Aron Kuppermann Arthur Amos Noyes Laboratory of Chemical Physics, * California Institute of ...

41 Pages·2013·1.47 MB·English

Aron Kuppermann
*
Arthur Amos Noyes Laboratory of Chemical Physics,
California Institute of Technology, Pasadena, CA 911 09
*
*
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ABSTRACT
The diffusion model of the radiation chemistry of aqueous solutions
is surveyed. Its ability to explain past experimental results and make
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over a time scale ranging from minutes down to picoseconds,
is assessed. The pertinence of this model to radiation biology is
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'discussed. ,
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NOTICE
This report was prepared as an account of work
qonwred by the United States Government. Nelther
the United States nor the United States Atomic Energy
Commission, nor any of their employees, nor any of
their contractors, subcontractors, or their employees,
makes any warranty, express or implied, or awumes any
legal liability or responsibility for the oeaueney, eom
pleteness or usefulness of any information, apparatus,
product or process disclosed, or represents that its use
would not infringe priuptely.owned rights.
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Work supported in part by the U. S. Atomic Energy Commission
Report Code CALT-767P4-127
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*
Contribution No. 4833
DISCLAIMER
This report was prepared as an account of work sponsored by an
agency of the United States Government. Neither the United States
Government nor any agency Thereof, nor any of their employees,
makes any warranty, express or implied, or assumes any legal
liability or responsibility for the accuracy, completeness, or
usefulness of any information, apparatus, product, or process
disclosed, or represents that its use would not infringe privately
owned rights. Reference herein to any specific commercial product,
process, or service by trade name, trademark, manufacturer, or
otherwise does not necessarily constitute or imply its endorsement,
recommendation, or favoring by the United States Government or any
agency thereof. The views and opinions of authors expressed herein
do not necessarily state or reflect those of the United States
Government or any agency thereof.
DISCLAIMER
Portions of this document may be illegible in
electronic image products. Images are produced
from the best available original document.
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1. HISTORICAL INTRODUCTION
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1
The first theory of diffusion kinetics was developed by Jaffe to -
explain the ionization currents obtained in gases and liquids bombarded by
., . . . .. .
. .
ionizing radiation, with and without.the presence of a collecting electric
L field. He introduced the idea of a cylindrical ionization track which was taken
.
2
over .and improved by Lea and applied to the radiation chemistry of aqueous
3 . 4
solutions Subsequently, Samuel and Magee introduced the idea of isolated
spherical spurs, rather than cylindrical tracks, to explain the chemical
effects of MeV y-rays. or electrons on aqueous solutions. These spurs were
. .
assumed to be made up of equal numbers of H and OH radicals within concentric
spherical regions of equal diameters according to ~amuel.andM agee, whereas
5 2
according to Platzman , and following the ideas of Lea , the characteristic
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radius of the H atom initial distribution should be much greater than that : r
. . .
n
of the OH. The reason for this difference between these two pictures was
that Samuel and Magee.assurned that after an ionization event prcduced a' low
.' energy electron (having an energy of 100 eV or less), the H~O+io n was able'
,
to rapidly recapture the electron, 'forming in the process 'an excited water
,
molecule which would dissociate within a picosecond into H + OH. On the
. .
other hand, Lea and Platzman assumed that the ionized e!ectron escaped .
thc parent H,O+ ion andbecame thermalized at a distance of 100 A or more
away from it, reacting then with wate; toform OH- + H. With the discovery
of the solvated electron6-*, it became widely accepted that this e- was the
aq
. . dominant reducing species in the spur, rather'than H atoms. In order to
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< ' I %' . . . ..C. ,. -.. . ..' ,. ~ .
.. ,. . .. .
C . C
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obtain agreement between theory and experiment, the diffusion model .. .
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requires, as described below, that the radius of the e- initial distribution
aq
be about three times larger than that of the OH, which corresponds to a
broader distribution of the reducing species than that assumed by Samuel-Magee,
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but not as broad as that of Lea-Platzman. In any event, it seems clear that
within the framework of the diffusion-kinetic.'model, the ionized electron does
H,o+.
escape recombination with the parent These ideas were extensively
discussed at a meeting on Physical and Chemical Aspects of Basic Mechanisms
in Radiobiology, similar in many aspects to the present one and held about
5 . /
twenty years ago Since then, the diffusion-kinetic equations resulting from
4
the spherical spur model for the effects of y-rays and high-energy electrons
. .
and for the cylindrical track m0de1~-f~or radiation& of high linear energy
transfer (4. E. T. ) were solved by the prescribed diffusion approximation4 , 9-11
and by accurate numerical techniques 12-14f or a variety of simple and of quite
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elaborate 9b9 14' reaction mechanisms.. -The cenhal objective of this paper
is to describe and assess the validity of the results of such calculations in the
fight of new and important experimental information obtained during the last
three years or so using the tebhniq~lo~f! soh-nanosecond pulse radiolysis
15.
invented by J. W. Hunt and his collaborators
2. DESCRIPTION OF MODEL
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. .
We have given an extensive description of.t he diffusion kinetics
model and its physical foundation elsewhere14b and will review it here only
very briefly. . .: I
@ . We assume that by about 1 to 10 picoseconds. after the passage of the
ionizing radiation through a solution, certain chemical species have been
. . .
.
.formed having certain inhomogeneous spacial distributions. The nature of
these species and the details of these initial distributions are determined by
the physical processes occurring in the time interval from about 10-16sec
-12
to about 10 sec after passage of the high-energy radiation through the region
of the medium being consideged. These. processes involve ionization and
excitation of the medium, dissociation of excited states, thermalization of
electrons and hot atoms or radicals and solvation of charged species. Our
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present knowledge about such processes i n liquid water is not adequate for
-12
an ab-initio prediction of the state of the system 10 sec after passage of
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radiation,. nor do adequate experimental tools presently exist for determining
. .
the nature and spacial distribution. of the chemical species present at that
time. For this reason, educated guesses a're made about these characteristics,
and the reasonability of these guesses are assessed by the extent of agreement
between the predictionsof the model and experiments conducted at a time
scale ranging from 10 picoseconds to minutes or. hours after passage of the
radiation. The presently assumed chemical species and their initial distribu-
tions are ciiscussed in the next section. It should be stressed, however, that - .
these are susceptible to change, since they are not an inherent part of the.
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diffusion model. What is inherent 9s that some initial set of species and c
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inhom.ogeneous distributions do exist, and an important goal of the model is
to obtain information about them by comparison with experiment at a later
time.
< The nature of the initial spacial inhomogeneity of the chemical species
.
is that their concentrations are high in the vicinity ofthe sites of substantial
energy deposition (spurs or. tracks). These species then pro'ceed to react
. .
with each other, or,to diffuse away 'from each other and react with radical
scavengers initially present. This strong spacial inhomogeneity and the
'consequent competition between the reaction and recombination processes just
mentioned constitute the real essence of the diffusion model. It assumes,
in addition, that the macroscopic laws of diffusion add reaction are valid when
14d
expressed in terms of ensemble averages of large numbers of spurs or tracks
,
Let us now exprkss the corresponding diffusion-kinetic equations qu.antitatively.
.
.
We will use the symbol ci (r t) to desigkte the probability density of finding
?.,
a particle of type i (one of the primary species or any other reactive substance
..
. .
in the solution) at time, t at a position r. The space and time dependence of
n
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this probability density which for simplicity's sake we will call: concentration
-
from here on satisfies the set of partial differential equations
v2
Here, Di is the diffusion coefficient of species of type i,, is the Laplacian
. ..-. .
:.: operator, and n is the number of different types of reactive species. The
reaction mechanism used for these diffusion equations has the general form
c L
where the Ai represent the formulas of the substances involved in the
reaction. They are reagents for positive aji and reaction products for
negative a.. v.. is the order of reaction j with respect to' substance Ai. . ..
11' 11
. .
The kj in Eq. (1) are the rate constants of reactions [I]. This generalized
.
0
.
.
manner of.representing a reaction mechanism is introduced for mathematical
. .
convenience.
The physical meaning of Eq. (1) is extremely simple. It states that
. .
the local change of concentration of species i in a small volume element of
the ,system is equal to the net amount of that species which diffuses into
that element (i. e., the difference between the amounts diffusing.in and out)
I .
divided its volume (which results in the Di ? ci term) plus the local rate of
formation of that species due to chemical reactions involving other species
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(as represented by the positive a. termi) minus its local rate of disappear-
J i
ance, due to reaction with other species (as represented by the negative
. .
a.. terms).
I1
Given the initial radical distributions, ci (ar ' o), diffusion coefficients,
.
,
reziction mechanism [I] and rate constants, it is possible to solve the system
. .
of E~;. (1) by numerical techniques1 4d using high-speed digital computers.
.
Once the ci (r t) are thus determined for every i, r and t it is possible to
A' n
calculate, by simple integrations over space and time, the total' amounts of
each reactiori product. These are related in a simple manner to the G
values (i. e., the number of molecules or radicals formed per 100 eV energy
deposition) of the several primary species for the spur or track described
by Eq. ( 1 ). For comparison with experiment, one must calculate averages
.. . . -
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. .
.
. . C ' t . .. 8 . !'. ' , . . ' ... . .
. -.
<.' '
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of these quantities overthe spectrum of energy degradation which character-
izes the radiation being considere". The present know1edge.about the details
. .
of such degradation spectra is somewhat limited, and relatively crude ones
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9b, llb, 14c. . .
have been employed
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3. INITIAL DISTRIBUTIONS
c
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As pointed out in the previous sectioo, due to the incomplete state
of knowledge of the aqueous system at about 1 to 10 picoseconds after the
.
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passage of the high-energy radiation, we make guesses about the nature and
' initial distributions of the chemically reactive species present at that time.
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The current view is that these species are OH, e- and.H ,O+
.. . . ' aq aq' are . .
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assumed to be formed as follows. The high-energy radiation, either directly
or indirectly (via secondary electrons), ionizes water molecules. ,E=
..-.
.. . 8 n
I. The H20+u ndergoes a rapid proton transfer reaction with a neighboring
rate molecule, according to
.. . .. .
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. . . . . . 5,3:,;.-I . ...
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and hecomes solvated into H,O+ Tlie electrons ejected in the ionization
acl'
process [2] would, in general, have, low energy, and after travelling a,
'
fewtens of angstroms would become thermalized and solvated into eaq.
..
kcording to this picture, the H,O+ and OH initial distributions have
. . . aq
A
essentially the same radius, of the order of magnitude of 10 (dep6nding
. .' . .
on how many ionizing events [ 21 occur in close spacial vicinity to oneanother),
whereas the-e - are initially more spread out. The processes just described
. . aq '. ,
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. . . are the major ones. In addition, some minor ones may take place, such as
0
. G the dissociation of excited or superexcited water molecules:
. . c
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.
, H,O ---H H,O . . [ 41.
. . The geometrical distribution of these primary species depends on
.
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the nature of the ionizing radiation being used. For example, the interaction
of 60 Co y-rays with water produces almost exclusively Compton recoil
. ..
. . electrons which further ionize moleculep producing secondary electrons, , <
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which can produce tertiary ones, etc. The LET of the high-energy electrons
is low and, .within the framework of the diffusion.mode1, produces in general
. . . . .
local depositions of energy typically of the order of magnitude of 100 eV. These
generate spherically symmetrical spurs which are sufficiently distant from
one-another so as not to interact. However, a certain fraction of the electrons
have low energy and produce spurs which do overlap, and:if there are
sufficient numbers of them they form cylindrical tracks. Furthermore, as a
high-energy electron slows down, it also produces spurs which overlap,
.. Therefore, one must consider the whole distribution of interspur distances
- -
corresponding to this spectrum of energy degradation before a meaningful .
. .
comparison with experiment can be made. However, this distribution is