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Cluster Size Dependent Kinetics: Analysis of Different Reaction

Mechanisms

Dmitry Yu. Murzin

1,2

Received: 7 June 2015 / Accepted: 3 August 2015 / Published online: 28 August 2015

Springer Science+Business Media New York 2015

Abstract

Quantitative description for turnover frequency

dependence on the metal cluster size is discussed for

competitive Langmuir–Hinshelwood mechanism showing

that the apparent reaction orders depend on the cluster size.

Position of the maximum rate of the turnover frequency for

a two-step sequence is a function on temperature and only

in a special case, maximum of the turnover frequency is

temperature independent on reaction temperature. For the

same reaction mechanism the impact of internal diffusion

limitations on structure sensitivity is discussed.

Graphical Abstract

0

2

4

6

0

1

2

3

2 /

/

2

3

)

)

(1(

3

d

B

t

B

A

t

A

d

B

t

B A

t

A

t

ePK PK

ePKPKk v

χ

χ

α

+

+

=

TOF, s

-1

radius, nm

Keywords

Structure sensitivity Kinetic analysis

Temperature dependence Optimum cluster size

Langmuir–Hinshelwood kinetics Eley–Rideal

mechanism Two step sequence

1 Introduction

Dependence of the catalytic activity on the size of clusters

attracted a very large attention in the recent decade,

because such activity in transition metal catalysis was

shown to strongly depend on the metal size and shape

[ 1

10

]. Such dependence expressed through turnover fre-

quency (TOF) can not only increase or decrease with

cluster size, but also pass through maxima. Several

attempts have appeared in the literature to quantify such

dependence.

One way of implementing the cluster size dependence in

reaction kinetics is to view reaction constants as size

independent. Then each type of sites (terraces and edges)

contributes to the overall rate according to the ratio

between terraces, corners and edges. Such analysis, when

any reaction sequence can be treated as a sum of contri-

butions from all these sites (terraces, corners and edges),

was considered in

[ 9

] leading to the dependence of TOF on

the cluster size for a cubo-octahedron cluster

&

Dmitry Yu. Murzin

dmurzin@abo.fi

1

A˚ bo Akademi University, Turku, Finland

2

St. Petersburg State Institute of Technology, St. Petersburg,

Russia

123

Catal Lett (2015) 145:1948–1954

DOI 10.1007/s10562-015-1604-6