Chemistry Reference
In-Depth Information
therefore, analysis of the laboratory data is usually performed by forward
convoluting tentative CM distributions over the experimental conditions.
In other words the CM angular and velocity distributions are assumed, ave-
raged and transformed to the LAB frame for comparison with the experi-
mental distributions and the procedure is repeated until a satisfactory fit of
the experimental distributions is obtained. The final outcome of a reactive
scattering experiment is the generation of a velocity flux contour map of the
reaction products, i.e., the plot of intensity as a function of angle and
velocity in the CM system, I
CM
(
, u) is called differential cross
section and is commonly factorized into the product of the velocity (or trans-
lational energy) distribution, P(u) (or P(E
0
T
)), and the angular distribu-
tion, T(
, u). The I
CM
(
).
The measurable quantities by this technique contain basic information.
The main advantage with respect to common flow reactors coupled with a
mass spectrometer is the possibility to measure product angular and velo-
city distributions, which allows one to directly derive the amount of the
total energy available to the products and, therefore, the energetics of the
reaction. This is crucial when more isomers with the same gross formula,
but different enthalpy of formation, can be produced, as exemplified in
Figure 14.3
for an ideal experiment relative to a reaction involving CN radi-
cals and a generic hydrocarbon RH. If two product isomers with the same
gross formula RCN are formed and if the energetics of the two channels is
significantly different, the two product isomers will be scattered within
different angular ranges. In the example of Figure 14.3 the enthalpy of
reaction for the channels leading to the two isomers (RCN)
0
and (RCN)
00
is
very different and so is the total energy available to product translational
motion. Recall that, because of the energy conservation rule, the total energy,
E
TOT
, is given by the sum of the initial collision energy, E
c
, and the heat of
reaction, E
TOT
¼
H
0
; in CMB experiments the internal energy of the
reactants is negligible because of the cooling during the supersonic expan-
sion. Since the energy available to the two isomers is very different, the maxi-
mum speed in the centre-of-mass frame that they can reach is different and
the limiting circles in the Newton diagram will define laboratory angular
ranges of different extent. When the difference is pronounced, the distinct
contributions to the observed signal will be easily separated during the data
analysis; when the difference is not sharp, accurate measurements of
product velocity distributions as a function of scattering angle usually allow
us to discriminate amongst different contributions.
Apart from what we learn from the energy release, the shape of the CM
angular distribution, T(
E
c
), can give us some information on the reactive
event as well [57,59]. Several shapes of the flux distributions are possible
corresponding to two different kinds of mechanism.
First, the T(
) and corresponding flux contour map I
CM
(
, u) are
90
; in this case the flux intensity is the same
symmetric with respect
¼
and 180
for each
pair. The ''forward-backward'' symmetric shape is
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