Shigeo Maruyama丸山 茂夫

東京大学大学院 工学系研究科 機械工学専攻e-mail: maruyama@photon.t.u-tokyo.ac.jphttp://www.photon.t.u-tokyo.ac.jp/~maruyama

分子熱流体工学 2014

表面エネルギー，濡れ性，吸着

Surface Tension

Add(Work)

)N/m(

xbA d2d

xbx d2d)Force(d(Work) 2: 両面

Young’s Equation (Macroscopic)

LG

SGSL

SGSLLG cos

LG

SLSG

cos

Solid

Liquid

Gas

AG

dd

可逆過程に対する第二法則

(1)

(2)

)1(')2()(

)2()1()()(

00)(

00

'0

Re

Ree

e

TdQ

TdQ

TdQ

RRCycleTdQ

）（可逆

)2()1()(12

)1(')2()(

)2()1()(

12)1(')2(

)(0

21)2()1(

)(0

0

0)(:)1(')2()1(

0)(:)1()2()1(

0

0

Re

Re

Re

Re

Re

TdQSS

TdQ

TdQ

SSTdQRR

SSTdQRR

サイクル

サイクル

)(eTdQdS )(eTdQdS

第一法則と組み合わせた表現

dLdSTdULawlstdLdQdU

TdQdS

e

e

)(

)(

)(

体積変化仕事のみの場合

dVpdSTdUdVpdL

ee

e

)()(

)(

一般力のある場合

dXjdVpdSTdUdVpdL

eee

e

)()()(

)(

Helmholtz自由エネルギー(Helmholtz Free Energy)

相変化，化学反応，混合のある場合

V

p

0

等温

等圧

等積

（均質物体）

A

B

等温等積変化

dXjTSUddXjdSTdUdVConstTT

e

ee

e

)(

)()(

)(

)(

0.,

dXjdF e)(

自由エネルギーHelmholtzTSUF 自由エネルギーHelmholtzTSUF

系が外部にする仕事ーj(e)dXは，一般にHelmholtz自由エネルギーの減少量ーdFより小さい

少する自由エネルギーは，減

の場合　

HelmholtzdFj e 00)(

Gibbs自由エネルギー(Gibbs Free Energy)

dXjTSpVUdConstTTConstpp

e

ee

)(

)()(

)(.,

等温等圧変化

dXjdG e)(

自由エネルギーGibbsTSHTSpVUG 自由エネルギーGibbsTSHTSpVUG

系が外部にする仕事ーj(e)dXは，一般にGibbs自由エネルギーの減少量ーdGより小さい

する自由エネルギーが減少

の場合　

GibbsdGj e 00)(

Liquid Droplet

Flat InterfaceLiquid-Vapor Interface

G

L)()( TNLG

z

zdzzPzP

0 100 200 300–40

–20

0

0

0.02

0.04

Z [Å]

Num

ber D

ensi

ty [1

/Å3 ]

Pres

sure

[MPa

]

8000 molecules in 6060300 box

Vm

mj

mi

Vm

mj

mi

mij FxvvmVP

Surface Tension

32000

1536

400

Liquid Droplet on Solid Surface

10 20

10

20

30

heig

ht (Å

)

Density Profile50

40

30 400

radius (Å)0

Liquid Droplet in Contact with a Surface

wettable

2-D Density Distributions for L-J Droplet

0 10 20 30 400

10

20

30

40

50

Radius [Å]

Hei

ght [

Å]

0 10 20 30 400

10

20

30

40

50

Radius [Å]0 10 20 30 40

0

10

20

30

40

50

Radius [Å]

0 10 20 30 400

10

20

30

40

50

Radius [Å]

Hei

ght [

Å]

0 10 20 30 400

10

20

30

40

50

Radius [Å]0 10 20 30 40

0

10

20

30

40

50

Radius [Å]

0.000 [Å-3]

0.025 [Å-3]E0 E1 E2

E3 E4 E5

Young’s Equation (Macroscopic)

LG

SGSL

SGSLLG cos

LG

SLSG

cos

Solid

Liquid

Gas

AG

dd

1 2 3 4–1

0

1

*SURF=SURF/AR

Con

tact

ang

le H

c/R1/

2 (=c

os

Bubble(100K)

Solid: DensityOpen: Potential

DropletBubble(110K)

cos → linear function of *SURF

*SURFdepth of integrated

effective surface potential

wettable

Contact angle correlated with *SURF

INT2

02

INT )/)(5/34( RSUFR

Nliq = 130T = 92 K = 71o

Nliq = 360T = 99 K = 85o

Nliq = 330T = 85 K = 90o

Nliq = 340T = 113 K = 86o

Nliq = 1600T = 92 K = 90o

Temperature & Size Effect

Asymptotic Macro-System

0 10000 20000 30000

0.4

0.5

0.6

0.7co

s

Number of Liquid Molecules

3/2

23/1

coscosL

L

NrN

LG

SLSG

cos

Sliced view (central 10Å)

All molecules

Snapshots of bubble formation for E3

0.025

0.000

h [Å]10

20

30

r [Å]

010 20 30 400

E1*SURF =1.29 =135.4

10

20

30

r [Å]

010 20 30 400

E2*SURF =1.86 =105.8

10

20

30

r [Å]

010 20 30 400

E3*SURF =2.42 =87.0

10

20

30

r [Å]

010 20 30 400

E4*SURF =2.99 =55.2

h [Å]

r [Å]

0

10

20

30

40

50

10 20 30 400

E2

r [Å]

0

10

20

30

40

50

10 20 30 400

E3

r [Å]

0

10

20

30

40

50

10 20 30 400

E4

r [Å]

0

10

20

30

40

50

10 20 30 400

E5

wettable

Two-dimensional density distributions

Experiments by Satish G. KANDLIKARRochester Institute of Technology

m = 1.15 x10-6 kg, = 0º, T = 22C, and = 22.05º.

0

10

20

30

40

50

60

0 10 20 30 40 50 60 70 80 90Surface Inclination, ( degree )

Con

tact

Ang

le,

( d

egre

e )

Advancing Angle

Receding Angle

19.6 torr Vacuum, 18 M de-ionized waterSurface roughness, Ra, value of 0.02 mModified RCA cleaning (1 part NH4OH, 3 parts H2O2, and 15 parts H2O)

System Configuration(water droplet on fcc(111) platinum surface)

100.

00 Å

3 LayersSolid

Surface

WaterDroplet

Mirror

Water-Water Potential

SPC/E

i j ij

ji

rqq

rr 0

6

OO

12

OO 44

-2q+q = 0.4238e1Å

47.1093/1cos2 11Å+q

0 5 10 15–40

–20

0

20

40

Intermolecular Distance [Å]

Pote

ntia

l Ene

rgy

[kJ/

mol

]

H. J. C. Berendsen, et al. (1987)

Cut-off Length25 Å

c/f Hydrogen Bond2.76 Å , 30 KJ/mol

a1 = 1.894210-16 J, b1 = 1.1004 Å-1a2 = 1.886310-16 J, b2 = 1.0966 Å-1a3 = 10-13 J, b3 = 5.3568 Å-1a4 = 1.74210-19 J, b4 = 1.2777 Å-1c = 1.1004 Å -1

Water-Platinum Potential (SH Potential)

E. Spohr & K. Heinzinger (1988)

PtHPtHPtHPtHOPtOPtPtOPtOH 212 , rrr frbafrbarba 1expexpexp 332211PtO rba 44PtH exp

2exp cf

r

Pt

= 0.8O-Pt = 2.70 Å, O-Pt = 6.6410-21 J, cO-Pt = 1.28H-Pt = 2.55 Å, H-Pt = 3.9110-21 J, cH-Pt = 1.2

Water-Platinum Potential (ZP Potential)

S.-B. Zhu and M. R. Philpott (1994)

j pjpj

p

pjpj

ppp zz

3

22

2Pt

6

22

2Pt

Ptan 4

r

j pj

pppp r

c10

10PtPt

Ptisr 4

r

kl lk

kl

rqq

,condOH 22

H

HisrHanOisrOancondOHsurfOH 22rrrr

r

Pt

Comparison of Water-Platinum Potential

S-H Potential Z-P Potential

0 5 10–60

–40

–20

0

20

Distance from Surface [Å]

Pote

ntia

l Ene

rgy

[kJ/

mol

]

A–top siteBridge siteHollow site

0 5 10–60

–40

–20

0

20

Distance from Surface [Å]Po

tent

ial E

nerg

y [k

J/m

ol]

A–top siteBridge siteHollow site

Experiment(STM)Morgensterm et. al. (1996) 400 meV = 40 kJ/mol

A-top

Hollow

Bridge

Snapshots of Water Droplet on Platinum Surface(N=2048, fcc(111), ZP Potential)

Velocity ScaledTemperature Control (350K)

0 10 20 30 40 50 600

10

20

30

Radius [Å]

0 10 20 30 40 50 600

10

20

30

Radius [Å]

0 10 20 30 40 50 600

10

20

30

Radius [Å]

Hei

ght [

Å]

0 10 20 30 40 50 600

10

20

30

Radius [Å]

Hei

ght [

Å]

Two Dimensional Density Profiles of Water Dropleton fcc(111) Platinum Surface

Z-P PotentialS-H Potential

N=864 N=864

N=2048 N=2048 0.00 [Å-3]

0.06 [Å-3]

Comparison of Surface Structure (Z-P Potential, N=864)

(111) (Pt: 0.150 Å-2) (100) (Pt: 0.130 Å-2) (110) (Pt: 0.093 Å-2)

Hydrogen Storage with Single-Walled Carbon Nanotubes

Mechanism of H2 Storage

High Storage Capacity is Possible?

Any Similar Structure Leads to Better Results

FUEL CELLS(PEFC) Distributed power supplyAutomobiles

Mobile machinesSupply of hydrogen

Storage problems for small light-weighted fuel cells

Liquid hydrogenHigh pressure gasMetal hydrideCarbon materials

Methanol Regenerator is heavyLow temperature, Energy loss

Weight of case

Heavy

Fuel Cell and Hydrogen Storage

A. C. Dillon et al., Nature, 386, (1997)

Energy Density of Hydrogen

0 5 100

20

40

60

80

水素重量密度 (wt%)

水素体積密度

(kg

H2m

–3)

DOE目標

液化

吸蔵合金

高圧ガス炭素ポリマー

60 MPa

40 MPa

20 MPa活性炭

2nm径1.63nm

1.22nm

SWNT

SWNT: (1mg sample, 0.1-0.2wt. % SWNT)A. C. Dillon et al., Nature, 386, 377 (1997).

5-10 wt.% (0.6-1.2 H/C) at less than 1 atm near room temperatureActivation energy: 19.6 KJ/molSWNT ropes:

Y. Ye et al., Appl. Phys. Lett., 74, 2307 (1999).8.25 wt.% (1H/C) at 80K, Phase transition?SWNT with Larger Diameter (1.85nm):

C. Liu et al., Science, 286, 1127 (1999).4.2 wt % at Room Temp., 10MPaHigh-Purity SWNT:

A. C. Dillon & M. J. Heben, Appl. Phys. A 72, 133 (2001).7 wt % at Room Temp., Atomspheric

? Ti ContaminationM. Hirscher et al., Appl. Phys. A 72, 129 (2001).

Hydrogen Storage in SWNTs

Graphite Nanofiber:A. Chambers et al., J. Phys. Chem. B, 102, 4253 (1998).

68 wt.%(8H/C) at 300K, 12MPa?Not reproducibleC. C. Ahn et al., Appl. Phys. Lett. 73, 3378 (1998).

Alkali-Doped Nanotube:P. Chen et al., Science, 285, 91 (1999).

20 wt %(200℃), 14 wt %(400℃)?Water contamination

R. T. Yang: Carbon 38, 623 (2000).

Hydrogen Storage with Graphite Nanofiber

HC = 0.442510-21 J = 2.76 meVHC = 3.179 Å

HH = 0.509510-21 J = 3.18 meVHH = 2.928 Å

H2-H2: Lennard-Jones

H2-C: Lennard-Jones (H2-Graphitic Wall)

612

4rr

U HHHHHHHH

02 r

–

21/6

Potential Function (H2-H2 and H2-C)

Van der Waals interaction of C atom and C atom from graphite

4

0

8

0 )(2

)( drdrU TTTTTTTT

Lennard-JonesCC = 0.384510-21 J = 2.40 meVCC = 3.37 Å

Interaction of SWNT and SWNT

612

4rr

U CCCCCCCC

10 20 30

–100

0

100

Tube Distance [Å]

Ener

gy [m

eV /

Å](8,8)

(10,10) (12,12)

10 20 30

–100

0

100

Tube Distance [Å]

Ener

gy [m

eV /

Å](8,8)

(10,10) (12,12)

d0 =13.6 Å

R = 16.7 Å

TT= 3.15 Å

Potential Function (SWNT-SWNT)

10 x 3.45 x 20 nm box

9504 Hydrogen Molecules

7 SWNTs Bundle (440 C atoms each)

3080 C atoms

Initial Configuration for (10,10) SWNTs

Initial 12 MPa

Transform = 0.05 = 1

Snapshots of Absorption for (10,10) SWNTs

Physisorption Sites

Endohedral

Interstitial

Outer

Potential Field

at 77 K，10 MPa-100 -50 0 [meV

]

-100

-50

0

[meV]

at 77 K，10 MPa

Phase Transformation

(a) 12 MPa (b) Transformed

(c) 6 MPa (d) Transformed

0 102

4

6

8

Gra

vim

etry

Ene

rgy

Den

sity

[wt%

]

Pressure [MPa]

(a)

(b)

(c)

(d)

Snapshots for Various SWNTs

(10,10) (16,16)

ClosePacked

InterstitiallyFilled

6.1 wt %

7.5 wt %

7.2 wt %

8.6 wt %

Definition of Adsorption

SWNT

High

Low

SWNT

High

Low

High

Low

SWNT

High

Low

SWNT

0 10 20

–50

00

0.1

Distance from SWNT's center [Å]

Pote

ntia

l Ene

rgy

[meV

]D

ensi

ty [Å

–3]

r0

HC HH 0.5HH

0 10 20

–50

00

0.1

Distance from SWNT's center [Å]

Pote

ntia

l Ene

rgy

[meV

]D

ensi

ty [Å

–3]

r0

HC HH 0.5HH

Position: r0+HC+1.5HHPotential: -18.7 meV(-3.010-21 J)

2-D Density Profile

2-D Potential Profile

Absolute and Surface Excess adV

ad

L

adab drrdrrn 0

adgabex Vnn

Solid Adsorption Layer Bulk

0 L

Bulk

Distance from solid surface

Den

sity

0

Solid Adsorption Layer Bulk

0 L

Bulk

Distance from solid surface

Den

sity

0

(10,10) 77 K, 10 MPa

(10,10) 300 K, 10 MPa0 5 10 150

1

2

3

0

2

40

20

40

Pressure [MPa]

(10,10) 77K

(10,10) 300K

Volumetric

Gravimetric Absolute

Gravimetric Excess

Adso

rptio

n[w

t%]

[wt%

][k

g H

2 m–3

]

Absorption Isotherms

Dependence on SWNT Diameter

(10,10) 77 K, 10 MPa

(16,16) 77K, 10 MPa

0 5 10 150

2

40

2

4

60

20

40

60

Pressure [MPa]

(16,16) 77K

(10,10) 77K

Volumetric

Gravimetric Absolute

Gravimetric Excess

Adso

rptio

n[w

t%]

[wt%

][k

g H

2 m–3

]