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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.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%.

歐亞書局 Chapter 25. Processes at solid surfaces P.915

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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歐亞書局 Chapter 25. Processes at solid surfaces P.922

歐亞書局 Chapter 25. Processes at solid surfaces P.923

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

歐亞書局 Chapter 25. Processes at solid surfaces P.924

歐亞書局 Chapter 25. Processes at solid surfaces P.925

RTEd

dAek/

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歐亞書局 Chapter 25. Processes at solid surfaces P.926

歐亞書局 Chapter 25. Processes at solid surfaces P.929

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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

歐亞書局 Chapter 25. Processes at solid surfaces P.930

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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