5.1 The Reactivity with Hydrogen
73
Fig. 5.2 Dependence of D 2 chemisorption reactivity R x on cluster size, for Nb x (a), Nb x
− (b), and
Nb x
+ (c), respectively. Two data points are included for Nb 9 , Nb 12 , and Nb l2
+ in order to reflect the
rapid and slow components of cluster depletion. The three curves are plotted on the same vertical
scale with typical uncertainties ±20%. Reproduced with permission from Ref. [52]. Copyright
1988 American Institute of Physics
demonstrated that clusters with closed electronic shells are less reactive to hydrogen
than those with unfilled shells, indicating similar pattern as the metal cluster reactivity with other diatomic gas molecules [1]. Considering the H 2 concentration as
a constant throughout the reaction region, the reactivity can be quantified within a
simple pseudo-first-order kinetic relationship,
−ln( f r ) = k[H 2 ]τ
(5.1)
where f r is the fraction of bare cluster remaining, k refers to the rate constant for the
addition of the first H 2 to the cluster, [H 2 ] is the concentration of the hydrogen, and τ
is the reaction time approximated as “reaction channel length/flow velocity”. Based
on Eq. (5.1), the constant k can be determined by measuring the mass spectra for a
series of H 2 flows and plotting out the logarithm values of the remaining bare cluster
signal versus reagent flow; and then the rate constants can be calculated.
73
Fig. 5.2 Dependence of D 2 chemisorption reactivity R x on cluster size, for Nb x (a), Nb x
− (b), and
Nb x
+ (c), respectively. Two data points are included for Nb 9 , Nb 12 , and Nb l2
+ in order to reflect the
rapid and slow components of cluster depletion. The three curves are plotted on the same vertical
scale with typical uncertainties ±20%. Reproduced with permission from Ref. [52]. Copyright
1988 American Institute of Physics
demonstrated that clusters with closed electronic shells are less reactive to hydrogen
than those with unfilled shells, indicating similar pattern as the metal cluster reactivity with other diatomic gas molecules [1]. Considering the H 2 concentration as
a constant throughout the reaction region, the reactivity can be quantified within a
simple pseudo-first-order kinetic relationship,
−ln( f r ) = k[H 2 ]τ
(5.1)
where f r is the fraction of bare cluster remaining, k refers to the rate constant for the
addition of the first H 2 to the cluster, [H 2 ] is the concentration of the hydrogen, and τ
is the reaction time approximated as “reaction channel length/flow velocity”. Based
on Eq. (5.1), the constant k can be determined by measuring the mass spectra for a
series of H 2 flows and plotting out the logarithm values of the remaining bare cluster
signal versus reagent flow; and then the rate constants can be calculated.