Transcript che 377 lectures - Classnotes For Professor Masel's Classes

ChE 553 Lecture 6
Equilibrium Adsorption
1
Objective
• Introduce Adsorption Isotherms
– How much gas adsorbs at equilibrium as a
function of pressure
– Qualitative features of isotherms
• Types 1-5
• More complex phase behavior
2
Topics
• Introduction to Adsorption Isotherms
Five types
• Langmuir Adsorption Isotherm
Simple Adsorption Isotherm
Finite number of surface spaces to hold
gas
• More complex behavior: surface phase
transitions due to adsorbate/adsorbate
interactions
3
Introduction To Adsorption
Isotherms
Adsorption Isotherm –
amount adsorbed
as a function of
pressure
S-shaped curve
typical at T>300K
4
Typical Behavior At Low
Temperature
Figure 4.2 Isotherms for adsorption of
krypton, argon at 77 K, argon at 91.3 K,
and ammonia on graphitized carbon black.
(Data of Putnam and Fart [1975], Ross and
Winkler [1955], Basset, Boucher, and
Zettlemoyer [1968], and Bomchil et al.
[1979], respectively.)
5
S-Shaped Curve At Low
Pressure
Figure 4.3 A blowup of the low-pressure part of the krypton data in Figure 4.2.
6
General Adsorption Isotherms
Figure 4.4 The five types of adsorption isotherms described by Brunauer [1945].
7
Next Langmuir’s Model Of
Adsorption:
Figure 4.5 Langmuir’s model of the structure of the adsorbed layer. The black dots
represent possible adsorption sites, while the white and mauve ovals represent adsorbed
molecules.
8
Key Features Of Langmuir’s
Model
• Finite sites to adsorb gas
• Ideal behavior in surface phase (no
interactions between adsorbed molecules?
• At low pressures coverages proportional to
pressure (or p1/2)
• Eventually surface fills up
– Adsorption limited by availability of sites
– If multiple species – competition for sites
– Maximum coverage 1ML
9
Kinetic Derivation Of
Langmuir’s Model
Assume equilibrium
A g  S  Aad
(4.1)
rad  k ad PA S 
(4.2)
At equilibrium rd=rad.
Solving
Aad 
PA S 

kad
kd

A
K equ
(4.4)
rd  k d  Aad 
(4.3)
10
Isotherm Arises From A Site
Balance
S0 [S] [A ad ]
(4.7)
equation (4.4) are 4.7 are two equations
in two unknowns ([S], [Aad]). Solving
yields
A 
A
K equ
PA
A
1 K equ
PA
(4.10)
11
Qualitative Features of
Langmuir’s Model
1.2
1.2
1
0.8
Cov erage
Cov erage
1
0.6
0.4
0.8
0.6
0.4
0.2
0.2
0
0
10
20
30
Pres s ure
40
50
0
0.01
0.1
1
10
100
Pres s ure
12
Derivation Of Langmuir Isotherm For
Competitive Adsorption
 Aad   K A Bad   K B
equ
equ
PA S 
PB S 
(4.22)
S S  Aad Bad 
(4.23)
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Solving Equations
Simultaneously
A

A
K equ
PA
1 
A
K equ
PA

B
K equ
PB
(4.24)
B 
B
K equ
PB
A
B
1 K equ
PA  K equ
PB
(4.25)
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1.2
1.2
1
1
0.8
0
0.1
1
5
10
0.6
0.4
Cov erage
Cov erage
Qualitative Picture
0.8
0.6
0.4
0
0.1
1
5
10
0.2
0.2
0
0
10
20
30
Pres s ure
40
50
0
0.01
0.1
1
10
100
Pres s ure
15
Derivation Of Langmuir Adsorption For
Dissociative Adsorption
1/2D2 + S  Dad
Dad   K D
equ
1/ 2
PD S 
2
Qualitatively the same
as non-dissociative
(4.26)
D 
D 1/ 2
K equ
P2
D 1/ 2
1 K equ
PD
2
(4.27)
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Comparison To Data
D
D
K equ
P21 / 2

1 
D
K equ
PD1 /22
(4.27)
1
Rearranging
1
D

1
1
D 1/ 2
Kequ P2
Figure 4.1 A plot of a series of adsorption isotherms for hydrogen adsorption on
Pt(111). Dotted lines are symbols: data. Solid Lines: fits to the Langmuir
adsorption isotherm. (Data of Ertl, Neuman, and Steit [1977].)
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Real Situation: Interactions
Between Molecules
Attractive interactions lead to islands
18
Repulsive Interactions Order
Overlayer Continued
19
Phase Diagrams For
Adsorption
Figure 4.13 A phase diagram for oxygen on W(110). (Adapted from one
presented by Lagally et al. [1980].)
20
Qualitative Behavior
1/RT
Strength of
Attraction
Figure 4.21 A replot of the data from Figure 4.20 as a function of dimensionless
pressure.
21
Universal Curve: Monolayer Adsorption: Only
Nearest Neighbor Interactions
Equilibrium
constant at half
coverage
Figure 4.23 A series of adsorption isotherms calculated via the lattice gas
method for adsorption on a square lattice with first nearest neighbor interactions.
Curves are shown for βh = -0.50, -0.25, 0, …, 2.0.
22
Complication: Multilayer
Adsorption
23
The BET Equation
Assume
• Random distribution of sites with
1, 2, 3… adsorbed molecules
• No lateral interactions between molecules
 A
cB xB
S 1 xB 1 cB 1xB 
(4.189)
Does not work that well in practice
24
A Comparison Of The Krypton Data In Figure 4.12
To The Best Fit With The BET Equation
25
Comparison Continued
Figure 4.45 A blowup of the portion of the date in Figure 4.44 below 4 torr.
Used anyway
26
Why 5 Types Of Adsorption
Isotherms?
27
Type I
• Type I arises when only
one type of site:
– Initially surface fills
randomly
– Eventually saturates when
surface filled (or pores filled
with a porous material)
28
Type III
• Type III arises when there
are strong attractive
interactions leading to
condensation
– Initially, no adsorption
– Pressure increases lead to
nucleation and growth of
islands
– Eventually liquids
condense on the surface
29
Type II
• Type II arises when the is
more than one adsorption site
– Initial rapid adsorption
– Saturates when first site filled
– Second rise when second site
fills
• Second site could be a
second monolayer, a second
site on the surface. In porous
materials, it can also be a
second type of pore.
30
Type V
• Type V is another case for
attractive interactions
– Initially no adsorption
– Next nucleation and growth
of islands or liquid drops
– Coverage saturates when
no more space to hold
adsorbates
31
Type IV
• Type V occurs when there
are multiple phase
transitions due to a
mixture of attractive and
repulsive interactions
• Can also arise in
multilayer adsorption
where adsorption on
second layer starts before
first layer saturates
32
Summary
• Introduction to Adsorption Isotherms
Five types
• Langmuir Adsorption Isotherm
Simple Adsorption Isotherm
Finite number of surface spaces to hold gas
• More complex behavior: surface phase transitions
due to adsorbate/adsorbate interactions
– Attractive Interactions: Classical two phase regions i.e.
solids and gases
– Repulsive interactions - adsorbate ordering
– Leads to universality (general phase diagrams that do not
depend on gas and solid)
33