡢ ྜ ィ TStorm࠺㸬ࡍ࡞ࢃࡕ㸪ୗᘧࢆほ ࢹ࣮ࢱ࡟ᑐࡋ࡚㏆ఝࡋ㸪ᮾி

(=145,440min)ࢆ⪃៖ࡋ࡚㸪ྛ㢼㏿࡟ᑐࡍࡿᭀ㢼௨እࡢ⣼⟶༊Ẽ㇟ྎ࡟࠾ࡅࡿ Weibull ಀᩘ C m ࠾ࡼࡧ k m ࢆ⟬ᐃ✚స⏝᫬㛫ࢆ㢼᪉ྥ࡟ᑐࡋ࡚௨ୗࡢࡼ࠺࡟⟬ᐃࡍࡿ㸬

ࡍࡿ㸬

Fm U

­ § U ·°¸¸
1  exp® ¨¨°̄ © C m ¹

°
¾
°¿

(7.1)

⥆࠸࡚㸪ᘓタᆅ࠾ࡼࡧẼ㇟ᐁ⨫ࡢᆅ⾲㠃⢒ᗘ༊ศࢆ⪃៖ࡋ࡚㸪Weibull ศᕸ࡟ᇶ࡙࠸ࡓᘓタᆅࡢ᳨ウ㧗ࡉ Z ࡟࠾ࡅࡿ㠀㉸㐣☜⋡ࢆୗᘧ࡛⟬ᐃࡍࡿ㸬

FDaily U

T Daily, k

T Dailyu FDaily U k  0.5  FDaily U k  0.5

TDaily60 u 24 u 365.2422 u N  TStormkm ½­° § U · k ½°
1  exp® ¨ ¸ ¾°̄ © C ¹ °¿

^

`

(7.6)
(7.7)

ࡲࡓ㸪
㢼┤஺᪉ྥ࡟ᑐࡋ࡚ࡣ㸪௨ୗࡢࡼ࠺࡟⟬ᐃࡍࡿ㸬
TDaily, r

TDailyu FDaily U r max  FDaily U r min

^

`

(7.8)

ᭀ㢼௨እ࡟ࡼࡿ⣼✚స⏝᫬㛫ࡢ⟬ᐃ⤖ᯝࢆ⾲ 7-5 ࠾ࡼ(7.2)

ࡧ⾲ 7-6 ࡟♧ࡍ㸬⚄ዉᕝ኱ᏛᕤᏛ◊✲ᡤᡤሗ ➨  ྕ⾲  ᭀ㢼௨እࡢ⣼✚స⏝᫬㛫 㢼᪉ྥ⏝ 
U Zk
(m/s)

ᭀ㢼௨እ䛾
㢼䛾㢖ᗘ

ᭀ㢼௨እ䛻䜘䜛
⣼✚స⏝᫬㛫
T Daily,k (min)

U Zk
(m/s)

ᭀ㢼௨እ䛾
㢼䛾㢖ᗘ

ᭀ㢼௨እ䛻䜘䜛
⣼✚స⏝᫬㛫
T Daily,k (min)

U Zk
(m/s)

ᭀ㢼௨እ䛾
㢼䛾㢖ᗘ

ᭀ㢼௨እ䛻䜘䜛
⣼✚స⏝᫬㛫
T Daily,k (min)53

6.816E-32

0351.361E-140173.034E-04

15,90752

9.379E-31

0347.842E-140166.970E-04

36,54351

1.231E-29

0334.301E-130151.516E-03

79,50350

1.539E-280322.245E-120143.122E-03

163,68849

1.836E-27

0311.115E-110136.078E-03

318,67648
47

2.087E-26
2.261E-25

0
0

30
29

5.268E-11
2.368E-10

0
0

12
11

1.118E-02
1.940E-02

586,065
1,016,895

46

2.334E-240281.012E-090103.170E-02

1,662,190

45

2.297E-23

027

4.117E-09094.872E-02

2,554,556

44

2.155E-220261.591E-08187.023E-02

3,681,864

43

1.925E-210255.848E-08379.459E-02

4,959,268

42

1.639E-20

0242.042E-071161.185E-01

6,211,408

41

1.330E-190236.776E-073651.369E-01

7,179,325

40

1.027E-180222.135E-06

112

41.442E-01

7,562,550

39

7.562E-18

0216.391E-06335

31.353E-01

7,094,490

38

5.301E-170201.816E-05952

2

1.074E-01

5,631,280

37

3.539E-160194.894E-05

2,566

1

6.132E-02

3,214,80236

2.249E-150181.252E-04

6,561

0

8.560E-03

448,8121.000E+00

52,428,399

䃂⾲  ᭀ㢼௨እࡢ⣼✚స⏝᫬㛫 㢼┤஺᪉ྥ⏝ 
fL(Hz)

U r min(m/s)

U r m ax(m/s)

T Daily, r
(min)

ᙉ㍈

209.22

66.5

95.8

0

ᙅ㍈

164.19

52.2

75.2

0

 㢼ᛂ⟅࡜⑂ປᦆയホ౯ᮏሗ࡛ࡣ㸪౽ᐅୖ㸪⥅ᡭࡢ࢝ࢸࢦ࣮ࣜࢆ⑂ປタィᣦ㔪  ⑂ປᦆയホ౯᪉ἲ(12)࡟࠾ࡅࡿࠕc) ⦪᪉ྥ⁐᥋⥅ᡭ 3. 㝮⫗⁐᥋⥅ᡭࠖ࡜ࡋ⑂ປタィᣦ㔪(12)࡟࠾ࡅࡿ⑂ປ᭤⥺ࡣ㸪ḟᘧࡢࡼ࠺࡞

࡚ᙉᗘ➼⣭ D (=100N/mm2)࡜ࡋ㸪⑂ປᘏᛶᣦᩘ m S ࡣ

Miner ๎࡟ᚑࡗࡓࡶࡢ࡜࡞ࡗ࡚࠾ࡾ㸪✀ࠎࡢ⥅ᡭᙧᘧ࡟mSࡘ࠸࡚♧ࡉࢀ࡚࠸ࡿ㸬ࡋ࠿ࡋ࡞ࡀࡽ㸪ᮏሗࡢࡼ࠺࡞᭤ࡆ

࡜ࡋ࡚ᡴษࡾ㝈⏺ᛂຊ 'V e ࢆ↓どࡋ㸪ಟṇ Miner ๎࡟ࡼᛂຊ࡟ᑐࡍࡿ⑂ປᦆയホ౯࡟㐺⏝࡛ࡁࡿ⑂ປ᭤⥺ࡣྠᣦࡗ࡚ホ౯ࡍࡿ㸬㔪࡟ࡶᥖ㍕ࡉࢀ࡚࠸࡞࠸㸬
n
D ¦ k
Nf

  㢼᪉ྥⲴ㔜࡟ࡼࡿ⑂ປᦆയᗘ

Nfm­§ 'V f · S°2 u 10 6 ¨¸¨ 'V ¸
®
k ¹
©
°
f
¯

(7.9)

3 ࡜ࡍࡿ㸬ࡲࡓ㸪⑂ປᦆയホ౯࡛ࡣᏳ඲ഃࡢホ౯㢼᪉ྥࡢྛ㢼㏿࡟࠾ࡅࡿᛂ⟅ࡣ㸪ᘧ(5.4)࡟ࡼࡾ q Z ࢆ㸪ᘧ(5.15)㸪(5.16)㸪(5.20)㸪(5.19)࠾ࡼࡧᘧ(5.29)࡟ࡼࡾ F 㸪'V k ! 'V e

(7.10)'V k d 'V eࡇࡇ࡟㸪 N f ࡣ◚᩿ࡀ⏕ࡌࡿ⧞㏉ࡋᅇᩘ㸪 n k ࡣᛂຊ

R D 㸪Q D 㸪 g D ࠾ࡼࡧ G D ࢆ㸪ࡉࡽ࡟㸪ᘧ(5.27)࠾ࡼࡧ

ᘧ(5.32)࡟ࡼࡾᖹᆒ࣍ࢵࢺࢫ࣏ࢵࢺᛂຊ V HD ࠾ࡼࡧ᭱኱
ኚື࣍ࢵࢺࢫ࣏ࢵࢺᛂຊ Vˆ HD ࡀᚓࡽࢀࡿ㸬⑂ປ᳨ウ⏝ࡢ࣍ࢵࢺࢫ࣏ࢵࢺᛂຊ᣺ᖜ ' V k ࡣᘧ(6.1)࡟♧ࡍࡼ࠺࡟᣺ᖜ 'V k ࡢ⧞㏉ࡋᅇᩘ㸪'V f ࡣ 2106 ᅇᇶᮏ⑂ປᙉᗘ㸪ࡇࡢᛂຊ Vˆ HD ࡢ 2 ಸࡢ್࡛࠶ࡿ㸬ࡲࡓ㸪ࡇࡢ ' V k ࡢ⧞

'V e ࡣᡴษࡾ㝈⏺ᛂຊ㸪 m S ࡣ⑂ປᘏᛶᣦᩘ࡛࠶ࡿ㸬㏉ࡋᅇᩘࡣᘧ(6.2)࡛⟬ᐃ࡛ࡁࡿ㸬ྛ㢼㏿࡟࠾ࡅࡿࡇࢀࡽ

⑂ປタィ౽ぴ(17)࡟ࡼࡿ࡜㸪᭤ࡆᛂຊ࡟ᑐࡍࡿᡴษࡾ㝈ࡢㅖᩘ್㸪࣍ࢵࢺࢫ࣏ࢵࢺᛂຊࡢ᭱኱್㸪⧞㏉ࡋᅇᩘ㸪⏺ᛂຊࡣ┤ᛂຊ࡟ᑐࡍࡿࡑࢀࡼࡾᑠࡉ࠸࡜࠶ࡿ㸬ࡍ࡞ࢃ⑂ປᦆയᗘࢆᙉ㍈࡟ࡘ࠸࡚⾲ 7-7 ࡟㸪ᙅ㍈࡟ࡘ࠸࡚⾲ 7-8ࡕ㸪⥅ᡭࡀྠࡌ࡛࠶ࡿሙྜ࡟㸪┤ᛂຊࡢ⑂ປ᭤⥺ࢆࡑࡢ࡟♧ࡍ㸬ࡲࡲ᭤ࡆᛂຊ࡟㐺⏝ࡍࢀࡤᏳ඲ഃࡢホ౯࡟࡞ࡿ࡜⪃࠼ࡽࢀࡿ㸬ᙉ㍈᪉ྥ࠾ࡼࡧᙅ㍈᪉ྥඹ࡟⣼✚⑂ປᦆയᗘ D ್ࡣ 1ࢆୗᅇࡿ್࡛㸪ᙉ㍈᪉ྥࡢ᪉ࡀ኱ࡁ࠸㸬ࡇࢀࡣ㸪➃㒊ࡢ㗰⟶㒊ᮦࡢ⡆᫆࡞⑂ປᦆയホ౯᪉ἲᅛᐃᗘࢆ⪃៖ࡋࡓࡇ࡜࡟ࡼࡗ࡚㸪ᙉ㍈᪉ྥࡢᅛ᭷᣺ືᩘ

࡛࠶ࡿ㸬ᙉ㍈࠾ࡼࡧᙅ㍈ඹ࡟᭱኱ࡢኚືᛂຊ᣺ᖜ࡛ࡇࡢ

ࡀᙅ㍈᪉ྥࡢࡑࢀ࡟ᑐࡋ 1.27 ಸ⛬ᗘ࡜ᕪ␗ࡀ኱ࡁࡃ࡞࠸

್ࢆୗᅇࡗ࡚࠾ࡾ㸪ᡴษࡾ㝈⏺ᛂຊࢆ⪃៖ࡋ࡚ Miner ๎ࡇ࡜㸪༢఩ኚ఩᣺ᖜ᫬ࡢᙉ㍈᪉ྥࡢ࣍ࢵࢺࢫ࣏ࢵࢺᛂຊ

࡛⑂ປᦆയᗘࢆホ౯ࡋࡓሙྜ࡟㸪୧᪉ྥඹ࡟ D ್ࡣ 0 ࡜

ࡀᙅ㍈᪉ྥࡢࡑࢀ࡟ᑐࡋ 2.57 ಸ࡜኱ࡁ࠸ࡇ࡜࡟ࡼࡿ㸬ホ౯ࡉࢀࡿࡇ࡜࡟࡞ࡿ㸬ᅉࡳ࡟㸪⑂ປタィᣦ㔪(12)࡟࠾࠸࡚ᙉᗘ➼⣭ࡀ D ࡢሙྜ㸪ᡴษࡾ㝈⏺ᛂຊ 'V e ࡣኚື᣺ᖜᛂຊࡢሙྜ࡛ 39N/mm2
⾲  㢼᪉ྥࡢ⑂ປᦆയホ౯⤖ᯝ㸦ࡑࡢ  ᙉ㍈ࡢሙྜ㸧
U Zk
(m/s)
53
52
51
50
49
48
47
46
45
44
43
42
41
40
39
38
37
36
35
34
33
32
31
30
29
28
27
26
25
24
23
22
21
20
19
18
17
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1

Tk
(s)
6.0E+02
0.0E+00
0.0E+00
1.2E+03
0.0E+00
6.0E+02
1.8E+03
1.8E+03
1.8E+03
3.0E+03
3.0E+03
5.4E+03
7.2E+03
9.0E+03
1.3E+04
1.7E+04
2.5E+04
3.4E+04
4.6E+04
6.5E+04
7.7E+04
1.1E+05
1.3E+05
1.7E+05
2.0E+05
2.4E+05
2.7E+05
3.0E+05
3.2E+05
3.4E+05
3.5E+05
3.7E+05
4.0E+05
4.5E+05
5.6E+05
8.2E+05
1.4E+06
2.7E+06
5.3E+06
1.0E+072.0E+07
3.6E+076.2E+07
1.0E+08
1.5E+08
2.2E+08
3.0E+08
3.7E+08
4.3E+08
4.5E+08
4.3E+08
3.4E+08
1.9E+08

q Zk(kN/m2)
1.713
1.649
1.587
1.525
1.465
1.405
1.347
1.291
1.235
1.181
1.128
1.076
1.025
0.976
0.928
0.881
0.835
0.791
0.747
0.705
0.664
0.625
0.586
0.549
0.513
0.478
0.445
0.412
0.381
0.351
0.323
0.295
0.269
0.244
0.220
0.198
0.176
0.156
0.137
0.120
0.103
0.088
0.074
0.061
0.049
0.039
0.030
0.022
0.015
0.010
0.005
0.002
0.001

F

RD

ȞD

gD

GD

1.4E-03
1.4E-03
1.4E-03
1.4E-03
1.4E-03
1.3E-03
1.3E-03
1.3E-03
1.3E-03
1.3E-03
1.2E-03
1.2E-03
1.2E-03
1.2E-03
1.2E-03
1.1E-03
1.1E-03
1.1E-03
1.1E-03
1.1E-03
1.0E-03
1.0E-03
1.0E-03
9.8E-04
9.6E-04
9.3E-04
9.1E-04
8.9E-04
8.7E-04
8.4E-04
8.2E-04
8.0E-04
7.7E-04
7.5E-04
7.2E-04
7.0E-04
6.7E-04
6.4E-04
6.2E-04
5.9E-04
5.6E-04
5.3E-04
5.0E-04
4.7E-04
4.4E-04
4.1E-04
3.7E-04
3.3E-04
3.0E-04
2.6E-04
2.1E-04
1.6E-04
1.0E-04

0.225
0.222
0.219
0.216
0.213
0.210
0.207
0.204
0.201
0.198
0.195
0.192
0.189
0.186
0.183
0.180
0.177
0.174
0.170
0.167
0.164
0.160
0.157
0.154
0.150
0.147
0.143
0.140
0.136
0.132
0.129
0.125
0.121
0.117
0.113
0.109
0.105
0.101
0.097
0.092
0.088
0.083
0.079
0.074
0.069
0.064
0.058
0.053
0.047
0.040
0.033
0.025
0.016

89.59
89.13
88.66
88.18
87.69
87.19
86.69
86.17
85.65
85.12
84.57
84.02
83.46
82.88
82.29
81.69
81.08
80.45
79.81
79.15
78.48
77.79
77.08
76.35
75.61
74.84
74.05
73.24
72.41
71.54
70.65
69.73
68.77
67.78
66.75
65.67
64.55
63.38
62.15
60.86
59.50
58.05
56.52
54.87
53.10
51.18
49.08
46.75
44.12
41.08
37.45
32.84
26.19

4.791
4.790
4.789
4.788
4.787
4.785
4.784
4.783
4.782
4.780
4.779
4.778
4.776
4.775
4.773
4.772
4.770
4.768
4.767
4.765
4.763
4.761
4.760
4.758
4.755
4.753
4.751
4.749
4.746
4.744
4.741
4.738
4.736
4.732
4.729
4.726
4.722
4.718
4.714
4.710
4.705
4.700
4.694
4.688
4.681
4.673
4.664
4.653
4.641
4.626
4.605
4.577
4.527

2.544
2.542
2.540
2.538
2.536
2.533
2.531
2.529
2.527
2.524
2.522
2.520
2.517
2.515
2.512
2.510
2.507
2.505
2.502
2.499
2.497
2.494
2.491
2.489
2.486
2.483
2.480
2.477
2.474
2.471
2.467
2.464
2.461
2.457
2.454
2.450
2.446
2.442
2.438
2.434
2.430
2.425
2.420
2.415
2.410
2.404
2.398
2.391
2.383
2.374
2.364
2.350
2.329

ı HD,kı^ HD,k䏓ı k(kN/m2) (N/mm2) (N/mm2)
9220
14.24
28.48
8875
13.69
27.37
8537
13.15
26.30
8206
12.62
25.24
7881
12.10
24.20
7562
11.60
23.19
7250
11.10
22.20
6945
10.62
21.24
6647
10.15
20.29
6354
9.69
19.37
6069
9.24
18.47
5790
8.80
17.60
5517
8.37
16.74
5252
7.95
15.91
4992
7.55
15.10
4740
7.16
14.31
4493
6.77
13.55
4254
6.40
12.80
4021
6.04
12.08
3794
5.69
11.38
3574
5.35
10.70
3361
5.02
10.04
3154
4.70
9.41
2954
4.40
8.79
2760
4.10
8.20
2573
3.82
7.63
2393
3.54
7.08
2219
3.28
6.55
2051
3.02
6.05
1891
2.78
5.56
1736
2.55
5.10
1589
2.33
4.65
1447
2.11
4.23
1313
1.91
3.83
1185
1.72
3.44
1063
1.54
3.08
949
1.37
2.74
840
1.21
2.42
739
1.06
2.12
643
0.92
1.84
555
0.79
1.59
473
0.67
1.35
397
0.56
1.13
328
0.46
0.93
266
0.37
0.75
210
0.29
0.59
161
0.22
0.45
118
0.16
0.33
82
0.11
0.23
53
0.07
0.14
30
0.04
0.08
13
0.02
0.04
3
0.00
0.01

Nf

nk

Dk

8.7E+079.7E+07
1.1E+08
1.2E+08
1.4E+08
1.6E+08
1.8E+08
2.1E+08
2.4E+08
2.8E+08
3.2E+08
3.7E+08
4.3E+08
5.0E+08
5.8E+08
6.8E+088.0E+08
9.5E+08
1.1E+09
1.4E+09
1.6E+09
2.0E+09
2.4E+09
2.9E+09
3.6E+09
4.5E+09
5.6E+09
7.1E+09
9.0E+09
1.2E+10
1.5E+102.0E+10
2.6E+10
3.6E+10
4.9E+10
6.8E+109.7E+10
1.4E+112.1E+11
3.2E+115.0E+118.2E+11
1.4E+122.5E+124.7E+129.7E+122.2E+13
5.6E+13
1.7E+14
6.7E+143.8E+15
4.5E+16
3.0E+18

1.3E+05
0.0E+00
0.0E+00
2.5E+05
0.0E+00
1.3E+05
3.8E+05
3.8E+05
3.8E+05
6.3E+05
6.3E+05
1.1E+06
1.5E+06
1.9E+06
2.6E+06
3.5E+06
5.1E+06
7.0E+06
9.5E+06
1.4E+07
1.6E+07
2.2E+072.8E+07
3.5E+07
4.2E+07
4.9E+07
5.6E+076.2E+076.6E+07
7.0E+07
7.4E+077.8E+078.4E+07
9.4E+07
1.2E+08
1.7E+08
2.9E+08
5.6E+08
1.1E+09
2.2E+09
4.1E+09
7.5E+09
1.3E+102.1E+10
3.2E+10
4.6E+10
6.2E+107.8E+109.0E+109.5E+108.9E+10
7.1E+10
4.0E+10ȈD k

1.4E-03
0.0E+00
0.0E+00
2.0E-03
0.0E+00
7.8E-04
2.1E-03
1.8E-03
1.6E-03
2.3E-032.0E-03
3.1E-03
3.5E-03
3.8E-03
4.5E-03
5.2E-03
6.4E-03
7.4E-03
8.4E-03
1.0E-02
9.8E-03
1.1E-02
1.2E-02
1.2E-02
1.2E-02
1.1E-02
1.0E-02
8.7E-03
7.3E-03
6.0E-03
4.9E-03
3.9E-03
3.2E-03
2.6E-03
2.4E-03
2.5E-033.0E-03
4.0E-03
5.3E-03
6.8E-038.2E-03
9.1E-03
9.2E-03
8.4E-03
6.8E-03
4.7E-03
2.8E-03
1.4E-03
5.3E-04
1.4E-04
2.3E-05
1.6E-06
1.3E-08
2.55E-01⚄ዉᕝ኱ᏛᕤᏛ◊✲ᡤᡤሗ ➨  ྕ⾲  㢼᪉ྥࡢ⑂ປᦆയホ౯⤖ᯝ㸦ࡑࡢ  ᙅ㍈ࡢሙྜ㸧
U Zk
(m/s)
53
52
51
50
49
48
47
46
45
44
43
42
41
40
39
38
37
36
35
34
33
32
31
30
29
28
27
26
25
24
23
22
21
20
19
18
17
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1

Tk
(s)
6.0E+02
0.0E+00
0.0E+00
1.2E+03
0.0E+00
6.0E+02
1.8E+03
1.8E+03
1.8E+03
3.0E+03
3.0E+03
5.4E+03
7.2E+03
9.0E+03
1.3E+04
1.7E+04
2.5E+04
3.4E+04
4.6E+04
6.5E+04
7.7E+04
1.1E+05
1.3E+05
1.7E+05
2.0E+05
2.4E+05
2.7E+05
3.0E+05
3.2E+05
3.4E+05
3.5E+05
3.7E+05
4.0E+05
4.5E+05
5.6E+05
8.2E+05
1.4E+06
2.7E+06
5.3E+06
1.0E+072.0E+07
3.6E+076.2E+07
1.0E+08
1.5E+08
2.2E+08
3.0E+08
3.7E+08
4.3E+08
4.5E+08
4.3E+08
3.4E+08
1.9E+08

q Zk(kN/m2)
1.713
1.649
1.587
1.525
1.465
1.405
1.347
1.291
1.235
1.181
1.128
1.076
1.025
0.976
0.928
0.881
0.835
0.791
0.747
0.705
0.664
0.625
0.586
0.549
0.513
0.478
0.445
0.412
0.381
0.351
0.323
0.295
0.269
0.244
0.220
0.198
0.176
0.156
0.137
0.120
0.103
0.088
0.074
0.061
0.049
0.039
0.030
0.022
0.015
0.010
0.005
0.002
0.001

F

RD

ȞD

gD

GD

1.7E-03
1.7E-03
1.6E-03
1.6E-03
1.6E-03
1.6E-03
1.6E-03
1.5E-03
1.5E-03
1.5E-03
1.5E-03
1.4E-03
1.4E-03
1.4E-03
1.4E-03
1.3E-03
1.3E-03
1.3E-03
1.3E-03
1.2E-03
1.2E-03
1.2E-03
1.2E-03
1.1E-03
1.1E-03
1.1E-03
1.1E-03
1.0E-03
1.0E-03
9.9E-04
9.6E-04
9.3E-04
9.1E-04
8.8E-04
8.5E-04
8.2E-04
7.9E-04
7.6E-04
7.2E-04
6.9E-04
6.6E-04
6.2E-04
5.9E-04
5.5E-04
5.2E-04
4.8E-04
4.4E-04
3.9E-04
3.5E-04
3.0E-04
2.5E-04
1.9E-04
1.2E-04

0.264
0.261
0.257
0.254
0.250
0.247
0.244
0.240
0.237
0.233
0.230
0.226
0.222
0.219
0.215
0.211
0.208
0.204
0.200
0.196
0.192
0.189
0.185
0.181
0.177
0.172
0.168
0.164
0.160
0.156
0.151
0.147
0.142
0.138
0.133
0.128
0.124
0.119
0.114
0.109
0.103
0.098
0.093
0.087
0.081
0.075
0.068
0.062
0.055
0.047
0.039
0.030
0.019

75.03
74.65
74.27
73.88
73.48
73.08
72.67
72.25
71.83
71.39
70.95
70.50
70.03
69.56
69.08
68.59
68.09
67.58
67.05
66.51
65.96
65.39
64.81
64.22
63.60
62.97
62.33
61.66
60.97
60.25
59.52
58.76
57.96
57.14
56.29
55.40
54.47
53.50
52.48
51.40
50.27
49.06
47.78
46.41
44.93
43.32
41.56
39.60
37.39
34.83
31.77
27.88
22.25

4.754
4.753
4.752
4.751
4.749
4.748
4.747
4.746
4.745
4.743
4.742
4.741
4.739
4.738
4.736
4.735
4.733
4.732
4.730
4.728
4.727
4.725
4.723
4.721
4.719
4.717
4.715
4.712
4.710
4.708
4.705
4.702
4.699
4.696
4.693
4.690
4.686
4.682
4.678
4.674
4.669
4.664
4.658
4.652
4.645
4.637
4.628
4.618
4.605
4.590
4.570
4.541
4.491

2.557
2.554
2.552
2.550
2.547
2.545
2.542
2.540
2.537
2.534
2.532
2.529
2.526
2.524
2.521
2.518
2.515
2.512
2.509
2.507
2.504
2.500
2.497
2.494
2.491
2.488
2.484
2.481
2.478
2.474
2.471
2.467
2.463
2.459
2.455
2.451
2.447
2.443
2.438
2.433
2.429
2.424
2.418
2.413
2.407
2.400
2.393
2.386
2.378
2.368
2.357
2.342
2.320

  㢼┤஺᪉ྥⲴ㔜࡟ࡼࡿ⑂ປᦆയᗘ

^ıı HD,k䏓ı kHD,k(kN/m2) (N/mm2) (N/mm2)
3102
4.83
9.66
2986
4.64
9.28
2872
4.46
8.92
2761
4.28
8.56
2651
4.10
8.20
2544
3.93
7.86
2439
3.76
7.52
2337
3.60
7.19
2236
3.44
6.87
2138
3.28
6.56
2042
3.13
6.25
1948
2.98
5.96
1856
2.83
5.67
1767
2.69
5.38
1680
2.55
5.11
1595
2.42
4.84
1512
2.29
4.58
1431
2.16
4.33
1353
2.04
4.08
1276
1.92
3.85
1203
1.81
3.62
1131
1.70
3.39
1061
1.59
3.18
994
1.48
2.97
929
1.38
2.77
866
1.29
2.58
805
1.19
2.39
746
1.11
2.21
690
1.02
2.04
636
0.94
1.88
584
0.86
1.72
534
0.78
1.57
487
0.71
1.42
442
0.64
1.29
399
0.58
1.16
358
0.52
1.04
319
0.46
0.92
283
0.41
0.82
248
0.36
0.71
216
0.31
0.62
187
0.27
0.53
159
0.23
0.45
134
0.19
0.38
110
0.16
0.31
89
0.13
0.25
71
0.10
0.20
54
0.08
0.15
40
0.06
0.11
28
0.04
0.08
18
0.02
0.05
10
0.01
0.03
4
0.01
0.01
1
0.00
0.00

Nf

nk

Dk

2.2E+09
2.5E+09
2.8E+09
3.2E+09
3.6E+09
4.1E+09
4.7E+09
5.4E+09
6.2E+09
7.1E+098.2E+09
9.5E+09
1.1E+10
1.3E+10
1.5E+10
1.8E+102.1E+10
2.5E+10
2.9E+10
3.5E+10
4.2E+105.1E+10
6.2E+10
7.6E+109.4E+10
1.2E+11
1.5E+11
1.9E+112.4E+113.0E+11
3.9E+115.2E+11
6.9E+119.3E+11
1.3E+121.8E+122.5E+123.7E+125.5E+128.4E+121.3E+132.2E+13
3.7E+13
6.6E+13
1.3E+142.6E+145.8E+14
1.5E+15
4.5E+15
1.8E+16
1.0E+17
1.2E+18
8.1E+19

9.9E+04
0.0E+00
0.0E+00
2.0E+05
0.0E+00
9.9E+04
3.0E+05
3.0E+05
3.0E+05
4.9E+05
4.9E+05
8.9E+05
1.2E+06
1.5E+06
2.1E+06
2.8E+06
4.0E+06
5.5E+06
7.5E+06
1.1E+07
1.3E+07
1.7E+07
2.2E+072.8E+07
3.3E+07
3.9E+07
4.4E+074.8E+075.2E+07
5.5E+075.8E+07
6.1E+076.6E+07
7.4E+07
9.3E+07
1.4E+08
2.3E+08
4.4E+088.7E+08
1.7E+09
3.2E+09
5.9E+09
1.0E+10
1.6E+10
2.5E+10
3.6E+10
4.9E+10
6.1E+10
7.1E+10
7.5E+107.0E+10
5.5E+10
3.2E+10ȈD k

4.4E-05
0.0E+00
0.0E+00
6.2E-05
0.0E+00
2.4E-05
6.3E-05
5.5E-05
4.8E-05
7.0E-05
6.0E-05
9.4E-05
1.1E-04
1.2E-04
1.4E-04
1.6E-04
1.9E-04
2.2E-04
2.5E-04
3.1E-04
3.0E-04
3.4E-04
3.5E-04
3.6E-04
3.5E-04
3.3E-04
3.0E-04
2.6E-04
2.2E-04
1.8E-04
1.5E-04
1.2E-04
9.5E-05
7.9E-05
7.2E-05
7.6E-05
9.1E-05
1.2E-04
1.6E-04
2.0E-04
2.4E-04
2.7E-04
2.8E-04
2.5E-04
2.0E-04
1.4E-04
8.4E-05
4.1E-05
1.6E-05
4.2E-06
6.9E-07
4.6E-08
3.9E-10
7.70E-03ྠ⾲࡟♧ࡍࡼ࠺࡟㸪ᙉ㍈᪉ྥ࡟ࡘ࠸࡚ࡣⓎ᣺㢼㏿ࡀ෌㢼┤஺᪉ྥࡢᛂ⟅ࡣ㸪ᘧ(5.35)㹼ᘧ(5.37)࡟ࡼࡾ㒊ᮦ୰⌧ᮇ㛫 500 ᖺࡢ㢼㏿ࢆୖᅇࡗ࡚࠸ࡿࡓࡵ㸪⑂ປ࡟ᑐࡋ࡚

ኸࡢኚ఩ࢆ㸪ᘧ(5.39)࡟ࡼࡾ᭱኱ኚື࣍ࢵࢺࢫ࣏ࢵࢺᛂຊ

ࡣᏳ඲࡛࠶ࡿ࡜ࡢ⤖ᯝ࡟࡞ࡗ࡚࠸ࡿ㸬୍᪉㸪ᙅ㍈࡟ࡘ࠸

Vˆ HL ࡀᚓࡽࢀࡿ㸬⑂ປ᳨ウ⏝ࡢ࣍ࢵࢺࢫ࣏ࢵࢺᛂຊ᣺ᖜ

࡚ࡣ㸪ഹ࠿ 10 ศ㛫ࡢ⣼✚స⏝᫬㛫࡛࠶ࡿࡀ㸪ኚ఩᣺ᖜ࠾

'V r ࡣ㸪㢼᪉ྥ࡜ྠᵝ࡟ᛂຊ Vˆ HL ࡢ 2 ಸࡢ್࡛࠶ࡿ㸬ࡼࡧ࣍ࢵࢺࢫ࣏ࢵࢺᛂຊࡀ኱ࡁ࠸ࡓࡵ㸪D ್ࡣ 2.3 ࡜ 1ࡲࡓ㸪ࡇࡢ 'V r ࡢ⧞㏉ࡋᅇᩘࡣᘧ(6.7)࡛⟬ᐃ࡛ࡁࡿ㸬㢼ࢆ㉸࠼࡚࠸ࡿ㸬┤஺᪉ྥࡢホ౯⤖ᯝࢆ⾲ 7-9 ࡟♧ࡍ㸬㗰⟶㒊ᮦࡢ⡆᫆࡞⑂ປᦆയホ౯᪉ἲ௨ୖࢆ㋃ࡲ࠼ࡿ࡜㸪㢼᪉ྥࡢ⑂ປᦆയ࡟ᑐࡋ࡚༑ศ࡟ճĂ ᚓࡽࢀࡓᅛᐃᗘࢆ⪃៖ࡋ࡚㸪ᅛ᭷᣺ື࣮ࣔࢻࢆ⟬Ᏻ඲࡛࠶ࡗ࡚ࡶ㸪୍ᗘ ບ᣺ࡀⓎ⏕ࡍࡿ࡜⮴࿨ⓗ࡞⑂ປᐃࡍࡿ᪉ἲࢆ♧ࡋ㸪ࡑࡢ᭷ຠᛶࢆ♧ࡋࡓ㸬ᦆയ࡟࡞ࡿྍ⬟ᛶࡀ࠶ࡿ࡜ゝ࠼ࡿ㸬մĂ ᭤ࡆ࣮࣓ࣔࣥࢺࡢ⟬ᐃᘧ㸪㟼ⓗศᕸⲴ㔜ࡢ⟬ᐃᘧ㸪୍⯡໬㉁㔞ࡢ⟬ᐃᘧࢆ♧ࡋࡓ㸬

FEM ࡟ࡼࡿ࣍ࢵࢺࢫ࣏ࢵࢺᛂຊ⟬ᐃ࡛ࡣ㸪⾲  㢼┤஺᪉ྥࡢᛂ⟅࡜⑂ປᦆയᗘ
ᙉ㍈
ȡD(kg/m3)(t/m3)
(m)

t
l

(m)
(m)

Ap
M

(m2)
(t)

ȡa

✵Ẽ

㒊ᮦ

kf
fL

᣺ື
≉ᛶ

ࡿࡼ࠺࡞್࡟࡞ࡿሙྜࡶ࠶ࡿ㸬ホ౯஦౛࡛ࡣ㸪

0.07630.0032նĂ 㢼᪉ྥ࡟ᑐࡍࡿ D ್ࡀ 1 ࢆୗᅇࡿᑠࡉ࡞್࡛࠶
ࡗ࡚ࡶ㸪㢼┤஺᪉ྥ㸪࠸ࢃࡺࡿ ບ᣺ࡀⓎ⏕ࡍࡿሙྜ࡟ࡣ D ್ࡀ 1 ࢆ㉸࠼ࡿࡼ࠺࡞್࡜࡞ࡿሙྜ

8.653E-03
1.0000209.22(kN/m2)
➼⣭
⑂ປ㝈

⑂ປ
≉ᛶ

0.5517164.19ձĂ CT ௨እࡢ⥅ᡭࡢሙྜࡢ⡆᫆࡞᣺ືᛶ≧ホ౯᪉ἲ↓100ղĂ ࣍ࢵࢺࢫ࣏ࢵࢺᛂຊࡢ⡆᫆࡞ホ౯᪉ἲࡢ☜❧㸬(N/mm2)

U Z, r =m ax 䈜U r m in

(m/s)
(m/s)

66.5

52.2

U r max
Tr

(m/s)
(min)

95.8
0.0

75.2
10.0

Ur*
YL
ı^ H L
nr
䏓ı r

⑂ປ
ᦆയ
ホ౯

ࡢ☜❧㸬
ճĂ ᭤ࡆᛂຊ࡟ᑐᛂࡋࡓ⑂ປᐇ㦂࡜⑂ປ᭤⥺03(N/mm2)մĂ ࣎ࣝࢺ࿘㎶ࡢᛂຊ㞟୰ࡢホ౯

19.7

᭱ᚋ࡟㸪ᮏሗ࡛ࡣಶᮦࡢ㢼࡟ࡼࡿ⑂ປᦆയࢆ⡆᫆࡟ホ52.9౯ࡍࡿ᪉ἲࢆ♧ࡋࡓࡀ㸪ᮏሗ࡛ࡢᥦ᱌(1 ❶ࡢ㡯┠ձ㹼ճ㸪

ྰ

↷ᰝ䛾せྰ
į

ࡀ࠶ࡿ㸬
ࡲࡓ㸪௨ୗࡢࡼ࠺࡞㡯┠ࡀ௒ᚋࡢㄢ㢟࡛࠶ࡿ㸬

4.440E+08 1.140E+08
0.005
D

䏓ı f
䏓ı e
mS
l /D

ບ
᣺䛾
ᛂ⟅
ホ౯

յĂ ࣍ࢵࢺࢫ࣏ࢵࢺᛂຊࡢᛂຊ㞟୰ಀᩘࡣ 10 ࢆ㉸࠼

1.5
7.349E-04

(Hz)

ıH
ȗ

ᙅ㍈
1.22
7.850

せ
51.03
5.06
0.00171(m)(kN/m2)(N/mm2)

1.954E+05
195.4

2(N/mm )

98514.2
390.7յ)ࢆ㌿⏝ࡋ㸪Ⲵ㔜࡟ࡘ࠸࡚ࡣⲴ㔜ᣦ㔪(7)ࢆ⏝࠸ࢀࡤ㸪㢼࡟ࡼࡿ㕲ሪ඲యࡢᛂ⟅࡟ࡼࡿ⑂ປᦆയࡶホ౯࡛ࡁࡿ㸬⿵㊊  ✚ศᐃᩘ✚ศᐃᩘ A1 㹼 A4 ࡢ㏆ఝ⢭ᗘୗᅗ࡟㸪✚ศᐃᩘ A1 㹼 A4 ࡢ⌮ㄽ್(ᅗ୰‫ࡼ࠾)ڧڹۑ‬ࡧ㏆ఝᘧ(2.9)㹼(2.12)ࢆẚ㍑ࡋ࡚♧ࡍ㸬ྠᅗղ♧ࡍࡼ࠺࡟ᥦ᱌ᘧࡣⰋࡃ㏆ఝࡋ࡚࠸ࡿ㸬

43589.1
2.3

Nf
D್

1
A2

䈜༳䠖᭱኱䛾↷ᰝ㢼㏿㸶㸬࠾ࢃࡾ࡟

ࡇࡇ࡛ࡢ᳨ウ࡜ᥦ᱌ࢆ஦౛࡟㐺⏝ࡍࡿࡇ࡜࡛ゎࡗࡓࡇ࡜ࢆࡲ࡜ࡵࡿ࡜ḟࡢࡼ࠺࡟࡞ࡿ㸬ࡲࡎ㸪⥅ᡭࡢᙳ㡪ࢆ⪃៖ࡋࡓ㗰⟶ࡢ᣺ືᛶ≧ࡢ⡆᫆࡞ホ౯ἲ࡛ࡣ㸪ձĂ ➃㒊࣎ࣝࢺࡢᮏᩘࡀᑡ࡞࠸⛬ᅛᐃᗘࡣᑠࡉࡃ࡞
ࡾ㸪࢙࢘ࣈࡢ➃㒊ᅇ㌿ᣊ᮰ຊࡀᑠࡉࡃ࡞ࡿ㸬ᮏሗ

A1, A2, A3, A4

0.5
A3=-A1
0

-0.5
-1
0

A4
0.5
kf

1

࡛ࡣ㸪ࡇࡢ࢙࢘ࣈࡢᣊ᮰ຠᯝࢆ➃㒊࣎ࣝࢺࡢᮏᩘ~  ୍⯡໬㉁㔞 M ࠾ࡼࡧ ) ࡢ㏆ఝᘧ࡜㛵㐃௜ࡅ࡚࢙࢘ࣈ᭷ຠ⋡ࢆᐃ⩏ࡋࡓ㸬

๓㏙ࡋࡓࡼ࠺࡟㸪㒊ᮦ୰ኸࡢኚ఩∦᣺ᖜࡀ 1 ࡛㸪➃㒊ղĂ 㒊ᮦ୰ኸ࠾ࡼࡧ 1/4 ࡢ఩⨨࡛ࡢኚ఩᣺ᖜࢆཧ↷ࡋ㸪ᅛᐃᗘࡀ k f ࡢሙྜࡢኚ఩࣮ࣔࢻ P x ࢆ㸪௨ୗࡢࡼ࠺࡟

ᅛᐃᗘࢆ⟬ᐃࡍࡿ᪉ἲࢆᥦ᱌ࡋࡓ㸬ࡉࡽ࡟㸪ᅛᐃ୧➃ࣆࣥࡢኚ఩࣮ࣔࢻ P pin x ࡜୧➃ᅛᐃࡢኚ఩࣮ࣔࢻ

ᗘࢆᇶ࡟ᅛ᭷᣺ືᩘࢆ⟬ᐃࡍࡿ᪉ἲࢆ♧ࡋ㸪ࡑࡢ

P fix x ࡢ୍ḟ⤖ྜ࡟ࡼࡗ࡚⾲ࢃࡉࢀࡿࡇ࡜ࢆ♧ࡋࡓ㸬᭷ຠᛶࢆ♧ࡋࡓ㸬⚄ዉᕝ኱ᏛᕤᏛ◊✲ᡤᡤሗ ➨  ྕ
P x

1  k f P pin x  k f P fix x

P pin xP fix x(2.13)෌ᥖ

sin Sx l(2.14) ෌ᥖ

B1 cos J f x  cosh J f x
 B2 sin J f x  sinh J f x(2.15) ෌ᥖ

B1 | 0.629665(2.16) ෌ᥖ

B 2 | 0.618647(2.17) ෌ᥖJ f l | 4.73004(2.18) ෌ᥖ(2) Ᏻ஭ඵ⣖㸪኱⇃Ṋྖ㸪㭯ぢಇ㞝㸪ᓥᒸಇ㍜㸸⥅ᡭࢆ⪃៖ࡋࡓ㗰⟶㒊ᮦࡢ⡆᫆࡞᣺ືᛶ≧ホ౯࡟㛵ࡍࡿ◊✲㸪ࡑࡢ 2. ᅛ᭷᣺ືᩘ࠾ࡼࡧ᣺ື࣮ࣔࢻࡢ⡆᫆ホ౯ἲ㸪᪥ᮏᘓ⠏Ꮫ఍኱఍Ꮫ
⾡ㅮ₇᱾ᴫ㞟㸪ᵓ㐀 I㸪No.20111㸪2013.8㸪
(3) ኱⇃Ṋྖ㸪୰㎸ᛅ⏨㸪୸ᕝẚబኵ㸸ᙉ㢼࡟ࡼࡿ㗰ᵓ㐀㦵⤌ࡢ⣼✚⑂ປᦆയ ࡑࡢ 1, ࡑࡢ 2㸪᪥ᮏᘓ⠏Ꮫ఍኱఍Ꮫ⾡ㅮ₇᱾
ᴫ㞟㸪pp.75-78㸪1988(4) ᡂཎᘯஅ㸪Ἠ‶㸪ὸぢ㇏㸸㢼Ⲵ㔜࡟ᑐࡍࡿ㧗ᒙ㗰ᵓ㐀㦵⤌ࡢ⑂ປタィ㸪᪥ᮏᘓ⠏Ꮫ఍ᵓ㐀⣔ㄽᩥ㞟㸪
➨465ྕ㸪
pp.129-137㸪
1994.11~
ࡇࡢ㏆ఝᘧࢆ⏝࠸ࢀࡤ㸪୍⯡໬㉁㔞 M ࠾ࡼࡧ࣮ࣔࢻ

(5) Ᏻ஭ඵ⣖㸪኱⇃Ṋྖ㸪ᘅᕝ㞞୍㸪ྜྷỤ៞♸㸪୸ᕝẚబኵ㸸㧗ࡢ✚ศ್ ) ࡣࡑࢀࡒࢀ௨ୗࡢࡼ࠺࡟⾲ࢃࡍࡇ࡜ࡀ࡛ࡁ㸪ᒙᘓ⠏≀ࡢ⑂ປᦆയホ౯࡟୚࠼ࡿᙉ㢼≉ᛶࡢࣔࢹࣝ໬ࡢᙳ

ࡑࢀࡒࢀᩚ⌮ࡍࡿ࡜ᘧ(5.24)㸪ᘧ(2.25)࡟୍⮴ࡍࡿ㸬㡪࡟㛵ࡍࡿ◊✲㸪ࡑࡢ 1 ᙉ㢼≉ᛶࡢࣔࢹࣝ໬㸪᪥ᮏᘓ⠏Ꮫ~M఍኱఍Ꮫ⾡ㅮ₇᱾ᴫ㞟㸪pp.185-186㸪2001.9

UAl>(6) ᪥ᮏᘓ⠏Ꮫ఍㸸㢼࡜ᆅ㟈࡟ࡼࡿ⧞㏉ࡋⲴ㔜ຠᯝ࡜⑂ປᦆയ㸪u 1  k f 2 ³01 P 2pin x c dx c
 k 2f ³01 P 2fix x c dx c
 2 1  k f k f ³01 P pin P fix x c dx c@

1  k f ³01 P pin x c dx c  k f ³01 P fix x c dx c

)
xc
1

(A.1)

xl

(8) ኱⇃Ṋྖ㸪Ᏻ஭ඵ⣖㸪ྜྷỤ៞♸㸸⑂ປᦆയホ౯ࡢࡓࡵࡢᭀ㢼(A.2)(5.3)෌ᥖ

³0 P pin x c dx c

0.5

(A.3)

1

0.396478

(A.4)

2

2

³0 P fix x c dx c
1

³0 P pin P fix x c dx c
10.878228ࢩ࣏ࣥࢪ࣒࢘㈨ᩱ㸪2003(7) ᪥ᮏᘓ⠏Ꮫ఍㸸ᘓ⠏≀Ⲵ㔜ᣦ㔪࣭ྠゎㄝ(2004)(A.5)³0 P pin x c dx c

0.636619(A.6)

1³0 P fix x c dx c

0.523164

(A.7)

ཧ⪃ᩥ⊩
(1) ᓥᒸಇ㍜㸪኱⇃Ṋྖ㸪㭯ぢಇ㞝㸪Ᏻ஭ඵ⣖㸸⥅ᡭࢆ⪃៖ࡋࡓࡢ⣼✚స⏝᫬㛫ࡢ⡆᫆ホ౯᪉ἲ㸪⚄ዉᕝ኱ᏛᕤᏛ◊✲ᡤ ᡤሗ㸪➨ 35 ྕ㸪pp.30-36㸪2012(9) ⏣ᮧᖾ㞝㸸෇⟄ࡢ ບ᣺࡟㛵ࡍࡿ◊✲㸪ࡑࡢ 2ບ᣺⌧㇟ࡢࣔࢹࣝ໬㸪᪥ᮏᘓ⠏Ꮫ఍ㄽᩥሗ࿌㞟㸪280㸪pp.67-77㸪1979(10) ⏣ᮧᖾ㞝㸪኱㔝ᫀᙪ㸸෇⟄ࡢ ບ᣺࡟㛵ࡍࡿ◊✲㸪ࡑࡢ 3 㐃⥆యࡢ ບ᣺ࣔࢹࣝ㸪᪥ᮏᘓ⠏Ꮫ఍ㄽᩥሗ࿌㞟㸪337㸪
pp.65-72㸪1984(11) ኱⇃Ṋྖ㸪⚄⏣㡰㸪⏣ᮧᖾ㞝㸸ᘓ⠏≀ࡢ⪏㢼タィ㸪㮵ᓥฟ∧఍㸪2004(12) ᪥ᮏ㗰ᵓ㐀༠఍㸸㗰ᵓ㐀≀ࡢ⑂ປタィᣦ㔪࣭ྠゎㄝ㸪2012(13) ⏣▮⹡⏨㸸᣺ື࣭⾪ᧁࡢᇶ♏⌮ㄽ࡜ࣛࣉࣛࢫኚ᥮<ୖ>㸪Ꮫ఍ฟ∧ࢭࣥࢱ࣮㸪1984(14) ᯇ஭ṇᏹ㸪኱⇃Ṋྖ㸪⏣ᮧᖾ㞝㸪㣤ሙṇ⣖㸪➉୰ᗣ㞝㸪ྜྷỤ៞♸㸸⪏㢼タィ࡛⣼✚ⓗⲴ㔜ຠᯝࢆホ౯ࡍࡿࡓࡵࡢᙉ㢼࢖࣋ࣥࢺࡢ➼౯⥅⥆᫬㛫㸪᪥ᮏᘓ⠏Ꮫ఍኱఍Ꮫ⾡ㅮ₇᱾ᴫ㞟 B㸪
pp.85-86㸪2011.8

㗰⟶㒊ᮦࡢ⡆᫆࡞᣺ືᛶ≧ホ౯࡟㛵ࡍࡿ◊✲㸪ࡑࡢ 1. ᭷㝈(15) ᘓタ㟁Ẽᢏ⾡༠఍㸸㏻ಙ㕲ሪタィせ㡿࣭ྠゎㄝ㸪2003

せ⣲ἲ࡟ࡼࡿᅛ᭷್ゎᯒ㸪᪥ᮏᘓ⠏Ꮫ఍኱఍Ꮫ⾡ㅮ₇᱾ᴫ㞟㸪(16) Ẽ㇟ᗇ HPᵓ㐀 I㸪No.20110㸪2013.8㸪

(17) ᪥ᮏᮦᩱᏛ఍㸸⑂ປタィ౽ぴ㸪1995㛗᪉ᙧᙧ≧ࡢ㉸ఏᑟࢽ࢜ࣈࢺࣥࢿࣝ᥋ྜࡢ
㉸ఏᑟ㟁ὶ࡜᭷㝈㟁ᅽ㟁ὶࢫࢸࢵࣉࡢ㸰ḟඖ☢⏺≉ᛶ୰ᒣ ᫂ⰾ㸨   㜿㒊 ᫴㸨㸨   ✰⏣ ဴኵ㸨㸨㸨

Two-dimensional Magnetic Field Characteristics
of Superconducting Current and Current Steps at Finite voltage of Niobium junctions
Akiyoshi NAKAYAMA㸨

Susumu ABE㸨㸨

Tetsuo ANADA㸨㸨㸨㸯㸬⥴ゝ ࢪࣙࢭࣇࢯࣥ᥋ྜࡣᇶᮏⓗ࡟஧➃Ꮚࡢ⣲Ꮚ࡛࠶ࡿ㸬㉸ ㉸ఏᑟࡣ  ᖺ࣐࢝ࣜࣥ࢜ࢿࢫ࡟ࡼࡾ㸪⣙ . ௨ୗఏᑟࢹࣂ࢖ࢫཬࡧ㉸ఏᑟ㞟✚ᅇ㊰ࡣ㸪㉸ఏᑟయࣂࣜ࢔

࡛Ỉ㖟ࡢ᢬ᢠ್ࡀ ᐃ࡛ࡁ࡞࠸࡯࡝ᑠࡉࡃ࡞ࡿ࡜࠸࠺࠿

㉸ఏᑟయࡢᵓ㐀ࢆᇶᮏ࡜ࡍࡿ㸰➃Ꮚࡢࢪࣙࢭࣇࢯࣥ᥋ྜ

ࡓࡕ࡛ࡣࡌࡵ࡚Ⓨぢࡉࢀ࡚࠸ࡿ㸬ࡇࡢ㉸ఏᑟࡢ≉ᚩⓗ࡞ࢆ୰ᚰⓗ࡞ᵓᡂ⣲Ꮚ࡜ࡋ࡚౑࠸㸪ᅇ㊰ⓗ࡟ᕤኵࡍࡿࡇ࡜

ᛶ㉁࡜ࡋ࡚ࡣ

࡛ࡇࢀࡲ࡛✀ࠎࡢ㉸ఏᑟᅇ㊰ࡀ〇సࡉࢀ࡚ࡁ࡚࠸ࡿ㸬 L ㉸ఏᑟయෆࡢ☢᮰ᐦᗘࡀ㞽㸦཯☢ሙࡢຠᯝ࡛☢᮰⥺ ᡃࠎࡢࢢ࣮ࣝࣉ࡛ࡣ㸪ࢽ࢜ࣅ࣒࢘㔠ᒓࢆ౑ࡗࡓ㉸ఏᑟࡀ㉸㟁ᑟయࡢእ࡬ᢲࡋฟࡉࢀࡿ㸧ⷧ⭷ሁ✚㸪ࣂࣜ࢔ᒙ⏝ࡢ࢔࣑ࣝࢽ࣒࢘ࡢሁ✚࡜ࡑࡢ⮬↛LL ┤ὶ᢬ᢠࡢᾘ⁛㓟໬ࣉࣟࢭࢫࡢ᭱㐺໬㸪ཬࡧࣇ࢛ࢺࢢࣛࣇ࢕࣮࡜㝧ᴟ㓟

LLL ㉸ఏᑟయ࡛ࡘ࡞ࡀࢀࡓ᥋ྜ㛫ࡢᖸ΅ຠᯝ㸦㉸ఏᑟ໬᪉ἲࢆ౑ࡗࡓ᥋ྜ㒊Ỵᐃࣉࣟࢭࢫࡢᨵၿ࡟ࡼࡾ㸪㉸ఏ㔞Ꮚᖸ΅ィ㸦Superconducting Quantum Interferenceᑟ஧➃Ꮚ⣲Ꮚ࠾ࡼࡧ㉸ఏᑟᖸ΅ィᵓ㐀ࢆ〇సࡋ㸪ࡑࡢᇶ

Devices㸧࡜࠸࠺࠿ࡓࡕ࡛฼⏝㸧 ᮏ≉ᛶࢆ ᐃࡋ࡚࠸ࡿ㸬ࡉࡽ࡟እ㒊࠿ࡽຍ࠼ࡿ☢⏺ࢆ᥋

LY ࣮࢜ࢲࣃ࣓࣮ࣛࢱ࡟ࡼࡾ⾲ࡉࢀࡿ㉸ఏᑟ≧ែྜ㠃ෆ࡛㸰ḟඖ㉮ᰝࡋ㸪እ㒊☢⏺࡟ᑐࡍࡿ㉸ఏᑟ᥋ྜࡢY ㉸ఏᑟࢧࣥࢻ࢖ࢵࢳᵓ㐀࡛ࡢ㉸ఏᑟ㟁Ꮚ㸦ࢡ࣮ࣃ࣮㟁ὶ㟁ᅽ≉ᛶ࡜㉸ఏᑟ㟁ὶࡢ≉ᛶࢆ ᐃࡍࡿ᪂ࡋ࠸ ᐃᑐ㸧ࡢࢺࣥࢿࣝຠᯝ

ᡭἲࢆ㛤Ⓨࡋ࡚ࡁ࡚࠸ࡿ㸬ࡀ࠶ࡿ㸬≉࡟ᛶ㉁ Y ࡟ࡘ࠸࡚㸪࢖ࢠࣜࢫࡢࢣࣥࣈࣜࢵࢪ
኱ᏛࡢࢪࣙࢭࣇࢯࣥẶࡣ㸰ᯛࡢ㉸ఏᑟయ࡛ⷧ࠸㓟໬⭷ࢆ㸰㸬ᐇ㦂ᣳࢇࡔࢧࣥࢻ࢖ࢵࢳᵓ㐀࡛㟁ὶࡀὶࢀ࡚ࡶ㟁఩ᕪࡀ⏕ࡌ࡞࠸ࡇ࡜ࢆ  ᖺ⌮ㄽⓗ࡟ண᝿ࡋ㸪ࡇࡢ⌧㇟ࡣ⩣ᖺᐇ㦂

2.1 ⣲Ꮚ〇స⏝ࢫࣃࢵࢱࣜࣥࢢ⿦⨨ⓗ࡟ほ ࡉࢀ࡚࠸ࡿ㸬௨᮶ࡇࡢᵓ㐀ࡣࢪࣙࢭࣇࢯࣥ᥋ྜ ☢⏺ࢭࣥࢧ࣮➼ࢆᛂ⏝࡜ࡵࡊࡍ㉸ఏᑟ᥋ྜࡢ〇సࡢࡓ࡜࿧ࡤࢀࡿ㸬ࡵ࡟ࡣ㸪࣐ࢢࢿࢺࣟࣥࢫࣃࢵࢱࣜࣥࢢ⿦⨨ࢆ౑࠺㸬ヨᩱ஺᥮ࡣ࣮ࣟࢻࣟࢵࢡᐊࡢࡳࡢ┿✵ࢆ◚ࡿࡇ࡜࡟ࡼࡾ▷᫬*ᩍᤵ 㟁Ẽ㟁Ꮚ᝟ሗᕤᏛ⛉Professor, Electronics and Informatics Frontiers**෸ᩍᤵ 㟁Ẽ㟁Ꮚ᝟ሗᕤᏛ⛉Associate Professor, Electronics and Informatics Frontiers***ᩍᤵ 㟁Ẽ㟁Ꮚ᝟ሗᕤᏛ⛉Professor, Electronics and Informatics Frontiers㛫࡛࠾ࡇ࡞࠺ࡇ࡜ࡀ࡛ࡁࡿ㸬୺᤼Ẽࡣࢱ࣮࣎ศᏊ࣏ࣥࣉ
࡜ࢻࣛ࢖࣏ࣥࣉ࡛࠶ࡿ㸬
2.2 ☢⏺≉ᛶ ᐃ⿦⨨ ෇ᙧࢥ࢖ࣝ[࣒࣊ࣝ࣍ࣝࢶࢥ࢖ࣝ]ࢆ㸱ᑐ౑࠸㸪㹶㸪㹷㸪㹸᪉ྥࡢእ㒊☢⏺ࢆ⏕ᡂࡍࡿ㸬ࣃ࣮ࢯࢼࣝࢥࣥࣆ࣮ࣗࢱ

⚄ዉᕝ኱ᏛᕤᏛ◊✲ᡤᡤሗ ➨  ྕ࡟ࡼࡾ GPIB ไᚚࡉࢀࡓ┤ὶ㟁※࡟ࡼࡾࢥ࢖ࣝ࡟㟁ὶࢆ㛗᪉ᙧ abcd ࡟㙐஺ࡍࡿ☢᮰')ࡢ 2S/)0 ಸ࡛࠶ࡿࡇ࡜࡟

ὶࡍ࡜㸪ࡑࡢ㟁ὶ࡟ẚ౛ࡋ࡚☢⏺ࡀ⏕ࡌࡿ㸬ࣉࣟࢢ࣒ࣛ

࡞ࡿ㸬ᩘᘧ࡛᭩ࡃ࡜ ࣇ࢓࢖࡛ࣝ࠶ࡽ࠿ࡌࡵタᐃࡋࡓ࢔ࣝࢦࣜࢬ࣒࡟ࡼࡾ㸪እ㒊☢⏺ࢆṇ☜࡟⏕ᡂࡋ㸪ࢹࢪࢱࣝ࢜ࢩࣟࢫࢥ࣮ࣉ࡛㟁ὶ-'J㟁ᅽ≉ᛶࢆィ ࡍࡿࡇ࡜ࡀྍ⬟࡜࡞ࡿ㸬

2S)00')      ࡛࠶ࡿ㸬≉࡟㸪㛗᪉ᙧ abcd ࡟㙐஺ࡍࡿ☢᮰ࡀ☢᮰㔞Ꮚ㸱㸬እ㒊☢⏺࡟ࡼࡿ㉸ఏᑟ㟁ὶࡢኚㄪ

)0 㸯 ಶ ศ ࡛ ࠶ ࢀ ࡤ 㸪 ఩ ┦ ࡢ ቑ ศ ࡣ 2S ࡛ ࠶ ࡿ 㸬iࠕ㠀ᖖ࡟ⷧ࠸⤯⦕⭷ࢆᣳࢇ࡛㸰ࡘࡢ㉸ఏᑟయࡀ࠶ࡿ࡜

sinJ

࡟ࡼࡾ㸪᥋ྜ඲య࡟ࡘ࠸࡚᥋ྜෆࡢྛⅬ࡛ࡁ㸪㸰ࡘࡢ㉸ఏᑟయࡢ㛫࡟㟁ὶࡀὶࢀ࡚࠸࡚ࡶ㸪㸰ࡘࡢࡢ㟁ὶ್ࡢ࿴ࢆ࡜ࡿࡇ࡜࡟ࡼࡾ㸪୚࠼ࡽࢀࡓ☢⏺࡟࠾ࡅ㉸ఏᑟయࡢ㛫ࡢ㟁఩ᕪࡀ㸮࡛࠶ࡾ࠺ࡿ࡜࠸࠺⌧㇟ࠖࡀ㸪ࡿ᥋ྜࢆὶࢀࡿ㟁ὶࡀᚓࡽࢀࡿ㸬≉ู࡞ሙྜ࡜ࡋ࡚㸪እࢪࣙࢭࣇࢯࣥ࡟ࡼࡾ⌮ㄽⓗ࡟ணゝࡉࢀ㸪⩣ᖺᐇ㦂࡟ࡼࡾ㒊☢⏺ࡀ࡞ࡅࢀࡤ㸪ࡇࡢ఩┦ᕪࡣ㸪᥋ྜෆ୍࡛ᐃ࡛㸪≉☜࠿ࡵࡽࢀ㸪
ࢪࣙࢭࣇࢯࣥຠᯝ࡜࿧ࡤࢀࡿࡇ࡜࡟࡞ࡗࡓ㸬࡟S/2 ࡢ࡜ࡁ㸪᭱኱ࡢ㟁ὶ Ic ࡀ᥋ྜࢆὶࢀࡿ㸬ࡇࡢ Ic ࡣࡇࡢ⌧㇟ࡣ㸪ゝ࠸᥮࠼ࡿ࡜㸪୍᪉ࡢ㉸ఏᑟయ࠿ࡽ௚᪉ࡢ

᥋ྜࡢ⮫⏺㟁ὶ್࡜ࡶ࿧ࡤࢀࡿ㸬㉸ఏᑟయ࡬㸪㟁Ꮚࡢࡳ࡞ࡽࡎ㸪࠸ࢃࡤ㸪㉸ఏᑟ㟁Ꮚᑐ㸦ࢡ ࡇࡢࡼ࠺࡟እ㒊࠿ࡽ☢⏺ࢆຍ࠼ࡿࡇ࡜࡟ࡼࡾ㸪ࢧࣥࢻ࣮ࣃ࣮ᑐ㸧ࡶࢺࣥࢿࣝࡍࡿ࡜࠸࠺ࢃࡅ࡛࠶ࡿ㸬࢖ࢵࢳᆺ㉸ఏᑟ᥋ྜࢆὶࢀࡿ㉸ఏᑟ㟁ὶࡣኚㄪࡍࡿ㸬ࡇ ࢧࣥࢻ࢖ࢵࢳᙧࡢ㉸ఏᑟ᥋ྜࢆ㟁ὶࡀὶࢀ࡚ࡶ㸪஧ࡘࡢ࡜ࡁ㸪ࢧࣥࢻ࢖ࢵࢳᆺ㉸ఏᑟ᥋ྜࡢ㓟໬⭷ࣂࣜ࢔⮬యࡢ㉸ఏᑟ㟁ᴟ㛫࡟㟁఩ᕪࡣ⏕ࡌ࡞࠸㸬ࡇࡢ࡜ࡁ㸪㸰ࡘࡢࢆᶓษࡿ⤒㊰࡟ἢࡗ࡚ࡢࢤ࣮ࢪ୙ኚ࡞఩┦ᕪࡣ㸪ࣂࣜ࢔㉸ఏᑟయ㛫࡟㟁఩ᕪ࡞ࡋ࡛㸪࠸ࡃࡽ࡛ࡶ኱ࡁ࡞㟁ὶࢆὶෆ㒊ࡢ☢⏺ࡢྥࡁ࡟ᆶ┤࡞᪉ྥ࡟✵㛫ⓗ࡟ኚㄪࡍࡿࢃࡅ

ࡏࡿࢃࡅ࡛ࡣ࡞ࡃ࡚㸪ὶࡋ࠺ࡿ࠶ࡿୖ㝈ࡢ್ࡀ࠶ࡿ㸬㸰࡛࠶ࡿ㸬ࡇࡢኚㄪ࿘ᮇࡣຍ࠼ࡿ☢⏺ࡢ኱ࡁࡉ࡟཯ẚ౛ࡍࡘࡢ㉸ఏᑟయࢆୗ㒊ࡢ㉸ఏᑟయ㟁ᴟཬࡧୖ㒊ࡢ㉸ఏᑟయࡿ㸬ࡇࡢࡼ࠺࡞ࢃࡅ࡛㸪㉸ఏᑟࢪࣙࢭࣇࢯࣥࢺࣥࢿࣝ㟁㟁ᴟ࡜࿧ࡪࡇ࡜࡟ࡍࡿ࡜㸪ࡇࡢୗ㒊㉸ఏᑟయ㟁ᴟ࠿ࡽୖὶࡢኚㄪ≉ᛶ࠿ࡽ㸪ࢺࣥࢿࣝࣂࣜ࢔ࡑࡢࡶࡢࡢ୍ᵝᛶ➼㒊㟁ᴟ࡟ྥ࠿ࡗ࡚㸪᥋ྜࢆ㟁఩ᕪ࡞ࡋ࡛ὶࢀࡿ㟁ὶ i ࡣ㸪

ࢆ デ ᩿ ࡍ ࡿ ࡇ ࡜ ࡀ ࡛ ࡁ ࡿ [1] 㸬 ࡇ ࢀ ࡲ ࡛ quartic஧ࡘࡢ㉸ఏᑟయ㟁ᴟ㛫ࡢࠕ㸦ࢤ࣮ࢪ୙ኚ࡞㸧఩┦ᕪJࠖࡢ

polynomial

sin ࡟ẚ౛ࡋ㸪    

normal-distribution-function ᙧ[4] ࡢ᥋ྜ࡟ࡘ࠸࡚ㄪ

sinJ࡭ࡽࢀ࡚ࡁ࡚࠸ࡿ㸬ࡓࡔࡋࡇࢀࡲ࡛㸪ࡇࡢࡼ࠺࡞☢⏺≉i              ࡢ㛵ಀࡀᡂࡾ❧ࡘ㸬ᇶ‽࡜࡞ࡿୗ㒊ࡢ㟁ᴟෆࡢ௵ពࡢⅬᙧ [2,3] ࡸ 㹶 ⥺ ゎ ᯒ ࡢ ࡓ ࡵ ࡢᛶࡣእ㒊☢⏺ࢆ୍ḟඖ᪉ྥ࡟㉮ᰝࡋ࡚ㄪ࡭ࡽࢀ࡚ࡁ࡚࠸
ࡿࡢࡀ⌧≧࡛࠶ࡿ㸬ࡇࢀ࡟ᑐࡋ࡚ᡃࠎࡣ㸰᪉ྥ㸪㸱᪉ྥa ࡢ࣮࢜ࢲࣃ࣓࣮ࣛࢱࡢ఩┦ࢆT(a)㸪ࡇࡢⅬ a ࠿ࡽᆶ┤࡟እ㒊☢⏺ࢆ㉮ᰝࡋ㸪Ic-H (Hx, Hy) ≉ᛶࢆㄪ࡭ࡿࡇ࡜ࢆ

࡟㓟໬⭷ࣂࣜ࢔ࢆᶓษࡗ࡚㸪ࡶ࠺୍᪉ࡢୖ㒊ࡢ㟁ᴟෆ࡟ᥦ᱌ࡋ࡚࠸࡚㸪ᐇ㝿࡟ᩘ್ゎᯒ࡜㸪ࡉࡲࡊࡲ࡞᥋ྜᙧ≧ධࡾⅬ b ࢆ⪃࠼ࡿ㸬ࡑࡢⅬࡢ఩┦ࢆT(b)࡜ࡋ࡚࠸ࡿ㸬᥋ࡢ⣲Ꮚ〇స㸪ᐇ㦂࡟ࡼࡾ ᐃ࡟ᡂຌࡋ࡚࠸ࡿ㸬ྜ㠃ࢆᆶ┤࡟ᶓษࡿ⤒㊰࡟ἢࡗࡓࢤ࣮ࢪ࡟ࡼࡽ࡞࠸ࠕࢤ
㸲㸬㛗᪉ᙧ᥋ྜࡢ㉸ఏᑟ㟁ὶ࣮ࢪ୙ኚ࡞఩┦ᕪJࠖࡣ㸪J

T b T a 

2S

ґ³ A  ds    )00 㸰᪉ྥ࡟እ㒊☢⏺ࢆ㉮ᰝࡋࡓ࡜ࡁ㸪᥋ྜ࡟ὶࢀࡿ㉸ఏᑟ㟁ὶࡀኚㄪࡉࢀࡿᵝᏊࢆ㸪㛗᪉ᙧࡢ᥋ྜࢆ౛࡟⪃࠼࡚࡛࠶ࡿ㸬ࡇࡇ࡛ࢤ࣮ࢪ୙ኚ࡞఩┦ᕪJࡢ๓༙ࡣ㸪ୖ㒊㟁ᴟࡳࡿ㸬〇సࡋࡓ㛗᪉ᙧࡢ᥋ྜࡢᵓ㐀ࢆᅗ㸯࡟♧ࡍ㸬⣲Ꮚ

ࡢⅬ b ࡢ఩┦T(b)࡜㸪ᇶ‽࡜࡞ࡿୗ㒊㟁ᴟࡢⅬ a ࡢ࣮࢜ࡣ࣐ࢢࢿࢺࣟࣥࢫࣃࢵࢱࣜࣥࢢἲ࡟ࡼࡾᡂ⭷ࡋࡓࡑࢀࡒ

ࢲࣃ࣓࣮ࣛࢱࡢ఩┦T( a)ࡢᕪ࡛࠶ࡿ㸬ᚋ༙ࡣⅬ a ࠿ࡽᆶࢀ 300,5,150nm ࡢࢽ࢜ࣅ࣒࢘/࢔࣑ࣝࢽ࣒࢘-࢔࣑ࣝࢽ࢘

┤࡟㓟໬⭷ࣂࣜ࢔ࢆᶓษࡗ࡚㸪ࡶ࠺୍᪉ࡢ㟁ᴟࡢⅬ b ࡲ࣒㓟໬⭷/ࢽ࢜ࣅ࣒࢘ࡢࢧࣥࢻ࢖ࢵࢳᵓ㐀࡛࠶ࡿ㸬࢔࣑࡛ࣝࡢ⤒㊰࡟ἢ࠺㟁☢ሙࡢ࣋ࢡࢺ࣏ࣝࢸࣥࢩࣕࣝAࡢ⥺✚ࢽ࣒࢘㓟໬⭷ࡣ㸪࢔࣑ࣝࢽ࣒࢘ⷧ⭷ሁ✚ᚋ㸪㓟໬ᐊ࡛⣧ศࡢ㡯ࡀධࡗ࡚࠸ࡿ㸬ࡉࡽ࡟㸪ୖ㒊㟁ᴟࡢⅬ c ࡜ୗ㒊㟁㓟⣲ࢆᑟධࡋ࡚⾲㠃ࢆ㓟໬ࡋᙧᡂࡋࡓ㸬ᅗ 1 ࡟♧ࡍ L

ᴟࡢⅬ d ࢆ㸲Ⅼ abcd ࡀ㛗᪉ᙧ abcd ࡟࡞ࡿࡼ࠺࡟⪃࠼࡚

W=150ȣm75ȣm ࡢ᥋ྜᑍἲࡣ㸪࣏ࢪࣞࢪࢫࢺ࡜ࢥ

ࡳࡿ㸬ࡇࡢ࡜ࡁ㸪⤒㊰ dc ࡟ἢ࠺ࢤ࣮ࢪ୙ኚ࡞఩┦ᕪJࡢ㸪ࣥࢱࢡࢺᘧ࣐ࢫࢡ࢔ࣛ࢖ࢼ࣮ࢆ౑ࡗࡓࣇ࢛ࢺࣜࢯࢢࣛࣇ

⤒㊰ ab ࡟ἢ࠺ࢤ࣮ࢪ୙ኚ࡞఩┦ᕪJ࡟ᑐࡍࡿᕪศ'Jࡣ㸪࢕࣮ᚋ࡛ࡢ⁐ᾮ୰ࡢ㝧ᴟ㓟໬ἲ࡛Ỵࡵࡓ㸬㛗᪉ᙧᙧ≧ࡢ㉸ఏᑟࢽ࢜ࣈࢺࣥࢿࣝ᥋ྜࡢ㉸ఏᑟ㟁ὶ࡜᭷㝈㟁ᅽ㟁ὶࢫࢸࢵࣉࡢ㸰ḟඖ☢⏺≉ᛶᐃࡣ GPIB (General Purpose Interface Bus)ࢩࢫࢸ࣒࡛
ไᚚࡉࢀࡓ㟁※࡟ࡼࡾ㸪᭱኱ 3000A/m ࡢ☢⏺ࢆⓎ⏕ࡉࡏ



)x)y
O  )0  P   ) 0)0  Q   ) 0 ࡿࡇ࡜ࡀ࡛ࡁࡿ࣒࣊ࣝ࣍ࣝࢶࢥ࢖ࣝᑐ࡟㟁ὶࢆὶࡋࡓ㸬⣲Ꮚ࡟ຍ࠼ࡿእ㒊☢⏺ࢆ㝵ẁⓗ࡟ኚ໬ࡉࡏࡿࡇ࡜࡛㸰ḟඖⓗ☢⏺≉ᛶ ᐃࢆ࠾ࡇ࡞ࡗࡓ㸬 ᐃࡣᾮయ࣒࣊ࣜ࢘୰
4.2K ࡛࠶ࡿ㸬

15

H
H

75
Pm

m
0P

Hy

Hy

Hx

H
Hx

T   ) 0  L   ) 0)0  N   ) 0 

Nb
AlOx
Nb
H
Hy

H

Hx

Hx

H   )0  ]   ) 0)0  K   ) 0 

Hx

Hy

Hy

H

ᅗ 㸬㛗᪉ᙧ᥋ྜ
እ㒊☢⏺ࡣ᥋ྜ㠃ෆ࡛㸪ࡑࢀࡒࢀࡢ㎶࡟ᖹ⾜࡟ +[+\ ᡂศ࡜ࡍࡿ㸬(mA)

Josephson current

9.0

Magnetic Field Hy (A/m)

400

H
Hy

Hy

H
Hx

H
Hx

E   ) 0  J   ) 0)0  G   ) 0

6.0
0

-400
-400

3.0

0.0
0

Hy

Hy

H

H
Hx
(A/cm2)+80D  )x)y   400

Magnetic Field Hx (A/m)
0ᅗ㸰㸬㛗᪉ᙧࡢ᥋ྜࡢ Ic-H (Hx, Hy)☢⏺≉ᛶࡢ ᐃ⤖ᯝ ᩘ್ゎᯒࡋࡓᅗ㸲ࡢᩘ್ゎᯒ⤖ᯝ࡜ࡢ୍⮴ࡣⰋ࠸࡜࠸࠼ࡿ. ࡸࡸᐇ㦂⤖ᯝ

Hy

Hx

-80

ࡢ᪉ࡀ୸ࡳࢆᖏࡧ࡚࠸ࡿࡢࡣ㸪ᐇ㝿࡟స〇ࡋࡓ᥋ྜࡢᙧࡢ࠿࡝ࡀ
୸ࡳࢆᖏࡧ࡚࠸ࡿࡇ࡜ࡢ཯࡛ᫎ࠶ࡿ.
ᅗ㸱㸬እ㒊☢⏺ࢆຍ࠼ࡓ࡜ࡁࡢ㛗᪉ᙧ᥋ྜෆࡢ㉸ఏᑟ᥋ྜ㟁ὶศᕸ⚄ዉᕝ኱ᏛᕤᏛ◊✲ᡤᡤሗ ➨  ྕ ࡇࡢ㉸ఏᑟ᥋ྜࡀ㛗᪉ᙧࡢሙྜࡢ Ic-H (Hy, Hz)☢⏺≉)0) ,  G ࡛ࡣ , )0)࡛࠶ࡿ㸬ࡇࡢሙྜࡣJ 2 =S࡛ᛶࡢ ᐃ⤖ᯝࢆᅗ㸰࡟♧ࡍ㸬᭱኱ࡢ᥋ྜ㟁ὶ್ࢆ࡜ࡿࡇ࡜࡟࡞ࡿ㸬ࡉࡽ࡟☢⏺ࢆቑࡸ ࡇࡢ ᐃ⤖ᯝࢆㄝ᫂ࡍࡿ࡟ࡣ㸪๓ࡢ➨㸱⠇࡛⪃࠼ࡓࡼࡋ࡚㸪 )x, )y ࡀ (H)࡛ࡣ  )0) (] ࡛ࡣ )0, )0) (K)࡛ࡣ

࠺࡟㸪᥋ྜ㠃ෆ࡟࠾࠸࡚እ㒊☢⏺࡟ᆶ┤࡞ྥࡁ࡟᥋ྜ㟁,)0)࡛࠶ࡿ㸬ࡇࡢ㸱౛࡛ࡣ㸪ኚㄪ࿘ᮇࡀࡕࡻ࠺࡝᥋ྜᑍ

ὶࡀ✵㛫ኚㄪࡋ࡚࠸ࡿ࡜௬ᐃࡍࡿ㸬✀ࠎࡢྥࡁཬࡧ኱ࡁ

ἲ࡟࡞ࡿࡢ࡛㸪 J 2 ࡢ್࡟ࡼࡽࡎ᥋ྜ㟁ὶ್ࡣ㞽࡛࠶ࡿ㸬ࡉࡢእ㒊☢⏺ࢆ㛗᪉ᙧ᥋ྜࡢ᥋ྜ㠃࡟ຍ࠼ࡓ࡜ࡁࡢ㸪᥋ࡉࡽ࡟㸪 )x, )y  ࡣ(T ࡛  )0), N ࡛ )0, )࡟࡞ࡿ

ྜ㠃ෆࡢ㉸ఏᑟ㟁ὶࡢศᕸࢆᅗ 3 ࡟♧ࡍ㸬㟁☢ሙࡢ࣋ࢡ࡜ኚㄪ࿘ᮇࡀ(2/3)L ࡟࡞ࡾ㸪࠾࠾ࡼࡑJ 2 = Sࡢ࡜ࡁ≉ࢺ࣏ࣝࢸࣥࢩࣕࣝA ࡢ࿘ᅇ✚ศࡣࡑࡢ୰ࢆ㈏ࡃ☢᮰㔞࡟ᛶ඲య࠿ࡽࡳ࡚㸰␒┠࡟኱ࡁ࡞ᴟ኱್࡟࡞ࡿ㸬ࡲࡓ㸪(L➼ࡋ࠸ࡢ࡛㸪௬࡟ x ᪉ྥ࡟☢⏺ࢆຍ࠼ࡓሙྜࡣ㸪᥋ྜྛ࡛ࡣ )x, )y  = )0, )0)࡛࠶ࡿࡀ㸪J 2 =S࡟࠾࠸࡚

㒊ࡢ఩┦ᕪ࡜㟁ὶᐦᗘࡣ y ᪉ྥ࡟ኚㄪࡉࢀࡿ㸬y ᪉ྥ࡟ᴟ኱್ࢆ࡜ࡿ.

☢⏺ࢆຍ࠼ࡓሙྜࡣ㸪᥋ྜྛ㒊ࡢ఩┦ᕪ࡜㟁ὶᐦᗘࡣ x ࡇࡢࡼ࠺࡟ศᕸࡍࡿ㉸ఏᑟ㟁ὶࢆ㛗᪉ᙧࡢ᥋ྜ඲య࡟

᪉ྥ࡟ኚㄪࡉࢀࡿࡇ࡜࡟࡞ࡿ㸬ࡲࡓ㸪ࡑࡢ✵㛫ኚㄪἼ㛗ࡘ࠸࡚ྜィࡍࡿ࡜㸪᥋ྜࢆὶࢀࡿ㉸ఏᑟ㟁ὶࢆᩘ್࡜ࡋ

ࡣ㸪ຍ࠼ࡿ☢⏺ࡢ኱ࡁࡉ࡟཯ẚ౛ࡍࡿ㸬࡚ồࡵࡿࡇ࡜ࡀ࡛ࡁࡿ㸬ࡑࡢ⤖ᯝࢆᅗ㸲࡟♧ࡍ㸬ᩘ್ゎᯒࡋࡓ⤖ᯝ࡜ᐇ㦂⤖ᯝࡢ୍⮴ࡣⰋ࠸㸬ᐇ㝿࡟స〇ࡋࡓ᥋ྜ࡛ࡣ㸪ࣞࢪࢫࢺࡢゅࡀ୸ࡃ࡞ࡾ㸪᥋ྜ⮬యࡶ୸ࡳࢆᖏ
ࡧ࡚࠸ࡿࡇ࡜࡟ࡼࡾ㸪≉ᛶࡑࡢࡶࡢࡶࡸࡸᐇ㦂⤖ᯝࡢ᪉ࡀ୸ࡳࢆᖏࡧ࡚࠸ࡿ㸬㸳㸬㟁ὶ㟁ᅽ≉ᛶࡢ᭷㝈㟁ᅽ࡛ࡢ㟁ὶඹ᣺ࢫࢸࢵࣉ ḟ࡟㟁ὶ㟁ᅽ≉ᛶࡢ᭷㝈㟁ᅽ࡟⌧ࢀࡿඹ᣺ࢫࢸࢵࣉ࡟
ࡘ࠸࡚ࡶ ᐃࡋࡓ㸬ᅗ 5 ࡟♧ࡍࡼ࠺࡟㸪㟁ὶ㟁ᅽ≉ᛶ࡟࠾࠸࡚ཧ↷㟁ᅽ Vr ࢆỴࡵࡇࡢ㟁ᅽࢆ୰ᚰ࡜ࡋ࡚s20ȣVࡢ⠊ᅖࡢ㟁ὶࡢ᭱኱್࡜᭱ᑠ್ࡢᕪࢆ㟁ὶࢫࢸࢵࣉ㧗ࡉ࡜ᐃ⩏ࡋࡓ㸬

I
search window
Ic
I-V CurveV
Vr resonant voltageᅗ㸳 ㉸ఏᑟ᥋ྜࡢ I-V ≉ᛶ࡟⌧ࢀࡿ㟁ὶࢫࢸࢵࣉ ᅗ㸴࡟ࡣ I-V ≉ᛶୖࡢࡢ㟁ὶࢫࢸࢵࣉ㧗ࡉࡀ㸪እ㒊࠿ࡽຍ࠼ࡓ☢⏺࡟ࡼࡾኚࢃࡿᵝᏊ(㸰ḟඖ☢⏺౫Ꮡᛶ)ࢆ♧ࡍ㸬ඹ᣺ࢫࢸࢵࣉࡢ⌧ࢀࡿ㟁ᅽ Vr (ᅗ 5 ཧ↷)ࢆࣃ࣓࣮ࣛ
ᅗ 4㸬㛗᪉ᙧ᥋ྜࢆὶࢀࡿ㉸ఏᑟ㟁ὶࡢᩘ್ゎᯒ⤖ᯝ ᅗ 3 ࡟࠾࠸࡚ )x, )y ࡣࡑࢀࡒࢀ᥋ྜࣂࣜ࢔㡿ᇦࢆ x᪉ྥ࠾ࡼࡧ y ᪉ྥ࡟㈏ࡃ☢᮰㔞࡜ࡍࡿ㸬)㸮ࢆ☢᮰㔞Ꮚh/(2e)࡜ࡋ࡚㸪(E ࡛ࡣ )x, )y =  )0) , J ࡛ࡣ )0,ࢱ࡜ࡋ࡚ኚ࠼࡚ ᐃࡋࡓ⤖ᯝࡀᅗ 6(a)-(l)࡛࠶ࡿ㸬㛗᪉ᙧᙧ≧ࡢ㉸ఏᑟࢽ࢜ࣈࢺࣥࢿࣝ᥋ྜࡢ㉸ఏᑟ㟁ὶ࡜᭷㝈㟁ᅽ㟁ὶࢫࢸࢵࣉࡢ㸰ḟඖ☢⏺≉ᛶ

Magnetic Field Hy (A/m)

400



(mA)

(e) Vr = 0.32(mV)

1.0

0

0.5

-400

0.0

Magnetic Field Hy (A/m)

400(f) Vr = 0.36 (mV)

0

-400

Magnetic Field Hy (A/m)

400(g) Vr = 0.40 (mV)

0

-400

Magnetic Field Hy (A/m)

400(h) Vr = 0.44 (mV)

0

-400
-400

0

Magnetic Field Hx (A/m)

400⚄ዉᕝ኱ᏛᕤᏛ◊✲ᡤᡤሗ ➨  ྕMagnetic Field Hy (A/m)

400

(mA)

(i) Vr = 0.48 (mV)

1.0

0

0.5
'y

'x

V(x,y'y)

-400

0.0

'y

Jy(x,y2'x

Jx(x,y)2

V(x'x,y)L(j) Vr = 0.52 (mV)

C

400

Magnetic Field Hy (A/m)(a)Vr=0.16mV ࡼࡾ(l)Vr=0.60mV ࡲ࡛⣲Ꮚࡢ㟁ὶ㟁ᅽ≉ᛶୖ࡛ඹ᣺ࢫࢸࢵࣉࡢ⌧ࢀࡿ㟁ᅽࢆࣃ࣓࣮ࣛࢱ࡜ࡋ࡚࠸ࡿ㸬I0

V(x,y)L

V(x,y'y)'yJy(x,y)2'x
Jx(x-,y)
2

0

C

I0

L
C

V(x'x,,y)

C

L

C

I0
y

I0

x

-400

Magnetic Field Hy (A/m)

400(k) Vr = 0.56 (mV)

ᅗ 7 ศᕸࡍࡿ L,C ཬࡧ㉸ఏᑟ᥋ྜ I0 せ⣲࠿ࡽ࡞ࡿ➼౯ᖹ㠃ᅇ㊰᭷㝈㟁ᅽࢫࢸࢵࣉࡣᅗ㸵࡟♧ࡍศᕸ /& ᅇ㊰࡟㉸ఏᑟ≉᭷ࡢ᥋ྜせ⣲㸦᥋ྜ⮫⏺㟁ὶ ,㸧ࢆ㏣ຍࡋࡓ➼౯ᅇ㊰࡛ゎᯒࡋࡓ㸬ᅗ㸵࡟♧ࡍࡼ࠺࡟㸪ࢧࣥࢻ࢖ࢵࢳᆺ㉸ఏᑟ᥋ྜࡣୖୗ

0ࡢ㉸ఏᑟ㟁ᴟ࡟ᣳࡲࢀࡓ㸪୍✀ࡢᖹ㠃ᅇ㊰࡛࠶ࡾ㸪኱㉺ඛ⏕ࡢࡈᥦ᱌ࡢ➼౯ᅇ㊰࡟㉸ఏᑟ᥋ྜせ⣲ࢆຍ࠼࡚㸪㧗࿘Ἴ➼౯ᅇ㊰ࢆᚓࡿ㸬ᅗ㸶࡟ࡣ㸪᭷㝈㟁ᅽ࡛ࡢ㟁ὶࢫࢸࢵࣉࢆ⏕ࡌࡉࡏࡿඹ

-400

Magnetic Field Hy (A/m)

400᣺࣮ࣔࢻࡢ᥋ྜෆ㟁ᅽศᕸࢆ♧ࡍ㸬ᅗ㸶ࡢୖഃࡣ㸪ᅗ 6(c)(l) Vr = 0.60 (mV)ࡢ୰࡛D1 ࡜D2 ࡛♧ࡋࡓඹ᣺࣮ࣔࢻ(1,0)ࢆㄝ᫂ࡍࡿ㸬ࡇࡢ࡜ࡁ㸪㙐஺☢᮰()x, )y)=())࡛࠶ࡾ㸪᥋ྜྛ㒊ࡢ㟁ᅽ Vࡣ఩┦ᕪࡢ᫬㛫ᚤศ࡟ẚ౛ࡋ㸪㟁ᅽ V ࡢᐃᅾἼࡣ᥋ྜෆࡢ y ᪉ྥ࡟୍Ἴ㛗࠶ࡿࡇ࡜࡟࡞ࡿ㸬ᅗ 8 ࡛ᅗࡢᕥഃࡣᇶ
‽᫬้ t=0㸪ྑഃࡣඹ᣺࿘ᮇࡢ༙ศࡔࡅᚋࡢ᫬้ࡢ᥋ྜ

0

-400
-400

ෆࡢᵝᏊ࡛࠶ࡿ㸬ᅗ(a1-a2)ࡣእ㒊☢⏺ࡢࡳࢆ♧ࡋ㸪☢᮰㔞Ꮚ㸯ಶศࡀ㙐஺ࡋ࡚࠸ࡿ㸬ᅗ(b1-b2)ࡣࡇࡢእ㒊☢⏺ࢆ㝖࠸ࡓඹ᣺࣮ࣔࢻࢆ♧ࡋ㸪୧⪅ࡢ࿴ࡀᅗ(c1-c2)࡛࠶ࡿ㸬ᅗ(d1-d2)ࡣ᥋ྜ㟁ὶࡢ᥋ྜෆศᕸࢆ♧ࡍ㸬ṇ᪉ྥࡢ㟁ὶ㡿ᇦࡀඹ᣺ࡢ⤖ᯝ㸪ቑ࠼࡚࠸ࡿࡇ࡜ࡀࢃ࠿ࡿ㸬
0400

Magnetic Field Hx (A/m)ᅗ㸴 ᭷㝈㟁ᅽࡢ㟁ὶࢫࢸࢵࣉࡢ ᐃ㛗᪉ᙧᙧ≧ࡢ㉸ఏᑟࢽ࢜ࣈࢺࣥࢿࣝ᥋ྜࡢ㉸ఏᑟ㟁ὶ࡜᭷㝈㟁ᅽ㟁ὶࢫࢸࢵࣉࡢ㸰ḟඖ☢⏺≉ᛶ⪃࠼ࡽࢀࡿ㸬
ࡉࡽ࡟㸪ཧ↷㟁ᅽ Vr ࡀ 0.52 mV ௨ୖࡢ⠊ᅖ࡛ࡣᅗ㸴ࡼࡾ㸪ඹ᣺㟁ὶࢫࢸࢵࣉࡢ☢⏺ H (Hx, Hy)౫Ꮡᛶࡣ࠾࠾ࡼ
ࡑ➼᪉ⓗ࡟࡞ࡿࡼ࠺࡟ࡳ࠺ࡅࡽࢀࡿ㸬᥋ྜࢪࣙࢭࣇࢯࣥ
㟁ὶࡢ఩┦㏿ᗘࡀࣂࣜ࢔㡿ᇦࡢ㟁☢Ἴࡢ఩┦㏿ᗘ c ࡜୍⮴ࡋࡓ࡜ࡁඹ᣺ࡀⓎ⏕ࡍࡿࡢ࡛㸪≉࡟㟁ᅽࡀẚ㍑ⓗ኱ࡁࡃ✵㛫Ἴ㛗ࡀᑠࡉ࠸㡿ᇦ࡛㸪᭱኱ࡢ㟁ὶࢫࢸࢵࣉࡢ⌧ࢀࡿඹ᣺㟁ᅽࡣእ㒊࠿ࡽࡢ༳ຍ☢⏺ࡢ኱ࡁࡉ࡟ẚ౛ࡍࡿ㸬 ࡞࠾㸪ᅗ 1-ᅗ 8 ࡣᩥ⊩[14]ࡼࡾᘬ⏝ࡋࡓ㸬 ᮏඹྠ◊✲ࡢᶵ఍ࢆ୚࠼࡚ࡃࡔࡉࡗࡓ⚄ዉᕝ኱ᏛᕤᏛ
◊✲ᡤ࠾ࡼࡧᕤᏛ◊✲ᡤᡤ㛗㸪ඹྠ◊✲ᑂᰝጤဨ఍࡟ឤ
ㅰ࠸ࡓࡋࡲࡍ㸬ཧ⪃ᩥ⊩(1) A. Barone and G. Paterno, "Physics and Applications of the Josephson
Effect," Wiley-Interscience, New York, (1982)(2) R.L. Peterson, Cryogenics, Vol. 31, Pages 132- ( 1991)(3) J. G. Gijsbertsen, E.P. Houwman, B.B.G. Klopman, J. Flokstra, H.
Rogalla, D. Quenter, S. Lemke, Physica Vol. C249, Pages 12- (1995)(4) K. Kikuchi, H. Myoren, T. Iizuka, S. Takada, Appl. Phys. Lett., Vol.77,
Pages.3660- (2000)(5) Akiyoshi Nakayama, Susumu Abe, Tatsuyuki Morita, Makoto Iwata,
and Yusuke Yamamoto, IEEE Trans.Mag.,Vol.36, Pages 3511-(2000)(6) A.Nakayama, S.Abe, T.Shoji, R.Aoki, and N.Watanabe, Physica Vol.
B329-333, Pages 1493- (2003)(7) Norimichi Watanabe, Akiyoshi Nakayama, Susumu Abe, Kunimori
Aizawa, J. Appl. Phys., Vol.97, Pages 10B116 1- May (2005)(8) N.Watanabe, A.Nakayama, S.Abe, K.Aizawa, J. Appl. Phys., Vol. 97,
Pages 10B116- (2005)(9) Akiyoshi NAKAYAMA, Susumu ABE, Tetsuya SHIMOYAMA,
Norimichi WATANABE,

Hsu Jui-Pang and Yoichi OKABE,

J.Phys.Conf.Ser.Vol. 43 Pages 1092- (2006)(10) N.Watanabe, A.Nakayama, S.Abe, J. Appl. Phys., Vol. 101, Pagesᅗ㸶 ඹ᣺ࢫࢸࢵࣉࡢ᥋ྜෆ㟁☢⏺ศᕸ

09G105- (2007)(11) N.Watanabe, A.Nakayama, S.Abe, et.al, J. Appl. Phys., Vol. 103,୍ ᪉ ࡛ ᅗ 8 ࡢ ୗ ༙ ศ (e1)-(h2) ࡛ ࡣ 㙐 ஺ ☢ ᮰ ()x,

Pages 07C707- (2008))y)=())࡛࠶ࡾ㸪㟁ᅽVࡢᐃᅾἼࡣࡸࡣࡾ☢᮰࡜ᆶ┤(12) N.Watanabe, A.Nakayama, S.Abe, et.al,, J. Appl. Phys., Vol. 105,࡞᪉ྥ࡟ኚㄪࡉࢀ㸪᥋ྜෆx᪉ྥ࡟୍Ἴ㛗࠶ࡿࡇ࡜࡟࡞ࡿ㸬

Pages 07E312- (2009)ࡇࡢሙྜࡶእ㒊☢⏺ศᕸ(e1)-(e2)࡜ࡇࡢඹ᣺࣮ࣔࢻ

(13) A.Nakayama,S.Abe,N.Watanabe, J. Appl. Phys., Vol.111. Pages(f1)-(f2)ࡢ⤌ࡳྜࢃࡏ࡛㸪ᐇ㝿ࡢඹ᣺ศᕸ(g1)-(g2)ࡣᡂࡾ

113907-1- (2012)❧ࡘ㸬ࡑࡢ⤖ᯝ㸪 ᥋ྜෆ࡛ࡣ(h1)-(h2)࡟♧ࡍࡼ࠺࡟᥋ྜ

(14) A.Nakayama,S.Abe,N.Watanabe,Y.Okabe, Microelectronic఩┦ᕪࡀ࡯࡯ȧ/2࡛㸪᥋ྜ㟁ὶṇࡢ㡿ᇦࡀᗈࡀࡾ㸪᫬㛫

Engineering., Vol.108. Pages 163-168 (2013)ⓗ࡟ᖹᆒࡋࡓ⤖ᯝ㸪ୗ㒊㟁ᴟ࠿ࡽୖ㒊㟁ᴟࡢྥࡁ࡟኱ࡁ
࡞㟁ὶࡀὶࢀ㸪㟁ὶ̾㟁ᅽ≉ᛶୖࡢ㟁ὶࢫࢸࢵࣉ࡟࡞ࡿ࡜ᣢ⥆ྍ⬟࡞࣮ࣜࣥ⏕⏘࣭≀ὶ࣐ࢿࢪ࣓ࣥࢺ୰ᓥ ೺୍㸨,ᯇ୸ṇᘏ㸨,ᯇ஭ṇஅ㸨

Lean manufacturing and logistics management for sustainability
Kenichi NAKASHIMA㸨, Masanobu MATSUMARU㸨, Masayuki MATSUI㸨㸯㸬ࡣࡌࡵ࡟

ࡲࡓ୍᪉࡛ࡣ㸪ᚠ⎔ᆺࢩࢫࢸ࣒ࢆ࠸࠿࡟ຠ⋡Ⰻࡃ㐠⏝ࡍ㏆ᖺ㸪ᗫᲠ≀ࡢቑຍ㸪㈨※ࡢᯤῬ࡞࡝ᆅ⌫⎔ቃࢆྲྀࡾࡿࡇ࡜ࡀ࡛ࡁࡿ࠿ࢆᐈほⓗ࡟♧ࡍࡓࡵ㸪ከࡃࡢ◊✲⪅࡟ᕳࡃ≧ἣࡣ㸪┈ࠎཝࡋ࠸ࡶࡢ࡜࡞ࡗ࡚ࡁ࡚࠸ࡿ㸬᪥ᮏ࡟ࡼࡾࢩࢫࢸ࣒ࡢࣔࢹࣝ໬ࢆ⏝࠸ࡓ◊✲ࡀ⢭ຊⓗ࡟⾜ࢃࢀ࠾࠸࡚ࡣ㸪୍⯡ᗫᲠ≀ࡢ᤼ฟ㔞ࡀ㸪 ᖺ௨㝆㸪ᖺ㛫࡚࠸ࡿ  㸬⣙  ୓ࢺࣥ࡜࡞ࡗ࡚࠾ࡾ㸪⏘ᴗᗫᲠ≀ࡢ᤼ฟ㔞ࡣ㸪ࡉࡽ࡟㸪᪥ᮏࢆྲྀࡾᕳࡃ࢔ࢪ࢔ᆅᇦ࡟࠾࠸࡚ࡶ㸪ࡶࡢᖺ㛫⣙  ൨ࢺࣥ࡜࡞ࡗ࡚࠸ࡿ㸬ࡇࡢࡼ࠺࡞≧ἣ࡟࠾࠸࡚㸪

࡙ࡃࡾᣐⅬࡢᒎ㛤࡟క࠺⎔ቃၥ㢟ࡀ㐍ࢇ࡛࠸ࡿ㸬౛࠼ࡤ

୍᪉㏻⾜ᆺࡢ〇ရࣇ࣮ࣟ࡟ࡼࡿᗫᲠ≀ࡢቑຍࢆᢚไࡍࡿ

௒᪥ࡑࡢྎ㢌ࡀ┠ぬࡲࡋ࠸୰ᅜ࡛ࡢ⮬ື㌴⏕⏘ࡣ㸪 ୡࡓࡵ㸪⡿ᅜ㸪ࢻ࢖ࢶࡸ᪥ᮏࢆࡣࡌࡵ࡜ࡍࡿྛᅜ࡛ࡣ㸪〇⣖ࡢ  ᖺ௦࡟ᪧࢯ㐃ࡢ᥼ຓ࡛タ❧ࡉࢀࡓ㛗᫓➨୍Ỷ㌴ရࡢࣜࢧ࢖ࢡࣝࡸ෌฼⏝ࢆಁ㐍ࡍࡿࡓࡵࡢἲᚊไᐃ➼㸪㸦ࠕỶ㌴ࠖ㸻㌴㸧࡟ࡼࡾጞࡵࡽࢀࡓ㸬➨୍Ỷ㌴ࡣ୺࡟ࠕゎᵝࠎ࡞ᑐᛂࡀ࡜ࡽࢀ࡚࠸ࡿ㸬ᨺࠖࣈࣛࣥࢻࡢ W ࢺࣛࢵࢡࢆ⏕⏘ࡋ࡚ࡁࡓࡀ㸪ẟἑᮾࢆᡃࡀᅜ࡟࠾࠸࡚ࡣ㸪ᗫᲠ≀ࡢⓎ⏕ࢆᢚไࡉࡏࡿࡓࡵ㸪ࣜࢧ࢖ࢡࣝࡢ᥎㐍㸪௻ᴗ࡞࡝ࡢ⎔ቃࢆ⪃៖ࡋࡓ〇ရ࡙ࡃࡣࡌࡵᨻᗓᣦᑟ⪅⏝ࡢ㧗⣭஌⏝㌴ࠕ⣚᪝ࠖࢆ⏕⏘ࡋࡓࡇ࡜࡛ࡶ᭷ྡ࡛࠶ࡿ㸬ࡾ㸪ᾘ㈝⪅ࡀ⎔ቃ࡬ࡢ㈇Ⲵࡢᑡ࡞࠸〇ရࡢ㉎ධࢆ᥎㐍ࡍ୰ᅜ࡛ࡣᑡ࡞ࡃ࡜ࡶ  ᖺ௦ࡲ࡛⮬ᐙ⏝㌴ࡣ࡯࡜ࢇ࡝

ࡿࡓࡵ࡟㸪ࢢ࣮ࣜࣥ㉎ධࢆ່ࡵ࡚࠸ࡿ㸬ࡲࡓ㸪⎔ቃᇶᮏ࡞࠿ࡗࡓ㸬ᨵ㠉㛤ᨺᚋ㸪Ḣ⡿ࡑࡋ࡚᪥ᮏ㸪㡑ᅜ࡞࡝ࡢୡ

ィ⏬࡛ࡣ㸪⤒῭ࢩࢫࢸ࣒࡟࠾ࡅࡿ≀㉁ࡢᚠ⎔ࢆಁ㐍ࡋ㸪⏺኱ᡭ⮬ື㌴࣓࣮࣮࢝ࡣ┦ḟࡂ୰ᅜ࡬㐍ฟࡍࡿ࡜ྠ᫬࡟㸪⎔ቃ࡬ࡢ㈇Ⲵࢆపῶࡉࡏࡿࡓࡵ࡟㸪ᗫᲠ≀ࡢⓎ⏕ᢚไ㸪୰ᅜᮏᅵࡢẸ᪘⣔⮬ື㌴࣓࣮࣮࢝ࡶྎ㢌ࡋ㸪ࡑࡢ⤖ᯝ㸪౑⏝῭ࡳ〇ရࡢ෌౑⏝㸪ᅇ཰ࡋࡓ〇ရࢆཎᮦᩱ࡜ࡋ࡚ࣜ

୰ᅜࡣୡ⏺୍ࡢ⮬ື㌴ᕷሙ࡜࡞ࡾ㸪ἢᾏᆅ༊ࡢ㒔఍ࡸྛࢧ࢖ࢡࣝࡍࡿ࣐ࢸࣜ࢔ࣝࣜࢧ࢖ࢡࣝ㸪ࡉࡽ࡟㸪ࣜࢧ࢖ࢡ┬ࡢ㤳ᗓᡤᅾᆅࡢ኱୰㒔఍࡛ࡣ⮬ᐙ⏝㌴ࡣ࠿࡞ࡾᬑཬࡋ

ࣝࡢᅔ㞴࡞ࡶࡢࡣ㸪࢚ࢿࣝࢠ࣮࡜ࡋ࡚౑⏝ࡍࡿࢧ࣮࣐ࣝ

࡚ࡁࡓ㸬 ᖺ࡟୰ᅜࡢ୍ேᙜࡓࡾࡢ *'3 ࡣึࡵ࡚ࣜࢧ࢖ࢡࣝࢆ᥎㐍ࡋ࡚࠸ࡿ㸬 ᖺ⎔ቃᗇ࡟ࡼࡿᚠ⎔ ࢻࣝࢆ㉸࠼㸪࠸ࢃࡺࡿࠕ࣮ࣔࢱࣜࢮ࣮ࢩࣙࣥࠖ⌧ᆺ⤒῭ࢩࢫࢸ࣒࡬ࡢᥦゝ௨᮶㸪 ᖺ࡟ࡣ㏻⏘┬࡟ࡼ㇟ࡣ୰ᅜෆᆅࡲ࡛㉳ࡇࡿࡼ࠺࡟࡞ࡾࡘࡘ࠶ࡿ㸬ࡑࢀ࡛ࡶࡿᗫᲠ≀ࡢ࢞࢖ࢻࣛ࢖ࣥࡢබ⾲㸪෌⏕㈨※฼⏝ಁ㐍ἲ ᖺᮎ⌧ᅾࡢ୰ᅜࡢ⮬ᐙ⏝⮬ື㌴ಖ᭷ྎᩘࡣேཱྀ࡛

 ᖺ 㸪⎔ቃᇶᮏἲ  ᖺ 㸪⤒ᅋ㐃⎔ቃ࢔ࣆ࣮ࣝ

๭ࡿ࡜ࢃࡎ࠿ே࡟ྎ࡟࡜࡝ࡲࡗ࡚࠾ࡾ㸪௒ᚋࡢ⮬ືᚠ⎔ᆺ♫఍ࡢᵓ⠏  ᖺ 㸪ᐜჾໟ⿦ࣜࢧ࢖ࢡࣝἲ

㌴ᕷሙࡢᣑ኱ࡍࡿవᆅࡣ࠿࡞ࡾ኱ࡁ࠸㸬୍᪉㸪୰ᅜࡢ ᖺ 㸪ᐙ㟁ࣜࢧ࢖ࢡࣝἲ  ᖺ 㸪ᘓタᕤ஦㈨ᮦ

&2 ᤼ฟ㔞ࡣ⮬ື㌴ಖ᭷㔞࡟ẚ౛ࡋ࡚ᖺࠎቑ࠼࡚࠸ࡿ㸬ࣜࢧ࢖ࢡࣝἲ  ᖺ 㸪㣗ရࣜࢧ࢖ࢡࣝἲ  ᖺ 㸪ᅜ㝿࢚ࢿࣝࢠ࣮ᶵ㛵㸦,($㸧ࡢⓎ⾲ࡋࡓࢹ࣮ࢱ࡟ࡼࡿ࡜㸪ᚠ⎔ᆺ♫఍ᙧᡂ᥎㐍ᇶᮏἲ  ᖺ 㸪ᨵṇᗫᲠ≀ฎ⌮

୰ᅜࡢ &2 ᤼ฟ㔞ࡣ  ᖺ࡟ึࡵ࡚࢔࣓ࣜ࢝ࢆ㉸࠼㸪ࡑἲ  ᖺ 㸪ᨵṇ෌⏕㈨※฼⏝ಁ㐍ἲ  ᖺ ࡞࡝ࡋ࡚ ᖺ࡟ࡣࡍ࡛࡟඲ୡ⏺ࡢ&2 ᤼ฟ㔞ࡢ㸣ࢆ༨ࡵḟࠎ࡜ᚠ⎔ᆺ♫఍࡟ྥࡅ࡚ࡢἲⓗᩚഛࡸᨻᗓ࡟ࡼࡿ⾜ᨻ࡚࠸ࡿ㸬ᣦᑟ㸪⏘ᴗ⏺࡟࠾ࡅࡿ⮬୺ⓗྲྀ⤌ࡳࡀᐇ᪋ࡉࢀ࡚࠸ࡿ㸬୰ᅜ⎔ቃಖㆤ㒊㸦┬㸧ࡢⓎ⾲࡟ࡼࡿ࡜㸪 ᖺࡢ୰ᅜࡢ኱୰㒔఍࡟࠾ࡅࡿ኱Ẽởᰁࡢ୺࡞ཎᅉࡣ⮬ື㌴ࡢ᤼Ẽ*ᩍᤵ ⤒ႠᕤᏛ⛉
Professor, Dept. of Industrial Engineering and Management࢞ࢫ࡟ࡼࡿࡶࡢ࡛࠶ࡿ㸬ᐇ㝿㸪ᖺ㛫 NP ㉮⾜ࡍࡿ㌴ࡣ㸪⇞㈝ NPO ࡞ࡽ㸪/ ࡢ࢞ࢯࣜࣥࢆᾘ㈝ࡋ㸪Ⓨᣢ⥆ྍ⬟࡞࣮ࣜࣥ⏕⏘࣭≀ὶ࣐ࢿࢪ࣓ࣥࢺ

⏕ࡍࡿ &2 ࡣ NJ ࡟ࡶ࡞ࡿ㸬ࡍ࡞ࢃࡕ㸪࠿࡞ࡾࡢ๭

ホ౯ࡀᚲせ࡜࡞ࡿ㸬ࡇࡇ࡛ࡣ㸪㈍኎ᚋࡢ〇ရࢆ௬᝿ⓗ࡞ྜ࡛㸪&2 ᤼ฟ㔞ࡢቑຍࡀ⮬ື㌴ࡢቑຍ࡜㛵ಀࡋ࡚࠸ࡿ

ᅾᗜရ࡜ࡋ࡚࡜ࡽ࠼㸪ࡑࡢᗫᲠ㔞ࡸ෌⏕⏘ࡉࢀࡿ๭ྜࢆ

ࡇ࡜ࡀࢃ࠿ࡿ㸬ࡑࡋ࡚୰ᅜࡢ ᖺࡢ⮬ື㌴ಖ᭷㔞ࡣ⪃៖ࡋࡓࢩࢫࢸ࣒ࡢホ౯ࣔࢹࣝࢆᥦ᱌ࡍࡿ㸬ࡉࡽ࡟㸪෌൨ྎ࡟㐩ࡍࡿ࡜ண ࡉࢀ࡚࠸ࡿ㸬ࡇࢀ࡟ᑐࡋ࡚㸪୰ᅜࡢ⏕⏘๭ྜࢆኚ໬ࡉࡏᖹᆒ㈝⏝ࢆ᭱ᑠ໬ࡋ㸪ࡉࡽ࡟ࣅࢪࢿ

ࠕ඲ᅜ஌⏝㌴ᕷሙಙᜥ⫃ᖍ఍ࠖࡢᖿ㒊ࡣ  ᖺ࡛ࡣ▼Ἔ⇞ࢫ࡟࠾ࡅࡿ✀ࠎࡢ≧ἣࢆ᝿ᐃࡋ࡚ࢥࢫࢺせᅉࡢỈ‽ࢆኚᩱࡀ  ൨ྎࡢ⮬ື㌴ࢆᨭ࠼ࡁࢀ࡞࠸࡜㆙࿌ࡋ࡚࠸ࡿ㸬໬ࡉࡏࡓᩘ್ᐇ㦂ࢆ⾜࠸㸪ᚓࡽࢀࡓᖹᆒ㈝⏝࡟㛵ࡍࡿศࡇࡢࡼ࠺࡟ࢢ࣮ࣟࣂࣝ࡞࡛ࣞ࣋ࣝࠊᚑ᮶ࡢ⏕⏘࣭≀ὶࢩࢫᩓศᯒ⤖ᯝࢆ♧ࡋ㸪ᣢ⥆ྍ⬟ࢩࢫࢸ࣒࡟ᑐࡍࡿࢥࢫࢺせࢸ࣒࡟࠾࠸࡚ࡣ⪃៖ࡉࢀ࡚࠸࡞࠿ࡗࡓࡀ㸪⎔ቃ࡬ࡢ㓄៖ࡸᅉࡢᙳ㡪ࢆ♧ࡍ㸬ᣢ⥆ྍ⬟࡞♫఍ࡢᐇ⌧࡟ࡴࡅ࡚ࡢྲྀࡾ⤌ࡳࡀᛴົ࡜࡞ࡗ࡚࠸ࡿ㸬㸰㸬ᚠ⎔ᆺࢩࢫࢸ࣒

ᮏ◊✲࡟࠾࠸࡚ࡣ㸪⏕⏘࣭≀ὶάືࡢ↓㥏ࢆ᤼㝖ࡋࡓ ୡ⣖ࡢ⤒῭άືࡣ㸪⏕⏘⪅୺ᑟᆺ࡛㐍ࡵࡽࢀ㸪➇த࣮ࣜࣥ⏕⏘࣭≀ὶࢩࢫࢸ࣒ᐇ⌧ࡢࡓࡵࡢ࣐ࢿࢪ࣓ࣥࢺࢩ

௚♫ࡼࡾࡶ㸪⏕⏘ᛶࡢຠ⋡໬࡜పࢥࢫࢺ໬ࡀồࡵࡽࢀ࡚ࢫࢸ࣒࠾ࡼࡧ࣮࢜࣌ࣞࢩࣙࣥࢩࢫࢸ࣒ࡢຠ⋡㐠⏝࡟ࡘ࠸ࡁࡓ㸬ࡇࢀ࡟ࡼࡾ㸪♫఍ࢩࢫࢸ࣒ࡣ㸪ࣇ࢛࣮ࢻ࣭ࢩࢫࢸ᳨࡚ウࢆ⾜࠸㸪㸪ᣢ⥆ྍ⬟♫఍ᵓ⠏࡬ࡢ㈉⊩ࢆ┠ᣦࡍ㸬࣒࡟㇟ᚩࡉࢀࡿ኱㔞⏕⏘኱㔞ᾘ㈝኱㔞ᗫᲠᆺࡢᙧែ࡜

࣮ࣜࣥ⏕⏘࣭≀ὶࢩࢫࢸ࣒ࡣ㸪⡿ᅜ 0,7 ࡟࠾ࡅࡿ◊✲⪅࡞ࡗࡓ㸬ࡇࡢ♫఍ࢩࢫࢸ࣒ࡣ㸪໬▼⇞ᩱ࡞࡝㸪᭷㝈ࡢ㈨ࡽࡀᥦၐࡋࡓࡶࡢ࡛㸪ࡑࡢᇶ♏࡜࡞ࡗ࡚࠸ࡿࢪࣕࢫࢺ࢖

※ࢆ኱㔞࡟౑࠸ᆅ⌫⎔ቃ࡟㈇Ⲵࢆ୚࠼࡞ࡀࡽᕤᴗ⏕⏘ࢆࣥࢱ࢖࣒㸦-XVW,Q7LPH-,7㸧⏕⏘ࢩࢫࢸ࣒ࡣ㸪᪥ᮏ࡟ᣑ኱ࡉࡏ࡚ࡁࡓ㸬ࡑࡢ⤖ᯝ㸪ࠥ ᖺ௦࡟ࡣ㸪බᐖ࠾ࡅࡿࡶࡢ࡙ࡃࡾࡢᐇ㊶ࡢሙ࠿ࡽ๰㐀ࡉࢀࡓຠ⋡ⓗ࡞ࢩၥ㢟ࡀⓎ⏕ࡋ㸪ࡑࡢᑐᛂ㸪㜵Ṇ࡬ࡢᑐ⟇࡟ከࡃࡢ௻ᴗࡀ

ࢫࢸ࣒࡜ࡋ࡚඲ୡ⏺࡟▱ࡽࢀ࡚࠸ࡿ㸬ඛ⾜◊✲ ࡛ࡣ㸪ྲྀࡾ⤌ࢇࡔ㸬ࡑࡋ࡚⌧ᅾ㸪㈨※ࡢᯤῬࡸ⎔ቃ࡬ࡢᑐᛂ࡞

࣮ࣜࣥ⏕⏘࣭≀ὶࢩࢫࢸ࣒࡟㛵ࡋ࡚ရ㉁࣭⎔ቃഃ㠃ࡼࡾࢺ࡝ᆅ⌫⎔ቃၥ㢟࡬ࡢྲྀࡾ⤌ࡳࡀ㔜せ࡟࡞ࡗ࡚ࡁ࡚࠸ࡿ㸬࣮ࢱࣝ࡞࣐ࢿࢪ࣓ࣥࢺࢩࢫࢸ࣒࡜ࡋ࡚ࡢศᯒ᳨࣭ウࢆ⾜ࡗ ࡇࡢࡼ࠺࡞⫼ᬒ࠿ࡽ㸪♫఍ࢩࢫࢸ࣒ࡣ㸪኱㔞⏕⏘኱㔞ࡓ㸬ᮏ✏࡛ࡣ㸪ࡉࡽ࡟ࡑࢀࢆ㐍ࡵ㸪᪉㔪⟶⌮࠾ࡼࡧ࣐ࢿࢪ

ᾘ㈝኱㔞ᗫᲠᆺ♫఍࠿ࡽ㸪ᆅ⌫⎔ቃࢆ㔜どࡋࡓᚠ⎔ᆺ♫࣓ࣥࢺࣞࣅ࣮ࣗࢆྵࡵࡓࢺ࣮ࢱ࣐ࣝࢿࢪ࣓ࣥࢺࢩࢫࢸ࣒ࣞ

఍࡬࡜⛣⾜ࡋ࡚ࡁࡓ㸬ࡑࡋ࡚㸪♫఍ࢩࢫࢸ࣒ࡀᚠ⎔ᆺ♫࣋ࣝ㸪࠾ࡼࡧᚠ⎔ᆺ♫఍ࢆᐇ⌧ࡍࡿࡓࡵࡢ࣮࢜࣌ࣞࢩࣙࣥ

఍࡬࡜ྥ࠿࠺୰࡛㸪ᚠ⎔ᆺࢩࢫࢸ࣒࡜࠸࠺ᴫᛕࡀ⏕ࡳฟࣞ࣋ࣝ࡟࠾ࡅࡿ㐠⏝࡟ࡘ࠸࡚ࡢ⪃ᐹࢆ⾜࠺㸬ࡇࡇ࡛ࡣ㟂ࡉࢀࡓ㸬ᚠ⎔ᆺࢩࢫࢸ࣒࡜ࡣ㸪᪂ࡓ࡞㈨※ࢆ⏝࠸ࡿࡢ࡛せ➼ࡢ☜⋡ⓗኚືࢆ⪃៖ࡋࡓࡶࡢ࡙ࡃࡾ⌧ሙ࡟࠾࠸࡚㸪ࡣ࡞ࡃ౑⏝῭ࡳࡢ㈨※ࢆ෌฼⏝ࡍࡿࡇ࡜࡟ࡼࡗ࡚㸪㈨※࣮ࣜࣥ⏕⏘࣭≀ὶࢩࢫࢸ࣒࣐ࢿࢪ࣓ࣥࢺᵓ⠏ࡢࡓࡵ㸪࢜࣌ࢆᚠ⎔ࡉࡏ࡚࠸ࡃ࡜࠸࠺⪃࠼᪉࡛࠶ࡿ㸬⏕⏘ࢩࢫࢸ࣒࡟

࣮ࣞࢩࣙࣥࡢ࡛ࣞ࣋ࣝ㸪ࢩࢫࢸ࣒ࢆ㞳ᩓ᫬㛫࣐ࣝࢥࣇࣔࢹ

࠾࠸࡚ࡣ㸪ࡓ࡜࠼ࡤ㸪〇ရᑑ࿨ࢆ⤊࠼ࡓ〇ရࢆ✚ᴟⓗ࡟ࣝ࡜ࡋ࡚ᐃᘧ໬ࢆ⾜࠸㸪ࢩࢫࢸ࣒せᅉࡢศᯒࢆ࠾ࡇ࡞࠺㸬ᅇ཰࣭ศゎࡋ࡚෌⏕⏘࡟⏝࠸ࡿࡇ࡜࡟ࡼࡾ㸪⎔ቃࡢᝏᙳࡲࡎ㸪㸰❶࡛ࡣᚠ⎔ᆺ♫఍࡟࠾ࡅࡿ⏕⏘ࢩࢫࢸ࣒ࡢ఩

㡪ࢆᴟຊᢚ࠼ࡓ⏕⏘ᙧែࡀ⪃࠼ࡽࢀ࡚࠸ࡿ㸬ࡑࡢࡓࡵ࡟

⨨࡙ࡅ࠾ࡼࡧ㸪ࡇࢀࡲ࡛ࡢᣢ⥆ྍ⬟࡞ࢩࢫࢸ࣒ࡢ◊✲࡟ࡣ㸪〇ရタィࡢẁ㝵࡛ศゎࡋࡸࡍ࠸〇ရࢆタィࡍࡿࡇ࡜㛵ࡋ࡚ᴫㄝࡍࡿ㸬㸱❶࡛ࡣࢺ࣮ࢱࣝ࡞࣐ࢿࢪ࣓ࣥࢺࢩࢫࡀ㔜せ࡜࡞ࡿ  㸬ࢸ࣒㐠⏝ୖࡣḞ࠿ࡏ࡞࠸㸪᪉㔪⟶⌮ࡸ࣐ࢿࢪ࣓ࣥࢺࣞࣅ ࡉࡽ࡟ᚠ⎔ᆺ♫఍࡟࠾ࡅࡿ෌⏕⏘ࡢຠ⋡ⓗ㐠⏝ࢆᐇ⌧࣮ࣗ࡟㛵ࡋ࡚ゎㄝࡋ㸪ᅜ㝿ᶆ‽つ᱁࡜ࡋ࡚▱ࡽࢀࡿࡍࡿࡓࡵ㸪⏕⏘⎔ቃ࡟࠾ࡅࡿ㟂せኚື➼ࡢ⌧ᐇⓗ࡞ၥ㢟,62 ࡜ࡢ㛵ಀᛶ࡟ࡘ࠸࡚㆟ㄽࡍࡿ㸬ࡇࢀࡽࡢࢩࢫࢸ

ࢆ⪃៖ࡋࡓ෌⏕⏘ࢩࢫࢸ࣒ࣔࢹࣝࡀ㸪ࡇࢀࡲ࡛࠸ࡃࡘ࠿

࣒ࡣ 3'&$ ࢧ࢖ࢡࣝ࡟ࡼࡿ⥅⥆ⓗᨵၿࢆᇶ♏࡜ࡋ࡚࠾ࡾ㸪ᥦ᱌ࡉࢀ࡚ࡁࡓ㸬ࡑࡢᨵၿࢆᐇ⌧ࡍࡿࡓࡵ࡟ࡣ⌧ሙࡢ࣮࢜࣌ࣞࢩࣙࣥࡀ㔜 ᐃᮇほ ࣔࢹࣝ࡜ࡋ࡚㸪&RKHQ ࡽ  ࡣ㸪ᅇ཰ࡉࢀࡓ〇せ࡜࡞ࡿ㸬ࡑࡇ࡛㸲❶࡛ࡣ㸪㟂せኚື➼ࡢ୙☜ᐇ࡞⎔ቃရࢆ┤᥋෌฼⏝ࡍࡿࣔࢹࣝࢆᥦ᱌ࡋ㸪᭱㐺ゎࢆ♧ࡋ࡚࠸ࡢࡶ࡜࡛㸪〇ရࡢࣛ࢖ࣇࢧ࢖ࢡࣝࢆ⪃៖ࡋࡓ〇ရᅇ཰㸫ࡿ㸬ࡉࡽ࡟㸪,QGHUIXUWK  ࡣ㸪Ⓨὀ࡜෌⏕⏘࡟࠾ࡅࡿࣜ

෌⏕⏘ࢩࢫࢸ࣒ࢆ⪃࠼㸪㞳ᩓ᫬㛫࣐ࣝࢥࣇ㐣⛬࡟ࡼࡿ࣮࢜ࢻࢱ࢖࣒ࡢᙳ㡪࡟ࡘ࠸࡚㆟ㄽࡋ࡚࠸ࡿ㸬㐃⥆ほ ࣔࢹ࣮࣌ࣞࢩࣙࣥࡢࣔࢹࣝ໬ࢆ⾜࠺㸬ᚑ᮶ࡣ㸪ᕤሙෆ㸪࠶ࡿࣝ࡜ࡋ࡚ࡣ㸪0XFNVWDGW ࡜ ,VDDF  ࡀ㸪 V4 ࣮ࣝࣝ࡟ᇶ

࠸ࡣ㈍኎๓ࡢ〇ရࡢࡳࢆᅾᗜ࡜ࡋ࡚࡜ࡽ࠼࡚ࢩࢫࢸ࣒ࡢ

࡙ࡃ࣮ࣜࢻࢱ࢖࣒࡜ࢩࢫࢸ࣒ࡢไᚚᨻ⟇ࢆ⪃៖ࡋࡓࣔࢹホ౯ࢆ࠾ࡇ࡞ࡗ࡚ࡁࡓࡀ㸪ᚠ⎔ᆺ♫఍ࢆ๓ᥦ࡜ࡋࡓ෌⏕ࣝࢆᥦ᱌ࡋ㸪YDQGHU/DDQ ࡽ  ࡣ㸪㟂せ࡜⊂❧࡟〇ရࡀ⏘ࢩࢫࢸ࣒࡟࠾࠸࡚ࡣ㸪㢳ᐈ࡬㈍኎ࡉࢀ㸪ᅇ཰ᚋ㸪෌⏕ᅇ཰ࡉࢀࡿࢩࢫࢸ࣒ࢆ⪃࠼㸪㐃⥆᫬㛫࣐ࣝࢥࣇࣔࢹࣝ࡜

⏘࡟฼⏝ࡉࢀࡿྍ⬟ᛶࡢ࠶ࡿ〇ရࢆྵࡵࡓ㸪ࢺ࣮ࢱࣝ࡞

ࡋ࡚ゎᯒࢆ⾜ࡗ࡚࠸ࡿ㸬ࡲࡓ YDQGHU/DDQ ࡜ 6DORPRQ ⚄ዉᕝ኱ᏛᕤᏛ◊✲ᡤᡤሗ ➨  ྕࡣ㸪᪂ရ࡜෌⏕⏘㒊ရࢆ⏝࠸ࡓ⏕⏘࡜ᅾᗜࢆ⤖ࡧࡘࡅࡿ

Nahmias (14)ࡢ Perishable Inventory ࣔࢹࣝࡢᴫᛕࢆᑟධࡋ㸪

386+DQG38// ᡓ␎ࢆᥦ᱌ࡋ࡚࠸ࡿ㸬ࡋ࠿ࡋ㸪ࡇࢀࡽࡢ㞳ᩓ᫬㛫࣐ࣝࢥࣇ㐣⛬ࢆ⏝࠸࡚㸪෌⏕⏘ࢩࢫࢸ࣒ࡢࣔࢹ

◊✲࡟࠾࠸࡚ࡣ㸪㈍኎ࡉࢀ࡚㢳ᐈࡀ౑⏝୰ࡢ〇ရࡣ⟶⌮ࣝ໬࡜ࢥࢫࢺศᯒࢆ⾜࠺㸬ࡢᑐ㇟࡜ࡣࡉࢀ࡚ࡇ࡞࠿ࡗࡓ㸬 Guide and Van Wassenhove (9) ࡣ㸪෌⏕⏘ศ㔝࡟࠾ࡅࡿ₯㸱㸬᪉㔪⟶⌮ࢩࢫࢸ࣒࡜࣐ࢿࢪ࣓ࣥࢺᅾⓗ࡞⤒῭ᛶศᯒ࡟㛵ࡍࡿ◊✲ࡀࡇࢀࡲ࡛࡟ᑡ࡞࠸ࡇ࡜

3.1 ᪉㔪⟶⌮࡜᪥ᖖ⟶⌮ࢆᣦ᦬ࡋ࡚࠸ࡿ㸬ᅗ㸯ࡣ㸪ᙼ➼ࡀᥦ᱌ࡋࡓࣅࢪࢿࢫศ㔝᪉㔪⟶⌮࡜᪥ᖖ⟶⌮ࢆṇࡋࡃ༊ูࡍࡿᚲせࡀ࠶ࡿࠋ᪥ᖖ࡟࠾ࡅࡿ〇ရᅇ཰ࡢ࣐ࢿࢪ࣓ࣥࢺ࡟࠾ࡅࡿᇶᮏⓗ࡞㛵ಀ⟶⌮ࡣ┠ᶆ࡟ࡼࡿ⟶⌮㸩᪉⟇㸪᪉㔪⟶⌮ࡣ⤌⧊ࡀ฿㐩ࡍࢆ♧ࡋ࡚࠸ࡿ㸬ࡿ┠ᶆ㸦ࢦ࣮ࣝ㸧ࢆᐃࡵ࡚㸪ࡑࡢ┠ᶆࢆ㐺ษ࡞᪉⟇࡛㐩ᡂࡍࡿάື࡛࠶ࡿ㸬ࡑࡇ࡟ࡣࣈ࣮ࣞࢡࢫ࣮ࣝ㸦⌧≧ᡴ◚㸧
Product Acquisition

ࡀᚲせ࡜࡞ࡾ㸪㔜Ⅼᣦྥࡀᚲせ࡜࡞ࡿࡀ㸪ࡸࡸࡶࡍࡿ࡜

Management᪉㔪⟶⌮࡜᪥ᖖ⟶⌮ࡣΰྠࡉࢀࡿࡇ࡜ࡀከ࠸㸬㧗࠸┠ᶆࡣ᪉㔪⟶⌮㸪ᶓ㏺࠸ࡢ┠ᶆࡣ᪥ᖖ⟶⌮࡜࠸࠺ࡼ࠺࡟࡜ࡽ
࠼ࡽࢀࡀࡕ࡛࠶ࡿࡀ㸪⌧ᅾࡢ౯್ほࢆそࡍ࡯࡝ࡢ㠉᪂ⓗRemanufacturing
Operational Issues

Remanufacturing࡞ࡇ࡜ࡀࠕ᪉㔪⟶⌮࡛ࠖ࠶ࡽࡡࡤ࡞ࡽ࡞࠸(15)㸬

Products Market
Development᪉㔪⟶⌮࡛ࡣ㡯┠ࢆࡓࡃࡉࢇᣲࡆࡿ࡭ࡁ࡛ࡣ࡞ࡃ㸪୍ᅗ㸯㸸〇ရᅇ཰࣐ࢿࢪ࣓ࣥࢺࢩࢫࢸ࣒ࡢࣇ࣮࣒࣮ࣞ࣡ࢡ

ᗘ࡟㠉᪂ⓗ࡞ࡇ࡜ࡀ࡛ࡁࡿ࡜⪃࠼ࡿ࡭ࡁ࡛ࡣ࡞࠸㸬୰࣭㛗ᮇ⤒Ⴀィ⏬㸪▷ᮇ⤒Ⴀィ⏬ࢆᐃࡵ࡚௻ᴗ⤌⧊඲యࡢཧ
⏬࡟ࡼࡾ㸪ຠ⋡ⓗ࡟┠ᶆࢆ㐩ᡂࡍࡿࡇ࡜ࡀ㔜せ࡛࠶ࡿ㸬〇ရᅇ཰ࡢࣉࣟࢭࢫࡣ㸪࣐ࢿࢪ࣓ࣥࢺࡀᚲせ࡜࡞ࡿ㔜┠ᶆ࡟ᑐࡍࡿ⤖ᯝࡢ※ὶཎᅉࢆ⢭ᰝࡋPDCAࢆࡲࢃࡋ࡚

せ࡞ศ㔝࡛࠶ࡾ㸪ࡇࡢ⤖ᯝ㸪෌฼⏝࣭෌⏕⏘ࡢάືࡀ࡝

ᑐᛂࡍࡿᚲせࡀ࠶ࡿ㸬⤖ᯝࢆ⟶⌮ࡍࡿࡇ࡜࡜㸪⤖ᯝ࡛⟶ࡢ⛬ᗘ⤒῭ⓗ࡞ࡶࡢ࡟࡞ࡿ࠿ࡀ㸪Ỵࡲࡿࡇ࡜࡜࡞ࡿ㸬ࡇ⌮ࡍࡿࡇ࡜ࡢ஧ࡘࡢ᪉ἲࢆ༊ูࡋ࡚⟶⌮ࡍࡿࡇ࡜ࡀ኱ษ

ࡢ⤫ྜ໬ࡉࢀࡓᯟ⤌ࡳࡣ㸪࣐ࢿࢪ࣮ࣕ࡟ᑐࡋ࡚㸪ࢢ࣮࡛ࣟ࠶ࡿ㸬ࣂࣝ࡞⤒῭ⓗ฼┈࡜〇ရᅇ཰ࣉࣟࢭࢫࡢᇶ♏࡜࡞ࡿᙺ๭
࡟↔Ⅼࢆᙜ࡚ࡉࡏࡿࡶࡢ࡛࠶ࡿ㸬ࡇࡢࡼ࠺࡞㸪㛢ࡌࡓࣝ

оಅƷችᅕ

˖ಅྸࣞ

ኺփ‫ۋ‬Ѭ

ᘍѣᙹር࣮ࣉࢆ௬ᐃࡋࡓ㸪⏕⏘ࢩࢫࢸ࣒ࡣࢡ࣮ࣟࢬࢻ࣭࣮ࣝࣉ⏕⏘ࢩࢫࢸ࣒࠶ࡿ࠸ࡣࢡ࣮ࣟࢬࢻ࣭࣮ࣝࣉࡢࢧࣉࣛ࢖࣭ࢳ
࢙࣮ࣥμᅈኺփ૾ᤆɶ᳽ ᧈ ஖ ᚘ ဒμᅈɶ஖ᴕᴳᴈᴎᴶᴵ

ኺփ Ʒ᣻ ᙲ૾ᤆʙಅஜᢿɶ஖૾ᤆ

ʙಅஜᢿᴕᴳᴈᴎ ᴶᴵ

ʙಅ ஜᢿ ᧈ૾ᤆ᣻ᙲ૾ᤆ࡜࿧ࡤࢀ㸪ࡑࡢຠ⋡ⓗ࠿ࡘຠᯝⓗ࡞㐠⏝࢔ࣉ࣮ࣟࢳࡢ᳨ウࡀồࡵࡽࢀ࡚࠸ࡿ㸬౛࠼ࡤ㸪Guide et al. (10)࡟
࠾࠸࡚ࡣ㸪ᦠᖏ㟁ヰࡢ౛ࢆ࡜ࡾ࠶ࡆ㸪฼┈᭱኱໬ࢆ⾜࠺࠰ࡇႸ೅͌᣻ໜ଀ሊ᳽ਦᤆ㟂せ࡜౪⤥ࡢ࣐ࢵࢳࣥࢢၥ㢟ࢆ㆟ㄽࡋ࡚࠸ࡿ㸬 ࢡ࣮ࣟࢬࢻ࣭࣮ࣝࣉ⏕⏘࡟࠾࠸࡚ࡣ㸪ᅇ཰ࡉࢀࡓ〇ရࡣ㸪௻ᴗ࡟࠾ࡅࡿ෌⏕⏘ࢩࢫࢸ࣒ࡢ࢖ࣥࣉࢵࢺせ⣲࡜࡞ܱ ଀ ଺ ஖ಅ ጚ Ⴘ ೅Э࠰ࡇƷɼƳӒႾໜʙಅ࿢‫ؾ‬Ʒ‫҄٭‬ʙಅஜᢿ᳨ഏɶ஖૾ᤆ
ʙಅஜᢿ᳨ഏɶ஖૾ᤆ᣻ਃ ࢘ ᢿ ᧉࡾ㸪ᚑࡗ࡚ࢥࢫࢺࢆ⪃៖ࡋࡓ㸪ရ㉁࣭㔞࣭ࢱ࢖࣑ࣥࢢࡢ
ၥ㢟ࡀ㔜せ࡜࡞ࡿ㸬Guide(11)࡛ࡣ㸪⡿ᅜ࡟࠾ࡅࡿᩘከࡃࡢ
෌⏕⏘௻ᴗ࡟㛵ࡍࡿࡇࡢศ㔝ࡢ஦౛ࡀ◊✲ࡉࢀ࡚࠸ࡿ㸬

ਦ
ᛢ ᫆

ໜ

Ӳ ᢿ ᧉ ᧈ ૾ ᤆࡲࡓ Nakashima et al. ࡛ࡣ㸪༢୍ࡢ〇ရᑑ࿨ࢆ⪃៖ࡋࡓ෌⏕⏘ࢩࢫࢸ࣒ࢆ⪃࠼㸪㞳ᩓ᫬㛫࣐ࣝࢥࣇࣔࢹࣝ࡜ࡋ
࡚ࢩࢫࢸ࣒ࢆᐃᘧ໬ࡋ㸪ࣃ࣓࣮ࣛࢱタᐃ࡟ࡼࡿࢩࢫࢸ࣒࠰ ࡇࡇ Ⴘ ᚘ೅ ဒ
͌
᣻

ໜ

଀

ሊ

ܱ଀଺஖

ਃ

࢘

ࡢศ㢮࡜≉ᛶࡸ᭱㐺ᨻ⟇࡟ࡘ࠸࡚㆟ㄽࡋ࡚࠸ࡿ㸬 ḟ❶࡛ࡣࡇࢀࡽࡢ࣮࢜࣌ࣞࢩࣙࣥᡓ␎ࡢᇶ♏࡜࡞ࡿ᪉μᅈኺփ૾ᤆஉ ഏ ౨ ᚛ ˟㔪⟶⌮ࡸࢺ࣮ࢱࣝ࡞࣐ࢿࢪ࣓ࣥࢺࢩࢫࢸ࣒࡟ࡘ࠸࡚ࡢ᳨ウࢆ⾜࠸㸪➨㸲❶࡟࠾࠸࡚ࡑࢀࡽࢆᒎ㛤ࡋࡓ࣮࢜࣌ࣞࢩ
࡛ࣙࣥࣞ࣋ࣝࡢ㸪㈍኎ᚋ〇ရࢆ෌⏕⏘࡟౑⏝ࡍࡿࡓࡵࡢ
௬᝿㒊ရᅾᗜ࡜ࡋ࡚࡜ࡽ࠼ࡓᐇົၥ㢟ࢆྲྀࡾୖࡆ㸪

ኺ

փ

˟

ᜭ

ᅈ

ȞȍǸȡȳȈȬȓȥȸ

ᧈ

ᚮ

ૺ

ȞȍǸȡȳȈȬȓȥȸᅗ  ᪉㔪⟶⌮ࡢ௙⤌ᣢ⥆ྍ⬟࡞࣮ࣜࣥ⏕⏘࣭≀ὶ࣐ࢿࢪ࣓ࣥࢺ



3.2 ᪉㔪⟶⌮ࡢ௙⤌ ᪉㔪⟶⌮࡟ࡣ㸪୰࣭㛗ᮇィ⏬࡜ᖺᗘィ⏬ࡀ࠶ࡿ㸬ࡇࢀ૾ࡸȬȓȥȸȝǤȳȈ

56'2

ኺփʙಅᚘဒ
ɶȷᧈ஖ʙಅᚘဒ
٥ɥȷМႩ᳋᳽Ჽ᳽Ჾ᳽Ჾ᳽᳍᳽Ჿ᳽᳇
ሁƷᢋ঺ཞඞ

ࡽࢆࠕ๰ᴗࡢ⢭⚄ࠖࠕ௻ᴗ⌮ᛕࠖ
ࠕ⤒Ⴀጼໃࠖ
ࠕ⾜ືつ⠊ࠖ
ࠕ඲♫୰ᮇࢫ࣮ࣟ࢞ࣥࠖ
ࠕ஦ᴗᮏ㒊ࢫ࣮ࣟ࢞ࣥࠖ
ࠕ඲♫⤒Ⴀ᪉㔪ࠖࠕ஦ᴗᮏ㒊㛗᪉㔪ࠖࠕ㒊㛛㛗᪉㔪ࠖ࡟ᒎ㛤ࡋ࡚
PDCA ࢆᅇࡋ࡚┠ᶆࢆ㐩ᡂࡍࡿάື࡛࠶ࡿ㸬ࡑࡢ┦஫㛵ಀࢆ♧ࡍ࡜ḟࡢ㏻ࡾ࡜࡞ࡿ㸬㸦ᅗ 2㸧Йૺȷൿ‫ܭ‬ȷϼፗ2&%#56'2
2&%#+51ᙲ൭Ȭșȫ
ƭƷǤȳȗȃȈ
ƭƷǢǦȈȗȃȈ

ᢘЏࣱ
ஊјࣱ
‫ࣱ࢘ڲ‬
јྙࣱ
ᚸų ̖
Ӓų Ⴞ
Ⴘ೅சᢋƷ
ᙲ‫׆‬Ўௌ

ഏ
஖
Ʒ
૾
ᤆ
ǁ

3.3 ⤒Ⴀ᪉㔪ᲢǹȑǤȩȫǢȃȗ᳊ᲾᲽ᲻Უ

ISO 9000s(16)ࡀせồࡋ࡚࠸ࡿရ㉁᪉㔪ࡣ㸪⤒Ⴀ᪉㔪࡜ࡋ࡚㹑㹕㹍㹒ศᯒࢆά⏝ࡋୗグࡢࡼ࠺࡟Ⓨᒎࡉࡏࡿࡇ࡜ࡀᚲせ࡛࠶ࡿ㸬
(1)ᅗ  ࢫࣃ࢖ࣛࣝ࢔ࢵࣉ㸰ẁ㝵᪉ᘧᇶᮏࣔࢹࣝISO ࡢせồ஦㡯ࢆ㉺࠼ࡿࡇ࡜㸬୰࣭㛗ᮇ⤒Ⴀィ⏬࡟࠾ࡅࡿ⤒Ⴀ᪉㔪࡟㸪ရ㉁㸪⎔ቃ㸪㈈ᅗ㸱࡟࠾ࡅࡿ㸵ࡘࡢ࢖ࣥࣉࢵࢺ࡜ࡣ㸪ձ┘ᰝࡢ⤖ᯝ㸪ົ㸪Ᏻ඲࡞࡝ရ㉁⤒Ⴀ᝟ሗయ⣔໬᪉㔪࡜ࡋ࡚Ⓨᒎࡉࡏࡿ㸬ղ㢳ᐈ࠿ࡽࡢࣇ࢕࣮ࢻࣂࢵࢡ㸪ճࣉࣟࢭࢫࡢᐇ᪋≧ἣཬ(2) ஦ᴗィ⏬㸪࣋ࣥࢳ࣐࣮࢟ࣥࢢ㸪ຠ⋡໬ࢆྵࡵࡓ⤒Ⴀࡧ〇ရࡢ㐺ྜᛶ㸪մண㜵ฎ⨨ཬࡧ᫝ṇฎ⨨ࡢ≧ἣ㸪յ๓᪉㔪㸪஦ᴗᮏ㒊㛗᪉㔪㸪㒊㛛㛗᪉㔪࡜ࡋ࡚ᒎ㛤ࡍࡿ㸬ᅇࡲ࡛ࡢ࣐ࢿࢪ࣓ࣥࢺࣞࣅ࣮ࣗࡢ⤖ᯝ࡟ᑐࡍࡿࣇ࢛࣮ࣟ

(3) ୰ᮇ⤒Ⴀィ⏬㸦཰┈ᵓ㐀ᨵ㠉㸪஦ᴗࡢ㔜Ⅼ໬࡞࡝㸧࢔ࢵࣉ㸪նရ㉁࣐ࢿࢪ࣓ࣥࢺࢩࢫࢸ࣒࡟ᙳ㡪ࢆཬࡰࡍྍ

ࡀ❧࡚ࡽࢀ࡚࠸ࡿ㸬⬟ᛶࡢ࠶ࡿኚ᭦㸪շᨵၿࡢࡓࡵࡢᥦ᱌㸪ࢆᣦࡋ࡚࠸ࡿ㸬(4) ISO ࡢつ᱁࡟ᑐࡍࡿ㐺ྜᛶ㸪᭷ຠᛶ࠿ࡽࣃࣇ࢛࣮࣐ ࡲࡓ㸪㸱ࡘࡢ࢔࢘ࢺࣉࢵࢺ࡜ࡣձရ㉁࣐ࢿࢪ࣓ࣥࢺࢩ

ࣥࢫࡢᨵၿࢆຠ⋡ࡼࡃ㐩ᡂࡍࡿάືࡀ⾜ࢃࢀ࡚࠸ࡿ㸬ࢫࢸ࣒ཬࡧࡑࡢࣉࣟࢭࢫࡢ᭷ຠᛶࡢᨵၿ㸪ղ㢳ᐈせồ஦(5) ရ㉁࣐ࢿࢪ࣓ࣥࢺ㸶ཎ๎ࡢᇶᮏࡀᐇ⾜ࡉࢀ࡚࠸ࡿ㸬㡯࡬ࡢ㐺ྜ࡟ᚲせ࡞〇ရࡢᨵၿ㸪ճ㈨※ࡢᚲせᛶ࡟㛵ࡍ

ձ

㢳ᐈ㔜ど

ࡿỴᐃཬࡧฎ⨨ࢆྵࡴࡇ࡜ࢆᣦࡍ㸬ղ࣮ࣜࢲ࣮ࢩࢵࣉ

ࡉࡽ࡟㸪ࣞࣅ࣮ࣗ࡜ࡣ ISO 9000 ࡟ࡼࡿ࡜ (3.8.7) タᐃ

ճ

ேࠎࡢཧ⏬

ࡉࢀࡓ┠ᶆࢆ㐩ᡂࡍࡿࡓࡵࡢ᳨ウᑐ㇟ࡢ㐺ษᛶ㸪ጇᙜᛶմࣉࣟࢭࢫ࢔ࣉ࣮ࣟࢳ

ཬࡧ᭷ຠᛶ (3.2.14)ࢆุᐃࡍࡿࡓࡵ࡟⾜ࢃࢀࡿάື࡜ᐃ

յ࣐ࢿࢪ࣓ࣥࢺ࡬ࡢࢩࢫࢸ࣒࢔ࣉ࣮ࣟࢳ

⩏ࡉࢀ࡚࠸ࡿ㸬ն⥅⥆ⓗᨵၿཧ⪃㸸ࣞࣅ࣮ࣗ࡟ࡣ㸪ຠ⋡㸦3.2.15㸧ࡢุᐃࢆྵࡴࡇ࡜ࡶ

շពᛮỴᐃ࡬ࡢ஦ᐇ࡟ᇶ࡙ࡃ࢔ࣉ࣮ࣟࢳ

࠶ࡿ㸬౛㸸࣐ࢿࢪ࣓ࣥࢺࣞࣅ࣮ࣗ㸪タィ࣭㛤Ⓨࡢࣞࣅࣗո౪⤥⪅࡜ࡢ஫ᜨ㛵ಀ࣮㸪㢳ᐈせồ஦㡯ࡢࣞࣅ࣮ࣗཬࡧ୙㐺ྜࡢࣞࣅ࣮ࣗ㸬᭷ຠᛶ㸦3.2.14㸧㸸ィ⏬ࡋࡓάືࡀᐇ⾜ࡉࢀ㸪ィ⏬ࡋࡓ⤖ᯝ

3.4 2 ẁ㝵᪉ᘧ࣐ࢿࢪ࣓ࣥࢺࣞࣅ࣮ࣗ
ISO 9001 ࡛せồࡉࢀ࡚࠸ࡿ࣐ࢿࢪ࣓ࣥࢺࣞࣅ࣮ࣗࡣ㸪ࡀ㐩ᡂࡉࢀࡓ⛬ᗘ㸬ຠ⋡㸦3.2.15㸧
㸸㐩ᡂࡉࢀࡓ⤖ᯝ࡜౑⏝ࡉࢀࡓ㈨※࡜ࡢ㛵ಀ㸬᪉㔪⟶⌮ࡢ௙⤌ࡳࡢ୰࡛⾜࠸㸪ISO 9001 ࡢせồ஦㡯ࡢ࣐ࢿࢪ࣓ࣥࢺࣞࣅ࣮ࣗ࡬ࡢ࢖ࣥࣉࢵࢺ㸪࢔࢘ࢺࣉࢵࢺࢆྵ

(1) STEP 1 ࡢࣞࣅ࣮࣏ࣗ࢖ࣥࢺ

ࡵ࡚㸪⤒Ⴀ఍㆟㸪♫㛗デ᩿࡞࡝࡛ PDCA ࢆࡲࢃࡋ࡚ࣇ࢛

ISO 9001 ࡢせồ஦㡯ࢆࣞࣅ࣮ࣗࡍࡿ㸬࣮ࣟࡍࡿࡼ࠺࡟ࡍࡿ㸬௙⤌ࡳࡣ㸦ᅗ㸱㸧࡟♧ࡍ㸬ձ㸵ࡘࡢ࢖ࣥࣉࢵࢺࢆྵࡴ㸪ղ㸱ࡘࡢ࢔࢘ࢺࣉࢵࢺࢆྵ

⤒Ⴀ⪅ࡣ⤒Ⴀୖࡢㄢ㢟㸪ၥ㢟Ⅼࢆᢕᥱࡋ㸪⮬♫ࡢ〇ရࡴ㸬௨ୖࡢࡇ࡜ࡔࡅ࡛ࡣ㸪⤌⧊ࡢ⤒Ⴀ⪅࡜ࡋ࡚ࡣᏳᚰ࡛

ࡀ㢳ᐈ࡟‶㊊ࡉࢀࡿయไࡀฟ᮶࡚࠸ࡿ࠿ࢆ⮬ࡽ࣮ࣜࢲ࣮

ࡁ࡞࠸㸬ࢫࣃ࢖ࣛࣝ࢔ࢵࣉࡀᚲせ࡛࠶ࡿ㸬ࢩࢵࣉࢆ࡜ࡗ࡚᥎㐍ࡍࡿᚲせࡀ࠶ࡿ㸬ISO ࡢㄆドྲྀᚓᚋ࣭ISO 9004 (JIS Q 9004)㸸ࣃࣇ࢛࣮࣐ࣥࢫࡢᨵၿࡢᣦ㔪 ࣭ࡢ⥔ᣢ࡟࠾࠸࡚ࡣ㸪ึᅇࡢ┠ⓗ࡟ᑐࡋ῝ࡳࢆቑࡍᚲせࡀ

JIS Q 9023㸸2003 ࣐ࢿࢪ࣓ࣥࢺࢩࢫࢸ࣒ࡢࣃࣇ࢛࣮࣐ࣥ࠶ࡿ㸬つ᱁࡟ᑐࡍࡿ༢࡞ࡿ㐺ྜᛶ㸪᭷ຠᛶࡔࡅ࡛࡞ࡃ㸪ࢫᨵၿࣃࣇ࢛࣮࣐ࣥࢫࡢᨵၿࢆຠ⋡ࡼࡃ㐩ᡂࡍࡿάືࡀᚲせ࡛㸫 ᪉㔪࡟ࡼࡿ࣐ࢿࢪ࣓ࣥࢺࡢᣦ㔪 㸫 ࡢά⏝ࢆ⾜࠺㸬࠶ࡿ㸬ࡇࢀࡽࢆຠᯝⓗ࡟㐍ࡵࡿࡓࡵ࡟ࢫࣃ࢖ࣛࣝ࢔ࢵࣉ
㸰ẁ㝵᪉ᘧࡢ࣐ࢿࢪ࣓ࣥࢺࣞࣅ࣮ࣗࢆᥦ᱌ࡍࡿ㸬⚄ዉᕝ኱ᏛᕤᏛ◊✲ᡤᡤሗ ➨  ྕ(2) STEP 2 ࡢࣞࣅ࣮࣏ࣗ࢖ࣥࢺ

ྛᅾᗜࣞ࣋ࣝࡢ᥎⛣ࡣ௨ୗࡢᘧ࡛୚࠼ࡽࢀࡿ㸬ձ ⤌⧊඲యࡢࣉࣟࢭࢫࡢ㐩ᡂ≧ἣ㸪ղ ࢩࢫࢸ࣒ࡢຠ⋡



ᛶࡢホ౯㸪
ճ ရ㉁࣐ࢿࢪ࣓ࣥࢺࡢ㸶ࡘࡢཎ๎࡟ᇶ࡙࠸ࡓ᪂ つ⏕⏘ 㔞P(t)ࣞࣅ࣮ࣗ㸪մ ࣃࣇ࢛࣮࣐ࣥࢫࡢ⟶⌮㸪յࣃࣇ࢛࣮࣐ࣥࢫ
ᨵၿィ⏬࡬ࡢ࢔࢘ࢺࣉࢵࢺ㸪ն⤌⧊ࡢᙉࡳ㸪ᙅࡳ࡞࡝㸬ࡑࡢࡓࡵࡢ୺࡞࢖ࣥࣉࢵࢺ࡜࢔࢘ࢺࣉࢵࢺ࡜ࡋ࡚ḟࡢࡼxI(t ) ᕤ ሙෆ〇 ရᅾᗜ㔞


$

$

$

D(t)

࠺࡞ࡶࡢࡀ࠶ࡿ㸬O1) ࢖ࣥࣉࢵࢺձ Ⴀᴗୖࡢㄢ㢟㸪ղ ฼ᐖ㛵ಀ⪅ࡢᏳᚰ㸪ճ ᢏ⾡࣭◊✲
㛤Ⓨ㸪௚♫➇ྜ〇ရࡢࣃࣇ࢛࣮࣐ࣥࢫ㸪մ ᕷሙࡢホ౯࣭㢳 ᐈ㟂せJ(t ) ௬᝿ 㒊ရᅾ ᗜ㔞ᡓ␎㸪յ ㈈ົ㛵ಀ㸦኎ୖ㸪฼┈ ௚㸧㸪ն ♫఍࣭⎔ቃࡢ≧ἣ㸪շ ἲ௧࣭つไせồ஦㡯ࡢኚ᭦ ࡞࡝2) ࢔࢘ࢺࣉࢵࢺ

Pձ ⤌⧊ࡢᡓ␎ィ⏬⟇ᐃ㸪஦ᴗィ⏬⟇ᐃ㸪ղ ᭷┈࡞᪂つ┠ᶆ㸪ճ ࣃࣇ࢛࣮࣐ࣥࢫᨵၿ┠ᶆ㸪մ ⤌⧊ᵓ㐀ࡢホ౯㸪⤌⧊ኚ᭦᳨ウ㸪յ ࣐࣮ࢣࢸ࢕ࣥࢢ㸪฼ᐖ㛵ಀ⪅ࡢ‶㊊࡟㛵ࡍࡿᡓ␎㸪ն ⏕ࡁṧࡿࡓࡵࡢᡓ␎ⓗィ⏬⟇ᐃ ࡞࡝ࡇࢀࡽࡢࣞࣅ࣮ࣗ࡟ᇶ࡙ࡃPDCAࢧ࢖ࢡ࣐ࣝࢿࢪ࣓ࣥᅗ 㸸෌⏕⏘ࢩࢫࢸ࣒







I (t  1) I (t )  P(t )  OJ (t)  D(t )    J (t )  OJ (t )  PJ (t )  D(t )   ࢺࢆࡲࢃࡍࡓࡵ࡟ࠊ࣮࢜࣌ࣞࢩ࡛ࣙࣥࣞ࣋ࣝࡢ⟶⌮ࡀ㔜 J (t  1)

せ࡜࡞ࡿ㸬ḟ⠇࡛ࡣ࣮࢜࣌ࣞࢩࣙࣥࣔࢹࣝ࡟ࡘ࠸࡚ࡢ᳨







ࡇࡇ࡛᪂つ⏕⏘㔞ࢆ P(t) = max{0, Imax-I(t)- J(t)}࡛୚࠼

ウࢆ⾜࠺㸬ࡽࢀࡿࡶࡢ࡜ࡋ㸪'PD[ӌ,PD[ ࡜௬ᐃࡍࡿ㸬ࡲࡓࢩࢫࢸ
㸲㸬ᚠ⎔ᆺࢩࢫࢸ࣒࣮࢜࣌ࣞࢩࣙࣥࣔࢹࣝ

࣒ࡢ≧ែ᥎⛣☜⋡ࡣ௨ୗࡢᘧ࡛୚࠼ࡽࢀࡿ㸬

4.1 ࣔࢹࣝ ᮏ❶࡛ࡣ㸪㟂せኚືࡢ୙☜ᐇᛶࡸ〇ရࡢ෌⏕⏘๭ྜ㸪

Ps ( t ) s ( t  1)ᗫᲠ๭ྜ➼ࡢኚືࢆ⪃៖ࡋࡓ༢୍ᕤ⛬࡛༢୍ရ✀ࢆ〇㐀ࡍࡿ෌⏕⏘ࢩࢫࢸ࣒ࢆ⪃࠼ࡿ㸦ᅗ㸲㸧㸬ྛᮇࡢ㟂せࡣ⊂❧࡛ྠ୍ࡢศᕸ࡟ᚑ࠺ࡶࡢ࡜ࡋ㸪᭱኱ࢆ 'PD[㸪᭱ᑠࢆ'PLQ㸪ᖹᆒࢆ ' ࡜ࡍࡿ㸬➨ W ᮇࡢ〇ရᅾᗜ㔞ࢆ , W ࡜ࡋ㸪­° Pr{ D (t )
®
°¯
0

d}

( I t  P (t )  OJ (t )  d ,J (t )  OJ (t )  PJ (t )  d ),otherwise.

if S (t  1)

(4)〇ရࡢ᭱኱ᅾᗜ㔞ࢆ,PD[ ࡛⾲ࡍࡶࡢ࡜ࡍࡿ㸬㢳ᐈ࡟㈍኎ࡉࢀࡓ〇ရࡣ෌⏕⏘࡟฼⏝ࡉࢀࡿ㒊ရࡢ௬᝿ᅾᗜ࡜࡞
ࡾ㸪➨ W ᮇࡢ௬᝿ᅾᗜ㔞ࢆ - W ࡜࠾ࡃ㸬ࡇࡢ௬᝿ᅾᗜࡢ

༢఩᫬㛫ᙜࡓࡾ㈝⏝ࡣ㸪࠺ࡕ㸪Ȣࡢ๭ྜ࡛〇ရࡢᅇ཰ࡀ⾜ࢃࢀ㸪ࡑࢀࡽࡣࡍ࡭࡚

Q(t) cP(t)  TOJ (t)  h[I (t)]  b[I (t)]  GPJ (t) (5)෌⏕⏘࡟౑⏝ࡉࢀࡿࡶࡢ࡜ࡍࡿ㸬୍᪉㸪ȣࡢ๭ྜ࡛〇ရࡢᗫᲠࡀ⾜ࢃࢀࡿࡶࡢ࡜ࡋ㸪Ȣȣӌ ࢆ௬ᐃࡍࡿ㸬 ࡲࡓ➨ W ᮇࡢ⏕⏘㔞ࡣ㸪᪂つࡢཎᮦᩱࢆ⏝࠸ࡿ᪂つ⏕࡜ࡋ㸪ࡇࡇ࡛㈝⏝ࣃ࣓࣮ࣛࢱࡣ௨ୗࡢ㏻ࡾ࡛࠶ࡿ㸬⏘ 3 W ࡜㢳ᐈ࠿ࡽᅇ཰ࡉࢀࡓ〇ရࢆ⏝࠸࡚⏕⏘ࢆ⾜࠺෌⏕⏘㔞Ȣ- W ࡢ࿴࠿ࡽ࡞ࡿࡶࡢ࡜ࡍࡿ㸬

K 〇ရᙜࡓࡾࡢᅾᗜಖ⟶㈝⏝ ࡇࡢ෌⏕⏘ࢩࢫࢸ࣒ࡣ㸪㞳ᩓ᫬㛫࣐ࣝࢥࣇ㐣⛬࡜ࡋ࡚

F 〇ရᙜࡓࡾࡢ᪂つ⏕⏘㈝⏝ḟࡢࡼ࠺࡟ᐃᘧ໬ࡉࢀࡿ>@㸬ȟ 〇ရᙜࡓࡾࡢ෌⏕⏘㈝⏝ ෌⏕⏘ࢩࢫࢸ࣒ࡢ➨ W ᮇ࡟࠾ࡅࡿ≧ែࡣ㸪ᡭᣢࡕࡢᅾ

E 〇ရᙜࡓࡾࡢ⧞ࡾ㉺ࡋ㈝⏝ᗜ㔞࡜௬᝿ᅾᗜ㔞ࡢ࣋ࢡࢺ࡛ࣝ⾲ࡉࢀࡿ㸬







 V W, W - W  ț 〇ရᙜࡓࡾࡢᗫᲠ㈝⏝ ࢩࢫࢸ࣒ࡢᐃᖖ≧ែ☜⋡ࢆィ⟬ࡍࡿࡇ࡜࡟ࡼࡾ㸪༢఩ᣢ⥆ྍ⬟࡞࣮ࣜࣥ⏕⏘࣭≀ὶ࣐ࢿࢪ࣓ࣥࢺ

᫬㛫ᙜࡓࡾࡢᖹᆒ㈝⏝ࢆồࡵࡿࡇ࡜ࡀ࡛ࡁ㸪ࢩࢫࢸ࣒ࡢ

⾲㸰㸸ศᩓศᯒ⾲せᅉᛶ⬟ホ౯ࡀྍ⬟࡜࡞ࡿ㸬
4.2 ࢥࢫࢺせᅉศᯒ 㟂せศᕸࢆ Pr{D(t)=2}=Pr{D(t)=3}=0.5࡜ࡋ㸪〇ရࡢ$ᗫᲠ㈝⏝%෌⏕⏘㈝⏝ㄗᕪィ᭱኱ᅾᗜ㔞ࢆ,PD[ ࡜ࡋ࡚㸪௨ୗࡢࣃ࣓࣮ࣛࢱࢆタ
ᐃࡍࡿ㸬



S

I

V

F0

920.3573
14.47400.08271934.914022
4
8

460.1786
7.237010.0206722254.74**
349.99**)  )  㸳㸬 ࠾ࢃࡾ࡟

F K E ȟ ț  ᮏ✏࡛ࡣ㸪ᣢ⥆ྍ⬟࡞࣮ࣜࣥ⏕⏘࣭≀ὶࢩࢫࢸ࣒ᵓ⠏࡟ࡴࡅࡓ࣐ࢿࢪ࣓ࣥࢺࢩࢫࢸ࣒ࡢ࠶ࡿ࡭ࡁጼ࡟ࡘ࠸࡚㸪

4.2.1෌⏕⏘ࢩࢫࢸ࣒ࡢᖹᆒ㈝⏝ࡘࡢほⅬ࠿ࡽ᳨ウࢆ࠾ࡇ࡞ࡗࡓ㸬୍ࡘࡣ㸪᪉㔪⟶⌮࠾ࡼࡇࡇ࡛ࡣ㸪ᗫᲠ๭ྜࢆȣ  ࡜ࡋࡓሙྜ࡟㸪෌⏕⏘ࡧ࣐ࢿࢪ࣓ࣥࢺࣞࣅ࣮ࣗࢆྵࡵࡓࢺ࣮ࢱ࣐ࣝࢿࢪ࣓ࣥࢺ

ࡢ๭ྜࢆኚ໬ࡉࡏ㸪ᩘ್ィ⟬ࢆ⾜ࡗࡓ㸦ᅗ 㸧㸬Ȣ ࢩࢫࢸ࣒࡛ࣞ࣋ࣝ࠶ࡾ㸪ࡶ࠺୍ࡘࡣࡑࢀࢆලయ໬ࡋ࡚ᚠ

ࡀ᭱㐺࡞෌⏕⏘๭ྜ࡜࡞ࡗ࡚࠾ࡾ㸪༢⣧࡟ᚠ⎔ࢆ㐍⾜ࡉ⎔ᆺ♫఍ࢆᐇ⌧ࡍࡿࡓࡵࡢ࣮࢜࣌ࣞࢩ࡛ࣙࣥࣞ࣋ࣝ࠶ࡿ㸬ࡏࡿࡔࡅ࡛ࡣ㸪ࢩࢫࢸ࣒ࢆ᭱㐺໬ฟ᮶࡞࠸ࡇ࡜ࢆ♧၀ࡋ⎔ቃኚ໬ࡢ⃭ࡋ࠸ࣅࢪࢿࢫ♫఍࡟࠾࠸࡚㸪࠸࠿࡟⤌⧊඲࡚࠸ࡿ㸬యࢆຠ⋡໬ࡉࡏ࡚࠸ࡃ࠿ࡀ௒ᚋࡢㄢ㢟࡛࠶ࡾ㸪ࢺࢵࣉࡢ࣐ࢿࢪ࣓ࣥࢺࣞࣅ࣮ࣗ➼኱ࡁ࡞࡛ࣞ࣋ࣝࡢ 3'&$ ࢧ࢖ࢡ㻞㻣ࣝࡢ᥎㐍ࡀᮇᚅࡉࢀࡿ㸬ࡲࡓ㸪ࡇࢀࡽࡢ᪉㔪ࢆ⌧ሙࣞ࣋㻞㻡࡛ࣝᐇ᪋ࡋ࡚࠸ࡃࡓࡵ࡟ࡣ㸪࣮࢜࣌ࣞࢩ࡛ࣙࣥࣞ࣋ࣝࡢ⟶⌮ࡶ㔜せ࡛࠶ࡾ㸪⌧ሙࡢ≧ἣ࡟ᛂࡌࡓ㐺ษ࡞࣐ࢿࢪ࣓

ᖹᆒ㈝⏝

㻞㻟

ࣥࢺࢩࢫࢸ࣒ࡀせồࡉࢀ࡚࠸ࡿ㸬ࡑࡢࡦ࡜ࡘࡢᣦ㔪࡜ࡋ㻞㻝࡚ᮏ◊✲࡛ࡢᡂᯝࡀά⏝ࡉࢀࢀࡤᖾ࠸࡛࠶ࡿ㸬㻝㻥௒ᚋࡲࡍࡲࡍࢢ࣮ࣟࣂࣝ࡞➇தࡀ⃭໬ࡍࡿࣅࢪࢿࢫ⎔䃛㻩㻜㻚㻡ቃ࡟࠾࠸࡚㸪ᣢ⥆ྍ⬟࡞ࡶࡢ࡙ࡃࡾࢩࢫࢸ࣒ࡢᵓ⠏ࡣ㸪㻝㻣㔜せ࡞ㄢ㢟࡛࠶ࡾ㸪ᡃࡀᅜࡢᡂ㛗ᡓ␎࡟ࡶ኱ࡁࡃᙳ㡪ࢆ

㻝㻡
䃚㻩㻜㻚㻝

䃚㻩㻜㻚㻞

䃚㻩㻜㻚㻟

䃚㻩㻜㻚㻠

䃚㻩㻜㻚㻡

୚࠼ࡿࡶࡢ࡜࠸࠼ࡿ㸬ᑓ㛛ศ㔝ࢆ㉺࠼ࡓࡇࡢ㡿ᇦ࡛ࡢᏛ㝿ⓗ࡞◊✲άືࡢ௒ᚋࡲࡍࡲࡍࡢάᛶ໬ࢆᮇᚅࡋࡓ࠸㸬

෌⏕⏘๭ྜ


ཧ⪃ᩥ⊩
ᅗ 㸸෌⏕⏘㔞ࡢᙳ㡪㸦ȣ 㸧 *81*25$DQG*837$60,VVXHVLQ

HQYLURQPHQWDOO\FRQVFLRXVPDQXIDFWXULQJDQGSURGXFW

4.2.2෌⏕⏘ࢩࢫࢸ࣒ࡢࢥࢫࢺศᯒUHFRYHU\DVXUYH\&RPSXWHUVDQG,QGXVWULDO(QJLQHHULQJ ࡇࡇ࡛ࡣ㸪Ȣ 㸪ȣ  ࡜ࡋ࡚㸪ᗫᲠ㈝⏝࡜෌⏕

⏘㈝⏝ࡢ㸰ࡘࡢᅉᏊࢆྲྀࡾୖࡆ㸪ྛ㸱Ỉ‽ࢆタᐃࡋ࡚ᖹ ୰ᓥ ೺୍ᯇ୸ṇᘏᯇ஭ṇஅ㸪ရ㉁࣭⎔ቃ ,62 ࡜ 740άᆒ㈝⏝ࢆồࡵࡓ㸦⾲㸯㸧㸬஧ඖ㓄⨨ࡢศᩓศᯒࢆ࠾ࡇ࡞

ື࡟ᇶ࡙ࡃ࣮ࣜࣥ⏕⏘࣐ࢿࢪ࣓ࣥࢺ⚄ዉᕝ኱ᏛᕤᏛ

ࡗࡓ⤖ᯝ㸪࠸ࡎࢀࡢせᅉࡶ㧗ᗘ࡟᭷ព࡜࡞ࡗ࡚࠸ࡿ㸦⾲◊✲ᡤᡤሗ  ྕ㸰㸧㸬 ᱵ⏣㟹ᚠ⎔ᆺ⏕⏘ࢩࢫࢸ࣒ᐇ⌧ࡢࡓࡵࡢㄢ㢟 ᪥ᮏ࢖ࣥࢲࢫࢺࣜ࢔࣭࢚ࣝࣥࢪࢽ࢔ࣜࣥࢢ༠఍ ,( ࣞࣅ࣮ࣗ
⾲㸯㸸ᩘ್ᐇ㦂⤖ᯝ

ᗫᲠ
㈝⏝

10
20
30

3
19.99
32.5
44.5



෌⏕⏘㈝⏝
6
21.5
34
46.5



9
23
35.5
47.8

  &2+(10$1$+0,$663,(56.$//$:3$G\QDPLF
LQYHQWRU\V\VWHPZLWKUHF\FOLQJ1DYDO5HVHDUFK/RJLVWLFV4XDUWHUO\ ,1'(5)857+.6LPSOHRSWLPDOUHSOHQLVKPHQWDQG
GLVSRVDOSROLFLHVIRUDSURGXFWUHFRYHU\V\VWHPZLWK⚄ዉᕝ኱ᏛᕤᏛ◊✲ᡤᡤሗ ➨  ྕ
OHDGWLPHV256SHNWUXP

 08&.67$'7-$DQG,6$$&0+$QDQDO\VLVRIVLQJOHLWHPLQYHQWRU\V\VWHPVZLWKUHWXUQV1DYDO5HVHDUFK/RJLVWLFV4XDUWHUO\
 9$1'(5/$$1($'HNNHU5DQG6$/202103URGXFWUHPDQXIDFWXULQJDQGGLVSRVDO$QXPHULFDOFRPSDULVRQRIDOWHUQDWLYHFRQWUROVWUDWHJLHV,QWHUQDWLRQDO-RXUQDORI

3URGXFWLRQ(FRQRPLFV
 9$1'(5/$$1($DQG6$/202103URGXFWLRQSODQQLQJDQGLQYHQWRU\FRQWUROZLWKUHPDQXIDFWXULQJDQG
GLVSRVDO(XURSHDQ-RXUQDORI2SHUDWLRQDO5HVHDUFK

 *8,'(-U9'5DQG:DVVHQKRYH/190DQDJLQJSURGXFWUHWXUQVIRUUHPDQXIDFWXULQJ3URGXFWLRQ2SHUDWLRQV0DQDJHPHQW *8,'(-U9'5DQG:DVVHQKRYH/19
&ORVHGORRSVXSSO\FKDLQV5$\HUV/$\UHVHGV$+DQGERRNRI,QVXGWULDO(FRORJ\(GZDUG(OJDU1RUWKDPSWRP0$ *8,'(-U9'53URGXFWLRQSODQQLQJDQG
FRQWUROIRUUHPDQXIDFWXULQJ-RXUQDORI2SHUDWLRQV

0DQDJHPHQW
 1$.$6+,0$.$5,0,768+126(7DQG.85,<$0$6$QDO\VLVRIDSURGXFWUHFRYHU\V\VWHP,QWHUQDWLRQDO-RXUQDORI3URGXFWLRQ5HVHDUFK

 1$.$6+,0$.$5,0,768+126(7DQG.85,<$0$6
&RVWDQDO\VLVRIDUHPDQXIDFWXULQJV\VWHP$Q

,QWHUQDWLRQDO-RXUQDO$VLD3DFLILF0DQDJHPHQW5HYLHZ

 1$+0,$662SWLPDODQGDSSUR[LPDWHRUGHULQJSROLFLHVIRUDSHULVKDEOHSURGXFWVXEMHFWWRVWRFKDVWLF
GHPDQG 3+''LVVHUWDWLRQ1RUWKZHVWHUQ8QLYHUVLW\ 㔠Ꮚᾈ୍㸪୰ᓥ೺୍㸪⬟ໃ㇏୍㸪㹇㹑㹍㹑࡜ 740 ࡢ⼥ྜ࡟ࡼࡿရ㉁⤒Ⴀ᝟ሗࡢయ⣔໬࡟㛵ࡍࡿ◊✲࢜ࣇ࢕ࢫ
࣮࢜ࢺ࣓࣮ࢩࣙࣥ ᪥ᮏつ᱁༠఍ 㸪-,6 ࣁࣥࢻࣈࢵࢡ ,62㸪
㸦㈈㸧᪥ᮏつ᱁༠఍

⎔ቃㄪ࿴ᆺ≀㉁ኚ᥮ཬࡧ࢚ࢿࣝࢠ࣮ࣉࣟࢭࢫ๰ฟࡢ
᪂ᇶ┙࡜࡞ࡿࢼࣀᵓ㐀ゐ፹ࡢ㛤Ⓨᘬᆅ ྐ㑻㸨   ෆ⸨ ࿘ᘤ㸨   ྜྷ⏣ ᬡᘯ㸨㸨   ୰⃝ 㡰㸨㸨

Development of Nano-scale Fine Structure Catalysts for Green Chemistry and Novel
Energy Processes
Shiro HIKICHI㸨

Shuichi NAITO㸨

Akihiro YOSHIDA㸨㸨Jun NAKAZAWA㸨㸨㸯㸬⥴ゝ✲࡛ࡣ㸪ᣢ⥆ྍ⬟࡞♫఍ᵓ⠏ࡢᇶ┙࡜࡞ࡿ㧗ᛶ⬟ゐ፹ࡢ‫ڧ‬2011 ᖺ 3 ᭶ࡢ㟈⅏௨㝆㸪ࢃࡀᅜࡢ㈨※࣭࢚ࢿࣝࢠ࣮஦

㛤Ⓨࢆ⾜࡞ࡗ࡚࠸ࡿ㸬ලయⓗ࡟ࡣ㸪㔠ᒓඖ⣲ࡀᣢࡘゐ፹᝟࡜ࡑࢀࢆྲྀࡾᕳࡃㅖၥ㢟ࡣ┈ࠎ῝้໬ࡋ࡚࠾ࡾ㸪ᣢ⥆ᛶ⬟ࢆᴟ㝈ࡲ࡛ᘬࡁฟࡍࡇ࡜ࡸ㸪ኳ↛ࡢ㧗ᛶ⬟ゐ፹࡛࠶ྍ⬟࡞♫఍ࢆ⠏࠸࡚࠸ࡃ࡟ࡣ㸪᪂ᢏ⾡ࡢ๰ฟࡀồࡵࡽࢀࡿ㓝⣲࡜ྠᵝ࡟㸪ᵝࠎ࡞ᶵ⬟ࢆేࡏᣢࡘゐ፹ࢹࣂ࢖ࢫࡢ

࡚࠸ࡿ㸬໬▼⇞ᩱ㈨※ࡣ㸪᪤Ꮡࡢࢩࢫࢸ࣒࡟࠾ࡅࡿ୺せᵓ⠏ࢆ┠ᣦࡋ࡚㸪ࢧࣈࢼࣀ㹼ࢼࣀࢫࢣ࣮࡛ࣝᵓ㐀ࡀไᚚ࡞࢚ࢿࣝࢠ࣮※࡛࠶ࡿ࡜ྠ᫬࡟ᡃࠎࡢ⏕άࢆᨭ࠼ࡿᵝࠎ

ࡉࢀࡓゐ፹㸪ࡍ࡞ࢃࡕ͆ࢼࣀᵓ㐀ゐ፹͇ࡢ㛤Ⓨࢆ᳨ウࡋ࡞≀㉁ࡢཎᮦᩱ࡛ࡶ࠶ࡿ㸬ᚑࡗ࡚㸪▼Ἔ࣭▼Ⅳ࣭ኳ↛࡚࢞࠸ࡿ㸬ࢫ➼ࡢ฼⏝ຠ⋡ࢆྥୖࡉࡏ㸪࠿ࡘ࢚ࢿࣝࢠ࣮ࡢ㐣๫ᾘ㈝ ⌧ᅾ◊✲㛤Ⓨ୰ࡢ᪂つࢼࣀᵓ㐀ゐ፹ࡣ㸪㧗࠸⪏⇕ᛶ࡜ࡸ⎔ቃ㈇Ⲵ≀㉁᤼ฟࢆᢚไࡋࡓ⎔ቃㄪ࿴ᆺ≀㉁ኚ᥮ࣉࣟ

ᶵᲔⓗᙉᗘࢆ᭷ࡋ㸪ࢼࣀࢫࢣ࣮࡛ࣝᵓ㐀ไᚚࡉࢀࡓ↓ᶵࢭࢫࢆᵓ⠏ࡍࡿࡇ࡜ࡣႚ⥭ࡢㄢ㢟࡛࠶ࡿ㸬ࡲࡓ㸪࢚ࢿࣝ㓟໬≀ከᏍయࢆᢸయ࡜ࡋ㸪ࡇࢀ࡟ศᏊᵓ㐀ࡸཎᏊ㓄ิࡀࢠ࣮ၥ㢟ࡢゎỴ࡟ࡣኴ㝧ග࡟௦⾲ࡉࢀࡿ෌⏕ྍ⬟࢚ࢿࣝไᚚࡉࢀࡓゐ፹άᛶⅬࢆᵓ⠏ࡋࡓࡶࡢ࡛࠶ࡿ㸬ᮏඹྠ◊ࢠ࣮ࡸỈ⣲࣭ࣂ࢖࣐࢜ࢫ➼ࡢ௦࢚᭰ࢿࣝࢠ࣮ࢆ㍈࡜ࡍࡿ✲࡛ࡣ㸪㸰ࡘࡢ◊✲ࢢ࣮ࣝࣉࡀಖ᭷ࡍࡿᢏ⾡ⓗ㛗ᡤࡢ⼥᪂ࡓ࡞࢚ࢿࣝࢠ࣮ኚ᥮ࢩࢫࢸ࣒ࡢ㛤Ⓨࡀᛴົ࡛࠶ࡿ㸬ࡉྜ࡟ࡼࡾ᪂つࢼࣀᵓ㐀ゐ፹ࡢ㛤Ⓨࢆ┠ᣦࡋ࡚࠸ࡿ㸬ෆ⸨㸪ࡽ࡟ࡇࢀࡽࡢ㛤Ⓨ࡟࠶ࡓࡗ࡚ࡣ㸪ᆅ⌫⎔ቃಖ඲ࡶྠ᫬࡟

ྜྷ⏣ࡢ◊✲ࢢ࣮ࣝࣉࡣ࢚ࢿࣝࢠ࣮ࡸ⎔ቃಖ඲࡟㛵ࢃࡿゐ㐩ᡂࡋ࡞ࡅࢀࡤᣢ⥆ྍ⬟࡞♫఍ࡣ⠏ࡅ࡞࠸㸬፹ࡢ㛤Ⓨᐇ⦼ࡀ࠶ࡾ㸪↓ᶵ㓟໬≀ከᏍయࡢᵓ㐀ไᚚ࡜ࡇ ໬Ꮫ཯ᛂ࡟ࡼࡿ≀㉁ኚ᥮ ≀㉁⏕⏘ࡸ⎔ቃởᰁ≀㉁ࡢ

ࢀࢆά⏝ࡋࡓゐ፹㧗ᛶ⬟໬࡟㛵ࡍࡿࣀ࢘ࣁ࢘ࢆ᭷ࡋ࡚࠸

↓ᐖ໬➼ ࡸ࢚ࢿࣝࢠ࣮ኚ᥮ࡢຠ⋡ྥୖ࡟㈨ࡍࡿゐ፹ࡣ㸪

ࡿ(1)㸬୍᪉ᘬᆅ㸪୰⃝ࡢ◊✲ࢢ࣮ࣝࣉࡣ㸪㓝⣲ࡢゐ፹ά⎔ቃㄪ࿴ᆺ≀㉁ኚ᥮࠾ࡼࡧ᪂࢚ࢿࣝࢠ࣮ࣉࣟࢭࢫ๰ฟࢆ

ᛶⅬ࡟ೌࡗࡓ㔠ᒓ㘒యゐ፹ࡢ㛤Ⓨ࡟ᦠࢃࡗ࡚࠾ࡾ㸪⢭ᐦ㐩ᡂࡍࡿࡓࡵ࡟Ḟࡃ࡭࠿ࡽࡊࡿࡶࡢ࡛࠶ࡾ㸪ࡑࡢ㧗ᛶ⬟ศᏊタィࡢᡭἲࢆ㥑౑ࡋࡓゐ፹άᛶⅬᵓ㐀ࡢไᚚ࡟ࡘ࠸

໬ࡣ௒࡞࠾♫఍࠿ࡽࡢせㄳࡀከ࠸᳨ウㄢ㢟࡛࠶ࡿ㸬ࡲࡓ࡚ࡢ◊✲ᐇ⦼ࢆ᭷ࡍࡿ(2)㸬ࡇࢀࡽࡢࣂࢵࢡࢢࣛ࢘ࣥࢻ࡟

ゐ፹࡟ࡣࡇࢀࡲ࡛㈗㔠ᒓࡀከ⏝ࡉࢀ࡚ࡁࡓࡀ㸪ᕼᑡ࡞㔠

ᇶ࡙ࡁ㈨※࣭࢚ࢿࣝࢠ࣮࣭⎔ቃၥ㢟ࡢゎỴ࡟㈨ࡍࡿ᪂つᒓ㈨※ࢆ⏝࠸⥆ࡅࡿࡇ࡜ࡣḟ➨࡟ᅔ㞴࡟࡞ࡾࡘࡘ࠶ࡾ㸪ゐ፹ࢆ㛤Ⓨࡍࡿࡇ࡜ࡀᮏඹྠ◊✲ࡢ㦵Ꮚ࡛࠶ࡿ㸬࠸ࢃࡺࡿ͆ඖ⣲ᡓ␎͇ࡢほⅬ࠿ࡽࡶゐ፹࡟⏬ᮇⓗ࡞㧗ᛶ⬟໬ࢆࡶࡓࡽࡍᢏ⾡㠉᪂ࡀồࡵࡽࢀ࡚࠸ࡿ㸬ࡑࡇ࡛ᮏ◊㸰㸬ゐ፹ᢸయ࡜ࡋ࡚ࡢከᏍయࢩࣜ࢝ࢤࣝ
‫ڧ‬ᅛయゐ፹ࡣ㸪Ẽ┦ࡸᾮ┦୰࡟Ꮡᅾࡍࡿ཯ᛂ≀࡟ᑐࡋ࡚㸪*ᩍᤵ ≀㉁⏕࿨໬Ꮫ⛉
Professor, Dept. of Material and Life Chemistry**≉ูຓᩍ ≀㉁⏕࿨໬Ꮫ⛉
Assistant Professor, Dept. of Material and Life Chemistryᅛ┦࡟Ꮡᅾࡍࡿゐ፹ࡀస⏝ࡍࡿࡇ࡜࡛໬Ꮫ཯ᛂࡀ㐍⾜ࡍࡿ୙ᆒ୍⣔཯ᛂ࡟౪ࡉࢀࡿ㸬ࡍ࡞ࢃࡕᅛయゐ፹࡟࠾࠸࡚㸪ゐ፹ᶵ⬟ࢆྖࡿάᛶⅬࡣ┦⏺㠃࡟఩⨨ࡍࡿࡇ࡜࠿ࡽ㸪⏺

⚄ዉᕝ኱ᏛᕤᏛ◊✲ᡤᡤሗ ➨  ྕ㠃࡛࠶ࡿᢸయ⾲㠃ࡢᵓ㐀ࡣゐ፹≉ᛶࡢᨭ㓄ᅉᏊ࡜࡞ࡿ㸬య⾲㠃࡬㐃⤖ྍ⬟࡞ࢩࣛࣀ࣮࢚ࣝࢫࢸࣝ㒊఩ࢆ᭷ࡍࡿ

ゐ፹ࡀ཯ᛂ≀࡜ྠ୍┦࡟Ꮡᅾࡍࡿᆒ୍⣔཯ᛂ࡟ẚ࡭㸪୙

NNO ᆺ 3 ᗙ࣮࢟ࣞࢺ࡛࠶ࡿ ȕ㸫ࢣࢳ࣑ࢼࢺ㓄఩Ꮚ L1 ࢆᆒ୍཯ᛂ࡛ࡣゐ፹࡜཯ᛂ≀ࡢ⾪✺㢖ᗘࡀపࡃ࡞ࡗ࡚ࡋࡲ

ྜᡂࡋ㸪⾲㠃✚ࡀ࡯ࡰྠ⛬ᗘ 600㹼700 m2/g ࡢ஧✀㢮ࡢ࠺㸬ࡑࡢࡓࡵᅛయゐ፹ࡢᢸయ࡜ࡋ࡚ࡣ༢఩య✚࠶ࡿ࠸ࡣࢩࣜ࢝⾲㠃࡟ᑐࡋ࡚ᢸᣢᐦᗘࡀ࡯ࡰ➼ࡋࡃ࡞ࡿࡼ࠺

༢఩㉁㔞࠶ࡓࡾࡢ⾲㠃✚ࡀ኱ࡁ࠸᪉ࡀᮃࡲࡋ࠸㸬࡜ࡇࢁ

0.08 ~ 0.09 molecule/nm2 ࡟ᅛᐃࡋࡓ SBA-L1, SiO2-L1 㸬࡛ᢸయ࡟ᚤ⣽ᏍࡀከࡃᏑᅾࡍࡿሙྜ㸪⾲㠃✚ࡣ኱ࡁࡃ࡞

࡞࠾ᢸయ⾲㠃࡟ṧ␃ࡍࡿỈ㓟ᇶ ࢩࣛࣀ࣮ࣝᇶ࡜⛠ࡉࢀࡿࡀ㸪ศᏊ࡛ࣞ࣋ࣝࡳࡿ࡜ࡑࡢ⾲㠃ᵓ㐀ࡣ⢒࠸ࡶࡢ࡜࡞

ࡿ Si–OH 㒊఩ ࡣ㸪ᅛᐃࡋࡓ㓄఩Ꮚ࡟ᑐࡍࡿ྾╔⬟࠾ࡼࡗ࡚࠸ࡿ㸬ࡇࡢࡼ࠺࡞ሙྜ㸪཯ᛂ≀ࡀ࢔ࢡࢭࢫ࡛ࡁ࡞࠸

ࡧ㔠ᒓ࢖࢜ࣥ࡟ᑐࡍࡿ㓄఩⬟ࢆ᭷ࡍࡿࡓࡵ࡟㸪ᆒ୍࡞ゐᚤ⣽Ꮝෆ㒊࡟ᙧᡂࡉࢀࡓゐ፹άᛶⅬࡣᶵ⬟ࡋ࡞࠸ࡓࡵ㸪፹άᛶⅬࡢᵓ⠏ࢆጉࡆࡿせ⣲࡜࡞ࡾ࠼ࡿ㸬ࡑࡇ࡛㓄఩Ꮚ┦ᑐⓗ࡟᭷ຠ࡞ゐ፹άᛶⅬࡀῶᑡࡋ࡚ࡋࡲ࠺㸬ࡲࡓᢸయᅛᐃᚋ࡟࣊࢟ࢧ࣓ࢳࣝࢪࢩࣛࢨࣥ (Me3Si)2NH ࢆస⏝ࡉ⾲㠃࡟㔠ᒓ㘒యゐ፹άᛶⅬࢆᅛᐃࡋࡓ㸪࠸ࢃࡺࡿᅛᐃ໬

ࡏࡿࡇ࡜࡛㸪
Ỉ㓟ᇶࢆࢺ࣓ࣜࢳࣝࢩࣜࣝ SiMe3 ࢚ࢫࢸࣝ㘒యゐ፹࡛ࡣ㸪ゐ፹άᛶⅬྠኈࡢ㛫㝸ࡀ⊃ࡲࡿࡇ࡜࡛఍

࡟ኚ᥮ࡋ㸪྾╔࣭㓄఩⬟ࢆ⁛ኻࡉࡏ࡚࠸ࡿ㸬࡞࠾ࡇࡢࢺ

ྜ≧ែࡀ⏕ࡌ㸪཯ᛂᛶࡀኚ໬ࡋ࡚ࡋࡲ࠺ࡇ࡜ࡶᠱᛕࡉࢀ

࣓ࣜࢳࣝࢩࣜࣝ໬ฎ⌮ࡢ᭷↓࡟ࡼࡗ࡚㸪ᢸయ⾲㠃ࡢ᭷ᶵࡿ㸬ࡉࡽ࡟᭷ᶵ㧗ศᏊࡸ࣑ࢭࣝ⭷➼ࡢᰂ㌾࡞ᵓ㐀ࢆᣢࡘᐁ⬟ᇶࡢ㓄⨨ࡀኚ໬ࡋ࡚ࡋࡲ࠺ࡇ࡜ࡣ᪤࡟ሗ࿌ࡉࢀ࡚࠸

ᢸయࢆ⏝࠸ࡿ࡜㸪ゐ፹ㄪ〇ࡸ཯ᛂ᫬࡟⁐ᾮ୰࡟ᾐࡍࡇ࡜

ࡿ(5, 6)㸬ࡇ࠺ࡋ࡚ᚓࡽࢀࡓ㓄఩Ꮚᅛᐃ໬ᢸయ࡟ᑐࡋ࡚ሷ໬

࡛⭾₶࡞࡝࡟ࡼࡗ࡚ᢸయ⮬㌟ࡀὶືᛶࢆᣢࡕ㸪⤖ᯝ࡜ࡋ㕲(III)ࢆస⏝ࡉࡏࡿࡇ࡜࡛ᅛᐃ໬㘒యゐ፹ Fe/SBA-L1 ࠾࡚ゐ፹άᛶⅬᵓ㐀ࡀኚ໬ࡋ࡚ࡋࡲ࠺ࡇ࡜ࡀ⪃࠼ࡽࢀࡿ㸬ࡼࡧ Fe/SiO2-L1 ࡟ㄏᑟࡋ㸪㔠ᒓ࡜㓄఩Ꮚࡢẚ⋡ࡑࡋ࡚㐣ᚑࡗ࡚ᮏ◊✲࡛ࡣ๛┤࡞ᵓ㐀ࢆᣢࡕ㸪⾲㠃✚ࡶ኱ࡁࡃ࠿

㓟໬Ỉ⣲ࢆ㓟໬๣࡜ࡋࡓࢩࢡࣟ࣊࢟ࢭࣥ㓟໬࡟ᑐࡍࡿά

ࡘ໬Ꮫಟ㣭ࡀᐜ᫆࡟⾜࠼ࡿᖹ⁥࡞⾲㠃ᵓ㐀ࢆ᭷ࡍࡿ↓ᶵᛶࢆホ౯ࡋࡓ㸬㓟໬≀ࢆᢸయ࡜ࡍࡿࡇ࡜࡜ࡋࡓ㸬ࡇࡢࡼ࠺࡞≉ᛶࢆഛ࠼࡜ࡇࢁ࡛㓄఩Ꮚࡢ㐠ືࡀไ㝈ࡉࢀ࡞࠸⁐ᾮ୰࡟࠾࠸࡚㸪ࡿࡶࡢ࡜ࡋ࡚㸪࣓ࢯከᏍᛶࢩࣜ࢝ࢤࣝࡢ୍✀࡛࠶ࡿ

L1 ࡣ㕲࢖࢜ࣥ࡟ᑐࡋ࡚ 2 ศᏊ⤖ྜࡍࡿࡇ࡜࡛⇕ຊᏛⓗ

SBA-15(3)ࡀᣲࡆࡽࢀࡿ㸬ࡇࢀࡣࣁࢽ࣒࢝ᵝࡢつ๎ⓗ࡞⣽࡟᭱ࡶᏳᐃ࡞ᵓ㐀య[Fe(L1)2] ࡀᙧᡂࡉࢀࡿࡀ㸪ࡇࢀࡣ㕲Ꮝᵓ㐀ࢆ᭷ࡋ㸪኱⾲㠃✚ 㹼1000 m2/g ࠾ࡼࡧ⣽Ꮝ┤ᚄ࢖࢜ࣥ୰ᚰ࡟㓟໬๣ࢆάᛶ໬ࡍࡿࡓࡵࡢ⤖ྜ㒊఩ 㓄఩

⣙ 5㹼10 nm ࡣᏍෆ࡬ࡢẚ㍑ⓗᐜ᫆࡞≀㉁ᣑᩓࢆಖ㞀ᗙ ࢆᣢࡓ࡞࠸ࡓࡵゐ፹άᛶࢆ♧ࡉ࡞࠸㸬୍᪉㸪ㄪ〇ࡋࡓࡍࡿ㸬ࡉࡽ࡟ཌ࠸⣽Ꮝቨ ⣙ 5 nm ࡣ༑ศ࡞ᶵᲔⓗ࠾ࡼࡧᅛᐃ໬㘒యゐ፹࡟࠾ࡅࡿ㓄఩Ꮚᑐ㔠ᒓࡢẚ⋡ࡣ㸪໬Ꮫⓗᙉᗘࢆ᭷ࡋ࡚࠸ࡿ㸬ࡑࡇ࡛ᡃࠎࡣࡲࡎࡇࡢ࣓ࢯከᏍᛶࢩࣜ࢝ᢸయࡢ᭷⏝ᛶ

Fe/SBA-L1 ࡛ࡣ 1:1 ࡛࠶ࡗࡓࡢ࡟ᑐࡋ࡚㸪Fe/SiO2-L1 ࡛ࡣ㕲ᢸᣢ㔞ࡀῶᑡࡋ࡚⣙ 2:1 ࡜࡞ࡗࡓ㸬ࡑࡋ࡚ゐ፹άᛶ࡟ࡘ࠸᳨࡚ドࡍࡿࡇ࡜࡜ࡋࡓ㸬≉࡟ᢸయ⾲㠃ࡢᵓ㐀㕲ཎᏊ 1 ಶ࠶ࡓࡾࡢゐ፹ᅇ㌿ᩘ ࡣ㸪Fe/SBA-L1 ࡢ 8.3

morphology ࡜ゐ፹≉ᛶࡢ┦㛵ࢆ᫂ࡽ࠿࡟ࡍࡿࡓࡵ㸪኱࡟ᑐࡋ࡚ Fe/SiO2-L1 ࡣ 5.2 ࡛࠶ࡗࡓ㸬ࡇࢀࡽࡢ⤖ᯝࡣḟᏍᚄ࠿ࡘᏍつ๎ᛶࡢ㧗࠸ SBA-15 ࡜㸪ᵝࠎ࡞ࢧ࢖ࢬࡢ⣽ࡢࡼ࠺࡟ゎ㔘࡛ࡁࡿ㸬⢒࠸⾲㠃ࢆ᭷ࡋ࡚࠸ࡿࡓࡵ࡟ᢸᣢ

Ꮝࡀΰᅾࡍࡿᕷ㈍ࡢከᏍᛶ࢔ࣔࣝࣇ࢓ࢫࢩࣜ࢝ࢤࣝ

L1 : Fe = 2 :1
ࡋࡓ㓄఩Ꮚࡀ㏆᥋ࡋ࡚࠸ࡿ Fe/SiO2-L1 ࡛ࡣ㸪

SiO2 ࢆᢸయ࡜ࡋࡓ㕲㘒యゐ፹ࢆ᪂ࡓ࡟㛤Ⓨࡋ㸪ࡑࡢᵓ࡛࠶ࡿࡇ࡜ࢆ⪃࠼ేࡏࡿ࡜㸪⁐ᾮ୰࡜ྠᵝ࡟㓄఩㣬࿴࡛㐀࠾ࡼࡧゐ፹άᛶࢆẚ㍑ࡋࡓ(4)㸬ᅗ 1 ࡢࡼ࠺࡟ࢩࣜ࢝ᢸ

ゐ፹άᛶࢆᣢࡓ࡞࠸[Fe(L1)2]+✀ࡀᙧᡂࡉࢀࡿࡶࡢ࡜⪃࠼ࡽࢀࡿ㸬ࡋ࠿ࡋ Fe/SiO2-L1 ࡣ Fe/SBA-L1 ࡢ 6 ๭⛬ᗘࡢάᛶࢆ᭷ࡋ࡚࠸ࡓࡇ࡜ࡼࡾ㸪ࡍ࡭࡚ࡢ㕲ࡀ[Fe(L1)2]+ࡢ≧ែ࡛ᢸᣢࡉࢀ࡚࠸ࡿࡢ࡛ࡣ࡞ࡃ㸪㓟໬๣⤖ྜ㒊఩ࢆᣢࡘゐ፹άᛶⅬ[Fe(L1)]2+ࡶᙧᡂࡉࢀ࡚࠾ࡾ㸪ࡉࡽ࡟ᚤ⣽Ꮝෆ㒊࡟఩⨨ࡋ࡚࠸ࡿࡓࡵ࡟㕲ࡀ㓄఩ࡋ࡚࠸࡞࠸ L1 ࡶᏑᅾࡋ࡚࠸ࡿࡇ࡜ࡀ⪃࠼ࡽࢀࡿ㸬୍᪉ᢸయ⾲㠃ࡀࡼࡾᖹ⁥࡞
Fe/SBA-L1 ࡛ࡣ㸪ᅛᐃࡉࢀ࡚࠸ࡿ L1 ࡢศᩓᗘࡀ㧗࠸ࡓ
ࡵ࡟ᐇ㉁ⓗ࡞άᛶⅬ࡛࠶ࡿ[Fe(L1)]2+㘒యࡀ┦ᑐⓗ࡟ከࡃᙧᡂࡉࢀ㸪ゐ፹άᛶࡀ㧗࠿ࡗࡓࡇ࡜ࡀ⪃࠼ࡽࢀࡿ ᅗ
2 㸬࡜ࡇࢁ࡛ Fe/SBA-L1 ࡢゐ፹άᛶࡣ㸪ࢃࡎ࠿࡞㔞 㕲࡜࡯ࡰ➼㔞 ࡢሷᇶࢆῧຍࡍࡿࡇ࡜࡟ࡼࡾྥୖࡍࡿࡀ㸪ࡑᅗ㸯㸬SBA-L1 ࠾ࡼࡧ SiO2-L1 ࡢㄪ〇ࡢάᛶࡣሷᇶࡢศᏊᵓ㐀࡟౫Ꮡࡋ࡚࠸ࡿࡇ࡜ࡶ᫂ࡽ࠿࡟

⎔ቃㄪ࿴ᆺ≀㉁ኚ᥮ཬࡧ࢚ࢿࣝࢠ࣮ࣉࣟࢭࢫ๰ฟࡢ᪂ᇶ┙࡜࡞ࡿࢼࣀᵓ㐀ゐ፹ࡢ㛤ⓎࡍࡿỈ㓟ᇶ࡟㓟ᛶ≀㉁ X–H ࡸ࢚ࢫࢸࣝ໬ྜ≀ X–ORࢆస⏝ࡉࡏࡿࡇ࡜࡛㸪Ỉࡸ࢔ࣝࢥ࣮ࣝࡢ⏕ᡂࢆకࡗ࡚᭷
ᶵᐁ⬟ᇶ X ࢆᢸయ⾲㠃࡟ᅛᐃࡍࡿ᪉ἲ㸪࠸ࢃࡺࡿ post
synthesis ἲࡀ୍⯡࡟ᗈࡃ⏝࠸ࡽࢀ࡚࠸ࡿ㸬๓⠇࡛㏙࡭ࡓ
ᅛᐃ໬㘒యゐ፹ࡶࡇࡢ᪉ἲ࡟ࡼࡾㄪ〇ࡋ࡚࠸ࡿ㸬ࡇࡢ᪉ἲࡣ⡆౽࡞᧯స࡛ᢸయࡢ໬Ꮫಟ㣭ࡀྍ⬟࡛࠶ࡿ࡜࠸࠺฼
Ⅼࢆ᭷ࡍࡿࡀ㸪ᢸయ⾲㠃ࡢ X ࡢᅛᐃᐦᗘ࠾ࡼࡧศᩓ≧ែࡢไᚚࡣᐜ࡛᫆ࡣ࡞࠸㸬ࡇࢀࡣᢸయ⾲㠃ࡢỈ㓟ᇶࡢ㔞ࡸศᕸࡣࡶࡕࢁࢇࡢࡇ࡜㸪ᅛᐃࡋࡼ࠺࡜ࡍࡿ࢚ࢫࢸࣝ໬ྜ
≀ X–OR ྠኈࡢ⦰ྜࡶ࠾ࡇࡾ࠼ࡿࡇ࡜㸪ࡉࡽ࡟ࡣ᭷ᶵ
ᐁ⬟ᇶ X ࡢᛶ㉁࡟ࡶ౫Ꮡࡍࡿࡓࡵ࡛࠶ࡿ㸬≉࡟ X ྠኈࡀ
Ỉ⣲⤖ྜ➼࡟ࡼࡾศᏊ㛫࡛┦஫స⏝ࡋࡸࡍ࠸ሙྜ࡟ࡣ㸪ᅗ㸰㸬Fe/SBA-L1 ࠾ࡼࡧ Fe/SiO2-L1 ࡢ᥎ᐃᵓ㐀㧗ศᩓ≧ែࢆ⥔ᣢࡋࡓࡲࡲ࡛ࡢᅛᐃࡣᅔ㞴࡜࡞ࡿ㸬ࡋ࠿ࡋ࡞ࡀࡽ㸪ᮏ◊✲࡛ᑟධࡋࡼ࠺࡜ࡍࡿᐁ⬟ᇶ X ࡜ࡣ㸪᭦࡞ࡿ໬Ꮫኚ᥮࡟ࡼࡾ㧗ḟᶵ⬟໬ࡀᅗࡿࡇ࡜ࡀ࡛ࡁࡿࡶࡢ
㓄఩Ꮚ࡜ࡢ㐃⤖ࡀྍ⬟࡞཯ᛂᛶ≀㉁ ࡸ㸪ࡑࡢࡶࡢ⮬యࡀ㔠ᒓᨭᣢ㓄఩Ꮚ࡜࡞ࡿࡶࡢ㸪࠶ࡿ࠸ࡣᇶ㉁ㄆ㆑⬟ࡸゐ፹ᶵ⬟ࢆᣢࡘࡶࡢ࡛࠶ࡾ㸪ࡇࢀࡽࡣࣝ࢖ࢫ࠶ࡿ࠸ࡣࣈࣞ

120ࣥࢫࢸࢵࢻሷᇶᛶࡲࡓࡣ㓟ᛶࢆ᭷ࡋ࡚࠸ࡿࡓࡵ࡟ᮏ㉁ⓗ࡟ศᏊ㛫࡛ࡢ┦஫స⏝ࢆ㉳ࡇࡋࡸࡍ࠸㸬ࡇࡢࡼ࠺࡞ X ྠ
80
TONኈ࡟ࡼࡿศᏊ㛫┦஫స⏝ࢆᢚไࡍࡿࡓࡵ࡟ࡣ㸪X ࡟㐺ษ࡞ಖㆤᇶࢆᑟධࡍࡿࡇ࡜ࡀ᭷ຠ࡛࠶ࡿ㸬Jones ࡽࡣ40

SBA-15 ࡟࢔ࣝ࢟ࣝ࢔࣑ࣀᇶ –CH2CH2CH2NH2 ࢆᅛᐃࡍNo additiveࡿ࡟࠶ࡓࡾ㸪ᮎ➃࢔࣑ࣀᇶ㒊఩ࢆ❧యⓗ࡟࠿ࡉ㧗࠸ࢺࣜ
0

0

60

120

180

240

ࢳࣝᇶ –C(C6H5)3 ࡛ಖㆤࡋࡓ≧ែ࡛ᅛᐃࡋ㸪ࡑࡢᚋ⬺ಖ

300

Time / min.

ᅗ㸱㸬ሷᇶῧຍ᫬ࡢ Fe/SBA-L1 ࡢゐ፹άᛶㆤࢆ⾜࠺ࡇ࡜࡟ࡼࡾ㸪᭷ᶵ࢔࣑ࣀᇶྠኈࡀ㧗ศᩓ≧ែ࡛ᅛᐃࡉࢀ࡚࠸ࡿࡇ࡜ࢆሗ࿌ࡋ࡚࠸ࡿ(5)㸬࡞࠾ᑟධࡍࡿಖ
ㆤᇶࡀࡉ࡯࡝❧యⓗ࡟࠿ࡉ㧗ࡃ࡞࠸ࣇ࢙ࢽࣝᇶ –C6H5

࡞ࡗࡓ ᅗ 3 㸬ࡇࡢࡇ࡜ࡣ㸪ゐ፹άᛶⅬࡣῧຍࡋࡓሷᇶ

ࡢሙྜ࡟ࡣ㸪ಖㆤᇶࢆᑟධࡏࡎ࡟ᅛᐃࡋࡓሙྜࡼࡾ࢔ࣝ

ࡸ㓟໬๣࡛࠶ࡿ㐣㓟໬Ỉ⣲⏤᮶ࡢ HOO–ࢆ⤖ྜࡍࡿవᆅ

࢟ࣝ࢔࣑ࣀᇶࡢᅛᐃ㔞ࡣῶᑡࡍࡿࡶࡢࡢ㸪ᅛᐃࡉࢀ࡚࠸

ࢆṧࡋࡓᵓ㐀 ࡇࡢࡼ࠺࡞≧ែࢆ͆㓄఩୙㣬࿴✀͇࡜࠸࠺ࡿ࢔࣑ࣀᇶྠኈࡣ᥋㏆ࡋ࡚࠸ࡿࡇ࡜ࡶྠ᫬࡟ሗ࿌ࡉࢀ࡚

࡛࠶ࡾ㸪ඛ࡟♧ࡋࡓ[Fe(L1)]2+ࡀάᛶⅬ࡛࠶ࡿࡇ࡜ࢆ♧၀࠸ࡿ㸬ࡍ࡞ࢃࡕ㸪ಖㆤᇶ࡟ࡘ࠸࡚ࡶ㐺ษ࡞ศᏊタィࢆ⾜ࡋ࡚࠸ࡿ㸬࡞࠺ࡇ࡜ࡀᚲせ࡛࠶ࡿ㸬㸱㸬ᢸయ⾲㠃ࡢ᭷ᶵศᏊ࡟ࡼࡿ໬Ꮫಟ㣭

one-pot synthesis ἲ࡟ࡼࡿ໬Ꮫಟ㣭࣓ࢯከᏍᛶࢩࣜ࢝ࡢྜ

 ୖ㏙ࡢࡼ࠺࡟㸪ᩘ್ୖࡣ㓄఩Ꮚᅛᐃᐦᗘࡀ࡯ࡰྠࡌ࡛

ᡂࡀ⾜࡞ࢃࢀࡿࡼ࠺࡟࡞ࡗ࡚ࡁࡓ㸬ࡇࢀࡣ࣓ࢯከᏍᛶࢩ

࠶ࡿ࡟ࡶ࠿࠿ࢃࡽࡎ㸪ᢸయ⾲㠃ࡢᵓ㐀 ᖹ⁥ࡉ ࡀ␗࡞ࡿࣜ࢝ࢤࣝࡀ㸪
͆Ꮝ͇ࡢ㉳※࡛࠶ࡿ㗪ᆺ๣ࡢ⾲㠃࡛㸪͆ࢩࣜ ࡑࡇ࡛㏆ᖺ post synthesis ἲ࡟᭰ࢃࡿࡶࡢ࡜ࡋ࡚㸪ࡇ࡜࡛㸪㓄఩Ꮚྠኈࡢ㛫㝸ࡀኚ໬ࡋ࡚ࡋࡲ࠺ࡓࡵ࡟ᢸయ

࢝※͇࡜࡞ࡿࢸࢺ࢚ࣛࢺ࢟ࢩࢩࣛࣥ(Si(OEt)4)ࡢຍỈศ⾲㠃࡟ᙧᡂࡉࢀࡿ㘒యศᏊࡢᵓ㐀ࡀኚ໬ࡋ࡚ࡋࡲ࠺ࡇ࡜

ゎ࣭⬺Ỉ⦰ྜࢆ⾜࠺ࡇ࡜࡛஧㓟໬ࢣ࢖⣲(SiO2)ࡢ͆ቨ͇ࢆ

ࡀ᫂ࡽ࠿࡟࡞ࡗࡓ㸬ࡑࡋ࡚ࡇࡢ⤖ᯝࡣ㸪ᖹ⁥࡞⾲㠃ᵓ㐀ᙧᡂࡉࡏࡓᚋ࡟㗪ᆺࢆ㝖ཤࡍࡿ࡜࠸࠺ࣉࣟࢭࢫ࡟ࡼࡾㄪ

ࢆᣢࡘ SBA-15 ࢆᢸయ࡜ࡋࡓሙྜ࡟ࡶ㸪㓄఩Ꮚࡸࡑࡢ௚

〇ࡉࢀ࡚࠸ࡿࡇ࡜࡟ᇶ࡙ࡃࡶࡢ࡛࠶ࡿ㸬ࡇࡇ࡛㗪ᆺ๣࡜ࡢ᭷ᶵศᏊࢆᅛᐃࡍࡿ㝿࡟ࡣ㸪ࡑࡢᅛᐃᐦᗘ࠾ࡼࡧศᩓ

ࡋ࡚⏝࠸ࡽࢀࡿࡶࡢࡣ࣏࣐࣮࣑ࣜࢭ࡛ࣝ࠶ࡿ㸬ࡑࡇ࡛㸪≧ែࢆไᚚࡍࡿᚲせࡀ࠶ࡿࡇ࡜ࢆព࿡ࡋ࡚࠸ࡿ㸬Si(OEt)4 ࡟ᑐࡋ㐺ᙜ㔞ࡢ᭷ᶵᐁ⬟ᇶࢆྵࡴࢺࣜ࢔ࣝࢥ࢟ ࢩࣜ࢝ࢤࣝࢆึࡵ࡜ࡍࡿ↓ᶵ㓟໬≀ࡢ⾲㠃࡟᭷ᶵ໬ྜ

ࢩࢩࣛࣥ XSi(OR)3 ࢆΰྜࡋࡓࡶࡢࢆ͆ࢩࣜ࢝※͇࡜ࡋ㸪≀ࢆᅛᐃࡍࡿ࡟ࡣ㸪↓ᶵ㓟໬≀ᢸయ⾲㠃࡟㒊ศⓗ࡟Ꮡᅾࡇࢀࢆ࣏࣐࣮࣑ࣜࢭࣝࡢ⾲㠃࡛ຍỈศゎ࣭⬺Ỉ⦰ྜࢆ⾜⚄ዉᕝ኱ᏛᕤᏛ◊✲ᡤᡤሗ ➨  ྕ࠺ࡇ࡜࡛᭷ᶵᐁ⬟ᇶXࢆྵࡴ࣓ࢯከᏍᛶࢩࣜ࢝ࢤࣝࡀᚓ

࠼ࡤ་⸆ရࡢሙྜ࡛ࡣᑐᤸయ࡟ࡼࡿ⏕⌮άᛶࡢ㐪࠸ࡀ⏕ࡽࢀࡿ㸬ࡇࡢ one-pot synthesis ἲ࡛ࡣ㸪X ࡢᑟධ㔞ࡣࢩࣜࡌࡿ㸬ᚑࡗ࡚㧗௜ຍ౯್᭷⏝໬Ꮫ≀㉁ ࣇ࢓࢖ࣥࢣ࣑࢝ࣝ

࢝※࡟࠾ࡅࡿ XSi(OR)3 ࡢ௙㎸ࡳẚ࡟ࡼࡾไᚚ࡛ࡁࡿ࡜ࢬ ࡢ⏕⏘⌧ሙ࡛ࡣ㸪୍᪉ࡢᑐᤸయࡢࡳࢆ㑅ᢥⓗ࡟సࡾฟ⪃࠼ࡽࢀࡿ㸬ࡲࡓ Si(OEt)4 ࡜ XSi(OR)3 ࡀ┦ศ㞳ࡍࡿࡇ࡜ࡍ ͆୙ᩧྜᡂ͇࡟㐺⏝࡛ࡁࡿゐ፹㸪࠸ࢃࡺࡿ͆୙ᩧゐ፹͇

࡞ࡃᆒ㉁࡟ΰࡊࡾྜࡗࡓ≧ែ࡛ࢩࣜ࢝ቨࡀᵓᡂࡉࢀ࡚࠸

࡟ࡼࡿྜᡂࣉࣟࢭࢫࡣ௒࡞࠾㛤Ⓨㄢ㢟࡜࡞ࡗ࡚࠸ࡿ㸬ࡃ᮲௳࡛ࡣ㸪X ࡢศᕸࡣࣛࣥࢲ࣒࡞ࡶࡢ࡜࡞ࡾ㸪X ࡢᑟ⌧ᅾ᪤࡟ᐇ⏝࡟౪ࡉࢀ࡚࠸ࡿ୙ᩧゐ፹ࡣ㸪ᆒ୍⣔཯ᛂධ㔞ࡀᑡ࡞࠸పᐦᗘ≧ែ࡛ࡣศᩓᗘࡶ㧗ࡃ࡞ࡿ࡜⪃࠼ࡽ࡟㐺⏝ࡉࢀࡿ㔠ᒓ㘒యゐ፹ࡸ᭷ᶵศᏊゐ፹࡛࠶ࡿࡀ㸪ࡇࢀࡿ㸬࡞࠾ SBA-15 ࡢㄪ〇࡟㝿ࡋ࡚㗪ᆺ๣࡜ࡋ࡚⏝࠸ࡽࢀࢆᅛయゐ፹໬ࡍࡿࡇ࡜ࡀ࡛ࡁࢀࡤ㸪ゐ፹ࡢᅇ཰ࡸ෌฼

ࢀࡿ࣏࣐࣮࣑ࣜࢭࣝ࡜ࡣ㸪␯Ỉᛶ࡜ぶỈᛶ㒊఩ࢆేࡏᣢ

⏝ᛶࡢྥୖ࡟ࡼࡾ㈗㔜࡞୙ᩧ※ࡢ᭷ຠ฼⏝࡟ࡘ࡞ࡀࡿ㸬ࡘ㧗ศᏊ ࣏ࣜ(࢚ࢳࣞࣥ࢜࢟ࢩࢻ)࡜࣏ࣜ(ࣉࣟࣆࣞࣥ࢜

ࡑࡇ࡛ᅛయᢸయୖ࡬ࡢ୙ᩧศᏊゐ፹ࡢᅛᐃ໬࡟ࡼࡿ୙ᆒ࢟ࢩࢻ)ࡢࣈࣟࢵࢡඹ㔜ྜయ ࡀỈ୰࡛␯Ỉᛶ㒊఩ࢆෆഃ୍⣔୙ᩧゐ፹ࡢ㛤Ⓨࡀヨࡳࡽࢀ࡚࠾ࡾ㸪ࡑࡢᅛయᢸయࡢ

࡟ྥࡅࡓ≧ែ࡛㞟ྜࡋࡓ఍ྜయ࡜࡞ࡗ࡚࠸ࡿࡶࡢ࡛࠶ࡿ㸬୰࡛ࡶ≉࡟ὀ┠ࡉࢀ࡚࠸ࡿࡢࡣ࣓ࢯከᏍᛶࢩ࡛ࣜ࢝࠶ࡿ㸬ᚑࡗ࡚ࡑࡢ⾲㠃࡟ Si(OEt)4 ࡜ XSi(OR)3 ࡀ㞟✚ࡋࡓ㝿㸪␯ࡇࢀࡣ㸪ࣉࣟ࢟ࣛࣝ࡞཯ᛂ≀ ࡑࡢ໬ྜ≀⮬యࡣ࢟ࣛࣜࢸ

Ỉᛶ࡛࠶ࡿ᭷ᶵᐁ⬟ᇶXࡣ࣏࣐࣮࣑ࣜࢭࣝࡢෆ㒊࡟ྥ࠿࢕࣮ࢆᣢࡓ࡞࠸ࡀ㸪ࡋ࠿ࡿ࡭ࡁ཯ᛂ࡟ࡼࡾ୍ẁ㝵࡛࢟ࣛࡗ࡚㓄ྥࡋࡸࡍࡃ㸪ࡇࢀࢆ⦰ྜࡋ࡚࠿ࡽ㗪ᆺ࡛࠶ࡿ࣏ࣜ

ࣜࢸ࢕࣮ࢆᣢࡘ໬ྜ≀࡟ኚ໬ࡍࡿศᏊ ࡢ✵㛫㓄⨨ࢆไ࣐࣮࣑ࢭࣝࢆ㝖ཤࡍࡿࡇ࡜࡛㸪⣽Ꮝෆቨ࡟ X ࡀᅛᐃࡉࢀ

㝈ࡍࡿࡇ࡜࡟ࡼࡗ࡚⏕ᡂ≀ࡢᑐᤸయ㑅ᢥᛶࡀྥୖࡍࡿࡇ

ࡓᵓ㐀యࡀᚓࡽࢀࡿ㸬ࡇࡇ࡟♧ࡋࡓ one-pot synthesis ἲ࡟࡜ࡀ▱ࡽࢀ࡚࠾ࡾ(8)㸪࣓ࢯከᏍᛶࢩࣜ࢝ࡀ᭷ࡍࡿࢼࣀࢫ

ࡼࡾᚓࡽࢀࡿ໬Ꮫಟ㣭 SBA-15 ࡢ࠺ࡕࠊ࢔ࣝ࢟ࣝ࢔ࢪࢻ

ࢣ࣮ࣝࡢ⣽Ꮝࡣ୕ḟඖᵓ㐀ࡀつᐃࡉࢀࡓ཯ᛂሙ✵㛫ࢆᵓ

ᇶ –CH2CH2CH2N3 ಟ㣭 SBA ࡢㄪ〇ἲࡣ㸪ᮏඹྠ◊✲ࡢ⠏ࡍࡿࡢ࡟㐺ࡋ࡚࠸ࡿ࡜⪃࠼ࡽࢀࡿࡓࡵ࡛࠶ࡿ㸬ࡑࡇ࡛࣓ࣥࣂ࣮ࡢ࠺ࡕࡢ 1 ྡ ୰⃝ ࡀ☜❧ࡋࡓࡶࡢ࡛࠶ࡾ㸪ᐇᮏ◊✲࡛ࡣ SBA-15 ࡢ࣓ࢯ⣽Ꮝࢆ࣏ࣜ࣌ࣉࢳࢻ࡛ಟ㣭ࡍ㝿࡟ࢩࣜ࢝※࡟࠾ࡅࡿ௙㎸ࡳẚ࡟ᛂࡌࡓXࡢᑟධ㔞ࡢไࡿࡇ࡜࡟ࡼࡗ࡚୕ḟඖ୙ᩧ཯ᛂሙࡢᵓ⠏ࢆィ⏬ࡋࡓ㸬ᚚࡀྍ⬟࡛࠶ࡿࡇ࡜ࡸ㸪ࡑࡢᅛᐃ≧ែ࡟࠾࠸࡚ࣛࣥࢲ࣒
࡞㓄⨨ࡀ㐩ᡂࡉࢀ࡚࠸ࡿࡇ࡜ࡶ᫂ࡽ࠿࡟ࡉࢀ࡚࠸ࡿ(7)㸬

㸱㸬㸯㸬㸯㸬✀ࠎࡢ࣏ࣜ࣌ࣉࢳࢻಟ㣭 6%$ ࡢྜᡂ ௨ୖࡢࡼ࠺࡞⫼ᬒࢆ㋃ࡲ࠼㸪ᮏඹྠ◊✲࡛ࡣ post࣓ࢯ࣏࣮ࣛࢫࢩࣜ࢝࡬ࡢ࣏ࣜ࣌ࣉࢳࢻࡢᑟධࡣ㸪⣽Ꮝsynthesis ἲ㸪one-pot synthesis ἲࡢ୧ᡭἲ࡟ࡼࡾᐁ⬟ᇶᑟෆࢆ࢔࣑ࣀᇶ࡛ಟ㣭ࡋࡓ SBA-15 ࡜άᛶ໬ࡋࡓ࢔࣑ࣀ㓟ධ㔞ࢆไᚚࡋࡓಟ㣭࣓ࢯከᏍᛶࢩࣜ࢝ᢸయ SBA-X (X =࡛࠶ࡿ NCA ࢆ㸪⬺Ỉ THF ࡲࡓࡣࣆࣜࢪࣥ୰࡛ࣜࣅࣥࢢ

NH2, N3)ࢆㄪ〇ࡋ㸪ࡇࡢಟ㣭ᐁ⬟ᇶ X ࢆᇶⅬ࡟㧗ḟᶵ⬟㔜ྜࡉࡏࡿࡇ࡜࡟ࡼࡾ⾜ࡗࡓ ᅗ 4 㸬Jones ࡽࡢሗ࿌(5)࡟

໬ࢆ᪋ࡍࡇ࡜࡛㸪᪂つゐ፹ࢆ㛤Ⓨࡋࡓ㸬≉࡟ 2012 ᖺᗘࡢೌ࠸㸪࠿ࡉ㧗࠸ಖㆤᇶࢆ᭷ࡍࡿ࢔࣑ࣀᇶಟ㣭๣ࢆ⏝࠸࡚◊✲࡛ࡣ㸪⏕యෆᶵ⬟ࢆᶍೌࡋࡓゐ፹㛤Ⓨ࡟ྲྀࡾ⤌ࢇࡔ㸬⣽Ꮝෆࡢ࢔࣑ࣀᇶᅛᐃᐦᗘࢆపୗࡉࡏࡿࡇ࡜࡛㸪⣽Ꮝෆ࡛ࡢ㛗㙐࣏ࣜ࣌ࣉࢳࢻ⏕ᡂࢆᮇᚅࡋࡓ㸬NCA ࡣ㸪ྛ✀࢔㸱㸬㸯㸬࣏ࣜ࣌ࣉࢳࢻಟ㣭࣓ࢯከᏍᛶࢩࣜ࢝࡟ࡼࡿ୙ᩧ࣑ࣀ㓟 ࣇ࢙ࢽࣝࢢࣜࢩࣥ(Phg)㸪ࣉࣟࣜࣥ(Pro)㸪࢔ࣛࢽࢼࣀ✵㛫཯ᛂሙࡢᵓ⠏࡜ゐ፹≉ᛶࡢゎ᫂ࣥ(Ala) ࡜ࢺࣜ࣍ࢫࢤࣥࡢ཯ᛂ࡟ࡼࡾྜᡂࡋࡓ㸬࣌ࣉࢳ D-࢔࣑ࣀ㓟ࡣࢱࣥࣃࢡ㉁ࡢᇶᮏᵓᡂせ⣲࡛࠶ࡿࡀ㸪⏕ࢻಟ㣭ᚋࡢヨᩱ࡟ࡘ࠸࡚ࡣ N2 ≀⌮྾╔ ᐃ࡟ࡼࡾ⾲㠃యᵓᡂせ⣲࡜ࡋ࡚㔜せ࡞≉ᛶࡢࡦ࡜ࡘ࡟ᑐᤸᛶ ࢟ࣛࣜ✚㸪⣽Ꮝయ✚㸪⣽Ꮝᚄࢆ㸪ࡲࡓ㓟⣲㞺ᅖẼୗ࡛ࡢ TG

ࢸ࢕࣮ ࡀ࠶ࡿ㸬ࢱࣥࣃࢡ㉁ࢆᵓᡂࡍࡿ࢔࣑ࣀ㓟ࡢ࠺ࡕ㸪ᐃ࡜ CHN ඖ⣲ศᯒࡼࡾ⣽Ꮝෆ࡟ᙧᡂࡋࡓ࣏ࣜ࣌ࣉࢳࢻ

ᑐᤸᛶࡀ࡞࠸ࢢࣜࢩࣥࢆ㝖ࡃ 19 ✀㢮ࡢᚲ㡲࢔࣑ࣀ㓟࡛ࡢᩘᖹᆒ㔜ྜᗘࢆ ᐃࡋࡓ㸬ࡣ୍᪉ࡢᑐᤸయ L య ࡢࡳࡀࢱࣥࣃࢡ㉁ࡢᵓᡂせ⣲࡜࡞ ྛ✀࣏ࣜ࣌ࣉࢳࢻ࡛ಟ㣭ࡋࡓ SBA-15 ࡢ N2 ྾╔ ᐃࡢࡾ࠼ࡿ㸬ࡇࡢࡓࡵࢱࣥࣃࢡ㉁࠿ࡽ࡞ࡿ✵㛫࡛㐍⾜ࡍࡿ⏕⤖ᯝࢆ⾲ 1 ࡟♧ࡍ㸬࣌ࣉࢳࢻᑟධ๓࡟ẚ࡭࡚⣽Ꮝᚄࡸ⣽యෆ཯ᛂ࡛ࡣ㸪ከࡃࡢሙྜᑐᤸᛶࡢ㆑ูࡀ⾜࡞ࢃࢀ㸪౛Ꮝయ✚ࡀῶᑡࡋࡓࡇ࡜࠿ࡽ㸪SBA-15 ࡢ⣽Ꮝෆ࡛࣏ࣜ࣌

ᅗ㸲㸬࣏ࣜ࣌ࣉࢳࢻಟ㣭 6%$ ࡢྜᡂ⎔ቃㄪ࿴ᆺ≀㉁ኚ᥮ཬࡧ࢚ࢿࣝࢠ࣮ࣉࣟࢭࢫ๰ฟࡢ᪂ᇶ┙࡜࡞ࡿࢼࣀᵓ㐀ゐ፹ࡢ㛤Ⓨࣉࢳࢻ㙐ࡀఙ㛗ࡋࡓࡇ࡜ࡀ᫂ࡽ࠿࡜࡞ࡗࡓ㸬ࡇࡢ㝿㸪

௜ຍయ UHP 㸪ᩘᖹᆒ㔜ྜᗘࡀ⣙ 30 ࡢྛ࣏ࣜ࣌ࣉࢳࢻ

SBA-15 ୖ࡟Ꮡᅾࡍࡿ㔜ྜ㛤ጞ๣ࡢ࢔࣑ࣀᇶ㔞࡟ᑐࡋࣔಟ㣭 SBA-15 ࢆຍ࠼࡚ᐊ ࡟࡚཯ᛂࢆ⾜ࡗࡓ࡜ࡇࢁ㸪ࣀ࣐࣮࡛࠶ࡿ NCA ࡢῧຍ㔞ࢆㄪ⠇ࡍࡿࡇ࡜࡛⣽Ꮝᚄࡸ

SBA-15 ࡣ⁐ゎࡏࡎ㸪࠸ࡎࢀࡢ࣏ࣜ࣌ࣉࢳࢻಟ㣭 SBA-15⣽Ꮝయ✚ࢆไᚚ࡛ࡁࡓ㸬❧యⓗ࡟࠿ࡉ㧗࠸ࣇ࢙ࢽࣝࢢࣜ

ࢆ⏝࠸ࡓ᫬ࡶ 90 %௨ୖࡢ཰⋡࡛࢚࣏࢟ࢩ࢝ࣝࢥࣥࡀᚓ

ࢩࣥ⏤᮶ࡢ NCA ࡛ࡣ㸪M/A NCA ࡢࣔࣝᩘ/࢔࣑ࣀᇶࡢ

ࡽࢀࡓ㸬⏕ᡂ≀ࡢගᏛάᛶయ㐣๫⋡ ee ࢆồࡵࡓ࡜ࡇࢁࣔࣝᩘ = 60 ࡢ᫬ࡢᩘᖹᆒ㔜ྜᗘࡀ 18㸪M/A = 30 ࡢ᫬ 4࣏ࣜ࢔ࣛࢽࣥಟ㣭 SBA-15 ࡟࡚ 82%ࡢ ee ࡀほ ࡉࢀࡓࡀ㸪

࡜࡞ࡾ㸪NCA ࡢ཯ᛂ⋡ࡀపࡃ㸪ᩘᖹᆒ㔜ྜᗘࡶప࠿ࡗࡓ㸬ࡑࡢ௚ࡢ࣏ࣜ࣌ࣉࢳࢻಟ㣭 SBA-15 ࡛ࡣࣛࢭ࣑యࡋ࠿ᚓ

୍᪉㸪ศᏊࢧ࢖ࢬࡢᑠࡉ࠸࢔ࣛࢽࣥ⏤᮶ࡢ NCA ࡛ࡣ㸪ࡽࢀ࡞࠿ࡗࡓ ⾲ 2 㸬ᮏ཯ᛂ࡛ࡣ࣏ࣜ࣌ࣉࢳࢻ㙐ࡢ Į-࣊

M/A = 30 ࡢ᫬ࡢ࣏ࣜ࣌ࣉࢳࢻ㙐㛗ࡀ 29㸪M/A = 60 ࡢ᫬ࣜࢵࢡࢫᵓ㐀ࡀከⅬⓗ࡞Ỉ⣲⤖ྜ࡟ࡼࡾᇶ㉁࡜ HOO–ࢆࡀ 40 ࡜࡞ࡾ㸪㧗࠸ NCA ཯ᛂ⋡࡜࣏ࣜ࣌ࣉࢳࢻ㙐ࡢఙ㛗ᅛᐃࡋ㸪ࡇࢀࡀ୙ᩧㄏᑟ࡟ࡘ࡞ࡀࡿࡇ࡜ࡀ᫂ࡽ࠿࡜࡞ࡗࡀほ ࡉࢀࡓ㸬ࡲࡓ㸪ศᏊࢧ࢖ࢬࡀ୧⪅ࡢ୰㛫࡛࠶ࡿࣉ

࡚࠸ࡿ(10)㸬௒ᅇ౑⏝ࡋࡓ࣏ࣜ࣌ࣉࢳࢻ୰࡛ࡣ࣏ࣜ࢔ࣛࢽ

࡛ࣟࣜࣥࡣ㸪NCA ࡢ཯ᛂ⋡ཬࡧ࣏ࣜ࣌ࣉࢳࢻ㙐㛗ࡣ୧⪅ࣥࡔࡅࡀ Į-࣊ࣜࢵࢡࢫᵓ㐀ࢆྲྀࡾ࠺ࡿࡇ࡜࠿ࡽ㸪࣏ࣜ࢔ࡢ୰㛫ࡢ್࡜࡞ࡗࡓ㸬ࣛࢽࣥಟ㣭 SBA-15 ࡢࡳࡀ㧗࠸ ee ࢆ♧ࡋࡓ࡜⪃࠼ࡽࢀࡿ㸬࡞࠾࣓ࢯ࣏࣮ࣛࢫࢩࣜ࢝⣽Ꮝෆ࡬ࡢࣜࣅࣥࢢ㔜ྜࢆ⏝࠸

⾲㸯SBA-polypeptide ࡢ N2 ≀⌮྾╔ ᐃ⤖ᯝ
a

M/A

⾲㠃✚
/m2g–1⣽Ꮝయ✚/cm3 g–1⣽Ꮝᚄ/nmࡓ࣏ࣜ࣌ࣉࢳࢻ㙐ࡢᑟධࡣࡍ࡛࡟ሗ࿌ࡉࢀ࡚࠸ࡿࡀ(11)㸪
bDPࡵ࡚࡛࠶ࡿ(12)㸬

SBA

ʊ

713

1.28

7.9

ʊ

SBA-NH2

ʊ

566

1.07

7.4

ʊ

SBA-poly(Ala)

30

269

0.59

7.3

29

60

243

0.46

6.0

40

30

294

0.61

7.5

22

60

266

0.46

6.7

35

30

412

0.82

7.1

4

60

303

0.53

6.1

18

SBA-poly(Pro)

SBA-poly(Phg)aᐇ㝿࡟ࡇࢀࢆ⏝࠸ࡓ୙ᩧ཯ᛂࢆᐇ⌧ࡋࡓ౛ࡣᮏ◊✲ࡀึ

M/A = NCA ࡢࣔࣝᩘ/࢔࣑ࣀᇶࡢࣔࣝᩘ
DP = ᩘᖹᆒ㔜ྜᗘ

⾲㸰SBA-polypeptide ࢆ⏝࠸ࡓJuliá-Colonna ࢚࣏࢟ࢩ໬Catalyst

Yield (%)

ee (%)

SBA-poly(Ala)30

94

82

SBA-poly(Pro)30

980SBA-poly(phg)30920㸱㸬㸯㸬㸰㸬࣏ࣜ࣌ࣉࢳࢻಟ㣭 6%$ ࢆ⏝࠸ࡓ୙ᩧ࢚࣏

Poly(Ala)30

55

89

࢟ࢩ໬཯ᛂ

Without peptide

93

0

b

 ㄪ〇ࡋࡓ࣌ࣉࢳࢻಟ㣭 SBA-15 ࢆ⏝࠸ࡓ୙ᩧ཯ᛂࡢ᳨

ḟ࡟㸪࣏ࣜ࢔ࣛࢽࣥಟ㣭 SBA-15 ࡜ᅛᐃ໬ࡋ࡚࠸࡞࠸

ウࢆ⾜ࡗࡓ㸬ࡲࡎ㸪࣏ࣜ࣌ࣉࢳࢻ㙐ᮎ➃ࡢ࢔࣑ࣀᇶ࡟⏤࣏ࣜ࢔ࣛࢽࣥࡢゐ፹≉ᛶࡢẚ㍑ࢆᵝࠎ࡞࣌ࣉࢳࢻ㙐㛗ࡢ᮶ࡍࡿሷᇶゐ፹⬟ࢆᮇᚅࡋ࡚㸪ᵝࠎ࡞཯ᛂ ࢩ࢔ࣀࢩࣜࣝ

ࡶࡢ࡛⾜ࡗࡓ ⾲ 3 㸬࣏ࣜ࢔ࣛࢽࣥಟ㣭 SBA-15 ࡛ࡣ㸪໬ࡸࢡࢿ࣮ࣇ࢙ࢼ࣮ࢤࣝ཯ᛂ㸪ࢽࢺࣟ࢔ࣝࢻ࣮ࣝ཯ᛂ

ᖹᆒ㔜ྜᗘ 10 ࡢ᫬࡟ ee ࡀ᭱㧗್ࡢ 91 %ࢆ♧ࡋࡓࡢ࡟ᑐࢆ᳨ウࡋࡓࡀ㸪࠸ࡎࢀࡢ࣏ࣜ࣌ࣉࢳࢻಟ㣭 SBA-15 ࡶࡇࡋ㸪ᅛᐃࡋ࡚࠸࡞࠸࣏ࣜ࢔ࣛࢽࣥ ⁐ᾮ≧ែ ࡛ࡣ㸪ᖹᆒࢀࡽࡢ཯ᛂ࡟άᛶࢆ♧ࡉ࡞࠿ࡗࡓ㸬ࡑࡇ࡛࣏ࣜ࣌ࣉࢳࢻ

㔜ྜᗘ 30 ࡢ᫬࡟ ee ࡀ᭱㧗್ࢆ♧ࡋࡓ㸬ࡲࡓ㸪ᖹᆒ㔜ྜࡀ୙ᩧㄏᑟ๣࡜ࡋ࡚ᶵ⬟ࡍࡿࡇ࡜ࡀ▱ࡽࢀ࡚࠸ࡿ

ᗘࡀ 3 ࡢሙྜ㸪SBA-15 ࡟ᅛᐃ໬ࡋࡓࡶࡢ࡛ࡣ 43 %㸪ᅛJuliá-Collona ࢚࣏࢟ࢩ໬཯ᛂ࡟ὀ┠ࡋࡓ㸬ࡇࡢ཯ᛂࡣ㸪ᐃࡋ࡚࠸࡞࠸ࡶࡢ࡛ࡣ 18 %࡜ SBA-15 ࡬ࡢᅛᐃ໬࡟ࡼࡾNaOH Ỉ⁐ᾮ࡜᭷ᶵ⁐፹ࡢ஧┦⣔࡛⾜ࢃࢀ㸪ሷᇶᛶ᮲௳

ee ࡀ኱ᖜ࡟ྥୖࡋࡓ㸬࡞࠾࢔࣑ࣀᇶಟ㣭 SBA-15 ࡟࣌ࣉୗ࡛㐣㓟໬Ỉ⣲࠿ࡽ⏕ᡂࡍࡿ HOO–ࡀ㟁Ꮚ୙㊊ࡢ࢜ࣞࣇࢳࢻᅛ┦ྜᡂἲࡢᡭἲ࡛ 3 ṧᇶࡢ࢔ࣛࢽࣥࢆ⦰ྜࡉࡏࡓ

࢕ࣥ࡬࡜ồ᰾௜ຍࡍࡿࡇ࡜࡛㐍⾜ࡍࡿ(9)㸬ࡋ࠿ࡋ㸪࣌ࣉࡶࡢࢆྜᡂࡋ㸪ྠᵝࡢ᮲௳࡛཯ᛂࢆ⾜ࡗࡓ࡜ࡇࢁ㸪ee ࡣࢳࢻಟ㣭࣓ࢯ࣏࣮ࣛࢫࢩࣜ࢝ࢆ஧┦⣔ࡢ཯ᛂ࡟⏝࠸ࡓ࡜

ࢃࡎ࠿ 4 %࡟࡜࡝ࡲࡗࡓ㸬࣏ࣜ࢔ࣛࢽࣥࡀᏳᐃ࡞D-࣊ࣜࡇࢁ㸪SBA-15 ࡢ NaOH Ỉ⁐ᾮ࡬ࡢ⁐ゎࡀ㉳ࡇࡾ㸪཯ᛂࢵࢡࢫᵓ㐀ࢆᙧᡂࡍࡿࡓࡵ࡟ࡣ㸪10 ṧᇶ⛬ᗘࡢ࣌ࣉࢳࢻ

ࡣ㐍⾜ࡋ࡞࠿ࡗࡓ㸬ࡑࡇ࡛㠀Ỉ᮲௳ୗ࡛཯ᛂࢆ⾜ࡗࡓ㸬㙐㛗ࡀᚲせ(9)࡛࠶ࡿࡇ࡜ࡀ▱ࡽࢀ࡚࠾ࡾ㸪3 ṧᇶ࡛ࡣ㙐㛗

THF ⁐፹࡟㸪ᇶ㉁ࡢ࢝ࣝࢥࣥ㸪DBU㸪ᒀ⣲–㐣㓟໬Ỉ⣲

୙㊊ࡢࡓࡵ࡟ Į-࣊ࣜࢵࢡࢫࡀᙧᡂ࡛ࡁࡎ ee ࡀ኱ᖜ࡟ప

⚄ዉᕝ኱ᏛᕤᏛ◊✲ᡤᡤሗ ➨  ྕࣛࢠࣥ㓟࠿ࡽ࡞ࡿࢪ࣌ࣉࢳࢻ H-Pro-Asp(OH)-OH ࡛ಟ㣭⾲㸱ྛ㙐㛗ࡢಟ㣭࠾ࡼࡧᮍಟ㣭࣏ࣜ࢔ࣛࢽࣥࡢ཯ᛂCatalystDPaee / %

63

43

b

30

4

ୖ࡬ࡢಟ㣭࡟⏝࠸࡚ࡶ㸪୍ᑐࡢ࢖࣑ࣀᇶ࡜࢝ࣝ࣎࢟ࢩᇶ

10

91

91

ࡀṧᏑࡍࡿ㸬ࡇࡢࡼ࠺࡞ࣉࣟࣜࣥ⏤᮶ࡢ࢖࣑ࣀᇶ࡜࢝ࣝ

30

70

81

࣎࢟ࢩᇶࢆᣢࡘ࢜ࣜࢦ࣌ࣉࢳࢻࡣ㸪ࣉࣟࣜࣥྠᵝ࡟࢔ࣝ

3

36

18

ࢻ࣮ࣝ཯ᛂ➼࡟ᑐࡍࡿ୙ᩧ᭷ᶵศᏊゐ፹࡜ࡋ࡚ᶵ⬟ࡍࡿ

10

30

80

30

60

92

3
SBA-poly(Ala)3poly(Ala)aDP = ᩘᖹᆒ㔜ྜᗘ,bࡋࡓ SBA-15 ࡢྜᡂ࡜㸪ࡑࡢ୙ᩧゐ፹⬟ࢆ᳨ウࡋࡓ㸬ࡇYield / %ࡢࢪ࣌ࣉࢳࢻࡣศᏊෆ࡟ 1 ࡘࡢ࢖࣑ࣀᇶ࡜ 2 ࡘࡢ࢝ࣝ࣎
࢟ࢩᇶࢆ᭷ࡋ࡚࠾ࡾ㸪࢝ࣝ࣎࢟ࢩᇶࡢ࠺ࡕ 1 ࡘࢆ SBA-15

ࡇ࡜ࡀ▱ࡽࢀ࡚࠸ࡿ(13)(14)㸬
SBA-Pro-Asp ࡣ㸪࣌ࣉࢳࢻᅛ┦ྜᡂἲࡢᡭἲࢆᛂ⏝ࡋ㸪࢔࣑ࣀᇶಟ㣭 SBA-15 ࡢ࢔࣑ࣀᇶ࡟ᑐࡋ㸪࣌ࣉࢳࢻ⦰ྜ

࣌ࣉࢳࢻᅛ┦ྜᡂἲ࡟࡚ఙ㛗ࡋࡓࡶࡢ

๣ࢆ⏝࠸࡚࢔࣑ࣀ㓟ࢆ㏲ḟⓗ࡟⦰ྜࡉࡏࡿࡇ࡜࡛ྜᡂࡋ

ୗࡋࡓ࡜⪃࠼ࡽࢀࡿ㸬ࡼࡗ࡚࣏ࣜ࢔ࣛࢽࣥಟ㣭 SBA-15

ࡓ ᅗ 5 㸬ᚓࡽࢀࡓ SBA-Pro-Asp ࡢ࣌ࣉࢳࢻಟ㣭㔞ࢆࡸᅛᐃࡋ࡚࠸࡞࠸࣏ࣜ࢔ࣛࢽࣥ࡟࠾࠸࡚㸪ᖹᆒ㔜ྜᗘࡀ

CHN ඖ⣲ศᯒ࡟ࡼࡾ⟬ฟࡋࡓ࡜ࡇࢁ㸪0.26 mmol/g ࡛࠶

3 ࡛࠶ࡗ࡚ࡶ࠶ࡿ⛬ᗘࡢ ee ࡀⓎ⌧ࡋ࡚࠸ࡿࡢࡣ㸪㔜ྜἲࡗࡓ㸬࡛ྜᡂࡋ࡚࠸ࡿࡓࡵ࡟㒊ศⓗ࡟㛗㙐࣏ࣜ࣌ࣉࢳࢻࡀᙧᡂ

ྜᡂࡋࡓ SBA-Pro-Asp ࢆ⏝࠸࡚࣋ࣥࢬ࢔ࣝࢹࣄࢻ࡜

ࡉࢀ࡚࠸ࡿࡓࡵ࡛࠶ࡿ࡜᥎ᐃࡋࡓ㸬ࡲࡓᅛᐃࡋ࡚࠸࡞࠸

࢔ࢭࢺࣥࡢ࢔ࣝࢻ࣮ࣝ཯ᛂࢆ⾜ࡗࡓ ⾲ 4 㸬ࡑࡢ⤖ᯝ࣏ࣜ࢔ࣛࢽࣥ࡟ẚ࡭࡚࣏ࣜ࢔ࣛࢽࣥಟ㣭 SBA-15 ࡛ࡼࡾ

SBA-Pro-Asp ࡟࠾࠸࡚72 ᫬㛫࡛཰⋡27 % ee 13 % ࡛⏕㧗࠸ ee ࡀほ ࡉࢀࡓࡇ࡜ࡣ㸪ᾮ┦ᆒ୍⣔࡛ࡢ㔜ྜ཯ᛂ࡟ᡂ≀ࡀᚓࡽࢀ㸪୙ᩧゐ፹཯ᛂࡀ㐍⾜ࡋࡓ㸬ᅛᐃ໬ࡢᙳ㡪ẚ࡭㸪SBA-15 ࡟ᅛᐃࡉࢀ࡚࠸ࡿ࢔࣑ࣀᇶࢆ㛤ጞ๣࡜ࡋࢆ᳨ドࡍࡿࡓࡵ㸪࢔࣑ࣀ࣓ࢳ࣏ࣝࣜࢫࢳࣞࣥࣞࢪࣥ࡟ࢪ

ࡓሙྜ㸪⣽Ꮝࡢධࡾཱྀ௜㏆࡞࡝ࡢ࢔ࢡࢭࢫᛶࡀ㧗࠸࢔࣑࣌ࣉࢳࢻࢆಟ㣭ࡋࡓࡶࡢ(resin-Pro-Asp)㸪ཬࡧ SBA-15 ࡬ࣀᇶୖ࡛ࡢ㔜ྜ཯ᛂࡀඃඛⓗ࡟㐍⾜ࡋࡸࡍࡃ㸪⤖ᯝ࡜ࡋࡢᅛᐃ໬ࡢࡓࡵࡢ࣮ࣜࣥ࢝ࢆ㐃⤖ࡋ࡚࠸ࡿ࢔ࢫࣃࣛࢠࣥ

࡚࢔࣑ࣀᇶ࡜ NCA ࡢ௙㎸ࡳࣔࣝẚࡀపࡃ࡚ࡶ㛗㙐࣏ࣜ㓟ࡢഃ㙐ࡢ࢝ࣝ࣎࢟ࢩᇶࢆ࣋ࣥࢪ࢚ࣝࢫࢸࣝ࡜ࡋࡓ

࣌ࣉࢳࢻࡢ⏕ᡂ㔞ࡀከ࠸ࡇ࡜ࡀཎᅉ࡜⪃࠼ࡽࢀࡿ㸬ࡲࡓ

H-Pro-Asp(OBn)-OH ࢆ⏝࠸࡚཯ᛂࡢẚ㍑ࢆ⾜ࡗࡓ㸬࣏ࣜ࢔ࣛࢽࣥಟ㣭 SBA-15 ࡛ࡣ㸪㙐㛗ࡀ 10 ࡢ᫬᭱ࡶ㧗࠸

resin-Pro-Asp ࡣ㸪SBA-Pro-Asp ࡜ྠᵝ࡟࢔ࣝࢻ࣮ࣝࢆ୚ee ࡀほ ࡉࢀ㸪㙐㛗ࡀ 30 ௨ୖ࡟࡞ࡿ࡜ ee ࡣపୗࡋࡓ㸬࠼ࡓࡀ㸪཰⋡ࡣ࠾ࡼࡑ༙ศ࡟పୗࡋࡓ㸬ࡇࢀࡽࡢᅛᐃ໬

ࡇࢀࡣ㸪ᅛᐃࡋ࡚࠸࡞࠸࣏ࣜ࣌ࣉࢳࢻࡢሙྜ࡜ࡣ␗࡞ࡿ

⾲㸲ࢪ࣌ࣉࢳࢻಟ㣭 SBA-15 ࢆゐ፹࡜ࡋࡓ࢔ࣝࢻ࣮ࣝ཯ᛂ

ᣲື࡛࠶ࡿ㸬ᮏ཯ᛂࡣ࣌ࣉࢳࢻࡀᏑᅾࡋ࡞࠸᮲௳ୗ࡛
HOO–࡜ᇶ㉁ࡀ཯ᛂࡋ㸪ࣛࢭ࣑యࢆ୚࠼ࡿ㸬ࡋࡓࡀࡗ࡚
SBA-15 ⣽Ꮝෆ࡛㛗㙐ࡢ࣏ࣜ࣌ࣉࢳࢻ㙐ࡀᙧᡂࡉࢀࡿ࡜㸪
HOO–ࡸᇶ㉁ࡢ࣌ࣉࢳࢻࡢ࢔ࢡࢭࢫᛶࡀపୗࡋ㸪HOO–࡜ᇶ㉁ࡢ┤᥋཯ᛂ࡟ࡼࡿࣛࢭ࣑యࡢᙧᡂࡀేⓎࡍࡿࡓࡵ㸪

Catalystsee ࡀపୗࡋࡓ࡜⪃࠼ࡽࢀࡿ㸬Time / hYield / %ee / %

72

27

13

SBA-Pro-Asp㸱㸬㸯㸬㸱㸬ࢪ࣌ࣉࢳࢻಟ㣭 SBA-15 ࡢྜᡂ࡜ゐ፹཯ᛂḟ࠸࡛㸪࢔࣑ࣀ㓟ࡀᮏ᮶ഛ࠼ࡿ㓟-ሷᇶゐ፹ᶵ⬟ࢆResin-Pro-Asp

72

14

15

H-Pro-Asp(OBn)-OH

72

46

54

SBA-15 ࡟௜୚ࡍࡿࡇ࡜ࢆ┠ᣦࡋ࡚㸪ࣉࣟࣜࣥ࡜࢔ࢫࣃ
O

OTMS
O Si
O
OMe

NH2 + HOt-BuOOC

H
N

Fmoc

O
OTMS
O
N
Si
O
H
OMe t-BuOOC

HBTU
HOBt
DMF

H
N

Fmoc

O
OTMS
O
N
Si
H
O
OMe t-BuOOC

Piperidine
DMF

SBA-NH2
HO
O

N
Boc

HBTU, HOBt
DMF

O
OTMS
O Si
N
H
O
OMe t-BuOOC

H
N
O

N
Boc

TFA

OTMS
O Si
O
OMe

O
N
H
HOOC

H
N

SBA-Pro-Aspᅗ㸳㸬ࢪ࣌ࣉࢳࢻಟ㣭 SBA-15 ࡢྜᡂ

O

NH2

N
H



⎔ቃㄪ࿴ᆺ≀㉁ኚ᥮ཬࡧ࢚ࢿࣝࢠ࣮ࣉࣟࢭࢫ๰ฟࡢ᪂ᇶ┙࡜࡞ࡿࢼࣀᵓ㐀ゐ፹ࡢ㛤Ⓨᢸయࢆẚ㍑ࡍࡿ࡜㸪࢔࣑ࣀ࣓ࢳ࣏ࣝࣜࢫࢳࣞࣥࣞࢪࣥࡣ

࠺ࡼ࠺࡞ሙྜ࡛ࡶ㸪㓄఩Ꮚࢆᅛయ⾲㠃࡟㐺ᙜ࡞㛫㝸ࢆಖ⾲㠃✚ࡀᴟࡵ࡚ஈࡋ࠸ࡢ࡟ᑐࡋ㸪࢔࣑ࣀᇶಟ㣭 SBA-15

ࡗ࡚ᅛᐃ࡛ࡁࢀࡤ㸪άᛶ࡞㓄఩୙㣬࿴㘒యࡀᢸయ⾲㠃࡛

ࡣ 566 m2/g ࡶࡢ⾲㠃✚ࢆ᭷ࡍࡿࡇ࡜࠿ࡽ㸪SBA-Pro-Aspᙧᡂࡉࢀ㸪ࡋ࠿ࡶࡑࡢ㛫㝸ࢆไᚚࡍࡿࡇ࡜࡛㘒యゐ፹ά

ࡢ᪉ࡀ resin-Pro-Asp ࡟ẚ࡭ᇶ㉁ࡢࢪ࣌ࣉࢳࢻࡢ᥋㏆ࡀ

ᛶⅬࡢᵓ㐀ไᚚ ༢᰾㔠ᒓ✀࡜ከ᰾㔠ᒓ✀ࡢ๰ࡾศࡅ ࡶᐜ࡛᫆࠶ࡗࡓࡓࡵ㧗࠸άᛶࢆ♧ࡋࡓࡶࡢ࡜᥎ ࡉࢀࡿ㸬ᮇᚅ࡛ࡁࡿ ᅗ 6 㸬ࡉࡽ࡟ᅛయࡢ≉ᛶࢆά࠿ࡋ࡚㸪ྠ୍୍᪉࡛㸪
H-Pro-Asp(OBn)-OH ࢆゐ፹࡜ࡋࡓᆒ୍⣔཯ᛂࡣ㸪ᢸయୖ࡟ᶵ⬟ࡢ␗࡞ࡿ㔠ᒓ㘒యࢆᅛᐃ໬ࡋࡓゐ፹ࢹࣂ࢖཰⋡㸪ee ඹ࡟ SBA-Pro-Asp ࡢ⤖ᯝࢆୖᅇࡗ࡚࠸ࡓ㸬ࡇࢀࢫࡢᵓ⠏ࡶྍ⬟࡟࡞ࡿ࡜⪃࠼ࡽࢀࡿ㸬௨ୖࡢⓎ᝿ࡢୗ㸪ࡣ SBA-Pro-Asp ࡛ࡣࢩࣜ࢝࡜ࢪ࣌ࣉࢳࢻࡢ࢝ࣝ࣎࢟ࢩ

ᮏ◊✲࡛ࡣ㘒యศᏊゐ፹ࡢᅛᐃ໬㘒యゐ፹࡬ࡢᒎ㛤ࢆ᳨ᇶ࡜ࡢỈ⣲⤖ྜࢆ௓ࡋࡓ┦஫స⏝ࡸ㸪ᅛయ⾲㠃࡟ᅛᐃ໬ウࡋࡓ㸬ࡉࢀࡓࡇ࡜࡟ࡼࡗ࡚ࢪ࣌ࣉࢳࢻࡢࢥࣥࣇ࢛࣓࣮ࢩࣙࣥࡀつไࡉࢀࡿࡇ࡜࡛ ee ࡢపୗࢆᣍ࠸ࡓࡇ࡜ࡀ⪃࠼ࡽࢀࡿ㸬ヲ⣽࡟ࡘ࠸࡚ࡣ⌧ᅾ᳨ウ୰࡛࠶ࡿ㸬(15)㸱㸬㸰㸬㸯㸬ᅛᐃ໬㘒యゐ፹ࡢタィ㘒యゐ፹ࢆᢸయ࡟ᅛᐃࡍࡿࡇ࡜࡛㸪ࡑࡢゐ፹άᛶࡸᶵ
⬟ࡀ኱ࡁࡃኚ໬ࡋ࡚ࡋࡲ࠺ࡇ࡜ࡀ࠶ࡿ㸬ࡑࡢせᅉࡢ୍㒊㸱㸬㸰㸬࢔ࢪࢻᇶಟ㣭࣓ࢯከᏍᛶࢩࣜ࢝ࢆ⏝࠸ࡓᅛᐃ໬

࡜ࡋ࡚㔠ᒓᨭᣢ㓄఩Ꮚ㒊ࡢᵓ㐀࣭ᛶ㉁࡜㸪ᢸయ࡬ࡢᅛᐃ㘒యゐ፹≧ែࡀᣲࡆࡽࢀ㸪ࡑࡢゎỴ࡟ࡣ㸪ձ㓄఩Ꮚ࡜ᢸయࡀᏳᐃ

⏕యෆ࡟࠾ࡅࡿⅣ໬Ỉ⣲࡬ࡢ㓟⣲ῧຍ཯ᛂࡣ㸪୺࡞ඹ᭷⤖ྜ࡟ࡼࡾ㐃⤖ࡉࢀࡿࡇ࡜ࡸ㸪ղゐ፹άᛶⅬ࡜࡞࡟㕲࣭㖡࡞࡝ࡢ㑄⛣㔠ᒓࢆάᛶ୰ᚰ࡜ࡍࡿ㓟⣲ῧຍࡿ㔠ᒓୖࡢ㓄఩୙㣬࿴ᗙ࡜ᢸయ⾲㠃ࡀ┤᥋┦஫స⏝ࡋ࡞㓝⣲࡟ࡼࡾゐ፹ࡉࢀ࡚࠸ࡿ㸬㓝⣲ࡢ≉␗࡞཯ᛂ≉ᛶ࠸ࡇ࡜㸪࡜࠸ࡗࡓ᮲௳ࢆ‶ࡓࡋࡓୖ࡛㸪ճ㓄఩Ꮚ㛫ࢆ㐺ࡣ㸪࢔࣑ࣀ㓟ࡸ࣏ࣝࣇ࢕ࣜࣥ࡞࡝ࡢ⿵ḞศᏊ᪘࡟ࡼ

ษ࡞㛫㝸ࢆಖࡗ࡚ᅛᐃࡋ㸪Ꮩ❧ࡋࡓ㘒యゐ፹άᛶⅬ࡜ࡋࡗ࡚⢭ᐦ࡟❧య࠾ࡼࡧ㟁Ꮚⓗ≉ᛶࡀไᚚࡉࢀࡓ㔠ᒓ࡚ᶵ⬟ࡉࡏࡿᚲせࡀ࠶ࡿ࡜⪃࠼ࡓ(17)㸬

㓄఩ሙ 㔠ᒓ㘒య (16)࡜㸪ࡑࡢ࿘ᅖࢆྲྀࡾᕳࡃ୕ḟඖࡑࡇ࡛ᮏ◊✲࡛ࡣ᭷ᶵ࢔ࢪࢻᇶಟ㣭࣓ࢯከᏍᛶࢩࣜ࢝

✵㛫཯ᛂሙ࡟ࡼࡾࡶࡓࡽࡉࢀࡿ㸬୕ḟඖ✵㛫཯ᛂሙࡣ㸪࢔ࢪࢻᇶࢤࣝ SBA –N3 (7)ࢆᢸయ࡜ࡍࡿࡇ࡜ࢆィ⏬ࡋࡓ㸬ᇶ㉁ㄆ㆑⬟ࡸ㟁Ꮚఏ㐩࣭㞺ᅖẼ ぶỈᛶ࣭␯Ỉᛶ ࡢไᚚࡣ࢔ࣝ࢟ࣥ㢮࡜ࡢ Huisugen[3+2]⎔໬௜ຍ཯ᛂ ࢡࣜࢵࢡ࡜࠸ࡗࡓ཯ᛂಁ㐍ࡸゐ፹Ᏻᐃ໬࡟㛵ࢃࡿ㔜せ࡞ᅉᏊ࡛࠶཯ᛂ ࡟ࡼࡾ 1,2,3-ࢺࣜ࢔ࢰ࣮ࣝ࡟ኚ᥮࡛ࡁࡿ㸬ࡼࡗ࡚㔠ࡿ㸬ࡍ࡞ࢃࡕ㓄఩Ꮚ࡟ࡼࡾᙧᡂࡉࢀࡿ㓄఩ᅪࡔࡅ࡛࡞ࡃ㸪ᒓᨭᣢ㓄఩Ꮚ୰࡟ᮎ➃࢔ࣝ࢟ࣥ㒊఩ࢆᑟධ࡛ࡁࢀࡤ㸪ࡑࢀࢆྲྀࡾᅖࡴ࿘㎶⎔ቃࡢᵓ㐀ࡸᛶ㉁ࡶ⪃៖ࡍࡿᚲせࡀ

SBA–N3 ࡢ᭷ᶵ࢔ࢪࢻᇶ࡜ࡢࢡࣜࢵࢡ཯ᛂ࡟ࡼࡗ࡚ᢸయ

࠶ࡿࡀ㸪ࡇࢀ࡟ࡣつ๎ⓗ࡞୕ḟඖᵓ㐀ࢆ᭷ࡋ㸪࠿ࡘ໬Ꮫୖ࡬ࡢඹ᭷⤖ྜࢆ௓ࡋࡓᅛᐃ໬ࡀ㐩ᡂ࡛ࡁࡿ㸬ࡇࡇ࡛⏝ಟ㣭࡟ࡼࡿぶ࿴ᛶࡢไᚚࡸᵝࠎ࡞ᶵ⬟ࡢ௜୚ࡀྍ⬟࡞ᅛ࠸ࡓ SBA–N3 ࡣ㸪ࢸࢺ࢚ࣛࢺ࢟ࢩࢩࣛࣥ Si(OEt)4 ࡟ᑐయ⾲㠃ࡢά⏝ࡀ᭷ຠ࡛࠶ࡿ࡜⪃࠼ࡽࢀࡿ㸬ࡲࡓ㔠ᒓ㘒యࡋ࡚௵ពࡢ㔞 ࢣ࢖⣲ࣔࣝẚ㸪x%㸹x = 0.5, 1.0, 2.0, 4.0 ࡢゐ፹ࡣ⁐ᾮෆ࡛ࡢ໬Ꮫᖹ⾮ࡸ㘒యศᏊ㛫࡛ࡢ୙ᆒ໬཯ᛂ

3- ࢔ ࢪ ࢻ ࣉ ࣟ ࣆ ࣝ ࢺ ࣜ ࢚ ࢺ ࢟ ࢩ ࢩ ࣛ ࣥ࡟ࡼࡾኻάࡋ࡚ࡋࡲ࠺ሙྜࡀ࠶ࡿࡀ㸪ࡇࢀࢆ㜵ࡄ࡟ࡣ㸪

N3CH2CH2CH2Si(OEt)3 ࢆῧຍࡋࡓࢩࣛࣀ࣮࢚ࣝࢫࢸࣝ

ᅛయ⾲㠃࡬ࡢ㘒యศᏊࡢᅛᐃ໬ࡀ᭷ຠ࡛࠶ࡿ࡜⪃࠼ࡽࢀΰྜ≀ࢆ㸪㗪ᆺ࡜࡞ࡿ࣏࣐࣮࣑ࣜࢭࣝࡢᏑᅾୗ࡛ຍỈศࡿ㸬≉࡟ᾮ┦୰࡛ࡣ୙άᛶ࡞㓄఩㣬࿴✀ࡀ⏕ᡂࡋ࡚ࡋࡲ

ゎ࣭⬺Ỉ⦰ྜࡍࡿࡇ࡜࡟ࡼࡾᵓ⠏ࡋࡓ SBA-15 㢮⦕య࡛R-H

࠶ࡿ㸬ࡇࡢ one-pot synthesis ἲ࡟ࡼࡾㄪ〇ࡋࡓ SBA–N3–x

R-H
M

R-OH

ࡣ㸪᭷ᶵ࢔ࢪࢻᇶࡢಟ㣭㔞ࡀཎᩱࢩࣛࣀ࣮࢚ࣝࢫࢸࣝࡢ

R-OH
M

M

௙㎸ࡳẚ x ࡟ࡼࡾไᚚ࡛ࡁࡿࡔࡅ࡛࡞ࡃ㸪᭷ᶵ࢔ࢪࢻᇶ

Mࡢศᕸࡀࣛࣥࢲ࣒࡛࠶ࡿ࡜࠸࠺≉ᚩࢆᣢࡘ(7)㸬

or㓄఩Ꮚ㛫㝸䠖୰㛫M㓄఩Ꮚ㛫㝸䠖⊃䛔ࡇࡢ SBA–N3–x ࡟ᅛᐃࡍࡿ㓄఩Ꮚ࡟ࡣ㸪ᮎ➃࢔ࣝ࢟ࣥ㓄఩Ꮚ㛫㝸䠖ᗈ䛔ᵓ㐀࡬ࡢㄏᑟࡀᐜ᫆࡞ࣅࢫ(ࣆࣜࢪ࣓ࣝࢳࣝ)࢔࣑ࣥᵓ㐀⁐ᾮ୰ࢆᇶᮏ㦵᱁࡜ࡍࡿࡶࡢࢆ⏝࠸ࡓ㸬ࡇࢀࡣ㸪࢔ࣝ࢝ࣥỈ㓟M໬ゐ፹࡜ࡋ࡚ᶵ⬟ࡍࡿࢽࢵࢣࣝ㘒య(18)ࡢ㔠ᒓᨭᣢ㓄఩ᏊMࢺࣜࢫ(ࣆࣜࢪ࣓ࣝࢳࣝ)࢔࣑ࣥ = TPA ࡢࣆࣜࢪࣝᇶࡢ 1M㓄఩㣬࿴㘒య䠄୙άᛶ䠅ᅗ㸴㸬㓄఩Ꮚᅛᐃ㛫㝸࡟ᛂࡌࡓ㘒యᵓ㐀ࡢไᚚಶࢆࣉࣟࣃࣝࢠࣝᇶ࡟⨨᥮ࡋࡓࡶࡢ࡛࠶ࡿ㸬ࡲࡓᢸయᅛ
ᐃ᫬࡟ࢡࣜࢵࢡ཯ᛂ࡟ࡼࡾ⏕ᡂࡍࡿࢺࣜ࢔ࢰࣜࣝᇶࡣ㸪㓄఩Ꮚ࡜ᢸయࢆࡘ࡞ࡄ࣮ࣜࣥ࢝࡜ࡋ࡚ࡢᶵ⬟ࢆᢸ࠺ࡔࡅ

⚄ዉᕝ኱ᏛᕤᏛ◊✲ᡤᡤሗ ➨  ྕ⾲㸳㸬M/SBA-L2-x ࡟࠾ࡅࡿ㓄఩Ꮚ࠾ࡼࡧ㔠ᒓᅛᐃ㔞Pluronic P123
࣏࣐࣮࣑ࣜࢭࣝ

(100 – x) mol%

x mol%

1) H2O / conc.HCl2) Soxhletᢳฟ

Catalyst

L2ᢸᣢ㔞 /
mmol·g–1

Mᢸᣢ㔞 /
mmol·g–1

L2‫؟‬M

Ni/SBA-L2-0.5

0.072

0.08

0.9‫؟‬1

Ni/SBA-L2-1

0.13

0.14

0.9‫؟‬1

Ni/SBA-L2-2

0.25

0.22

1.1‫؟‬1

Ni/SBA-L2-4

0.33

0.19

1.7‫؟‬1

Co/SBA-L2-0.5

0.080

0.080

1.0‫؟‬1

Co/SBA-L2-4

0.32

0.23

1.4‫؟‬1ᅗ㸵㸬one-pot synthesis ἲ࡟ࡼࡿ SBA-L2-x ࡢㄪ〇࡛ࡣ࡞ࡃ㸪≧ἣ࡟ࡼࡗ࡚ࡣ㔠ᒓ㓄఩ᇶ࡜࡞ࡿࡇ࡜ࡶ᝿ᐃ
ࡋ࡚࠸ࡿ㸬࡞࠾㓄఩Ꮚᅛᐃᚋࡢᢸయ࡟࣊࢟ࢧ࣓ࢳࣝࢪࢩ
ࣛࢨࣥ (Me3Si)2NH ࢆస⏝ࡉࡏࡿࡇ࡜࡛㸪⾲㠃࡟ṧᏑࡋ࡚࠸ࡿỈ㓟ᇶࢆࢺ࣓ࣜࢳࣝࢩࣜࣝᇶ࡛୙άᛶ໬ࡋࡓ
SBA–L2–x ࡬࡜ㄏᑟࡋࡓ ᅗ 7 㸬ࡇࢀ࡟ࢽࢵࢣࣝ(II)࠶ࡿ
࠸ࡣࢥࣂࣝࢺ(II)㓑㓟ሷࢆస⏝ࡉࡏࡿࡇ࡜࡟ࡼࡾ㸪ᑐᛂࡍࡿᅛᐃ໬㘒యゐ፹ M/SBA-L2-x ࡜ࡋࡓ(19)(20)㸬
㸱㸬㸰㸬㸰㸬ᢸయୖࡢ㓄఩Ꮚᅛᐃᐦᗘ࡜ゐ፹≉ᛶࡢ┦㛵ㄪ〇ࡋࡓ M/SBA-L2-x ࡢ㓄఩Ꮚᢸᣢ㔞ࡣ㸪SBA–N3–x
ㄪ〇᫬ࡢ࢔ࢪࢻᇶ௙㎸ࡳẚ⋡ x ࡟ᛂࡌ࡚༢ㄪ࡟ኚ໬ࡋ࡚
࠸ࡓࡀ㸪㓄఩Ꮚᢸᣢ㔞࡜㔠ᒓ࢖࢜ࣥᅛᐃ㔞ࡢẚࡣ㓄఩Ꮚᢸᣢ㔞࡟ᛂࡌ࡚␗࡞ࡗ࡚࠸ࡓ ⾲ 5 㸬
Ni/SBA-L2-x ࡟࠾ࡅࡿ㓄఩Ꮚᢸᣢ㔞࡜ࢽࢵࢣࣝ࢖࢜ࣥᅛᐃ㔞ࡢẚࡣ㸪x = 0.5
㹼2 ࡛ࡣ࡯ࡰ L2㸸Ni = 1㸸1 ࡛࠶ࡗࡓࡢ࡟ᑐࡋ࡚ x = 4 ࡢࡶࡢ࡛ࡣ L2㸸Ni = 2㸸1 ࡟㏆ࡃ࡞ࡗࡓ㸬ࡲࡓ Co/SBA-L2-x
࡛ࡣ x = 0.5 ࡛ࡣ L2㸸Co = 1㸸1 ࡛ࢽࢵࢣࣝࡢሙྜ࡜ྠᵝ࡛࠶ࡗࡓࡀ㸪x = 4 ࡛ࡣ L2㸸Co = 1.4㸸1 ࡛ࢽࢵࢣࣝゐ፹
࡜㍑࡭࡚㔠ᒓࡢẚ⋡ࡀ㧗࠿ࡗࡓ ⾲ 5 㸬࡜ࡇࢁ࡛
SBA–N3–x ࡟᭰࠼࡚ tert-ࣈࢳࣝ࢔ࢪࢻ(tBuN3)࡜ࡢ཯ᛂ࡟
ࡼࡾᚓࡓ㓄఩Ꮚ L2tBu ࢆ⏝࠸ู࡚㏵㔠ᒓ㘒యࢆྜᡂࡋ㸪ࡑࡢᵓ㐀ゎᯒࢆ⾜࡞࠺ࡇ࡜࡟ࡼࡾᢸయୖ࡟ᙧᡂࡉࢀ࡚࠸
ࡿ㘒య✀ࡢᵓ㐀࡟ࡘ࠸࡚⪃ᐹࡋࡓ㸬ࢽࢵࢣࣝ㘒యࡢሙྜ㸪᮲௳࡟ᛂࡌ࡚ L2㸸Ni = 1㸸1 ࡛࠶ࡿ[Ni(L2tBu)(OAc)2(OH2)]= Ni/L2tBu ; ᅗ 8(a) ࠾ࡼࡧ L2㸸Ni = 2㸸1 ࡢ⤌ᡂ࠿ࡽ࡞
ࡿ[Ni(L2tBu)2](BF4)2 = Ni/2L2tBu ; ᅗ 8(b) ࡀᚓࡽࢀࡓࡀ㸪࡝ࡕࡽࡢ㘒య࡟࠾࠸࡚ࡶࢺࣜ࢔ࢰࣜࣝᇶࡣࢽࢵࢣࣝ࡟㓄఩ࡋ࡚࠸࡞࠸ࡇ࡜ࡀุ᫂ࡋࡓ(19)㸬୍᪉ࢥࣂࣝࢺ㘒య࡛ࡣࢺࣜ࢔ࢰࣜࣝᇶࡶࢥࣂࣝࢺ࢖࢜ࣥ࡟⤖ྜࡋ࡚ L2tBu 㓄఩Ꮚࡀᅄᗙ࣮࢟ࣞࢺ࡜ࡋ࡚ᶵ⬟ࡋࡓ[Co(L2tBu)(OAc)]+=Co/L2tBu ; ᅗ 8(c) ࡀᚓࡽࢀࡓ(20)㸬ᚑࡗ࡚㔠ᒓ✀࡟ࡼࡾtBu

ᅗ㸶㸬L2 ࢆ㓄఩Ꮚ࡜ࡍࡿ㘒యࡢศᏊᵓ㐀

L2 ࡢ⤖ྜᵝᘧࡣ␗࡞ࡗ࡚࠾ࡾ㸪M/SBA-L2-x ࡟࠾࠸࡚ࡶ
ྠᵝ࡞㘒య✀ࡀᢸయ⾲㠃࡟ᙧᡂࡉࢀ࡚࠸ࡿࡶࡢ࡜᥎ ࡋࡓ㸬ࡇࢀࡽࡢゐ፹࡟ࡘ࠸࡚㸪mCPBA ࢆ㓟໬๣࡜ࡍࡿࢩࢡ
ࣟ࣊࢟ࢧࣥ㓟໬άᛶࢆẚ㍑ࡍࡿࡇ࡜࡛㸪ᢸయୖࡢ㓄఩Ꮚᅛᐃᐦᗘࡀゐ፹άᛶ࡟ཬࡰࡍᙳ㡪ࢆ᳨ウࡋࡓ࡜ࡇࢁ㸪㔠ᒓ✀࡟ࡼࡾᣲືࡀ␗࡞ࡿࡇ࡜ࡀ᫂ࡽ࠿࡟࡞ࡗࡓ ⾲ 6 㸬ࢽࢵࢣࣝࢆ୰ᚰ㔠ᒓ࡜ࡋࡓሙྜ㸪Ni(ClO4)2 ➼ࡢ༢⣧࡞㔠ᒓሷࡣゐ፹άᛶࢆ♧ࡉ࡞࠸ࡇ࡜ࡀ᪤࡟ሗ࿌ࡉࢀ࡚࠾ࡾ(21)㸪
άᛶࡢⓎ⌧࡟ࡣ㐺ษ࡞㓄఩ᏊࡢᏑᅾࡀᚲ㡲࡛࠶ࡿ㸬ᮏ◊✲ู࡛㏵ྜᡂࡋࡓ㘒య Ni/L2tBu ࢆゐ፹࡜ࡋࡓᾮ┦ᆒ୍⣔
཯ᛂࡣ㏿ࡸ࠿࡟㐍⾜ࡋ㸪཯ᛂ㛤ጞ࠿ࡽ 1 ᫬㛫ᚋ࡟ࢩࢡࣟ
࣊࢟ࢧࣀ࣮ࣝࡢ⏕ᡂ㔞ࡀ㔠ᒓ࠶ࡓࡾࡢゐ፹ᅇ㌿ᩘ
TON ࡟᥮⟬ࡋ࡚⣙ 600 ᅇ࡟㐩ࡋࡓ࡜ࡇࢁ࡛཯ᛂࡀ೵Ṇࡋࡓ㸬ࡇࢀࡣୡ⏺࡛᭱ึ࡟ሗ࿌ࡉࢀࡓ࢔ࣝ࢝ࣥỈ㓟໬࡟άᛶࢆ♧ࡍࢽࢵࢣࣝ㘒యゐ፹ TPA ࢆ㓄఩Ꮚ࡜ࡍࡿࢽࢵ
ࢣࣝ㘒య (18)࡜ྠ➼ࡢ཯ᛂᛶ࡛࠶ࡿ㸬୍᪉㸪ᅛᐃ໬㘒యゐ፹࡛ࡣ཯ᛂ㏿ᗘࡣపୗࡋ࡚࠸ࡓࡀ㸪≉➹ࡍ࡭ࡁࡣ㓄఩Ꮚᢸᣢ㔞࡟ᛂࡌ࡚άᛶࡀ␗࡞ࡗ࡚࠸ࡓࡇ࡜࡛࠶ࡿ㸬
Ni/SBA-L2-x ࡢሙྜ㸪཯ᛂ⏕ᡂ≀࡟࠾ࡅࡿ࢔ࣝࢥ࣮ࣝ A࡜ࢣࢺࣥ K ࠾ࡼࡧࡑࡢ㓟໬య࡛࠶ࡿࣛࢡࢺࣥ L ࡢẚ⋡ࡣ㸪㓄఩Ꮚᢸᣢ㔞࡟ࡼࡽࡎ Ni/L2tBu ࡸ TPA 㘒యࡢሙྜ࡜኱ࡁࡃኚ໬ࡋ࡚࠸࡞࠸ࡇ࡜࠿ࡽ㸪཯ᛂ࣓࢝ࢽࢬ࣒ࡣྠ
୍࡛࠶ࡿ࡜⪃࠼ࡽࢀࡿ㸬ࡋࡓࡀࡗ࡚㓄఩Ꮚᅛᐃ㔞ࡀᑡ࡞࠸ሙྜ x = 0.5, 1, 2 ࡟ࡣ㸪Ni/L2tBu ࡜ྠᵝ࡞Ꮩ❧ࡋࡓ㘒య
ゐ፹άᛶⅬࡀᵓ⠏ࡉࢀ࡚࠸ࡿࡓࡵ࡟⁐ᾮ୰࡜ྠᵝ࡞཯ᛂᛶࢆ⥔ᣢࡋ࡚࠸ࡓࡶࡢࡢ㸪㓄఩Ꮚᅛᐃ㔞ࡀከ࠸⎔ቃㄪ࿴ᆺ≀㉁ኚ᥮ཬࡧ࢚ࢿࣝࢠ࣮ࣉࣟࢭࢫ๰ฟࡢ᪂ᇶ┙࡜࡞ࡿࢼࣀᵓ㐀ゐ፹ࡢ㛤Ⓨ⾲㸴㸬M/SBA-L2-x ࡢゐ፹άᛶ

Co/SBA-L2-x ࡟࠾࠸࡚ࡣ㸪㓄఩Ꮚᢸᣢ㔞࡜ゐ፹άᛶࡢ┦㛵ࡀ๓㏙ࡢࢽࢵࢣࣝゐ፹ࡢࡑࢀ࡜ࡣ㏫ࡢഴྥࢆ♧ࡋࡓ㸬⯆࿡῝࠸ࡇ࡜࡟㸪㧗ᢸᣢ㔞ࡢࡶࡢ x = 4 ࡀ⏕ᡂ≀཰㔞࣭࢔ࣝࢥ࣮ࣝ㑅ᢥᛶ࡜ࡶ࡟ Co/L2tBu ࢆゐ፹࡜ࡍࡿᆒ୍⣔཯ᛂࡼࡾࡶ㧗࠿ࡗࡓ㸬཯ᛂ㏵୰࡟ゐ፹ࢆࢁ㐣ࡍࡿࡇ࡜࡟ࡼ
ࡾ㝖ཤࡋࡓ⁐ᾮ࡛ࡣ㸪⁐ฟࡋࡓࢥࣂࣝࢺ࢖࢜ࣥࡢస⏝࡟
ࡼࡾゐ፹཯ᛂࡀ㐍⾜ࡍࡿࡶࡢࡢ㸪⏕ᡂ≀࡟༨ࡵࡿ࢔ࣝࢥ
࣮ࣝࡢ๭ྜࡀῶᑡࡋ࡚࠸ࡓࡇ࡜ࢆ⪃࠼ేࡏࡿ࡜㸪ᢸయୖ࡟㧗ᐦᗘ࡛Ꮡᅾࡍࡿ㓄఩Ꮚ L2 ࡀࢥࣂࣝࢺ࢖࢜ࣥࡢὶฟ
ࢆᢚไࡋ㸪㓄఩Ꮚ L2 ࡟ಖᣢࡉࢀࡓ㘒య✀࡜ࡋ࡚㛗᫬㛫άᛶࢆ⥔ᣢ࡛ࡁࡓ஦ࡀάᛶྥୖࡢせᅉ࡜⪃࠼ࡽࢀࡿ(20)㸬
௨ୖ࡟♧ࡋࡓᢸయୖࡢ㓄఩Ꮚᅛᐃᐦᗘࡀゐ፹άᛶ࡟ཬ
ࡰࡍᙳ㡪ࡢ┦㐪ࡣ㸪୍⩏ⓗ࡟ࡣ㔠ᒓ✀࡟ᛂࡌ࡚Ᏻᐃ࡞㘒యศᏊᵓ㐀࠾ࡼࡧ㓄఩ᖹ⾮ࡀ␗࡞ࡿࡓࡵ࡜ゎ㔘࡛ࡁࡿࡀ㸪ᾮ-ᅛ⏺㠃 ୙ᆒ୍⣔ ࡜⁐ᾮ≧ែ ᆒ୍⣔ ࡛ࡣᖹ⾮ᣲືࡀ␗࡞ࡿࡇ࡜ࡶゐ፹≉ᛶࡢᨭ㓄ᅉᏊ࡜࡞ࡗ࡚࠸ࡿࡶࡢ࡜
᥎ᐹࡉࢀࡿ㸬࡞࠾ᅛᐃ໬㘒యゐ፹ࡢ㛤Ⓨ࡜୪⾜ࡋ࡚㸪ࢽࢵࢣࣝ㘒యゐ፹࡟ࡼࡿ᭷ᶵ㐣㓟ࢆ㓟໬๣࡜ࡍࡿ㑅ᢥⓗ࢔ࣝ࢝ࣥỈ㓟໬཯ᛂࡢᶵᵓゎ᫂ࡶヨࡳ࡚࠾ࡾ㸪ࡈࡃ᭱㏆㸪
ゐ፹཯ᛂࡀ㘒య཯ᛂሙ࡟࠾࠸࡚㐍⾜ࡋ࡚࠸ࡿࡇ࡜ࢆ♧ࡍドᣐࢆᚓࡿࡇ࡜ࡸ㸪ゐ፹཯ᛂ㐣⛬࡛⏕ᡂࡍࡿ୰㛫యࡢ᳨ฟ࡟ᡂຌࡋࡓ(22)(23)㸬ࡇࢀࡽࡢᡂᯝࡣ㔠ᒓᨭᣢ㓄఩Ꮚࡢ⢭ᐦศᏊタィ࡟ࡼࡾ఩⨨࠾ࡼࡧ❧య㑅ᢥⓗ࡞࢔ࣝ࢝ࣥỈ㓟
໬ゐ፹ࡀᵓ⠏࡛ࡁࡿྍ⬟ᛶࢆ♧ࡍࡶࡢ࡛࠶ࡾ㸪ࡇࢀ࡜ᮏ◊✲ࡢᡂᯝ࡜⤌ࡳྜࢃࡏࡿࡇ࡜࡛ࣇ࢓࢖ࣥࢣ࣑࢝ࣝࢬࡢ
ྜᡂࣉࣟࢭࢫ࡟㐺⏝ྍ⬟࡞୙ᩧᅛయ㓟໬ゐ፹ࡢ㛤Ⓨࡀᮇᚅ࡛ࡁࡿ㸬ᅗ㸷㸬Ni/SBA-L2-x ࡢ᥎ᐃάᛶⅬᵓ㐀

Ni/SBA-L2-4.0 ࡛ࡣ㸪L2㸸Ni ࡀ 2㸸1 ࡟㏆࠸ࡇ࡜࠿ࡽ㸪ᢸయ⾲㠃࡟ࡣ୙άᛶ࡞㘒య✀[Ni(L2)2]2+ ࡀከࡃᙧᡂࡋ࡚࠸
ࡿࡶࡢ࡜⪃࠼ࡽࢀࡿ ᅗ 9 㸬࡜ࡇࢁ࡛ L2㸸Ni = 2㸸1 ࡛࠶ࡿ㘒య Ni/2L2tBu ࡣᾮ┦ᆒ୍⣔཯ᛂ࡟࠾࠸࡚ Ni/L2tBu ࡜඲ࡃྠᵝ࡞ゐ፹άᛶࢆ♧ࡋࡓࡇ࡜࠿ࡽ㸪⁐ᾮ୰࡛ࡣ[Ni(L2tBu)2]2+ ࡟࠾ࡅࡿ L2tBu ࡣ⨨᥮άᛶ࡛࠶ࡿ࡜⪃࠼ࡽࢀࡿ㸬ࡋ࠿ࡋ Ni/SBA-L2-4.0 ࡛ࡣ L2 ࡀᢸయ࡟ᅛᐃࡉࢀࡓࡇ
࡜࡛㐠ືᛶࡀపୗࡋ࡚ᖹ⾮≧ែࡀ኱ࡁࡃኚ໬ࡋࡓࡓࡵ࡟㸪ᢸయ⾲㠃࡟ᙧᡂࡉࢀࡓ[Ni(L2)2]2+ࡣ⨨᥮୙άᛶ࡛࠶ࡾゐ፹άᛶⅬ࡜ࡣ࡞ࡾ࠼࡞࠿ࡗࡓࡶࡢ࡜᥎ ࡉࢀࡿ(19)㸬
୍᪉㸪ࢥࣂࣝࢺࢆ୰ᚰ㔠ᒓ࡜ࡋࡓሙྜ࡟ࡣ㸪ࢽࢵࢣࣝゐ፹࡜ࡣᣲືࡀ␗࡞ࡗࡓ㸬ࡲࡎ኱ࡁ࡞㐪࠸ࡣ༢⣧࡞ࢥࣂࣝࢺ(II)ሷࡀゐ፹άᛶࢆ᭷ࡍࡿࡇ࡜࡛࠶ࡿ(21)㸬ᆒ୍⣔࡟࠾࠸࡚ࡣࢥࣂࣝࢺ࢖࢜ࣥࡀ㓄఩Ꮚ L2tBu ࡟ಖᣢࡉࢀࡿࡇ࡜
࡟ࡼࡾ㸪཯ᛂ㏿ᗘࡀ㢧ⴭ࡟పୗࡍࡿ࡜࡜ࡶ࡟࢔ࣝࢥ࣮ࣝ
⏕ᡂ≀ࡢ㑅ᢥᛶࡀྥୖࡋࡓ㸬ࡑࡋ࡚ᅛᐃ໬㘒య㸲㸬⤖ゝࡇࢀࡲ࡛ࡢ◊✲࡛㸪࣓ࢯከᏍᛶࢩࣜ࢝ᢸయࡢࢼࣀࢫࢣ
࣮ࣝ⣽Ꮝෆ㒊ࡢ᭷ᶵᐁ⬟ᇶ࡟ࡼࡿ໬Ꮫಟ㣭ἲࢆ☜❧ࡍࡿࡇ࡜࡟ᡂຌࡋࡓ㸬ᑟධࡍࡿᐁ⬟ᇶࡢ✀㢮ࡸᵓ㐀≉ᛶ࡟ᛂࡌ࡚㸪ணࡵㄪ〇ࡋࡓከᏍᛶࢩࣜ࢝࡜࠿ࡉ㧗࠸ᐁ⬟ᇶࢆ᭷ࡍࡿࢩࣛࣥ࢝ࢵࣉࣜࣥࢢ๣ࡢ⦰ྜ࡟ࡼࡿ post synthesis ἲ㸪࠶ࡿ࠸ࡣࢩࣜ࢝ㄪ〇᫬࡟ᡤᮃࡢᐁ⬟ᇶࢆ᭷ࡍࡿࢩࣛࣥ࢝
ࢵࣉࣜࣥࢢ๣ࢆᡤᐃࡢ๭ྜ࡛ᑟධࡍࡿ one-pot synthesisἲ࡟ࡼࡾᢸయ࡬ࡢᐁ⬟ᇶᑟධᐦᗘࢆไᚚࡋࡓ㸬ᑟධࡋࡓᐁ⬟ᇶᮎ➃ࢆ཯ᛂ㛤ጞⅬ࡜ࡍࡿࡇ࡜࡛㸪⣽Ꮝෆቨࢆ࣏ࣜ
࣌ࣉࢳࢻ࡛ಟ㣭ࡋࡓ͆୙ᩧࢼࣀ✵㛫͇ࢆᵓ⠏ࡋࡓ࡜ࡇࢁ㸪㛗㙐࣏ࣜ࣌ࣉࢳࢻࡢ㸱ḟඖᵓ㐀࡟㉳ᅉࡍࡿᇶ㉁ㄆ㆑⬟ࡀⓎ⌧ࡋ࡚㸪❧య㑅ᢥⓗ࡞㓟໬཯ᛂࡀ㐍⾜ࡍࡿࡇ࡜ࡀ᫂ࡽ
࠿࡟࡞ࡗࡓࡀ㸪ᢸయୖ࡛ࡢ࣏ࣜ࣌ࣉࢳࢻ㙐㛗ࡢไᚚἲࢆ
☜❧ࡍࡿ࡟ࡣ⮳ࡗ࡚࠸࡞࠸㸬ࡲࡓ୙ᩧゐ፹࡜ࡋ࡚ᶵ⬟ࡍࡿࢪ࣌ࣉࢳࢻಟ㣭ࢩࣜ࢝ࡢ㛤Ⓨ࡟ᡂຌࡋࡓࡀ㸪ᆒ୍⣔᭷ᶵศᏊゐ፹࡜ྠ➼ࡢάᛶࢆᚓࡿ࡟ࡣ㸪ከࡃࡢ᳨ウㄢ㢟ࡀ⚄ዉᕝ኱ᏛᕤᏛ◊✲ᡤᡤሗ ➨  ྕᏑᅾࡍࡿࡇ࡜ࡶ᫂ࡽ࠿࡟࡞ࡗࡓ㸬୍᪉ᅛᐃ໬㘒యゐ፹࡟

Top. Catal., 52 (2009) 845.

ࡘ࠸࡚ࡣ㸪ᢸయ࡬ࡢᐁ⬟ᇶᑟධᐦᗘ࡟ᛂࡌ࡚㸪ᐁ⬟ᇶᮎ(7) (a) J. Nakazawa, T. D. P. Stack, J. Am. Chem. Soc., 130 (2008)➃࡟㐃⤖ࡋࡓ㔠ᒓ㘒యゐ፹ࡢᵓ㐀࠾ࡼࡧゐ፹≉ᛶࡀኚ໬

14360; J. Nakazawa, B. J. Smith, T. D. P. Stack, J. Am. Chem. Soc.,

ࡍࡿࡇ࡜ࡀ᫂ࡽ࠿࡟࡞ࡾ㸪㐺ษ࡞タィࢆ⾜࡞࠼ࡤ⁐ᾮ୰134 (2012) 2750.

࡛ࡢゐ፹άᛶࢆᦆ࡞࠺ࡇ࡜࡞ࡃ㸪ᅛయゐ፹࡬࡜ᒎ㛤ࡍࡿ(8) J. M. Thomas, R. Raja, Acc. Chem. Res., 41 (2008), 708.

ࡇ࡜ࡀྍ⬟࡛࠶ࡿࡇ࡜ࡀᐇド࡛ࡁࡓ㸬ࡇࢀࡽࡢ▱ぢࡣ(9) S. Juliá, J. Guixer, J. Masana, J. Rocas, S. Colonna, R. Annuziata, H.

ᵝࠎ࡞᭷ᶵ̿↓ᶵࣁ࢖ࣈࣜࢵࢻᮦᩱࡸ✀ࠎࡢ࣎ࢺ࣒࢔ࢵ
ࣉᆺࢼࣀᵓ㐀ᶵ⬟ᮦᩱࢆタィ࣭ᵓ⠏ࡍࡿୖ࡛᭷┈࡞▱ぢ࡜࡞ࢁ࠺㸬௒ᚋࡣᮏ✏࡛⤂௓ࡋࡓ㸪⢭ᐦ᭷ᶵྜᡂࡢ⎔ቃㄪ࿴ᆺࣉ

Molinari, J. Chem. Soc., Perkin Trans.1, (1982) 1317.
(10) D. R. Kelly, E. Caroff, R. W. Flood, W. Heal, S. M. Roberts, Chem.
Comm., (2004) 2016.
(11) J. D. Lunn, D. F. Shantz, Chem. Mater., 21 (2009) 3638.

ࣟࢭࢫࡢᵓ⠏࡟㈉⊩ࡋ࠼ࡿゐ፹ࡢ᭦࡞ࡿ㧗ᛶ⬟໬ࢆ᥎ࡋ(12) బ⸨ 㝯௓㸪ྜྷ⏣ ᭐ᘯ㸪ෆ⸨ ࿘ᘤ㸪͆✀ࠎࡢ࣏ࣜ࣌ࣉࢳࢻಟ

㐍ࡵࡿ࡜࡜ࡶ࡟㸪ࡇࢀࡲ࡛࡟ᚓࡓ͆ࢼࣀᵓ㐀ゐ፹͇ࡢタ㣭࣓ࢯ࣏࣮ࣛࢫࢩࣜ࢝ࡢྜᡂ࡜୙ᩧゐ፹཯ᛂ࡬ࡢᛂ⏝͇㸪➨ィ࣭ᵓ⠏࡟㛵ࢃࡿ▱ぢࢆࡶ࡜࡟㸪࢚ࢿࣝࢠ࣮ࡸ⎔ቃၥ㢟ࡢゎỴ࡟㈉⊩ࡋ࠼ࡿゐ፹ࡢ㛤Ⓨࡶ⾜࡞ࡗ࡚࠸ࡃィ⏬࡛࠶ࡿ㸬

108 ゐ፹ウㄽ఍, 1G22 (2011 ᖺ 9 ᭶).
(13) B. List, R. A. Lerner, C. F. Barbas III, J. Am. Chem. Soc., 122 (2000)
2395.
(14) P. Krattiger, R. Kovasy, J. D. Revell, S. Ivan, H. Wennemers, Org.

ཧ⪃ᩥ⊩

Lett., 7 (2005) 1101.

(1) (a) T. Miyao, K. Minoshima, Y. Kurokawa, K. Shinohara, W. Shen,(15) బ⸨ 㝯௓, ྜྷ⏣ ᭐ᘯ, ෆ⸨ ࿘ᘤ,͆୙ᆒ୍⣔୙ᩧゐ፹ㄪ〇ࡢ

S. Naito, Catal. Today, 132, 132 (2008); (b) W. Shen, K.

ࡓࡵࡢ࣓ࢯ࣏࣮ࣛࢫࢩࣜ࢝⣽Ꮝෆ࡬ࡢ࣌ࣉࢳࢻᑟධἲࡢ㛤

Komatsubara, T. Hagiyama, A. Yoshida, S. Naito, Chem. Commun.,
6490 (2009); (c) W. Shen, K. Komatsubara, T. Saito, A. Yoshida, S.
Naito, Catal. Today, 171, 150 (2011); (d) W. Shen, Y. Nitta, A.
Yoshida, S. Naito, J. Catal., 280, 161 (2011).
(2) (a) S. Hikichi, H. Okuda, Y. Ohzu, M. Akita, Angew. Chem. Int. Ed.,Ⓨ͇㸪➨ 111 ゐ፹ウㄽ఍, 2P58 (2013 ᖺ 3 ᭶).
(16) (a) ᘬᆅ ྐ㑻, ᅛయ≀⌮, 43 (2008) 733; (b) ᘬᆅ ྐ㑻, ゐ፹,
46 (2004) 262.
(17) ᘬᆅ ྐ㑻, ୰⃝ 㡰, ゐ፹, 52 (2010) 243.
(18) (a) T. Nagataki, Y. Tachi and S. Itoh, Chem. Commun., (2006) 4016;

48 (2009) 188; (b) S. Hikichi, C. Kobayashi, M. Yoshizawa, M.

(b) T. Nagataki, K. Ishii, Y. Tachi and S. Itoh, Dalton Trans., (2007)

Akita, Chem. Asian J., 5 (2010) 2086; (c) J. Nakazawa, H. Ogiwara,

1120.

Y. Kashiwazaki, A. Ishii, N. Imamura, Y. Samejima, S. Hikichi,
Inorg. Chem., 50 (2011) 9933.
(3) (a) D. Zhao, J. Feng, Q. Huo, N. Melosh, G.H. Fredrickson, B.F.
Chmelka, G.D. Stucky, Science, 279 (1998) 548; (b) D. Margolese,
J.A. Melero, S.C. Christiansen, B.F. Chmelka, G.D. Stucky, Chem.
Mater., 12 (2000) 2448.
(4) T. Akashi, J. Nakazawa, S. Hikichi, J. Mol. Catal. A: Chem., 371(2013) 42.
(5) J. C. Hicks, R. Dabestani, A. C. Buchanan III, C. W. Jones, Chem.
Mater., 18 (2006) 5022.
(6) S. Hikichi, M. Kaneko, Y. Miyoshi, N. Mizuno, K. Fujita, M. Akita,(19) J. Nakazawa, T. Hori, T. D. P. Stack, S. Hikichi, Chem. Asian J., 8(2013) 1191.
(20) J. Nakazawa, A. Yata, T. Hori, T. D. P. Stack, Y. Naruta, S. Hikichi,
Chem. Lett., 42(2013)1197.
(21) W. Nam, J. Y. Ryu, I. Kim and C. Kim, Tetrahedron Lett., 43(2002) 5487.
(22) S. Hikichi, K. Hanaue, T. Fujimura, H. Okuda, J. Nakazawa, Y.
Ohzu, C. Kobayashi, M. Akita, Dalton Trans., 42 (2013) 3346.
(23) J. Nakazawa, S. Terada, M. Yamada, S. Hikichi, J. Am. Chem. Soc.,
135 (2013) 6010.

87✵Ẽ㟁ụ⏝㟁ᴟゐ፹࠾ࡼࡧ㧗ศᏊ㟁ゎ㉁⭷ࡢ㛤Ⓨᯇᮏ ኴ 1࣭⏣୰ Ꮫ 2࣭༡㒊 ඾⛱ 3࣭ᓊᒸ ┿ஓ 4

Development of Electrocatalyst and Polymer Electrolyte Membrane for Air-Battery
Futoshi MATSUMOTO࣭Manabu TANAKA࣭Noritoshi NANBU࣭Shin-ya KISHIOKA㸯㸬⥴ゝ 

࡛ࡣ㸪✵Ẽ㟁ụࡢ୰࡛ࡶ✵Ẽᴟ࡟࠾ࡅࡿゐ፹ᮦᩱࢆ㧗౯ ✵Ẽ㟁ụࡣ㸪ࣜࢳ࣒࢘஧ḟ㟁ụࡢ㈇ᴟ࡜⇞ᩱ㟁ụࡢ✵࡞㔠ᒓࢆ⏝࠸࡞ࡃ࡚ࡶゐ፹⬟ࢆⓎ᥹࡛ࡁࡿᮦᩱࡀከࡃ᳨

Ẽᴟࢆ⏝࠸࡚㟁ụࢆసࡿࡇ࡜࡟ࡼࡾ㸪ࣜࢳ࣒࢘஧ḟ㟁ụウ࡛ࡁࡿࡼ࠺࡟㟁ゎ㉁ࢆ࢔ࣝ࢝ࣜᛶỈ⁐ᾮ࡜ࡋ㸦Ỉ㓟໬࡜⇞ᩱ㟁ụࡢ㛗ᡤࢆྜࢃࡏᣢࡘ㟁ụ Fig. 1 ࡜࡞ࡗ࡚࠾

≀࢖࢜ࣥఏᑟᆺ㸧
㸪㈇ᴟ࡟ࡣ Zn ࡢࡼ࠺࡞㔠ᒓ㈇ᴟࢆ⏝࠸ࡾ㸪᪤Ꮡࡢࣜࢳ࣒࢘஧ḟ㟁ụࡢ඘ᨺ㟁ᐜ㔞ࡢ㸱ಸ௨ୖࡢࡿ✵Ẽ㟁ụࡢ㛤Ⓨࢆ┠ⓗ࡜ࡋ࡚◊✲ࢆ⾜ࡗ࡚࠸ࡿ㸬ࡇࡢᛶ⬟ࢆ᭷ࡍࡿࡇ࡜࠿ࡽ㏆ᖺὀ┠ࡉࢀ࡚࠸ࡿ[1-4]㸬⌧ᅾ㸪㟁ụࡣ⌮ㄽ㟁ᅽ 2.5 V඘ᨺ㟁ᐜ㔞ࡣ 860 mAh/g ࡛࠶ࡾ㸪✵Ẽ㟁ụࡣ㸪
⿵⫈ჾ⏝ࡢ㸯ḟ㟁ụ࡜ࡋ࡚౑ࢃࢀ࡚࠸ࡿࡀ㸪⌧ᅾࡢࣜࢳ࣒࢘஧ḟ㟁ụࡢ⌮ㄽᐜ㔞ࡀ 274 mAh/g ࡛࠶ࡿ஧ḟ㟁ụ࡜ࡋ࡚ࡢᕷ㈍ရࡣ↓࠸㸪ࡇࡢ⌮⏤ࡣ㸪✵Ẽᴟ࡟ࡇ࡜ࢆ⪃࠼ࡿ࡜ 3 ಸࡢᐜ㔞ࢆᣢࡘࡇ࡜࡟࡞ࡿ㸬㈇ᴟ࡟ࣜ

࠾ࡅࡿ඘㟁࣭ᨺ㟁཯ᛂࢆప࠸㐣㟁ᅽ࡛㉳ࡇࡍᏳ౯࡞ゐ፹ࢳ࣒࢘㔠ᒓࢆ⏝࠸࡞࠸ࡓࡵ㸪㟁ụࡢ⌮ㄽ㟁ᅽࡣࣜࢳ࣒࢘ᮦᩱࢆぢ࠸ࡔࡏ࡞࠸ࡇ࡜࡞࡝࡟ࡼࡿ[5,6] 㸬ࡑࡇ࡛ᮏ◊✲㔠ᒓࢆ౑ࡗࡓሙྜ࡟ẚ࡭ 1.7 V ⛬ᑠࡉ࠸ࡀ㸪ࣜࢳ࣒࢘㔠ᒓ࡟ࡼࡿ⇿Ⓨࡢ༴㝤ᛶࡀ࡞࠸ࡇ࡜ࡀ኱ࡁ࡞฼Ⅼ࡛࠶ࡿ㸬ࡲࡓ㸪㟁ゎ㉁⭷࡜ࡋ࡚㧗ศᏊ⭷ࢆ⏝࠸ࡿࡇ࡜࡟ࡼࡾⓎⅆ࣭ᘬⅆࡢ༴㝤ᛶࡀᚑ᮶ࡢࣜࢳ࣒࢘஧ḟ㟁ụ࡛⏝࠸ࡽࢀࡿࡼ࠺࡞᭷ᶵ⁐፹ࢆ⏝࠸ࡿሙྜ࡟ẚ࡭࡚ᑠࡉࡃ࡞ࡿࡇ࡜
ࡶ≉ᚩ࡛࠶ࡿ㸬ࡇࡢ࢔ࣝ࢝ࣜỈ⁐ᾮࢆ⏝࠸ࡓ✵Ẽ㟁ụࡢ㻲㼕㼓㻚㻌㻝㻌 䜰䝹䜹䝸ᆺ✵Ẽ㟁ụ䛾ᶍᘧᅗ㻌

1: ෸ᩍᤵ ⚄ዉᕝ኱ᏛᕤᏛ㒊≀㉁⏕࿨໬Ꮫ⛉
Associate Professor, Dept. of Material and Life
Chemistry, Kanagawa University
2: ຓᩍ 㤳㒔኱Ꮫᮾி኱Ꮫ㝔㒔ᕷ⎔ቃ⛉Ꮫ◊✲⛉ศᏊᛂ⏝໬Ꮫᇦ
Assistant Professor, Dept. of Applied Chemistry,
Tokyo Metropolitan University
3: ෸ᩍᤵ ᮾிᕤⱁ኱ᏛᕤᏛ㒊⏕࿨⎔ቃ໬Ꮫ⛉
Associate Professor, Dept. of Life Science andSustainable Chemistry, Tokyo Polytechnic University
4: ෸ᩍᤵ ⩌㤿኱Ꮫᩍ⫱Ꮫ㒊⌮⛉ᩍ⫱ㅮᗙ
Associate Professor, Dept. of Chemistry Faculty of
Education, Gunma University㻲㼕㼓㻚㻌 㻞㻌 㻼㼠㻙㻾㼡 ྜ㔠䛸 㻼㼠㻼㼎 㔠ᒓ㛫໬ྜ≀䛾⤖ᬗᵓ㐀䛸⾲㠃ᵓ㐀㻌⚄ዉᕝ኱ᏛᕤᏛ◊✲ᡤᡤሗ ➨  ྕࡲࡓ㸪⤖ᬗᵓ㐀ࡀ㔠ᒓ㛫໬ྜ≀ࢆᙧᡂࡍࡿࡇ࡜࡟ࡼࡗ࡚Ᏻᐃ໬
ࡋ࡚࠸ࡿࡓࡵ㸪㛗᫬㛫ࡢ౑⏝࡟ࡼࡗ࡚⤖ᬗᵓ㐀ࡀኚ໬ࡍࡿၥ㢟ࡣ࡯࡜ࢇ࡝࡞࠸㸬㟁Ẽ໬Ꮫⓗ࡞ほⅬ࠿ࡽぢ࡚ࡳࡿ࡜㸪Pb ࡣ㓟ᛶ⁐ᾮ୰࡟࠾࠸࡚㸪㟁Ẽ໬Ꮫⓗ࡟⁐ゎࡋࡸࡍ࠸㔠ᒓ࡛࠶ࡾ㸪ࡇࢀ
ࡲ࡛ Pb ࢆ⏝࠸ࡓ໬ྜ≀ࡀゐ፹࡜ࡋ࡚⪃៖ࡉࢀ࡚ࡇ࡞࠿ࡗࡓࡢ
㻲㼕㼓㻚㻌㻟㻌 ⓑ㔠㟁ᴟୖ䜈䛾 㻯㻻 䛾྾╔㻌ᐇ⏝໬ࡢࡓࡵ࡟ࡣከࡃࡢⅬ࡟࠾࠸࡚ᨵⰋࡀᚲせ࡛࠶ࡿࡀ㸪ᮏࣉࣟࢪ࢙ࢡࢺ࡛ࡣ௨ୗࡢ୕ࡘࡢせ⣲ᢏ⾡࡟ࡘ࠸࡚ࡢᮦ
ᩱ㛤Ⓨࢆ┠ⓗ࡟᳨ウࢆ⾜ࡗ࡚࠸ࡿ㸬(1) Pt ࡞࡝ࡢ㧗౯࡞ᮦᩱࡢ౑⏝㔞ࢆᴟຊᑡ࡞ࡃࡍࡿゐ፹ᮦᩱࡢ㛤Ⓨ
(2)࢔ࢽ࢜ࣥ஺᥮㧗ศᏊ㟁ゎ㉁ࡢ㛤Ⓨ㸸࢔ࢽ࢜ࣥఏᑟᛶ
ࢆ 10-3 Scm-1 ⛬ᗘࢆᣢࡕ㸪✵Ẽࢆྲྀࡾධࢀࡿሙྜ࡟஧㓟໬
Ⅳ⣲ࢆྠ᫬࡟㟁ụෆ࡟ྲྀࡾ㎸ࡲ࡞࠸ࡼ࠺࡟࢞ࢫศ㞳⭷ᶵࡣ㸪ࡇࡢ⌮⏤ࡢࡓࡵ࡛࠶ࡿ㸬ࡋ࠿ࡋ㸪㔠ᒓ㛫໬ྜ≀ࡢ⏕ᡂ࡟ࡼࡿᏳᐃ໬ࡢຠᯝ࡟ࡼࡾ㸪Pb ࡀ㟁Ẽ໬Ꮫⓗ࡟⁐ฟࡍࡿ㟁఩ࡀ኱ࡁࡃṇ㟁఩ഃ࡟ࢩࣇࢺࡋ㸪᭷ᶵపศᏊࡢ㓟໬཯ᛂࡀ㉳ࡇࡿ㟁఩⠊ᅖ࡟࠾࠸࡚ࡶPtPb ゐ፹࡜ࡋ࡚Ᏻᐃ࡟ാࡃࡇ࡜ࡀ࡛ࡁࡿ㸬ࡇࡢⅬࡀ㔠ᒓ㛫໬ྜ≀ࢆ฼⏝ࡍࡿ฼Ⅼ࡜ࡋ࡚ᙉࡃ୺ᙇࡉࢀࡿⅬ࡛࠶ࡿ
㸦Fig. 4㸧㸬Pb ࡣ㓟ᛶ⁐ᾮ࡟࠾࠸࡚㸪-0.13 V (vs. NHE)௜㏆࡛⁐ゎࡍࡿ㸬୍᪉㸪Pt ୖ࡟ᩓࡾࡤࡵࡽࢀࡓPb ཎᏊ㸦࢔ࢻ࢔ࢺ࣒Pb㸧
ࡢሙྜࡣPt ࡜ᙉࡃ┦஫స⏝ࡍࡿࡢ࡛㸪Ᏻᐃ໬ࡋ㸪⁐ゎ㟁఩ࡀṇ㟁఩ഃ࡟ࢩࣇࢺࡋ㸪ࡑࡢ್ࡣ⣙0.53 V ࡛࠶ࡿ㸬ࡉࡽ࡟㔠ᒓ㛫໬⬟ࢆ᭷ࡍࡿ≉ᛶࢆᣢࡓࡏࡿ㸬(3)ゐ፹ୖ࡬ࡢ㓟⣲࢞ࢫࡢ༑ศ࡞౪⤥ࠊ㓟⣲㑏ඖ⏕ᡂ≀࡛࠶ࡿỈ㓟໬≀࢖࢜ࣥࡢゐ፹⾲㠃࠿ࡽ㟁ゎ㉁⭷ࡲ࡛ࡢࢫ࣒࣮ࢬ࡞⛣ືࢆᐇ⌧ࡍࡿ㟁ᴟゐ፹㟁ゎ㉁⭷ࡢ୕ᒙ⏺㠃ࡢᵓ⠏ᮏሗ࡛ࡣ㸪せ⣲ᢏ⾡(1), (2)࡟ࡘ࠸࡚ 2012 ᖺᗘ᳨ウࡋࡓ⤖ᯝ࡟ࡘ࠸࡚ሗ࿌ࡍࡿ㸬㸰㸬㔠ᒓ㛫໬ྜ≀ࢆ⏝࠸ࡓ㓟⣲㑏ඖゐ፹ࡢ㛤Ⓨ㓟⣲㑏ඖゐ፹ࡣ Pt ࡀ⏝࠸ࡽࢀ࡚࠸ࡿࡀ㸪Pt ࢆ⏝࠸ࡓሙྜ࡟
࠾࠸࡚ࡶ㸪㧗࠸㐣㟁ᅽࢆ⏕ࡌࡿࡓࡵⓎ㟁ຠ⋡ࡀᝏ࠸࡞࡝ࡢၥ㢟ࡀṧࡗ࡚࠸ࡿ㸬ᡃࠎࡣPt ࣮࣋ࢫࡢ㔠ᒓ㛫໬ྜ≀ࢆ⇞ᩱᴟࡢ㟁ᴟゐ፹࡜ࡋ࡚㐺⏝ࡍࡿࡇ࡜࡟ࡼࡾ㸪ゐ፹άᛶ࡜ࡑࡢάᛶࡢᏳᐃᛶ

㻲㼕㼓㻚㻌㻡㻌 ྜᡂ䛧䛯ྛ✀䝃䞁䝥䝹䛾 㼄 ⥺ᅇᢡᅗᙧ㻌ࡀ኱ࡁࡃྥୖࡍࡿࡇ࡜ࢆሗ࿌ࡋ࡚ࡁ࡚࠸ࡿ[7-9]㸬㔠ᒓ㛫໬ྜ≀ࡣ㸪⤖ᬗ᱁Ꮚ୰࡟࠾࠸࡚㸪 ࠶ࡿ࠸ࡣ  ✀㢮ࡢඖ⣲ࡀつ๎ṇࡋࡃ㓄ิࡋ࡚࠾ࡾ(Fig. 2)㸪つ๎ṇࡋࡃ㓄ิࡍࡿࡇ࡜࡟ࡼࡾ㸪኱ࡁ࡞Ᏻᐃ໬࢚ࢿࣝࢠ࣮ࡀ⏕ࡌࡿ㸬㔠ᒓ㛫໬ྜ≀ࡣ㸪≉ᐃࡢඖ⣲ࡢ⤌ࡳྜࢃࡏ࡛ᙧᡂࡍࡿ㸬౛࠼ࡤ㸪ⓑ㔠㖄 PtPb ࡢሙྜࡢ౛ࢆ
Fig. 2 (b) ࠾ࡼࡧ (d)࡟♧ࡍ㸬PtPb 㔠ᒓ㛫໬ྜ≀࡛ࡣ㸪Pt ཎᏊ㛫ࡢ㊥㞳ࡣ Pb ཎᏊࡀ᱁Ꮚ㛫࡟ᤄධࡉࢀࡿࡓࡵ࡟ቑຍࡍࡿ㸬ࡑࡢ⤖ᯝ㸪PtཎᏊ㛫࡟ࡲࡓࡀࡗ࡚྾╔ࡍࡿࢱ࢖ࣉࡢCO྾╔ Fig. 3 ࡣ㉳ࡇࡾ࡙ࡽࡃ㸪CO ⿕ẘࡀ㍍ῶࡉࢀࡿ࡜⪃࠼ࡿࡇ࡜ࡀ࡛ࡁࡿ㸬㻲㼕㼓㻚㻚㻌㻢㻌 ྜᡂ䛧䛯 㻼㼠㻟㼀㼕㻌㻛㻌㻯㻮㻌㻔㼍㻕ཬ䜃 㻢㻜㻜㻌㼻㻯㻌㻔㼎㻕㻘㻌㻥㻜㻜㻌㼻㻯㻔㼏㻕䛷䜰䝙䞊䝹ฎ⌮䛧䛯 㻼㼠㻟㼀㼕㻛㻯㻮 䝃䞁䝥䝹䛾 㼀㻱㻹 ീ䛚䜘䜃⢏Ꮚᚄศᕸ㻚㻌㻔㼐㻕㻦㻌㻥㻜㻜㻌㼻㻯 䛷䜰䝙䞊䝹ฎ⌮䛧䛯 㻼㼠㻟㼀㼕㻛㻯㻮 䝃䞁䝥䝹䛾㧗ಸ⋡ 㼀㻱㻹 ീ㻌㻲㼕㼓㻚㻌㻠㻌 㻼㼎 䛾⁐ゎ㟁఩㻌89✵Ẽ㟁ụ⏝㟁ᴟゐ፹࠾ࡼࡧ㧗ศᏊ㟁ゎ㉁⭷ࡢ㛤Ⓨྜ≀ࡢᙧᡂ࡟ࡼࡿ⮬⏤࢚ࢿࣝࢠ࣮ኚ໬ࡣ㸪⣙-51 kJmol-1࡛࠶ࡾ㸪ࡁ࡚࠸ࡿࡇ࡜ࢆ☜ㄆࡋࡓ㸬ࡲࡓ㸪ࡍ࡭࡚ࡢࢧࣥࣉࣝ࡟࠾

ࡇࡢᏳᐃ໬ࡣ+0.26V ࡢ⁐ゎ㟁఩ࡢࢩࣇࢺ࡟┦ᙜࡍࡿ㸬ࡘࡲࡾ࠸࡚ Pt3Ti NPs ᚄࡣኚ໬ࡏࡎ㸪⤖ᬗ໬ᗘྜ࠸ࡢࡳࡀኚ໬

㔠ᒓ㛫໬ྜ≀୰ࡢPb ࡣ⣙0.8 V ௜㏆ࡲ࡛⁐ゎࡍࡿࡇ࡜ࡀ࡞࠸㸬ࡋ࡚࠸ࡿࡇ࡜ࢆ⢏Ꮚᚄศᕸ࠿ࡽ☜ㄆࡋࡓ㸬Fig. 8 ࡟ࡇࢀᮏ◊✲࡛ࡣ㸪㓟⣲ᴟഃࡢ㟁ᴟゐ፹㸦㓟⣲㑏ඖ(ORR)ゐ፹㸧࡟╔┠ࡋ㸪ゐ፹⾲㠃ࡢ⤖ᬗᵓ㐀㸪㟁Ꮚ≧ែࢆኚ໬ࡉ
ࡏࡿࡇ࡜࡟ࡼࡗ࡚㸪㓟⣲㑏ඖ཯ᛂࡢゐ፹άᛶࡀ࡝ࡢࡼ࠺࡟ ኚ ໬ ࡍࡿ ࠿࡟ ࡘ ࠸ ᳨࡚ ウࢆ ⾜ ࡗ ࡓ㸬 ᙜヱ ᮦ ᩱ(Pt3Ti/carbon black(CB,Vulcan-72R), PtPb/CB, PtPb/TiO2,
Pt3Nb)ࡢࢼࣀ⢏Ꮚ(NPs)ࡢྜᡂࡣ㸪ࡍ࡭࡚ Schlenk line ࢆ⏝࠸࡚㸪ᐊ 㸪୙άᛶ㞺ᅖẼୗ࡛⾜ࡗࡓ㸬๓㥑య࡜ࡋ࡚
PtCODCl, H2PtCl6, Ti(THF)2Cl4, Pb(CH3COO)2 ࢆ⏝࠸ࡓ㸬
ࡉࡽ࡟Pt3Ti NPs࡟࠾࠸࡚ࡣྜᡂࡉࢀࡓࢧࣥࣉࣝࢆ␗࡞ࡗࡓ ᗘ(300㹼900°C)࡛࢔ࢽ࣮ࣝฎ⌮ࢆ᪋ࡍࡇ࡜࡟ࡼ
ࡾ㸪ཎᏊ⛛ᗎᛶࡢ␗࡞ࡗࡓ NPs ࢆᚓࡓ㸬㟁ᴟゐ፹άᛶࡢホ౯ࡣ㸪┤ᚄ 6 mm ࡢࢢࣛࢵࢩ࣮࣮࢝࣎ࣥ㟁ᴟୖ࡟Nafion ࢆ⏝࠸࡚ NPs/CB ࠶ࡿ࠸ࡣ NPs/TiO2 ࢆᅛᐃࡋ㸪㓟⣲㣬࿴ 0.1 M H2SO4 Ỉ⁐ᾮ୰࡟࠾࠸࡚㸪200 rpm, 10 mVs-1
ࡢ᮲௳ࢆ⏝࠸࡚ᅇ㌿㟁ᴟ࣎ࣝࢱ࣓ࣥࢺ࣮ࣜࢆ⾜ࡗࡓ㸬

Pt3Ti-NPs ࡢ⤖ᬗᵓ㐀࡜ ORR άᛶࡢ㛵ಀ㻲㼕㼓㻚㻚㻌 㻤㻌 㻌 㻼㼠㻛㻯㻮䠈ྜᡂ䛧䛯 㻼㼠㻟㼀㼕㻛㻯㻮 ཬ䜃ྛ ᗘ䛷ฎ⌮䛧䛯㻼㼠㻟㼀㼕㻛㻯㻮 䛾 㻻㻾㻾 άᛶ䛻㛵䛩䜛䝪䝹䝍䝰䜾䝷䝮㻌

Fig. 5࡟ྜᡂࡋࡓPt3Ti࠾ࡼࡧྛ ᗘ࡛࢔ࢽ࣮ࣝฎ⌮ࡋࡓࢧࣥࣉࣝࡢ XRDᐃ⤖ᯝࢆ♧ࡍ㸬Pt3Ti 㔠ᒓ㛫໬ྜ≀

Pb/TiO2

ࡀᣢࡘ Cu3Au ࢱ࢖ࣉࡢ⤖ᬗ⣔࡛ィ⟬ࡉࢀࡿ(111)㠃ࡢࣆ࣮ࢡࡀ 40°࡟࠾࠸࡚࢔ࢽ࣮ࣝ ᗘࡢୖ᪼࡟క࠸ቑຍࡋ࡚
࠸ࡿࡇ࡜ࡀほᐹࡉࢀࡓ㸬ࡇࢀࡽࡢ(111)㠃ࡢࣆ࣮ࢡࡣ Pt
࡜ Ti ࡀ୙つ๎࡟୪ࢇࡔ FCC ࢱ࢖ࣉࡢ⤖ᬗᙧ࡟࠾࠸࡚ࡶ

Pb/TiO2

ほᐹࡉࢀࡿࡀ㸪700, 900°C ࡛࢔ࢽ࣮ࣝࡋࡓࢧࣥࣉࣝࡢ㧗ಸ⋡ TEM ീ(Fig. 6)࠿ࡽุ᩿ࡋ࡚㸪Pt ࡜ Ti ࡀつ๎ⓗ࡟୪ࢇࡔ㔠ᒓ㛫໬ྜ≀ࢆᙧᡂࡋ࡚࠸ࡿࡇ࡜ࢆ☜ㄆࡋ㸪࢔ࢽ࣮ࣝ ᗘࡢୖ᪼࡟కࡗ࡚ FCC ᵓ㐀࠿ࡽ Cu3Au ᵓ㐀࡟ኚ໬ࡋ࡚࠸ࡿࡇ࡜ࡀࢃ࠿ࡗࡓ㸬ࡉࡽ࡟㸪XPS ࡢࢹ࣮ࢱ࠿ࡽࡶ
ࣂࣝࢡᮦᩱ࡜ࡋ࡚ྜᡂࡋࡓ Pt3Ti ࡜ Pt3Ti NPs ࡢ 3d ㌶㐨
ࡢࣆ࣮ࢡ್ࡀ୍⮴ࡋࡓࡇ࡜࠿ࡽࡶ(Fig. 7)㸪900°C ࡛࢔ࢽ࣮ࣝࡋࡓࢧࣥࣉࣝ࡟࠾࠸࡚ Pt3Ti 㔠ᒓ㛫໬ྜ≀ࡀྜᡂ࡛㻲㼕㼓㻚㻚㻌 㻥㻌 㻼㼠㻛㻯㻮䠈㻼㼠㻛㼀㼕㻻㻞 ཬ䜃 㻼㼠㻼㼎㻛㼀㼕㻻㻞 䛾 㻻㻾㻾 άᛶ䛻㛵䛩䜛䝪䝹䝍䝰䜾䝷䝮㻌

ࡽࡢࢧࣥࣉࣝࡢ ORR άᛶ ᐃ⤖ᯝࢆ♧ࡍ㸬ORR άᛶࡣ࢔ࢽ࣮ࣝࢆ⾜ࢃ࡞࠿ࡗࡓࢧࣥࣉࣝࡀ᭱ࡶ㧗ࡃ㸪⤖ᬗ໬ࡢᗘྜ࠸ࡀ㧗ࡃ࡞ࡿ࡜άᛶࡀపୗࡍࡿᣲືࡀほᐹࡉࢀࡓ㸬ࡇࡢ⌮⏤ࡣ TEM ീ࠿ࡽ⤖ᬗ໬ࡢᗘྜ࠸ࡀ኱ࡁࡃ࡞ࡿ࡟
ᚑࡗ࡚㸪(111)࡜(001)㠃ࡀ NPs ⾲㠃࡟㟢ฟࡋ㸪ࡇࡢ㠃ࡢゐ፹άᛶࡀప࠸ࡇ࡜࡟ࡼࡿ࡜⪃ᐹࡋࡓ㸬

TiO2 ᢸᣢ PtPb-NPs ࡢ ORR άᛶࡢྥୖ࡜Ᏻᐃ໬

 Fig.9 ࡟ Pt/TiO2, PtPb/TiO2 ࡢ ORR ࡟㛵ࡍࡿ࣎ࣝࢱࣔࢢ
㻲㼕㼓㻚㻌㻣㻌㻼㼠㻛㻯㻮㻔㼍㻕㻘㻌㻼㼠㻟㼀㼕㻛㻯㻮㻌㻔㻥㻜㻜㻌㼻㻯 䛷䜰䝙䞊䝹ฎ⌮㻕㻔㼎㻕㻘㻌㻼㼠㻟㼀㼕 㔠ᒓ㛫໬ྜ≀䠄䝞䝹䜽䠅㻔㼏㻕䛾 㻼㼠㻔㻟㼐㻕䛻㛵䛩䜛 㼄㻼㻿 ᐃ⤖ᯝ㻌࣒ࣛ㸪Fig.10 ࡟ Pt/CB, Pt/TiO2, PtPb/TiO2 ࢆ⏝࠸࡚ ORR
άᛶࢆ ᐃࡋࡓ᫬ࡢ㑏ඖ㟁ὶ್ࡀほᐹࡉࢀࡿ㟁఩(Onset⚄ዉᕝ኱ᏛᕤᏛ◊✲ᡤᡤሗ ➨  ྕ

potential)ࡢ㟁఩ࢧ࢖ࢡࣝ࡟ᑐࡍࡿኚ໬ࢆ♧ࡍ㸬PtPb/TiO2

࡞ࡗ࡚࠸ࡿ㸬
ࡇࡢၥ㢟ࢆゎỴࡍࡿࡓࡵ࡟ࡣ✵Ẽᴟ࡟࠾ࡅࢆ⏝࠸ࡓ ORR ࡟㛵ࡍࡿ Onset Potential ࡀ 0.66 V ࡟ほᐹࡿ㓟⣲ࡢ㑏ඖ཯ᛂཬࡧࡑࡢ㏫཯ᛂࡢゐ፹ࢆ㛤Ⓨࡍࡿᚲせࡉࢀ࡚࠸ࡿࡀ㸪
Pt/TiO2 ࡢሙྜ࡟ࡣ 0.49 V ࡜࡞ࡗ࡚࠾ࡾ㸪ࡀ࠶ࡿ㸬㏆ᖺ㸪MnO2 ࢆゐ፹࡜ࡋ࡚✵Ẽ㟁ụ࡟⤌ࡳ㎸ࢇ

PtPb/TiO2 ࡟࠾࠸࡚ ORR ࡀಁ㐍ࡉࢀ࡚࠸ࡿ⤖ᯝࡀほᐹࡉࡔ᫬࡟㸪㐣㟁ᅽࡀపῶࡉࢀࡓ࡜࠸࠺ሗ࿌ࡀὀ┠ࢆ㞟ࡵ࡚ࢀࡓ(Fig. 9)㸬ࡉࡽ࡟㟁఩ࢧ࢖ࢡࣝࢆ⧞ࡾ㏉ࡋࡓሙྜ㸪ᚑ࠸ࡿ[11,12]㸬ࡑࡇ࡛ᮏ◊✲࡛ࡣ㸪Į-MnO2 ࡢ୍㒊ࢆ␗✀ࡢ

᮶ἲࡢPt/CB (Fig.10-a)ࡣOnset Potential ࡀ኱ࡁࡃపୗࡋ㸪㔠ᒓ࡛⨨᥮ࡍࡿࡇ࡜࡛㸪ゐ፹ᛶ⬟ࡢ᭦࡞ࡿྥୖࢆᅗࡿࡇ

ᛶ⬟ࡢຎ໬ࢆ♧ࡋ࡚࠸ࡿࡀ㸪TiO2 ࢆᢸᣢయ࡟⏝࠸ࡓሙྜ࡜ࢆ┠ⓗ࡜ࡋࡓ㸬
Į-MnO2 ࡣࠊMn(CH3COO)2 Ỉ⁐ᾮ࡜ KMnO4 Ỉ⁐ᾮࢆ཯ᛂࡉࡏ࡚⏕ࡌࡓỿẊࢆࢁ㐣࣭Ὑίࡋࡓᚋ 350 Υ࡛ 10 h ↝ᡂ ࡍ ࡿ ࡇ ࡜ ࡛ ᚓ ࡓ 㸬 㔠 ᒓ ࢻ ࣮ ࣉ Mn 㓟 ໬ ≀ ࡣMn(CH3COO)2 Ỉ⁐ᾮ࡟␗✀㔠ᒓࡢሷ໬≀ࢆຍ࠼ࡓୖ࡛

㻲㼕㼓㻚㻚㻌㻝㻜㻌 㻌 㻼㼠㻌㻛㻌㻯㻮㻌㻔㼍㻕㻘㻌㻼㼠㻌㻛㻌㼀㼕㻻㻞㻔㼎㻕ཬ䜃 㻼㼠㻼㼎㻌㻛㻌㼀㼕㻻㻞㻔㼏㻕䛻䛚䛡䜛䝫䝔䞁䝅䝱䝹䝃䜲䜽䝹䛻క䛖 㻻㼚㼟㼑㼠㻌㻼㼛㼠㼑㼚㼠㼕㼍㼘 䛾ኚ໬㻌㻲㼕㼓㻚㻌㻝㻝㻌 ྜᡂ䛧䛯ྛ✀䝃䞁䝥䝹䛾 㼄 ⥺ᅇᢡᅗᙧ㻌(Fig.10-b,c)㸪Onset Potential ࡢపୗࡣほᐹࡉࢀ࡞࠿ࡗࡓ㸬KMnO4 Ỉ⁐ᾮ࡜཯ᛂࡉࡏࡓ㸬⥆࠸࡚ KOH Ỉ⁐ᾮ࡛୰࿴ࡇࡢ⌧㇟ࢆ☜ㄆࡍࡿࡓࡵ࡟ 50 ࢧ࢖ࢡࣝᚋࡢ NPs ࡢᙧែࡋ 6 h ᧠ᢾࡋࡓᚋ㸪ࢁ㐣࣭Ὑίࢆ⾜ࡗ࡚ 350 Υ࡛ 10 h ↝ほᐹࢆ⾜ࡗࡓ࡜ࡇࢁ㸪Pt/CB ࡢሙྜ㸪NPs ࡀจ㞟ࡋ࡚࠸ᡂࡍࡿࡇ࡜࡟ࡼࡾྜᡂࡋࡓ㸬RuO2 ࡣ RuCl3 ࢆ⣧Ỉ࡟⁐࠿ࡿࡇ࡜ࡀほᐹࡉࢀ㸪୍᪉㸪Pt/TiO2PtPb/TiO2 ࡢሙྜࡣࡋ㸪NaOH Ỉ⁐ᾮࢆ pH7㹼8 ࡟࡞ࡿࡲ࡛⁲ୗࡋ 110 Υ࡛NPs ࡢจ㞟ࡣほᐹࡉࢀࡎ㸪TiO2 ࡀ NPs ࡢจ㞟ࢆ㜵ࡄຠᯝ୍ᬌ஝⇱ᚋ㸪500 Υ࡛ 5 h ↝ᡂࡋྜᡂࡋࡓ㸬ྜᡂࡋࡓヨࢆᣢࡗ࡚࠸ࡿࡇ࡜ࢆぢฟࡍࡇ࡜ࡀ࡛ࡁࡓ㸬௒ᚋࡢ᪉㔪࡜ᩱ࡟ࡘ࠸࡚ XRD㸪SEM㸪BET ࢆ⏝࠸࡚≀ᛶホ౯ࢆ⾜ࡗࡋ࡚௨ୗࡢ 2 Ⅼ࡟ࡘ࠸᳨࡚ウࢆ⾜࠺㸬1)Pt3Ti ࡢ⤖ᬗ⾲ࡓ㸬ࡲࡓ㟁Ẽ໬Ꮫศᯒ࡜ࡋ࡚ࢧ࢖ࢡࣜࢵࢡ࣎ࣝࢱ࣓ࣥࢺ

㠃࡜ ORR άᛶࡢ㛵ಀࢆ᫂ࡽ࠿࡟ࡍࡿ㸬2) NPs ࢆᢸᣢࡍࡿ㔠ᒓ㓟໬≀ࡢ✀㢮ࢆኚ࠼㸪㔠ᒓ㓟໬≀࡜ゐ፹≉ᛶࡢ㛵ಀࢆ᫂ࡽ࠿࡟ࡍࡿ㸬㸬㔠ᒓ㓟໬≀ࢆ⏝࠸ࡓ %LIXQFWLRQDO 㟁ᴟゐ፹ࡢ㛤Ⓨ✵Ẽ㟁ụࡣṇᴟά≀㉁࡜ࡋ࡚✵Ẽ୰ࡢ㓟⣲ࢆ⏝࠸㸪㓟⣲ศᏊࢆ㑏ඖࡍࡿࡇ࡜࡟ࡼࡗ࡚Ⓨ㟁ࢆ⾜࠺ࡇ࡜࠿ࡽ㸪Li㔠ᒓࢆ㈇ᴟ࡟⏝࠸ࡿ࡜ᚑ᮶ࡢࣜࢳ࣒࢘㟁ụࡢ 10 ಸ௨ୖࡢ࢚ࢿࣝࢠ࣮ᐦᗘࢆ♧ࡍ᪂ᆺ㟁ụ࡜ࡋ࡚ὀ┠ࡉࢀ࡚࠸ࡿ
>@㸬ࡋ࠿ࡋ࡞ࡀࡽ㸪඘ᨺ㟁࡟㧗࠸㐣㟁ᅽࢆせࡍࡿ࠺࠼࡟㸪Ⓨ㟁ຠ⋡ࡶప࠸ࡇ࡜ࡀࡇࡢ㟁ụ㛤Ⓨࡢ኱ࡁ࡞ၥ㢟࡜㻲㼕㼓㻚㻌㻝㻞㻌 㻌 ྜᡂ䛧䛯ྛ✀䝃䞁䝥䝹䛾㓟⣲㑏ඖ཯ᛂ䛻㛵䛩䜛䝪䝹䝍䝰䜾䝷䝮㻚㻌㻜㻚㻝㻌㻹㻌㻷㻻㻴㻌㻔㻻㻞 㞺ᅖẼୗ㻕㻌✵Ẽ㟁ụ⏝㟁ᴟゐ፹࠾ࡼࡧ㧗ศᏊ㟁ゎ㉁⭷ࡢ㛤Ⓨ91Ruࢻ࣮ࣉ0Q㓟໬≀ࡢ㓟⣲㑏ඖ཯ᛂ࡟࠾ࡅࡿ࣎ࣝࢱࣔࢢࣛ
࣒ࢆ♧ࡍ㸬ࡇࡢ᭤⥺࡟࠾࠸࡚Ruࢆῧຍࡋ࡞࠸≧ែ࠿ࡽ
Ru30%࡟࡞ࡿࡲ࡛ࣆ࣮ࢡ㟁ὶᐦᗘࡀୖ᪼ࡋࡑࡢᚋపୗ
ࡋ࡚࠸ࡿࡇ࡜ࡀほᐹࡉࢀࡓ㸬30%ῧຍࡋࡓ㝿࡟ࡣ-0.3 V࡟࠾࠸࡚Į-MnO2࡜ẚ㍑ࡋ࡚2ಸࡢ㟁ὶᐦᗘࡀᚓࡽࢀࡿࡢࢆ
☜ㄆࡋࡓ㸬ࡉࡽ࡟㸪Fig. 13࡟㑄⛣㔠ᒓ࢖࢜ࣥࢆMn㓟໬≀࡟ࢻ࣮ࣉࡋࡓࢧࣥࣉࣝࡢゐ፹άᛶࡢホ౯⤖ᯝࡢࡑࡢ௚ࡢ
౛࡜ࡋ࡚Irࢻ࣮ࣉMnO2ࡢ⤖ᯝࢆ♧ࡍ㸬㑏ඖ཯ᛂ࡟ᑐࡋ࡚᭷ຠ࡞ゐ፹ࡣ㓟໬཯ᛂࡢゐ፹ᛶ⬟ࡀప࠸ࡇ࡜ࡀࢃ࠿ࡿ㸬ࡑࡇ࡛㸪࡝ࡢࢧࣥࣉࣝࡀBifunctionalゐ፹࡜ࡋ࡚᭷ຠ࡛࠶ࡿࡢ࠿ࢆホ౯ࡍࡿࡓࡵ࡟㸪୍ᐃ㟁ὶ್࡟࠾ࡅࡿOH-ࡢ㓟໬཯ᛂࡢ㟁఩࡜O2ࡢ㑏ඖ཯ᛂࡢ㟁఩ࡢᕪࢆẚ㍑ࡋࡓࡶࡢࢆFig. 14࡟♧ࡍ㸬෇⁥࡞඘ᨺ㟁཯ᛂࢆᐇ⌧ࡍࡿ࡟ࡣ㓟໬࡜㑏ඖ㟁఩ᕪࡀᑠࡉ࠸ࢧࣥࣉࣝࡀᮃࡲࡋ࠸ゐ፹࡛࠶ࡿ࡜⪃࠼ࡿࡇ࡜ࡀ࡛ࡁ㸪MnO2 ㄏᑟయࡢ࠺ࡕ᭱ࡶ᭷ᮃ࡞㔠ᒓ㓟໬≀ࡣ
Ru0.8Mn0.2Ox࡛࠶ࡿࡇ࡜ࡀ᫂ࡽ࠿࡜࡞ࡗࡓ㸬㻲㼕㼓㻚㻌 㻝㻟㻌 㻌 ྜᡂ䛧䛯ྛ✀䝃䞁䝥䝹䛾 㻻㻴㻙䜲䜸䞁䛾㓟໬཯ᛂ㻔㻭㻕䛚䜘䜃㓟⣲㑏ඖ཯ᛂ㻔㻮㻕䛻㛵䛩䜛䝪䝹䝍䝰䜾䝷䝮㻚㻌 㻜㻚㻝㻌 㻹㻌 㻷㻻㻴㻌 Ỉ⁐ᾮ㻔㻻㻞 㣬࿴ୗ㻕㻚㻌㸬࢔ࢽ࢜ࣥ஺᥮㧗ศᏊ⭷ࡢྜᡂ࡜ᛶ⬟ホ౯࢔ࢽ࢜ࣥ஺᥮㧗ศᏊ⭷ࢆ✵Ẽ㟁ụ࡟⏝࠸ࡿࡇ࡜࡟ࡼࡾ㸪௨ୗࡢຠᯝࡀᮇᚅࡉࢀࡿ㸬1) Ⓨⅆ࣭ᘬⅆࡢ༴㝤ᛶࡢ࠶ࡿ࣮ࣜࢆ⾜ࡗࡓ㸬 ᐃ᮲௳ࡣ࢔ࣝ࢝ࣜ㟁ゎᾮ୰࡛ᤲᘬ㏿ᗘ
-1

10 mVsec 㸪㟁ᴟᅇ㌿ᩘ 2000 rpm ࡜ࡋࡓ㸬㟁ὶᐦᗘࡢィ⟬࡟ࡣゐ፹⢏Ꮚࡢ BET ⾲㠃✚ ᐃ⤖ᯝࢆ⏝࠸ࡓ㸬
Fig.11࡟ྜᡂࡋࡓĮ-MnO2㸪RuO2ཬࡧRuࢻ࣮ࣉMn㓟໬≀ࡢX⥺ᅇᢡᅗᙧࢆ♧ࡍ㸬Ruࢻ࣮ࣉMn㓟໬≀࡟࠾࠸࡚Į-MnO2
ࡢࣆ࣮ࢡ࡜RuO2ࡢࣆ࣮ࢡࡀΰᅾࡋ࡚࠸ࡿࡇ࡜࠿ࡽ㸪ΰྜ≀ࡢ≧ែ࡛࠶ࡿ࡜᥎ ࡉࢀࡿ㸬Fig.12࡟Į-MnO2ࠊRuO2ཬࡧ

᭷ᶵ⁐፹ࢆ౑⏝ࡍࡿᚲせࡀ࡞ࡃ㸪ࡉࡽ࡟㟁ụࡢᑠᆺ࣭㍍
㔞໬࡟ࡶᐤ୚࡟ࡍࡿ㸬2)ከᵝ࡞ゐ፹ᮦᩱࡢ✵Ẽᴟ࡬ࡢ㐺⏝ࢆྍ⬟࡜ࡍࡿ࢔ࣝ࢝ࣜᛶỈ⁐ᾮࡢ᥹Ⓨࢆ㜵ࡂ㸪㟁ụࡢ㛗ᮇ㛫฼⏝ࢆྍ⬟࡟ࡍࡿ㸬3) ✵Ẽᴟ࠿ࡽࡢ஧㓟໬Ⅳ⣲ࡢྲྀࡾ㎸ࡳࢆᢚไࡍࡿࡇ࡜࡛㸪࢔ࣝ࢝ࣜᛶỈ⁐ᾮ୰ࡢ㟁ゎ㉁ࡢᯒฟࠊ≉ᛶຎ໬ࢆపῶࡍࡿࡇ࡜ࡀ࡛ࡁࡿ㸬4) ✵Ẽᴟ࡟࢔ࢽ࢜ࣥఏᑟᛶ࢔࢖࢜ࣀ࣐࣮ ࣂ࢖ࣥࢲ࣮ ࢆ⏝࠸ࡓ㝿ࡢぶ࿴ᛶࡀྥୖࡍࡿ㸬ୖグࡢ฼Ⅼࢆᘬࡁฟࡍࡓࡵ࡟ࡣ࢔
ࢽ࢜ࣥ஺᥮㧗ศᏊࡢ⢭ᐦ࡞ศᏊタィ࡜ᐇ⏝࡟౪ࡋ࠺ࡿ㟁ゎ㉁⭷ࡢస〇ࡀ୙ྍḞ࡛࠶ࡿ㸬ࡋ࠿ࡋ࡞ࡀࡽ㸪࢔ࢽ࢜ࣥ஺᥮㧗ศᏊ⭷ࢆ✵Ẽ㟁ụ࡟ᛂ⏝ࡋࡓ౛ࡣ㝈ࡽࢀ࡚࠾ࡾ
[12]㸪ࡑࡢศᏊタィᣦ㔪ࡸඃඛࡍ࡭ࡁ≉ᛶ࡟ࡘ࠸࡚㸪ࡇࢀࡲ࡛࡯࡜ࢇ࡝◊✲ࡉࢀ࡚ࡁ࡚࠸࡞࠸㸬ᮏ◊✲࡛ࡣ㸪✵Ẽ㟁ụ࡬ࡢᛂ⏝ࢆ┠ᣦࡋ㸪ྛ✀࢔ࢽ࢜ࣥఏᑟ㧗ศᏊࢆྜᡂ࡜ࡑࡢᇶ♏≀ᛶ ࢔ࢽ࢜ࣥఏᑟᛶࠊẼయ㏱㐣ᛶ࡞࡝ ࢆホ౯ࡍࡿࡇ࡜ࢆ┠ⓗ࡜ࡍࡿ㸬࢔ࢽ࢜ࣥ஺᥮㧗ศᏊࡢྜᡂ

✵Ẽ㟁ụ⏝࢔ࢽ࢜ࣥ஺᥮㧗ศᏊ࡜ࡋ࡚㸪ձඃࢀࡓ࢔ࢽ
࢜ࣥఏᑟᛶ ᐊ ࡛ 6FP ⛬ᗘ ࢆ᭷ࡋ㸪ղ஧㓟໬Ⅳ
㻲㼕㼓㻚㻌 㻝㻠㻌 㻌 ྜᡂ䛧䛯ྛ✀䝃䞁䝥䝹䛾 㻻㻴㻙䜲䜸䞁䛾㓟໬཯ᛂ䛻䛚䛡䜛㟁఩䛚䜘䜃 㻻㻞 㑏ඖ཯ᛂ䛻䛚䛡䜛㑏ඖ㟁఩ᕪ䠄㓟໬཯ᛂ䠖㻜㻚㻜㻞㻌㼙㻭㼏㼙㻙㻞 䛻䛚䛡䜛㟁ᴟ㟁఩䠈㑏ඖ཯ᛂ䠖㻙㻜㻚㻜㻞㻌 㼙㻭㼏㼙㻙㻞 䛻䛚䛡䜛㟁ᴟ㟁఩㻌 䠅㻌

⣲ࡢ㏱㐣ᛶࡀపࡃ㸪ճඃࢀࡓ⇕ⓗ࣭ᶵᲔⓗ࣭໬ᏛⓗᏳᐃᛶࢆ᭷ࡍࡿ㧗ศᏊࢆタィࡍࡿᚲせࡀ࠶ࡿ㸬ᮏ◊✲࡛ࡣ㸪࢔ࣝ࢝ࣜ⇞ᩱ㟁ụࢆ◊✲ࡋ࡚ࡁࡓᡃࠎࡢᚑ᮶ࡢ▱ぢ[13-15]ࢆᇶ࡟㸪࢔ࢽ࢜ࣥ஺᥮ᇶ࡜ࡋ࡚࢔ࢽ࢜ࣥఏᑟᛶ࡟
ඃࢀࡓᅄ⣭࢔ࣥࣔࢽ࣒࢘ᇶ࠾ࡼࡧᏳᐃᛶ࡟ඃࢀࡓᅄ⣭࢖࣑ࢲࢰ࣒ࣜ࢘ᇶࢆ㑅ᢥ㸪୺㙐㦵᱁࡜ࡋ࡚㧗࠸࢞ࣛࢫ㌿⛣⚄ዉᕝ኱ᏛᕤᏛ◊✲ᡤᡤሗ ➨  ྕ

Number of chloromethyl groups
per repeating unit

Ⅼ(Tg㸼150Υ)ࢆ᭷ࡋ㸪ᶵᲔⓗ㸪໬ᏛⓗᏳᐃᛶࡀ㧗ࡃ㸪ࡉࡽ࡟⭷ᙧᡂ⬟࡟ࡶඃࢀࡓ࣏ࣜ ࢔࣮࢚࣮ࣜࣞࣥࢸࣝ 㦵᱁ࢆ㑅ᢥࡋࡓ㸬௦⾲ⓗ࡞ྜᡂࢫ࣮࣒࢟ࢆ Fig. 15 ࡟♧ࡍ㸬࣏ࣜ ࢔࣮࢚࣮ࣜࣞࣥࢸࣝ ࡣࢪ࣮࢜ࣝࣔࣀ࣐࣮࡜ࢪࣇࣝ
࢜ࣟࣔࣀ࣐࣮ࡢ㔜⦰ྜ࡟ࡼࡾྜᡂࡋࡓ㸬ࢤࣝᾐ㏱ࢡ࣐ࣟ
ࢺࢢࣛࣇ࢕࣮(GPC)࡟ࡼࡿศᏊ㔞 ᐃࡢ⤖ᯝ㸪㔜㔞ᖹᆒศᏊ㔞ࡣ⣙ 20 ୓࡜㸪㟁ゎ㉁⭷࡜ࡋ࡚ᙧᡂࡀᐜ᫆࡞༑ศ
㧗࠸ศᏊ㔞࡛࠶ࡗࡓ㸬ࢡ࣓ࣟࣟࢳ࣓ࣝࢳ࢚࣮ࣝࢸࣝ㸪ሷ໬ள㖄ࢆ⏝࠸ࡓ㧗ศᏊ཯ᛂ࡟ࡼࡿ๓㥑ࢡ࣓ࣟࣟࢳࣝ໬࣏
࣐࣮ࣜࢆ⤒࡚㸪ࢺ࣓ࣜࢳࣝ࢔࣑ࣥ࠶ࡿ࠸ࡣ࣓ࢳࣝ࢖࣑ࢲ

1

0.5

0
0

ࢰ࣮ࣝ࡜཯ᛂࡉࡏࡿࡇ࡜࡛࢔ࢽ࢜ࣥ஺᥮ᇶ࡬࡜ㄏᑟࡋࡓ㸬

10
20
Reaction time (h)30㐺ษ࡞᮲௳ࡢ㑅ᢥ࡟ࡼࡾᅄ⣭໬཯ᛂࡣᐃ㔞ⓗ࡟㐍⾜ࡍࡿ㻲㼕㼓㻚㻌 㻝㻢㻌 㻌 䜽䝻䝻䝯䝏䝹໬཯ᛂ᫬㛫䛻䜘䜛㧗ศᏊ⧞䜚㏉䛧༢఩ᙜ䛯ࡓࡵ㸪ࢡ࣓ࣟࣟࢳࣝᇶࡢᑟධ㔞ࡢไᚚࡀ࢔ࢽ࢜ࣥ஺᥮ᇶ

䜚䛾䜽䝻䝻䝯䝏䝹ᇶᑟධ㔞䛾ไᚚ㻌ࡢᑟධ㔞ࢆỴࡵࡿ㔜せ࡞せ⣲࡛࠶ࡿ㸬ࢡ࣓ࣟࣟࢳࣝ໬཯
ᛂ᮲௳ࢆ᭱㐺໬ࡍࡿࡇ࡜࡛㸪཯ᛂ᫬㛫࡟ᛂࡌࡓࢡ࣓ࣟࣟ

PAESࢳࣝᇶᑟධ㔞ࡢไᚚࡀྍ⬟࡜࡞ࡗࡓ(Fig. 16)㸬ᅄ⣭໬཯ᛂ



b

d

a,c

ࡢ㐍⾜ࡣ㸪1H NMR(Fig. 17)࠾ࡼࡧ FT-IR ࡟ࡼࡾ☜ㄆࡋ㸪๪཯ᛂ࡞ࡃ཯ᛂࡀ㐍⾜ࡋ㸪┠ⓗࡢ࢔ࢽ࢜ࣥ஺᥮㧗ศᏊࡀᚓࡽࢀ࡚࠸ࡿࡇ࡜ࢆ᫂ࡽ࠿࡟ࡋࡓ㸬ࢡ࣓ࣟࣟࢳࣝ໬཯ᛂ
᫬㛫ࢆ 18 ᫬㛫࡜ࡋࡓሙྜ㸪㧗ศᏊ⧞ࡾ㏉ࡋ༢఩ᙜࡓࡾ
0.91 ಶࡢࢡ࣓ࣟࣟࢳࣝᇶࡀᑟධࡉࢀ㸪ᅄ⣭໬࡟ࡼࡗ࡚ᚓ
ࡽࢀࡓ࢔ࢽ࢜ࣥ஺᥮㧗ศᏊࡢ࢖࢜ࣥ஺᥮ᐜ㔞(Ion
CM-PAES

Exchange Capacity: IEC)ࡣ 1.89 meq/g ࡜࡞ࡗࡓ㸬
ࡑࡢ࡯࠿㸪

b

࢖࢜ࣥ஺᥮ᇶࡢᙳ㡪ࢆ᳨ドࡍࡿࡓࡵ㸪IEC ್ࡢ␗࡞ࡿ୍
㐃ࡢ㧗ศᏊࡸ㸪ᅄ⣭࢖࣑ࢲࢰ࣒ࣜ࢘ᇶࢆ᭷ࡍࡿ࢔ࢽ࢜ࣥ

dd’ d’’a,cc’஺᥮㧗ศᏊ࡞࡝ࡶྠᵝ࡟ྜᡂࡋࡓ㸬


e
O
S
O

F

ab

F

S
O

cd

O

d'

O

e

ab

O

d'' c' m
CM-PAES

cd
O

d'

TMA-PAESn

CH3OCH2Cl, ZnCl2,
CHCl2CHCl2

f
O
S
O

O

PAES

Cl

ab

OH

cd

O
S
O

Cl

ab O

HO
K2CO3, CaCO3,
DMAc, toluene

O
S
O

e

ab

O

d'' c' m
TMA-PAES

O
S
O

f

cd
O

O
n

e

N(CH3)3, H2O
N

a,c,c’
b,d’,d,d’’

cd
O

O



n



㻲㼕㼓㻚㻌 㻝㻣㻌 㻌 ᅄ⣭䜰䞁䝰䝙䜸໬䝫䝸䜰䝸䞊䝺䞁䜶䞊䝔䝹䝇䝹䝩䞁㻲㼕㼓㻚㻌㻝㻡㻌 㻌 䜰䝙䜸䞁஺᥮㧗ศᏊ䛾ྜᡂ䝇䜻䞊䝮䛾୍౛㻔ᅄ⣭䜰䞁䝰㻔㼀㻹㻭㻙㻼㻭㻱㻿㻕䛚䜘䜃䛭䛾๓㥑య㧗ศᏊ䛾 㻝㻴㻌 㻺㻹㻾 䝇䝨䜽䝖䝹㻔ྛ䝙䜸໬䝫䝸䜰䝸䞊䝺䞁䜶䞊䝔䝹䝇䝹䝩䞁 㼀㻹㻭㻙㻼㻭㻱㻿 䛾ྜᡂ㻕㻌䝢䞊䜽䛿 㻲㼕㼓㻚㻌㻝㻡 䛾ྛ䝥䝻䝖䞁䛻ᖐᒓ㻕㻌࢔ࢽ࢜ࣥ஺᥮㧗ศᏊ⭷ࡢస〇࡜㟁ゎ㉁⭷ホ౯㟁ゎ㉁⭷ࡣ⁐፹࢟ࣕࢫࢺἲ࡟ࡼࡾస〇ࡋࡓ㸬⁐፹᥹Ⓨ

93✵Ẽ㟁ụ⏝㟁ᴟゐ፹࠾ࡼࡧ㧗ศᏊ㟁ゎ㉁⭷ࡢ㛤Ⓨ᮲௳ ⁐፹✀㸪 ᗘ㸪஝⇱᫬㛫➼ ࢆ᳨ウࡋ㸪⦓ᐦ࡛ᙉ㠌ࢽ࢜ࣥ஺᥮㧗ศᏊ⭷ࢆ⏝࠸ࡿࡇ࡜࡛㸪㟁ụෆ㒊࡬ࡢ஧㓟࡞⭷ࢆస〇ࡍࡿࡇ࡜࡟ᡂຌࡋࡓ㸬ᚓࡽࢀࡓ⭷ࡣῐ㯤Ⰽ㏱

໬Ⅳ⣲ࡢ౵ධ࡟ࡼࡿ࢔ࣝ࢝ࣜ㟁ゎᾮࡢᯒฟࡣᢚไ࡛ࡁࡿ

࡛᫂㸪⭷ཌࡣ 30-100 m ࡢ⠊ᅖ࡛ไᚚྍ⬟࡛࠶ࡗࡓ㸬ࡶࡢ࡜ᮇᚅࡉࢀࡿ㸬㟁ゎ㉁⭷ホ౯࡜ࡋ࡚᭱ࡶ㔜せ࡞࢔ࢽ࢜ࣥఏᑟᗘࡢ ᐃ⤖ᯝࢆ Fig. 18 ࡟♧ࡍ㸬༑ศ㧗࠸ IEC ್ࢆ᭷ࡍࡿ࢔ࢽ࢜ࣥ

㼀㼍㼎㼘㼑㻌㻝㻚㻌 㼀㻹㻭㻙㻼㻭㻱㻿 ⭷䛚䜘䜃 㻺㼍㼒㼕㼛㼚 䛾㓟⣲㏱㐣 ᐃ⤖ᯝ㻌஺᥮⭷ࢆస〇ࡋࡓࡓࡵ㸪ᐊ ௜㏆࡛ࡶ 10-3 S cm-1 ࢆ㉸࠼

㏱㐣ಀᩘ P[cm3(STP) /cm2sec cmHg]

ᣑᩓಀᩘ D[cm2 /sec]⁐ゎᗘಀᩘ S[cm3(STP) /cm3 cmHg]

TMA-PAES⭷

3.0㽢10-11

1.9㽢10-9

1.6㽢10-2

Nafion117

1.1㽢10-10

4.6㽢10-8

2.3㽢10-3ࡿඃࢀࡓ࢔ࢽ࢜ࣥఏᑟᛶࢆ♧ࡋࡓ㸬࡞࠾ࠊ✵Ẽ㟁ụ࡜ࡋ࡚సືࡍࡿሙྜ㸪ఏᑟࡍࡿ࢔ࢽ࢜ࣥ✀ࡣỈ㓟໬≀࢖࡛࢜ࣥ࠶ࡿࡀ㸪Ỉ㓟໬≀࢖࢜ࣥࡣ✵Ẽ୰ࡢ஧㓟໬Ⅳ⣲࡜ᐜ᫆࡟⨨᥮ࡋ㸪Ⅳ㓟࢖࢜ࣥ࠶ࡿ࠸ࡣⅣ㓟Ỉ⣲࢖࢜ࣥ࡟⨨ࡁ᥮ࢃࡾࡸࡍ࠸ࡓࡵ㸪௒ᅇࡣሷ໬≀࢖࢜ࣥఏᑟᗘࢆ ᐃࡋࡓ㸬✵Ẽᴟ࡬ࡢ㐺⏝ࢆ┠ᣦࡋࡓ࢔ࢽ࢜ࣥ஺᥮㧗ศᏊࡢศᏊタィ࡜ྜᡂ

Ỉ㓟໬≀࢖࢜ࣥࡣሷ໬≀࢖࢜ࣥࡼࡾᩘಸ㧗࠸࢖࢜ࣥ⛣ືᗘࢆ᭷ࡋ࡚࠾ࡾ㸪ᐇ㝿ࡢ✵Ẽ㟁ụ฼⏝⎔ቃ ࢔ࣝ࢝ࣜỈ࢔ࢽ࢜ࣥ஺᥮㧗ศᏊࡣ✵Ẽᴟ࡟࠾ࡅࡿࣂ࢖ࣥࢲ࣮࡜ࡋ

⁐ᾮ࡟᥋ゐ ୗ࡛ࡣࠊFig.18 ࡢ⤖ᯝࡼࡾ 2-3 ಸ㧗࠸࢖࡚࢜ࣥࡢᛂ⏝ࡶᮇᚅࡉࢀࡿ㸬࢔ࢽ࢜ࣥ஺᥮㧗ศᏊࣂ࢖ࣥࢲ࣮

ఏᑟᗘࢆ♧ࡍ࡜ண᝿ࡉࢀࡿ㸬ࢆ⏝࠸ࡿࡇ࡜࡛ࠊձ✵Ẽᴟ࡟࠾ࡅࡿ࢔ࢽ࢜ࣥఏᑟ⤒㊰ࡢ☜ಖ㸪ղ㟁ᴟ཯ᛂࢆ᭷ຠ࡟⾜࠺ࡓࡵࡢỈಖᣢ⬟㸪ճ⏕ᡂࡋࡓỈ࡟ࡼࡿࣇࣛࢵࢹ࢕ࣥࢢ ࢞ࢫᣑᩓ⤒㊰ࡢ㜼ᐖ ࡢᢚ

o

10-1

Temperature / C
80
60
40

20

10-1

࣮ࡣ࢔ࢽ࢜ࣥ஺᥮㧗ศᏊ⭷࡜ࡣ␗࡞ࡿ≉ᛶࡶせồࡉࢀࡿ-1

10Anion conductivity / S cm

Anion conductivity / S cm -1

ไ࡞࡝ࡢຠᯝࡀᮇᚅࡉࢀࡿ㸬✵Ẽᴟ⏝ࡢ㧗ศᏊࣂ࢖ࣥࢲ

oat 90 Cat 95% RH

-2

10

10-3

10-4

ࡓࡵ㸪᪂ࡓ࡞ศᏊタィࡀᚲせ࡜࡞ࡿ㸬ᮏ◊✲࡛ࡣ㸪ࡑࢀ

-2ࡒࢀ≉ᚩࡢ␗࡞ࡿ௨ୗࡢ 4 ✀ࡢ࢔ࢽ࢜ࣥ஺᥮㧗ศᏊࣂ࢖ࣥࢲ࣮ࢆタィ㸪ྜᡂࡋࡓ(1H NMR㸪FT-IR㸪GPC㸪IEC

10-3

2.8

3.0
3.2
1000 T -1 / K-1

3.4

10-4
50

ᐃ࡞࡝࡟ࡼࡾ┠ⓗ≀ࡀᚓࡽࢀ࡚࠸ࡿࡇ࡜ࢆ☜ㄆ 㸬1) 㧗 IEC(2.25 meq/g)ᆺ TMA-PAES
60 70 80 90 100
Relative humidity / %࢔ࣝࢥ࣮ࣝ➼࡟ྍ⁐ ゐ፹ᒙస〇ࡀᐜ᫆ ࡜࠸࠺฼Ⅼࡀ࠶ࡿ㸬୍᪉ࠊྵỈ࡟ࡼࡿ㐣ᗘ࡞⭾₶ 㓟⣲࢞ࢫᣑᩓࢆ㜼ᐖ㻲㼕㼓㻚㻌 㻝㻤㻌 㻌 㼀㻹㻭㻙㻼㻭㻱㻿㻔㻵㻱㻯㻩㻝㻚㻤㻥㻌 㼙㼑㼝㻛㼓㻕䛾ሷ໬≀䜲䜸䞁ఏᑟᗘ䛾ᗘ౫Ꮡᛶ䛚䜘䜃‵ᗘ౫Ꮡᛶ㻌㧗࠸࢔ࢽ࢜ࣥఏᑟᛶ(5.35×10-2 @80oC,95%RH)ࢆ᭷ࡋ㸪ࡶᠱᛕࡉࢀࡿ㸬 ప IEC(0.70 meq/g)ᆺ TMA-PAES ࢔ࢽ࢜ࣥఏᑟᛶ࡟ຍ࠼㸪Ẽయࡢࣂࣜ࢔ᛶࡣ✵Ẽ㟁ụ࡟ ྵỈ࡟ࡼࡿ㐣ᗘ࡞⭾₶ࡀᑡ࡞࠸ 㓟⣲࢞ࢫᣑᩓ࡟᭷฼

࠾ࡅࡿ㧗ศᏊ⭷࡟ồࡵࡽࢀ࡚࠸ࡿ㔜せ࡞せ⣲࡛࠶ࡿ㸬Ẽ

࡜࠸࠺฼Ⅼࡀ࠶ࡿ୍᪉࡛㸪ప࢔ࢽ࢜ࣥఏᑟᛶ(1.27×10-3@యࡢࣂࣜ࢔ᛶ(Ẽయ㏱㐣ಀᩘ)ࡣᕪᅽἲ࡟ࡼࡾ ᐃࡋࡓ㸬

80oC,95%RH)㸪࢔ࣝࢥ࣮ࣝ➼࡟୙⁐ ゐ፹ᒙస〇᫬࡟㧗Ἓࡇࡢᡭἲࡣ ᐃᑐ㇟⭷ࡢ୧ᴟ࡟ᅽຊᕪࢆ⏕ࡌࡉࡏ㸪Ẽయ

Ⅼ⁐፹ࡀ୙ྍḞ ࡜࠸࠺ၥ㢟Ⅼࡀ࠶ࡿ㸬ࡋ࠿ࡋ㸪ゐ፹⿕

ࡢ㏱㐣㔞ࢆ⤒᫬ⓗ࡟ ᐃࡍࡿࡇ࡜࡛㸪㧗ศᏊ⭷ࡢ㏱㐣ಀẘࡢᠱᛕࡀ࡯࡜ࢇ࡝࡞࠸࡜࠸࠺฼Ⅼࡶᣢࡕྜࢃࡏࡿ㸬ᩘ P ࢆ⟬ฟࡍࡿᡭἲ࡛࠶ࡿ㸬ࡲࡓ㸪 ᐃึᮇࡢẼయࡢ㧗 ࢖࣑ࢲࢰ࣒ࣜ࢘⨨᥮ PAES(IM-PAES)

ศᏊ⭷࡬ࡢ⁐ゎᣲື࠿ࡽ㸪Ẽయࡢ⁐ゎᗘಀᩘ S ࠾ࡼࡧᣑ໬ᏛⓗᏳᐃᛶ࡟ඃࢀࡿ㸪ྵỈ࡟ࡼࡿ㐣ᗘ࡞⭾₶ࡀᑡ࡞ᩓಀᩘ D ࡶู㏵⟬ฟྍ⬟࡛࠶ࡿ㸬Table 1 ࡟ TMA-PAES࠸ 㓟⣲࢞ࢫᣑᩓ࡟᭷฼ ࡜࠸࠺฼Ⅼࡀ࠶ࡿ୍᪉㸪ẚ㍑ⓗࡢ㓟⣲㏱㐣 ᐃࡢ⤖ᯝࢆ㸪௦⾲ⓗ࡞㧗ศᏊ㟁ゎ㉁⭷࡛࠶ప࠸࢔ࢽ࢜ࣥఏᑟᛶࠊ
࢔ࣝࢥ࣮ࣝ୙⁐࡜࠸࠺ḞⅬࡶ࠶ࡿ㸬ࡿ Nafion ࡢ⤖ᯝ࡜ඹ࡟♧ࡍ㸬TMA-PAES ⭷ࡢ㏱㐣ಀᩘ P

N

ࡣ Nafion ࡼࡾ 1 ᱆పࡃ㸪㧗࠸Ẽయࣂࣜ࢔ᛶࢆ᭷ࡋ࡚࠸ࡿ
ࡇ࡜ࡀ᫂ࡽ࠿࡜࡞ࡗࡓ㸬ࡇࡢཎᅉࡣ㸪ᣑᩓಀᩘ D ࡀྠᵝ࡟ 1 ᱆ప࠸ࡇ࡜࠿ࡽ㸪Nafion ࡜ẚ㍑ࡋ࡚ TMA㸫PAES
ࡀࡼࡾ⦓ᐦ࡞ࣃࢵ࢟ࣥࢢᵓ㐀ࢆ᭷ࡋ࡚࠸ࡿ࡜⪃࠼ࡽࢀࡿ㸬஧㓟໬Ⅳ⣲ࡸ❅⣲࡞࡝ࡑࡢ௚ࡢẼయ࡟ᑐࡋ࡚ࡶྠᵝ࡟㧗࠸ࣂࣜ࢔ᛶࢆ᭷ࡋ࡚࠸ࡿࡇ࡜ࡀ᫂ࡽ࠿࡜࡞ࡗ࡚࠾ࡾ㸪࢔

Cl
O
S
O

O

N

O
m

O
S
O

O

㻲㼕㼓㻚㻌㻝㻥㻌 㻌 㻵㻹㻙㻼㻭㻱㻿 䛾໬Ꮫᵓ㐀㻌

O
n





⚄ዉᕝ኱ᏛᕤᏛ◊✲ᡤᡤሗ ➨  ྕ  㧗⮬⏤య✚ᆺ

%LIXQFWLRQDO ゐ፹ᮦᩱࡢ㛤Ⓨ㸪  ஧㓟໬Ⅳ⣲࡟ᑐࡍࡿ  Fig. 20 ࡢ໬Ꮫᵓ㐀࠾ࡼࡧศᏊࢩ࣑࣮ࣗࣞࢩࣙࣥ࠿ࡽ

㑅ᢥᛶࢆ᭷ࡍࡿ࢔ࢽ࢜ࣥ஺᥮㧗ศᏊ㟁ゎ㉁ࡢ㛤Ⓨ㸪 ᫂ࡽ࠿࡞ࡼ࠺࡟㸪ࣅࢼࣇࢺ࣮ࣝࣔࣀ࣐࣮ࢆ౑⏝ࡍࡿࡇ࡜

㛤Ⓨࡉࢀࡓゐ፹㸪㧗ศᏊ㟁ゎ㉁ࢆ⏝࠸ࡓ㟁ᴟゐ፹㟁ゎ࡛㧗ศᏊ୺㙐㦵᱁࡟ᢡࢀ᭤ࡀࡾᵓ㐀ࢆᑟධࡍࡿࡇ࡜ࡀ࡛

㉁⭷ࡢ୕ᒙ⏺㠃ࡢᵓ⠏࡟ࡘ࠸᳨࡚ウࢆ⾜ࡗ࡚࠾ࡾ㸪ᮏᖺࡁࡿ㸬ࡑࡢ⤖ᯝ㸪㧗࠸⮬⏤య✚ࡀᚓࡽࢀ㸪㓟⣲ᣑᩓ࡟᭷ᗘࡣ㸪㟁ᴟゐ፹㸪㧗ศᏊ㟁ゎ㉁⭷ࡢ᳨ウࢆ⾜ࡗࡓ㸬ᐇ⏝฼࡛࠶ࡿ࡜ண᝿ࡉࢀࡿ㸬ࡲࡓ㸪ྵࣇࢵ⣲ᵓ㐀࡟ࡼࡾ㸪㧗໬࡟࠸ࡓࡿ࡟ࡣ༑ศ࡞ᛶ⬟ࡀⓎ᥹࡛ࡁ࡚࠸࡞࠸ࡀ㸪⌧ᅾ࠸᧕Ỉᛶࢆ᭷ࡋ࡚࠾ࡾ㸪ࣇࣛࢵࢹ࢕ࣥࢢࡢᢚไࡶᮇᚅࡉ

ࡢ✵Ẽ㟁ụࡢ㛤Ⓨ࡟࠾ࡅࡿၥ㢟Ⅼࢆ༑ศ࡟⪃៖ࡋࡓୖ࡛

ࢀࡿ㸬ࡋ࠿ࡋ㸪Ỉಖᣢ⬟࡟ஈࡋࡃ㸪᮲௳࡟ࡼࡗ࡚ࡣప࢔ࡢ᳨ウ࡛࠶ࡾ㸪௒ᚋ㸪ᮦᩱᨵၿࢆ⾜࠺ࡇ࡜࡟ࡼࡗ࡚㸪࢔ࢽ࢜ࣥఏᑟᛶ࡜࡞ࡿ㸬ࣝ࢝ࣜᛶࡢ✵Ẽ㟁ụࡢᐇ⏝࡛ࣞ࣋ࣝࡢ᳨ウ࡟ධࡗ࡚࠸ࡅ

ࡿ࡜⪃࠼ࡿ㸬ᮏ᳨ウ࡟࠾࠸࡚㛤Ⓨࡉࢀࡓゐ፹㸪ᅛయ㟁ゎ
F

F F㉁⭷ࡣ㸪࢔ࣝ࢝ࣜᆺࡢ⇞ᩱ㟁ụ࡟࠾࠸࡚ࡶ㐺⏝ྍ⬟࡛࠶

F
F

F F

F

ࡾ㸪௒ᚋ㸪⇞ᩱ㟁ụᛶ⬟ヨ㦂ࡶྠ᫬࡟⾜ࡗ࡚࠸ࡃணᐃ࡛

O
O
F

F F

F

n

N
N

࠶ࡿ㸬

O
O
F

F F

F



1-n

ཧ⪃ᩥ⊩

Cl



Y. Zhang, C. Wang, N. Wan, Z. Mao, International Journal of
Hydrogen Energy , 32 (2007) 400.

N.-L. Wu, W.-R. Liu, S.-J. Su, Electrochim. Acta, 48 (2003)
1567.

MM2ィ⟬䛻䜘䜛6㔞యᵓ㐀

S. D. Beattie, D. M. Manolescu, S. L. Blair, J. J. Pettersson, B.
Ramsey, D. Harrison, J. Power Sources, 157(2006) 28.

㻲㼕㼓㻚㻌㻞㻜㻌 㻌 㧗⮬⏤య✚ᆺ䜰䝙䜸䞁஺᥮㧗ศᏊ䛾໬Ꮫᵓ㐀䛸ศᏊ䝅䝭䝳䝺䞊䝅䝵䞁䛻䜘䜛᝿ᐃ❧యᵓ㐀㻌

N. Krstaji a, S. Trasatti, J. Electrochem. Soc., 142(1995) 2675.



K. C. Neyerlin, G. Bugosh, R. Forgie, Z. Liu, P. Strasser, J.

Electrochem. Soc., 156(2009) B363.

ࡇࢀࡽ᪂つ࢔ࢽ࢜ࣥ஺᥮㧗ศᏊࣂ࢖ࣥࢲ࣮ࡣ㸪㢮ఝࡢ

Govindachetty Saravanan et al., Electrochim. Acta, 99 (2013) 15.

◊✲ࡀ࡯࡜ࢇ࡝࡞ࡃ㸪ୖグࣂ࢖ࣥࢲ࣮ࡢ≉ᛶࢆ᫂ࡽ࠿࡟



Futoshi Matsumoto, Electrochemistry, 80 (2012), 132.

ࡍࡿࡓࡵ࡟ࡣࡑࡢホ౯᪉ἲ⮬య࠿ࡽ᳨ウࡍࡿᚲせࡀ࠶ࡿ㸬Hideki Abe et al., J. Am. Chem. Soc., 130 (2008) 5452.

௒ᚋ㸪ゐ፹࡜ࡢ⤌ࡳྜࢃࡏ࡟ࡼࡿ㟁Ẽ໬Ꮫⓗホ౯㸪㟁ụG. Girishkumar et al., J. Phys. Chem. Lett., 1 (2010) 2193.

ࢭࣝస〇࡟ࡼࡿྛ✀᮲௳ୗ࡛ࡢⓎ㟁ホ౯࡞࡝࡟ࡼࡾ㸪᭱

T. Ogasawara et al., J. Am. Chem. Soc., 128 (2006) 1390.

㐺࡞ࣂ࢖ࣥࢲ࣮ᵓ㐀ࡀ᫂ࡽ࠿࡟࡞ࡗ࡚࠸ࡃࡶࡢ࡜ᮇᚅࡉ



J. Read, J. Electrochem. Soc., 149 (2002) A1190.

ࢀࡿ㸬



N. Fujiwara et al., J. Power Sources, 196 (2011) 808.



M. Tanaka et al., Macromolecules, 43, (2010) 2657.

㸬ࡲ࡜ࡵ



M. Tanaka et al., Polym. Chem., 2, (2011) 99.

 ᮏࣉࣟࢪ࢙ࢡࢺ࡛ࡣ㸪 Ᏻ౯࡞ᮦᩱࢆ⏝࠸ࡓ M. Tanaka et al., J. Am. Chem. Soc., 133, (2011) 10646.

࣮࢝࣎ࣥࢼࣀࢳ࣮ࣗࣈෆ㒊ࡢ ḟඖⓗࢼࣀ✵㛫࡟㛢ࡌ㎸ࡵࡽࢀࡓỈࡢㄏ㟁≀ᛶᯇ⏣ ࿴அ㸨, ┦⃝ ၨோ㸨㸨, ┿ᗞ ㇏㸨㸨㸨

Dielectric Properties of Water Confined Inside Pseudo-one-dimensional Nanoscopic
Space of Carbon Nanotubes
Kazuyuki MATSUDA㸨, Hirohito AIZAWA㸨㸨, Yutaka MANIWA㸨㸨㸨㸯㸬ࡣࡌࡵ࡟ ༢ᒙ࣮࢝࣎ࣥࢼࣀࢳ࣮ࣗࣈ (SWNT: Single Walled
Carbon Nanotubes) ࡣ㸪࣐࢖ࢡ࣓࣮ࣟࢱ࣮࣮࢜ࢲ࣮ࡢ㛗ࡉࢆᣢࡕ㸪┤ᚄࡣࢼࣀ࣓࣮ࢺ࣮ࣝ࢜ࢲ࣮࡜࠸࠺኱ࡁ࡞⦪ᶓ
ẚࢆ᭷ࡍࡿ⌮᝿ⓗ࡞ 1 ḟඖᵓ㐀ࢆࡋ࡚࠸ࡿ(1)㸬SWNT ࡢ❧యᵓ㐀ࡣࢢࣛࣇ࢙ࣥࢩ࣮ࢺࢆ୸ࡵ࡚ࡘ࡞ࡂྜࢃࡏࡓ෇
⟄ᵓ㐀࡛࠶ࡿ㸬ᅗ 1 ࡟࣮࢝࣎ࣥࢼࣀࢳ࣮ࣗࣈࡢᒎ㛤ᅗ࡜࢝࢖ࣛࣝ࣋ࢡࢺࣝ Ch ࢆ♧ࡍ㸬࢝࢖ࣛࣝ࣋ࢡࢺࣝࡣ 2 ḟඖභゅ᱁Ꮚࡢᇶᮏ୪㐍࣋ࢡࢺࣝ a, b ࢆ⏝࠸࡚ Ch㸻na + mb
(n, m ࡣᩚᩘ) ࡜⾲ࡉࢀ㸪ಀᩘࡢ⤌ (n, m) ࢆ࢝࢖ࣛࣝᣦᩘ
࡜࿧ࡪ㸬ࡇࡢࡼ࠺࡟ࢢࣛࣇ࢙ࣥࢩ࣮ࢺࡢᕳࡁ᪉࡟ࡼࡾ┤ᚄࡢ␗࡞ࡿ SWNT ࢆࡘࡃࡿࡇ࡜ࡀ࡛ࡁ㸪ࡑࡢᵓ㐀࡟ࡼࡾ㟁Ꮚ≧ែࡀኚ໬ࡋ࡚༙ᑟయᆺ SWNT ࡸ㔠ᒓᆺ SWNT ࡜
࡞ࡿ㸬㏻ᖖ㸪SWNT ࡣᩘ༑࠿ࡽᩘⓒᮏࡀ᮰࡟࡞ࡗ࡚ࣂࣥ
ࢻࣝ࡜࿧ࡤࢀࡿ⤖ᬗࢆ⤌ࢇ࡛࠸ࡿࡓࡵ㸪ࡇࡢࣂࣥࢻࣝࡢ
㝽㛫ࡸ SWNT ෆ㒊࡟ࡉࡲࡊࡲ࡞ศᏊࡸཎᏊࢆ྾ⶶࡍࡿ
ࡇ࡜ࡀ࡛ࡁࡿ㸬ࡇࡢࡼ࠺࡞ࢼࣀࢧ࢖ࢬࡢ✵㛫࡟྾ⶶࡉࢀ
ࡓ≀㉁ࡣࣂࣝࢡ࡛ࡣぢࡽࢀ࡞࠸⛛ᗎᵓ㐀ࡸ┦㌿⛣ᣲື࡞࡝ࢆ♧ࡍࡇ࡜ࡀከᩘሗ࿌ࡉࢀ࡚࠸ࡿ㸬ࢼࣀ✵㛫୰࡛≉␗࡞᣺ࡿ⯙࠸ࢆࡍࡿ≀㉁ࡢ 1 ࡘ࡟Ỉࡀ࠶ࡿ㸬Ỉࡣ wet-dry ㌿⛣࡛▱ࡽࢀ࡚࠸ࡿࡼ࠺࡟㸪1 Ẽᅽ࡛ࡣ␯Ỉᛶࡢ~1500 nm ࡢ⊃࠸✵㛫࡟ࡣᾐධ࡛ࡁ࡞࠸㸬ࡋ࠿ᅗ 㻝㻚㻌 ༢ᒙ䜹䞊䝪䞁䝘䝜䝏䝳䞊䝤䠄㻿㼃㻺㼀䠅䛾ᒎ㛤ᅗ䠄ୖᅗ䠅䠊▮༳䛷♧䛧䛯㻞 ᮏ䛾䜹䜲䝷䝹䝧䜽䝖䝹䛜෇࿘䛸䛺䜛䜘䛖䛻䜾䝷䝣䜵䞁䝅䞊䝖䜢෇⟄≧䛻୸䜑䜛䛸䠈䛭䜜䛮䜜䜹䜲䝷䝹ᣦᩘ㻌 㻌 㻔㻝㻜㻘㻜㻕㻌 䛸㻌㻔㻢㻘㻢㻕㻌 䛾 㻿㼃㻺㼀 䛸䛺䜛䠊㻌 䜹䜲䝷䝹ᣦᩘ㻌 㻔㻝㻜㻘㻝㻜㻕㻌 䛾༢ᒙ䜹䞊䝪䞁䝘䝜䝏䝳䞊䝤䠄㻔㻝㻜㻘㻝㻜㻕㻌㻿㼃㻺㼀䠅䛾ᵓ㐀䠄ୗᅗ䠅䠊㻌ࡋ㸪ࢼࣀ✵㛫࡛࠶ࡿ SWNT ୰࡟ࡣ SWNT ቨ࡜ࡢ┦஫స⏝࡟ࡼࡗ࡚ከ㔞ࡢỈࢆ྾ⶶࡍࡿࡇ࡜ࡀ࡛ࡁࡿ㸬ᐇ㝿࡟*෸ᩍᤵ ≀⌮Ꮫᩍᐊ
Associate Professor, Institute of Physics**≉ูຓᩍ ≀⌮ᏛᩍᐊResearch associate, Institute of Physics***ᩍᤵ 㤳㒔኱Ꮫᮾி
Professor, Tokyo Metropolitan University

SWNT ࡣ␯Ỉᛶ࡛࠶ࡿ࡟ࡶ㛵ࢃࡽࡎከ㔞ࡢỈࢆࢳ࣮ࣗࣈෆ㒊࡟྾ⶶࡍࡿࡇ࡜ࡀ⢊ᮎ X ⥺ᅇᢡ㸦XRD㸧ᐇ㦂࡟ࡼࡗ࡚᫂ࡽ࠿࡟ࡉࢀ࡚࠸ࡿ(2),(3)㸬ᐊ ࡛ SWNT ࢆỈ࡟ࡉࡽࡍࡇ࡜࡛ᐜ᫆࡟Ỉࢆ྾ⶶࡉࡏࡿࡇ࡜ࡀྍ⬟࡛࠶ࡿࡀ㸪⚄ዉᕝ኱ᏛᕤᏛ◊✲ᡤᡤሗ ➨  ྕᅗ㻟䠊㻔㼍㻕㻌 ༢ᒙ䜹䞊䝪䞁䝘䝜䝏䝳䞊䝤୰䛻ᙧᡂ䛧䛯㻡ဨ⎔䜰䜲䝇䝘䝜䝏䝳䞊䝤䛾ᵓ㐀䝰䝕䝹䠊㻌㻔㼎㻕㻌 ỈศᏊ䛾Ọஂ㟁Ẽ཮ᴟᏊ䝰䞊䝯䞁䝖㻌 㼜㻌㻚㻌㻔㼏㻕㻌 ศᏊືຊᏛ䝅䝭䝳䝺䞊䝅䝵䞁䛻䜘䜚ᚓ䜙䜜䛯 㻡 ဨ⎔䜰䜲䝇䝘䝜䝏䝳䞊䝤䛾ᵓ㐀䠊኱䛝䛺⌫䛿㓟⣲ཎᏊ䠈ᑠ䛥䛺ⓑ⌫䛿Ỉ⣲ཎᏊ䜢⾲䜟䛧䛶䛔䜛䠊㻌㻔㼐㻕㻌 䜰䜲䝇䝘䝜䝏䝳䞊䝤䜢ᵓᡂ䛩䜛Ỉ䝏䜵䞊䞁䛾ᵓ㐀䛸䛭䛾㟁Ẽ཮ᴟᏊ䝰䞊䝯䞁䝖㻌 㻼㻌㻚㻌ᅗ 㻞䠊㻿㼃㻺㼀 ෆ㒊䛾Ỉ䛾䜾䝻䞊䝞䝹┦ᅗ䠊䕔䛸䖃䛿䛭䜜䛮䜜㻺㻹㻾 䛸 㼄㻾㻰 ᐇ㦂䛻䜘䜚Ỵᐃ䛥䜜䛯┦㌿⛣ ᗘ㻔㻞㻕㻙㻔㻡㻕䠊䜎䛯䠈Ⅼ⥺䛿䝞䝹䜽Ỉ䛾ᾮయ㻙ᅛయ┦㌿⛣ ᗘ䛛䜙䛾እᤄ䜢♧䛧䛶䛔䜛䠊䕕䛸䕧䛿䠈䛭䜜䛮䜜ሷぢ䜙䛸㧗ᒾ䜙䛻䜘䜛ィ⟬ᶵ䝅䝭䝳䝺䞊䝅䝵䞁䛛䜙ᚓ䜙䜜䛯┦㌿⛣ ᗘ㻔㻣㻕㻘㻌 㻔㻤㻕䠊ᤄධᅗ䛿䠈䛭䜜䛮䜜 㻡㻘㻌 㻢㻘㻌 㻣㻘㻌 㻤ဨ⎔ 㼕㼏㼑㻙㻺㼀㼟 䜢㍈᪉ྥ䛛䜙ぢ䛯ᵓ㐀䝰䝕䝹䠊㻌ࡼࡃ▱ࡽࢀ࡚࠸ࡿࡼ࠺࡟ỈศᏊࡣ኱ࡁ࡞Ọஂ㟁Ẽ཮ᴟᏊ࣮࣓ࣔࣥࢺ ( p ~ 6.210-30 C࣭m ) ࢆ᭷ࡍࡿᴟᛶศᏊ࡛
࠶ࡿ㸬ࡋ࠿ࡋ㸪Ỉࡣࣂࣝࢡࡢᾮయ≧ែ࡛ࡣ⮬Ⓨศᴟࡣ⏕ࡌࡎ㸪⤖ᬗᛶᅛయ≧ែ࡛࠶ࡗ࡚ࡶ 1 ᪉ྥ࡟ỈศᏊࡢ᪉ྥ
ࡀᥞ࠺ࡇ࡜ࡣ࡞ࡃ⮬ⓎศᴟࡣⓎ⏕ࡋ࡞࠸㸬୍᪉㸪Ice-NT࡛ࡣᅗ 3(d)࡟♧ࡍỈࢳ࢙࣮ࣥࢆᵓᡂࡍࡿỈศᏊࡢ㓄ྥ࡟ࡼࡗ࡚⮬Ⓨศᴟࢆᣢࡘࡇ࡜ࡀ♧၀ࡉࢀࡿ㸬ࡍ࡛࡟㏙࡭ࡓᐊ ࡼࡾ㧗 㸦~330 K㸧࡛ࡣ㸪ᾮయẼయ┦㌿⛣ࢆ㉳ࡇࡋ㸪ࡼ࠺࡟㸪ᅗ 3(c)࡛ࡣỈ⣲ࢆୖ࡟ྥࡅࡓࢳ࢙࣮ࣥࡀ 3 ᮏ㸪ෆໟࡉࢀ࡚࠸ࡓỈࡀࢳ࣮ࣗࣈࡢእ࡬ᨺฟࡉࢀࡿ㸬㓟⣲ࢆୖ࡟ྥࡅࡓࢳ࢙࣮ࣥࡀ 2 ᮏ࠶ࡿ㸬ࡍ࡞ࢃࡕ㸪5 ဨࡲࡓ㸪ప ࡛ࡣෆໟỈࡣᾮయᅛయ┦㌿⛣ࢆ㉳ࡇࡋ㸪࢔࢖ࢫࢼࣀࢳ࣮ࣗࣈ (Ice-NT) ࡜࿧ࡤࢀࡿ⛛ᗎᵓ㐀ࢆ࡜ࡿࡇ࡜ࡀ XRD ᐇ㦂ࡸྂ඾ศᏊືຊᏛ㸦MD㸧ィ⟬࡟ࡼࡗ࡚(2)-(8)⎔Ice-NT ࡣ඲య࡜ࡋ࡚Ỉࢳ࢙࣮ࣥ1 ᮏศࡢ⮬Ⓨศᴟࢆᣢࡘࣇ࢙ࣜᙉㄏ㟁య࡛࠶ࡿ࡜⪃࠼ࡿࡇ࡜ࡀ࡛ࡁࡿ㸬୍᪉㸪അᩘဨ⎔࡛࠶ࡿ 6 ဨ⎔ Ice-NT ࡣỈ⣲ཎᏊࢆྥࡅ

㸬ᅗ 2 ࡟ࡇࢀࡲ࡛ࡢ◊✲࡛ᚓࡽࡓࢳ࢙࣮ࣥ࡜㓟⣲ࢆྥࡅࡓࢳ࢙࣮ࣥࡀྠᩘ࡛Ᏻᐃᵓ㐀࡜ࢀ࡚࠸ࡿ SWNT ෆໟỈࡢࢢ࣮ࣟࣂࣝ┦ᅗࢆ♧ࡍ(5)㸬

࡞ࡾ㸪Ice-NT ඲య࡜ࡋ࡚ࡣ㟁Ẽ཮ᴟᏊ࣮࣓ࣔࣥࢺࢆᣢࡓ

Ice-NT ࡣỈ⣲⤖ྜ࡟ࡼࡾ 5 ಶ࠿ࡽ 8 ಶࡢỈศᏊࡀࣜࣥࢢ

࡞࠸㸬ࡋ࠿ࡋ㸪ಶࠎࡢࢳ࢙࣮ࣥࡣศᴟࢆᣢࡘࡇ࡜࠿ࡽ 6≧࡟㓄ิࡋ㸪ࡑࡢࣜࣥࢢࢆ㔜ࡡࡓࢳ࣮ࣗࣈ≧ࡢᵓ㐀ࢆࡋဨ⎔ Ice-NT ࡣ཯ᙉㄏ㟁య࡛࠶ࡿ࡜ண᝿ࡉࢀࡿ㸬᫂ࡽ࠿࡟ࡉࢀ࡚࠸ࡿ

࡚࠸ࡿ㸬ࡇࡢ n ಶࡢỈࣜࣥࢢ࠿ࡽ࡞ࡿ Ice-NT ࢆ n ဨ⎔㏆ᖺࡢ㟁Ꮚᶵჾࡢᑠᆺ㧗ᛶ⬟໬࡟ࡼࡾ㸪ᙉㄏ㟁య୙᥹

Ice-NT ࡜࿧ࡪ㸬౛࡜ࡋ࡚ᅗ 3(a) ࡟ SWNT ෆ࡟ᙧᡂࡋࡓ

Ⓨ࣓ࣔࣜࡸ✚ᒙࢥࣥࢹࣥࢧ࣮࡞࡝ࡢࢹࣂ࢖ࢫᮦᩱ࡜ࡋ࡚

5 ဨ⎔ Ice-NT ࡢᵓ㐀ࢆ♧ࡍ㸬୍⯡࡟Ỉࡢ⼥Ⅼࡣ⊃࠸✵㛫ࡢㄏ㟁యࡶᚤ⣽໬ࡀ㐍ࢇ࡛࠾ࡾ㸪ࡇࡢࡼ࠺࡞ᚤ⣽໬࡟࡜࡯࡝ୗࡀࡿࡇ࡜ࡀ▱ࡽࢀ࡚࠸ࡿࡀ㸪ᅗ 2 ࡟♧ࡍࡼ࠺࡟ࡶ࡞࠺ㄏ㟁≉ᛶࡢኚ໬ࡀ㔜せ࡞◊✲ㄢ㢟࡜࡞ࡗ࡚࠸ࡿ㸬

Ice-NT ࡢ⼥Ⅼ (Tm) ࡣ SWNT ┤ᚄࡀ⣽࠸࡯࡝㧗ࡃ࡞ࡿ㸬≉࡟㸪ᚑ᮶ࡢ◊✲࡛ࡣㄏ㟁యᮦᩱࡢࢧ࢖ࢬࡀᑠࡉࡃ࡞ࡾᅗ 3(c) ࡟ MD ィ⟬࡟࡚ᚓࡽࢀࡓ 5 ဨ⎔ Ice-NT ࡢᵓ㐀ࢆࡍࡂࡿ࡜㸪ᙉㄏ㟁య┦ࡀᾘኻࡍࡿࡇ࡜ࡀሗ࿌ࡉࢀ࡚࠾ࡾ㸪♧ࡍ㸬ࡇࡢ 5 ဨ⎔ Ice-NT ᵓ㐀ࡣ 5 ᮏࡢỈࢳ࢙࣮ࣥ࠿ࡽᵓ

ࡇࡢᚤᑠ㝈⏺ࢧ࢖ࢬࢆ᫂ࡽ࠿࡟ࡍࡿࡇ࡜ࡣ㔜せ࡛࠶ࡿ㸬ᡂࡉࢀ࡚࠸ࡿ࡜ࡶぢࡿࡇ࡜ࡀ࡛ࡁࡿ㸬ᅗ 3(c) ࡟♧ࡍ 5 ဨᮏ✏࡛ࡣ㸪MD ࢩ࣑࣮ࣗࣞࢩࣙࣥ࡟ࡼࡿ SWNT ෆໟỈࡢ

⎔ Ice-NT ࢆୖ࠿ࡽぢࡓᅗ࡛ࡣ㸪Ỉ⣲ཎᏊ㸦ᅗࡢᑠࡉ࠸ⓑㄏ㟁≉ᛶண ࡜㸪Ice-NT ࡢㄏ㟁≉ᛶ ᐃ࡟ᚲせ࡜࡞ࡿ㧗⌫㸧ࢆୖ࡟ྥࡅࡓࢳ࢙࣮ࣥ 3 ᮏ࡜㓟⣲ཎᏊࢆୖ࡟ྥࡅࡓ

⣧ᗘࡢ༙ᑟయᆺ࣭㔠ᒓᆺ SWNT ࡢ≀ᛶ ᐃࡢ⤖ᯝ࡟ࡘ࠸ࢳ࢙࣮ࣥ 2 ᮏࡀ࠶ࡿࡇ࡜ࡀࢃ࠿ࡿ㸬࡚⤂௓ࡍࡿ㸬

࣮࢝࣎ࣥࢼࣀࢳ࣮ࣗࣈෆ㒊ࡢ  ḟඖⓗࢼࣀ✵㛫࡟㛢ࡌ㎸ࡵࡽࢀࡓỈࡢㄏ㟁≀ᛶ㸰㸬ྂ඾ศᏊືຊᏛィ⟬ἲ

VWW ᮏ✏࡛ࡣ㸪ࡲࡎྂ඾ศᏊືຊᏛ㸦MD㸧ィ⟬࡟ࡼࡾㄪ࡭ࡓ SWNT ෆࡢỈࡢㄏ㟁≉ᛶ࡟ࡘ࠸࡚⤂௓ࡍࡿ㸬ྂ඾



12
6
­°§ V
·
§V
· ½°
4H ww ®¨¨ WW ¸¸  ¨¨ WW ¸¸ ¾  VCoulomb°̄© rww ¹© rww ¹ °¿MD ἲ࡛ࡣᑐ㇟࡜࡞ࡿከᩘࡢཎᏊࡸศᏊ࡟ࡘ࠸࡚㐠ື᪉ࡇࡇ࡛㸪rww ࡣ O ཎᏊ㛫ࡢ㊥㞳㸪İww 㸪ıww ࡣ Lennard Jones⛬ᘧࢆᩘ್ⓗ࡟ゎࡁ㸪ྛ᫬้࡟࠾ࡅࡿࡑࡢ఩⨨࡜㐠ື㔞ࣃ࣓࣮ࣛࢱ࡛࠶ࡿ㸬ࢆỴᐃࡍࡿ㸬ྛ⢏Ꮚ࡟ᑐࡋ࣏ࢸࣥࢩࣕࣝ㛵ᩘ࡜ึᮇ≧ែ

SWNT ࡣ✵㛫࡟ᅛᐃࡋࡓࡓࡵ㸪ศᏊෆ᣺ືࡸ୪㐍࣭ᅇ㸦ึᮇ㓄⨨㸪ึ㏿ᗘ㸧ࢆ୚࠼ࢀࡤ㸪ࡇࡢධຊ᝟ሗࢆࡶ࡜

㌿ࡢ⮬⏤ᗘࡣ࡞࠸㸬ỈศᏊ࡜ SWNT ࡢ C ཎᏊ࡜ࡢ㛫ࡢ࡟㐠ື᪉⛬ᘧࢆᩘ್✚ศࡍࡿࡇ࡜࡟ࡼࡾ⣔ࡢ㐠ືࡢ᫬㛫┦஫స⏝ࡣ 12-6 Lennard Jones ᆺ࣏ࢸࣥࢩࣕࣝ㛵ᩘࢆ⏝Ⓨᒎࢆồࡵࡿࡇ࡜ࡀ࡛ࡁࡿ㸬࠸࡚ࡍ࡞ࢃࡕ i ␒┠ࡢ⢏Ꮚࡢ㐠ື᪉⛬ᘧࡀFi§ d 2r ·mi ¨¨ 2i ¸¸© dt 0 ¹

VCW­°§ V ·12 § V ·6 ½°
4H CW ®¨¨ CW ¸¸  ¨¨ CW ¸¸ ¾
°̄© rCW ¹© rCW ¹ °¿࡜ࡋࡓ㸬ࡇࡇ࡛㸪rCW ࡣ SWNT ෆࡢ C ཎᏊ࡜ỈศᏊࡢ O

࡛୚࠼ࡽࢀࡿ࡜ࡍࡿ࡜㸪ࢩ࣑࣮ࣗࣞࢩࣙࣥࡢ㛤ጞ᫬㛫ࢆཎᏊ࡜ࡢ㊥㞳࡛࠶ࡿ㸬ࣃ࣓࣮ࣛࢱࡣ௨ୗ࡟♧ࡍt0 ࡜ࡋ࡚㸪௨ୗࡢ୍㐃ࡢᡭ⥆ࡁࢆ⧞ࡾ㏉ࡍࡇ࡜࡟ࡼࡾ⣔Lorenz-Berthelot ๎ࢆ⏝࠸࡚⟬ฟࡋࡓ㸬ࡢ㐠ືࡢ᫬㛫Ⓨᒎࢆồࡵ࡚࠸ࡿ㸬H i, j(1) ᫬้ t㸻t0 ࡟࠾ࡅࡿཎᏊ㓄⨨ࡢୗ࡛ྛཎᏊ㸪ศᏊ࡟ാV i, jࡃຊ Fi ࢆィ⟬ࡍࡿ㸬(2) ồࡵࡽࢀࡓຊ࡟ᚑ࠸㸪ྛࠎࡢཎᏊ࣭ศᏊ࡟ࡘ࠸࡚ᩘ

Vi V j2

C ཎᏊࡢ Lennard Jones ࣃ࣓࣮ࣛࢱࡣ㸪
İCC=28 K㸪ıCC=3.4 ύ㸪್✚ศ࡟ࡼࡾ㐠ື᪉⛬ᘧࢆゎࡃ㸬(3) ᫬้ t=t0+ǻt ࡟࠾ࡅࡿྛཎᏊࡢᗙᶆࢆồࡵࡿ㸬

Hi H jTIP3P ࣔࢹࣝࡢ Lennard Jones ࣃ࣓࣮ࣛࢱࡣ㸪(4) t0+ǻt ĺ t0 ࡜⨨ࡁ᥮࠼࡚ (1) ࡟ᡠࡿ㸬

İww=76.6 K㸪ıww=3.15061 ύ
࡛࠶ࡿ㸬
ࡼࡗ࡚㸪
Lorenz-Berthelot ๎࡟ࡼࡾ C ཎᏊ
㸦SWNT㸧

ࡉࡽ࡟㸪ᚓࡽࢀࡓ⤖ᯝࢆゎᯒࡍࡿࡇ࡜࡟ࡼࡾ㸪ືᚄศᕸ㛵ᩘࡸᣑᩓಀᩘ࡞࡝ࡢ≀⌮㔞ࢆᚓࡿࡇ࡜ࡀ࡛ࡁࡿ㸬ྂ㸫O ཎᏊ㸦TIP3P㸧 㛫┦஫స⏝ࡢ Lennard Jones ࣃ࣓࣮ࣛࢱࡣ㸪İC,W=46.3 K㸪ıC,W=3.27531 ύ

඾ MD ἲࡣ≀㉁ࡢ㟼ⓗ࣭ືⓗᛶ㉁ࢆホ౯࣭ண ࡍࡿࡇ࡜ࢆྍ⬟࡜ࡍࡿ᭷ຊ࡞ࢩ࣑࣮ࣗࣞࢩࣙࣥᢏἲࡢ୍ࡘ࡛࠶ࡿ㸬࡜ồࡲࡗࡓ㸬

ᮏ◊✲࡛ࡣྂ඾ศᏊືຊᏛࢩ࣑࣮ࣗࣞࢩࣙࣥࢯࣇࢺ࢙࢘

⢏Ꮚᩘ N ࡜ᇶᮏࢭࣝࡢయ✚ V ࡣ୍ᐃ࡜ࡋ㸪 ᗘ T ࢆไ࢔㸪㸦ᰴ㸧ᐩኈ㏻ Materials Explorer㸪Scigress ࢆ౑⏝ࡋࡓ㸬

ᚚࡍࡿ NVT ࢔ࣥࢧࣥࣈࣝࢆ⏝࠸ࡓ㸬 ᗘไᚚࡣ㏿ᗘࢫࢣ

SWNT ෆࡢ᭱㏆᥋ࡢC ཎᏊ㸫CཎᏊ㛫ࡢ⤖ྜ㛗ࡣ1.42 ύ࣮ࣜࣥࢢἲ࡛⾜ࡗࡓ㸬㏿ᗘࢫࢣ࣮ࣜࣥࢢἲ࡛ࡣྛཎᏊࡢ

࡜ࡋ㸪ཎᏊᗙᶆࢆᅛᐃࡋ࡚ィ⟬ࡋࡓ㸬ࡲࡓ㸪ỈศᏊ࡟ࡣࡶࡘ㐠ື࢚ࢿࣝࢠ࣮ࡢ⥲࿴ࡀ⣔ࡢタᐃ ᗘ Tex ࡜ཎᏊ⣔TIP3P ࣔࢹࣝࢆ⏝࠸ࡓ㸬TIP3P ࣔࢹ࡛ࣝࡣ㸪ࡢ඲⮬⏤ᗘ g ࠿ࡽᚓࡽࢀࡿ⇕࢚ࢿࣝࢠ࣮࡟➼ࡋࡃ࡞ࡿࡼ

࣭O ཎᏊ-H ཎᏊ㛫࠺࡟ྛཎᏊࡢ㏿ᗘࢆ୍ᵝ࡟ࢫࢣ࣮ࣝࡍࡿ㸬ࢫࢣ࣮ࣝ๓ࡢ

⤖ྜ㛗 rO-H = 0.9572 ύ⤖ྜゅ҆HOH = 104.52°

㹼ཎᏊࡢ㏿ᗘࢆ vi 㸪ࢫࢣ࣮ࣝᚋࡢཎᏊࡢ㏿ᗘࢆv i ࡜ࡋࡓ࡜࣭O ཎᏊࡢ㟁Ⲵ㸸-0.834e [C]ࡁ㸪ࢫࢣ࣮ࣜࣥࢢࡢᘧࡣ

࣭H ཎᏊࡢ㟁Ⲵ㸸+0.417e [C]D vi࡛࠶ࡿ㸬ࡇࡇ࡛ e ࡣ㟁Ẽ⣲㔞 1.602×10-19 [C]࡛࠶ࡿ㸬⢏Ꮚ࡟ຍࢃࡿຊFi ࡣ࣏ࢸࣥࢩࣕࣝ㛵ᩘ࡛୚࠼ࡽࢀࡿ㸬
TIP3P ࣔࢹࣝࡢỈศᏊ㛫┦஫స⏝࣏ࢸࣥࢩࣕࣝࡣ㸪O ཎ

v~i

D

§1
· § 1
2·
¨ gk BTex ¸ / ¨ ¦ mi vi ¸©2
¹ © i 2¹࡛୚࠼ࡽࢀࡿ㸬Ꮚ㛫࡟ാࡃ 12-6 Lennard Jones ᆺࡢ┦஫స⏝࣏ࢸࣥࢩࣕ

ࢫࢣ࣮ࣜࣥࢢ᧯సࡣࢩ࣑࣮ࣗࣞࢩࣙࣥࢫࢸࢵࣉ 1 ࢫࢸࣝ࡜㸪O ཎᏊ࡜ H ཎᏊ࡟⨨࠿ࢀࡓ㟁Ⲵ㛫࡟ാࡃࢡ࣮ࣟࣥ

ࢵࣉࡈ࡜࡟⾜ࡗࡓ㸬ࡲࡓ㸪᫬㛫✚ศ࡟ࡣ Gear ἲ㸦ண Ꮚ┦஫స⏝࣏ࢸࣥࢩࣕࣝ VCoulomb ࡢ࿴࡛୚࠼ࡽࢀࡿ㸸ಟṇᏊἲ㸧ࢆ⏝࠸ࡓ㸬⚄ዉᕝ኱ᏛᕤᏛ◊✲ᡤᡤሗ ➨  ྕ



300K

200K

(a) (9,8)SWNT
2R=1.153nm

300K
ᅗ 㻡䠊㻡㻘㻌㻢㻘㻌㻣 ဨ⎔䜰䜲䝇䝘䝜䝏䝳䞊䝤䠄㻵㼏㼑㻙㻺㼀䠅䛾⏕ᡂ⁐ゎ䜢♧䛩䝫䝔䞁䝅䝱䝹䜶䝛䝹䜼䞊䛾 ᗘ౫Ꮡᛶ㻚㻌 ప 䛷 㻵㼏㼑㻙㻺㼀 䛜⏕ᡂ䛩䜛䛸䝫䝔䞁䝅䝱䝹䜶䝛䝹䜼䞊䛜ᛴⴠ䛩䜛䠊䝫䝔䞁䝅䝱䝹䜶䝛䝹䜼䞊䛾ᛴⴠ ᗘ䛿 㼄 ⥺ᅇᢡᐇ㦂䛾⤖ᯝ䛛䜙Ỵᐃ䛥

200K

䜜䛯䛭䜜䛮䜜䛾 㻵㼏㼑㻙㻺㼀 䛾⼥Ⅼ㻌 㼀㼙㻌 䛸䜘䛟୍⮴䛧䛶䛔䜛䠊㻌㸱㸬ࢮࣟ㟁ሙ࡟࠾ࡅࡿ࢔࢖ࢫࢼࣀࢳ࣮ࣗࣈࡢ≀ᛶホ౯(b) (9,9)SWNT
2R=1.221nm
300Kࡇࡇ࡛ࡣࢮࣟ㟁ሙ࡛ࡢSWNTෆ࡟ෆໟࡉࢀࡓỈࡢMDࢩ࣑࣮ࣗࣞࢩࣙࣥࡢ⤖ᯝࢆ⤂௓ࡍࡿ㸬 ࢮࣟ㟁ሙ࡟࠾ࡅࡿỈࡢᵓ㐀Ꮩ❧ࡋࡓ SWNT ࢆ⪃࠼㸪Ỉࢆ SWNT ෆ㒊࡟㓄⨨ࡋ㸪3✀㢮ࡢ࢝࢖ࣛࣜࢸ࢕ࡀ␗࡞ࡿ SWNT ࡟ࡘ࠸࡚ࢩ࣑ࣗࣞ
࣮ࢩࣙࣥࢆ⾜࡞ࡗࡓ㸬SWNT ࡢᣦᩘ㸪┤ᚄ 2R㸪ෆໟࡋࡓỈศᏊᩘࡣ௨ୗࡢ㏻ࡾ࡛࠶ࡿ㸬

170K
࣭(9,8)SWNT:

2R =1.153 nm , 104 ಶ࣭(9, 9)SWNT:

2R =1.221 nm, 83 ಶ࣭(10, 10)SWNT: 2R =1.356 nm, 98 ಶ(c) (10,10)SWNT
2R=1.356nm

SWNT ࡢ୧➃࡟ࡣ┦஫స⏝ࡢᑠࡉ࠸ཎᏊࢆ௬ᐃࡋቨ
࡜ࡋ࡚ᅛᐃࡋ㸪ࡇࡢቨ࡟ࡼࡾ㧗 ࡸ㠀⇕ᖹ⾮࡟࠾࠸࡚ᅗ 㻠䠊ศᏊືຊᏛ䝅䝭䝳䝺䞊䝅䝵䞁䛷ᚓ䜙䜜䛯㻔㻥㻘㻤㻕㻘㻌㻔㻥㻘㻥㻕㻘㻌㻔㻝㻜㻘㻝㻜㻕㻌㻿㼃㻺㼀㼟 ෆໟỈ䛾ᵓ㐀䠊ୖ䛻䛿䝏䝳䞊䝤㍈᪉ྥ䛛䜙ぢ䛯ᅗ䠈ୗ䛻䛿ᶓ䛛䜙ぢ䛯ᅗ䠄㻿㼃㻺㼀 䛿⾲♧䛧䛶䛔䛺䛔䠅䜢♧䛧䛶䛔䜛䠊㧗㻟㻜㻜㻌 㻷 䛷䛿Ỉ䛿ᾮయ≧ែ䛷䛒䜛䛜䠈ప 䛷䜰䜲䝇䝘䝜䝏䝳䞊䝤䜢ᙧᡂ䛧䛶䛔䜛䛾䛜ぢ䛶䛸䜜䜛䠊㻌

SWNT ෆ࠿ࡽỈࡀ↓㝈㐲࡟㣕ࡧཤࡗ࡚ࡋࡲ࠺ࡇ࡜ࢆ㜵࠸ࡔ㸬ࡲࡓ㸪SWNT ୰࡟ྠᵝࡢ௬᝿ཎᏊ 1 ಶࢆ㓄⨨ࡋ㸪Ỉࢡࣛࢫࢱ඲యࡀ୪㐍㐠ືࡸᅇ㌿㐠ືࢆ⾜࡞࠺ࡇ࡜ࢆ㜵࠸࡛࠸ࡿ㸬SWNT ࡜ቨࡣᅛᐃࡋỈࡣ๛య࡜ࡋࡓ㸬ࢡ࣮ࣟ
ࣥ࠾ࡼࡧLennard Jones࣏ࢸࣥࢩࣕࣝࡢ࢝ࢵࢺ࢜ࣇ㊥㞳ࢆ
20 ύ࡜ࡋ㸪࿘ᮇⓗቃ⏺᮲௳ࡣ౑⏝ࡏࡎ㸪ࡲࡓ Ewald ἲࡣ⏝࠸࡚࠸࡞࠸㸬(9,8)㸪(9.9)㸪(10.10) SWNTs ࡑࢀࡒࢀࡢ
⣔ࡢィ⟬᮲௳ࢆ⾲ 1 ࡟♧ࡍ㸬࣮࢝࣎ࣥࢼࣀࢳ࣮ࣗࣈෆ㒊ࡢ  ḟඖⓗࢼࣀ✵㛫࡟㛢ࡌ㎸ࡵࡽࢀࡓỈࡢㄏ㟁≀ᛶ

XRD ᐇ㦂࡛ࡣ Ice-NT ⏤᮶ࡢ 1 ḟඖࡢࣈࣛࢵࢢࣆ࣮ࢡ⾲ 㻝䠊㻹㻰 ィ⟬䛾᮲௳㻌ࡀฟ⌧ࡍࡿ ᗘ㸪MD ィ⟬࡛ࡣ࣏ࢸࣥࢩ࢚ࣕࣝࢿࣝࢠ࣮

䜹䜲䝷
䝹ᣦᩘ

┤ᚄ
[nm]

㛗䛥
[nm]

H2O㻌
[ಶ]

(9,8)

1.153

6.2

104

ᗘኚ໬䛾
㏿ᗘ[K/ns]67

ែ࠿ࡽ Ice-NT ࡬ࡢ┦㌿⛣ࢆ෌⌧ࡍࡿࡇ࡜࡟ᡂຌࡋ࡚࠸
ࡿࡇ࡜ࡀ☜ㄆ࡛ࡁࡿ㸬

(9,9)

1.221

4.3

83

67

(10,10)

1.356

4.3

98

22

ࡀⴠࡕጞࡵࡿ ᗘࢆ Tm ࡜ࡋࡓ㸬௨ୖࡢࡼ࠺࡟㸪ᮏ MDࢩ࣑࣮ࣗࣞࢩࣙࣥࡣ XRD ᐇ㦂࡛ぢฟࡉࢀ࡚࠸ࡿᾮయ≧ࡲࡎ 300 K ࡛ 1 ns ಖᣢࡋࡓᚋ㸪 ᗘࢆ⾲ 1 ࡟♧ࡋࡓ㏿ᗘ࡛෭༷ࡋࡓ㸬᭱ప ࡟฿㐩ᚋ㸪ྠࡌ㏿ᗘ࡛᪼ 㐣⛬ࢆ
㏣㊧ࡋࡓ㸬✚ศࡁࡊࡳᖜࡣ 1.0 fs ࡜ࡋ㸪5 ps ࡈ࡜࡟ᗙᶆ
࡜㏿ᗘࢆฟຊࡋࡓ㸬
300 K ࡜ྛ᭱ప ᗘ㸦200 K ࡲࡓࡣ 170 K㸧࡛ࡢᵓ㐀ࢆ
ᅗ 4 ࡟♧ࡍ㸬ᅗࡢ 300 K ࡢ≧ែࡣ༑ศ᫬㛫 (~1 ns) ࡀ⤒㐣ࡋࡓᚋࡢ≧ែ࡛࠶ࡾ㸪⇕ᖹ⾮≧ែ࡟㐩ࡋ࡚࠸ࡿ㸬300 K࡜᭱ప ᗘࡢᵓ㐀ࢆẚ㍑ࡍࡿ࡜㸪300 K ࡛ࡣỈࡣ஘ࢀࡓ≧ែ࡛࠶ࡿࡢ࡟ᑐࡋ㸪ప ࡛ࡣつ๎ⓗ࡟㓄ิࡋ Ice-NT ࢆᙧᡂࡋ࡚࠸ࡿࡇ࡜ࡀࢃ࠿ࡿ㸬ࡍ࡞ࢃࡕ 300 K ࡛ࡣᾮయⓗ≧ែ࡛࠶ࡾ㸪ప ࡛ࡣỈࡀ⤖ᬗ໬ࡋ࡚࠸ࡿ㸬ࡇࡢᾮయᅛయ┦㌿⛣ࡣ⣔඲యࡢ࣏ࢸࣥࢩ࢚ࣕࣝࢿࣝࢠ࣮ (PE) ࡢᗘኚ໬࠿ࡽ᫂☜࡟ぢࡿࡇ࡜ࡀ࡛ࡁࡿ㸬ᅗ 5 ࡟ ᗘ࡜Ỉศ
Ꮚ 1 ಶᙜࡓࡾࡢ࣏ࢸࣥࢩ࢚ࣕࣝࢿࣝࢠ࣮ࡢ㛵ಀࢆ♧ࡋࡓ㸬
3 ✀㢮ࡢ SWNT ࡟ࡘ࠸࡚㸪࣏ࢸࣥࢩ࢚ࣕࣝࢿࣝࢠ࣮ࡣ࠶ࡿ ᗘ௨ୗ࡛ᛴⴠࡋ㸪ᾮయ࠿ࡽᅛయ࡬ࡢ┦㌿⛣ᣲື࡟ᑐᛂࡋ࡚࠸ࡿ࡜⪃࠼ࡽࢀࡿ㸬ᛴⴠࢆ♧ࡍ ᗘࡣ XRD ᐇ㦂࡟ࡼࡗ࡚Ỵᐃࡉࢀࡓᾮయᅛయ┦㌿⛣ ᗘ࡟㏆࠸㸬ḟ࡟㓟⣲࡜Ỉ⣲ࡢᗙᶆ࠿ࡽỈ 1 ศᏊ࠶ࡓࡾࡢࢳ࣮ࣗࣈ
㍈᪉ྥࡢ㟁Ẽ཮ᴟᏊ࣮࣓ࣔࣥࢺ㸦P㸧ࢆồࡵࡓ㸦ᅗ 6㸧㸬࣏ࢸࣥࢩ࢚ࣕࣝࢿࣝࢠ࣮ࡀᛴⴠࢆ♧ࡍ࢜ࣥࢭࢵࢺ ᗘࢆᅗ 㻢䠊㻔㻥㻘㻤㻕㻘㻌㻔㻥㻘㻥㻕㻘㻌㻔㻝㻜㻘㻝㻜㻕㻌㻿㼃㻺㼀㼟 ෆ䛾Ỉ 㻝 ศᏊ䛒䛯䜚䛾㟁Ẽ཮

Ice-NT ࡢ⼥Ⅼ㸦Tm㸧࡜⪃࠼ࡿ࡜㸪Tm ௨ୖ࡛ࡣ P ࡀࡤࡽࡘᴟᏊ䝰䞊䝯䞁䝖㻌 㻼㻌 䛾 ᗘ౫Ꮡᛶ䠊㻼 䛿䝏䝳䞊䝤㍈᪉ྥᡂศ䛸࠸࡚࠸ࡿࡢ࡟ᑐࡋ㸪Tm ௨ୗ࡛ࡣ P ࡀ୍ᐃࡢ್ࢆ࡜ࡗ࡚࠾

䛧䛶ồ䜑䛶䛔䜛䠊ወᩘဨ⎔䛾 㻡㻘㻣 ဨ⎔䜰䜲䝇䝘䝜䝏䝳䞊䝤㻌ࡾ㸪ỈศᏊࡀ㓄ྥࡋ࡚࠸ࡿࡇ࡜ࡀࢃ࠿ࡿ㸬ࡲࡓഅᩘဨ⎔㻔㻵㼏㼑㻙㻺㼀㻕㻌 䛜ᙧᡂ䛥䜜䜛㻔㻥㻘㻤㻕㻘㻌㻔㻝㻜㻘㻝㻜㻕㻌㻿㼃㻺㼀㼟 䛷䛿ప 䛷 㻼 䛿᭷

ࡣ P=0 ࡛Ᏻᐃࡋ࡚࠸ࡿࡢ࡟ᑐࡋ㸪ወᩘဨ⎔ࡣ᭱ప ࡛ศ㝈್䛸䛺䜛䛜䠈അᩘဨ⎔㻌 䛾 㻢 ဨ⎔ 㻵㼏㼑㻙㻺㼀㻌 䛜ᙧᡂ䛥䜜䜛㻔㻥㻘㻥㻕㻌ᴟࡋࡓ≧ែ࡟࠶ࡾ P ࡣ᭷㝈ࡢ୍ᐃ್ࢆ࡜ࡗ࡚࠸ࡿ㸬㻿㼃㻺㼀 䛷䛿䝊䝻䛸䛺䜛䠊㻌࣏ࢸࣥࢩ࢚ࣕࣝࢿࣝࢠ࣮࡜㟁Ẽ཮ᴟᏊ࣮࣓ࣔࣥࢺࡣ
(9,8)㸪(9,9) SWNTs ࡛ࡣ 75 ps ࡈ࡜ࡢᖹᆒࢆ࡜ࡾ㸪(10,10)


SWNT ࡛ࡣ 200 ps ࡈ࡜ࡢᖹᆒࢆ࡜ࡗࡓ㸬XRD ᐇ㦂ࡢ⤖ᯝ࡜ MD ィ⟬ࡢ⤖ᯝࡢẚ㍑ࢆ⾲ 2 ࡟♧ࡍ㸬 ࢔࢖ࢫࢼࣀࢳ࣮ࣗࣈࡢᏳᐃᛶ㸸ࡺࡽࡂ⾲ 㻞䠊㻹㻰 ィ⟬䛸 㼄㻾㻰 ᐇ㦂䛻䜘䜚ᚓ䜙䜜䛯 㼀㼙 䛾ẚ㍑㻌ḟඖ⣔࡛ࡣ㢧ⴭ࡞ࡺࡽࡂࢆ♧ࡍࡇ࡜ࡀᮇᚅࡉࢀࡿ㸬ࡑࡇ

SWNT ෆ㒊ࡣ 1 ḟඖⓗࢼࣀ✵㛫࡛࠶ࡿ㸬ࡇࡢࡼ࠺࡞ 1

XRD
ᖹᆒ┤ᚄ
[nm]
1.17
1.26
1.35

MD ┤ᚄ
[nm]

⎔ᵓ㐀

1.153
1.221
1.356

5 ဨ⎔
6 ဨ⎔
7 ဨ⎔

XRD
Tm㻌
[K]
300
280
225

MD
Tm 㻌 㻌
[K]
290
260
220

࡛ 5 ဨ⎔ Ice-NT ࡟ࡘ࠸࡚ࡑࡢᵓ㐀ࡢ᫬㛫ⓗ࡞Ᏻᐃᛶ㸦ࡺࡽࡂ㸧ࢆㄪ࡭ࡓ㸬(9,8) SWNT ࡟ࡘ࠸࡚㸪࣏ࢸࣥࢩࣕࣝ
௨ୗࡢప࢚ࢿࣝࢠ࣮ࡀᛴⴠࡋጞࡵࡿ ᗘ
㸦Tm㸧

100, 175 ,

200, 225, 250, 270, 290 K ࠾ࡼࡧ㸪Tm ௨ୖࡢ㧗

310 K ࡟ࡘ࠸୍࡚ᐃ᫬㛫ಖᣢࡋ࡚Ỉࡢᵓ㐀ࡢ᫬㛫ኚ໬ࢆ⚄ዉᕝ኱ᏛᕤᏛ◊✲ᡤᡤሗ ➨  ྕ

1.2 10

-30

1 10

-30

8 10

-31

6 10

-31

4 10

-31

2 10

-31

P [C.m]



0
100

150

200
250
Temperature [K]300ᅗ 㻤䠊Ỉ 㻝 ศᏊ䛒䛯䜚䛾㟁Ẽ཮ᴟᏊ䝰䞊䝯䞁䝖䛾⤯ᑐ್㻌 㼨㻌 㻼㻌 㼨䛾 ᗘ౫Ꮡᛶ䠊㻡 ဨ⎔䜰䜲䝇䝘䝜䝏䝳䞊䝤⏕ᡂ䛻క䛔㻌 㼨㻌㻼㻌㼨㻌 䛿time [ns]

ቑ኱䛧䠈ప

40
35
30
25
20
15
10
5
0

㻝㻣㻡㻌㻷 ௨ୗ䛷㣬࿴䛩䜛䠊㻌

0.00380.004

0.00420.0044Temperature [1/K]ᅗ 㻥䠊㻡 ဨ⎔䜰䜲䝇䝘䝜䝏䝳䞊䝤䜢ᵓᡂ䛩䜛Ỉ䝏䜵䞊䞁䛾཯㌿᫬㛫䛾 ᗘ౫Ꮡᛶ䠊㻌Tm ௨ୖࡢ㧗

310 K ࡛ࡣ P~0 ࡛ࡺࡽ࠸࡛࠸ࡿࡇ࡜࠿ࡽ㸪ỈศᏊࡣ㓄ྥࡋ࡚࠾ࡽࡎ㸪Ỉࡀᾮయ≧ែ࡛࠶ࡿࡇ࡜࡜▩┪ࡋ࡞࠸㸬Tm (~290 K) ௨ୗ࡛ࡣ P ࡢࡺࡽࡂࡀ኱ࡁࡃ࡞
ࡾỈศᏊࡀ㓄ྥࡋጞࡵ࡚࠸ࡿࡇ࡜ࢆ♧၀ࡋ࡚࠸ࡿ㸬 ᗘࡀపࡃ࡞ࡿ࡟ࡘࢀ㸪ࡇࡢࡺࡽࡂࡢ᣺ᖜࡣ኱ࡁࡃ࡞ࡗ࡚࠸ᅗ 㻣䠊୍ᐃ ᗘ᮲௳ୗ䛷䛾㻔㻥㻘㻤㻕㻌㻿㼃㻺㼀 ෆ䛾Ỉ 㻝 ศᏊ䛒䛯䜚䛾㟁Ẽ཮ᴟᏊ䝰䞊䝯䞁䝖㻌 㻼㻌 䛾᫬㛫ኚ໬䠊㻼 䛿䝏䝳䞊䝤㍈᪉ྥᡂศ䛸䛧䛶ồ䜑䛶䛔䜛䠊ྑᅗ䛿ྛ᫬㛫䛻䛚䛡䜛䠈䝏䝳䞊䝤㍈᪉ྥ䛛䜙ぢ䛯㻿㼃㻺㼀୰ኸ㒊ศ䛾Ỉ䛾ᵓ㐀䠊㧗 㻟㻝㻜㻌㻷䛷䛿ෆໟỈ䛿ᾮయ≧ែ䛻䛒䜛䛯䜑䠈㻼㻌 䛿䝊䝻䛻㏆䛔್䛷ᦂ䜙䛔䛷䛔ᙧᡂࡋ࡚࠸ࡿࡀ᫬㛫ⓗ࡟Ᏻᐃࡋ࡚࠸࡞࠸㸬ࡲࡓ Ice-NT ࢆᵓᡂࡍࡿỈࢳ࢙࣮ࣥ࡟ࡶḞᦆࡸࢻ࣓࢖ࣥࡀከࡃぢࡽࢀࡿ㸬
250 K ௨ୗ࡛ࡣ P ࡣ࠶ࡿ୍ᐃࡢ್࡟࡞ࡿࡀ㸪ࡇࡢ ᗘ㡿ᇦ࡛ࡣ SWNT ෆໟỈࡣᏳᐃࡋࡓ 5 ဨ⎔ Ice-NT ࢆᙧᡂࡋ࡚࠾ࡾỈࢳ࢙࣮ࣥ࡟Ḟᦆࡣ࡯࡜ࢇ࡝ぢࡽࢀ࡞࠸㸬䜛䠊㻌పࡿ㸬ࡇࡢ࡜ࡁ SWNT ෆໟỈࡢᵓ㐀ࡣ㒊ศⓗ࡟ Ice-NT ࢆ㻝㻣㻡㻌㻷 ௨ୗ䛷䛿䠈㻡 ဨ⎔䜰䜲䝇䝘䝜䝏䝳䞊䝤䜢ᵓᡂ䛩䜛Ỉ䝏䜵䞊䞁䛾཯㌿㐠ື䛜෾⤖䛧䛶䛔䜛䛯䜑䛻㻌 㻼㻌 䛜᭷㝈䛾୍ᐃ್䛸䛺䜛䠊㻌

ࡇࡇ࡛ P ࡀṇࡢ୍ᐃ್࡛ࡣ z ㍈ࣉࣛࢫ᪉ྥ࡟ 3 ᮏࡢỈࢳ࢙࣮ࣥࡢỈ⣲ཎᏊࡀྥ࠸ࡓ≧ែ࡛࠶ࡾ㸪㈇ࡢ୍ᐃ್࡛
ࡣ 3 ᮏࡀ࣐࢖ࢼࢫ᪉ྥࢆྥ࠸ࡓ≧ែ࡛࠶ࡿ㸬ࡍ࡞ࢃࡕ㸪
250 K ௨ୗࡢṇ㈇ࡢ཯㌿ࡣ㸪Ice-NT ࢆᵓᡂࡋ࡚࠸ࡿỈࢳ

㏣㊧ࡋࡓ㸬ྛ ᗘ࡟࠾ࡅࡿศᏊࡢึᮇ㓄⨨ࡣ 3-1 ࡟♧ࡋ࢙࣮ࣥ1ᮏ༢఩ࡢ཯㌿࡛࠶ࡿ㸬ᅗ7࠿ࡽ᫂ࡽ࠿࡞ࡼ࠺࡟㸪ࡓࢩ࣑࣮ࣗࣞࢩࣙࣥ࡟ࡼࡾᚓࡽࢀࡓᵓ㐀ࢆ௬ᐃࡋ࡚࠸ࡿ

Ỉࢳ࢙࣮ࣥࡀ཯㌿ࡋࡓ┤ᚋ࡛࠶ࡗ࡚ࡶ㟁Ẽ཮ᴟᏊ࣮࣓ࣔ㸦ᅗ 4㸧㸬ィ⟬⤖ᯝࢆᅗ 7 ࡟♧ࡍ㸬⦪㍈ P ࡣỈศᏊ 1 ಶ࠶ࣥࢺࡢ್ࡣ஘ࢀ࡚࠸࡞࠸㸬ࡼࡗ࡚Ỉࢳ࢙࣮ࣥࡣ཯㌿ࡍࡿࡓࡾࡢ㟁Ẽ཮ᴟᏊ࣮࣓ࣔࣥࢺࡢ್࡛࠶ࡾ㸪1.0 ns ࡈ࡜ࡢ㝿࡟ Ice-NT ࢆቯࡍࡇ࡜ࡣ࡞࠸㸬ࡲࡓ㝆 ࡟క࠸Ỉࢳ࢙࣮ᖹᆒࡢ್࡛࠶ࡿ㸬ࣥࡢ཯㌿ࡢ᫬㛫ࡣ㛗ࡃ࡞ࡾ㸪175 K ௨ୗ࡛ࡣ 20 ns ࡲ࡛཯㌿ࡣ㉳ࡇࡗ࡚࠸࡞࠸㸬࣮࢝࣎ࣥࢼࣀࢳ࣮ࣗࣈෆ㒊ࡢ  ḟඖⓗࢼࣀ✵㛫࡟㛢ࡌ㎸ࡵࡽࢀࡓỈࡢㄏ㟁≀ᛶ ᅗ 8 ࡟㟁Ẽ཮ᴟᏊ࣮࣓ࣔࣥࢺࡢ⤯ᑐ್ |P| ࡢ ᗘ౫Ꮡᛶࢆ♧ࡍ㸬|P| ࡣ Tm ௨ୗ࡛ቑຍࡋጞࡵ㸪250 K ௜㏆࠿ࡽഴࡁࡀ⦆ࡸ࠿࡟࡞ࡾ㣬࿴ࡍࡿ㸬Tm ௨ୗ㸦≉࡟ 250 K ௨ୗ㸧ࡢ|P| ࡢ᫬㛫ኚ໬ࡣ㸪Ice-NTࢆᙧᡂࡍࡿỈࢳ࢙࣮ࣥࡢ཯㌿࡟ࡼࡿࡇ࡜ࡀࢃ࠿ࡗࡓ㸬ᅗ
7 ࠿ࡽ

ᗘ 270, 250, 225 K ࡢỈࢳ࢙࣮ࣥࡀ཯㌿ࡍࡿᖹᆒⓗ࡞᫬㛫 Ĳ ࡣ௨ୗࡢࡼ࠺࡟ぢ✚ࡶࡽࢀࡿ㸬
࣭270 K: Ĳ = 20/6 = 3.3 ns
࣭250 K: Ĳ = 30/4 = 7.5 ns
࣭225 K: Ĳ = 75/2 = 37.5 ns
ᗘ T [K]࡜Ỉࢳ࢙࣮ࣥࡢ཯㌿ࡀ㉳ࡇࡿ᫬㛫 Ĳ [ns]࡜ࡢ
㛵ಀࢆᅗ 9 ࡟♧ࡍ㸬ࡇࡢ ᗘ౫Ꮡᛶ࡟ᑐࡋ༢⣧࡞⇕άᛶᆺࢆ௬ᐃࡍࡿ࡜㸪௨ୗࡢࡼ࠺࡟⾲ࢃࡉࢀࡿ㸬W | 5 . 88 u 10

6

u exp(

3525 . 6)
T㸲㸬㟁ሙ୰࡛ࡢ࢔࢖ࢫࢼࣀࢳ࣮ࣗࣈࡢ≀ᛶホ౯
ࡍ࡛࡟㏙࡭ࡓࡼ࠺࡟㸪࢔࢖ࢫࢼࣀࢳ࣮ࣗࣈࡣࡑࢀࢆᵓ
ᡂࡍࡿỈࢳ࢙࣮ࣥࡀ㟁Ẽ཮ᴟᏊ࣮࣓ࣔࣥࢺࢆ᭷ࡍࡿࡓࡵ
࡟㸪ወᩘဨ⎔࢔࢖ࢫࢼࣀࢳ࣮ࣗࣈ࡛ࡣ⮬Ⓨศᴟࡀ⏕ࡌࡿࡇ࡜ࡀ᫂ࡽ࠿࡜࡞ࡗࡓ㸬ࡇࡇ࡛ࡣ࢔࢖ࢫࢼࣀࢳ࣮ࣗࣈ࡟
㟁ሙࢆ༳ຍࡋࡓሙྜࡢศᴟ㐣⛬࡟ࡘ࠸࡚ࡢMD ィ⟬⤖ᯝࢆ⤂௓ࡍࡿ㸬

ᅗ㻝㻜䠊ప 䠄㻝㻜㻜㻌㻷䠅䛷䛾 㻡 ဨ⎔䜰䜲䝇䝘䝜䝏䝳䞊䝤䛾ึᮇศᴟ㐣⛬䠊ୗ䛻䛿䝏䝳䞊䝤㍈᪉ྥ䛛䜙ぢ䛯䠈㻿㼃㻺㼀 ୰䛻⏕ᡂ䛧䛯䜰䜲䝇䝘䝜䝏䝳䞊䝤ᵓ㐀䛸༳ຍ☢ሙ䛾ྥ䛝䜢♧䛧䛶䛔䜛䠊ෆໟỈศᏊ䛾Ỉ⣲ཎᏊ䛿ᑠ䛥䛺ⓑ⌫䛷⾲䜟䛧䛶䛚䜚䠈༳ຍ㟁ሙ䛜኱䛝䛟䛺䜛䛻䛴䜜䠈Ỉ䝏䜵䞊䞁䛜཯㌿䛩䜛ᵝᏊ䛜ぢ䛶䛸䜜䜛䠊㻌 ࢔࢖ࢫࢼࣀࢳ࣮ࣗࣈࡢึᮇศᴟ㐣⛬(9,8), (9,9), (10,10) SWNTs ෆࡢ 5, 6, 7 ဨ⎔ Ice-NTs ࡢ㟁ࡇࡢỈࢳ࢙࣮ࣥࡢ཯㌿࡜ྠ᫬࡟㟁Ẽ཮ᴟᏊ࣮࣓ࣔࣥࢺ

ሙ౫Ꮡᛶࢆ MD ࢩ࣑࣮ࣗࣞࢩࣙࣥ࡟ࡼࡾㄪ࡭ࡓ㸬 ᗘ

P ࡀࢫࢸࢵࣉ≧࡟ኚ໬ࡋ࡚࠸ࡿ㸬ࡍ࡞ࢃࡕỈศᏊࡢỌஂ

100 K ୍࡛ᐃ࡟ࡋࡓ≧ែ࡛㸪㟁ሙࢆࢳ࣮ࣗࣈ㍈᪉ྥ࡟༳཮ᴟᏊ࣮࣓ࣔࣥࢺࡀ㟁ሙ᪉ྥ࡟ຊࢆཷࡅ㸪Ỉࢳ࢙࣮ࣥ 1ຍࡋ㸪ࢮࣟ࠿ࡽࢫࢸࢵࣉ≧࡟༳ຍ㟁ሙࢆቑຍࡉࡏࡓ㸬⮬ᮏࡀ཯㌿ࡋ࡚࠸ࡿ㸬അᩘࡢ 6 ဨ⎔ Ice-NT ࡟ࡘ࠸࡚ࡶወᩘ

Ⓨศᴟࡢ᪉ྥ࡟ᑐࡋ࡚ṇ㈇ࡢ୧᪉ࡢྥࡁ࡟ࡘ࠸࡚ィ⟬ࡋࡢ 5, 7 ဨ⎔ Ice-NTs ࡜ྠᵝ࡟ P ࡀࢫࢸࢵࣉ≧࡟ኚ໬ࡍࡿ

࡚࠸ࡿ㸬ࡇࡢ࡜ࡁ㸪༳ຍ㟁ሙࢆኚ໬ࡉࡏࡓᚋ㸪ྛ㟁ሙ࡛⤖ᯝࢆᚓ࡚࠸ࡿ㸬

500 ps ಖᣢࡋࡓ㸬ึᮇᵓ㐀ࡣ 3-1 ࡛ᚓࡽࢀࡓ᭱ప ࡢ 5㸪
6㸪7 ဨ⎔ Ice-NTs ᵓ㐀࡜ࡋࡓ㸬ࢩࢫࢸ࣒ࢧ࢖ࢬࡣ⾲ 1 ࡟♧ࡋ࡚࠶ࡿ㸬

  ဨ⎔࢔࢖ࢫࢼࣀࢳ࣮ࣗࣈࡢศᴟᒚṔ
5 ဨ⎔ Ice-NT ࡟ࡘ࠸࡚ࢳ࣮ࣗࣈ㍈᪉ྥ࡟㟁ሙࢆ༳ຍࡋ㸪

5 ဨ⎔࡜ 7 ဨ⎔ Ice-NTs ࡛ࡢ⤖ᯝࢆࡑࢀࡒࢀᅗ 10㸪11ヲ⣽࡞ศᴟ㐣⛬ࢆㄪ࡭ࡓ㸬ึᮇᵓ㐀ࡣ 4-1 ࡜ྠᵝ࡟ 5 ဨ࡟♧ࡍ㸬㟁Ẽ཮ᴟᏊ࣮࣓ࣔࣥࢺ P ࡣྛ㟁ሙ୰࡛ 500 ps ಖ

⎔Ice-NT ᵓ㐀࡜ࡋ㸪ྛ㟁ሙ࡛500 ps ಖᣢࡋ㸪 ᗘ100, 175,ᣢࡋ㸪ࡑࡢ࠺ࡕࡢ 400 ps ࠿ࡽ 500 ps ࡢ᫬㛫ᖹᆒࢆ࡜ࡗࡓ㸬200, 225, 250 K ࡟ࡘ࠸࡚ィ⟬ࡋࡓ㸬༳ຍ㟁ሙ E=0 V/m ࠿ᅗࡢୗഃ࡟ࡣࢳ࣮ࣗࣈ㍈᪉ྥ࠿ࡽぢࡓ Ice-NT ࡢᵓ㐀ࡶ

ࡽ z ㍈᪉ྥ࡟㟁ሙࢆᙉࡃࡋ࡚࠸ࡁ㸪5 ᮏࡍ࡭࡚ࡢỈࢳ࢙♧ࡋ࡚࠸ࡿ㸬ᅗࡢ Ice-NT ᵓ㐀࡟࠶ࡿᑠࡉ࡞ⓑ⌫ࡣỈ⣲ཎ࣮ࣥࡀᥞࡗࡓ࡜ࡇࢁ࡛㸪z ㍈ࡢ㏫᪉ྥ࡟㟁ሙࢆᙉࡃࡋ࡚

Ꮚࢆ⾲ࢃࡋ࡚࠾ࡾ㸪༳ຍ㟁ሙࡀ኱ࡁࡃ࡞ࡿ࡟ᚑ࠸ Ice-NT࠸ࡃ࡜࠸࠺᧯సࢆ⧞ࡾ㏉ࡋ㸪ศᴟࣄࢫࢸࣜࢩࢫ࣮ࣝࣉࢆ

ᵓ㐀ࢆಖᣢࡋࡓࡲࡲỈࢳ࢙࣮ࣥࡀ཯㌿ࡋ࡚࠸ࡿࡇ࡜ࡀぢほᐹࡋࡓ㸬ࡲࡓ 320 K ࡟ࡘ࠸࡚ࡣᾮయ≧ែࡢึᮇᵓ㐀ࢆ࡚࡜ࢀࡿ㸬⏝࠸࡚⾜࡞ࡗࡓ㸬⚄ዉᕝ኱ᏛᕤᏛ◊✲ᡤᡤሗ ➨  ྕᅗ㻝㻝䠊ప 䠄㻝㻜㻜㻌㻷䠅䛷䛾 㻣 ဨ⎔䜰䜲䝇䝘䝜䝏䝳䞊䝤䛾ึᮇศᴟ㐣⛬䠊ୗ䛻䛿䝏䝳䞊䝤㍈᪉ྥ䛛䜙ぢ䛯䠈㻿㼃㻺㼀 ୰䛻⏕ᡂ䛧䛯䜰䜲䝇䝘䝜䝏䝳䞊䝤ᵓ㐀䛸༳ຍ☢ሙ䛾ྥ䛝䜢♧䛧䛶䛔䜛䠊ෆໟỈศᏊ䛾ᑠ䛥䛺ⓑ⌫䛿Ỉ⣲ཎᏊ䜢⾲䜟䛧䛶䛔䜛䠊㻌ᅗ 12 ࡟ᚓࡽࢀࡓศᴟࣄࢫࢸࣜࢩࢫ࣮ࣝࣉࢆ♧ࡍ㸬ࡇࡇ࡛ࡢ཮ᴟᏊ࣮࣓ࣔࣥࢺ P ࡣỈ 1 ศᏊ࠶ࡓࡾࡢ್࡛㸪ྛ㟁ሙ୰࡛ 500 ps ಖᣢࢆ⾜࡞ࡗࡓ࠺ࡕࡢ 400 ps ࠿ࡽ 500 psࡢᖹᆒࢆ࡜ࡗ࡚࠸ࡿ㸬225 K ௨ୗࡢศᴟ㐣⛬ࡣࢫࢸࢵࣉ
≧ࡢኚ໬ࢆ♧ࡋ࡚࠾ࡾ㸪ప ࡯࡝ࡑࡢࢫࢸࢵࣉࡀࡣࡗࡁᅗ 㻝㻞䠊୍ᐃ䛾 ᗘ䛷ಖᣢ䛧䛯䛸䛝䛾㻌 㻔㻥㻘㻤㻕㻌 㻿㼃㻺㼀 ෆໟỈ䠄㻡 ဨ⎔䜰䜲䝇䝘䝜䝏䝳䞊䝤䠅䛾ศᴟ㐣⛬䠊㻌ࡾ࡜ぢ࠼ࡿ㸬ࡲࡓ 175 K ௨ୗ࡛ࡣṧ␃ศᴟࡀ኱ࡁࡃ㸪175
K ࡛ࡣ 4.6 ᮏ㸪100 K ࡛ࡣ 5 ᮏࡢỈࢳ࢙࣮ࣥࡀᥞࡗࡓ≧ែࢆಖᣢࡋ࡚࠸ࡿ㸬ࡇࢀࡣ Ice-NT ࡀప ࡛ᙉㄏ㟁య࡜࡞ࡿࡇ࡜ࢆ♧ࡋ࡚࠸ࡿ㸬୍᪉㸪ᾮయ≧ែࡢ 320 K ࡛ࡣᖖㄏ㟁ᛶࡢ᣺ࡿ⯙࠸ࢆ♧  ဨ⎔ ,FH17 ࡢ㟁ሙ୰ࡢ෭༷
᭷㝈㟁ሙ୰࡛ࡢෆໟỈࡢᾮయ࠿ࡽ Ice-NT ࡬ࡢ┦㌿⛣ᣲືࢆ᫂ࡽ࠿࡟ࡍࡿࡓࡵ㸪㟁ሙ୰࡛ࡢ (9,8) SWNT ࡢෆࡋ㸪ࣄࢫࢸࣜࢩࢫࡣぢࡽࢀ࡞࠸㸬ᅗ 13 ࡟ 225 K ௨ୗ࡟࠾ໟỈࡢ෭༷㐣⛬ࢆ MD ィ⟬࡟ࡼࡾㄪ࡭ࡓ㸬㟁ሙ E ࡣࡅࡿศᴟࣄࢫࢸࣜࢩࢫ࣮ࣝࣉࢆ♧ࡍ㸬ప ࡛ࡣ඲య࡜ࡋ

SWNT ㍈᪉ྥ࡬༳ຍࡋࡓ㸬350 K ࡛ 1.5 ns ಖᣢࡋ㸪ࡑࡢ࡚ᙉㄏ㟁ᛶࡢࣄࢫࢸࣜࢩࢫࢆᣢࡘࡇ࡜ࡀࢃ࠿ࡿ㸬ᚋ㸪㝆 ㏿ᗘ 12.5 K/ns ࡛ 200 K ࡲ࡛෭༷ࡋࡓ㸬౑⏝ࡋࡇࡢᙉㄏ㟁ᛶࣄࢫࢸࣜࢩࢫ࡟ᑐᛂࡍࡿ༳ຍ㟁ሙ᪉ྥ㸦z㍈ṇ᪉ྥ㸧ࢆྥ࠸࡚࠸ࡿỈࢳ࢙࣮ࣥᩘࡢ㟁ሙ౫Ꮡᛶࢆᅗ
14 ࡟♧ࡍ㸬ࡇࢀࡽᅗ 13, 14 ࠿ࡽ᫂ࡽ࠿࡞ࡼ࠺࡟㸪Ice-NTࡓ⣔ࡣ 3.1 ࡢࢩ࣑࣮ࣗࣞࢩ࡛ࣙࣥ⏝࠸ࡓ(9,8) SWNT ࡛࠶ࡿ㸬
350 K ࡛ 1.5 ns ಖᣢࡋࡓᚋࡢᵓ㐀࡜ 200 K ࡢᵓ㐀ࢆᅗࡢศᴟࣄࢫࢸࣜࢩࢫ࣮ࣝࣉ࡟≉᭷࡞ࢫࢸࢵࣉ≧ࡢኚ໬ࡣ

15 ࡟♧ࡍ㸬ࢮࣟ㟁ሙ࡜ྠᵝ࡟㸪㟁ሙ࡟࠾࠸࡚ࡶ 5 ဨ⎔

Ice-NT ࡢศᴟࡀỈࢳ࢙࣮ࣥ 1 ᮏ༢఩ࡢศᴟ࡛㉳ࡇࡗ࡚࠸

Ice-NT ࡬ࡢ㌿⛣ࡀぢࡽࢀࡿ㸬Ỉ 1 ศᏊ࠶ࡓࡾࡢ㟁Ẽ཮ᴟࡿࡇ࡜࡟㉳ᅉࡋ࡚࠸ࡿ㸬Ꮚ࣮࣓ࣔࣥࢺ P ࡢᗘ౫Ꮡᛶࢆᅗ 16 ࡟♧ࡍ㸬P [C.m]࣮࢝࣎ࣥࢼࣀࢳ࣮ࣗࣈෆ㒊ࡢ  ḟඖⓗࢼࣀ✵㛫࡟㛢ࡌ㎸ࡵࡽࢀࡓỈࡢㄏ㟁≀ᛶ

6 10

-30

4 10

-30

2 10

-30



225K
100K
200K

0
-2 10

-30

-4 10

-30

-6 10

-30

175K

9

9

-2.4 10-1.6 10 -8 10

8

8

0

9

8 10 1.6 10 2.4 10

9E [V/m]ᅗ 㻝㻟䠊୍ᐃ ᗘ䠄䖃䠖㻝㻜㻜㻌㻷䠈䕔䠖㻝㻣㻡㻌㻷䠈䕺䠖㻞㻜㻜㻌㻷䠈䕦䠖㻞㻞㻡㻌㻷䠅䛷᪉ྥࢆྥ࠸࡚࠸ࡿỈࢳ࢙࣮ࣥࡢᩘ>ಶ@䛾 㻡 ဨ⎔䜰䜲䝇䝘䝜䝏䝳䞊䝤䛾ศᴟ䝠䝇䝔䝸䝅䝇䝹䞊䝥䠊㻌

225K

5
100K

4

200K

3
2
175K

1
0
9

9

-2.4 10-1.6 10 -8 10

8

0

8

9

8 10 1.6 10 2.4 10

9E[V/m]

ᅗ 㻝㻡䠊㟁ሙ୰䛷䛾㻔㻥㻘㻤㻕㻌㻿㼃㻺㼀 ෆໟỈ䛾ᵓ㐀䠊ୖ䛻䛿䝏䝳䞊䝤㍈᪉ྥ䛛䜙ぢ䛯ᅗ䠈ୗ䛻䛿ᶓ䛛䜙ぢ䛯ᅗ䠄㻿㼃㻺㼀 䛿⾲♧䛧䛶ᅗ㻝㻠䠊㻡ဨ⎔䜰䜲䝇䝘䝜䝏䝳䞊䝤୰䛾㟁ሙ᪉ྥ䜢ྥ䛔䛯Ỉ䝏䜵䞊䞁䛾ᮏᩘ䠄䖃䠖㻝㻜㻜㻌㻷䠈䕔䠖㻝㻣㻡㻌㻷䠈䕺䠖㻞㻜㻜㻌㻷䠈䕦䠖㻞㻞㻡㻌㻷䠅䠊㻌࡞࠾㸪ࡇࡢ್ࡣ 400 ps ࡈ࡜ࡢᖹᆒ್࡜ࡋ࡚ồࡵ࡚࠸ࡿ㸬䛔䛺䛔䠅䜢♧䛧䛶䛔䜛䠊㟁ሙ䜢༳ຍ䛧䛯ሙྜ䛷䜒䠈ప 䛷 㻡 ဨ⎔䜰䜲䝇䝘䝜䝏䝳䞊䝤䛜⏕ᡂ䛧䛶䛔䜛䛾䛜ぢ䛶䛸䜜䜛䠊㻌୍᪉㸪ᅗ 5 ࡜ᅗ 17 ࡢ࣏ࢸࣥࢩ࢚ࣕࣝࢿࣝࢠ࣮ PE ࡢྛࢢࣛࣇࡢᕥࡢᩘᏐࡣ᭱ప ࡢ 200 K ࡛㟁ሙ༳ຍ᪉ྥ㸦zᗘ౫Ꮡᛶࢆẚ㍑ࡍࡿ࡜㸪༳ຍ㟁ሙࡀ኱ࡁࡃ࡞ࡿ࡟ᚑ࠸㌿㍈ṇ᪉ྥ㸧ࢆྥ࠸࡚࠸ࡿỈࢳ࢙࣮ࣥࡢᮏᩘ࡛࠶ࡿ㸬ࡇࡢ⛣ ᗘ Tm ┤ୗ࡟ぢࡽࢀࡿ PE ࡢᛴ⃭࡞ῶᑡࡣぢ࠼࡟ࡃᗘ౫Ꮡᛶ࠿ࡽ 300 ~ 280 K ࠶ࡓࡾ࠿ࡽỈࢳ࢙࣮ࣥࡢྥ

ࡃ࡞ࡗ࡚࠸ࡿࡢࡀࢃ࠿ࡿ㸬ࡇࡢ┦㌿⛣ᣲືࡢ෭༷㐣⛬࡟ࡁࡀᥞ࠺ࡇ࡜ࡀࢃ࠿ࡾ㸪ࡇࡢ ᗘࡣࢮࣟ㟁ሙ࡛ࡢ 5 ဨ⎔ࡼࡿኚ໬ࢆㄪ࡭ࡿࡓࡵ࡟㸪ྠࡌ⣔ࢆ⏝࠸࡚ 300 K ࡛ 1 ns

Ice-NT ㌿⛣ ᗘ Tm ࡟࡯ࡰ୍⮴ࡋ࡚࠸ࡿ㸬ࡍ࡞ࢃࡕ㸪㌿ಖᣢࡋࡓᚋ࡟㝆 ㏿ᗘ 50 K/ns ࡛ 200 K ࡲ࡛෭༷ࡍࡿィ⛣ᗘ Tm ࡣ ༳ ຍ 㟁 ሙ ࡟ ࡼ ࡽ ࡎ ୍ ᐃ ࡛ ࠶ ࡿ 㸬⟬ࡶ⾜ࡗࡓࡀྠᵝࡢ⤖ᯝࡀᚓࡽࢀࡓ㸬⚄ዉᕝ኱ᏛᕤᏛ◊✲ᡤᡤሗ ➨  ྕᅗ㻝㻢䠊㟁ሙ୰䛷䛾㻔㻥㻘㻤㻕㻌㻿㼃㻺㼀ෆ䛾Ỉ㻝ศᏊ䛒䛯䜚䛾㟁Ẽ཮ᴟᏊ䝰䞊䝯䞁䝖㻌 㻼㻌 䛾 ᗘ౫Ꮡᛶ䠊ప 䛷 㻡 ဨ⎔䜰䜲䝇䝘䝜䝏䝳䞊䝤䛜ᙧᡂ䛥䜜䜛䛯䜑䠈㻼 䛿୍ᐃ್䛸䛺䜛䠊㻌ᅗ 㻝㻤䠊㻔㼍㻕㻌 ༙ᑟయᆺ䠈㻔㼎㻕㻌 㔠ᒓᆺ䠈㻔㼏㻕㻌 ᮍศ㞳 㻿㼃㻺㼀 䝞䞁䝗䝹ヨᩱ䛾⢊ᮎ 㼄 ⥺ᅇᢡ䝟䝍䞊䞁䠊ᤄධᅗ䛿䝏䝳䞊䝤㍈᪉ྥ䛛䜙ぢ䛯 㻿㼃㻺㼀 䝞䞁䝗䝹ᵓ㐀䛾୕ゅ᱁Ꮚ㻔㻥㻕䠊㻌ᅗ 㻝㻣䠊㟁ሙ୰䛷䛾 㻡 ဨ⎔䜰䜲䝇䝘䝜䝏䝳䞊䝤䛾⏕ᡂ䜢♧䛩䝫䝔䞁䝅䝱䝹䜶䝛䝹䜼䞊䛾 ᗘ౫Ꮡᛶ㻚㻌㸳㸬༙ᑟయᆺ࣭㔠ᒓᆺ࣮࢝࣎ࣥࢼࣀࢳ࣮ࣗࣈࡢ≀ᛶ
ࡍ࡛࡟㏙࡭ࡓࡼ࠺࡞࢔࢖ࢫࢼࣀࢳ࣮ࣗࣈࡢᙉㄏ㟁≉ᛶࢆ ᐃࡍࡿ࡟ࡣ㸪㧗⣧ᗘ࡞༙ᑟయ SWNT ヨᩱࡀᚲせ࡛࠶ࡿ㸬ࡋ࠿ࡋ㸪୍⯡࡟ SWNT ࡣ༙ᑟయᆺ࡜㔠ᒓᆺࡀΰᅾࡋ
ࡓࣂࣥࢻࣝヨᩱ࡜ࡋ࡚స〇ࡉࢀ㸪ࡲࡓ㔠ᒓゐ፹ࡸ࢔ࣔࣝ
ࣇ࢓ࢫⅣ⣲➼ࡢ୙⣧≀ࢆྵࢇ࡛࠸ࡿ㸬ࡑࡇ࡛ᐦᗘ໙㓄㐲ᚰศ㞳ἲ࡟ࡼࡾᮍ⢭〇 SWNT ヨᩱ࠿ࡽ༙ᑟయᆺ࡜㔠ᒓᆺ࡟ศ㞳ࡋࡓ SWNT ヨᩱࢆస〇ࡋ㸪ࡑࡢ≀ᛶホ౯ࢆ⾜ࡗࡓ㸬ᅗ㻝㻥䠊༙ᑟయᆺ䠈㔠ᒓᆺ䠈䜹䞊䝪䞁䝘䝜䝏䝳䞊䝤䛾ᅛయ 㻝㻟㻯㻌 ᰾☢Ẽඹ㬆䝇䝨䜽䝖䝹㻔㻥㻕䠊༙ᑟయヨᩱ䛿⢭〇᮲௳䛜␗䛺䜛 㻞 ✀㢮䠄㻏㻝 䛸㻏㻞䠅䛾䝇䝨䜽䝖䝹䜢♧䛧䛶䛔䜛䠊ཧ⪃䛾䛯䜑䛻䝣䝷䞊䝺䞁 㻯㻢㻜 ⤖ᬗ䛾䝇䝨䜽䝖䝹䜒⾲♧䛧䛶䛔䜛䠊ᤄධᅗ䛿ᮍศ㞳ヨᩱ䛾䝇䝨䜽䝖䝹㻔㻝㻜㻕䠊㻌࣮࢝࣎ࣥࢼࣀࢳ࣮ࣗࣈෆ㒊ࡢ  ḟඖⓗࢼࣀ✵㛫࡟㛢ࡌ㎸ࡵࡽࢀࡓỈࡢㄏ㟁≀ᛶ

ᅗ 18 ࡟ᮍศ㞳㸪༙ᑟయᆺ㸪㔠ᒓᆺ SWNT ࣂࣥࢻࣝヨᐃ࡛ࡣ㸪༙ᑟయᆺ࣭㔠ᒓᆺศ㞳 SWNT ヨᩱࡢಶయ 13C

ᩱࡢ⢊ᮎ XRD ࣃࢱ࣮ࣥࢆ♧ࡍ㸬3 ࡘࡢヨᩱࡍ࡭࡚࡟ࡘ࠸

NMR ಙྕࢆୡ⏺࡛ึࡵ࡚ほ ࡋ㸪ᚤどⓗ࡞㟁Ꮚ≧ែࢆ࡚Ἴᩘ Q ~ 4 nm-1 ௜㏆࡟ࡣࣂࣥࢻࣝᵓ㐀ࡢ୕ゅ᱁Ꮚ࡟⏤᫂ࡽ࠿࡟ࡋࡓ㸬௒ᚋ㸪ࡇࡢ㧗⣧ᗘ༙ᑟయᆺ SWNT ヨᩱࢆ᮶ࡍࡿࣆ࣮ࢡࡀ☜ㄆ࡛ࡁࡿ㸬ࡇࢀࡽࡢ XRD ࣃࢱ࣮ࣥ࠿

⏝࠸ࡿࡇ࡜࡟ࡼࡾ㸪MD ࢩ࣑࣮ࣗࣞࢩࣙࣥ࡟ࡼࡾ♧ࡉࢀ

ࡽ SWNT ᖹᆒ┤ᚄࡣ 1.44 nm ࡜Ỵᐃࡉࢀࡿ㸬ࡲࡓග྾཰

ࡓ࢔࢖ࢫࢼࣀࢳ࣮ࣗࣈࡢᙉ࣭཯ᙉㄏ㟁≉ᛶࢆ᳨ฟࡍࡿࡇ

ࢫ࣌ࢡࢺࣝ ᐃ⤖ᯝ࠿ࡽศ㞳ヨᩱࡢ⣧ᗘࡣ㸼㹼95%࡜ぢ࡜ࡀᮇᚅࡉࢀࡿ㸬✚ࡶࡽࢀࡿ㸬ࡇࢀࡽࡢヨᩱࢆ⏝࠸࡚㸪㔠ᒓᆺ SWNT ヨᩱᮏ◊✲ࡣ㸪୕ୖྐグ㸪ᐈ㔝㐶㸪ᰗ࿴ᘯ෸ᩍᤵ㸦㤳㒔኱࡜༙ᑟయᆺ SWNT ヨᩱࡢᅛయ 13C NMR ࢫ࣌ࢡࢺࣝほᏛᮾி㸧㸪∦ᾆᘯ㐨༤ኈ㸦⏘ᴗᢏ⾡⥲ྜ◊✲ᡤ㸧ࢆࡣࡌࡵ࡟ୡ⏺࡛ึࡵ࡚ᡂຌࡋࡓ㸦ᅗ 19㸧㸬ᅗ࠿ࡽ᫂ࡽ࠿࡞ࡼ࠺

࡜ࡍࡿከࡃࡢ᪉ࠎ࡜ࡢඹྠ◊✲࡛࠶ࡿ㸬ඹྠ◊✲⪅ࡢ࡟㸪ᮍศ㞳ヨᩱ࡟ẚ㍑ࡋ㸪㔠ᒓᆺ࣭༙ᑟయᆺࡢヨᩱࡢඹ᪉ࠎ࡟῝ࡃឤㅰ࠸ࡓࡋࡲࡍ㸬㬆⥺ᖜࡣ༑ศᑠࡉࡃ㸪ࡲࡓ C60 ࣇ࣮ࣛࣞࣥ⤖ᬗ࡜ྠᵝ࡟
sp2 ࣮࢝࣎ࣥ≉᭷ࡢ㠀ᑐ⛠ࢫ࣌ࢡࢺࣝ࡜࡞ࡗ࡚࠸ࡿ㸬ࡇࢀཧ⪃ᩥ⊩ࡣศ㞳⢭〇࡟ࡼࡾ㸪ヨᩱ୰ࡢ㔠ᒓゐ፹ࡀ࡯ࡰࡍ࡭࡚ྲྀࡾ

(1) S. Iijima and T. Ichihashi, Nature, 363 (1993) 603.

㝖࠿ࢀ࡚࠸ࡿࡇ࡜ࢆ♧ࡋ࡚࠸ࡿ㸬ࡇࢀࡽほ ࡉࢀࡓ༙ᑟ

(2) Y. Maniwa, H. Kataura, M. Abe, S. Suzuki, Y. Achiba, H. Kira and K.

యᆺ SWNT ࡢ 13C NMR ࢩࣇࢺࡣ㸪sp2 ΰᡂ㌶㐨࡟ࡼࡿ໬

Matsuda: J. Phys. Soc. Jpn., 71 (2002) 2863.

Ꮫࢩࣇࢺ࡜እ㒊☢ሙㄏ㉳⎔㟁ὶ࡟ࡼࡿ໬Ꮫࢩࣇࢺ㸪㔠ᒓ(3) Y. Maniwa, H. Kataura, M. Abe, A. Udaka, S. Suzuki, Y. Achiba, H.

ᆺSWNT ࡛ࡣࡇࢀࡽ2 ࡘࡢ໬Ꮫࢩࣇࢺ࡟ఏᑟ㟁Ꮚࢫࣆࣥ

Kira, K. Matsuda, H. Kadowaki and Y. Okabe: Chem. Phys. Lett., 401

࡟ࡼࡿ Knight ࢩࣇࢺࢆຍ࠼ࡿࡇ࡜࡟ࡼࡾㄝ࡛᫂ࡁࡿࡇ

(2005) 534-538.

(9)࡜ࢆ᫂ࡽ࠿࡟ࡋࡓ 㸬(4) K. Matsuda, T. Hibi, H. Kadowaki and Y. Maniwa: Phys. Rev. B 74
(2006) 073415.

㸴㸬ࡲ࡜ࡵỈศᏊࢆෆໟࡋࡓ SWNT ࡢ MD ࢩ࣑࣮ࣗࣞࢩࣙࣥࢆ

(5) H. Kyakuno, K. Matsuda, H. Yahiro, T. Fukuoka, Y. Miyata, K.
Yanagi, Y. Maniwa, H. Kataura, T. Saito, M. Yumura, and S. Iijima: J.

⾜࠸㸪ወᩘဨ⎔࢔࢖ࢫࢼࣀࢳ࣮ࣗࣈࡣࣇ࢙ࣜᙉㄏ㟁య㸪

Phys. Soc. Jpn., 79 (2010) 083802.

അᩘဨ⎔࢔࢖ࢫࢼࣀࢳ࣮ࣗࣈࡣ཯ᙉㄏ㟁య࡜࡞ࡾ㸪ࡇࢀ(6) K. Koga, G. T. Gao, H. Tanaka and X. C. Zeng: Nature, 412 (2001)ࡽ࢔࢖ࢫࢼࣀࢳ࣮ࣗࣈࡢศᴟࡢྥࡁࡣእ㒊㟁ሙ࡟ࡼࡾไ

802.

ᚚྍ⬟࡛࠶ࡿࡇ࡜ࡀ᫂ࡽ࠿࡟࡞ࡗࡓ㸬ࡇࢀࡽࡢ⤖ᯝࡣ㸪(7) J. Shiomi, T. Kimura, and S. Maruyama: J. Phys. Chem. C 111 (2007)࢔࢖ࢫࢼࣀࢳ࣮ࣗࣈࡣཎ⌮ⓗ࡟ᴟᚤᑠࡢከ್ㄏ㟁య࣓ࣔ

12188.

ࣜᮦᩱ࡜ࡋ࡚฼⏝ྍ⬟࡛࠶ࡿࡇ࡜ࢆ♧ࡋ࡚࠸ࡿ㸬୍⯡࡟(8) D. Takaiwa, I. Hatano, K. Koga, and H. Tanaka: Proc. Natl. Acad. Sci.

SWNT ࡣ㔠ᒓᆺ࡜༙ᑟయᆺࡀΰᅾࡋࡓࣂࣥࢻࣝ࡜ࡋ࡚

USA. 105 (2008) 39.

స〇ࡉࢀࡿࡀ㸪ࡇࢀࡽࡢㄏ㟁≉ᛶࢆほ ࡍࡿ࡟ࡣ㧗⣧ᗘ(9) K. Matsuda, K. Yanagi, H. Kyakuno, S. Sagitani, H. Kataura, and Y.

ࡢ༙ᑟయᆺ SWNT ヨᩱࡀᚲせ࡜࡞ࡿ㸬ࡑࡇ࡛㸪ᐦᗘ໙㓄

Maniwa: J. Phys. Soc. Jpn. 82 (2013) 015001.

㐲ᚰศ㞳ἲ࡟ࡼࡾ༙ᑟయᆺ࡜㔠ᒓᆺࡢ㧗⣧ᗘ SWNT ヨ(10) K. Matsuda, Y. Maniwa, and H. Kataura: Phys. Rev. B 77 (2008)ᩱ㸦>㹼95%㸧ࢆస〇ࡋ≀ᛶホ౯ࢆ⾜ࡗࡓ㸬≉࡟ NMR

075421.

ࢡ࢜ࣥࢸ࢖ࣝ࡜᏶ഛ࡭ࡁ➼ᕥ༙⎔ࡢ⾲⌧ᐃ⌮す⃝ ᘯẎ㸨   ྂ⃝ ோ㸨㸨

Representation Theorems for Quantales and Complete Idempotent Left Semirings
Koki NISHIZAWA㸨

Hitoshi FURUSAWA㸨㸨are binary relations on ܳ. However, the order of the quantale

㸯㸬Introduction
This paper shows representation theorems for quantales andis not given by inclusion, but the opposite order of inclusion.
Brown and Gurr(9) show that a completely coprime algebraic

complete idempotent left semirings.
(1)

Quantales were introduced by Mulvey in order to provide aquantale ܳ is isomorphic to a sub-quantale of the quantale

constructive formulation of foundations of quantum mechanics.

whose elements are binary relations on ܳ and whose order is

They are complete join semilattices together with a monoid

given by inclusion. However, the unit of the monoid structure

structure satisfying the distributive laws. In the literature, theyof the quantale is not equal to the identity relation.

are also known as complete idempotent semirings or standard(2)

Kleene algebras .

Palmigiano and Re(10) give a sufficient condition for aquantale to be isomorphic to a sub-quantale of the quantale

There is a relational quantale whose elements are binary

whose elements are binary relations on a set and whose order isrelations on a set, whose order is given by inclusion, and whose

given by inclusion and whose monoid structure is given by

monoid structure is given by relational composition and therelational composition and the identity relation. Indeed, thisidentity relation. Relational quantales play an important role inresult means `relational representation theorem'. It is importantcomputer science. For example, they are models for the

point to embed a quantale ܳ in the relations not on ܳ but on(3,4)

semantics of non-deterministic while-programs , they also
provides a sound and complete class of models for linear
intuitionistic logic(5), and so on.

the set of all atoms of ܳ.
However, the result given in the paper(10) is a relational
representation theorem for `unital involutive quantales'. A

In Stone's representation theorem for Boolean algebra orquantale ܳ is involutive if it is endowed with a unary

Priestley's representation theorem for bounded distributive

operation ݂. such that, for all ܽǡ ܾ ‫ ܳ א‬and every ܵ ‫ܳ ك‬,

lattices, a powerset is regarded as a standard Boolean algebra
(6,7)

1.

݂ሺ݂ሺܽሻሻ ൌ ܽ,or a standard bounded distributive lattice . On the other hand,2.

݂ሺܽ ‫ܾ ڄ‬ሻ ൌ ݂ሺܾሻ ‫݂ ڄ‬ሺܽሻ,

since a relational quantale has been regarded as a `standard3.

݂ሺ‫ܵڀ‬ሻ ൌ ሼ݂ሺܽሻȁܽ ‫ܵ א‬ሽ.

quantale', some results called `relational representation theorem

This paper gives a relational representation theorem forfor quantales' have been shown in the literature.
However, relational quantales in their results are not equal to
the standard relational quantales.
(8)

For example, Valentini

shows that a quantale ܳ isisomorphic to a sub-quantale of the quantale whose elements*෸ᩍᤵ ᝟ሗࢩࢫࢸ࣒๰ᡂᏛ⛉Associate Professor, Dept. of Information Systems Creation**෸ᩍᤵ ᩘ⌮᝟ሗ⛉Ꮫᑓᨷ 㮵ඣᓥ኱Ꮫ኱Ꮫ㝔
Associate Professor, Dept. of Mathematics and Computer
Science, Kagoshima University

quantales which are not in general involutive. Similarly to thepapers(10,11), our representation theorem shows that a quantale
ܳ satisfying some condition is isomorphic to a sub-quantale ofthe quantale whose elements are binary relations on the set of
all atoms of ܳ(12,13).
The main theorem Theorem 4 of this paper says that for aquantale ܳ, the following are equivalent.
1.

ܳ has a relational representation in our way and it is
CCP-invertible.

ࢡ࢜ࣥࢸ࢖ࣝ࡜᏶ഛ࡭ࡁ➼ᕥ༙⎔ࡢ⾲⌧ᐃ⌮2.

ܳ is isomorphic to Եሺܺሻ as complete jointerminology in this section relies on the paper(9).

semilattice for some set ܺ.

Definition 1 (complete join semilattice).



A complete join semilattice is a tupleሺ‫ܭ‬ǡ ൑ǡ ‫ڀ‬ሻ with the3.

ܳ is atom-algebraic and it is a frame.

4.

ܳ is atom-algebraic and its atoms are completely

following properties:

coprime.

1.

ሺ‫ܭ‬ǡ ൑ሻ is a partially ordered set.

ܳ2.

‫ ܵڀ‬is the join (i.e., the least upper bound) for each5.

is completely coprime algebraic and its

subset ܵ of ‫ܭ‬.

completely coprime elements are atoms.
6.

ܳ is is completely coprime algebraic and the order of

A complete join semilattice must have the least element,
which is the join of the empty subset. We write ٣ for it.

its completely coprime elements is discrete.
This theorem asserts that a quantale has a relational

A complete join semilattice must be a complete lattice, since

representation, if it is isomorphic to a powerset as complete

the meet of a subsetܵ is the join of all lower bounds ofܵ. We

join semilattice. A powerset quantale has four other equivalent

writeܽ ‫ ܾ ר‬for the meet of ሼܽǡ ܾሽ.

conditions. The notion of a CCP-invertible quantale is defined

Definition 2.
An element ‫ ݔ‬of a complete join semilatticeܳ is calledin this paper. When a quantale is CCP-invertible, it has arelational representation in our way if and only if it iscompletely coprime (or completely join-prime), if

isomorphic to a powerset as complete join semilattice.

‫ ݔ‬൑ ሧ ܵ  ฻  ‫ܵ א ܽ׌‬Ǥ ‫ ݔ‬൑ ܽPowerset quantales are examples of `completely coprime
algebraic quantales' which is the sufficient condition given infor each subset ܵ of ܳ.

(9)

We write ۱۱‫۾‬ሺܳሻ for the set of all completely coprime

the paper . However, our result is not an application of theresult in the paper(9) to powerset quantales, since ourelements of ܳ.

representation theorem embeds a quantaleܳ in the relations

Remark 1.

not onܳ but on the set of all atoms ofܳ.

٣ is not completely coprime, since ٣ൌ ‫׎ڀ‬.

Similarly to quantales, we also show a representation theorem
for powerset complete idempotent left semirings(14). Complete

Definition 3 (completely coprime algebraic).
A complete join semilattice ܳ is called completely coprime

idempotent left semirings are a relaxation of quantales byalgebraic (or CCPA) if for each ܽ ‫ܳ א‬, the following equation

giving up strictness and distributivity of composition overholds.

arbitrary joins from the left. We show that powerset completeܽ ൌ ሧሼ‫ א ݔ‬۱۱‫۾‬ሺܳሻȁ‫ ݔ‬൑ ܽሽ

idempotent left semirings can be represented not only byrelations but also by multirelations.

Definition 4 (quantale (or complete idempotent semiring)).

This paper is organized as follows. Section 2 defines

A quantale is a tuple ሺ‫ܭ‬ǡ ൑ǡ ‫ڀ‬ǡ‫ ڄ‬ǡͳሻ with the following

completely coprime algebraic quantales and Section 3 defines

properties:

powerset quantales. Section 4 shows that a quantale has a1.

ሺ‫ܭ‬ǡ‫ ڄ‬ǡͳሻ is a monoid.

relational representation, if it is isomorphic to a powerset as2.

ሺ‫ܭ‬ǡ ൑ǡ ‫ڀ‬ሻ is a complete join semilattice.

complete join semilattice. Section 5 shows that a quantale3.

ሺ‫ܵڀ‬ሻ ‫ ܽ ڄ‬ൌ ‫ڀ‬ሼܾ ‫ܽ ڄ‬ȁܾ ‫ܵ א‬ሽ for each element ܽ andeach subset ܵ of ‫ܭ‬.

satisfies the condition, if it has a relational representation in ourway and it is CCP-invertible. Section 6 shows a multirelationalܽ ‫ ڄ‬ሺ‫ܵڀ‬ሻ ൌ ‫ڀ‬ሼܽ ‫ܾ ڄ‬ȁܾ ‫ܵ א‬ሽ for each element ܽ and4.

each subset ܵ of ‫ܭ‬.

representation theorem for powerset complete idempotent leftsemirings. Section 7 summarizes this work and discusses

A quantale ሺ‫ܭ‬ǡ ൑ǡ ‫ڀ‬ǡ‫ ڄ‬ǡͳሻ is called completely coprime
algebraic if ሺ‫ܭ‬ǡ ൑ǡ ‫ڀ‬ሻ is completely coprime algebraic.

future work.

Example 1.
㸰㸬Completely Coprime Algebraic Quantales

For a set ‫ ܣ‬, the tuple‫ܔ܍܀‬ሺ‫ܣ‬ሻ ൌ ሺ‫ܭ‬ǡ ൑ǡ ‫ڀ‬ǡ‫ ڄ‬ǡͳሻ forms a

In this section, we recall the notion of completely coprime

quantale where

algebraic quantales and show some examples. A quantale isz‫ ܭ‬is the set of all binary relations on ‫ܣ‬,

called completely coprime algebraic depending only on itsz൑ is the inclusion ‫ك‬,z‫ ڀ‬is the union operator ‫ڂ‬,underlying

completejoinsemilattice

structure.

The⚄ዉᕝ኱ᏛᕤᏛ◊✲ᡤᡤሗ ➨  ྕzܴ ‫ ܳ ڄ‬is the composition of ܴ and ܳ, andzͳis the identity (diagonal) relation on ‫ܣ‬.

z‫ ܵ ڀ‬is the minimum number of ܵ except for‫ڀ‬ሼ߱ሽ ൌ ‫ ׎ ڀ‬ൌ ߱,

Here, the composition ܴ ‫ ܳ ڄ‬is defined as follows.
ሺǡ ሻ ‫ ܳ ڄ ܴ א‬฻ ‫ܣ א ܿ׌‬Ǥ ሺܽǡ ܿሻ ‫ܴ א‬ሺܿǡ ܾሻ ‫)ܳ א‬zܽ ‫ ܾ ڄ‬isܽ ൅ ܾexcept for ɘ ‫  ڄ‬ൌ ܽ ‫ ߱ ڄ‬ൌ ߱, andzͳis the zero number.

A binary relation on ‫ ܣ‬is completely coprime in ‫ܔ܍܀‬ሺ‫ܣ‬ሻ ifThis quantale is completely coprime algebraic and ۱۱‫۾‬ሺԳ ‫׫‬and only if it is a singleton subset of ‫ ܣ‬ൈ ‫ܣ‬. ‫ܔ܍܀‬ሺ‫ܣ‬ሻ isሼ߱ሽሻ ൌ Գ.

completely coprime algebraic, since forܴ ‫ܔ܍܀ א‬ሺ‫ܣ‬ሻ,㸱㸬Powerset Quantales
In this section, we recall the notion of atom and define theራሼܳ ‫ א‬۱۱‫۾‬ሺ‫ܔ܍܀‬ሺ‫ܣ‬ሻሻȁܳ ‫ܴ ك‬ሽnotion of atom-algebraic. We compare a powerset semilatticewith the four conditions based on completely coprime elementsൌ ራሼሼሺܽǡ ܽԢሻሽȁሼሺܽǡ ܽԢሻሽ ‫ܴ ك‬ሽor atoms. Finally, we define the notion of powerset quantale.

ൌ ሼሺܽǡ ܽԢሻȁሺܽǡ ܽԢሻ ‫ܴ א‬ሽDefinition 5 (atom).

ൌܴ

An atom of a complete join semilatticeܳ is an element‫ ݔ‬with‫ז‬

the following properties:1.

‫് ݔ‬٣.

gives only two examples for monoids.

2.

ܽ ൏ ‫ ݔ‬implies ܽ ൌ٣.

Example 2.

We write ‫ܕܗܜۯ‬ሺܳሻ for the set of all atoms of ܳ.

The powerset of a monoid forms a quantale. This paper

For a set ȭ , the tuple Եሺȭ ‫ כ‬ሻ ൌ ሺ‫ܭ‬ǡ ൑ǡ ‫ڀ‬ǡ‫ ڄ‬ǡͳሻ forms a

Definition 6 (atom-algebraic).

quantale where

A complete join semilattice ܳ is called atom-algebraic if forz‫ ܭ‬is the powerset of ȭ ‫ כ‬where ȭ ‫ כ‬is the set of alleach ܽ ‫ܳ א‬, the following holds.

finite sequences of elements of ȭ,z൑ is the inclusion ‫ك‬,z‫ ڀ‬is the union operator ‫ڂ‬,ܽ ൌ ሧሼ‫ܕܗܜۯ א ݔ‬ሺܳሻȁ‫ ݔ‬൑ ܽሽ
We also recall the notion of frame.

zܴ ‫ ܳ ڄ‬is ሼߪߨȁߪ ‫ܴ א‬ǡ ߨ ‫ܳ א‬ሽ, andDefinition 7 (frame).

zͳis the singleton set of the empty sequence on ‫ܣ‬.

A complete join semilattice ܳ is called a frame if

A subset of ȭ ‫ כ‬is completely coprime if and only if it is aܽ ‫ ר‬ሧ ܵ ൌ ሧሼܽ ‫ݏ ר‬ȁ‫ܵ א ݏ‬ሽsingleton subset. Եሺȭ ‫ כ‬ሻ is completely coprime algebraic.
Example 3.

for each element ܽ and each subset ܵ of ܳ.

The tuple ԵሺԺଶ ሻ ൌ ሺ‫ܭ‬ǡ ൑ǡ ‫ڀ‬ǡ‫ ڄ‬ǡͳሻ forms a quantale where

Example 5.
In‫ܔ܍܀‬ሺ‫ܣ‬ሻ of Example 1, Եሺȭ ‫ כ‬ሻ of Example 2, and ԵሺԺଶ ሻz‫ܭ‬Ժଶ ൌ ሺሼͲǡͳሽǡ ൅ǡͲǡ െሻ,of Example 3, an element is an atom if and only if it is az

൑ is the inclusion ‫ك‬,

singleton subset. They are atom-algebraic and they are frames.

z‫ ڀ‬is the union operator ‫ڂ‬,

Theorem 1.

z‫ ܤ ڄ ܣ‬is ሼܽ ൅ ܾȁܽ ‫ܣ א‬ǡ ܾ ‫ܤ א‬ሽ, andFor a complete join semilattice ܳ, the following are equivalent.

zͳis the set ሼͲሽ.

1.

ܳ is isomorphic to Եሺܺሻ for some set ܺ.

A subset of Ժଶ is completely coprime if and only if it is a2.

ܳ is atom-algebraic and it is a frame.

singleton subset. This quantale is completely coprime3.

ܳ is atom-algebraic and its atoms are completely

is

the

powerset

of

the

group

algebraic.
Example 4.

coprime.
4.

The tuple Գ ‫ ׫‬ሼ߱ሽ ൌ ሺ‫ܭ‬ǡ ൑ǡ ‫ڀ‬ǡ‫ ڄ‬ǡͳሻ forms a quantale wherez‫ ܭ‬is the set of all natural numbers and the additional

coprime elements are atoms.
5.

element ɘ,zܳ is completely coprime algebraic and its completely
ܳ is completely coprime algebraic and the order of its
completely coprime elements is discrete.

ܽ ൑ ܾ if and only if ܽ ൌ ߱, ܽ ൌ ܾ, or ܽ is a

Proof.

natural number greater than ܾ,(ͳ ֜ ʹ)ࢡ࢜ࣥࢸ࢖ࣝ࡜᏶ഛ࡭ࡁ➼ᕥ༙⎔ࡢ⾲⌧ᐃ⌮

A subset ܻ of ܺ is an atom in Եሺܺሻ if and only if ܻ is a

Since the order of ۱۱‫۾‬ሺܳሻ is discrete, an arbitrary subset of

singleton subset. Եሺܺሻ is an atom-algebraic frame.

۱۱‫۾‬ሺܳሻ is down-closed. Therefore, ܻ ‫ ك‬۱۱‫۾‬ሺܳሻ satisfies(ʹ ֜ ͵)݂ሺ݃ሺܻሻሻ

Let us show that an atom ‫ ݔ‬of a frame ܳ is completely
coprime, that is,ൌ ሼ‫ א ݔ‬۱۱‫۾‬ሺܳሻȁ‫ ݔ‬൑ ሧ ܻሽൌ ሼ‫ א ݔ‬۱۱‫۾‬ሺܳሻȁ‫ܻ א ݕ׌‬Ǥ ‫ ݔ‬൑ ‫ݕ‬ሽ‫ ݔ‬൑ ሧ ܵ  ฻  ‫ܵ א ݏ׌‬Ǥ ‫ ݔ‬൑ ‫ݏ‬ൌ ܻ.

for each subset ܵ of ܳ. RHS implies LHS, since ‫ ݔ‬൑ ‫ ݏ‬൑‫ז‬‫ܵ ڀ‬. To show that LHS implies RHS, assume that ‫ ݔ‬൑ ‫ܵ ڀ‬.

When these conditions are satisfied by a quantale, we call it

Sinceܳ is a frame and ‫ ݔ‬൑ ‫ܵ ڀ‬, we have ‫ ݔ‬ൌ ‫ ܵ ڀ ר ݔ‬ൌ

a powerset quantale. Every powerset quantale ܳ satisfies‫ڀ‬ሼ‫ݏ ר ݔ‬ȁ‫ܵ א ݏ‬ሽ . Since‫ ݔ‬is an atom, we have ‫ڀ‬ሼ‫ר ݔ‬۱۱‫۾‬ሺܳሻ ൌ ‫ܕܗܜۯ‬ሺܳሻ.

‫ݏ‬ȁ‫ܵ א ݏ‬ሽ ്٣ . Therefore, there exists ‫ ܵ א ݏ‬satisfying

Example 6.

‫് ݏ ר ݔ‬٣. Since‫ݔ‬is an atom and ٣് ‫ ݏ ר ݔ‬൑ ‫ݔ‬, we have‫ܔ܍܀‬ሺ‫ܣ‬ሻ in Example 1, Եሺȭ ‫ כ‬ሻ in Example 2, and ԵሺԺଶ ሻ in‫ ݏ ר ݔ‬ൌ ‫ݔ‬. Therefore, we have ‫ ݔ‬൑ ‫ݏ‬.

Example 3 are powerset quantales.

(͵ ֜ Ͷ)We also give an example of completely coprime algebraic

Let ܳ be atom-algebraic and assume that its atoms arequantale which is not a powerset quantale.

completely coprime. ܳ is completely coprime algebraic, since

Example 7.

the following holds.

Գ ‫ ׫‬ሼ߱ሽ in Example 4 is completely coprime algebraic and it
is a frame. However, it has no atoms. Therefore, it is not aܽ ൌ ሧሼ‫ܕܗܜۯ א ݔ‬ሺܳሻȁ‫ ݔ‬൑ ܽሽ

powerset quantale.

൑ ሧሼ‫ א ݔ‬۱۱‫۾‬ሺܳሻȁ‫ ݔ‬൑ ܽሽ㸲㸬Representation Theorem for Powerset Quantales൑ ܽ

This section shows that a powerset quantale has a relationalLetܽbe completely coprime. The following holds.

representation.

ܽ ൑ ܽ

Theorem 2.
Let ሺܳǡ ൑ǡ ‫ڀ‬ǡ‫ ڄ‬ǡͳሻ฻ ܽ ൌ ሧሼ‫ܕܗܜۯ א ݔ‬ሺܳሻȁ‫ ݔ‬൑ ܽሽ

be a quantale. If ܳ is a powerset

quantale, then the following function ߟ ‫ ܳ ׷‬՜ ‫ܔ܍܀‬ሺ۱۱‫۾‬ሺܳሻሻ฻ ‫ܕܗܜۯ א ݔ׌‬ሺܳሻǤ ܽ ൑ ‫ ݔ‬൑ ܽ

is an injective homomorphism of quantales.
ߟሺܽሻ ൌ ሼሺ‫ݔ‬ǡ ‫ݕ‬ሻȁ‫ א ݔ‬۱۱‫۾‬ሺܳሻǡ ‫ א ݕ‬۱۱‫۾‬ሺܳሻǡ ‫ ݔ‬൑ ܽ ‫ݕ ڄ‬ሽ฻ ܽ ‫ܕܗܜۯ א‬ሺܳሻ
Therefore,ܽ is an atom.

Proof.

(Ͷ ֜ ͷ)By Theorem 1, ܳ is completely coprime algebraic and theLet ܳ be completely coprime algebraic and assume that its

order of its completely coprime elements is discrete.

completely coprime elements are atoms. Assume that there are(ߟ preserves joins)completely coprime elements ܽǡ ܾ satisfying ܽ ൑ ܾ andܽ ് ܾ. Since ܾ is also an atom, ܽ ൌ٣. But since ܽ is also
an atom, ܽ ്٣. It is a contradiction. Therefore, the order ofcompletely coprime elements is discrete.
(ͷ ֜ ͳ)Let ܳ be completely coprime algebraic and assume that theሺ‫ݔ‬ǡ ‫ݕ‬ሻ ‫ߟ א‬ሺሧ ܵሻ฻ ‫ ݔ‬൑ ሺሧ ܵሻ ‫ݕ ڄ‬฻ ‫ ݔ‬൑ ሧሼܽ ‫ݕ ڄ‬ȁܽ ‫ܵ א‬ሽorder of its completely coprime elements is discrete. Let ݂ be

฻ ‫ܵ א ܽ׌‬Ǥ ‫ ݔ‬൑ ܽ ‫ݕ ڄ‬

a function ݂ ‫ ܳ ׷‬՜ Եሺ۱۱‫۾‬ሺܳሻሻ such that ݂ሺܽሻ ൌ ሼ‫א ݔ‬฻ ‫ܵ א ܽ׌‬Ǥ ሺ‫ݔ‬ǡ ‫ݕ‬ሻ ‫ߟ א‬ሺܽሻ۱۱‫۾‬ሺܳሻȁ‫ ݔ‬൑ ܽሽ

.

Let

݃

be

a

function݃ ‫ ׷‬Եሺ۱۱‫۾‬ሺܳሻሻ ื ܳ such that ݃ሺܵሻ ൌ ‫ ܵ ڀ‬. We have(by ‫ א ݔ‬۱۱‫۾‬ሺܳሻ)฻ ሺ‫ݔ‬ǡ ‫ݕ‬ሻ ‫ א‬ራሼߟሺܽሻȁܽ ‫ܵ א‬ሽǤܽ ൌ ݃ሺ݂ሺܽሻሻ for all ܽ ‫ ܳ א‬, since ݃ሺ݂ሺܽሻሻ ൌ ‫ڀ‬ሼ‫א ݔ‬(ߟ preserves ‫)ڄ‬۱۱‫۾‬ሺܳሻȁ‫ ݔ‬൑ ܽሽ and ܳ is completely coprime algebraic.

ሺ‫ݔ‬ǡ ‫ݕ‬ሻ ‫ߟ א‬ሺܽ ‫ܽ ڄ‬Ԣሻ⚄ዉᕝ኱ᏛᕤᏛ◊✲ᡤᡤሗ ➨  ྕSince ۱۱‫۾‬ሺ‫ܔ܍܀‬ሺ‫ܣ‬ሻሻ is the set of singleton subsets of ‫ ܣ‬ൈ ‫ܣ‬,฻ ‫ ݔ‬൑ ܽ ‫ܽ ڄ‬Ԣ ‫ݕ ڄ‬ߟ can be also given as follows.

฻ ‫ ݔ‬൑ ܽ ‫ ڄ‬ሧሼ‫ א ݖ‬۱۱‫۾‬ሺܳሻȁ‫ ݖ‬൑ ܽԢ ‫ݕ ڄ‬ሽߟሺܴሻൌ ሼሺሼሺ‫ݏ‬ǡ ‫ݐ‬ሻሽǡ ሼሺ‫ݑ‬ǡ ‫ݒ‬ሻሽሻȁ‫ݏ‬ǡ ‫ݐ‬ǡ ‫ݑ‬ǡ ‫ܣ א ݒ‬ǡ ሺ‫ݏ‬ǡ ‫ݐ‬ሻ ‫ ڄ ܴ א‬ሼሺ‫ݑ‬ǡ ‫ݒ‬ሻሽሽ฻ ‫ ݔ‬൑ ሧሼܽ ‫ݖ ڄ‬ȁ‫ א ݖ‬۱۱‫۾‬ሺܳሻǡ ‫ ݖ‬൑ ܽԢ ‫ݕ ڄ‬ሽൌ ሼሺሼሺ‫ݏ‬ǡ ‫ݐ‬ሻሽǡ ሼሺ‫ݑ‬ǡ ‫ݐ‬ሻሽሻȁ‫ݏ‬ǡ ‫ݐ‬ǡ ‫ܣ א ݑ‬ǡ ሺ‫ݏ‬ǡ ‫ݐ‬ሻ ‫ ڄ ܴ א‬ሼሺ‫ݑ‬ǡ ‫ݐ‬ሻሽሽ฻ ‫ א ݖ׌‬۱۱‫۾‬ሺܳሻǤ ‫ ݔ‬൑ ܽ ‫ ݖݖ ڄ‬൑ ܽԢ ‫ݕ ڄ‬ൌ ሼሺሼሺ‫ݏ‬ǡ ‫ݐ‬ሻሽǡ ሼሺ‫ݑ‬ǡ ‫ݐ‬ሻሽሻȁ‫ܣ א ݐ‬ǡ ሺ‫ݏ‬ǡ ‫ݑ‬ሻ ‫ܴ א‬ሽ฻ ‫ א ݖ׌‬۱۱‫۾‬ሺܳሻǤ ሺ‫ݔ‬ǡ ‫ݖ‬ሻ ‫ߟ א‬ሺܽሻሺ‫ݖ‬ǡ ‫ݕ‬ሻ ‫ߟ א‬ሺܽԢሻ

Example 9.

(ߟ preserves ͳ)

Similarly, Եሺȭ ‫ כ‬ሻ in Example 2 has a relational representation.

ሺ‫ݔ‬ǡ ‫ݕ‬ሻ ‫ߟ א‬ሺͳሻ

The

is

injective

‫כ‬

from

Եሺȭ ‫ כ‬ሻto‫כ‬‫ܔ܍܀‬ሺ۱۱‫۾‬ሺԵሺȭ ሻሻሻ ؆ ‫ܔ܍܀‬ሺȭ ሻ . The map ߟ is given as฻‫ ݔ‬൑ͳ‫ݕڄ‬฻‫ݔ‬൑‫ݕ‬฻‫ݔ‬ൌ‫ݕ‬ߟ

mapfollows.
ߟሺܴሻ ൌ ሼሺܲǡ ܳሻȁܲǡ ܳ ‫ א‬۱۱‫۾‬ሺԵሺȭ ‫ כ‬ሻሻǡ ܲ ൑ ܴ ‫ܳ ڄ‬ሽ(since CCP(Q) is discrete)(ߟ is injective)

Since ۱۱‫۾‬ሺԵሺȭ ‫ כ‬ሻሻ is the set of singleton subsets of ȭ ‫ כ‬, ߟ

For all ܽ ‫ܳ א‬, we have the following equation.

can be also given as follows.

ܽߟሺܴሻ ൌ ሼሺሼߪሽǡ ሼߨሽሻȁߪǡ ߨ ‫ א‬ȭ ‫ כ‬ǡ ሼߪሽ ‫ ڄ ܴ ك‬ሼߨሽሽ

ൌܽ‫ͳڄ‬

ൌ ሼሺሼߪሽǡ ሼߨሽሻȁߪǡ ߨ ‫ א‬ȭ ‫ כ‬ǡ ߪ ‫ ڄ ܴ א‬ሼߨሽሽൌ ሼሺሼ߬ߨሽǡ ሼߨሽሻȁߨ ‫ א‬ȭ ‫ כ‬ǡ ߬ ‫ܴ א‬ሽൌ ሧሼ‫ א ݔ‬۱۱‫۾‬ሺܳሻȁ‫ ݔ‬൑ ܽ ‫ͳ ڄ‬ሽ

Example 10.

ൌ ሧሼ‫ א ݔ‬۱۱‫۾‬ሺܳሻȁ‫ ݔ‬൑ ܽ ‫ ڄ‬ሧሼ‫ א ݕ‬۱۱‫۾‬ሺܳሻȁ‫ ݕ‬൑ ͳሽሽSimilarly, ԵሺԺଶ ሻ in Example 3 has a relational representation.
The injective map ߟ from ԵሺԺଶ ሻ to ‫ܔ܍܀‬ሺ۱۱‫۾‬ሺԵሺԺଶ ሻሻሻ
is given as follows.

ൌ ሧሼ‫ א ݔ‬۱۱‫۾‬ሺܳሻȁ‫ ݔ‬൑ ሧሼܽ ‫ݕ ڄ‬ȁ‫ א ݕ‬۱۱‫۾‬ሺܳሻǡ ‫ ݕ‬൑ ͳሽሽߟሺ‫ܣ‬ሻ ൌ ሼሺ‫ܤ‬ǡ ‫ܥ‬ሻȁ‫ܤ‬ǡ ‫ א ܥ‬۱۱‫۾‬ሺԵሺԺଶ ሻሻǡ ‫ ܤ‬൑ ‫ܥ ڄ ܣ‬ሽSince ۱۱‫۾‬ሺԵሺԺଶ ሻሻ is the set of singleton subsets of Ժଶ , ߟൌ ሧሼ‫ א ݔ‬۱۱‫۾‬ሺܳሻȁ‫ א ݕ׌‬۱۱‫۾‬ሺܳሻǤ ‫ ݔ‬൑ ܽ ‫ݕ ڄ‬ǡ ‫ ݕ‬൑ ͳሽ

can be also given as follows.
ߟሺ‫ܣ‬ሻ ൌ ሼሺሼܾሽǡ ሼܿሽሻȁܾǡ ܿ ‫ א‬Ժଶ ǡ ሼܾሽ ‫ ڄ ܣ ك‬ሼܿሽሽൌ ሧሼ‫ א ݔ‬۱۱‫۾‬ሺܳሻȁ‫ݕ׌‬Ǥ ሺ‫ݔ‬ǡ ‫ݕ‬ሻ ‫ߟ א‬ሺܽሻǡ ‫ ݕ‬൑ ͳሽൌ ሼሺሼܾሽǡ ሼܿሽሻȁܾǡ ܿ ‫ א‬Ժଶ ǡ ܾ ‫ ڄ ܣ א‬ሼܿሽሽ

Here, if ܽǡ ܽԢ ‫ ܳ א‬satisfy ߟሺܽሻ ‫ߟ ك‬ሺܽԢሻ , then we haveൌ ሼሺሼܽ ൅ ܿሽǡ ሼܿሽሻȁܿ ‫ א‬Ժଶ ǡ ܽ ‫ܣ א‬ሽܽ ൑ ܽԢ as follows.

Example 11.

ܽ

For a frame ሺܳǡ ൑ǡ ‫ڀ‬ሻ, the tuple ሺܳǡ ൑ǡ ‫ڀ‬ǡ‫ר‬ǡ ሻ is a quantale
where T is the greatest element. If it is also atom-algebraic,ൌ ሧሼ‫ א ݔ‬۱۱‫۾‬ሺܳሻȁ‫ݕ׌‬Ǥ ሺ‫ݔ‬ǡ ‫ݕ‬ሻ ‫ߟ א‬ሺܽሻǡ ‫ ݕ‬൑ ͳሽ

then it has a relational representation by Theorem 2 andTheorem 1.

൑ ሧሼ‫ א ݔ‬۱۱‫۾‬ሺܳሻȁ‫ݕ׌‬Ǥ ሺ‫ݔ‬ǡ ‫ݕ‬ሻ ‫ߟ א‬ሺܽԢሻǡ ‫ ݕ‬൑ ͳሽൌ ܽԢ

㸳㸬CCP-invertible Quantale‫ז‬Section 4 shows that a powerset quantale has a relational

Since the above function ߟ is an injective homomorphism,

representation. Conversely, if a quantale has a relational

the image of ܳ by ߟ is isomorphic to ܳ and it is a

representation in the same way as Section 4, is it then a

sub-quantale of ‫ܔ܍܀‬ሺ۱۱‫۾‬ሺܳሻሻ.

powerset quantale? The answer is 'Yes', if it is CCP-invertible.

We give some examples.

Definition 8 (CCP-invertible).

Example 8.

A quantale ܳ is called CCP-invertible, if for all ‫ݔ‬ǡ ‫א ݕ‬‫ܔ܍܀‬ሺ‫ܣ‬ሻ in Example 1 is a powerset quantale. Therefore, by۱۱‫۾‬ሺܳሻ, for all ܽ ‫ܳ א‬, the following holds.

Theorem 2, ‫ܔ܍܀‬ሺ‫ܣ‬ሻ has a relational representation. The‫ ݔ‬൑ ܽ ‫ ݕ ڄ‬฻ ‫ א ݖ׌‬۱۱‫۾‬ሺܳሻǤ ‫ ݔ‬൑ ‫ ݖݕ ڄ ݖ‬൑ ܽ

injective map ߟ from ‫ܔ܍܀‬ሺ‫ܣ‬ሻ to ‫ܔ܍܀‬ሺ۱۱‫۾‬ሺ‫ܔ܍܀‬ሺ‫ܣ‬ሻሻሻ is

Theorem 3.

given as follows.

Let ሺܳǡ ൑ǡ ‫ڀ‬ǡ‫ ڄ‬ǡͳሻ be a quantale.

ߟሺܴሻ ൌ ሼሺܲǡ ܳሻȁܲǡ ܳ ‫ א‬۱۱‫۾‬ሺ‫ܔ܍܀‬ሺ‫ܣ‬ሻሻǡ ܲ ൑ ܴ ‫ܳ ڄ‬ሽequivalent.

The following areࢡ࢜ࣥࢸ࢖ࣝ࡜᏶ഛ࡭ࡁ➼ᕥ༙⎔ࡢ⾲⌧ᐃ⌮

1.

2.



The following function ߟ ‫ ܳ ׷‬՜ ‫ܔ܍܀‬ሺ۱۱‫۾‬ሺܳሻሻ

Example 14.

ߟሺܽሻ ൌ ሼሺ‫ݔ‬ǡ ‫ݕ‬ሻȁ‫ݔ‬ǡ ‫ א ݕ‬۱۱‫۾‬ሺܳሻሻǡ ‫ ݔ‬൑ ܽ ‫ݕ ڄ‬ሽԵሺԺଶ ሻ in Example 3 is CCP-invertible, since ‫ ݖ‬in Definition

is an injective homomorphism of quantales and ܳ is

8 is given by ‫ ݖ‬ൌ ሼ‫ ݏ‬൅ ‫ݐ‬ሽ ൌ ሼ‫ ݏ‬െ ‫ݐ‬ሽ where ‫ ݔ‬ൌ ሼ‫ݏ‬ሽ and

CCP-invertible.

‫ ݕ‬ൌ ሼ‫ݐ‬ሽ.

ܳ is a powerset quantale.

Example 15.

Proof.

Գ ‫ ׫‬ሼ߱ሽ in Example 4 is CCP-invertible, since ‫ ݖ‬in(ͳ ฺ ʹ)Definition 8 is given by ‫ ݔ‬െ ‫ݕ‬. However, the order of its

Let ܽ be an element of ܳ. Since ߟ is a homomorphism ofcompletely coprime elements is not discrete. Therefore, by

quantales and ܳ is CCP-invertible, we have the following

Theorem 3, ߟ is not an injective homomorphism of quantales.

diagram.

Example 16.
The ordered set of Fig 1 forms a quantale where ܽ ‫ ܾ ڄ‬ൌ ܽ ‫ר‬ߟሺሧሼ‫ א ݖ‬۱۱‫۾‬ሺܳሻȁ‫ ݖ‬൑ ܽሽሻܾ except for ͳ ‫ ܽ ڄ‬ൌ ܽ ‫ ͳ ڄ‬ൌ ܽ . It is not CCP-invertible,
since the set of its completely coprime elements is ሼ‫ݏ‬ǡ ‫ݐ‬ሽ andൌ ራሼߟሺ‫ݖ‬ሻȁ‫ א ݖ‬۱۱‫۾‬ሺܳሻǡ ‫ ݖ‬൑ ܽሽ‫ ݐ‬൑ ͳ ‫ ݐ ڄ‬but ‫ݐ ڄ ݏ ح ݐ‬.

ൌ ሼሺ‫ݔ‬ǡ ‫ݕ‬ሻȁ‫ א ݖ׌‬۱۱‫۾‬ሺܳሻǡ ሺ‫ݔ‬ǡ ‫ݕ‬ሻ ‫ߟ א‬ሺ‫ݖ‬ሻǡ ‫ ݖ‬൑ ܽሽTൌ ሼሺ‫ݔ‬ǡ ‫ݕ‬ሻȁ‫ݔ‬ǡ ‫ א ݕ‬۱۱‫۾‬ሺܳሻǡ ‫ א ݖ׌‬۱۱‫۾‬ሺܳሻǡ ‫ ݔ‬൑ ‫ݕ ڄ ݖ‬ǡ‫ ݖ‬൑ ܽሽൌ ሼሺ‫ݔ‬ǡ ‫ݕ‬ሻȁ‫ݔ‬ǡ ‫ א ݕ‬۱۱‫۾‬ሺܳሻǡ ‫ ݔ‬൑ ܽ ‫ݕ ڄ‬ሽ

1ൌ ߟሺܽሻ

tMoreover, since ߟ is injective, we have ൌ ሧሼ‫ א ݖ‬۱۱‫۾‬ሺܳሻȁ‫ ݖ‬൑ ܽሽs

Therefore, ܳ is completely coprime algebraic.

٣

Since ߟ preserves 1, for ‫ݔ‬ǡ ‫ א ݕ‬۱۱‫۾‬ሺܳሻ,  ൑  if andonly if  ൌ Ǥ Therefore, the order of completely coprimeelements of ܳ is discrete.

Fig.1. A quantale which is not CCP-invertible(ʹ ฺ ͳ)Example 17.

By Theorem 2, ߟ is an injective homomorphism of quantales.

The ordered set of Fig 2 forms a quantale where ܽ ‫ ܾ ڄ‬ൌ ܽ ‫ר‬Let ܽ be an element of ܳ and ‫ݔ‬ǡ ‫ ݕ‬elements of ۱۱‫۾‬ሺܳሻ.

ܾ

Since ܳ is completely coprime algebraic, we have

CCP-invertible. However, this quantale is not completely‫ ݔ‬൑ܽ‫ݕڄ‬

coprime algebraic, since the set of its completely coprime

exceptfor ͳ ‫ ܽ ڄ‬ൌ ܽ ‫ ͳ ڄ‬ൌ ܽ .

Thisquantaleelements is ሼ‫ݏ‬ǡ ͳሽ, but ‫ڀ ് ݐ‬ሼ‫ݏ‬ሽ. Therefore, by Theorem 3,฻ ‫ ݔ‬൑ ቀሧሼ‫ א ݖ‬۱۱‫۾‬ሺܳሻȁ‫ ݖ‬൑ ܽሽቁ ‫ݕ ڄ‬

ߟ is not an injective homomorphism of quantales.

฻ ‫ ݔ‬൑ ሧሼ‫ݕ ڄ ݖ‬ȁ‫ א ݖ‬۱۱‫۾‬ሺܳሻǡ ‫ ݖ‬൑ ܽሽT฻ ‫ א ݖ׌‬۱۱‫۾‬ሺܳሻǤ ‫ ݔ‬൑ ‫ ݖݕ ڄ ݖ‬൑ ܽ
Therefore, ܳ is CCP-invertible.
‫ז‬

t
1

Example 12.
‫ܔ܍܀‬ሺ‫ܣ‬ሻ in Example 1 is CCP-invertible, since ‫ ݖ‬inDefinition 8 is given by ‫ ݕ ڄ ݔ‬ι where ‫ ݕ‬ι is the oppositesrelation of ‫ݕ‬.
Example 13.

٣‫כ‬Եሺȭ ሻ in Example 2 is CCP-invertible, since ‫ ݖ‬in Definition
8 is given by ሼߪሽ where ‫ ݔ‬ൌ ሼߪߨሽ and ‫ ݕ‬ൌ ሼߨሽ.

isFig. 2. A quantale which is CCP-invertible⚄ዉᕝ኱ᏛᕤᏛ◊✲ᡤᡤሗ ➨  ྕRemark that there exist other relational representations ofsemiring consisting of up-closed multirelations, in which all

Example 17, for example, the following function ߟԢ ‫ ܳ ׷‬՜

joins, the least element, multiplication, and the unit element are‫ܔ܍܀‬ሺሼߙǡ ߚǡ ߛሽሻ(9).

respectively given by unions, empty multirelations, theߟԢሺܶሻ ൌ ሼሺߙǡ ߚሻǡ ሺߙǡ ߙሻǡ ሺߚǡ ߚሻǡ ሺߛǡ ߛሻሽ

multirelational composition, and the membership relation.

ߟԢሺ‫ݐ‬ሻ ൌ ሼሺߙǡ ߚሻǡ ሺߙǡ ߙሻǡ ሺߚǡ ߚሻሽ

Definition 9 (complete idempotent left semiring).

ߟԢሺ‫ݏ‬ሻ ൌ ሼሺߙǡ ߚሻǡ ሺߙǡ ߙሻሽ

A complete idempotent left semiring is a tupleሺ‫ܭ‬ǡ ൑ǡ ‫ڀ‬ǡ‫ ڄ‬ǡͳሻߟԢሺͳሻ ൌ ሼሺߙǡ ߙሻǡ ሺߚǡ ߚሻǡ ሺߛǡ ߛሻሽwith the following properties:ߟԢሺ٣ሻ ൌ ‫׎‬1.

ሺ‫ܭ‬ǡ‫ ڄ‬ǡͳሻ is a monoid.

Example 18.

2.

ሺ‫ܭ‬ǡ ൑ǡ ‫ڀ‬ሻ is a complete join semilattice.

ሺܳǡ ൑ǡ ‫ڀ‬ǡ‫ר‬ǡ ܶሻ in Example 11 is CCP-invertible, since ‫ ݖ‬in3.

ሺ‫ܵڀ‬ሻ ‫ ܽ ڄ‬ൌ ‫ڀ‬ሼܾ ‫ܽ ڄ‬ȁܾ ‫ܵ א‬ሽ for each element ܽ andeach subset ܵ of ‫ܭ‬.

Definition 8 is given by ‫ ݖ‬ൌ ‫ݔ‬.
We can summarize our results for quantales as follows.
(10)

A complete idempotent left semiringሺ‫ܭ‬ǡ ൑ǡ ‫ڀ‬ǡ‫ ڄ‬ǡͳሻ is calledshow `relational representation theorem'

completely coprime algebraic if ሺ‫ܭ‬ǡ ൑ǡ ‫ڀ‬ሻ is completelyfor `unital involutive quantales'. On the other hand, ourcoprime algebraic. A powerset complete idempotent left

relational representation theorem can be applied to quantales

semiring is a complete idempotent left semiring which is

Palmigiano and Re

which are not in general involutive.

isomorphic to Եሺܺሻ as complete join semilattice for some set

Theorem 4.

ܺ.

For a quantale ܳ, the following are equivalent.

Definition 10 (multirelation).

The following function ߟ ‫ ܳ ׷‬՜ ‫ܔ܍܀‬ሺ۱۱‫۾‬ሺܳሻሻ1.

A multirelation on a set ‫ ܣ‬is a subset of ‫ ܣ‬ൈ Եሺ‫ܣ‬ሻ. A
multirelation ܴ on a set ‫ ܣ‬is called up-closed if ሺܽǡ ܺሻ ‫ܴ א‬ߟሺܽሻ ൌ ሼሺ‫ݔ‬ǡ ‫ݕ‬ሻȁ‫ݔ‬ǡ ‫ א ݕ‬۱۱‫۾‬ሺܳሻǡ ‫ ݔ‬൑ ܽ ‫ݕ ڄ‬ሽ2.

is an injective homomorphism of quantales and ܳ isand ܺ ‫ ܻ ك‬imply ሺܽǡ ܻሻ ‫ܴ א‬.

CCP-invertible.

Example 19.

ܳ is isomorphic to Եሺܺሻ as complete join semilattice

For a set ‫ܣ‬, the tuple‫ܔ܍܀ۻ܃‬ሺ‫ܣ‬ሻ ൌ ሺ‫ܭ‬ǡ ൑ǡ ‫ڀ‬ǡ‫ ڄ‬ǡͳሻ forms afor some set ܺ.

complete idempotent left semiring where3.

ܳ is atom-algebraic and it is a frame.

z‫ ܭ‬is the set of all multirelations on ‫ܣ‬,4.

ܳ is atom-algebraic and its atoms are completelyz൑ is the inclusion ‫ك‬,

coprime.

z‫ ڀ‬is the union operator ‫ڂ‬,ܳ is completely coprime algebraic and its completelyzܴ ‫ ܳ ڄ‬is defined by5.

ሼሺܽǡ ܺሻȁ‫ܻ׌‬Ǥ ሺܽǡ ܻሻ ‫ܴ א‬ǡ ‫ܻ א ݕ׊‬Ǥ ሺ‫ݕ‬ǡ ܺሻ ‫ܳ א‬ሽ,

coprime elements are atoms.
ܳ is completely coprime algebraic and the order of its

6.

completely coprime elements is discrete.

zͳis ሼሺܽǡ ܺሻȁܽ ‫ܣ א‬ǡ ܺ ‫ܣ ك‬ሽ.

The next theorem means that a powerset complete

Proof.

idempotent left semiring has a multirelational representation.

This theorem is implied by Theorem 1 and Theorem 3.

This theorem is proved in the paper(14).
‫ז‬Theorem 5.
Let ሺܳǡ ൑ǡ ‫ڀ‬ǡ‫ ڄ‬ǡͳሻ be a complete idempotent left semiring. If㸴 㸬 Representation Theorem for Powerset Completeܳ is a powerset complete idempotent left semiring, then the

Idempotent Left Semirings

followingThis section shows a representation theorem for powerset
complete idempotent left semirings.
It is known that the set of up-closed multirelations over a set
forms a complete idempotent left semiring together with union,functionߟ ‫ ܳ ׷‬՜ ‫ܔ܍܀ۻ܃‬ሺ۱۱‫۾‬ሺܳሻሻisaninjective homomorphism of complete idempotent left semirings.
ߟሺܽሻ ൌ ሼሺ‫ݔ‬ǡ ߜሺܾሻሻȁ‫ א ݔ‬۱۱‫۾‬ሺܳሻǡ ܾ ‫ܳ א‬ǡ ‫ ݔ‬൑ ܽ ‫ܾ ڄ‬ሽHere, we write ߜሺܾሻ for the following set of completely
coprime elements.
ߜሺܾሻ ൌ ሼ‫ א ݕ‬۱۱‫۾‬ሺܳሻȁ‫ ݕ‬൑ ܾሽ

multirelational composition, the empty multirelation, and themembership relation. Similarly to quantales, this section shows

Example 20.

the powerset condition is sufficient for a complete idempotent

The ordered set of Fig 3 forms a complete idempotent left

left semiring to be isomorphic to a complete idempotent leftsemiring where ܽ ‫ ܾ ڄ‬ൌ ܽ ‫ ܾ ר‬except for ͳ ‫ ܽ ڄ‬ൌ ܽ ‫ ͳ ڄ‬ൌ ܽࢡ࢜ࣥࢸ࢖ࣝ࡜᏶ഛ࡭ࡁ➼ᕥ༙⎔ࡢ⾲⌧ᐃ⌮and ʹ ‫  ڄ‬ൌ . It is a powerset complete idempotent left



It is also future work.

semiring but not a powerset quantale.
Acknowledgements

T

This work was supported by JSPS Grant Numbers 24700017 and
22500016.

1

2

References(1) C.J.Mulvey, “&”, In Second Topology Conference. Rendiconti delCircolo Matematico di Palermo, ser.2, supplement no. 12 (1986)٣

pp.99--104.
(2) J. H. Conway, “Regular Algebra and Finite Machines”, Chapman and

Fig. 3. A powerset complete idempotent left semiring

Hall, London, (1971).
(3) He Jifeng, C. A. R. Hoare, “Weakest Prespecification”, Information

Our multirelational representation theorem for powerset
complete idempotent left semirings can be also extended as(14)

Processing Letters, vol. 24 (1987).
(4) S. Vickers, “Topology via Logic”, Cambridge University Press

follows. The proof is described in the paper .

(1989).

Theorem 6.

(5) D. N. Yetter, “Quantales and (Noncommutative) Linear Logic”,

Let ሺܳǡ ൑ǡ ‫ڀ‬ǡ‫ ڄ‬ǡͳሻ be a complete idempotent left semiring.

Journal of Symbolic Logic vol. 55 (1990) pp.41--64.

The following are equivalent.

(6) B. A. Davey and H. A. Priestley, “Introduction to Lattices and Order”,

1.

The following function ߟ ‫ ܳ ׷‬՜ ‫ܔ܍܀ۻ܃‬ሺ۱۱‫۾‬ሺܳሻሻ is

2nd edn. Cambridge University Press (2002).

an injective homomorphism of complete idempotent left

(7) Peter T. Johnstone, “Stone Spaces”, Cambridge University Press

semirings, ܳ is CCP-invertible, and ߟ reflects the(1982).

order.

(8) Silvio Valentini, “Representation Theorems for Quantales”, Math.

ߟሺܽሻ ൌ ሼሺ‫ݔ‬ǡ ߜሺܾሻሻȁ‫ א ݔ‬۱۱‫۾‬ሺܳሻǡ ܾ ‫ܳ א‬ǡ ‫ ݔ‬൑ ܽ ‫ܾ ڄ‬ሽܳ is a powerset complete idempotent left semiring.

2.

Log. Q. vol. 40 (1994) pp.182--190.
(9) Carolyn Brown and Doug Gurr, “A Representation Theorem for
Quantales”, Journal of Pure and Applied Algebra vol. 85 (1993)

㸵㸬Conclusion

pp.27--42.

Our main theorem is a relational representation theorem for(10) B. Jo’nsson and A. Tarski, “Relational Representation of Groupoid

powerset quantales. Conversely, if a quantale has a relational

Quantales”, Order (2011) pp.1--19.

representation in the same way and it is CCP-invertible, then it(11) A. Palmigiano and R. Re, “Boolean algebras with operators. Part II”,

isAmer. J. Math. vol.74 (1952) pp.127--162.

apowersetquantale.

Similarly,amultirelational

representation theorem for powerset complete idempotent left(12) H. Furusawa, K. Nishizawa, “Relational and multirelationalsemirings is also proved.

representation theorem for complete idempotent left semirings”. LNCS,

It is future work to extend our representation theorem to a
Stone-type duality(7).

vol. 6663, Springer (2011) pp.148—163.
(13) K. Nishizawa, H. Furusawa, “Relational representation theorem

As shown in Example 15, ߟ for Գ ‫ ׫‬ሼ߱ሽ is not anfor powerset quantales”. LNCS vol. 7560, Springer(2012) pp.207–218.

injective homomorphism. However, we do not know whether(14) H. Furusawa, K. Nishizawa, “Multirelational representation theorem

there exist other relational representations of Գ ‫ ׫‬ሼ߱ሽ than ߟ.

for complete idempotent left semirings”. submitted.





⚄ዉᕝ኱Ꮫ 21 ᖺ㛫ࡢゐ፹◊✲ෆ ⸨ ࿘ ᘤ㸨Study on the Heterogeneous Catalysis for Twenty-one Years at Kanagawa
University
Shuichi NAITO㸨㸯㸬ࡣࡌࡵ࡟ ⚾ࡀ⚄ዉᕝ኱ᏛᕤᏛ㒊≀㉁⏕࿨໬Ꮫ⛉㸦ᙜ᫬, ᛂ⏝໬Ꮫ⛉㸧ࡢࠕ≀⌮໬Ꮫ◊✲ᐊࠖ࡟Ᏻ┒ᒾ㞝ඛ⏕ࡢᚋ௵࡜ࡋ

ࣇࣟࣥࢸ࢕࢔ࠖࢆ❧ࡕୖࡆࡿࡇ࡜ࡀฟ᮶, ኱ᆺ⿦⨨࡜ࡋ
࡚23ྕ㤋8㝵࡟࠶ࡿ༢⤖ᬗୖ࡛ࡢゐ፹཯ᛂࢆほᐹྍ⬟࡞⾲㠃ゎᯒ⿦⨨ࢆᩚഛࡍࡿࡇ࡜ࡀ࡛ࡁࡓ

࡚╔௵ࡋࡓࡢࡣ 1993 ᖺ࡛࠶ࡗࡓ ᙜ᫬ࡶ௒࡜ྠࡌ༞ᴗ

⚾ࡢᑓ㛛ศ㔝ࡣゐ፹࣭⾲㠃໬Ꮫࡢ◊✲࡛࠶ࡿࡀ, ᪂ࡋ◊✲㓄ᒓ࣮࡛ࣝࣝࡑࡢᖺࡢ๭ࡾᙜ࡚ேᩘࡢ༙ᩘࡀ᪂௵◊࠸⿦⨨సࡾࡸ࢞ࣛࢫ⣽ᕤࢆࡍࡿࡇ࡜ࡶዲࡁࡔࡗࡓ ௒✲ᐊ࡟㓄ᒓࡉࢀ࡚࠸ࡓࡀ, ወࡋࡃࡶ௒ᖺࡢ๭ࡾᙜ࡚ேᩘ

࡛ࡶᏛ⏕ࡀቯࡍ࡜࢞ࣛࢫ⿦⨨ࡢಟ⌮ࡸ࢞ࣛࢫ〇཯ᛂ⟶ࡢ

14 ྡࡢ༙ศ࡛࠶ࡗࡓ࡜グ᠈ࡋ࡚࠸ࡿ ╔௵┤ᚋࡢ 4 ᭶〇సࡣ⪁║㙾ࢆ࠿ࡅ࡞ࡀࡽ⾜ࡗ࡚࠸ࡿ ᙜ᫬ࡢᡃࠎࡢ

ึࡵ࡟⚾ࡢᡭ〇ࡢ࣐࢖ࢡࣟἼศගჾ࡜௜ᒓ࢞ࣛࢫ⣔┿✵ศ㔝࡛ࡣ, ゎᯒ⿦⨨ࡣฟ᮶ࡿࡔࡅ⮬ศ࡛タィࡋ, ḧࡋ࠸ࣛ࢖ࣥ, ࡑࢀ࡜ᑠᆺࡢ㉸㧗┿✵⿦⨨ࢆ๓௵ᆅ࡛࠶ࡗࡓᮏ

᝟ሗࢆ࠺ࡲࡃධᡭ࡛ࡁࡿᕤኵࡀᚲせ࡛࠶ࡗࡓ 2 ᅇ࡟㒓ࡢᮾ኱⌮Ꮫ㒊࠿ࡽ 2 t ࢺࣛࢵࢡ࡛, ༞◊⏕࡟ᡭఏࡗ࡚

ࢃࡓࡾ⋓ᚓ࡛ࡁࡓ⛉◊㈝B ࡛ࣇ࣮࢚ࣜኚ᥮࣐࢖ࢡࣟἼศ

ࡶࡽ࠸࡞ࡀࡽᶓ὾࢟ࣕࣥࣃࢫࡢᪧ 4 ྕ㤋ࡲ࡛㐠ࢇ࡛ࡁࡓගჾࢆヨసࡋࡓࡋ, ๓㏙ࡢ XPS ⿦⨨࡟ in-situ ࢭࣝࢆ௜タࡇ࡜ࡀఱ࡜ࡶ᠜࠿ࡋࡃᛮ࠸ฟࡉࢀࡿ

ࡋ࡚ᵝࠎ࡞๓ฎ⌮ᚋࡢ⾲㠃ࡑࡢሙほᐹࢆྍ⬟࡟ࡋࡓ

4 ᭶ 1 ᪥࡟㎡௧ࢆࡶࡽࡗࡓᚋ㸪Ᏻ┒◊࠿ࡽṧࡗ࡚࠸ࡓࣔࢵࢺ࣮࡛࠶ࡿࠕゐ፹཯ᛂࡢ⌧ሙࢆほᐹࡋ, ཯ᛂᶵᵓࡢ

᪂஭஬㑻ຓᡭ(ᚋ࡟໬ᏛᕤᏛ◊✲ᐊຓᩍᤵ)࡜ 2 ே࡛, 7ヲ⣽ࢆゎ᫂ࠖࡍࡿࡓࡵ࡟, 5 ྎࡢࣇ࣮࢚ࣜኚ᥮㉥እศගྡࡢ༞ᴗ◊✲⏕ࡢࡓࡵ࡟ៃࡓࡔࡋࡃゐ፹཯ᛂ࡜ᅛయ⾲㠃ჾ࡜ᡭ〇ࡢࡶࡢࡶྵࡵࡿ࡜ 20 ྎ㏆࠸࢞ࢫࢡ࣐ࣟࢺࢢࣛ

ゎᯒࡢࡓࡵࡢ⿦⨨ࢆ❧ࡕୖࡆ࡚◊✲ࢆ㛤ጞࡋࡓ ࡑࡢࣇࢆ㥑౑࡛ࡁࡓࡢࡶ, Ꮫ⛉࣭Ꮫ㒊ࡸ኱Ꮫᙜᒁࡢ᥼ຓ࡜⌮ᖺ,Ꮫ⛉࡟๭ࡾᙜ࡚ࡽࢀࡓ≉ูண⟬࡛, ༙ࡤᡭ〇ࡢゎࡀ࠶ࡗࡓ࠿ࡽࡔ࡜ឤㅰࡋ࡚࠸ࡿ

LEED࣭AES ゎᯒ⿦⨨ࢆ㉎ධࡋ࡚㡬࠸ࡓࡇ࡜ࡣ኱ኚ᭷㞴࠿ࡗࡓ ࡇࡢ⿦⨨ࡣࡑࡢᚋ, 2001 ᖺ࡟⌧ᅾࡢ 23 ྕ㤋㸰㸬⚄ዉᕝ኱ᏛᕤᏛ㒊࡛ࡢゐ፹◊✲࡟⛣㌿ࡋࡓ࡜ࡁ࡟ᗫᲠࡉࢀࡓ ྠࡌ 2001 ᖺ࠿ࡽ 5 ᖺ㛫㸪

2.1 ྠ఩యࣉ࣮ࣟࣈἲ࡟ࡼࡿ཯ᛂゎᯒ࡜ゐ፹タィ⚾❧኱ᏛᏛ⾡◊✲㧗ᗘ໬᥎㐍஦ᴗࠕࣁ࢖ࢸࢡ࣭ࣜࢧ࣮ࢳ

ゐ፹཯ᛂࡢάᛶ࣭㑅ᢥᛶᨭ㓄ᅉᏊࡢゎ᫂࡟ࡣཎᏊࣞ

ࢭࣥࢱ࣮ࠖࡀబ⸨♸୍ඛ⏕ࢆࣉࣟࢪ࢙ࢡࢺ࣭࣮ࣜࢲ࣮࡜

࡛࣋ࣝࡢゐ፹⾲㠃ࡢᵓ㐀࡜྾╔✀ࡢືⓗᣲືࡢほᐹࡀࡋ࡚Ⓨ㊊ࡋ, ⌧ᅾࡣᕤᏛ◊✲ᡤᡤᒓ࡜࡞ࡗ࡚࠸ࡿ㏱㐣ᆺ୙ྍḞ࡛࠶ࡿ⚾ࡀ⚄ዉᕝ኱Ꮫ࡟᮶࡚᭱ึ࡟ᡭ᥃ࡅࡓ

㟁Ꮚ㢧ᚤ㙾(TEM)࡜ X ⥺ග㟁Ꮚศග⿦⨨㸦XPS㸧ࢆ㉎ධ◊✲ࡣ㔠ᒓ࣭㓟໬≀࣭ࣂ࢖࣓ࢱࣜࢵࢡࢡࣛࢫࢱ࣮ࡸ࢝

࡛ࡁ, ⚄ዉᕝ኱Ꮫ࡛ࡢ⾲㠃໬Ꮫ◊✲ࡶ඘ᐇࡋ࡚ࡁࡓ

ࣝ࣎ࢽࣝࢡࣛࢫࢱ࣮ࡢ⢏Ꮚᚄ࣭⤌ᡂ࡞࡝ࢆኚ໬ࡉࡏࡓ

᭦࡟, 2006 ᖺ㹼2011 ᖺ 3 ᭶ࡲ࡛⚾ࡀࣉࣟࢪ࢙ࢡࢺ࣭ࣜᢸᣢゐ፹ୖ࡛ࡢࣉࣟ࣌ࣥศᏊࡢ㛵୚ࡍࡿỈ⣲໬࣭␗ᛶ࣮ࢲ࣮ࢆົࡵࡓ⚾❧኱ᏛᏛ⾡◊✲㧗ᗘ໬᥎㐍஦ᴗࠕᏛ⾡໬࣭㓟໬࣭ࣄࢻ࣑ࣟ࣍ࣝࣝ໬཯ᛂ୰࡟㔜Ỉ⣲ࢆ⏝࠸ࡓྠ఩య஺᥮཯ᛂࢆ࢝ࢵࣉࣝࡉࡏࡓࡶࡢ࡛࠶ࡗࡓࡇࢀ

*ᩍᤵ ≀㉁⏕࿨໬Ꮫ⛉
Professor, Dept. of Material and Life Chemistryࡽࡢ཯ᛂ୰࡟⏕ᡂࡍࡿ㔜Ỉ⣲໬ࣉࣟ࣌ࣥࡢྠ఩యศᕸ
ࢆ࣐࢖ࢡࣟἼศගἲ࡛ゎᯒࡋࣉࣟ࣌ࣥࡢ྾╔≧ែࢆ⚄ዉᕝ኱Ꮫ  ᖺ㛫ࡢゐ፹◊✲ࣉ࣮ࣟࣈ࡜ࡋ࡚ゐ፹ᵓ㐀࡜཯ᛂ୰㛫యᵓ㐀ࡢ┦㛵ࢆㄪࡀ㠀ᖖ࡟ࡼࡃ໬▼⇞ᩱ࡟௦ࢃࡿ࢚ࢿࣝࢠ࣮※࡜ࡋ࡚ࡣ⌮࡭㸪௚ࡢᡭἲ࡛ࡣᚓࡽࢀ࡞࠸ࠕ཯ᛂ୰ࡢືⓗᣲືࠖ࠿᝿ⓗ࡞ࡶࡢ࡛࠶ࡿ ୍᪉, ⇞ᩱ㟁ụࡣ࢚ࢿࣝࢠ࣮ኚ᥮

ࡽάᛶⅬᵓ㐀ࡢタィᣦ㔪ࢆᚓࡿࡇ࡜࡟ᡂຌࡋࡓ ࡇຠ⋡ࡀ኱ࡁࡃ⇞↝࡟క࠺᤼ฟ≀ࡀᑡ࡞࠸Ⅼ࠿ࡽඃࢀࡓ࢚

ࡢ◊✲࡜ᚋ㏙ࡢࠕCO-H2 ཯ᛂࡢ཯ᛂᶵᵓࡢゎ᫂ࠖࢆ୰ࢿࣝࢠ࣮౪⤥ࢩࢫࢸ࣒࡛࠶ࡿࡀ, ࡑࡢ⇞ᩱ࡜ࡋ࡚Ỉ⣲ࡀ

ᚰ࡟ 2009 ᖺ 3 ᭶࡟ࡣゐ፹Ꮫ఍࠿ࡽᏛ఍㈹㸦Ꮫ⾡㒊㛛㸧᭱㐺࡛࠶ࡿ ࡋ࠿ࡋ, Ỉ⣲࢚ࢿࣝࢠ࣮♫఍࡟࠾࠸࡚⇞ࢆ㡬ࡃࡇ࡜ࡀฟ᮶ࡓ㸬ᩱ㟁ụࢆ୍⯡ᐙᗞࡸ⮬ື㌴࡟฼⏝ࡍࡿࡓࡵ࡟ࡣ, ⣧⢋࡞

2.2 ࣓ࢱࣥࡢྜᡂ࢞ࢫࡸ࣋ࣥࢮࣥ࡬ࡢ㌿᥮཯ᛂỈ⣲ࢆ࡛ࡁࡿࡔࡅᏳ౯࡟〇㐀ࡋ, Ᏻ඲࡟㈓ⶶ࣭౪⤥࡛ࡁኳ↛࢞ࢫࡣ࣓ࢱࣥࢆ୺ᡂศ࡜ࡋ࡚࢚ࢱࣥ࡞࡝ᑡ㔞ࡢపࡿᢏ⾡ࡢ㛤Ⓨࡀ୙ྍḞ࡛࠶ࡿ

⣭࢔ࣝ࢝ࣥࢆྵࢇࡔྍ⇞ᛶ࢞ࢫࢆ࠸࠸, ▼Ἔ࡟༉ᩛࡍࡿ ⇞ᩱ㟁ụ࡟࠾ࡅࡿ཯ᛂࢆ⪃࠼ࡓሙྜ, 㓟⣲㸫Ỉ⣲཯ᛂྍ᥇ᇙⶶ㔞ࢆ᭷ࡍࡿ ࡉࡽ࡟㸪᭱㏆ὀ┠ࡉࢀ࡚࠸ࡿ࣓

ࡀ⌮᝿ⓗ࡛ࡣ࠶ࡿࡀ, Ỉ⣲ࡢ㐠ᦙ࣭㈓ⶶࢆ⪃៖ࡍࢀࡤ࣓

ࢱࣥࣁ࢖ࢻ࣮ࣞࢺࡢ㛤Ⓨࡀᮏ᱁໬ࡍࢀࡤࡑࡢᇙⶶ㔞ࡣ㣕ࢱࣀ࣮ࣝࢆ┤᥋⇞ᩱ㟁ụࡢ㈇ᴟ(⇞ᩱᴟ㸧࡟౪⤥ࡋ CO2㌍ⓗ࡟ቑ኱ࡍࡿࡇ࡜ࡀᮇᚅࡉࢀࡿ ⌧ᅾ, ୡ⏺ࡢ୍ḟ࡟㓟໬ࡍࡿ┤᥋ᙧ࣓ࢱࣀ࣮ࣝ⇞ᩱ㟁ụ(DMFC)ࡀ᭷ᮃ࡛

࢚ࢿࣝࢠ࣮ࡢ⣙ 20%ࢆ౪⤥ࡋ࡚࠸ࡿࡀ, ᭱኱ࡢၥ㢟Ⅼࡣ࠶ࡿ DMFC ࡢ᭱኱ࡢḞⅬࡣฟຊ࢚ࢿࣝࢠ࣮ᐦᗘࡢప

Ẽయ࡛࠶ࡿࡓࡵᾮయ⇞ᩱ࡜ẚ㍑ࡋ࡚㍺㏦ᛶ࣭㈓ⶶᛶ࡟ຎ

࠸Ⅼ࡟࠶ࡾ, ప ࡛ࡢ࣓ࢱࣀ࣮ࣝኚ᥮ຠ⋡ࢆୖࡆࡿࡓࡵ

ࡿⅬࡀᣲࡆࡽࢀࡿ ኳ↛࢞ࢫࢆ໬Ꮫᕤᴗཎᩱ࡟ኚ᥮ࡍ

࡟⇞ᩱᴟ࡛ࡢ㧗ຠ⋡࡛⪏ஂᛶࡢ㧗࠸ゐ፹ࡢ㛤Ⓨࡀᮃࡲࢀࡿ᪉ἲ࡜ࡋ࡚ࡣ, ࡲࡎ୺ᡂศࡢ࣓ࢱࣥࢆỈࡸ㓟⣲, CO2࡚ࡁࡓ ୍᪉, ୙ᆒ୍⣔ゐ፹཯ᛂࡢほⅬ࠿ࡽ࣓ࢱࣀ࣮

ࢆ⏝࠸࡚ᨵ㉁཯ᛂ㸦reforming㸧ࢆ⾜࠸ྜᡂ࢞ࢫ(CO-H2)

ࣝࡢỈ⵨Ẽᨵ㉁࡛Ỉ⣲ࢆᚓࡿ཯ᛂࡣྂࡃ࠿ࡽ᳨ウࡉࢀ,࡟㌿᥮ࡋࡓᚋ, ࣓ࢱࣀ࣮࣭࢚ࣝࢳ࣭ࣞࣥ㧗⣭Ⅳ໬Ỉ⣲ࢆCu ⣔ゐ፹ࡀ㧗άᛶࢆ♧ࡍࡇ࡜ࡀ▱ࡽࢀ࡚࠸ࡿ Cu ⣔ྜᡂࡍࡿ㛫᥋ἲ࡜, ྜᡂ࢞ࢫࢆ⤒⏤ࡍࡿࡇ࡜࡞ࡃ୍ẁ㝵ゐ፹࡛ࡣ཯ᛂࡣ HCOOCH3 ࢆ⤒࡚㐍⾜ࡍࡿࡓࡵ CO2 ࡬ࡢࡢ཯ᛂ࡛ࡇࢀࡽࢆྜᡂࡍࡿ┤᥋ἲࡀ࠶ࡿ ࣓ࢱࣥࡢࢫࢳ࣮࣒ࣜࣇ࢛࣮࣑ࣥࢢ཯ᛂࡣ᪤࡟ᕤᴗ໬ࡉ

㑅ᢥᛶࡀ㧗࠸ࡀ㸪VIII ᪘㔠ᒓゐ፹࡛ࡣ HCHO ࡢศゎࡢࡓ
ࡵ࡟COࡢ๪⏕ࡀከ࠸ ཪ, ࡇࡢ཯ᛂࡣⴭࡋ࠸ᢸయຠᯝ

ࢀ࡚࠸ࡿࡀ, Ni/Al2O3 ゐ፹ࢆ⏝࠸ 20-40 Ẽᅽ, 800°C ๓ࢆ♧ࡍࡇ࡜ࡶ▱ࡽࢀ࡚࠾ࡾ, Pd ࡢሙྜ ZnO ᢸయ࡟ศᩓ

ᚋࡢ཯ᛂ ᗘ࡛⾜ࢃࢀࡿ ࡇࡢ཯ᛂࡣ྾⇕཯ᛂ࡛࠶ࡿ

ࡉࡏࡓࡶࡢ࡛ࡣ PdZn ྜ㔠ࡢ⏕ᡂ࡟ࡼࡾ㠀ᖖ࡟㧗࠸άᛶࡓࡵ, ୍⯡࡟㧗 ࡢ཯ᛂ ᗘࡀᚲせ࡛࠶ࡾ, ཯ᛂ㏿ᗘ⮬ࢆ♧ࡍࡇ࡜ࡀሗ࿌ࡉࢀ࡚࠸ࡿ ࡋ࠿ࡋᾮ┦ࡢ࣓ࢱࣀ࣮

యࡣⴭࡋࡃ኱ࡁࡃᣑᩓᚊ㏿࡟࡞ࡗ࡚࠸ࡿ ᡃࠎࡣࡇࡢ

ࣝᨵ㉁཯ᛂ࡛ࡢỈ⣲⏕ᡂࢆྲྀࡾᢅࡗࡓ◊✲౛ࡣ㠀ᖖ࡟ᑡ

Ⅼࢆᨵၿࡍࡿࡓࡵ࡟, つ๎ⓗ࣓ࢯ⣽Ꮝࢆࡶࡘ࢔࣑ࣝࢼᢸ

࡞ࡃ, ࡑࡢ࡯࡜ࢇ࡝ࡀ DMFC ࡟㛵ࡍࡿࡶࡢ࡛࠶ࡗࡓ

యࡢ⣽Ꮝෆ࡟ 1L 㔠ᒓ࡜ຓゐ፹ࡢ 0J ࢆ㧗ศᩓᢸᣢࡉࡏࡓ

๓㏙ࡢࣁ࢖ࢸࢡ࣭ࣜࢧ࣮ࢳࢭࣥࢱ࣮ࣉࣟࢪ࢙ࢡࢺࡀጞࡇࡢゐ፹࡛ࡣ 750Υ, 30 ᫬㛫ᚋ࡛ࡶάᛶຎ໬ࡣṤ࡝࡞ࡲࡿ┤๓ࡢ 2000 ᖺࡇࢁ࠿ࡽᡃࠎࡣୡ⏺࡟ඛ㥑ࡅ࡚ᢸᣢࡃ 1L ⢏Ꮚᚄࡣ QP ࡟ಖࡓࢀ, Ⅳ⣲⵳✚ࡶ 1-2 wt%࡟ᢚ

8-10 ᪘㔠ᒓゐ፹࡟ࡼࡿ࣓ࢱࣀ࣮ࣝᾮ┦ᨵ㉁཯ᛂࡢ◊✲ࢆ࠼ࡽࢀࡓ ୍᪉, ࣓ࢱࣥࡢ┤᥋ኚ᥮ἲ࡛ࡣ㑏ඖ㞺ᅖẼ㛤ጞࡋࡓ ࡲࡎ, ✀ࠎࡢᢸᣢ Pt㸪Ir㸪Rh ゐ፹ୖ࡛ࡢ࣓ࢱ

ୗ࡛ࡢ࣓ࢱࣥࡢάᛶ໬ࡀὀ┠ࡉࢀ, ᢸᣢ Pt ࡸ Ru ゐ፹ୖࣀ࣮ࣝᾮ┦ᨵ㉁཯ᛂ࡟ᑐࡍࡿ Ru, Mo, W, Re ࡞࡝ࡢῧຍ࡛ࡢప ࡟࠾ࡅࡿ⬺Ỉ⣲࡟ࡼࡿ⾲㠃Ⅳ⣲ࡢ⵳✚࡜ࡑࢀ࡟ຠᯝࢆ᳨ウࡋࡓࡀ㸪Pt/TiO2 ゐ፹࡟ 1:1 ࡢࣔࣝẚ࡛ Ru, Mo,⥆ࡃỈ⣲໬࡟ࡼࡾ C2 ௨ୖࡢ㛗㙐ࡢⅣ໬Ỉ⣲ࡸⰾ㤶᪘໬ཪࡣ W ࢆῧຍࡍࡿ࡜ CO2 ࡬ࡢ㑅ᢥᛶࡣഹ࠿࡟ୗࡀࡿࡶ

ྜ≀ࡢ⏕ᡂࡀሗ࿌ࡉࢀࡓ ᭦࡟ ZSM-5 ࡸ SiO2 ࡟ᢸᣢࡉࡢࡢ, H2 ⏕ᡂࡢTOF ࡣ3㹼5 ಸ࡟ྥୖࡍࡿࡇ࡜ࢆぢฟࡋࢀࡓ Mo2C ୖ࡛㢮ఝࡢ཯ᛂࡀ᳨ウࡉࢀ, 㧗 (973K)࡛ࡣ

ࡓ ≉࡟ Mo ῧຍࡢሙྜ㸪ࡲࡎࣔࣜࣈࢹࣥ㓟࢔ࣥࣔࢽ࢘

࠶ࡿࡀ࣋ࣥࢮࣥࡀ㧗࠸㑅ᢥ⋡(60-100%)࡛⏕ᡂࡍࡿࡇ࡜

࣒ࢆྵᾐᚋ, 㧗 㓟໬ฎ⌮࡛ Mo 㓟໬≀⿕⭷ࢆᙧᡂᚋ,ࡀぢฟࡉࢀ࡚࠸ࡓ ᡃࠎࡶ, ࢩࣜ࢝ᢸᣢ Rh, Ru, Pd ゐ፹

Pt ࢆྵᾐࡉࡏࡿ᪉ἲ㸦ᚋྵᾐἲ㸧࡛ㄪ〇ࡋࡓゐ፹ࡣ, Moୖ࡛ࡢ࣓ࢱࣥ࡜୍㓟໬Ⅳ⣲ࡢ཯ᛂࢆ 573-723K ࡢ ᗘ㡿ࡢ࢔࣮ࣥ࢝ຠᯝ࡟ࡼࡾ㧗ศᩓࡢ Pt ᚤ⢏Ꮚࡀᚓࡽࢀ,ᇦ᳨࡛ウࡋ, Ⅳ໬Ỉ⣲ࡢ୰࡛ࡣ࣋ࣥࢮࣥࡀ㑅ᢥⓗ࡟⏕ᡂPt-Mo/TiO㸰ゐ፹(ᚋྵᾐ)ࡀ᳨ウࡋࡓࡶࡢࡢ୰࡛ࡣ᭱኱ࡢ

ࡍࡿࡇ࡜ࢆึࡵ࡚ぢฟࡋࡓ 

TOF ࢆ♧ࡋࡓ

2.3 Ỉ⣲〇㐀ࡢࡓࡵࡢ࣓ࢱࣀ࣮ࣝࡸ࢚ࢱࣀ࣮ࣝᾮ┦ᨵ▼Ἔ࡞࡝ࡢ໬▼㈨※ࡢᯤῬ࡟క࠸,carbon-neutral ㈨㉁ゐ፹ࡢ◊✲※࡜ࡋ࡚ࣂ࢖࢚࢜ࢱࣀ࣮ࣝࡸࣂ࢖࢜࢜࢖ࣝ(㓑㓟ࡀ୺ᡂ ໬▼⇞ᩱࡢᯤῬ࡜⇞↝࡟క࠺⎔ቃởᰁၥ㢟ゎỴࡢࡓࡵศ)࠿ࡽࡢỈ⣲⏕ᡂࡀὀ┠ࡉࢀጞࡵࡓࡢࡣ, ࡈࡃ᭱㏆ࡢ࡟, ௦᭰⇞ᩱࡢ㛤Ⓨࡀ⥭ᛴࡢㄢ㢟࡛࠶ࡿ Ỉ⣲ࡣ⇞↝ࡇ࡜࡛࠶ࡿ ᡃࠎࡣ⌧ᅾ, ✀ࠎࡢᢸᣢ 8-10 ᪘㔠ᒓゐ፹⏕ᡂ≀ࡀỈࡢࡳ࡛࠶ࡾ, ࡑࡢ㧗࠸཯ᛂᛶࡢࡓࡵ࡟⇕ຠ⋡࡟ࡼࡿ࢚ࢱࣀ࣮ࣝࡸ㓑㓟Ỉ⁐ᾮ࠿ࡽࡢỈ⣲⏕ᡂࡢ◊✲ࢆ⚄ዉᕝ኱ᏛᕤᏛ◊✲ᡤᡤሗ ➨  ྕ⾜࠸㧗ศᩓࡢ Ru/TiO2 ゐ፹࡟ Re ࢆῧຍࡋࡓࡶࡢࡀ㧗άࢩࣜ࢝⢏Ꮚゐ፹ࡢㄪ〇࡜཯ᛂᶵᵓࡢゎ᫂ᛶ࣭㧗㑅ᢥᛶࢆ♧ࡍࡇ࡜ࢆぢฟࡋ࡚࠸ࡿ

๓⠇࡛㏙࡭ࡓࡼ࠺࡟, ✀ࠎ8-10 ᪘㔠ᒓ࢔࣑ࣥࣥ㘒య

2.4 ୍㓟໬Ⅳ⣲ࡢỈ⣲໬཯ᛂᶵᵓࡢゎ᫂࡜ࢼࣀᵓ㐀ࢆࢆ㗪ᆺ࡜ࡋ࡚, ࡑࡢ⤖ᬗ⾲㠃࡛ TEOS ࢆຍỈศゎࡍࡿࡶࡘ㧗㑅ᢥゐ፹ࡢ㛤Ⓨ࡜ෆ㒊✵㛫࡜ቨ୰࡟ QP ࣮࢜ࢲ࣮ࡢ㔠ᒓᚤ⢏Ꮚࢆෆໟࡍ

)7 ྜᡂࡣ 1923 ᖺ,  Fischer ࡜ Tropsch ࡟ࡼࡾึࡵ࡚

ࡿ SiO2 ࢼࣀࢳ࣮ࣗࣈ(nt)ࡸࢼࣀ࢝ࣉࢭࣝ(nc)ࢆㄪ〇࡛ࡁሗ࿌ࡉࢀࡓྂ࠸ゐ፹཯ᛂ࡛࠶ࡿࡀ1980 ᖺ௦ึ㢌࡟ࡣࡿ ࡇࢀࡽࡢࢼࣀᵓ㐀యࢆ᭦࡟㧗 ࡛↝ᡂࡍࡿࡇ࡜

C1 ໬Ꮫ࡜ࡋ࡚෌Ⓩሙࡋࡓࡑࡢᐇ⏝ୖࡢ㔜せᛶࡣ௒ࡶ࡟ࡼࡾ, ቨࡢᙧᡂࡍࡿ SiO2 ࡢ⥙┠ᵓ㐀ࡀ⦓ᐦ໬ࡋ,ኚࢃࡽࡎ≉࡟㧗㑅ᢥᛶࢆ♧ࡍゐ፹ࡢ◊✲ࡀ⥆ࡅࡽࢀ࡚Ỉ⣲ศᏊࡢࡳࢆ㏱㐣ࡍࡿ࣑ࢡࣟ⣽Ꮝࢆᙧᡂࡋ,  CO ࡢ࠸ࡿ௚᪉CO㸫H2 ཯ᛂࡣ⡆༢࡞ 2 ཎᏊศᏊ࠿ࡽ✀ࠎ

10 ಸ௨ୖࡢỈ⣲㈓ⶶ⬟ࢆᣢࡘࡼ࠺࡟࡞ࡿ ࡢⅣ໬Ỉ⣲ࡸྵ㓟⣲໬ྜ≀࡛ࡁࡿ⯆࿡῝࠸ゐ፹཯ᛂ࡛᭦࡟ᡃࠎࡣ, ࡇࢀࡽࡢ㔠ᒓ㸫㓟໬≀ࢼࣀᵓ㐀యࡢㄪ࠶ࡿ≉࡟࢔ࣝࢹࣄࢻࡸ࢔ࣝࢥ࣮ࣝࢆྜᡂࡍࡿάᛶ

〇ࢆ㏫࣑ࢭࣝไ㝈཯ᛂሙෆ࡛⾜࡞࠸ከ㔞ࡢỈ⣲྾ⶶ⬟Ⅼᵓ㐀ࡢゎ᫂ࡣ㧗㑅ᢥゐ፹ࡢタィ࡟࡜ࡗ࡚㔜せ࡛࠶ࡿ

⣙㸯wt% ࡸỈ⣲໬཯ᛂ࡟㧗άᛶ࡞ゐ፹⬟ࢆࡶࡘ Ir, Rh,ᡃࠎࡣࡑࡢึᮇࡢ◊✲ẁ㝵࡟࠾࠸࡚ᢸయୖ࡛㔠ᒓᚤPt ࡞࡝ࡢ㔠ᒓࢼࣀࢡࣛࢫࢱ࣮ࢆෆໟࡋࡓ୰✵ࢩࣜ࢝⢏⢏Ꮚ࡜࢔ࣝ࢝ࣜ㔠ᒓ࡞࡝ࡢῧຍ≀࢖࢜ࣥࢆᐦ᥋࡟᥋ྜᏊࡢㄪ〇࡟ึࡵ࡚ᡂຌࡋࡓIr-SiO2 ࢼࣀ࣮࣍ࣟ ࡢሙࡉࡏࡿࡇ࡜ࡀྵ㓟⣲໬ྜ≀୰㛫యࢆᏳᐃ໬ࡋ㑅ᢥᛶࡢ

ྜIR,XAFS,XPS ➼ࡢ⾲㠃ศගἲࡸྠ఩య㏣㊧ἲࢆ㥑ྥୖ࡟᭷ຠ࡞ࡇ࡜ࢆぢฟࡋࡓࡇࡢᵓ㐀ࡣ㔠ᒓ࢖࢜ࣥ౑ࡋ࡚ ྾╔ࡢ㝿ࡣ SiO㸫Ir+ୖ࡛ゎ㞳Ỉ⣲ࡣ SiOH ࡜࡜ῧຍ≀࢖࢜ࣥࢆྠ᫬࡟ྵࡴゐ፹๓㥑యࢆᢸయୖ࡟ྵ

IrH ࡜࡞ࡾ hydride cluster ࡜ࡋ࡚จ㞟ࡍࡿࡀ⬺㞳ࡢ㝿ᾐࡉࡏࢀࡤᵓ⠏ྍ⬟࡛࠶ࡗࡓࡀ㔠ᒓ⢏Ꮚᚄࡸῧຍ≀ࡣ SiO㸫Ir+࡜࡞ࡗ࡚෌ศᩓࡍࡿ≉␗࡞Ỉ⣲྾ᨺฟᶵᵓࢆ

ࡢ๭ྜࢆไᚚࡍࡿࡼ࠺࡞ࠕάᛶⅬᵓ㐀ࡢタィࠖ࡜࠸࠺ゎ᫂ࡋࡓ

ほⅬ࠿ࡽࡣ㝈⏺ࡀ࠶ࡗࡓࡑࡢᚋࡇࡢᴫᛕࡣ Pd/CeO2

2.6 ❅⣲㓟໬≀㈓ⶶ㑏ඖゐ፹ࡢ㛤Ⓨゐ፹ୖ࡛ࡢ࣓ࢱࣥ࡜࣓ࢱࣀ࣮ࣝ⏕ᡂࡢάᛶⅬᵓ㐀ࡢゎ⮬ື㌴ࡢ࢚ࣥࢪࣥࡸᕤሙ࣎࢖࣮ࣛ࡞࡝࠿ࡽࡢ᤼࢞ࢫ
୰࡟ࡣ CO, CO2, NOx, SOx Ⅳ໬Ỉ⣲ࡀྵࡲࢀ࡚࠾ࡾ,᫂࡬࡜⧅ࡀࡗࡓ
᭦࡟ 2006 ᖺ࠿ࡽጞࡲࡗࡓᏛ⾡ࣇࣟࣥࢸ࢕࢔ࠕ໬Ꮫ✵࠸ࡎࢀࡶ኱Ẽởᰁࡢ㔜せ࡞ཎᅉ≀㉁࡜࡞ࡿ ࡇࡢ࠺㛫ࡢタィ࡜ไᚚ࡛ࠖࡣ඲ࡃ㏫ࡢⓎ᝿࠿ࡽ㔠ᒓ๓㥑యࡕ,  SOx ࢆῶᑡࡉࡏࡿࡓࡵ࡟ࡣ㸪⇞ᩱ୰࠿ࡽ◲㯤ศࢆ⤖ᬗࢆ㗪ᆺ࡜ࡋࡑࡢ⾲㠃࡟ᢸయ࡛࠶ࡿ㓟໬≀ቨࢆࢯ㝖ཤࡍࡿᚲせࡀ࠶ࡾ, ⌧ᅾ▼Ἔ⢭〇㐣⛬࡛ゐ፹ࢆ⏝࠸࣭ࣝࢤࣝἲ࡛ㄪ〇ࡍࡿࡇ࡜࡛ゐ፹άᛶⅬ࡜࡞ࡿ㔠ᒓ࡚Ỉ⣲໬⬺◲ࡀ⾜ࢃࢀ࡚࠸ࡿ ୍᪉㸪NOx ࡣ⇞↝཯ᛂᚤ⢏Ꮚࡢ࿘ࡾࡢࢼࣀ཯ᛂሙࢆタィ࣭ไᚚ࡛ࡁࡿࢼࣀᵓ

ࡢ㝿࡟ N2 ࡜ O2 ࠿ࡽ⏕ࡌࡿࡢ࡛ NOx ࡢ⏕ࡌ࡟ࡃ࠸࢚ࣥ

㐀యࡢྜᡂ࡟ึࡵ࡚ᡂຌࡋࡓ๓㥑య⤖ᬗࡢ⾲㠃࡟Ỉࢪࣥࡸ࣎࢖࣮ࣛࢆ㛤Ⓨࡍࡿ࠿, ᤼࢞ࢫฎ⌮࡟ࡼࡾᑐฎ

㓟໬≀⿕⭷ࢆᙧᡂࡍࡿ㝿࡟㘒యࡀ⿕⭷୰࡟෌⁐ゎࡍࡿࡋ࡞ࡅࢀࡤ࡞ࡽ࡞࠸ ⇞↝⿦⨨࠿ࡽⓎ⏕ࡋࡓ NOx ࢆ⌧㇟ࢆ࠺ࡲࡃ฼⏝ࡍࢀࡤ↝ᡂᚋฟ᮶ୖࡀࡿ㓟໬≀ቨ୰పῶࡍࡿ᪉ἲ࡜ࡋ࡚ⅆຊⓎ㟁ᡤࡢ኱ᆺ࣎࢖࣮ࣛ➼ࡢ᤼࡟ࡣ௚ࡢᡭἲ࡛ࡣㄪ〇ᅔ㞴࡞㔠ᒓࢼࣀࢡࣛࢫࢱ࣮ࢆᆒ

࢞ࢫࡣ V2O5/TiO2 ➼ࡢ㓟໬≀⣔ゐ፹࡟ࡼࡿ࢔ࣥࣔࢽ࢔

୍࡟ศᩓࡉࡏࡿࡇ࡜ࡀྍ⬟࡜࡞ࡗࡓ

㑅ᢥ㑏ඖ(SCR)ἲࡀᐇ⏝໬ࡉࢀ࡚࠸ࡿ ࡲࡓ⮬ື㌴᤼

Pt-TiO2 ࢼࣀࢳ࣮ࣗࣈࡢሙྜቨ୰࡟ࡣ 1 nm ௨ୗࡢ࢞ࢫ࡟ࡣ, Ⅳ໬Ỉ⣲, CO, NOx ࢆྠ᫬࡟㓟໬ཪࡣ㑏ඖį+Pt ࢡࣛࢫࢱ࣮ࡀᏑᅾࡋ TiO2 ቨࡣ Ti ࡢ≉␗࡞㟁Ꮚ≧ែࡍࡿ୕ඖゐ፹ࡀᐇ⏝໬ࡉࢀ࡚࠾ࡾ㸪ࣁࢽ࣒࢝≧ࡢᇶᯈࢆ࡜ࡾࡇࢀࡀ CO ࡢỈ⣲໬཯ᛂ࡛࣓ࢱࣀ࣮ࣝࢆ㑅ᢥ࡟ Pt-Pd-Rh ⣔ࡢ㈗㔠ᒓࢆᢸᣢࡋࡓ࢔࣑ࣝࢼゐ፹࡟ Ceⓗ࡟ྜᡂࡍࡿάᛶⅬ࡜࡞ࡿࡇ࡜ࢆ᫂ࡽ࠿࡟ࡋࡓࡇࡢ

࡞࡝ࢆῧຍࡋࡓࡶࡢࡀ⏝࠸ࡽࢀ࡚࠸ࡿ ࡋ࠿ࡋ୕ඖ

TiO2 ቨ୰࡛ࡢ≉␗࡞㔠ᒓࢡࣛࢫࢱ࣮ࡢᙧᡂࡣ㸪㔠ᒓཬゐ፹ࡣࢹ࢕࣮ࢮ࢚ࣝࣥࢪࣥ࡞࡝ࡢ㓟⣲㐣๫㞺ᅖẼୗ࡛

3+ࡧࡑࡢ๓㥑యࡢᛶ㉁࡟ⴭࡋࡃ౫Ꮡࡋ Rh ࢔࣑ࣥࣥ㘒యࡣ౑⏝࡛ࡁ࡞࠸ࡇ࡜ࡸ, ୺ᡂศ࡛࠶ࡿ Rh ࡢ㈨※ⓗไࡢሙྜ, Ti ࢔ࣝࢥ࢟ࢩࢻࡢຍỈศゎ୰㸪㘒యࡢ Ti(OH)4⣙࠿ࡽ᪂ࡓ࡞ゐ፹ࡢ㛤Ⓨࡀᮃࡲࢀ࡚࠸ࡿ ቨ࡬ࡢ⁐ゎࡣ㉳ࡇࡽࡎ,  Rh 㔠ᒓࡢ TiO2 ቨ࡬ࡢศᩓࡣ

⚄ዉᕝ኱Ꮫ࡟㉱௵ࡋࡓ┤ᚋ,  Pd 㔠ᒓ࡟ In ࡸ Ga ࢆ㧗 ↝ᡂࡢ㐣⛬࡛ RhO ࡜ࡋ࡚㐍⾜ࡋࡓ ࡑࡢ⤖ᯝ,ῧຍࡋ࡚࡛ࡁࡿ㔠ᒓ㛫໬ྜ≀ࡀ NO ࡢ CO ࡟ࡼࡿ㑏ඖ↝ᡂᚋ࢝ࣉࢭࣝ୰✵ෆ࡟ᩘ nm ࡢ Rh ᚤ⢏Ꮚࡀṧࡾ, ቨ཯ᛂ࡟ⴭࡋ࠸㧗άᛶࢆ♧ࡋ, ᐊ ᇦ࡛ࡶ཯ᛂࡢ㐍⾜ࡍ୰ࡢ Rh ࢡࣛࢫࢱ࣮㔞ࡶࡉ࡯࡝ከࡃ࡞ࡃ,  CO-H2 ཯ᛂࡿࡇ࡜ࢆぢฟࡋࡓ ゐ፹ࡣྛሷ໬≀Ỉ⁐ᾮ࡟ࢩࣜ࢝

࡛ࡢ࣓ࢱࣀ࣮ࣝ㑅ᢥᛶࡶࡉ࡯࡝㧗ࡃࡣ࡞࠿ࡗࡓ ࢆྵᾐᢸᣢࡍࡿࡇ࡜࡟ࡼࡾㄪ〇ࡋ,  733K ࡛ 5 ᫬㛫Ỉ

2.5 Ỉ⣲㑅ᢥ㏱㐣⭷࡜Ỉ⣲྾ⶶ⬟ࢆᣢࡘ㔠ᒓෆໟ୰✵⣲㑏ඖࢆ⾜ࡗࡓࡶࡢࢆゐ፹࡜ࡋࡓ ✀ࠎࡢฎ⌮ࢆ᪋⚄ዉᕝ኱Ꮫ  ᖺ㛫ࡢゐ፹◊✲ࡋࡓ Pd-In /SiO2 ゐ፹ࡢ⢊ᮎ X ⥺ᅇᢡ(XRD)ࡢ⤖ᯝ࠿ࡽ, ࡢᏛ㛗࠿ࡽ 2006 ᖺᗘ኱Ꮫ㝔タ⨨ᇶ‽ࡢ୍㒊ᨵṇ࡟క࠸

733K ࡛㑏ඖᚋࡢ㧗࠸ NO-CO ཯ᛂάᛶࢆ♧ࡍヨᩱࡣ⩏ົ໬ࡉࢀࡓࠕᩍ⫱ෆᐜᨵၿࡢࡓࡵࡢ⤌⧊ⓗ࡞◊ಟ➼ࠖ

Pd0.48In0.52 ࡢ㔠ᒓ㛫໬ྜ≀࡟ྠᐃࡉࢀࡿ ࡇࡢヨᩱࢆ࡟ࡘ࠸࡚Ꮫົጤဨ఍᳨࡛ウࡍࡿࡼ࠺࡟࡜ࡢㅎၥࢆཷࡅࡓ

733K ࡛㓟໬ࡍࡿ࡜㔠ᒓ㛫໬ྜ≀ࡣ᏶඲࡟◚ቯࡉࢀ PdO

ࡇࢀࢆᶵ࡟, ᮏᏛ࡛ FD άືࢆ඲Ꮫⓗ࡞⤌⧊࡜ࡍࡿ㆟ㄽ࡜ In2O3 ࡀ୺࡟ほ ࡉࢀࡓࡀ, ࡇࡢ≧ែࡢ཯ᛂάᛶࡣ

ࡀ㛤ጞࡉࢀࡓ2008 ᖺ 10 ᭶࠿ࡽせ⥘࡟ᇶ࡙ࡃ FD ඲Ꮫ୍᱆௨ୖపୗࡋࡓ ᭦࡟ 733K ࡛෌㑏ඖࡋࡓヨᩱ࡛ࡣ,ጤဨ఍ࡀࢫࢱ࣮ࢺࡋ, 2009 ᖺ 4 ᭶࠿ࡽࡣṇᘧ࡞つᐃࡶᅇᢡࣃࢱ࣮࣭ࣥゐ፹άᛶ࡜ࡶඖ࡟ᡠࡗࡓ ᚑࡗ࡚ᩚഛࡉࢀࡓࡑࡢᚋ 2 ᖺ㛫㸪FD ඲Ꮫጤဨ఍ጤဨ㛗ࢆ௵

Pd0.48In0.52 ࡜࠸࠺㔠ᒓ㛫໬ྜ≀ࡀ NO-CO ཯ᛂࡢಁ㐍࡟ࡉࢀ, ࡑࢀࡲ࡛✚ࡳṧࡉࢀ࡚ࡁࡓ඲Ꮫⓗᠱ᱌࡛࠶ࡗࡓ㔜せ࡞ᙺ๭ࢆᯝࡓࡋ࡚࠸ࡿࡇ࡜ࡀ⤖ㄽࡉࢀࡓ 

FYS ᤵᴗෆᐜࡸᐇ᪋᪉ἲࡢᨵၿ, Ꮫ⏕⏕άᐇែㄪᰝࡸᤵ

ࢺࣚࢱ⮬ື㌴ࡣ๓㏙ࡢ୕ඖゐ፹ࡢḞ㝗ࢆඞ᭹ࡍࡿ᪂

ᴗ࢔ࣥࢣ࣮ࢺࡢෆᐜࡢぢ┤ࡋ࡜⤖ᯝࡢබ㛤࡟ࡼࡿ⤌⧊ⓗࡋ࠸⮬ື㌴᤼࢞ࢫゐ፹࡜ࡋ࡚❅⣲㓟໬≀㈓ⶶ㑏ඖά⏝, ᩍ⫱ᨭ᥼ࢭࣥࢱ࣮タ❧࡟ྥࡅࡓཎ᱌ࡢసᡂ࡞࡝࡟

(NSR)ゐ፹ Pt-Ba/Al2O3 ࢆୡ⏺࡟ඛ㥑ࡅ࡚㛤Ⓨࡋࡓ ࡇྲྀࡾ⤌ࢇࡔᩥ⛉⣔࣭⌮ᕤ⣔࡛ࡶࡢࡢ⪃࠼᪉ࡀࡎ࠸ࡪࢇࡢゐ፹࡛ࡣ᤼࢞ࢫ୰ࡢ❅⣲㓟໬≀ࡣ㓟⣲㐣๫㞺ᅖẼ࡛㐪࠺ࡇ࡜ࢆᐇឤࡋࡓࡢࡣࡇࡢ࡜ࡁࡔࡗࡓ୧⪅ࢆ௰❧ࡕ

Ba(NO3)2 ࡜ࡋ࡚㈓ⶶࡉࢀࡿ
ࡣ Pt ୖ࡛ NO㸰࡟㓟໬ࡉࢀ㸪

ࡍࡿࠕゐ፹ࠖࡢᙺ┠ࢆᯝࡓࡍࡘࡶࡾ࡛࠶ࡗࡓࡀ, ࠶ࡲࡾ⇞ᩱ㐣๫ࡢ㑏ඖ㞺ᅖẼ࡟࡞ࡿ࡜◪㓟ሷࡣ BaO ࡟ᡠࡾ,ᛶ⬟ࡢࡼ࠸ゐ፹࡛ࡣ࡞࠿ࡗࡓ࡜⮬ᡄࡋ࡚࠸ࡿ

NO㹶㈓ⶶ⬟ࡀᅇ᚟ࡍࡿᡃࠎࡣ᭱㏆, 㢮ఝࡢ㈓ⶶ㑏ඖ⬟ࢆࡶࡘゐ፹࡜ࡋ࡚ K-Titanate (K2Ti4O17)ᢸయ࡟ⓑ㔠࡜㸲㸬 ྡవࡾࡢ༞ᴗ◊✲⏕࣭኱Ꮫ㝔⏕࡜ඹ࡟◪㓟࣒࢝ࣜ࢘ࢆᢸᣢࡋࡓ᪂ࡋ࠸ゐ፹⣔ࢆ㛤Ⓨࡋࡓࡇ ࡇࡢ㛫㸪⚾ࡢ◊✲ᐊ࡟㓄ᒓࡉࢀࡓ 250 ྡవࡢᏛ㒊 4 ᖺ

ࡢゐ፹ࡣࢺࣚࢱゐ፹࡟ẚ࡭ 3 ಸࡢ NO㹶㈓ⶶ⬟࡜㢮ఝࡢ⏕࡜, 60 ேవࡢ኱Ꮫ㝔ಟኈ࣭༤ኈㄢ⛬ࡢᏛ⏕࡜࡜ࡶ࡟,NO㹶㝖ཤ⬟ࢆ♧ࡋࡓ

ୡ⏺ࡢ➨୍⥺࡛➇ྜฟ᮶ࡿゐ፹◊✲ࢆ┠ᣦࡋ࡚㡹ᙇࡗ࡚ࡁࡓ21 ᖺ࡜࠸࠺ᖺ᭶ࡣ㛗ࡃࡶ࠶ࡿࡀ, ᛮ࠸㏉ࡍ࡜࢔㸱㸬Ꮫ⛉࣭඲Ꮫጤဨ࡞࡝
⚄ዉᕝ኱Ꮫ࡟㉱௵ࡋ࡚᭱ึ࡟Ꮫ⛉ጤဨ࡜ࡋ࡚๭ࡾᙜ࡚

ࢵࢺ࠸࠺㛫࡛࠶ࡗࡓࡼ࠺࡞Ẽࡶࡍࡿࡲࡔࡲࡔ, ࡸࡾṧࡋࡓࡇ࡜ࡀἑᒣ࠶ࡿࡼ࠺࡞࣭࣭࣭࣭࣭

ࡽࢀࡓࡢࡣࠕ᝟ሗฎ⌮ࢭࣥࢱ࣮㐠Ⴀጤဨ࡛ࠖ࠶ࡗࡓ1998

 ᭱ᚋ࡟㸪300 ྡవࡾࡢ⚾ࡢ◊✲ᐊࢆ༞ᴗࡋࡓᏛ⏕࡟ࡘ

ᖺ࠿ࡽ2000ᖺ3᭶ࡲ࡛Ꮫ⛉ே஦ࡢ㛵ಀ࡛Ꮫ⛉୺௵ࢆ௵ࡉ

࠸࡚㏙࡭ࡓ࠸ࡼࡃゝࢃࢀࡿࡇ࡜࡛࠶ࡿࡀ ୍⯡࡟⚄ࢀࡓࡕࡻ࠺࡝, ᪂ᕤᏛᲷ 23 ྕ㤋ࡢタィ࣭㠃✚๭࣭⛣㌿ዉᕝ኱Ꮫ࡟ධᏛࡋ࡚ࡃࡿᏛ⏕ࡣ⣲┤࡛኱ேࡋ࠸ᛶ᱁ࡢ

ࡢ᫬ᮇ࡟࠶ࡓࡾᕤᏛ㒊௚Ꮫ⛉ࡢ⌮ゎࢆᚓ࡚⌧ᅾࡢ 23 ྕேࡀከ࠸ ࡇࢀࡣ୍ࡘ࡟ࡣ⚄ዉᕝ኱Ꮫࡢὴᡭ࡛࡞࠸

㤋 7࣭8 㝵࡟≀㉁⏕࿨໬Ꮫ⛉࡜ࡋ࡚ࡲ࡜ࡵ࡚㡬࠸ࡓࡑ

ࢫࢡ࣮࣮ࣝ࢝ࣛ࡟ࡶᐤࡿ࡜ࡇࡀ኱ࡁ࠸࡜ᛮࢃࢀࡿ

ࡢᚋ, 2000 ᖺ 4 ᭶࠿ࡽ 7㹼8 ᖺࡢ㛫㸪ᛂ⏝໬Ꮫᑓᨷࡢ኱

ࡋ࠿ࡋ  ᖺࡢ༞ᴗ◊✲࡟╔ᡭࡋ࡚◊✲ࡍࡿࡇ࡜ࡢ㠃Ꮫ㝔㐠Ⴀጤဨࢆົࡵࡓࡑࡢ㛫, ᕤᏛ◊✲⛉࠿ࡽ඲Ꮫࡢⓑࡉࢆ▱ࡿ࡜ ேࡀኚࢃࡗࡓࡼ࠺࡟✚ᴟⓗ࡟࡞ࡾ

኱Ꮫ㝔Ꮫົጤဨ఍࡟ฟᖍࡋࡓࡀ2005ᖺ࠿ࡽ3ᖺ㛫Ꮫົጤ኱Ꮫ㝔࡟㐍ᏛࡋᏛ఍Ⓨ⾲࡞࡝ࡶ❧ὴ࡟ࡇ࡞ࡍࡼ࠺࡟࡞

ဨ఍ጤဨ㛗ࢆົࡵࡓ

ࡿ㸬ࡇࡇ࡛㏙࡭ࡓ ⚾ࡢ 21 ᖺ㛫ࡢ◊✲ᡂᯝࡶᙼࡽࡢ

⚾ࡀ⚄ዉᕝ኱Ꮫࡢࣇ࢓࢝ࣝࢸ࢕࣭ࢹ࣋ࣟࢵࣉ࣓ࣥࢺ
(FD)࡜῝ࡃ㛵ࢃࡿࡼ࠺࡟࡞ࡗࡓࡢࡣࡇࡢ㡭ࡔࡗࡓᙜ᫬

ດຊࡢ㈷≀࡛࠶ࡿ㸬ࡇࡇ࡟ឤㅰࡢពࢆ⾲ࡋࡓ࠸㸬






㧗ศᏊᚤ⢏Ꮚ࡜ 50 ᖺᕝཱྀ ᫓㤿㸨  

My Life of Research Devoted to Polymeric Micro-Particles
Haruma KAWAGUCHIฎ⌮ࡸ VOC ࡟㉳ᅉࡍࡿㅖၥ㢟࡟ᝎࡲࡉࢀ࡞࠸࡛ࡍࡴ

㸯㸬㉳
ࡶ࠺ 50 ᖺ㏆ࡃ㧗ศᏊᚤ⢏Ꮚࡢ◊✲࡟㛵ࢃࡗ࡚ࡁࡓࡇ

ࡲࡓ㸪ங໬㔜ྜ࠿ࡽࡣ㧗ศᏊࡀᚤ⢏Ꮚศᩓᾮ࡜ࡋ࡚ᚓࡽ

࡜࡟࡞ࡿ㸬ࡑࡢ⥴ࡣ༞ᴗ◊✲࡛࠶ࡗࡓ㸬ࠗங໬㔜ྜ⣔㸦ᅗࢀࡿࡢ࡛཯ᛂᚋࡢ⏕ᡂ≀ࡢྲྀࡾᢅ࠸ࡸᚋฎ⌮ࡀᐜ࡛᫆࠶

㸧ࡢ ᗘኚ໬࠘࡜࠸࠺ࡢࡀ༞ㄽࡢ◊✲ࢸ࣮࣐࡛㸪ங໬㔜ࡿ㸪➼ࠎ㸬ࡑࢇ࡞ங໬㔜ྜ࡟࠾࠸࡚ఱࡼࡾࡶ⯆࿡῝࠿ࡗྜ⣔ࡢ ᗘࡢほ ࡟ࡼࡗ࡚㔜ྜࡢ㐍ࡳලྜࢆࣜ࢔ࣝࢱ࢖

ࡓࡢࡣ㸪㔜ྜ㛤ጞ๣ࣛࢪ࢝ࣝࡀ⏕ࡌࡿሙ ࡍ࡞ࢃࡕ㔜ྜࡀ࣒࡛ᢕᥱࡍࡿࡇ࡜ࢆ┠ⓗ࡜ࡍࡿ◊✲ࡔࡗࡓ㸬 ◊✲ࢆጞጞࡲࡿሙ ࡜㸪ࣔࣀ࣐࣮ࡀᏑᅾࡍࡿሙ㸦ࡍ࡞ࢃࡕ㔜ྜࡀ㐍ࡵ࡚࡯࡝࡞ࡃங໬㔜ྜ࢜ࢱࢡ࡟࡞ࡗࡓ㸬ሢ≧㔜ྜࡸ⁐ᾮࡴሙ㸧࡜ࡀ␗࡞ࡿ࡜࠸࠺࣑ࢫࢸࣜ࢔ࢫ࡞⯙ྎࡢタᐃ࡛࠶㔜ྜ࡞࡝௚ࡢ୍⯡ⓗ࡞㔜ྜ࡟ࡣ࡞࠸ከࡃࡢ㠃ⓑࡉࢆ㸪ஙࡗࡓ㸬໬㔜ྜࡀᣢࡕྜࢃࡏ࡚࠸ࡿ࠿ࡽ࡛࠶ࡿ㸬౛࠼ࡤ㸪୍⯡ࡢ㔜ྜSmith &
ࡇࢀࢆゎࡁ᫂࠿ࡋࡓ Harkins ࡢㄽᩥ(1947)㸪
Ewart ࡢㄽᩥ(1948)ࢆㄞࢇ࡛㸪୙ᆒ୍⣔㔜ྜ࡟ഴಽࡋࡓ㸬࡛ࡣ㔜ྜᗘ࡜㔜ྜ㏿ᗘࡀ཯ẚ౛ࡍࡿ㛵ಀ࡟࠶ࡿࡢ࡟ᑐ
ࡋ࡚㸪ங໬㔜ྜ⣔࡛ࡣ㧗㔜ྜᗘࡢ࣏࣐࣮ࣜࢆ㧗㏿࡛ᚓࡿࡇ࡜ࡀ࡛ࡁࡿ㸬ங໬㔜ྜࡣỈ⣔࡛ࡢ㔜ྜ࡞ࡢ࡛཯ᛂ⇕ࡢ㸰㸬ᢎ㸦ᨾ㸧኱ሯಖ἞ᩍᤵᣦᑟࡢࡶ࡜㸪༤ኈㄽᩥࡢㄢ㢟ࡣ㸪ࠗங໬๣ࡀ㛤ጞ๣ࡢ୍ᡂศ࡜ࡋ࡚ാࡃங໬㔜ྜ࡛࠘࠶ࡗ
ࡓ㸬ලయⓗ࡟ࡣ㸪ࣀࢽ࢜ࣥᛶங໬๣ࡢ࢚ࢳࣞࣥ࢜࢟ࢩࢻ
㙐࡜ࢭ࣒ࣜ࢘࢖࢜ࣥ࡜ࡀᙧᡂࡍࡿࣞࢻࢵࢡࢫ⣔ࢆ౑ࡗࡓప 㔜ྜࡢᶵᵓ࡜㏿ᗘㄽ࡟ࡘ࠸࡚◊✲ࡋࡓ㸬ࡇࡇ࡛ࡢங

*≉௵ᩍᤵ ໬ᏛᩍᐊProfessor, Dept. of Chemistryg㧗ศᏊᚤ⢏Ꮚ࡜  ᖺ໬๣ࡣ㸪ங໬๣࡜㛤ጞ๣ࡢ㸰ᙺࢆ₇ࡌ࡚࠾ࡾ㸪ᚋ࡟ࡇࡢࣔࣀ࣐࣮ྍ⁐࣏࣐࣮ࣜ୙⁐ࡢ⁐፹୰࡛㔜ྜࢆ⾜࠺࡜㸪㔜ศ㔝࡛ά㌍ࡍࡿ㸪࠸ࢃࡺࡿ inisurf (initiator㸩surfactant)ࡢ

ྜࡢ㐍⾜࡟కࡗ࡚࣏࣐࣮ࣜࡀỿẊࡍࡿ㸬⢒኱࡞ỿẊ≀ࡀ㉮ࡾ࡜ゝ࠼ࡿࡶࡢ࠿ࡶࡋࢀ࡞࠸㸬  ⏕ᡂࡍࡿࡇ࡜ࡀከ࠸ࡀ㸪ࣔࣀ࣐࣮⁐๣㛤ጞ๣ࡢ⤌ࡳྜࡑࡢᚋ㸪ࢯ࣮ࣉࣇ࣮ࣜங໬㔜ྜ㸪␯Ỉᛶࣔࣀ࣐࣮ぶỈࢃࡏ࡟ࡼࡗ࡚ࡣ༢ศᩓ㧗ศᏊᚤ⢏Ꮚࢆ⏕ᡂࡍࡿࡇ࡜ࡀྍ

ᛶࣔࣀ࣐࣮ࡢࢯ࣮ࣉࣇ࣮ࣜங໬ඹ㔜ྜ࡟ᡭࢆᰁࡵࡓ㸬ᚋ

⬟࡛࠶ࡿ㸬
ࡇࢀࡀ㸪
ᚤ⢏Ꮚ⏕ᡂࡢࡓࡵࡢỿẊ㔜ྜ࡛࠶ࡾ㸪⪅࡟࠾࠸࡚ぶỈᛶࣔࣀ࣐࣮ࣘࢽࢵࢺࡣ⏕ᡂࡍࡿ㧗ศᏊᚤ

Pelton ࡣ N-࢖ࢯࣉࣟࣆࣝ࢔ࢡࣜࣝ࢔࣑ࢻ (N-isopropyl-⢏Ꮚ⾲㠃ᒙ࡟ᒁᅾࡋ࡚⢏ᏊࡢᏳᐃ໬࡟ᐤ୚ࡍࡿࡤ࠿ࡾ࡛

acrylamide 㸪 NIPAM) ࡢỈ⣔ỿẊ㔜ྜ࡛༢ศᩓ࣏ࣜ

࡞ࡃ㸪⢏Ꮚࡢᶵ⬟Ⓨ⌧࡟ࡶ㈉⊩࡛ࡁࡿࡇ࡜ࢆᏛࢇࡔ㸬඾

NIPAM (PNIPAM) ࡢྜᡂࢆᐇ⌧ࡋࡓࡀ㸪ࢃࢀࢃࢀࡣ㸪࢔ᆺⓗ࡞␯Ỉᛶࣔࣀ࣐࣮࡛࠶ࡿࢫࢳࣞࣥ࡜ぶỈᛶࣔࣀ࣐࣮

ࣝࢥ࣮ࣝ୰࡛ࡢ acrylamide ࡜ methacrylic acid ࡢỿẊඹ㔜࡛࠶ࡿ࢔ࢡࣜࣝ࢔࣑ࢻࢆ⤌ࡳྜࢃࡏ࡚ࢯ࣮ࣉࣇ࣮ࣜங໬

ྜ࡛ࢧ࢖ࢬศᕸࡢ⊃࠸࣏࣐࣮ࣜ⢏Ꮚࢆᚓࡓ㸬ᚓࡽࢀࡓ࣑

㔜ྜࢆ⾜࠸㸪
␯Ỉᛶࢥ࢔ぶỈᛶࢩ࢙ࣝ࠿ࡽᡂࡿࢥ࢔ࢩ࢙

ࢡࣟࢤࣝࢆᨵ㉁ࡍࡿ࡜୧ᛶ࣑ࢡࣟࢤࣝࡀᚓࡽࢀࡓ㸬ࡇࡢࣝ⢏Ꮚࢆᚓ࡚㸪ࢩ࢙ࣝࡀ♧ࡍ⾲㠃≉ᛶ㸪໬Ꮫⓗᛶ㉁ࡸ⏺

⢏Ꮚࡢㅖ≉ᛶࡢ S+ ౫Ꮡᛶࡣ㸪࠶ࡿ⢾ࢱࣥࣃࢡ⢏Ꮚ࡜㢮ఝࡇࡢ㛫࡟㸪U.

ࡋ࡚࠸ࡓ㸬  ࡑࡢࡇ࡜࡟㛵ᚰࢆᣢࡓࢀ㸪ࢩ࢔ࢺࣝ࡟タ❧㠃㟁Ẽ໬Ꮫⓗ≉ᚩ࡟ࡘ࠸࡚◊✲ࡋࡓ㸬

Mass. Amherst㸪ࡍ࡞ࢃࡕ࣐ࢧࢳࣗࢭࢵࢶᕞ❧኱Ꮫ㸦࢔ࡉࢀࡓ㹂㹂㹑㛵㐃࣋ࣥࢳ࣮ࣕ఍♫ࡢ࣮࣎ࢻ࣓ࣥࣂ࣮࡟ᣍ

࣐࣮ࢫࢺᰯ㸧࡟  ࢝᭶ᅾ⡠ࡋ㸪ࡑࢀࡲ࡛࡜඲ࡃ␗࡞ࡿ⎔⪸ࡉࢀࡓ㸬ࡇࡢ࣮࣎ࢻ࡟ࡣ㸪࣡ࢩࣥࢺࣥ኱ᏛࡢProfessor A.

ቃ࡛◊✲⏕άࢆ㏦ࡗࡓ㸬ࡑࡇ࡛ࡢᣦᑟᩍᤵࡣ㧗ศᏊ◊✲

Hoffman㸪MIT ࡢ Professor T. Tanaka㸪Mayo Clinic ࡢࢭࣥࢱ࣮Professor O. Vogl㸬ࢸ࣮࣐ࡣங໬㔜ྜ࠿ࡽ㞳ࢀ

Professor J. Fernandez ࡽࡀྠᖍࡋ㸪࢚࢟ࢧ࢖ࢸ࢕ࣥࢢ࡞᫬

࡚ Head-to-Head polymer (H-H ࣏࣐࣮ࣜ ࡢྜᡂ࡜࢟

㛫ࢆ࿡ࢃ࠼ࡓ㸬ࡋ࠿ࡋഹ࠿ 3 ᖺ࡛㸪኱ᡭ௻ᴗ࡟ࡼࡿ࣋ࣥ

ࣕࣛࢡࢱࣜࢮ࣮ࢩ࡛ࣙࣥ࠶ࡗࡓ㸬 H-H ࣏࣐࣮ࣜࡣ

ࢳ࣮ࣕ఍♫ࡢ㈙཰࡟ࡼࡾ㸪ࡑࡢᴦࡋ࠸≀ㄒࡣ⤊ࢃࡗࡓ㸬

㸦-CH2-CHX-CHX-CH2-㸧ࡢ⧞ࡾ㏉ࡋ༢఩ࢆᣢࡘ࣏ࣜ

࣑ࢡࣟࢤࣝࡣࢯࣇࢺ࣐ࢱ࣮࡛࠶ࡾ㸪ࡑࡢࢯࣇࢺࢿࢫࡢ

࣐࣮࡛㸪ࡑࡢྜᡂ࡟ṇ㠃࠿ࡽྲྀࡾ⤌ࢇࡔࡽ୍ᮅ୍ኤ࡛ࡣ

㉳※ࡣྍኚⓗ࡞ྵỈᛶ࡟࠶ࡾ㸪ᵝࠎ࡞ศ㔝ࡢ◊✲⪅ࡢ㛵∦௜࠿࡞࠸㸬⚾ࡀఏᤵࡉࢀࡓ᪉ἲࡣ㸪ࣈࢱࢪ࢚ࣥ

ᚰࢆ࿧ࢇࡔ㸬࡜ࡾࢃࡅὀ┠ࡉࢀࡓ࣑ࢡࣟࢤࣝࡣ ᗘᛂ⟅

㸦-CH2-CH=CH-CH2-㸧࡟ࣁࣟࢤࣥ࢞ࢫ(Cl2 ࡸ Br2) ࢆ྿ࡁ㎸ࢇ࡛ H-H ࣏ࣜሷ໬ࣅࢽࣝࡸ H-H ࣏ࣜ⮯໬ࣅࢽࣝࢆᚓࡿ࡜࠸࠺ࢺࣜࢵ࣮࢟࡞ࡶࡢ࡛㸪H-H ᵓ㐀ࡀ ㉸࡜ࢡࣟࢤࣝࢆྲྀࡾୖࡆࡓ◊✲ࡣ 1990 ᖺ௦ࡣᖺࢆ㏣࠺ࡈ࡜

࠸࠺ࡶࡢࡀ࡛ࡁࡓ㸬 ࡑ࠺࠸࠺◊✲ࡢྜ㛫࡟㸪ᖐᅜࡋࡓ࠶ࡿ࠸ࡣ࣊࢔ᒙ࡜ࡍࡿ⢏Ꮚࢆྲྀࡾୖࡆ㸪 ᗘᛂ⟅ᛶࡀ⏕ࡽఱࢆࡋࡼ࠺࠿⪃࠼࡚࠸ࡓ㸬㧗ศᏊᚤ⢏Ꮚࡢྜᡂ࡟࡜࡝

ࡳฟࡍᶵ⬟ࢆ㏣ồࡋࡓ㸬PNIPAM ࣑ࢡࣟࢤࣝࡣ 32Υ௜㏆ࡲࡿࡇ࡜࡟㣬ࡁ㊊ࡽ࡞࠸ᛮ࠸ࡣເࡗ࡚࠸࡚㸪సࡗࡓᚤ⢏࡟య✚㌿⛣ ᗘࢆᣢࡕ㸪ࡑࢀ௨ୗࡢ ᗘ࡛ࡣ㧗ᗘ࡟⭾₶Ꮚࡢᶵ⬟ࢆ⏕࠿ࡍ◊✲࡟㔜ᚰࢆ⛣ࡍពᚿࢆᣢࡗ࡚ᖐᅜࡋ
ࡓ㸬

㸱㸬㌿
ᶵ⬟ᛶᚤ⢏Ꮚ࡜ࡋ࡚ࡲࡎ╔┠ࡋࡓࡢࡣ㸪๓㏙ࡢぶỈᛶࢩ࢙ࣝ┦ࢆᣢࡘ⢏Ꮚ㸬ぶỈᛶ⾲㠃ࡣ⏕య㐺ྜᛶࡀࡼ࠸ࡇ
࡜࠿ࡽ㸪ࡑࢀࡽ⢏Ꮚࡢࣂ࢖࢜ศ㔝࡬ࡢᛂ⏝ࢆᡭ᥃ࡅࡓ㸬ᚤ⢏Ꮚࡢ⣽⬊࡜ࡢ┦஫స⏝㸪ࢱࣥࣃࢡ㉁࡜ࡢ┦஫స⏝㸪┦஫స⏝࡬ࡢᚤ⢏Ꮚ⾲㠃໬Ꮫᵓ㐀ࡢᙳ㡪㸪࡞࡝ࡢ◊✲ࢆᒎ㛤ࡋࡓ㸬ࣂ࢖࢜ศ㔝ࡢ◊✲ᣑᙇࡢࡓࡵ㸪ி㒔኱Ꮫ⟁⩏ேඛ⏕࡟ࡈ⤂௓࠸ࡓࡔ࠸࡚㸪◊✲ᐊ࡟⸨ᮏၨ஧༤ኈࢆ㏄࠼ࡓ㸬ࡇࢀ௨㝆ࡢ◊✲ᐊࡢ㊰⥺ࡣ㸪኱ࡁࡃ  ࡘ࡟ศ㢮ࡉࢀࡿ㸬୍ࡘࡣ࣑ࢡࣟࢤࣝ㸪௚ࡢ୍ࡘࡣ」ྜ⢏Ꮚ࡛࠶ࡿ㸬ࡲࡎ㸪࣑ࢡࣟࢤࣝ࠿ࡽ㏙࡭ࡿ㸬ࢃࢀࢃࢀࡀྲྀࡾୖࡆࡓࡢࡣ㸪࣑ࢡࣟࢤࣝࡢ࠺ࡕࡢ࣑ࢡࣟࣁ࢖ࢻࣟࢤࣝ㸪ࡍ࡞ࢃࡕ㸪Ỉࢆᢪ࠼㎸ࡴࢯࣇࢺ࣐ࢱ࣮㸬ࡑࡢస〇ࡣỿẊ㔜ྜ࡟ࡼࡗࡓ㸬ᛶ࣏࣐࣮࣑ࣜࢡࣟࢤ࡛ࣝ㸪୰࡛ࡶඛ࡟㏙࡭ࡓ PNIPAM ࣑࡟ຍ㏿ⓗ࡟ቑ኱ࡋࡓ㸬ᡃࠎࡣ㸪࣏ࣜ NIPAM ࢆࢩ࢙ࣝᒙ㸪⚄ዉᕝ኱ᏛᕤᏛ◊✲ᡤᡤሗ ➨  ྕࡋ㸪ࡑࢀ௨ୖ࡛ࡣ཰⦰ࡋࡓ㸬ኚ໬ࡣయ✚࡟࡜࡝ࡲࡽࡎ㸪ぢ࠿ࡅࡢȝ࣏ࢸࣥࢩࣕࣝ㸪ࢤࣝ⢏Ꮚࡢぶ␯Ỉᛶࡶ┦㌿⛣(6)ࡀ௒࡛ࡶᏑ❧ࡋ࡚࠸ࡿ㸬」ྜ⢏Ꮚ࡟ࡘ࠸࡚ࡣ㸪↓ᶵࢼࣀ⢏Ꮚྵ᭷࣑ࢡࣟࢤࣝࡢ

ᗘ௜㏆࡛኱ࡁࡃኚືࡋࡓ㸬 ࡇࡢ≉ᚩࢆ฼⏝ࡋ࡚㸪ࢤ◊✲ࢆ  ᖺ㐣ࡂ࠿ࡽጞࡵ㸪௒ࡶ⥅⥆୰࡛࠶ࡿ㸬⌧ᅾಙࣝ⢏Ꮚࢆ౑࠺࡜㸪 ᗘ࡟ࡼࡗ࡚ࢱࣥࣃࢡ㉁ࡢ྾⬺╔ࢆไᕞ኱Ꮫ‽ᩍᤵࡢ㕥ᮌ኱௓༤ኈࡀ୰ᚰ࡜࡞ࡗ࡚㸪ձ࣑ࢡࣟ

(7)

ᚚ࡛ࡁࡓ㸬

ࡲࡓ㸪࣏ࣜ NIPAM ⢏Ꮚࢆᩜࡁワࡵࡓࢩ࣮ࢤࣝ࡬ࡢ㔠ᒓ࢖࢜ࣥࡢᑟධ㸪ղ㔠ᒓ࢖࢜ࣥࡢࡑࡢሙ㑏ඖࢺࡢୖ࡟᧛✀ࡉࢀࡓ⣽⬊ࡣ࡯࡜ࢇ࡝่⃭ࢆཷࡅ࡞࠸ࡇ࡜㸪࡟ࡼࡿࢼࣀ⢏Ꮚ࡬ࡢኚ᥮㸪࡜࠸࠺ࣉࣟࢭࢫ࡛࠸ࡃࡘ࠿ࡢ

ࡑࡢ⣔ࡢ ᗘࢆ 25Υ࠿ࡽ 37Υ࡟ኚ࠼ࡿ࡜⣽⬊ࡣࡦ࡝ࡃᶵ⬟ᛶ」ྜᚤ⢏Ꮚࢆᚓࡓ㸬ࡑࡢ࠺ࡕࡢ୍ࡘ㸪㔠ࢼࣀ⢏Ꮚ่⃭ࡉࢀࡿࡇ࡜࡞࡝ࡢ▱ぢࢆᚓࡿࡇ࡜ࡀ࡛ࡁࡓ㸬(8) 㸦ᅗྵ᭷ 31,3$0 ࣑ࢡࣟࢤࣝࡣ㸪 ᗘୖ᪼࡟ࡼࡾศᩓᾮࡢⰍࡀ

3㸪࡞࠾㸪࣏ࣜࢫࢳࣞࣥ⢏Ꮚࢆᩜࡁワࡵࡓࢩ࣮ࢺୖ࡛ࡣ㸪ኚ໬ࡍࡿ࡜࠸࠺⌧㇟ࢆ♧ࡋࡓ㸬ࡇࢀࡣ㸪㌿⛣ ᗘࢆ㉸࠼␯Ỉᛶ⾲㠃ࡀⱞᡭ࡞⣽⬊ࡣ⃭ࡋࡃάᛶ໬ࡉࢀࡓ㸬㸧࡚㸪࣑ࢡࣟࢤࣝࡀ཰⦰ࡋ㸪ࢤࣝෆࡢ㔠ࢼࣀ⢏Ꮚࡢศᕸࡀ

ࡲࡓ㸪࣑ࢡࣟࣁ࢖ࢻࣟࢤࣝ࡟ࡣ⮬ᕫ㞟✚ᛶࡀ࠶ࡿࡇ࡜
ࡀ☜ㄆࡉࢀࡓ㸬࣑ࢡࣟࢤࣝศᩓᾮࡢ୍⁲ࢆᇶᯈୖ࡟ⴠ࡜

ኚ໬ࡋ࡚㸪⾲㠃ࣉࣛࢬࣔࣥ྾཰ࡢἼ㛗ࡀኚ໬ࡋࡓࡓࡵ࡟
㉳ࡇࡗࡓࡇ࡜࡟ࡼࡿ㸬  ࡋ࡚஝⇱ࡍࡿ࡜㸪⮬ᕫ㞟✚࡟ࡼࡾ⢏Ꮚࡀ୍ᐃࡢ㝽㛫ࢆ࠶ࡅ࡚(9) 2 ḟඖつ๎㓄ิᵓ㐀ࢆᙧᡂࡋ(ᅗ 4)㸪ᵓ㐀Ⰽࡀほ㸲㸬⤖ࡉࢀࡓ㸬(10) Ꮫ⾡ࣇࣟࣥࢸ࢕࢔஦ᴗ࡛ࡣࠗศᏊ࣭㉸ศᏊ࣭㉸ᵓ㐀య⌮ᕤᏛ࠘࡜࠸࠺₎Ꮠࡔࡅࡢྡ⛠ࡢࣉࣟࢪ࢙ࢡࢺࢆࢹ࢕ࣞ
ࢡࢱ࣮࡜ࡋ࡚㸪ࡲࡓ㸪 ୡ⣖ &2( ࣉࣟࢢ࣒࡛ࣛࡣ㸪ࠗࣛ࢖ࣇࢥࣥࢪࣗࢤ࣮ࢺࢣ࣑ࢫࢺ࣮ࣜ࠘࡜࠸࠺࢝ࢱ࢝ࢼࡤ࠿
ࡾࡢྡ⛠ࡢࣉࣟࢪ࢙ࢡࢺࢆᣐⅬ࣮ࣜࢲ࣮࡜ࡋ࡚ᚤຊ࡞ࡀ
ࡽ᮰ࡡࡘࡘ㸪
⮬ࡽࡣୖ㏙ࡢࢸ࣮࣐࡟⢔ࠎ࡜ᦠࢃࡗ࡚ࡁࡓ㸬 ᖺ࠿ࡽࡢ ᖺ㛫ࡣ៞᠕̿㈨⏕ᇽඹྠ◊✲ࣉࣟࢪ࢙ࢡ
ࢺࠗ⏕య⾲㠃࡜ᮦᩱ࡜ࡢ⏺㠃┦஫స⏝࠾ࡼࡧࡑࡢᛂ⏝࠘ࢆ⤫ᣓࡉࡏ࡚࠸ࡓࡔࡁ㸪௒ᰤᮾὒᏊඛ⏕ࡢᙉ኱࡞ࡈຓຊ
ࡢࡶ࡜㸪⏕య⾲㠃࡟㐺⏝࡛ࡁࡑ࠺࡞ᮦᩱࡢ◊✲㛤Ⓨ࡜ࡑࡇ࡛ぢࡽࢀࡿ⌧㇟ࡢゎ᫂࡟ᚑ஦ࡋࡓ㸬ᅄ௳ࡢࢸ࣮࣐ࡢ ௳ࠗศᏊ࢖ࣥࣉࣜࣥࢺ㧗ศᏊᚤ⢏Ꮚࡢ๰〇࡜ࡑࡢᶵ⬟࠘ࢆ⤂௓ࡍࡿ㸬   ศᏊ࢖ࣥࣉࣜࣥࢺࡣ㸪ศᏊࡢᙧែࢆ≀㉁࡟้༳㸦࢖ࣥࣉࣜࣥࢺ㸧ࡍࡿࡇ࡜ࢆព࿡ࡋ㸪ࡑࡢศᏊࡢ㑅ᢥⓗᤕ㞟ࡸ」ྜ⢏Ꮚࡢ୰࡛ࡣ㸪ࡲࡎ㸪ྜᡂ㧗ศᏊ࡜⏕యศᏊ࡜ࡢ

ศ㞳ࡢࢶ࣮ࣝࢆసࡾฟࡍࡇ࡜࡟฼⏝ࡉࢀࡿ㸬ᚑ᮶ࡢศᏊ

」ྜ࡟ࡼࡾᙧᡂࡉࢀࡿ࢔ࣇ࢕ࢽࢸ࢕ࣛࢸࢵࢡࢫ࡟ὀ┠ࡋ࢖ࣥࣉࣜࣥࢺࡣ◳࠸ᶞ⬡ࡢ୰࡟ศᏊࡢᙧࢆ้ࡳ㎸ࡴࡶࡢࡓ㸬࢔ࣇ࢕ࢽࢸ࢕ࣛࢸࢵࢡࢫࡣ㸪⏕య⣔࡛≉␗ⓗ࡟࢔ࣇ࡛㸪ຠ⋡ࡢᨵၿࡀㄢ㢟࡛࠶ࡗࡓ㸬ࢃࢀࢃࢀࡢ◊✲࡛ࡣ㸪࢕ࢽࢸ࢕ࢆ♧ࡍ࢝ࢵࣉࣝࡢ୍᪉ࢆ⢏Ꮚ࡟ᅛᐃࡋ㸪ࡑࡢ⢏ẚ⾲㠃✚ࡀ኱ࡁ࡞ࢯࣇࢺ࡞ᚤ⢏Ꮚࡢ⾲㠃ࢆ࢖ࣥࣉࣜࣥࢺ

Ꮚศᩓᾮࢆ౑ࡗ࡚㸪⏕యศᏊࡢΰྜ≀ࡢ୰࠿ࡽ㸪┦⿵ⓗࡢሙ࡜ࡋ࡚⏝࠸ࡿࡇ࡜ࢆ≉ᚩ࡜ࡋ࡚㸪ᅗ  ࡟♧ࡍᡭ㡰࡛࡞ᡂศࡔࡅࢆ㑅ᢥⓗ࡟㔮ࡾୖࡆࡿᶵ⬟ࢆᣢࡘࡶࡢࢆᣦࡍ㸬┠ⓗ≀ࢆᚓࡓ㸬ᢠయࢆᅛᐃࡋ㸪ᢠཎࡢ᳨ฟ࡟౑࠺㸪࠸ࢃࡺࡿࣛࢸࢵࢡࢫ
デ᩿⸆ࡀࡑࡢⲡศࡅ࡜ゝࡗ࡚࠸࠸㸬࢔ࣇ࢕ࢽࢸ࢕ࣛࢸࢵ
ࢡࢫ࡟౑ࢃࢀࡿᚤ⢏Ꮚ࡟ᚲせ୙ྍḞ࡞≉ᛶࡣ㸪㠀≉␗྾╔ࢆ࠾ࡇࡉ࡞࠸஦࡛࠶ࡿ㸬ᮾᕤ኱༙⏣ᏹᩍᤵ࡜ࡢඹྠ◊✲࡛㸪ࡑࡢࡓࡵࡢ᭱㐺࡞⢏Ꮚ࡜ࡋ࡚㸪ࢫࢳࣞࣥࢢࣜࢩࢪ
࣓ࣝࢱࢡ࣮ࣜࣞࢺඹ㔜ྜయ⢏Ꮚࢆタィࡋࡓ㸬ࡑࡢ⢏Ꮚ࡟㸪
≉ᐃࡢሷᇶ㓄ิࡢ '1$ ࡸࢱࣥࣃࢡ㉁㸪⸆๣ࢆᅛᐃࡋ㸪┦⿵ⓗ࡞ᡂศࢆศ㞳ࡋࡓࡾᅇ཰ࡋࡓࡾࡍࡿ⏝㏵࡟౪ࡋࡓ㸬࢔ࣇ࢕ࢽࢸ࢕ࣛࢸࢵࢡࢫ࡟ࡘ࠸࡚ᚓࡽࢀࡓ≉チ࡟ᇶ࡙ࡁฟ᮶ୖࡀࡗࡓ࣋ࣥࢳ࣮ࣕ఍♫ࡣ㸪ᙧࡇࡑኚࢃࡗࡓ

㧗ศᏊᚤ⢏Ꮚ࡜  ᖺᅗ  ࡢ୰࡛㸪LQLIHUWHU㸦 㸧ࡣࣜࣅࣥࢢ㔜ྜࡢ㛤ጞࡢࡓࡵࡢศᏊ࡛㸪ࡇࡇࢆ㛤ጞⅬ࡜ࡋ࡚࢔ࢡࣜࣝ࢔࣑ࢻࡢࣜ
ࣅࣥࢢࢢࣛࣇࢺ㔜ྜࢆ࠾ࡇ࡞ࡗ࡚㸪ཌࡉࡀࢱ࣮ࢤࢵࢺศ
Ꮚ㸦ࡇࡇ࡛ࡣ࣊ࣔࢢࣟࣅࣥศᏊ㸧ࡢࢧ࢖ࢬ࡟࡯ࡰ➼ࡋ࠸ࢩ࢙ࣝᒙࢆసࡗࡓ㸬㠀≉␗྾╔ࢆᢚ࠼ࡁࢀ࡞࠿ࡗࡓࡀ㸪࢖ࣥࣉࣜࣥࢺࡋࡓሙࡣ᫂☜࡟ࢱ࣮ࢤࢵࢺศᏊ㑅ᢥᛶࢆ♧ࡋࡓ㸬⏘Ꮫࡢᐦ࡞㐃ᦠࡢᴦࡋࡉ࡜㞴ࡋࡉࢆ࿡ࢃࡗࡓ㈗㔜࡞ ᖺ㛫ࢆ⤊࠼ࡓᚋ㸪⚄ዉᕝ኱Ꮫ໬Ꮫᩍᐊ࡟㏄࠼࡚࠸ࡓࡔ࠸
ࡓ㸬ᑠࡌࢇࡲࡾ࡛ࡣ࠶ࡾ࡞ࡀࡽ◊✲ᐊࢆᣢࡘࡇ࡜ࡶㄆࡵ
ࡽࢀ㸪◊✲ࢆ⥆ࡅࡿࡇ࡜ࡀ࡛ࡁࡓ㸬டᒣᩔᩍᤵࡢ◊✲ᐊᏛ⏕ㅖྩࡢ༠ຊࡶ࠸ࡓࡔࡁ࡞ࡀࡽᡭࡀࡅࡓࢸ࣮࣐ࡣ㸪ࠗศᏊ࢔ࢭࣥࣈࣜࣥࢢ࡟ࡼࡿ᪂ወ࣑ࢡࣟࢤࣝࡢྜᡂ࠘ࠗ↓ᶵࢼࣀ⢏Ꮚྵ᭷࣑ࢡࣟࢤࣝࡢྜᡂ࡜ᶵ⬟่⃭࠘ࠗᛂ⟅ᛶ࣑ࢡ
ࣟࢤࣝࢆ⏝࠸ࡓࣆࢵ࢝ࣜࣥࢢ࢚࣐ࣝࢩࣙࣥࡢ⏕ᡂ࡜ࡑࡢ≉ᛶ࠘ࠗ᪂ࡓ࡞ᡂศࢆඹᏑࡉࡏࡓங໬㔜ྜࡢ཯ᛂ࡜⏕ᡂ≀࡟㛵ࡍࡿ≉ᚩ࠘࡞࡝࡛࠶ࡿ㸬ᅗ  ࡣࠗ↓ᶵࢼࣀ⢏Ꮚྵࣞࣇ࢓ࣞࣥࢫ

᭷࣑ࢡࣟࢤࣝࡢྜᡂ࡜ᶵ⬟࠘୰࡛ᚓࡽࢀࡓ㸪㖟ࢼࣀ⢏Ꮚ(1) ⸨஭࣭኱ሯ࣭ᕝཱྀ 㧗ศᏊ໬Ꮫ 26, 163 (1969) ྵ᭷࢝ࣝ࣎࢟ࢩ࣓ࢳࣝࢭ࣮ࣝࣟࢫ࣑ࢡࣟࢤࣝࡢ㉸ⷧษ∦෗┿࡛࠶ࡿ㸬

෇ᙧࡢ୰࡟ⅬᅾࡍࡿᩘከࡃࡢⅬࡀ㖟ࢼ(2)኱ሯ࣭ᕝཱྀ࣭㔠㇂ 㧗ศᏊㄽᩥ㞟31, 87 (1974)(3).Y.Ohtsuka,

H. Kawaguchi, Y. Sugi, J. Appl. Polym. Sci. 26, 1637 (1981)ࣀ⢏Ꮚ࡛࠶ࡿ㸬ࡇࡢ࣑ࢡࣟࢤࣝࡢᵓ㐀ࢆゎᯒࡋ㸪㑏ඖ཯(4) H. Kawaguchi, Y. Sumida, J. Muggee, O. Vogl, Polymer, 23, 1805

ᛂゐ፹࡜ࡋ࡚ࡢᶵ⬟ホ౯ࢆ㐍ࡵ࡚࠸ࡿ㸬

(1982)

(5) M. Kashiwabara, K. Fujimoto, H. Kawaguchi, Colloid Polym. Sci.,273, 339 (1995)

(6) K. Fujimoto, Y. Nakajima, H. Kawaguchi, Polym Intl., 30, 237

(1993)

(7) H. Kawaguchi, K. Fujimoto, Y. Mizuhara, Colloid Polym. Sci., 270,



53 (1992)
(8) M. Miyaki, K. Fujimoto, H. Kawaguchi, Colloids Surfaces A, 153,



603 (1999)(9) S. Tsuji, H. Kawaguchi, Macromolecules, 39(13) 4338 82006)(10) S. Tsuji, H. Kawaguchi, Langmuir, 21, 2434 (2005)㸳㸬➹ࢆ⨨ࡃ๓࡟

(11) H. Kawaguchi, A. Asai, Y. Ohtsuka, H. Watanabe, T. Wada, H..

 㧗ศᏊᚤ⢏Ꮚࡢᮏ᱁ⓗ◊✲ࡢ㯪᫂ᮇࡣ㸪 ᖺ௦࡜࠸Handa, Nucleic Acids Res., 17, 6229-6240(1989)࠼ࡿ㸬⤊ᡓࡢᚋ㸪ங໬㔜ྜἲࡢ῝໬࡜ᣑᙇ㸪ᶵჾศᯒࡢ(12) N. Shimizu, M. Hatakeyama, H. Kawaguchi, H. Watanabe, H.

Ⓨ㐩㸪ࢼࣀ࣭࣓ࣞ࣋ࣝࢰࣞ࣋ࣝࡢ⛉Ꮫࡢ㐍໬㸪ቃ⏺㡿ᇦ

Handa, et al. Nature Biotech., 18, 877 (2000)◊✲ࡢⓎᒎ࡞࡝ࡢᚋᢲࡋࡀ࠶ࡗ࡚㸪 ୡ⣖ᚋ༙ࡣᚤ⢏Ꮚ(13) D. Suzuki, H. Kawaguchi, Langmuir, 22, 3818 (2006)◊✲ⰼ┒ࡾࡢ᫬௦࡛࠶ࡗࡓ㸬⾲  ࡟ࡑࢀࢆ♧ࡍ㸬ࡑࡢ᫬(14) H. Ugajin, T. Oka, N. Ueno, T. Abe, H. Kawaguchi, Colloid Polym.

௦࡟ᙜヱศ㔝ࡢ◊✲⪅࡛࠸ࡽࢀࡓࡇ࡜ࢆᖾࡏ࡟ᛮ࠺㸬

Sci., 291,109 (2013)

ᴫ㏙ࡋࡓ⣙  ᖺࡢ◊✲ࡢ㏵ୖ࡛ฟ఍࠸ࡈᨭ᥼࠸ࡓࡔ
࠸ࡓ◊✲⪅ࡢⓙᵝ㸪࠸ࡘࡶᑠ⫋ࡢ◊✲ᐊࢆᨭ࠼┒ࡾୖࡆ࡚ୗࡉࡗࡓ㝔⏕࣭Ꮫ㒊⏕ㅖྩ㸪࡟⾺ᚰࡼࡾ࠾♩ࢆ⏦ࡋୖࡆࡲࡍ㸬(15) Y. Sano, not published yet.





2012 ᖺᗘ㸦ᖹᡂ 24 ᖺᗘ㸧ᕤᏛ◊✲ᡤᖺḟሗ࿌㸯㸬ே஦ 㸯㸧㐠Ⴀጤဨᡤ  㛗        ᪂୰ ᪂஧ ᩍᶵᲔᕤᏛ⛉ᤵ     ᕤ⸨ 㑥⏨ ᩍ ᤵ㟁Ẽ㟁Ꮚ᝟ሗᕤᏛ⛉≀㉁⏕࿨໬Ꮫ⛉   ᒣཱྀ ᰤ㞝 ᩍ

  

ᤵ

 బ⸨ ᠇୍ ᩍ ᤵ᝟ሗࢩࢫࢸ࣒๰ᡂᏛ⛉    ዟ㔝 ⚈஧ ຓ ᩍ⤒ႠᕤᏛ⛉       ୰ᓥ ೺୍ ᩍ ᤵᘓ⠏Ꮫ⛉ 

Ᏻ⏣ ὒ௓ ෸ᩍᤵ     ᩘᏛᩍᐊ      ᒣᓮ ᩍ᫛ ᩍ ᤵ 㸰㸧◊✲ᡤᐈဨᩍᤵす  ࿴ኵ㸦2012.4㹼2013.3㸧       ᮤ  ᮽ 㸦2012.10㹼2013.9㸧
኱⇃ Ṋྖ㸦2012.4㹼2013.3㸧

ᇼ㔝 ᐃ㞝㸦2012.4㹼2013.3㸧

బ⸨ ♸୍㸦2012.4㹼2013.3㸧       ኱⃝ ᗣᙪ㸦2012.10㹼2013.9㸧
ᑠᔱ ⱥ୍㸦2012.4㹼2013.3㸧

⛙㔝 ṇ἞㸦2012.10㹼2013.9㸧

ᮡཎ ῟ 㸦2012.4㹼2013.3㸧

㜿㒊 ⱥᶞ㸦2012.10㹼2013.9㸧

チ  ⍞㑥㸦2012.10㹼2013.9㸧

ఀᮾ ᆂᫀ㸦2012.4㹼2013.3㸧

Ṋ⏣ 㔜႐㸦2012.10㹼2013.9㸧     ᒣ⏣ ಖ἞㸦2012.4㹼2013.3㸧

 㸱㸧◊✲ᡤᐈဨ◊✲ဨ኱࿴ ⿱ᖾ㸦2008.10㹼2013.3㸧       ᕝୖ ༤ྖ㸦2011.4㹼2013.3㸧
ஂಖ Ⓩ 㸦2008.10㹼2013.3㸧       ྖ  ᏹಇ㸦2011.10㹼2013.9㸧
㱟  㔜ἲ㸦2008.10㹼2013.3㸧       Li ZhiGang㸦2012.4㹼2013.3㸧
▼಴ ⌮᭷㸦2008.10㹼2013.3㸧       ᣢ⏣ ⏤ᖾ㸦2012.4㹼2014.3㸧
▼ᕝ ༤ᩄ㸦2008.10㹼2013.3㸧       㔠  ᚨ༳㸦2012.10㹼2014.9㸧
⸼  ᮅ㍤㸦2009.10㹼2013.9㸧       㔠Ꮚ ಙᝅ㸦2012.10㹼2013.9㸧
࿘  ᘓᮾ㸦2009.10㹼2013.9㸧

 㸲㸧◊✲ᡤ≉ู◊✲ဨ໭ᓥ ๰ 㸦2008.10㹼2013.3㸧       ➉ෆ ㄔ 㸦2012.4㹼2014.3㸧

㸳㸧◊✲ᡤ⫋ဨᩍົᢏ⾡⫋ဨ  ⴗཎ ೺ྖ         ᢏ⾡ဨ  ඵ㧗 ඃ຾    㸰㸬ண ⟬
ᖹᡂ 24 ᖺᗘࡢண⟬࣭Ỵ⟬㢠ࢆ⾲㸫㸯࡟♧ࡍࠋ      ⾲㸫㸯     㸦༢఩㸸༓෇㸧
ᴗ

ົ

㡯

┠

ண ⟬ 㢠

*ᕤᏛ◊✲ᡤඹྠ◊✲ෆヂỴ ⟬ 㢠◊✲ᡤ㐠Ⴀ㈝

2,537

2,533

኱ᆺඹྠタഛ⟶⌮㐠Ⴀ

4,000

3,960

୰ᒣ

ᩍᤵ

3,000

ᕤᏛ◊✲ᡤඹྠ◊✲*14,00014,049

୰ᓥ

ᩍᤵ

2,100

㸦≉㸧ࢸࢡࣀࣇ࢙ࢫࢱ

2,877

2,364

   ᘬᆅ

ᩍᤵ

2,100

223

0

ᯇᮏ ෸ᩍᤵ

 3,000

1,500

916

ᯇ⏣ ෸ᩍᤵ

3,800

25,137

23,828ィ

14,000㸦≉㸧ⱝ⪅࡜ㄒࡿ
㸦≉㸧ࢸࢡࣀࢧ࣮ࢡࣝྜ    ィඹྠ◊✲௦⾲⪅ண⟬㢠㸦༓෇㸧㸱㸬ඹྠ◊✲㸭ࣉࣟࢪ࢙ࢡࢺ◊✲ᖹᡂ 24 ᖺᗘࡢᕤᏛ◊✲ᡤඹྠ◊✲㸭ࣉࣟࢪ࢙ࢡࢺ◊✲ࢆ⾲㸫㸰࡟♧ࡍ
⾲㸫㸰
ඹྠ◊✲

☢ᛶయᮦᩱ࡜㉸ఏᑟయᮦᩱࢆ౑ࡗࡓ㔞Ꮚຠᯝࢹࣂ࢖ࢫࡢヨసᣢ⥆ྍ⬟♫఍ᐇ⌧ࡢࡓࡵࡢ࣮ࣜࣥ⏕⏘࣭≀ὶࢩࢫࢸ࣒࡟㛵ࡍࡿ◊✲⎔ቃㄪ࿴ᆺ≀㉁ኚ᥮࠾ࡼࡧ᪂࢚ࢿࣝࢠ࣮ࣉࣟࢭࢫ๰ฟࡢᇶ┙࡜࡞ࡿࢼࣀᵓ㐀ゐ፹ࡢ㛤ⓎᏳ඲࣭Ᏻ౯࡞᪂ᆺ✵Ẽ㟁ụ㛤Ⓨࡢࡓࡵࡢせ⣲ᢏ⾡ࡢ᳨ウ㺔㺎㺬㺼㺻㺣㺧㺟㺋㺎㺪㺼ෆ㒊ࡢࢼࣀ✵Ὕࢆ฼⏝ࡋࡓỈศᏊ㓄ྥไᚚ࡟ࡼࡿᴟᚤᑠ
ㄏ㟁యࡢ๰〇࡜ࡑࡢ≀ᛶゎ᫂୰ᒣ ᫂ⰾ㸭㟁Ẽ㟁Ꮚ᝟ሗᕤᏛ୰ᓥ ೺୍㸭⤒ႠᕤᏛᘬᆅ ྐ㑻㸭≀㉁⏕࿨໬Ꮫᯇᮏ ኴ㸭≀㉁⏕࿨໬Ꮫᯇ⏣ ࿴அ㸭≀⌮⚄ዉᕝ኱ᏛᕤᏛ◊✲ᡤᡤሗ ➨  ྕࣉࣟࢪ࢙ࢡࢺ◊✲㸿㧗࿘Ἴᅇ㊰ࡢゎᯒ࣭タィ⌮ㄽࡢᩚഛ࡜ᑐᛂࢯࣇࢺ㛤Ⓨ㸫ᅛ᭷࣮ࣔࢻ࡟ᇶ࡙ࡃཝᐦ࡞➼౯ᅇ㊰ࢆ㐺⏝ࡋ࡚㸫✰⏣ ဴኵ㸭㟁Ẽ㟁Ꮚ᝟ሗᕤᏛ

㹁኱Ẽ⎔ቃ໬Ꮫ◊✲ᡤ஭ᕝ Ꮫ㸭≀㉁⏕࿨໬Ꮫ㹁㧗Ᏻᚰ࣭㉸Ᏻ඲஺㏻◊✲ᡤ㸦㹉㹓㸫㹕㹇㹎㹄㸧ᯇᾆ ᫓ᶞ㸭⤒ႠᕤᏛ㹁㜵⅏ࡲࡕ࡙ࡃࡾᨭ᥼◊✲ࢭࣥࢱ࣮ⲥᮏ Ꮥஂ㸭ᘓ⠏㹁ᆅඖఫẸ࡜༠ຊࡋ࡚ᐇ᪋ࡍࡿ⏫࡙ࡃࡾ◊✲ᡤࡢ๰タ࡜㐠Ⴀෆ⏣ 㟷ⶶ㸭ᘓ⠏㸿ᵓ㐀≀ࡢ⪏㟈Ᏻ඲ᛶཬࡧ⪏ஂᛶࡢホ౯᪉ἲ࡟㛵ࡍࡿ◊✲㉿ ⾝๛㸭ᘓ⠏㸿㧗ᛶ⬟⇕㟁Ⓨ㟁ᮦᩱࡢ㛤Ⓨᒣᮧ ༤㸭≀㉁⏕࿨໬Ꮫ㸿᪂ࡓ࡞పⅣ⣲࢚ࢿࣝࢠ࣮♫఍࡟ᑐᛂࡋࡓ᪂ᆺ㟁ụࡢ㛤Ⓨᯇᮏ ኴ㸭≀㉁⏕࿨໬Ꮫ㸿ᐇ⏝ࢫࢱ࣮ࣜࣥࢢ࢚ࣥࢪࣥࡢ㛤Ⓨ࡜ࡑࡢᛂ⏝ཎᮧ ჆ᙪ㸭ᶵᲔᕤᏛ㸿୕ḟඖ࿘Ἴᩘศᯒࢆ⏝࠸ࡓ᣺ືࣔࢹࣝ໬ᢏ⾡ࡢᵓ⠏ᒣᓮ ᚭ㸭ᶵᲔᕤᏛ㸿ከศᒱ࣏࣐࣮ࣜ⣔ࢼࣀࣁ࢖ࣈࣜࢵࢻᮦᩱࡢ㛤Ⓨ࡜ᛂ⏝ᶓ⃝ ຮ㸭≀㉁⏕࿨໬Ꮫ㸲.ㅮ₇఍ࠕᬽࡽࡋࡢ୰ࡢࢧ࢖࢚ࣥࢫࠖ㐃⥆ㅮ₇఍ࢸ࣮࣐㸸ࠗࣄࢺ࣭ࣔࣀ࣭࢝ࢿࡢ࣐ࢿࢪ࣓ࣥࢺ࠘    ̿⤒ႠᕤᏛ࡛ၥ㢟ゎỴ̿ሙ ᡤ㸸⚄ዉᕝ኱Ꮫࡳ࡞࡜ࡳࡽ࠸࢚ࢡࢫࢸࣥࢩࣙࣥࢭࣥࢱ࣮

࣮࢜࢞ࢼ࢖ࢨ࣮㸸୰ᓥ ೺୍㸦⚄ዉᕝ኱ᏛᕤᏛ㒊ᩍᤵ㸧‫ ➨ە‬1 ᅇ 2012 ᖺ 9 ᭶ 29 ᪥㸦ᅵ㸧13:30㹼16:50
1 ⌧㇟ࢆぢ࠼ࡿ໬ࡋࡼ࠺㸫ၥ㢟ゎỴࡣࡌࡵࡢ୍Ṍ  ⚄ዉᕝ኱ᏛᕤᏛ㒊ᩍᤵ  ୰ᓥ ೺୍ ඛ⏕
2 ඈࡅࡿ௙⤌ࡳࢆ⪃࠼ࡼ࠺㸫࠾㔠ࡢ▱㆑ࡣࡌࡵࡢ୍Ṍ  㧗ᗘ⫋ᴗ⬟ຊ㛤Ⓨಁ㐍ࢭࣥࢱ࣮  ⛅ᒣ 㝯 ඛ⏕‫ ➨ە‬2 ᅇ 2012 ᖺ 10 ᭶ 20 ᪥㸦ᅵ㸧13:30㹼16:50
1 ▱㆑ࡀ⏕ࡲࢀࡿ⤌⧊㸦ᐙᗞ㸧㸫఍㆟ࡢ㐍ࡵ᪉ࡣࡌࡵࡢ୍Ṍ  ओKANJIE ASSOCIATES ௦⾲  ⏣୰ ᾈྖ ඛ⏕
2 ⤌⧊ࡢຠ⋡࢔ࢵࣉ㸟㸫ࡇ࡜ࡤࡢ▱㆑ࡣࡌࡵࡢ୍Ṍ  ओࢥࢽ࣑࢝ࣀࣝࢱࢸࢡࣀࣟࢪ࣮ࢭࣥࢱ࣮࢖ࣀ࣮࣋ࢩࣙࣥࢭࣥࢱ࣮㛗  ཎ㈡ ⚽᫛ ඛ⏕㸳㸬⚄኱ࢸࢡࣀࣇ࢙ࢫࢱ㸰㸮㸯㸰 ̿ᬽࡽࡋ࡜⎔ቃࡢᮍ᮶̿
᪥᫬㸸2012 ᖺ 12 ᭶ 14 ᪥㸦㔠㸧12:00㸫17:30
ሙᡤ㸸⚄ዉᕝ኱Ꮫᶓ὾࢟ࣕࣥࣃࢫ 2 ྕ㤋₇⩦ᐊ࣭1 ྕ㤋 804 ᐊᐇ᪋ෆᐜ㸯㸧ㅮ₇఍㸦1 ྕ㤋 308 ᐊ㸧  ᕤᏛ⣔ㅮ₇ࠗ㟁Ẽ࣭ᶵᲔ࣭ᘓ⠏Ꮫ࠿ࡽࡳࡓ㡢㡪࡜⎔ቃࡢ㛵ࢃࡾ࠘3 ௳≉ูㅮ₇ ࠗ㟁ụᢏ⾡࡜ḟୡ௦㟁ື㌴୧࠘᪥⏘⮬ື㌴ओ⥲ྜ◊✲ᡤ ඛ➃ᮦᩱ◊✲ᡤ  ୺⟶◊✲ဨ ⛙㔝 ṇ἞ Ặ㸦⚄ዉᕝ኱ᏛᕤᏛ◊✲ᡤ ᐈဨᩍᤵ㸧㸰㸧◊✲࣏ࢫࢱ࣮Ⓨ⾲㸦2 ྕ㤋₇⩦ᐊ㸧  ኱Ꮫ㝔⏕࡟ࡼࡿ࣏ࢫࢱ࣮Ⓨ⾲࣭సရᒎ♧ 67 ௳  Ꮫ㒊⏕࡟ࡼࡿ࣏ࢫࢱ࣮Ⓨ⾲ 29 ௳  ࢸࢡࣀࢧ࣮ࢡࣝ࡟ࡼࡿ࣏ࢫࢱ࣮Ⓨ⾲࣭సရᒎ♧ 5 ௳   ⥲ィ 101 ௳㸱㸧ᐇ₇ᒎ♧ 3 ௳㸦᪥⏘࣮ࣜࣇࠊ㺨㺼㺎㺟㺊㺷ᆅ⌫ྐ༤≀㤋ᫎീࠊᏱᐂ࢚࣮ࣞ࣋ࢱ㸧㸲㸧௻ᴗᒎ♧ 30 ♫ࠊ1 ྠ❆఍㸦2 ྕ㤋₇⩦ᐊ㸧㸳㸧◊✲┦ㄯ❆ཱྀ㸦2 ྕ㤋₇⩦ᐊ㸧㸴㸧ᢏ⾡࣭᝟ሗ஺᥮఍㸦10 ྕ㤋 3 㝵Ꮫ⏕ࣛ࢘ࣥࢪ 18:00㸫19:30㸧

⚄ዉᕝ኱ᏛᕤᏛ◊✲ᡤᡤሗ ➨  ྕ㸴㸬኱ᆺ⿦⨨౑⏝ᐇ⦼ᖹᡂ  ᖺᗘࡢ኱ᆺ⿦⨨⿦⨨౑⏝ᐇ⦼ࢆ⾲㸫㸱࡟♧ࡍࠋ                  ⾲㸫㸱           㸦᫬㛫㸧


◊✲ᐊྡ

㼀㻱㻹

㻿㻱㻹

㼄㻾㻰

㼀㻲㻙㼄㻾㻰

㼄㻼㻿

㻵㻯㻼

㻯㻯㻰

㻺㻯㻿㻹



ᶵᲔᕤᏛ⛉

㻜

㻜

㻝㻠㻞

㻜

㻜

㻜

㻜

㻠㻜



ᕤ⸨◊✲ᐊ

㻝㻝㻤

➉ᮧ◊✲ᐊ

㻝㻜㻠㻚㻡

㻞㻠

୰ᑿ◊✲ᐊ
㟁Ẽ㟁Ꮚ᝟ሗᕤᏛ⛉

㻠㻜
㻜

㻞㻟㻤㻚㻡

㻟㻝

ᖹᡭ◊✲ᐊ

㻞㻝㻟

㻞㻞

ᒣཱྀ◊✲ᐊ

㻞㻡㻚㻡

㻥

㻠㻥㻟㻚㻡

㻤㻟㻜

㻜

㻜

㻜

㻜

㻜

㻡㻡

㻝㻠㻣㻚㻡

㻝㻟㻜㻡

㻝㻡㻝㻟

㻜

୰ᒣ◊✲ᐊ

≀㉁⏕࿨໬Ꮫ⛉

㻟㻢㻜㻚㻡

஭ᕝ◊✲ᐊ
ụཎ◊✲ᐊ

㻝㻜㻚㻡
㻞㻟

㻡㻢㻟
㻝㻥㻜

ᒸᮏ◊✲ᐊ

㻝㻢

ᑠ㔝◊✲ᐊ
㔠◊✲ᐊ

㻞㻝㻣
㻡㻞㻚㻡

ᑠฟ◊✲ᐊ
ෆ⸨◊✲ᐊ

㻝㻢㻡㻚㻡

㻝㻤㻥

㻡

㻝㻞
㻤㻥

㻣㻟㻡

㻠㻥㻚㻡

㻢㻟

ᘬᆅ◊✲ᐊ
ᯇᮏ◊✲ᐊ

㻟㻤
㻡㻢

㻝㻥㻢

ᒣᮧ◊✲ᐊ
໬Ꮫᩍᐊ

㻡㻜

㻝㻞

டᒣ◊✲ᐊ

㻞㻝㻝

㻝㻡㻣

㻠㻡

㻞㻣㻤

㻞㻟㻚㻡

㻢㻥㻜

㻣㻟㻚㻡

㻠㻟㻣㻚㻡

㻡㻡

㻢

㻟㻝㻚㻡

㻜

㻜

㻜

㻜

㻜

㻜

㻜

㻜

㻞㻢㻤

㻜

㻞㻠

㻜

㻤㻚㻡

ᕝཱྀ◊✲ᐊ

㻝㻞

㻝㻡

⌮Ꮫ㒊

㻜

㻜

ᕝᮏ◊✲ᐊ

㻞㻠㻚㻡

㔝ᐑ◊✲ᐊ

㻡㻚㻡

ᒣཱྀ◊✲ᐊ

㻞㻟㻤

㻞㻠

୕┦ங໬䝥䝻䝆䜵䜽䝖

㻢㻟

㻞㻠

㻢㻠

㻢㻚㻡

㻝㻤

㻜

㻜

㻜

ྜィ᫬㛫

㻠㻟㻡㻚㻡

㻣㻣㻥㻚㻡

㻝㻜㻢㻣

㻢㻝㻚㻡

㻠㻟㻟㻚㻡

㻝㻟㻜㻡

㻝㻡㻟㻣

㻠㻜

ᶵᲔᕤᏛ⛉䠄䠂䠅

㻜㻚㻜

㻜㻚㻜

㻝㻟㻚㻟

㻜㻚㻜

㻜㻚㻜

㻜㻚㻜

㻜㻚㻜

㻝㻜㻜

㟁Ẽ㟁Ꮚ᝟ሗᕤᏛ⛉䠄䠂䠅

㻜㻚㻜

㻟㻜㻚㻢

㻞㻚㻥

㻜㻚㻜

㻜㻚㻜

㻜㻚㻜

㻜㻚㻜

㻜

≀㉁⏕࿨໬Ꮫ⛉䠄䠂䠅

㻤㻞㻚㻤

㻢㻟㻚㻟

㻣㻣㻚㻤

㻤㻥㻚㻠

㻟㻠㻚㻜

㻝㻜㻜㻚㻜

㻥㻤㻚㻠

㻜

ඹ㏻ᩍᐊ䠄䠂䠅

㻞㻚㻤

㻟㻚㻜

㻜㻚㻜

㻜㻚㻜

㻜㻚㻜

㻜㻚㻜

㻜㻚㻜

㻜

⌮Ꮫ㒊䠄䠂䠅

㻜㻚㻜

㻜㻚㻜

㻜㻚㻜

㻜㻚㻜

㻢㻝㻚㻤

㻜㻚㻜

㻝㻚㻢

㻜

୕┦ங໬䠄䠂䠅

㻝㻠㻚㻡

㻟㻚㻝

㻢㻚㻜

㻝㻜㻚㻢

㻠㻚㻞

㻜㻚㻜

㻜㻚㻜

㻜



⚄ዉᕝ኱ᏛᕤᏛ◊✲ᡤᡤሗᇳ➹つ⛬ ᖺ㸦᫛࿴  ᖺ㸧 ᭶㸳᪥ᨵゞ  ᖺ㸦᫛࿴  ᖺ㸧 ᭶  ᪥ᨵゞ  ᖺ㸦ᖹᡂ㸰ᖺ㸧 ᭶  ᪥ᨵゞ  ᖺ㸦ᖹᡂ㸱ᖺ㸧 ᭶  ᪥ᨵゞ  ᖺ㸦ᖹᡂ㸴ᖺ㸧 ᭶  ᪥ᨵゞ  ᖺ㸦ᖹᡂ  ᖺ㸧 ᭶  ᪥㸯㸬ᢞ✏㈨᱁

㸲㸬ᥦฟᮇ᪥

ᢞ✏➹㢌⪅ࡣཎ๎࡜ࡋ࡚⚄ዉᕝ኱ᏛᕤᏛ㒊ᒓᩍ⫋ဨ࡜ࡍࡿ㸬ࡓࡔࡋཎ✏ࢆ⦅㞟ጤဨ఍ࡀ౫კࡍࡿሙྜࡣࡇࡢ㝈ࡾ࡛ࡣ࡞࠸㸬ࡲࡓ㐃ྡ⪅࡟ࡘ࠸࡚ࡣไ㝈ࡋ࡞࠸㸬ࡑࡢᖺᗘ࡟ࡼࡾᐃࡵࡿ㸬㸳㸬㡫ᩘ௨ୗࡢ㡫ᩘࡣࡍ࡭࡚ࠝๅࡾୖࡾࠞࡢࡶࡢࢆ♧ࡍ㸬㸰㸬グ஦ࡢ✀㢮⥲ྜ ㄽ ᩥ  ཎ๎࡜ࡋ࡚ 20 㡫௨ෆ㸬࿴ᩥࡢሙྜࡣࠝḢᩥᕳ 㢌
  ゝ ෆᐜᴫせ㸦1 㡫௨ෆ㸧ࠞ㸪Ḣᩥࡢ࡜ࡁࡣࠝ࿴ᩥㄽ   ㄝ  Ꮫၥ࣭ᢏ⾡࣭ᮏ◊✲ᡤࡢ஦ᴗ࣭ືྥ࡞࡝࡟ෆᐜᴫせ㸦1 㡫௨ෆ㸧ࠞࢆࡘࡅࡿࡇ࡜ࡀ࡛ࡁࡿ㸬㛵ࡍࡿㄽㄝ㸪ពぢ㸬⥲ ྜ ㄽ ᩥ  ᑓ㛛ࡢᏛ༠఍࡞࡝࡟Ⓨ⾲ࡉࢀࡓ◊✲ㄽᩥࢆ㦵Ꮚ࡜ࡋ࡚㸪ⴭ⪅ࡢ୍㐃ࡢ◊✲ࢆࡲ࡜ࡵ㸪ࡇࢀ࡟ࡑࡢศ㔝࡟࠾ࡅࡿᆅ఩ࢆ᫂ࡽ࠿࡟ࡍ
ࡿࡼ࠺࡞ゎㄝࢆⱝᖸࡘࡅࡓࡶࡢ㸬ඹྠ◊✲ሗ࿌ Ⓨ㊊᫬Ⅼ࡛ࡣࠝඹྠ◊✲ࡢ⤂௓ࠞ㸪୰㛫᫬Ⅼㄽㄝ࣭㝶᝿ ཎ๎࡜ࡋ࡚ 4 㡫௨ෆ㸬⥲ㄝ࣭ࢺࣆࢵࢡࢫ࣭ࡑࡢ௚ࡢグ஦ ཎ๎࡜ࡋ࡚ 8 㡫௨ෆ㸬㸴㸬ཎ✏ࡢ᭩ࡁ᪉
ཎ✏ࡢ᭩ࡁ᪉ࡣ㸪ࡇࡢࠝつ⛬ࠞ࡞ࡽࡧ࡟ࠝ⚄ዉᕝ኱Ꮫ ᕤᏛ◊✲ᡤ ᡤሗ ᇳ➹せ㡿ࠞ࡟ࡼࡿ㸬㸵㸬ཎ✏ࡢ㈐௵࡜ᶒ฼

࡛ࡣࠝඹྠ◊✲ࡢ⌧ἣࠞ㸪◊✲⤊஢ࡲࡓࡣ୍

ᥖ㍕ࡉࢀࡓㄽᩥ࡞࡝ࡢෆᐜ࡟ࡘ࠸࡚ࡢ㈐௵ࡣⴭ⪅ࡀ㈇࠺

ẁⴠࡢ᫬Ⅼ࡛ࡣࠝඹྠ◊✲ࡢᡂᯝせ⣙ࠞ࡜ࡶࡢ࡜ࡍࡿ㸬ࡲࡓࡑࡢⴭసᶒ㺃⦅㞟ฟ∧ᶒࡣࠝ⚄ዉᕝ኱Ꮫ

ࡋ࡚㸪ࡑࡢ⌧≧ࡀሗ࿌ࡉࢀࡿ㸬ᕤᏛ◊✲ᡤࠞ࡟ᒓࡍࡿ㸬⥲    ㄝ ⥲ྜㄽᩥ࡜␎ྠ୍ᛶ᱁ࡢグ஦࡛࠶ࡿࡀ㸪ゎㄝⓗⰍᙬࡢᙉ࠸ࡶࡢ㸬
ࢺࣆࢵ

ࢡ
 ࢫ
  ࡑࡢ᫬ࠎࡢࢺࣆࢵࢡࢫ࡟ࡘ࠸࡚ࡢᒎᮃ࠶ࡿ࠸ࡣゎㄝ㸬㝶    ᝿ ◊✲࣭㛤Ⓨ࡞࡝ࡢᛮ࠸ฟ㸪ពぢ㸪ឤ᝿㸪⤒㦂ㄯ࡞࡝㸬ᅜ㝿஺ὶ◊✲ Ꮫእ㸦ᅜෆ㸪ᅜእ㸧࡟࠾ࡅࡿ◊✲࣭ㅮ⩏࣭ฟᙇ࡟㛵ࡍࡿ⤒㦂ㄯ࡞࡝㸬≉    㞟 ࡑࡢྕࡢ≉㞟࡜ࡋ࡚≉ูグ஦ࢆタࡅࡿࡇ࡜
ࡀ࠶ࡿ㸬
㸱㸬⏝ㄒ
⏝ㄒࡣ࿴ᩥ࡜ࡍࡿ㸬ࡓࡔࡋ⥲ྜㄽᩥ࡟㝈ࡾḢᩥ࡛ࡶࡼ࠸㸬ࡲࡓࠝⱥᩥ┠ḟࠞసᡂࡢࡓࡵ㸪ཎ✏࡟ࡣࠝⱥᩥ㢟┠ࠞࡢ࡯࠿ࠝⴭ⪅Ặྡࠞ࠾ࡼࡧࠝ⫋ྡ㸪ᡤᒓࠞࡢⱥㄒྡࢆࡘࡅࡿ㸬㸶㸬᥇ྰཎ✏ࡢ᥇ྰ࠾ࡼࡧศ㢮ࡣࠝ⚄ዉᕝ኱Ꮫ ᕤᏛ◊✲ᡤ ⦅㞟ጤဨ఍ࠞ࡟࠾࠸࡚⾜࠺㸬㸷㸬ཎ✏ࡢᥦฟඛ
ཎ✏ࡢᥦฟඛࡣࠝ⚄ዉᕝ኱Ꮫ ᕤᏛ◊✲ᡤ ஦ົᐊࠞ࡜
ࡍࡿ㸬ࡑࡇ࡛ཷ㡿ࡋࡓ᪥ࢆཎ✏ཷ௜᪥࡜ࡍࡿ㸬㸯㸮㸬ࡑࡢ௚
㸦㸯㸧 ཎ✏ࡢᯛᩘࡀつᐃ㝈ᗘࢆ㉸㐣ࡍࡿሙྜࡣጤဨ఍
ࡢᢎㄆࢆせࡍࡿࡀ㸪≧ἣ࡟ࡼࡾ㉸㐣ศࡢᐇ㈝ࢆᚩ
ࡍࡿࡇ࡜ࡀ࠶ࡿ㸬㸦㸰㸧 ᅗࡀ༳ๅ࡟୙㐺ᙜ࡞ሙྜࡣ㸪ᑓ㛛ᐙ࡟౫კࡋ࡚᭩
┤ࡍࡇ࡜ࡀ࠶ࡿ㸬ࡇࡢሙྜࡢ⤒㈝ࡣⴭ⪅㈇ᢸ࡜ࡍ
ࡿ㸬



ᕤᏛ◊✲ᡤᡤሗᇳ➹せ㡿ᕤᏛ ኴ㑻㸨   ◊✲ᡤ ⰼᏊ㸨㸨

Making Reports of Research Institute for Engineering
Taro KOUGAKU㸨

Hanako KENKYUJO㸨㸨㸯㸬⥴ゝ㸱㸬グྕཬࡧ༢఩ࡢ᭩ࡁ᪉

‫ࡢࡇڧ‬ᕤᏛ◊✲ᡤᇳ➹せ㡿ࡣ㸪ࡇࡢࣇ࢓࢖ࣝ⮬యࡀᡤሗ‫ڧ‬ㅖグྕࡢᏐయࡣḟࡢ࡜࠾ࡾ࡜ࡍࡿ㸬ཎ✏ࡢࢸࣥࣉ࣮ࣞࢺ࡟࡞ࡗ࡚࠸ࡿࡢ࡛㸪ⴭ⪅ࡀู࡟ࢱ࢖  㸦✀ ู㸧   㸦Ꮠ య㸧   㸦౛㸧ࣉࡋ࡚࠶ࡿཎ✏ࢆࡇࡢᵝᘧෆ࡟࣮࣌ࢫࢺࡍࢀࡤ㸪௨ୗ࡟ ᩘᏛⓗ₇⟬グྕ   ❧ య   sin㸪sinh

グ㍕ࡍࡿయ⿢ࡢཎ✏ࡀసᡂࡉࢀࡿ㸬  ༢఩グྕ     ❧ య   cm㸪kg㸪MȐ‫ࡣࣝ࢖࢓ࣇࢺ࣮ࣞࣉࣥࢸڧ‬ᕤᏛ◊✲ᡤ஦ົᐊ࠿ࡽⴭ⪅࠶  ࣋ࢡࢺࣝ㔞  ᩳయࢦࢩࢵࢡ  ㏿ᗘ 9㸪ຊ )࡚࡟࣓࣮ࣝ࡟ࡼࡾ㏦௜ࡍࡿ㸬   㔞グྕ     ᩳ య   ࿘Ἴᩘ f㸪㛗ࡉ l‫ڧ‬ཎ✏ࡣ㸪ࢸࣥࣉ࣮ࣞࢺ㸦A4 ∧㸧࡟ᚑࡗ࡚ᇳ➹ࡋ㸪ᥦฟ  ໬Ꮫグྕ     ❧ య   H2O㸪BaTiO2

ࡢ㝿ࡣ㸪༳ๅࡋࡓཎ✏㸦ࣁ࣮ࢻࢥࣆ࣮㸧࡜ࡑࡢࢹࢪࢱࣝ

⾲ 1 ࡟♧ࡍ࡜࠾ࡾ࡜ࡍࡿ㸬‫ڧ‬ᩥᏐࡢ኱ࡁࡉࡣ⾲ࢹ࣮ࢱ㸦ࣇ࢓࢖ࣝ㸧ࢆᥦฟࡍࡿ㸬ࣇ࢓࢖ࣝࡣ MS Word㸦Windows ࡲࡓࡣ Mac㸧ࡲࡓࡣ TEX࡜ࡍࡿ㸬‫ڧ‬ཎ✏グ㍕ࡢ㡰ᗎࡣ㸪ᶆ㢟㸪ᮏᩥ㸪ᩥ⊩㸪௜㘓㸪࡛࠶ࡿ㸬㸲㸬ᅗ㸪෗┿ཬࡧ⾲ࡢసᡂ‫ڧ‬ᅗ㸪෗┿ཬࡧ⾲ࡀ༢ẁ㸦∦ഃ㸧࡟཰ࡲࡽ࡞࠸ሙྜࡣ 2ẁ㸦୧ഃ㸧࡟ࡲࡓࡀࡗ࡚᭩ࡃࡇ࡜ࡀ࡛ࡁࡿ㸬㸰㸬ᮏᩥཬࡧཎ✏ࡢయ⿢඲⯡‫ڧ‬ᅗ㸪෗┿ཬࡧ⾲ࡢᶓ࡟✵ⓑࡀ࡛ࡁ࡚ࡶ㸪ࡑࡢ✵ⓑ㒊࡟‫ڧ‬A4 ∧⏝⣬ࢆ⏝࠸㸪ᮏᩥࣞ࢖࢔࢘ࢺ
㸦㸯࣮࣌ࢪ࠶ࡓࡾࡢᩥᏐᩘ㸧ࡣᮏᩥࢆグධࡋ࡞࠸㸬ࡣ㸪25 Ꮠ×45 ⾜×2 ẁ=2250 Ꮠ࡜ࡍࡿ㸬ࡓࡔࡋࢱ࢖ࢺࣝࡢࡳࡣ1‫ڧ‬ᅗ㸪෗┿㸪⾲࡜ᮏᩥཬࡧᅗ⾲┦஫ࡢ㛫ࡣ㸯⾜వⓑࢆ࡜ẁ⤌࡛࠶ࡿ㸬

ࡿ㸬‫ڧ‬06:RUG ࡢ࣮͆࣌ࢪࡢタᐃ͇ࡢ͆ᩥᏐᩘ࡜⾜ᩘ͇ࡢࢱࣈ୰ࡢ

‫ڧ‬ᅗ㸪෗┿㸪⾲ࡢぢฟࡋࡣᮏᩥ࡜ྠ୍ゝㄒ࡜ࡍࡿ㸬ᅗཬタᐃࡣࣇ࢛ࣥࢺࢧ࢖ࢬ㸶㸪ẁᩘ㸰࡛ᩥᏐᩘ 㸪⾜ᩘ  ࡜ࡋ㸪ࡧ෗┿ࡢぢฟࡋࡣࡑࡢୗ࡟㸪⾲ࡢぢฟࡋࡣୖ࡟᭩ࡃ㸬͆వⓑ͇ࡢࢱࣈ୰ࡢタᐃࡣୖ ୗ ᕥ ྑ ࡜ࡋ࡚࠶ࡿ㸬‫ڧ‬ᅗ㸪⾲୰ࡢグྕ㢮ࡣ㸪ᑠࡉࡍࡂุู࡚୙⬟࡟࡞ࡽ࡞࠸

‫ڧ‬࿴ᩥᩥᏐࡣMS ᫂ᮅ㸪ⱥᩥᩥᏐࡣTimes New Roman ࡜ࡍࡿ㸬ࡼ࠺࡟ࡍࡿ㸬ࡲࡓ㸪」㞧࡞グྕ㢮ࡣ㸪኱ࡁࡵ࡟ᥥࡃࡼ࠺

ࡓࡔࡋ㸪グྕ࡞࡝࡟Symbol ࢆ⏝࠸ࡿࡇ࡜ࡀฟ᮶ࡿ㸬࡟ࡍࡿ㸬‫ڧ‬ᮏᩥ㸪ᅗ㸪⾲ཬࡧᘧࡣཎ๎࡜ࡋ࡚ᕥྑࡢẁ࡟ࡲࡓࡀࡽ

‫ڧ‬෗┿ࡣᮏᩥ࡟㈞ࡿࡔࡅ࡛࡞ࡃ㸪෗┿ࡢࣇ࢓࢖ࣝࢆῧ௜

࡞࠸ࡼ࠺࡟᭩ࡃ㸬ࡍࡿ㸬‫ڧ‬ᑠᩘⅬࡣࠝ㸬ࠞࢆ⏝࠸㸪࣐࢝ࣥࠝ㸪ࠞࢆ⏝࠸࡞࠸㸬‫ྃڧ‬ㄞⅬࡣࠝ㸪
ࠞ
ࠝ㸬
ࠞ࡜ࡋ㸪
ࠝࠊ
ࠞ
ࠝࠋ
ࠞࢆ⏝࠸࡞࠸㸬‫⬮ڧ‬ὀࡣ࡞ࡿ࡭ࡃ㑊ࡅࡿ㸬㸳㸬ᩘᘧ‫ڧ‬ᩘᘧ࢚ࢹ࢕ࢱࢆ⏝࠸࡚グ㍕ࡍࡿ㸬‫ڧ‬ᘧࡣ༢ิ࡟᭩ࡃࡼ࠺࡟ᩚᙧࡍࡿ㸬‫ڧ‬Ꮠయࡣ Times New Roman ࢆ౑࠺㸬ࡓࡔࡋ㸪Symbol ࡣ*ᩍᤵ ᶵᲔᕤᏛ⛉
Professor, Dept. of Mechanical Engineering**ຓᡭ ᘓ⠏Ꮫ⛉Research associate, Dept. of Architecture౑⏝࡛ࡁࡿ㸬
‫ڧ‬ᩘᘧࡣཎ๎࡜ࡋ࡚ᩥ❶ࡢ⾜ࡢ୰࡟ධࢀ࡞࠸㸬ࡸࡴࢆᚓࡎᤄධࡍࡿሙྜ࡟ࡣ㸪1 ⾜㧗ࡉࢆᏲࡿ㸬౛㸯ࠝศᩘᘧࡢ౛ࠞ

ࢫࢆసࡗ࡚ࢸ࢟ࢫࢺ࣎ࢵࢡࢫࢆᤄධࡋ㸪ࡑࡢ୰࡟ᅗ࡞࡝

͐ࡇࢀࡣ ( a  b) / ( c  d ) ࡢᙧࢆྲྀࡿ㸬ࢆ࣮࣌ࢫࢺ㸪࠶ࡿ࠸ࡣࣇ࢓࢖ࣝ࠿ࡽࡢᤄධࢆࡍࡿ㸬౛㸰ࠝᣦᩘᘧࡢ౛ࠞ‫ ➨ڧ‬1 ࣮࣌ࢪࡢ⬮ὀ㸦ⴭ⪅ᡤᒓ࡞࡝㸧࡟ࡣ㸪┤᥋ධຊࡋ͐㟁ὶࡣ iI exp(  t / x ) ࡢᙧ࡜࡞ࡿ㸬࡚ࡶ㸪ࢥࣆ࣮ࡋࡓෆᐜࢆ࣮࣌ࢫࢺࡋ࡚ࡶⰋ࠸㸬ࡓࡔࡋࠊ‫ڧ‬ᩥ୰࡛࡞ࡃ㸪ᘧࢆู⾜࡟ࡍࡿሙྜ࡟ࡣ㸪ḟࡢࡼ࠺࡟᭩

MS Word ࡢไ㝈࡟ࡼࡾࠊ⬮ὀࡢᶵ⬟ࢆඛ㢌ࡢ͆㸬⥴ゝ͇࠸࡚ࡶⰋ࠸㸬ࡑࡢ⤖ᯝ㸪ࠝୖ౛ࡢᘧࠞࡣḟࡢᙧࢆྲྀࡿ㸬ࡢᚋࢁ࡟ぢ࠼࡞࠸ࡼ࠺࡟ⓑᩥᏐ࡛͆㸨͇ࢆࡘࡅ࡚࠶ࡿ㸬౛㸯ࠝศᩘᘧࡢ౛ࠞ

ࡇࡇࢆ๐㝖ࡍࡿ࡜⬮ὀࡶᾘ࠼࡚ࡋࡲ࠺ࡢ࡛ὀពࡀᚲせ࡛͐ࡑࡢ⤖ᯝ㸪ࡇࢀࡣḟᘧࡢᙧࢆྲྀࡿ㸬
ab
cd

࠶ࡿ㸬
㸦ᶆ㢟ୗࡢⴭ⪅ྡ࡟⬮ὀࡢᶵ⬟ࢆࡘࡅࡿ࡭ࡁࡔࡀ㸪(1)ࡑࡢሙྜࡣ⬮ὀࡀ୧ẁ࡟ࡲࡓࡀࡗ࡚ࡋࡲ࠺ࡓࡵ㸪ࡇࡢᙧᘧࢆ᥇⏝ࡋࡓ㸧‫࡚࠸ࡘ࡟ࢺ࣮ࣞࣉࣥࢸࡢࡇڧ‬୙᫂࡞Ⅼࡀ࠶ࡿሙྜࡣ㸪ᕤ౛㸰ࠝᣦᩘᘧࡢ౛ࠞ

Ꮫ◊✲ᡤ ஦ົᒁ࡟ၥ࠸ྜࢃࡏࡿ㸬͐ࡑࡢ⤖ᯝ㸪㟁ὶࡣḟᘧࡢᙧ࡜࡞ࡿ㸬i

Ie t / x

(2)

㸶㸬⤖ゝ
‫ڧ‬ᰯṇࡣⴭ⪅࡟౫㢗ࡍࡿࡢ࡛㸪ᰯṇๅࡾࡀ฿╔ᚋ㸪㏿ࡸ㸴㸬ᩥ⊩グ㍕᪉ἲ࠿࡟ᰯṇࢆ῭ࡲࡏ࡚㸪ᕤᏛ◊✲ᡤ ஦ົᐊࡲ࡛㏉㏦ࡍࡿ㸬‫ڧ‬ᩥ୰ࡢᩥ⊩ᘬ⏝ࡣ㸪ᘬ⏝⟠ᡤ࡟ᩥ⊩ࢼࣥࣂ࣮ࢆୖ௜ࡁ

ᰯṇࡣ㸪ෆᐜࡀⴭ⪅ᥦฟࡢࣁ࣮ࢻࢥࣆ࣮࡜୍⮴ࡍࡿࡇ࡜࢝ࢵࢥ࡛ࡘࡅࡿ㸬ࢆ☜࠿ࡵࡿࡶࡢ࡛࠶ࡗ࡚㸪ኚ᭦ࢆຍ࠼ࡿࡇ࡜ࡣ࡛ࡁ࡞࠸㸬‫ڧ‬ཧ⪃ᩥ⊩㸦References㸧ࡣࢼࣥࣂ࣮࡟㸦 㸧ࢆ௜ࡋ࡚ᮏ

‫ࡢ⪅ⴭڧ‬㈐௵࡟ࡼࡿಟṇࡀ⏕ࡌࡓሙྜ࡟ࡣ㸪ࡑࡢಟṇ࡟ᩥᮎ࡟ิグࡍࡿ㸬ᚲせ࡞ᐇ㈝ࢆᚩ཰ࡍࡿ㸬ᘬ⏝ᩥ⊩ࡣཎ๎࡜ࡋ࡚௨ୗࡢ A㸪B ࡢࡼ࠺࡟グ㍕ࡍࡿ㸬㸦A㸧㞧ㄅࡢሙྜ
(No.) ⴭ⪅ྡ㸪͆ᶆ㢟͇㸪㞧ㄅྡ㸪ᕳ㸫ྕ㸦Ⓨ⾜ᖺ-᭶㸧㸪p.࣮࣌ࢪ㸬⾲㸯 ᩥᏐཬࡧࢧ࢖ࢬ౛㢟┠

06 ᫂ᮅ ࣏(x) ㉥ᆏ᠇ኵ㸪㟷ᒣᖾኵ㸪ᐑୗಇኵ㸪͆ᗈᖏᇦቑᖜჾࡢ≉ᛶ͇
㸪㟁

ⴭ⪅ྡ

06 ᫂ᮅ

 ࣏

Ḣᩥ㢟┠

7LPHV1HZ
5RPDQ

12 ࣏Ḣᩥⴭ⪅ྡ

7LPHV1HZ
5RPDQ

9 ࣏

06 ᫂ᮅ ࣏ᮏᩥࡢྛ⠇࣭ᑠ㡯┠

06 ࢦࢩࢵࢡ ࣏ᅗ࣭⾲ࡢぢฟࡋ

06 ࢦࢩࢵࢡ ࣏ཧ⪃ᩥ⊩࣭⬮ὀMS ᫂ᮅ࣏

Ꮚ㏻ಙᏛ఍ㄅ㸪52㸫192㸦1977-8㸧
㸪p.1125㸬(x) E. W. Euller and R. F. Stoessel, “͐͐”, Mech. Engng., 90-3 (1968-3),
p.42㸬

㸦B㸧༢⾜ᮏࡢሙྜ
(No.) ⴭ⪅ྡ㸪͆᭩ྡ͇㸪Ⓨ⾜ᡤྡ㸪
㸦Ⓨ⾜ᖺ㸧㸪p.࣮࣌ࢪ㸬౛(x) ⏣㒊ᾈ୕㸪➉ୗ ㄔ㸪͆ሷ㓟ゐ፹͇
㸪⏘ᴗᅗ᭩㸪
㸦1976㸧
㸪
p.1225㸬ᮏᩥ㸵㸬ཎ✏సᡂୖࡢࣄࣥࢺ
‫ ࡣࢺ࣮ࣞࣉࣥࢸࡢࡇڧ‬Windows MS Word 97 ࡛సᡂࡋ࡚
࠶ࡿ㸬ⴭ⪅ࡀู࡟᭩࠸ࡓཎ✏ࢆࢥࣆ࣮࣮࣌ࢫࢺࡍࢀࡤ㸪⮬ືⓗ࡟๭௜ࡀỴᐃࡍࡿ㸬‫ڧ‬Word ࠿ࡽࢥࣆ࣮࣮࣌ࢫࢺࡍࡿ㝿㸪᭩ᘧ᝟ሗ↓ࡋࡢࢸ࢟ࢫࢺࡢࡳࢆ࣮࣌ࢫࢺࡍࡿ࡟ࡣ㸪ࢥࣆ࣮ࡋࡓᚋ࡟࣓ࢽ࣮ࣗ
ࡢ͆⦅㞟͇࠿ࡽ͆ᙧᘧࢆ㑅ᢥࡋ࡚㈞ࡾ௜ࡅ...͇ࢆ㑅ᢥࡋ㸪͆ࢸ࢟ࢫࢺ͇ࢆ㑅ࡪ㸬ཧ⪃ᩥ⊩‫ ➨ڧ‬1 ࣮࣌ࢪᶆ㢟㒊ศࡣ 1 ẁ⤌࡛࠶ࡿ㸬ࡇࡢ㒊ศ࡛ࡣ㸪(1) ᕤᏛኴ㑻㸪◊✲ᡤⰼᏊ㸪͆ᇳ➹せ㡿͇
㸪ᕤᏛ◊✲ᡤᡤሗ㸪27 ྕ㡯┠ࡈ࡜࡟ࢥࣆ࣮࣮࣌ࢫࢺࡀᚲせ࡛࠶ࡿ㸬㸦2004㸫11㸧㸪p.126㸬‫ڧ‬ᮏᩥࡣⴭ⪅ཎ✏࠿ࡽᅗ㸪⾲㸪⬮ὀࢆ㝖࠸࡚ࢥࣆ࣮ࡋ㸪㸦㞧ㄅࡢሙྜ㸧ࢸࣥࣉ࣮ࣞࢺ࡟࣮࣌ࢫࢺࡍࡿ㸬ࡑࡢᚋ࡛㸪ᅗ➼ࡢࢫ࣮࣌(2) ᕤᏛኴ㑻㸪◊✲ᡤⰼᏊ㸪͆ᕤᏛ◊✲ᡤᡤሗ 27 ྕ͇ᕤᏛ◊✲ᡤ㸪
㸦2004㸧
㸪p.126㸬

Information Systems Creation㸦༢⾜ᮏࡢሙྜ㸧

Industrial Engineering and Management᝟ሗࢩࢫࢸ࣒๰ᡂ
⤒ႠᕤᏛArchitecture

ᘓ⠏Ꮫ

௜㘓

Mathematicsᩘ Ꮫ㹙ཧ ⪃㹛◊✲ᡤᡤሗࡢ㓄ᕸ

Physics≀⌮Ꮫๅୖࡀࡗࡓᡤሗࡣ௨ୗࡢྛ⪅࡟ 1 㒊ᐄ㉗࿊ࡍࡿ㸬Chemistry໬ Ꮫ㸦㸯㸧ᮏᏛ⌮஦࠾ࡼࡧᕤᏛ㒊ᡤᒓᩍ⫋ဨ㸬

Biology⏕≀Ꮫ㸦㸰㸧⌮㸪ᕤᏛ㒊ࢆ᭷ࡍࡿᅜෆࡢ኱Ꮫࡲࡓࡣࡑࢀ࡟‽ࡎࡿᏛᰯ㸬

Professor㸦㸱㸧ᐁබᗇࡢ◊✲ᶵ㛵㸬

Professor Emeritusྡ㄃ᩍᤵ㸦㸲㸧୺せࡢᏛ༠఍㸬

Associate Professor෸ᩍᤵ㸦㸳㸧Ẹ㛫ࡢ୺せ◊✲ᶵ㛵㸬

Assistant Professorຓ ᩍ㸦㸴㸧ࡑࡢ௚ጤဨ఍ࡀㄆࡵࡓࡶࡢ㸬Research Associateຓ ᡭTechnical Assistantᢏ⾡ဨ㹙㈨ ᩱ㹛ⱥᩥ⏝ㄒ୍ぴ

Graduate㸦M.C.㸧

኱Ꮫ㝔㸦༤ኈ๓ᮇㄢ⛬㸧Graduate㸦D.C.㸧

኱Ꮫ㝔㸦༤ኈᚋᮇㄢ⛬㸧Research Student◊✲⏕

Research Institute for EngineeringᕤᏛ◊✲ᡤScience Reports of Research Institute for EngineeringᕤᏛ◊✲ᡤᡤሗ
Faculty of Engineering

Dean

ᕤᏛ㒊

Chairman of Dept. of ͐

Department㸦Dept.㸧ofᏛ ⛉Abstract

Mechanical EngineeringᶵᲔᕤᏛElectrical and Electronic Information Engineering≀㉁⏕࿨໬Ꮫ

Ꮫ㒊㛗
Ꮫ⛉୺௵
ᴫ せ

ὀ㸸ᕤᏛ㒊㸪෸ᩍᤵ㸪ຓᡭ㸪ᢏ⾡ဨ㸪◊✲⏕࡞࡝࡟ࡘ࠸࡚ࡣ✀ࠎࡢ࿧⛠ࡀ࠶ࡿࡀ㸪ୖグࡢࡼ࠺࡟⤫୍ࡍࡿ㸬㟁Ẽ㟁Ꮚ᝟ሗᕤᏛ
Material and Life Chemistry

ᩍ ᤵ



⦅㞟ᚋグ

⦅㞟ጤဨ࡞ࡽࡧ࡟ᕤᏛ◊✲ᡤ஦ົ⫋ဨࡢࡈ༠ຊࡢࡶ࡜ࠊᕤᏛ◊✲ᡤᡤሗ➨㸱㸴ྕࡀห⾜࡜࡞ࡾࡲࡋࡓࠋ࠾ᛁࡋ࠸࡜ࡇࢁࠊ㐍ࢇ࡛ཎ✏ࢆ࠾ᐤࡏୗࡉ࠸ࡲࡋࡓඛ⏕᪉࡟ཌࡃ࠾♩⏦ࡋୖࡆࡲࡍࠋ
ᡤሗࡢ⦅㞟࡟࠶ࡓࡗ࡚ࡣࠊᡤሗࢆ㏻ࡋ࡚ᕤᏛ◊✲ᡤࡢᖺ㛫άື࠾ࡼࡧᡤဨࡢ◊✲ศ㔝ࡢ⤂௓࡜◊✲ࡢ࣏ࢸࣥࢩࣕࣝࡢ㧗ࡉࢆ▱ࡗ࡚ᡝࡅࡿࡼ࠺㓄៖ࡋࡲࡋࡓࠋ᪂௵ࡢᩍဨ
࡟ࡣࠊࡇࢀࡲ࡛ࡸࡗ࡚ࡇࡽࢀࡓᑓ㛛ศ㔝ࡢ◊✲ࢆᏑศ࡟࢔ࣆ࣮ࣝࡋ࡚㡬ࡅࡿࡼ࠺࡟ࠊ
⥲ㄝࢆᇳ➹㡬ࡁࡲࡋࡓࠋࡲࡓࠊᮏᖺᗘࢆࡶࡗ࡚㏥⫋ࡉࢀࡿᩍဨ࡟ࡣ኱㚷ࢆ▷ࡃ⧳ࡵࡓ㝶᝿ࢆᇳ➹㡬ࡁࡲࡋࡓࠋࡉࡽ࡟ࠊᕤᏛ◊✲ᡤඹྠ◊✲ࡢᡂᯝሗ࿌࡟ຍ࠼࡚ᕤᏛ◊✲ᡤࡢᖺ㛫άືࡀ୍┠࡛ศ࠿ࡿᖺḟሗ࿌➼ࢆグ㍕ࡋ࡚࠶ࡾࡲࡍࠋ⏘ᐁᏛ࡜㐃ᦠࡋ࡚◊✲άືࢆ⾜ࡗ࡚࠸ࡿඛ⏕᪉ࡢάືࡸ◊✲ᡂᯝࡶྍ⬟࡞⠊ᅖ࡛ᕤᏛ◊✲ᡤᡤሗ࡟බ⾲ࡋ࡚࠸ࡃᚲせࡀ࠶ࡲࡍࠋࡇࢀ࡟ࡼࡾࠊ⏘ᐁ࡜ᕤᏛ◊✲ᡤ࡜ࡢࡼࡾ⥭ᐦ࡞㛵ಀࡀ☜❧ࡉࢀࡲࡍࠋ
ᕤᏛ◊✲ᡤ࡜ࡢ⥭ᐦ࡞㛵ಀࡢ୰࡛⏘ᐁᏛ༠ྠ◊✲ࡀࡉࡽ࡟Ⓨᒎࡍࡿࡇ࡜ࢆᮇᚅࡋ࡚࠸
ࡲࡍࠋ࡞࠾ࠊᡤሗࢆ࣮࣒࣮࣍࣌ࢪ࡟ࡶᥖ㍕ࡋࡲࡋࡓࡢ࡛ࠊࡼࡾከࡃࡢ᪉ࠎ࡟࠾ㄞࡳ㡬ࡅࡿࡶࡢ࡜ᛮ࠸ࡲࡍࠋⓎห࡟࠶ࡓࡾࡈ༠ຊ㡬ࡁࡲࡋࡓ᪉ࠎ࡟ᨵࡵ࡚ᩗពࢆ⾲ࡍࡿ࡜࡜ࡶ࡟ࠊ
ࡈ༠ຊ࡟ឤㅰ⏦ࡋୖࡆࡲࡍࠋ
≀㉁⏕࿨໬Ꮫ⛉ బ⸨ ᠇୍ᕤᏛ◊✲ᡤᡤሗ㸦No. 36㸧ᕤᏛ◊✲ᡤ ᡤ㛗᪂୰ ᪂஧

ᕤᏛ◊✲ᡤ ᡤሗ ⦅㞟ጤဨ఍              ጤ ဨ 㛗 బ⸨ ᠇୍ 㸦≀㉁⏕࿨໬Ꮫ⛉㸧ጤဨ ఀᮾ ᘯ⾜ 㸦ᶵᲔᕤᏛ⛉㸧ᒣཱྀ ᰤ㞝 㸦㟁Ẽ㟁Ꮚ᝟ሗᕤᏛ⛉㸧ዟ㔝 ⚈஧ 㸦᝟ሗࢩࢫࢸ࣒๰ᡂᏛ⛉㸧              ୰ᓥ ೺୍ 㸦⤒ႠᕤᏛ⛉㸧                   ㉿  ⾝๛ 㸦ᘓ⠏Ꮫ⛉㸧ᒣᓮ ᩍ᫛ 㸦ᩘᏛᩍᐊ㸧

SCIENCE
Research Institute
Director of the Institute

REPORTS㸦No. 36㸧
offor Engineering (KANAGAWA University)

Shinji SHINNAKA

Chief Editor

Kenichi SATO

(Dept. of Material and Life Chemistry)

EditorHiroyuki ITO(Dept. of Mechanical Engineering)

Shigeo YAMAGUCHI(Dept. of Electrical, Electronics andInformation Engineering)

Shouji OKUNO(Dept. of Information Systems Creation)

Kenichi NAKASHIMA(Dept. of Industrial Engineering and Management)

Yan-Gang ZHAOO(Dept. of Architectonics)

Noriaki YAMAZAKI(Dept. of Mathematics)⚄ዉᕝ኱ᏛᕤᏛ◊✲ᡤᡤሗ➨ྕᖺ᭶᪥  ༳ ๅᖺ᭶᪥  Ⓨ ⾜⦅㞟වⓎ⾜⪅  ⚄ዉᕝ኱ᏛᕤᏛ◊✲ᡤࠛ ᶓ὾ᕷ⚄ዉᕝ༊භゅᶫ ༳ ๅ  ᡤ  ඹ❧㏿グ༳ๅᰴᘧ఍♫ᮾி㒔༓ ௦⏣༊ 㣤 ⏣ᶫ RESEARCH INSTITUTE FOR ENGINEERING
KANAGAWA UNIVERSITY
3-27 Rokkakubashi, Kanagawa-ku, Yokohama, 221-8686, Japan