ᚑくᄢቇℂᎿቇ⎇ⓥႎ๔
J. Fac. Sci. Tech., Seikei Univ.
Vol.45 No.2 (2008) pp.85-87
㧔․೎⎇ⓥ⾌ߦଥࠆ⺰ᢥ㧕὇⚛᧚ᢱ⇇㕙ߩ⿥ẢṖ․ᕈߩᢙ୯⊛⎇ⓥ૒‫ ᧁޘ‬ᚑᦶ*1㧘᧼᧛ ⾫᣿*2, ਃᶆ ᶈᴦ*3

Numerical Study of Suerlubricity of Carbon-Materials Interface
Naruo SASAKI㧖1, Noriaki ITAMURA㧖2, Kouji MIURA㧖3
ABSTRACT㧦Superlubricity of the graphite/C60/graphite interface is numerically investigated andcompared with that of the graphite/graphite/graphite interface. Simulated interlayer distances ofabout 1.3nm are in good agreement with previous experimental results. The atomic-scale friction
coefficient of the graphite/C60/graphite interface decreases to about 30% of that of thegraphite/graphite/graphite interface.
Keywords㧦 Superlubricity, Friction, Fullerene, C60, Graphite, Molecular Mechanics Simulation, AtomicForce Microscopy

㧔Received September 24, 2008㧕㧝㧚ߪߓ߼ߦ㨪⿥ẢṖࠪࠬ࠹ࡓߩ᭎ᔨ࠽ࡁߩࠪ࡯࠻ ࠣ࡜ࡈࠔࠗ࠻ ᐥߩ਄ߦ⋥ធ᧼ࠍ⟎޿ߡṖࠄߖࠆߩߣ㧘ࡄ࠴ࡦࠦ₹ࠍᐥߦ߫ࠄ߹޿ߡߘߩ਄߆ࠄ᧼ࠍ⟎޿ߡṖࠄߖࠆߩߣߢߪ㧘ᒰὼᓟ⠪ߩᣇ߇Ṗࠅ߿ߔ޿‫ߪࠇߎޕ‬ᐥߣ᧼ߣߩ㑆ߦ௛ߊ࠽ࡁߩࡏ࡯࡞
㧔C60៺ᡂ߇㧘ࡄ࠴ࡦࠦ₹ߩォ߇ࠅߦࠃߞߡシᷫߐࠇࠆߚ߼ߢ޽ࠆ‫ߪ₹ࠦࡦ࠴ࡄߩߎޕ‬ᯏ᪾Ꮏቇߩಽ㊁ߢ⸒߁ࡏ࡯࡞ࡌߔߴࠅ‫ޔ‬ᝄേ‫ޔ‬ォ߇ࠅࠕ࡝ࡦࠣߩᓎഀࠍᨐߚߒߡ޿ࠆ‫ߣࠇߎޕ‬หߓ᭴ㅧࠍ࠽ࡁࠨࠗ࠭ߩ਎⇇ߢ૞ߞߡߺߚࠄ៺ᡂߪዊߐߊߥࠆߩߢߪߥ޿߆㧫ਃᶆ㧘૒‫ ࠄᧁޘ‬1)-4)ߪ㧘࠽ࡁߩ‫࡜ࠣߡߒߣޠ᧼ޟ‬ࡈࠔࠗ࠻(㤥㋦)ߣ޿߁὇⚛ߩੑᰴరࠪ࡯࠻㧘࠽ࡁߩ‫ޠ⃿ޟ‬࠽ࡁߩࠪ࡯࠻ ࠣ࡜ࡈࠔࠗ࠻ߣߒߡ਎⇇ᦨዊߩࠨ࠶ࠞ࡯ࡏ࡯࡞ߣ๭߫ࠇࠆࡈ࡜࡯࡟ࡦC60 ࠍ↪޿ࠆ੐ࠍ⠨߃ߚ‫ߺ⚵ߩࠄࠇߎޕ‬วࠊߖߪᒝ޿ൻቇ࿑㧝නಽሶࡌࠕ࡝ࡦࠣឬ௝⚿วࠍ⺃⿠ߒߥ޿╫ߥߩߢࠬࡓ࡯࠭ߥേ߈߇ᦼᓙ಴᧪ࠆ‫ ޕ‬C60 ಽሶߩ౐ຬⅣߣ਄ਅጀߩࠣ࡜ࡈࠔࠗ࠻ߩ౐ຬⅣߣ߇㧘㧞㧚⿥ẢṖ὇⚛⭯⤑ߩ᷹ቯࠛࡀ࡞ࠡ࡯⊛ߦ቟ቯߥ AB Ⓧጀߩ㈩⟎ࠍขࠆ੐ࠍ⠨ᘦߒߡ਄ጀࠣ࡜ࡈࠔࠗ࠻⭯⤑ࠍṖࠄߖࠆߣ㧘C60 ಽሶߩ਄ਅߦ࠻࡞ࠢ߇߆߆ߞߡ C60 ಽሶ߇ォ߇ࠆ੐߇੍ᗐߐࠇࠆ(࿑1)‫ᧄޕ‬Ⓜߢߪ㧘ᐔᚑ 19 ᐕᐲ․೎⎇ⓥߦ߅޿ߡ‫ޟ‬὇⚛᧚ᢱ⇇㕙ߩ⿥ẢṖ․ᕈߩᢙ୯⊛⎇ⓥ‫ࠍޠ‬ផㅴߒߡᓧࠄࠇߚ⚿ᨐࠍႎ๔ߔࠆ‫ޕ‬ࠣ࡜ࡈࠔࠗ࠻ࠍ⎣㉄ߣ⎫㉄ߩᷙ㉄ਛߢ߆ߊߪࠎߒߚᓟ
᳓ᵞ޿ߒ㧘1000͠એ਄ߦ଻ߞߡ C60 ☳ᧃߣ౒ߦ 2 ㅳ㑆߶ߤ଻ߟߣ㧘࿑ 2(a),(b)ߩㅘㆊ㔚ሶ㗼ᓸ㏜௝߇␜ߔࠃ߁ߦ㧘
C60 ߇ኽ౉ߐࠇߚࠣ࡜ࡈࠔࠗ࠻ߩ⭯⤑߇૞⵾ߐࠇࠆ‫࡜ࠣޕ‬ࡈࠔࠗ࠻[0001]㕙ౝߢߪ C60 ಽሶߪᦨኒలႯ᭴ㅧࠍขࠆ(࿑ 2(a)) ৻ᣇ㧘[0001]ゲᣇะߦߪ C60 නಽሶጀ߇⚂ 1.3nm*1㧦ᚑくᄢቇℂᎿቇㇱ ‛⾰↢๮ℂᎿቇ⑼ ᢎ᝼*㧞naru@st.seikei.ac.jp㧦ᚑくᄢቇℂᎿቇㇱ ‛⾰↢๮ℂᎿቇ⑼ ഥᚻ*㧟㧦ᗲ⍮ᢎ⢒ᄢቇ ‛ℂቇᢎቶ ᢎ᝼ߩ㑆㓒ߢⓍጀߔࠆ᭴ㅧࠍขߞߡ޿ࠆ(࿑ 2(b))‫ޕ‬៺ᡂജ㗼ᓸ㏜᷹ቯߩ⚿ᨐ㧘࿑ 3 ߦ␜ߔࠃ߁ߦ㧘ੑᰴర៺ᡂജ௝ߣ᳓ᐔജ࡞࡯ࡊ߇ᓧࠄࠇߚ‫ޕ‬100nN એਅߢߪ㧙㧙ᡂജ(ᐔဋ᳓ᐔജ)߽࠯ࡠࠍ␜ߔߎߣ㧘߅ࠃ߮៺ᡂଥᢙ߇(b)

C60

1.3nm

C60C60graphene࿑㧠[0001 ]

2nm

2nm

࿑㧞C60ኽ౉ࠣ࡜ࡈࠔࠗ࠻ࡈࠖ࡞ࡓߩㅘㆊ㔚ሶ㗼ᓸ㏜௝‫(ޕ‬0001)㕙ߦ C ᐔⴕ D ု⋥ᣇะߩࡄ࠲࡯ࡦ‫ޕ‬⩄㊀ 0nN2nm

210-1-2

᳓ᐔജFL (nN)៺ᡂജ௝FzU

2eV

01.0nm[0110]

࿑㧟d(b)

1-1

1.31

1.5

Distance between graphenes
d [nm]C C60ࡌࠕ࡝ࡦࠣ♽ߩࠪࡒࡘ࡟࡯࡚ࠪࡦࡕ࠺࡞‫ ޕ‬D ࠣ࡜ࡈࠔࠗ࠻ጀ㑆〒㔌dߩ㑐ᢙߣ ߒ ߡ ߩ ု ⋥ ജ Fz ߣ ో ࠛ ࡀ ࡞ ࠡ ࡯ U ‫ޕ‬
Fz=0 Uߪᭂዊ ߣߥࠆd=PO߇ᐔⴧ〒㔌ߢ޽ࠆ੐߇ಽ߆ࠆ‫ޕ‬ߎߎߢߪ C60 ಽሶߩ౐ຬⅣߣࠣ࡜ࡈࠔࠗ࠻ߩ౐ຬⅣ߇

AB Ⓧጀࠍ⛽ᜬߒߡ C60 ಽሶ߇Ṗࠆࡕ࡯࠼(࿑ 5(a))ߣ㧘C60_ಽሶ߇ォ߇ࠆࡕ࡯࠼(࿑ 5(b))ࠍ⚫੺ߔࠆ‫[ޕ‬1010]ᣇะߩ⿛

᳓ᐔജ࡞࡯ࡊ
⩄㊀ 0nNᩏߦኻߒߡ㧘C60 ಽሶ߇Ṗࠆࡕ࡯࠼ߢߪ࿑ 5(a)ߩࠃ߁ߦࠬ

࠹ࠖ࠶ࠢࠬ࡝࠶ࡊߦ઻߁ࡅࠬ࠹࡝ࠪࠬࠍᜬߟ 0.44nm ๟ᦼߩ᳓ᐔജ࡞࡯ࡊ㧘C60 ಽሶ߇ォ߇ࠆࡕ࡯࠼ߢߪ࿑ 5(b)ߩࠃ߁ߦਇㅪ⛯࿁ォߦ↱᧪ߔࠆᓸዊߥࡅࠬ࠹࡝ࠪࠬࠍᜬ

04

⿛ᩏ૏⟎ (nm)ߟ 2.56nm ๟ᦼߩ᳓ᐔജ࡞࡯ࡊ߇ᓧࠄࠇߚ‫ޕ‬Ṗࠅࡕ࡯࠼8ߩ៺ᡂଥᢙߪ㧘ࠣ࡜ࡈࠔࠗ࠻ߩ⸘▚୯ 0.0082 ߩ 30㧑એਅ㧘
0.0023 ߦᛥ߃ࠄࠇࠆ੐߇ಽ߆ߞߚ(࿑ 5 ਅ)‫ޕ‬

C60 ኽ౉ࠣ࡜ࡈࠔࠗ࠻ࡈࠖ࡞ࡓߩု⋥⩄㊀ߦኻߔࠆ៺ᡂജ௝ߣ᳓ᐔജ࡞࡯ࡊ‫ޕ‬᷹ቯ♖ᐲએਅߢേ៺ᡂജ ᐔဋ᳓ᐔജ ߽ᦨᄢ㕒ᱛ៺ᡂജ߽࠯ࡠߦㄭ޿⁁ᴫ߇ᚑ┙ߒߡ޿ࠆ‫ޕ‬㧟㧚⿥ẢṖ὇⚛⭯⤑ߩࠪࡒࡘ࡟࡯࡚ࠪࡦ
ಽሶജቇࠪࡒࡘ࡟࡯࡚ࠪࡦࠍ↪޿ߡ㧘⿥ẢṖ⭯⤑ߩ᭴ㅧࠍ⺞ߴߚ 6)-11)‫ޕ‬࿑ 4(a)ߩࠃ߁ߦ C60 නጀ⭯⤑ࠍੑᨎߩࠣ࡜ࡈࠔࠗ࠻නጀ⤑(ࠣ࡜ࡈࠚࡦ)ߢ᜽ࠎߛ๟ᦼࡕ࠺࡞ࠍ⠨߃㧘C60 ಽሶౝߣ C60 ಽሶ̆ࠣ࡜ࡈࠔࠗ࠻㑆ߦㆡᒰߥ⚿ว㧘㕖⚿ว⋧੕૞↪ࡐ࠹ࡦࠪࡖ࡞㑐ᢙࠍㆡ↪ߒߡ㧘ጀ㑆〒㔌d ߩ㑐ᢙߣߒߡု⋥⩄㊀ Fz ߣోࠛࡀ࡞ࠡ࡯U ࠍ⸘▚ߒߚߣߎࠈ㧘਄ਅࠣ࡜ࡈࠚࡦጀ㑆㑆㓒߇ 1.31nm ߩᚲߢ቟ቯ᭴ㅧ߇⃻ࠇߚ㧔࿑ 4(b)㧕‫ޕ‬૒‫ᧁޘ‬㧘ਃᶆߪઁߦ߽ⶄᢙߩḰ቟ቯ᭴ㅧࠍ⷗಴ߒߚ߇㧘޿ߕࠇ߽⚂ 1.3nm ㄭறߩጀ㑆〒㔌ࠍ␜ߒߚ‫ ߦ߁ࠃߩߎޕ‬TEM ᷹ቯߢᓧࠄࠇߚጀ㑆〒㔌ࠍ⺑᣿಴᧪ߚ6)-11)

Total Energy U [eV]Fz

0.001 ᧂḩߢ޽ࠆ੐߇ಽ߆ߞߚ 4)-9)‫ޕ‬(a)graphene

Normal Load Fz [eV /Έ](a)

0.1nN ߩ᷹ቯᯏེߩಽ⸃⢻એਅߢᦨᄢ㕒ᱛ៺ᡂജ߽േ៺A࿑㧡 C C60ಽሶࡌࠕ࡝ࡦࠣߦ߅ߌࠆ=?ᣇะߩ C Ṗࠅࡕ࡯࠼ D ォ߇ࠅࡕ࡯࠼ߩ᭎ᔨ࿑
ߣ᳓ᐔജ࡞࡯ࡊ‫ߣ♽࠻ࠗࠔࡈ࡜ࠣޕ‬Ṗࠅࡕ࡯࠼ߩ៺ᡂଥᢙߩᲧセ‫ޕ‬‫ޕ‬ᰴߦ਄ጀࠣ࡜ࡈࠔࠗ࠻ࠍ᳓ᐔ⿛ᩏߒߡ៺ᡂ․ᕈࠍ⺞ߴߚߣߎࠈ㧘C60 ࡌࠕ࡝ࡦࠣࠪࠬ࠹ࡓߩ⿥ẢṖᕈߩ⿠Ḯߣ⠨߃ࠄࠇࠆ㧘ౖဳ⊛ߥ C60 ಽሶߩㆇേ߇಴⃻ߒߚ 10),11)‫ޕ‬㧙㧙એ਄ߩ⚿ᨐߪ㧘ࠣ࡜ࡈࠔࠗ࠻ߩጀ㑆ߦࠣ࡜ࡈࠔࠗ࠻ࠪ
࡯࠻ࠍ᜽߻႐วࠃࠅ߽㧘C60 ಽሶࠍ᜽߻႐วߩᣇ߇㧘C60
ಽሶߩᓸዊ࿁ォ࡮ਗㅴㆇേߩ⥄↱ᐲߦࠃߞߡ㧘ోࡐ࠹ࡦࠪࡖ࡞ࠛࡀ࡞ࠡ࡯ߩࠃࠅૐ޿⚻〝߇㐿߈߿ߔߊߥࠅ㧘ߕࠇᔕജ߇ᷫዋߔࠆ㧘ߣ޿߁ේሶ࡟ࡌ࡞ߩ⿥ẢṖࠪ࠽࡝ࠝߢ⺑᣿಴᧪ࠆ 10),11)‫ޕ‬㧠㧚߅ࠊࠅߦ ᧄⓂߢߪ․೎⎇ⓥ⾌⺖㗴ࠍផㅴߒߡᓧࠄࠇߚ⚿ᨐߣߒߡ㧘⿥ẢṖ C60 ಽሶࡌࠕ࡝ࡦࠣߩ FFM ᷹ቯ෸߮ಽሶജቇࠪࡒࡘ࡟࡯࡚ࠪࡦ⎇ⓥߩ⃻⁁ࠍ⚫੺ߒ㧘C60 ಽሶߩᓸዊ࿁ォ࡮ਗㅴㆇേߩ⥄↱ᐲ߇ේሶ࡟ࡌ࡞⿥ẢṖࠍ⺃⿠ߔࠆน⢻ᕈࠍᜰ៰ߒߚ‫⿥♽ࡦࡏ࡯ࠞޕ‬ẢṖ⭯⤑ߩ⎇ⓥߪ㧘නߦᓥ᧪ߩ࠽ࡁࠬࠤ࡯࡞៺ᡂߩ⊒ዷ⊛⎇ⓥ⺖㗴ߢ޽ࠆߛߌߢ
ߥߊ㧘ⅣႺ࡮ࠛࡀ࡞ࠡ࡯໧㗴߆ࠄක≮ᛛⴚ߹ߢ޽ࠄࠁࠆಽ㊁߳ߩㆡ↪น⢻ᕈࠍᜬߞߡ߅ࠅ㧘ࠃࠅ⼾߆ߥ␠ળ↢ᵴߩታ⃻ߦነਈߔࠆ੐߇ᦼᓙߐࠇࠆ‫ޕ‬ෳ⠨ᢥ₂1) K. Miura, S. Kamiya and N. Sasaki: Phys. Rev. Lett. 90,p.055509 (2003).

2) N. Sasaki and K. Miura: Jpn. J. Appl. Phys.43, p.4486(2004).

3) ૒‫ᧁޘ‬ᚑᦶ, ਃᶆᶈᴦ: ࠽ࡁࡑ࠹࡝ࠕ࡞ࡂࡦ࠼ࡉ࠶ࠢ, ࠛ࠿࡮࠹ࠖ࡯࡮ࠛࠬ, pp. 51-59 (2005).

4) ૒‫ᧁޘ‬ᚑᦶ: ᣣ⚻࠽ࡁࡆࠫࡀࠬ 4 ᦬ 11 ᣣภ, pp. 18-21(2005).

5) K. Miura, D. Tsuda, N. Sasaki: e-J. Surf. Sci. Nanotech.3,p.21 (2005).

6) K. Miura, D. Tsuda, N. Itamura, N. Sasaki: Jpn. J. Appl.
Phys. 46, p.5269 (2007).

7) ૒‫ᧁޘ‬ᚑᦶ, ਃᶆᶈᴦ: ࠽ࡁ࠹ࠢߩߚ߼ߩ‛ℂ౉㐷,౒┙಴, pp. 37-58 (2007).

8) ਃᶆᶈᴦ, ૒‫ᧁޘ‬ᚑᦶ: ࠽ࡁࠞ࡯ࡏࡦࡂࡦ࠼ࡉ࠶ࠢ,ࠛ࠿࡮࠹ࠖ࡯࡮ࠛࠬ, pp.680-685 (2007).

9) N. Sasaki, N. Itamura, D. Tsuda, K. Miura: Current
Nanoscience. 3, p.105 (2007).

10) N. Sasaki, N. Itamura, K. Miura: J. Phys.: Conference
Series 89, p.012001 (2007).

11) N. Sasaki, N. Itamura, K. Miura: Jpn. J. Appl. Phys. 46,p.L1237 (2007).

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