Kinetics and Reaction Rate Theory:

Surface Reactions

a tutorial

J W NiemantsverdrietSchuit Institute of Catalysis

Eindhoven University of Technology

adsorption

desorption

The Catalytic Cycle

reaction

Langmuir - Hinshelwood Kinetics

Irving Langmuir1881 - 1957

Nobel Prize 1932

Cyril NormanHinshelwood

1897 - 1967Nobel Prize 1956

1915Langmuir Isotherm

1927 Kinetics of Catalytic Reactions

The Arrhenius Equation

A B AB

k+

k = v e -Eact /RT

r = = k [A][B]d[AB]

dt

Svante Arrhenius1859 - 1927

Nobel Prize 1903

reaction parameter

E

Eact+

Empirical !

Temperature Dependence of the Rate

r = = k [A] [B]d [AB]

d tA + B ABk

R = 8,2

0

100

200

300

400

500

600

700

800

900

1000

1 200 400 600 800 1000T (K)

rate

k = v e- Eact / RT

Arrhenius:

ln k =ln v Eact / RT

ln k

1000 / T

Reaction Rate Theory(Transition State Theory)

to rationalize

preexponential factors of surface reactions adsorption desorption dissociation

sticking coefficients direct versus precursor-mediated adsorption

catalytic mechanisms Langmuir-Hinshelwood versus Eley-Rideal

Reaction Rate Theory

Molecules collide, but ..only a small fraction of the collisions is reactive

collision theory

transition state theory

Reaction Rate Theory

E

reaction parameter

Collision Theory of Reaction Rates:

Reaction:

Hard SpheresHard SpheresH + Br2 [H-Br-Br]# HBr + Br

Redistribution ofKinetic Energy:

H + Br2 [H-Br-Br]# H + Br2

Collision Theory of Reaction Rates:

Reaction:

H + Br2 [H-Br-Br]# HBr + Br

Redistribution ofKinetic Energy:

Hard SpheresHard Spheres

H + Br2 [H-Br-Br]# H + Br2

Collision Theory

reaction if collision energy > barrier energy

incidentally successful

usually predicts prefactors that are too high

major problem: disagrees with vant Hoff

equation for the equilibrium constant

Reaction Rate TheoryCollision Theory:hard spheres scatter or react upon collision

Transition State Theorymolecules possess internal degrees of freedom translation vibration rotation described by statistical thermodynamics(partition functions)

Ludwig Boltzmann(1844-1906)

S = k ln (W )

x ie

e

RTi /

=

i =

0

RTi /

Boltzmann Statistics:the basis of statistical thermodynamics

Partition Function:

i=

0q e i B k T/=

thermodynamical function of state,contains information on energy and entropy

Partition Function: q e i Bk Ti

= =

/0

energy(average)

chemicalpotential

entropy

= kT2 lnqT

= -kT ln q

kT ln qT

s =

Partition Function: q e i Bk Ti

= =

/0

chemicalpotential

equilibriumconstant

= -kT ln q

qproducts qreactants

i

i

K =

All Molecules

vibrate

rotate

translate

Partition Function:i=

0

e=q i B k T/

translation vibration rotationq l

m k Thtrans

B= ( ) /2 1 2

may be large iflength l over which molecule moves is large

(per dimension!)

q Ik Throt

B=8 2

2

large:H2: 2.9 at 500 KCO: 180 at 500 KCl2: 710 at 500 K(2-dimensional!)

(per dimension!)

qevib h k TB

=

11 /

usually equals 1unless vibrations have very low frequency

(per vibration!)

TransitionState

Theory

CHads Cads + Hadson noble metals, e.g. Rh(100)

Eb

reaction coordinate

ECHads

Cads+Hads

CHads#

CHads Cads + HadsTransition statePaco Ample, Dani Curulla, TU/e, 2004

Transition State Theory

R R# PK#

k ThB

k TB= K#kTST hHenry Eyring1901 - 1981

M.G. Evans & M. Polanyi

q#k TB Eb= -e k TB/h q

Transition State Theory: The Assumptions

Eb

reaction coordinate

E

R

P

R# passage over barrier only inforward direction

equilibrium between reactantsand products for all degrees offreedom, except for reactioncoordinate

passage over barrier is classicalevent, described by one reaction coordinate only

= K#[R]d[P] k T

hB

K#k T

hB

dt

R R# PK#

k T

hB = [R]

q#

q-

ek TB/Ebk T

hB

How to Compare

Transition State Theory

Expressions

with the

Arrhenius Equation?

How to Compare Transition State Theory Expression

with Arrhenius Equation?

Eact = kT2

Tln kTSTKey:

= em q#

qkThB

Eact = Eb + m k TBin transition state theory the activation energy is not precisely

equal to the barrier energy

m: number of times T appears in the rate expression

The meaning of

Preexponential

Factors

Meaning of Preexponentials

= em q#

qkThB

Standard case:q# q; m = 1

= ek T

hB 1013 s-1

transition state and reactants have same degrees of freedom and similar entropy

Loose TST:q# >> q; m 1

1013

Loose TST:q# >> q

Tight TST:q# 0

E

R

P

reaction coordinate

109 < < 1013 s-1 1013 < < 1017 s-1

Application to

Surface Reactions:

Adsorption

Adsorption

direct:

precursor mediated (trapping mediated):(high sticking probability)

(low sticking probability)

or

Adsorption in TST

precursor mediated (trapping mediated):mobile transition state

rad s = [AB]q#

q-

ek TB/Ebk T

hB = [AB]

(qtrans)2k T

hB

#

(qtrans)3

qvib#

qvib

qrot#

qrot

Collision frequencygas - surface

Sticking coefficient

direct adsorptionqvibadskBT

qtrans3 qrot qvib qtrans2kBTh

qtrans2 qvib#

Collision stickingfrequency coefficient

#kads = qtrans3 qrot qvibh

extremely small rate of adsorption due to lack of mobility in the transition state !

precursor mediated adsorption

kBT qtrans2 qrot qvib

# #

kads = qtrans3 qrot qvibhcollision stickingfrequency coefficient

largest possible rate of adsorption: mobility and free rotation in the precursor state !

Adsorption

direct: immobile transition statelow sticking probability:

Application to

Surface Reactions:

Desorption

Desorption of Atoms and MoleculesAdsorbed Transition Desorbed Preexponential

state state state factor

mobile

immobile

1015 s-1

1013 s-1

mobile 1014-17 s-1

immobile 1013 s-1

Temperature Programmed Desorption

Temperature

Controller

QuadrupoleMass Analyzer

Ultra High Vacuum

ToPumps

Thermocouple

Heatingwires

Single Crystal

Temperature

Rate

of des

orpt

ion

300 400 500 600

CO

0 .04 ML0 .08 ML0 .11 ML0 .17 ML0 .25 ML0 .33 ML0 .43 ML0 .47 ML

0 .62 ML0 .59 ML

0 .68 ML0 .70 ML0 .77 ML0 .80 ML

0 .82 ML

CO/Rh(100)

Ta ds

Preexponential Factorsfor Desorption at Low Coverages

CO Co(0001) 28 kcal/mol 1015 s-1

CO Ni(111) 31 1015

37 1017

30 1015

CO Ni(100) 31 1014

CO Cu(100) 16 1014

CO Ru(0001) 38 1016

CO Rh(111) 32 1014

CO Pd(111) 34 1014

CO 35 1015

CO Pd(100) 38 1016

CO Pd(211) 35 1014

CO Ir(110) 37 1013

CO Pt(111) 32 1014

from V.P. Zhdanov, Elementary Physicochemical Processes at Surfaces,Plenum, New York, 1991

Ammonia on Rh(111): Peculiar TPD patterns

Rh atom

NH3

Rh (111) - (2x2) NH3

LEED of Rh (111) + 0.25 ML NH3 NH 3

Des

orpt

ion

Rat

e [a

.u.]

200 300 400 500100Temperature [K]

Lateral Interactions?Preexponential Factor?

(2x2) NH3

R. M. van Hardeveld, R.A. van Santen and J.W. Niemantsverdriet Surface Sci. 369 (1996) 23

NH3 on Rhodium, TPD and Calculations

NH3 on coverage Eads (kJ/mol)TPD Calculated

Rh(111) 0 81.53.00.11 820.25 70

Rh(100) 0 90.04.00.11 910.25 81

F. Frechard, R.A. van Santen, A. Siokou, J.W. Niemantsverdriet and J. HafnerJ. Chem. Phys., 111 (1999) 8124

Lateral Interactions cannot explain the large shift in TPD !

Better explanation: mobile adsorption state, which becomes hindered at higher coverage

Dissociation:

The CO molecule dissociates in the transition state:

optimal overlap between d- and 2*-orbitals

De Koster and Van Santen

Dissociation of Adsorbed Molecules

O2 Ag(110) 7.8 kcal/mol 1.7 109 s-1

Ag(111) 8.3 1.7 107

O2 Pt(111) 2.5 9.0 1011

N2 Fe(111) 4.3 7.0 107

C2H6 Pt(111) 16.4 8.0 109

C2H2 Pt(111) 13.2 3.0 1012

CH4 Rh film 11 2. 1010

from C T Campbell, Y K Sun and W H Weinberg, Chem. Phys. Lett. 179 (1991) 53

Dissociation proceeds through tight transition stateswith prefactors smaller than for desorption

Application to

Surface Reactions:

CO Oxidation

LH or ER?

CO oxidation (surface-mediated)

+

adsorption reaction desorption

CO

O2

catalyst

CO2

E

adsorption reaction desorption

reaction coordinate

Eley - Rideal Mechanismdirect reaction between gas phase

and adsorbed species

How likely is an E-R event ???

Eley-Rideal orLangmuir-Hinshelwood

CO + Oads = CO2

CO + Oads

CO2COads + Oads CO2,ads

CO + 1/2 O2

E

reaction coordinate

- 42.5

- 74.1

26.8

- 73.3- 67.9

0

on Rhodium (111)

kcal/mol

-6

+

in the most favorable case for ER (Eact = 0): kER / kLH = 7 x 10W H Weinberg, in Dynamics of Gas-Surface Interactions, (C.T. Rettner and M.N.R. Ashfold, eds.) Royal Society of Chemistry, Cambridge,1991

ammonia

synthesi

s

Langmu

ir

Hinshelw

oodCom

putation

al

chemistry

Berzeliu

s

Equilibr

ium

hermody

namics

1800 1900 2000

TST

Know

ledge

Fundamental & Applied CatalysisHow much do we know?

IR

Surface

Science

T

Schuit Institute of Catalysis

TPD-TPSIMS-HREELSMarco Hopstaken (now Philips)Martijn van Hardeveld (now Shell)Herman Borg (now Philips)Wouter van Gennip (now Philips)Davy NieskensSander van Bavel

Acknowledgements

Collaborations

TU/e:Prof Rutger van SantenProf Peter HilbersDr Johan Lukkien

Univ TarragonaProf Josep Ricart

DFT CalculationsDr Daniel CurullaPaco Ample (Univ Tarragona)Tracy Bromfield (Sasol)

FundingNWO, NCF, Spanish Ministerio de EduacionCatalan GovernmentEindhoven University of Technology

Concepts of Modern Catalysis and Kinetics I. Chorkendorff & J.W. NiemantsverdrietCopyright 2003 WILEY-VCH Verlag GmbH & Co. KGaA, WeinheimISBN: 3-527-30574-2Price: 69 Euro

Langmuir - Hinshelwood KineticsPartition Function:Partition Function:Partition Function:All MoleculesPartition Function:CO oxidation (surface-mediated)