表面エネルギー,濡れ性,吸着...第一法則と組み合わせた表現 du t ds dl du...
TRANSCRIPT
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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: [email protected]://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)(
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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
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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
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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
]