Phenomenological kinetics (PK) is widely used in the study of the reaction rates in heterogeneous catalysis, and it is an important aid in reactor design. PK makes simplifying assumptions: It neglects the role of fluctuations, assumes that there is no correlation between the locations of the reactants on the surface, and considers the reacting mixture to be an ideal solution. In this article we test to what extent these assumptions damage the theory. In practice the PK rate equations are used by adjusting the rate constants to fit the results of the experiments. However, there are numerous examples where a mechanism fitted the data and was shown later to be erroneous or where two mutually exclusive mechanisms fitted well the same set of data. Because of this, we compare the PK equations to “computer experiments” that use kinetic Monte Carlo (kMC) simulations. Unlike in real experiments, in kMC the structure of the surface, the reaction mechanism, and the rate constants are known. Therefore, any discrepancy between PK and kMC must be attributed to an intrinsic failure of PK. We find that the results obtained by solving the PK equations and those obtained from kMC, while using the same rate constants and the same reactions, do not agree. Moreover, when we vary the rate constants in the PK model to fit the turnover frequencies produced by kMC, we find that the fit is not adequate and that the rate constants that give the best fit are very different from the rate constants used in kMC. The discrepancy between PK and kMC for the model of CO oxidation used here is surprising since the kMC model contains no lateral interactions that would make the coverage of the reactants spatially inhomogeneous. Nevertheless, such inhomogeneities are created by the interplay between the rate of adsorption, of desorption, and of vacancy creation by the chemical reactions.

1.
A. B.
Bortz
,
M. H.
Kalos
, and
J. L.
Lebowitz
,
J. Comput. Phys.
17
,
10
(
1975
).
2.
K. A.
Fichthorn
and
W. H.
Weinberg
,
J. Chem. Phys.
95
,
1090
(
1991
).
3.
P. A.
Maksym
,
Semicond. Sci. Technol.
3
,
594
(
1988
).
4.
A. F.
Voter
,
Phys. Rev. B
34
,
6819
(
1986
).
5.
V. P.
Zhdanov
,
Surf. Sci.
500
,
966
(
2002
).
6.
R. M.
Ziff
,
E.
Gulari
, and
Y.
Barshad
,
Phys. Rev. Lett.
56
,
2553
(
1986
);
[PubMed]
B. J.
Brosilow
and
R. M.
Ziff
,
Phys. Rev. A
46
,
4534
(
1992
).
[PubMed]
7.
G. M.
Buendia
,
E.
Machado
, and
P. A.
Rikvold
,
J. Mol. Struct.: THEOCHEM
769
,
189
(
2006
).
8.
D. J.
Liu
and
J. W.
Evans
,
J. Chem. Phys.
117
,
7319
(
2002
).
9.
D. J.
Liu
and
J. W.
Evans
,
Multiscale Model. Simul.
4
,
424
(
2005
).
10.
D. J.
Liu
and
J. W.
Evans
,
J. Chem. Phys.
124
,
154705
(
2006
).
11.
F. J.
Gracia
and
E. E.
Wolf
,
Chem. Eng. Sci.
59
,
4723
(
2004
).
12.
E.
Machado
,
G. M.
Buendia
,
P. A.
Rikvold
, and
R. M.
Ziff
,
Phys. Rev. E
71
,
016120
(
2005
).
13.
N. V.
Petrova
and
I. N.
Yakovkin
,
Surf. Sci.
578
,
162
(
2005
).
14.
A.
Provata
and
V. K.
Noussiou
,
Phys. Rev. E
72
,
066108
(
2005
).
15.
D. Y.
Hua
and
Y. Q.
Ma
,
Phys. Rev. E
66
,
066103
(
2002
).
16.
D. Y.
Hua
,
S. J.
Shao
, and
S.
Lin
,
Phys. Rev. E
69
,
046114
(
2004
).
17.
R. H.
Goodman
,
D. S.
Graff
,
L. M.
Sander
,
P.
LerouxHugon
, and
E.
Clement
,
Phys. Rev. E
52
,
5904
(
1995
).
18.
N.
Pavlenko
,
J. W.
Evans
,
D. J.
Liu
, and
R.
Imbihl
,
Phys. Rev. E
65
,
016121
(
2002
).
19.
Y.
Suchorski
,
J.
Beben
,
R.
Imbihl
,
E. W.
James
,
D. J.
Liu
, and
J. W.
Evans
,
Phys. Rev. B
63
,
165417
(
2001
).
20.
E.
Clement
,
P.
LerouxHugon
, and
L. M.
Sander
,
Phys. Rev. E
52
,
5997
(
1995
).
21.
K.
Reuter
,
D.
Frenkel
, and
M.
Scheffler
,
Phys. Rev. Lett.
93
,
116105
(
2004
).
22.
K.
Reuter
and
M.
Scheffler
,
Phys. Rev. Lett.
90
,
046103
(
2003
).
23.
K.
Reuter
and
M.
Scheffler
,
Phys. Rev. B
73
,
045433
(
2006
).
24.
G. F.
Froment
,
Catal. Rev. - Sci. Eng.
47
,
83
(
2005
).
25.
E.
Kotomin
and
V.
Kuzovkov
, in
Comprehensive Chemical Kinetics
, edited by
R. G.
Compton
and
G.
Hancock
(
Elsevier
,
Amsterdam
,
1996
), Vol.
34
, p.
1
.
26.
J. M.
White
, in
Comprehensive Chemical Kinetics
, edited by
C. H.
Bamford
and
C. F. H.
Tipper
(
Elsevier
,
Amsterdam
,
1972
), Vol.
6
, p.
201
.
27.
H.
Metiu
,
Physical Chemistry: Thermodynamics
, 1st ed. (
Taylor & Francis
,
London
,
2006
), Vol.
1
.
28.
R. K.
Boyd
,
Chem. Rev. (Washington, D.C.)
77
,
93
(
1977
).
29.
K.
Denbigh
,
The Principles of Chemical Equilibrium
(
Cambridge University Press
,
Cambridge
,
1993
).
30.
E.
Clement
,
P.
Lerouxhugon
,
L. M.
Sander
, and
P.
Argyrakis
,
J. Phys. Chem.
98
,
7274
(
1994
).
31.
R.
Dickman
,
Phys. Rev. A
34
,
4246
(
1986
).
32.
J. W.
Evans
,
D. J.
Liu
, and
M.
Tammaro
,
Chaos
12
,
131
(
2002
).
33.
J.
Wang
,
C. Y.
Fan
,
K.
Jacobi
, and
G.
Ertl
,
Surf. Sci.
481
,
113
(
2001
).
34.
K.
Reuter
,
M. V.
Ganduglia-Pirovano
,
C.
Stampfl
, and
M.
Scheffler
,
Phys. Rev. B
65
,
165403
(
2002
).
35.
K.
Reuter
and
M.
Scheffler
,
Surf. Sci.
490
,
20
(
2001
).
36.
K.
Reuter
and
M.
Scheffler
,
Phys. Rev. B
65
,
035406
(
2001
).
37.
K.
Reuter
and
M.
Scheffler
,
Phys. Rev. B
68
,
045407
(
2003
).
38.
K.
Reuter
,
C.
Stampfl
,
M. V.
Ganduglia-Pirovano
, and
M.
Scheffler
,
Chem. Phys. Lett.
352
,
311
(
2002
).
39.
J.
Assmann
,
V.
Narkhede
,
L.
Khodeir
,
E.
Loffler
,
O.
Hinrichsen
,
A.
Birkner
,
H.
Over
, and
M.
Muhler
,
J. Phys. Chem. B
108
,
14634
(
2004
).
40.
V.
Narkhede
,
J.
Assmann
, and
M.
Muhler
,
Z. Phys. Chem.
219
,
979
(
2005
).
41.
Y. D.
Kim
,
H.
Over
,
G.
Krabbes
, and
G.
Ertl
,
Top. Catal.
14
,
95
(
2001
).
42.
Y. D.
Kim
,
A. P.
Seitsonen
, and
H.
Over
,
Surf. Sci.
465
,
1
(
2000
).
43.
Y. D.
Kim
,
A. P.
Seitsonen
, and
H.
Over
,
Phys. Rev. B
63
,
115419
(
2001
).
44.
Y. D.
Kim
,
A. P.
Seitsonen
,
S.
Wendt
,
J.
Wang
,
C.
Fan
,
K.
Jacobi
,
H.
Over
, and
G.
Ertl
,
J. Phys. Chem. B
105
,
3752
(
2001
).
45.
H.
Madhavaram
,
H.
Idriss
,
S.
Wendt
,
Y. D.
Kim
,
M.
Knapp
,
H.
Over
,
J.
Assmann
,
E.
Loffler
, and
M.
Muhler
,
J. Catal.
202
,
296
(
2001
).
46.
H.
Over
,
Y. D.
Kim
,
A. P.
Seitsonen
,
S.
Wendt
,
E.
Lundgren
,
M.
Schmid
,
P.
Varga
,
A.
Morgante
, and
G.
Ertl
,
Science
287
,
1474
(
2000
).
47.
H.
Over
and
M.
Muhler
,
Prog. Surf. Sci.
72
,
3
(
2003
).
48.
H.
Over
,
A. P.
Seitsonen
,
E.
Lundgren
,
M.
Schmid
, and
P.
Varga
,
J. Am. Chem. Soc.
123
,
11807
(
2001
).
49.
H.
Over
,
A. P.
Seitsonen
,
E.
Lundgren
,
M.
Schmid
, and
P.
Varga
,
Surf. Sci.
515
,
143
(
2002
).
50.
H.
Over
,
A. P.
Seitsonen
,
E.
Lundgren
,
M.
Smedh
, and
J. N.
Andersen
,
Surf. Sci.
504
,
L196
(
2002
).
51.
K.
Reuter
and
M.
Scheffler
,
Appl. Phys. A: Mater. Sci. Process.
78
,
793
(
2004
).
52.
A. P.
Seitsonen
,
Y. D.
Kim
,
M.
Knapp
,
S.
Wendt
, and
H.
Over
,
Phys. Rev. B
65
,
035413
(
2002
).
53.
S.
Wendt
,
M.
Knapp
, and
H.
Over
,
J. Am. Chem. Soc.
126
,
1537
(
2004
).
54.
S.
Wendt
,
A. P.
Seitsonen
,
Y. D.
Kim
,
M.
Knapp
,
H.
Idriss
, and
H.
Over
,
Surf. Sci.
505
,
137
(
2002
).
55.
S.
Wendt
,
A. P.
Seitsonen
, and
H.
Over
,
Catal. Today
85
,
167
(
2003
).
56.
D. A.
McQuarrie
,
Statistical Mechanics
, 2nd ed. (
University Science Books
,
Sausalito
,
2000
).
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