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Towards the positronium and radiolytic hydrogen
formation mechanism in saturated hydrocarbons
V.M. Byakov and S.V. Stepanov
A fast positron in a condensed molecular medium initiates numerous chemical
transformations. These are similar to chemical processes in tracks of electrons
with the same initial energy. Therefore, joint analysis of experimental data of
positron spectroscopy and radiation chemistry provides better insight into
intratrack reactions which duration is comparable with the positron lifetime.
That is why we discuss together the yields of radiolytic hydrogen and Ps in
liquid hydrocarbons.
Our discussion will be based on our unified model describing
formation of Ps in molecular condensed matter and that of
radiolytic hydrogen in water and aqueous solution. The model
consists in the following intratrack reactions:
e+ + e- => Ps
(H2O, H2O)+ + e- => (H2O, H2O)* => H2 + 2OH
According to this model it is seen that formation process of
radiolytic hydrogen is very similar to that of Ps formation.
1) An approximate
equality between
relative formation
probabilities of Ps and
radiolytic H2 in aqueous
solutions
1
GH2(cS)/GH2(cS=0)
There are several
effects which support
the suggested
mechanism:
0.8
0.6
0.4
IO3Cu2+
Cd22+
Cr2O72-
H2O2
NO3-
0.2
PPs(cS)/PPs(cS=0)
0
0
0.2
0.4
0.6
0.8
1
2) Identical isotopic effects replacement on Ps and H2 yields
3) Approximate equality of Ps
and H2 yields at different T
30 I3 , %
1.5
1.4
relative yields
H 2O
25
D 2O
20
0.4
GH 2
0.45
0.5
H2
1.3
1.2
Ps
1.1
Ps
1.0
0.9
0
50
100 150 200 250
T, oC
Experimental data of T.Hirade (Ps: +);
J.-Ch. Abbe and G.Duplatre (Ps: Δ);
Y. Katsumura (H2: ○, □)
We will try to explain this
anticorrelation effect basing
on the above formulated
concept of Ps and H2
formation.
H2 yield, molec/100 eV
6
c-alkanes
5.5
n-alkanes
5
4.5
6
4
8
10
12
number of C atoms in the molecule
40
ortho-Ps yield, %
In hydrocarbons Ps and H2
yields behave quite in another
way.
The hydrogen yields in calkanes (●) exceed the yields
in normal alcanes (■). On the
contrary, Ps yields are below
than in normal alkanes.
Therefore, Ps and H2 yield
change oppositely, when the
molecular structure is
changed from the normal to
the cyclic form. Thus, the
proportionality between Ps
and H2 yields is violated for
saturated hydrocarbons.
n-alkanes
35
30
c-alkanes
25
20
4
6
8
10
12
Scheme of radiolytic hydrogen formation in cyclohexane
From the scheme it is seen that hydrogen formation is initiated by a decay of
excited molecules, C6H12*. They produce H2 molecules directly or through
intermediate formation of H atoms. The H2 yield is equal to the yield of excited
molecules: G(H2) = G(exc). Explanation of the anticorrelation effect is based on
a remarkable distinction of primary holes in cyclic hydrocarbons: their unusually
high mobility, one or two orders of magnitude higher than in normal
hydrocarbons. Because of that intratrack hole-electron recombination in cyclic
hydrocarbons is much more rapid than in normal ones, the hydrogen yield is
greater, the Ps yield is reduced. Note, that the formation of excited molecules
occurs via electron-hole recombination. Its rate constant is controlled by a
diffusion of reactants. In the e+ blob the electron-hole recombination competes
with e+/e- recombination. Therefore, Ps formation probability depends on the
ratio of their rate constants, k+e/ kpe
Ps and H2 yields given by quantitative model of intratrack
processes based on the above reaction scheme
For n-alkanes (k+e/ kpe <<1) both yields are constant in agreement
with experiment. Therefore,
As a result in n-alkane PPs is higher than in cyclic whereas Gexc is
reduced.
Conclusion
The unified (re)combination model for the Ps and
radiolytic H2 formation explains not only direct
correlations between Ps and H2 yields in aqueous
solutions, but also their anticorrelations in liquid alkanes.
The obtained results give an independent support
of the idea on unusually high mobility of primary holes in
cyclic hydrocarbons. They demonstrate that the role of
intrablob electron-hole recombination may be important
in the Ps formation processes. The anticorrelation effect
is not a peculiarity of liquid alkanes only. It becomes
apparent also in aqueous solutions.
Alkalization of water increases the Ps yield, but
reduces the yield of radiolytic hydrogen.
GH2(cS)/GH2(cS=0)
1
0.8
0.6
0.4
IO3-
OH-
Cu2+
Cd22+
Cr2O72-
H2O2
NO3-
0.2
PPs(cS)/PPs(cS=0)
0
0
0.2
0.4
0.6
0.8
1
The approximate equality between relative formation probabilities
of Ps and radiolytic H2 is violated in alkaline aqueous solutions.
Alkalization of water increases the Ps yield, but reduces the yield
of radiolytic hydrogen
Similar linear dependencies of reciprocal Ps and hydrogen yields
on various electron acceptor concentration
NO3-
NO3-
5
4
4
3
H 2 O2
Cd2+
2
1
2+
Zn , Tl
+
HClO4
PPs(0) / PPs(cS)
GH2(0) / GH2(cS)
5
3
H 2 O2
2
Cd2+
HClO4
1
Zn2+, Tl+
0
0
0
0.2
0.4
0.6
cS , M
0.8
1
0
0.2
0.4
0.6
cS , M
0.8
1
The more a given solute S suppresses H2 yield, the stronger it inhibits the
formation of Ps.
Similar variations of Mu, Ps and 57Fe2+ yields with
temperature and aggregate state
1.5
relative yields
Aggregate state similarly
influences on the
formation yields of Mu
and Ps. In frozen
amorphous aqueous
solutions the yields are
practically the same as in
liquid ones. In crystalline
systems the yields are
increased against their
values in liquid solutions
due to much longer
duration of the lifetime of
presolvated electrons.
Ps
ice
Mu
1
H2
Ps
Fe2+
0.5
10 M
H2SO4
100
200
water
300
400
temperature, Ê
500
Ps and H2 in saturated hydrocarbons
The above experimental corroborations give weighty
arguments in favour of the suggested mechanism.
However, they all refer to pure water or to aqueous
solutions only.
Quite in another way Ps and radiolytic H2 behave in
saturated hydrocarbons. The proportionality between
Ps and H2 yields is violated for liquid alkanes. Instead of
direct correlation between the yields which takes place
in water and aqueous solutions anticorrelation between
Ps and H2 yields becomes apparent.
Scheme of the structure of a fast positron track in aqueous milieu
-- - - - - -++ +
+ +
+ +
+
+
+
+
asp
-
-
-
-
-
+
+
+
+
+
+
e+ isolated ion-electron spurs
1 MeV  3 keV
Reactions in spurs and blobs:
(H2O,H2
O)+ + e- H
2
+ 2 OH
e- + S S(H2O,H2O)+ + S Products
e+ blob
+
+
+
-
track

--
-electron
Both (re)combination reactions
compete against each other in the
terminal positron blob. In addition,
the reaction of H2 formation
occurs also in all track elements of
any ionizing particle.
+
 - e- blob
- - -- -- - - -- - - - - - - - -
+
+ +
++ +
+ + +
+ +
cylindrical +
column
3 keV  1 keV
+ +
++ +
+
+
+ + ++ +
+ +
+
Ps
e+
abl  40 Å
Ps formation in the terminal blob
e+ + e-  Ps