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Announcements
• A 3-h open book exam on December 12, 2013 Monday 9:10 – 12:00 am • November 14 & 21: Chapter 25 (Atkins/Paula) Processes at solid surfaces
• November 21 & 28: Chapter 20 (Atkins/Paula) The solid state
• December 5: Single molecule spectroscopic methods
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Atkins / Paula
《 Physical Chemistry, 8th Edition 》
Chapter 25.
Processes at solid surfaces
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The growth and structure of solid surfaces 25.1 Surface growth 25.2 Surface composition
P.909
The extent of adsorption 25.3 Physisorption and chemisorption 25.4 Adsorption isotherms 25.5 The rates of surface processes
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Processes at electrodes 25.8 The electrode-solution interface 25.9 The rate of charge transfer 25.10 Voltammetry 25.11 Electrolysis 25.12 Working galvanic cells 25.13 Corrosion
P.909
Heterogeneous catalysis 25.6 Mechanisms of heterogeneous catalysis 25.7 Catalytic activity at surfaces
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歐亞書局 Chapter 25. Processes at solid surfaces P.910
25.1 Surface growth
歐亞書局 Chapter 25. Processes at solid surfaces P.910
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歐亞書局 Chapter 25. Processes at solid surfaces P.911
歐亞書局 Chapter 25. Processes at solid surfaces P.911
歐亞書局 Chapter 25. Processes at solid surfaces P.911
歐亞書局 Chapter 25. Processes at solid surfaces P.912
25.2 Surface composition
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Surface characterization tools:
1. Electron microscopy (Impact I8.1)
2. Scanning probe microscopy (Impact I9.1)
3. Ionization techniques
4. Vibrational spectroscopy
5. Electron spectroscopy
6. Surface-extended X-ray absorption fine structure spectroscopy
7. Low-energy electron diffraction
8. Molecular beam techniques
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歐亞書局 Chapter 25. Processes at solid surfaces P.912
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歐亞書局 Chapter 25. Processes at solid surfaces P.913
On-top site
Bridge site
歐亞書局 Chapter 25. Processes at solid surfaces P.914
歐亞書局 Chapter 25. Processes at solid surfaces P.914
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歐亞書局 Chapter 25. Processes at solid surfaces P.914
LEED
Electron energy: 10-200 eV
Wavelength: 100-400 pm
The de Broglie wavelength:
歐亞書局 Chapter 25. Processes at solid surfaces P.915
歐亞書局 Chapter 25. Processes at solid surfaces P.915
The results of LEED experiments show that the surface of a crystal rarely has exactly the same for as a slice through the bulk. As a general rule, it is found that metal surfaces are simply truncations of the bulk lattice, but the distance between the top layer of atoms and the one below is contracted by ~5%.
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The interpretation of LEED data is much more complicated than the interpretation of bulk X-ray data.
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Thermogravimetric Analysis (TGA)
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歐亞書局 Chapter 25. Processes at solid surfaces P.917
Hydrogen bond energy between H2O molecules?
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Kp
Kp
k
kK
Nkdt
d
Desorption
pNkdt
d
Adsorption
d
a
d
a
1
:
)1(
:
A(g) + M(surface) ↔ AM(surface)
N is the total number of sites
歐亞書局 Chapter 25. Processes at solid surfaces P.918
CO on charcoal
mm
m
KVV
p
V
p
Kp
Kp
V
V
1
1
歐亞書局 Chapter 25. Processes at solid surfaces P.920
R
H
T
p
or
RT
H
T
K
T
p
constpK
Kp
ad
ad
)/1(ln
lnln.lnln
1
2
At constant θ
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The van 't Hoff equation The equation that relates the change in temperature T to the change in the equilibrium constant K in chemical thermodynamics,
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2/1
2/1
2
2
)(1)(
)1(
Kp
Kp
kdt
d
Desorption
pkdt
d
Adsorption
d
a
Dissociative adsorption, X2(g) → 2X(surface)
歐亞書局 Chapter 25. Processes at solid surfaces P.920
RTHH
mon
vapdesec
p
pz
where
zcz
cz
V
V
/)(
*
])1(1)[1(
BET isotherm
(Brunauer, Emmett, Teller)
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● BET theory aims to explain the physical adsorption of gas molecules on a solid surface and serves as the basis for an important analysis technique for the measurement of the specific surface area of a material. ● In 1938, Stephen Brunauer, Paul Hugh Emmett, and Edward Teller published an article about the BET theory J. Am. Chem. Soc., 1938, 60, 309 for the first time. ● “BET” consists of the first initials of their family names.
Edward Teller (1/15/1908 – 9/9/2003)
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Derivation of the BET isotherm Consider a surface:
Definition:
0, 1, ..., n = Surface area covered by 0, 1, ..., n layers of adsorbed molecules.
At equilibrium, 0 must remain constant,
Rate of evaporation from 1st layer = Rate of condensation onto bare surface
(I)
Similarly at equilibrium, 1 must remain constant,
Rate of condensation onto bare surface + Rate of evaporation from the 2nd layer
= Rate of condensation on the 1st layer + Rate of evaporation from the 1st layer
(II)
11122201 kpkkpk
0111 pkk
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Substituting into (I) gives
Extending this argument to other layers,
(III)
Since the total surface area,
the total volume of gas molecules adsorbed on surface is
where V0 is the volume of gas adsorbed per unit area when the surface is covered with
a complete layer. Defining Vm, the volume of gas adsorbed when the entire surface is
covered with a complete monolayer, the average number of layers is then
1222 pkk
1 iiii pkk
0i
iA
0
0i
iiVV
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(IV)
From eq. (III)
If we assume that the properties of the 1st, 2nd, ... layers are equivalent, then,
From eq. (III)
or
(V)
,
0
0
0
i
i
i
i
m
i
AV
V
V
V
gk
k
k
k
i
i
...2
2
0111 pkk 001
11 yp
k
k
0001 )/( iii
i czzzyyz
1 iiii pkk 11
11
1
ii
ii
ii zgpp
k
k
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Substituting (V) into (IV) yields
Mathematically, it is known
also
,
1
1
100
01
0
0
1i
i
i
i
i
i
i
i
i
i
i
i
mzc
izc
cz
iczi
V
V
x
xxxx
i
i
i
i
101
21
3232
1
)1()
1()(
...)4321(....32
x
x
x
x
dx
dxx
dx
dx
xxxxxxxix
i
i
i
i
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Finally,
or or
Note that at the saturation gas pressure, p*, an infinite number of adsorbate layers
must build up on the surface, i.e. V → ∞. This is possible only when z =1. Since
z ≡ gp, it means gp* = 1 or g = 1/p*. Alternatively,
,
)1)(1(1
1
1)1(1
2
1
1czzz
cz
z
czz
cz
zc
izc
V
V
i
i
i
i
m
])1(1)[1( zcz
czVV m
*)]/)(1(1*))[/(1(*)/(
])1(1)[1( ppcpp
ppcV
zcz
czVV mm
cV
zc
cVzV
z
mm
)1(1)1(
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*)]/)(1(1*))[/(1(*)/(
ppcpp
ppc
V
V
m
What is c?
歐亞書局 Chapter 25. Processes at solid surfaces P.921
Interaction between adsorbates
RTHH
des
vap
con
ad
ii
vapdesec
K
K
K
K
pkk
pkk
z
yc
/)(
11
)/()/(
cV
zc
cVzV
z
mm
)1(1)1(
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Assuming that the value of c is sufficiently large, then c–1 ~ c.
At p/p* << 1, the above equation can be reduce to the Langmuir
equation as
pc
pc
ppc
ppc
V
V
m *1*
*)/(1*)/(
BET isomtherm is a generalized form of the Langmuir model
*)]/)(1(1*))[/(1(*)/(
ppcpp
ppc
V
V
m
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Srate of adsorption
rate of collision
Sticking probability:
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According to the kinetic model of gases, the rate of collision with a surface:
(25.1a)
where p is the pressure and m is the mass of the molecule.
• For air at 1 atm and 25 °C, the collision flux is 3 × 1027 m-2s-1. Because 1 m2 of metal surface consists of about 1019 atoms, each atom is struck about 108 times each second. If S = 1, it will take only 10 ns to form a monolayer.
• In UHV, where the pressure is 10-9 Pa (or 10-14 atm), the collision flux is reduced to 3 × 1013 m-2s-1, meaning that each surface atom is hit once every 105 - 106 s, or about once a day.
mkT
pZW
2
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歐亞書局 Chapter 25. Processes at solid surfaces P.924
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RTEd
dAek/
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Unimolecular decomposition
– Rate is proportional to the surface coverage only
– PH3(ad) on W
k
kKp
Kp
kKpk
1
when Kp << 1 first-order decomposition when Kp >> 1 zeroth-order decomposition
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Langmuir-Hinshelwood (LH) mechanism
– Reactions take place by encounters between molecular fragments and atoms adsorbed on the surface
– O(ad) + CO(ad) → CO2(g)
2)1(
1
1
BBAA
BABA
BBAA
BBB
BBAA
AAA
BA
PKpK
ppKkK
PKpK
pK
PKpK
pK
k
PBA
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Eley-Rideal (ER) mechanism
– A surface-catalyzed reaction, a gas-phase molecule collides with another molecule already adsorbed on the surface
– Almost all thermal surface-catalyzed reactions are thought to take place by this mechanism
– H(g) + D(ad) → HD(g)
A
BA
BA
Kp
pkKp
pk
PBA
1
When KpA >> 1, the rate determining step is the collision of B with adsorbed fragments.
Bkp
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Zeolites are microporous aluminosilicates with the formula of
where Mn+ cations and H2O molecules bind inside the cavities or pores of the Al-O-Si framework.
Chapter 25. Processes at solid surfaces P.931
{[Mn+]x/n[H2O]m}{[AlO2]x[SiO2]y}x–
歐亞書局 Chapter 25. Processes at solid surfaces P.931
Some zeolites for which M=H+ are very strong acids and catalyse a variety of reactions, including the dehydration of methanol to form hydrocarbons such as gasoline and other fuels:
xCH3OH → (CH2)x + xH2O