adsoprtion laws

1. Lecture 2—Adsorption at Surfaces
1. Adsorption/Desorption
2. Overlayers, lifting reconstruction
3. Dissociative and Associative adsorption
4. 1st and 2nd order desorption, kinetics
Reading—
Lecture on Langmuir adosrption isotherm
P. A. Redhead, Vacuum 12 (1962) 203-211
Smentkowski and Yates, Surf. Sci. 232 (1990) 1

2. S S S S
S S
A
A
A
A A
Adsorption at open
site: S = S0
No adsorption at
occupied site: S = 0
Monolayer Adsorption:
Assume an Adsorbate (A) can adsorb at an empty surface site with sticking coefficient S0.
If a surface site is already occupied, then no adsorption occurs (S = 0)
2

3. (1x1) unit cell
3

4. Adsorbate forming a (2x2) overlayer on the
(1x1) substrate surface
4

5. Unused surface bonds can interact, causing change in surface structure
Surface dimerization
5

6. Surface dimerization
Dissociative adsorption of H2
H
H
H
H
H
H
Adsorption can induce or lift surface
reconstructions (e.g., H/Si(100)
6

7. Associative Adsorption adsorbate does
not break bonds during chemisorption,
e.g., CO/W
W W W W W W
CO
CO
CO
CO
CO
7

8. W W W W W W
H H
H2
Dissociative adsorption: molecular
bonds broken during adsorption
3.g., H2 on W
8

9. Consider adsorption (assoc. or dissoc.) at a
surface
In this process, note that the average sticking
coefficient will depend on the fractional
surface coverage (Θ).
At zero or low coverage, the sticking
coefficient will be S0: 0<S0<1
At Θ = 1 (full coverage), S = 0
For 0<Θ<1, we have S = S0(1-Θ)
9

10. We can therefore model adsorption as an
equilibrium between adsorbate, and surface
sites:
[A] + [S] [AS]
Therefore:
(1) Kads = [AS]/[A][S]
We can then rewrite [AS] and [S] in terms of Θ:
(2) [AS]/[S] = Θ/(1-Θ)
Given that [A] is some constant (C), we can re-
write (1) as
Kads = Θ/C(1-Θ), or
(3) Θ = KadsC/(1+KadsC)
(the usual form for the Langmuir Isotherm)
10

11. (3) Allows us to determine the fractional surface coverage as a function of C
(typically proportional to pressure)
For small C, KadsC << 1, and
Θ ~ KadsC
For large C, we have KadsC >> 1
And Θ ~ 1
Θ
C
Θ~ KadsC
Θ~1
11

12. In many laboratory situations, adsorption at a given
temperature is, for all practical purposes, irreversible.
Kads is very large, and the equilibrium fractional surface
coverage is 1.
However, we are often concerned with the kinetics of coverage,
as we can control the total exposure of a gas to the surface.
Assuming that once adsorbed at a given temperature, A will not
desorb, we have
Θ = SFt where S = sticking coefficient, F = flux to the surface
(suitably normalized, and proportional to pressure), and t =
time.
Ft = “exposure”. Typically, exposure is measured in “Langmuirs”
(L) where L = 10-6 Torr-sec
12

13. Note, however, the S is not constant.
We have S = S0(1-Θ)
We then have :
(4) Θ = S0(1-Θ)cPt where c is a constant, and P = Pressure
Differentiating both sides of (4) with respect to t,
(5) dΘ/dt = S0cP – S0cP(dΘ/dt)
For Θ << 1, we have
dΘ/dt ~ S0cP, and coverage will increase linearly with exposure
For Θ ~ 1,
(6) then dΘ/dt = 0, and coverage is constant with time
13

14. Θ
P x t
14

15. Interrogating adsorption and desorption
Temperature Programmed Desorption (TPD)
Temperature Programmed Reaction Spectroscopy
(TPRS)
Typical experimental apparatus
(Gates, et al., Surf. Sci. 159 (1985) 233
Typically need:
•QMS with line of site
•Controlled dosing
•Temperature control with linear
ramp
•Another method to monitor surface
composition/structure (Auger, XPS,
LEED…) 15

16. TPD
Step 1:
Adsorption at
Low Temp
Step 2:
Desorption vs.
temperature:
dT/dt ~ 1-10 K/sec
QMS
16

17. 1st and 2nd order desorption
1st order, desorption occurs from a
surface site
2nd order, desorption occurs
after surface reaction and
combination, e.g.;
Hads + Hads  H2 desorbed
17

18. In monitoring desorption from a surface, the desorption rate
(N(t); molecules/cm2-sec) is proportional to two pressure-dependent
terms (see Redhead)
aN(t) = dp/dt + p/λ
a = constant (dependent on surface area)
p = pressure
λ = pumping time (reciprocal of pumping rate)
In modern vacuum systems, λ is very small, and p/λ
becomes the dominant term.
The desorption rate is therefore proportional to the
(partial) pressure as measured by the QMS:
N(t) = kp
18

19. We can therefore monitor the desorption rate by looking at the change
in partial pressure of the desorbing species (e.g., H2, CO, etc.) in the
QMS:
PCO
T ( = T0 + βt) 
Temperature of desorption rate
maximum
19

20. We can (Redhead) express N(t) as the product of an Arrhenius
rate equation:
(7) N(t) = -dѳ/dt = vnѳn exp(-E/RT)
v = rate constant
n = order of the reaction
ѳ = concentration of adsorbates (molecules/cm2)
E = activation energy
20

21. Given that T = T0 + βt (the linear heating rate is critical), we can solve (7) for the
temperature at which N(t) is a maximum (T = TP) (Redhead, again)
For n = 1 (1st order) (v1 is the first order rate constant)
(8a)E/(RTp
2) = ( v1/β)exp(-E/RTp)  TP independent of surface coverage
(note: this assumes E does not vary with surface coverage; not always true)
For n = 2 (2nd order)
(8b) E/RTP
2 = (σ0v2/β)exp(-R/TP)  TP is a function of initial surface coverage (σ0)
21

22. From 8a, b, we can see that one way to distinguish 1st from 2nd order desorption
processes is to due the same desorption expt at different surface coverages:
Initial coverage, 0.7 ML
Initial coverage, 0.4 ML
Initial coverage, 0.4 ML
1st order reaction, temp. of peak maximum is invariant
with initial coverage.
22

23. 2nd Order: Peak temperature decreases with increasing
initial coverage (desorption of H2 from W: Redhead)
23