The Optical Approximation, Primary Radiation Chemical Yields, and

36 The Optical Approximation, Primary Radiation Chemical Yields, and Structure of the Track of an Ionizing Particle

Downloaded by UNIV LAVAL on July 11, 2016 | http://pubs.acs.org Publication Date: January 1, 1968 | doi: 10.1021/ba-1968-0081.ch036

IVAN SANTAR and JAROSLAV BEDNÁŘ The Nuclear Research Institute, Czechoslovak Academy of Sciences, Řež, Czechoslovakia

A survey is given of the theory of the physical stage of radiolysis. Using the optical approximation to cross sections for the interaction between fast electrons and molecules, expressions have been derived for the yield g ° of primary optical activations, and for the total absorbed energy Q It is shown that the total yield g of primary activations is conveniently discussed as a sum g ° + g , where the first term includes the action of fast electrons, while g describes the action of slow electrons (kinetic energy less than about 100 e.v.) on molecules of the medium. This approach is com pared withPlatzman'sconsiderations on primary yields and the differences are pointed out. Finally, theoretical results of the present approach are applied to the analysis of the initial structure of the track of a fast electron, consisting of spurs, blobs, and short tracks. tot.

8

8

>Tphere is no doubt that of all phenomena connected with the interaction of high-energy radiation with matter, the radiation-chemical response of matter is the most complicated one. Between the primary acts by which the radiative energy is transferred to the medium and the resulting chemical changes there lies a complicated interplay of subse quent physicoehemieal and chemical processes. However, the whole present experience of radiation chemistry, brought together in the ubiqui tous term "radiation-chemical yield," suggests a proportionality between the measured effects and the amount of initially absorbed energy of radiation. This fact should stimulate the efforts towards the theoretical description of radiolytic processes. A

523 Hart; Radiation Chemistry Advances in Chemistry; American Chemical Society: Washington, DC, 1968.

524

RADIATION CHEMISTRY

1

T h e a b s o r p t i o n of energy of r a d i a t i o n passing t h r o u g h a m e d i u m c a n b e t h e o r e t i c a l l y i n v e s t i g a t e d at three levels of i n c r e a s i n g c o m p l e x i t y : ( 1 ) Q u i t e p r a g m a t i c a l l y as a process o c c u r r i n g c o n t i n u o u s l y i n t h e w h o l e i r r a d i a t e d v o l u m e . C o n s e q u e n t l y , w e c h a r a c t e r i z e this process b y a single q u a n t i t y c a l l e d the dose, w h i c h gives t h e a m o u n t of e n e r g y a b s o r b e d i n a v o l u m e or mass u n i t . T h i s w a s t h e p r a g m a t i c basis f o r t h e i n t r o d u c t i o n of t h e e m p i r i c a l n o t i o n of t h e "100 e . v . - y i e l d . " ( 2 ) A s a process o c c u r r i n g c o n t i n u o u s l y a l o n g the paths of i n d i v i d u a l i o n i z i n g particles. T h e n t h e d e c i s i v e q u a n t i t y appears t o b e t h e L E T g i v i n g t h e m e a n e n e r g y loss of t h e p a r t i c l e p e r u n i t p a t h - l e n g t h .


( 3 ) A s a n ensemble of i n d i v i d u a l e l e m e n t a r y acts of energy transfer, as i t corresponds to the p h y s i c a l r e a l i t y of this p h e n o m e n o n . E x c e p t f o r t h e w o r k of P l a t z m a n ( 5 , 12, 13) a n d M a g e e (6, 7), t h e t h e o r e t i c a l considerations i n r a d i a t i o n c h e m i s t r y h a v e b e e n l i m i t e d to the first t w o items o n l y . R e c e n t l y , t h e most general p r o c e d u r e ( i t e m 3 ) has b e e n a p p l i e d to b o t h t h e t h e o r y of p r i m a r y r a d i a t i o n c h e m i c a l y i e l d ( J , 14, 16,17,19)

a n d to the t h e o r y of i n i t i a l structure of the t r a c k of a n

i o n i z i n g p a r t i c l e (10,19).

T h e p u r p o s e of this p a p e r is to c o m p a r e these

t w o aspects of a b s o r p t i o n of i o n i z i n g r a d i a t i o n . Primary

Radiation

Chemical

Yield

T h e most characteristic t y p e of p r i m a r y activations are t h e e l e c t r o n i c transitions of m o l e c u l e s w h i c h are m u c h faster t h a n other response of the i r r a d i a t e d m e d i u m .

T h i s enables o n e to c o n s i d e r separately t h e

p h y s i c a l stage of r a d i o l y s i s , at the e n d of w h i c h a c e r t a i n ensemble of e x c i t e d a n d i o n i z e d m o l e c u l e s is f o r m e d i n t h e m e d i u m . E a c h of t h e a c t i v a t e d m o l e c u l e s possesses a p a r t i c u l a r a m o u n t of energy f o r subsequent

processes.

available

T h e i n i t i a l d i s t r i b u t i o n a n d y i e l d s of i n d i

v i d u a l p r i m a r y activations

are dealt w i t h b y t h e t h e o r y o f p r i m a r y

r a d i a t i o n c h e m i c a l y i e l d ( P R C Y ) . W e h a v e s t u d i e d t h e a p p l i c a t i o n of this t h e o r y to t h e r a d i o l y s i s of gases i n d e t a i l d u r i n g t h e last years T h u s , i n t h e f o r m a l expression—see (5),

17, 18, 19, 20). G(X) =

$ g (X) n

n

n

(16,

for the yield

of a p a r t i c u l a r ( f i n a l or i n t e r m e d i a r y ) p r o d u c t X ,

w e are p r i m a r i l y interested i n the p r i m a r y g - v a l u e s f o r t h e i n d i v i d u a l n

types of p r i m a r y activations.

T h e p r o b a b i l i t i e s ; 100 e.v. excite a n d i o n i z e

m o l e c u l e s p r e d o m i n a n t l y i n o p t i c a l collisions i n d u c i n g the same t y p e of transitions of v a l e n c e electrons as does the a b s o r p t i o n of photons.

This

a b u n d a n t t y p e of p r i m a r y activations shows, therefore,

close

c o n n e c t i o n w i t h the o p t i c a l spectra of m o l e c u l e s .

a very

T h u s , f o u n d a t i o n s are

l a i d for the use of the so-called o p t i c a l a p p r o x i m a t i o n i n r a d i a t i o n c h e m istry, as suggested b y P l a t z m a n ( 1 3 ) .

M o r e e x p l i c i t l y , the t h e o r y

cross sections for o p t i c a l collisions leads i n first a p p r o x i m a t i o n to

of the

f o l l o w i n g f o r m u l a f o r the y i e l d of a p a r t i c u l a r electronic t r a n s i t i o n n : g = const X f /E n

Here E

n

n

(1)

n

is the energy of the t r a n s i t i o n a n d f

n

is the c o r r e s p o n d i n g o p t i c a l

oscillator strength, c h a r a c t e r i z i n g the relative c o n t r i b u t i o n of that t r a n s i t i o n to the o p t i c a l s p e c t r u m of the m o l e c u l e . I n a d d i t i o n , sufficiently energetic electrons i n d u c e , i n a s m a l l y i e l d , the o p t i c a l transitions of i n n e r electrons [g

K

b e i n g (1, 11)

of the o r d e r of

Hart; Radiation Chemistry Advances in Chemistry; American Chemical Society: Washington, DC, 1968.

526

RADIATION CHEMISTRY

T a b l e I.

1

S t r u c t u r e of

diluted PRCY


Theory Primary activation

isolated

Development of the activation

isolated

System

ionizing particle + molecule

Statistics

homogeneous (degradation spec trum + ensemble of isolated mole cules)

Space and time element The theory -operates i n stage -extensible to stages

physical ( P ) physicochemical ( P C ) chemical ( C )

0.01 f o r the K - e l e c t r o n s of the elements f r o m the s e c o n d p e r i o d ] . C h a r a c teristic result of these transitions is the A u g e r effect. Its i m p o r t a n c e as a specific m i n o r effect i n r a d i a t i o n c h e m i s t r y stems f r o m the d e e p d e s t r u c t i o n of t h e m o l e c u l e i n t o s m a l l fragments

(11).

F i n a l l y , fast electrons also u n d e r g o i n f r e q u e n t h a r d collisions w i t h m o l e c u l e s , i n w h i c h the latter are i o n i z e d a n d s e c o n d a r y electrons

with

a p p r e c i a b l e k i n e t i c energy of the o r d e r of h u n d r e d s of e.v. are ejected (δ-electrons). g* ^

T h e s e collisions thus c o n t r i b u t e (6,17)

b y a small amount

0.1 to the y i e l d of i o n i z a t i o n s . A d i s t i n c t specific role of t h e m is

a p p a r e n t o n l y i n r a d i o l y s i s of c o n d e n s e d m e d i a , w h e r e they

constitute

a p r o n o u n c e d s t r u c t u r a l track effect a n d m a y c o n t r i b u t e to c e r t a i n m i n o r processes (see

below).

N o c o r r e s p o n d i n g d e t a i l e d theory of the a c t i o n of s l o w exists.

electrons

T h e i r f r a c t i o n i n the d e g r a d a t i o n s p e c t r u m is nevertheless

so

s u b s t a n t i a l that their c o n t r i b u t i o n to t h e r a d i o l y s i s m u s t b e c o n s i d e r e d as v e r y i m p o r t a n t .

T h e reason is that t h e y are f o r m e d a b u n d a n t l y as

s e c o n d a r y electrons f r o m o p t i c a l i o n i z a t i o n s a n d c o n t r i b u t e c o n s i d e r a b l y


36.

SANTAR AND BEDNÂR

Track of an Ionizing

527

Particle

Radiation-Chemical Theories M

E

D

I

U

M dense

Magee

Fano

not existing yet

isolated

non-isolated

non-isolated non-isolated


non-isolated track of ionizing particle i n isolated molecules

ionizing particle + matrix of mole cules

track of ionizing particle i n matrix of molecules

i n track (individual parti cle + ensemble of isolated molecules)

homogeneous (degradation spec trum + plasma of molecular electrons)

i n track (degradation spec trum + plasma of molecular electrons + ensemble of i n teracting molecules)

+

+

+

Ρ (PC, C ) ?

PC,C - F U T U R E PROGRESS

Î

to the excitations a n d i o n i z a t i o n s of v a l e n c e electrons, the latter u s u a l l y b e i n g precursors of a major p a r t of the c h e m i c a l changes o b s e r v e d . T h e g e n e r a l m e t h o d for the c a l c u l a t i o n of y i e l d s is i n a p p l i c a b l e to s l o w electrons,

therefore

w i l l be r e p l a c e d b y a n a p p r o a c h c o m b i n i n g

the c o n v e n i e n t use of the o p t i c a l a p p r o x i m a t i o n f o r fast electrons

with

the p o s s i b i l i t y of a v o i d i n g a n y n e e d for d e t a i l e d k n o w l e d g e of the d i s t r i b u t i o n a n d the interactions of s l o w electrons.

I n v i e w of the f a c t that

the s m a l l y i e l d s of h a r d collisions a n d i n n e r - s h e l l i o n i z a t i o n s

represent

at most a f e w p e r cent of the t o t a l i o n i z a t i o n , a n d that, m o r e o v e r , the δand

A u g e r electrons p r o d u c e d are fast a n d lose most of t h e i r

energy

a g a i n i n o p t i c a l collisions, s e c o n d a r y electrons f r o m o p t i c a l i o n i z a t i o n s c a u s e d b y fast electrons m a y b e s a i d to p r a c t i c a l l y p r e d o m i n a t e i n the s l o w r e g i o n of the d e g r a d a t i o n s p e c t r u m . t h e o r y of P R C Y is (17,

18)

T h e essential p o i n t of

the

therefore a c o r r e s p o n d i n g s u b d i v i s i o n of the

d e g r a d a t i o n s p e c t r u m i n t o the fast a n d s l o w regions w h o s e c o n t r i b u t i o n s to the t o t a l y i e l d g of p r i m a r y activations are c o n s i d e r e d separately

(see

Figure 1 ) : g = go + gs


(2)

528

RADIATION CHEMISTRY

Table II. D F

A

E s

G

R

A

D

S u r v e y of Types A


g° —' 4 - 5

g

%

I

O

N

EL

O p t i c a l excitations of

0

T

ECTRONS Τ > 100 e.v.

r

Hard collisions

Process valence electrons (100 e.v. > E > E )

1

inner electrons ( E '—' IK)

g

K

50-60%

( E > 100 e.v.)

— 0.01-0.02

g * — 0.1-0.2

0.1-0.2%

1-2%

Qtot

T h e o p t i c a l y i e l d g ° c a u s e d b y the fast electrons c a n be

expressed

e x p l i c i t l y u s i n g the o p t i c a l a p p r o x i m a t i o n . I n the d i f f e r e n t i a l f o r m c o n c e r n i n g the energy t r a n s f e r r e d b e t w e e n Ε a n d Ε + (16,17,18,

dE

we then obtain

19):

(3)

-(E)dE=™±±*jLdE.

g

Z°eff is the effective n u m b e r of v a l e n c e electrons i n the m o l e c u l e , is the d i f f e r e n t i a l f o r m of the oscillator strength f

n

df/dE

f r o m E q u a t i o n 1.

E s s e n t i a l l y a l l s l o w electrons o r i g i n a t e i n i o n i z i n g o p t i c a l collisions a n d t h e i r k i n e t i c energy, t h o u g h d i s s i p a t e d i n a n u m b e r of

subsequent

interactions, is thus i n t e g r a l l y i n c l u d e d i n the energies Ε of these c o l lisions. T h i s is the reason w h y the t o t a l a b s o r b e d energy m a y b e a p p r o x i m a t e d b y the energy t r a n s f e r r e d i n o p t i c a l collisions of fast electrons. F r o m the o p t i c a l a p p r o x i m a t i o n ( E q u a t i o n 3 ) , it m a y t h e n be s h o w n

(17)

that the t o t a l a b s o r b e d energy vJtot is Qtot = const X Z °

e f {

,

(4)

f r o m w h e r e the i m p o r t a n c e of v a l e n c e electrons i n the p a r t i t i o n of energy


36.

SANTAR AND BEDNAR


529

Particle

of Primary Activations S

P

E

C

T

R

U

M SUBEXCITATION TT> E 0

Excitations optically


allowed

r

Other processes (vibrational excitations, electron cap ture, . . . )

forbidden

—3-4

gse varying between 0 and g

important perhaps for low-lying lowest triplets

25-35%

ELECTRONS 0

i o n

10-15%

small fraction?

i n m i x t u r e s c a n c l e a r l y b e seen.

It f u r t h e r f o l l o w s f o r the d i s t r i b u t i o n of

a b s o r b e d energy a m o n g the v a r i o u s o p t i c a l collisions that 1

t{

T h e o p t i c a l s p e c t r u m df/dE, t r u m (l/E)(df/dE)

ÉL

dQ dE

eff

(5)

dE '

a n d the d e r i v e d e x c i t a t i o n (14)

spec

are thus seen to b e the most i m p o r t a n t characteris

tics of a m o l e c u l e e v e n f r o m the p o i n t of v i e w of its r a d i o l y t i c properties. B y i n t e g r a t i n g the d i f f e r e n t i a l y i e l d s g i v e n b y E q u a t i o n 3 o v e r r e l e v a n t parts of m o l e c u l a r spectra w e c a n , of course, o b t a i n the p a r t i a l y i e l d s f o r p a r t i c u l a r types of transitions—e.g., the y i e l d s of a l l excitations, i o n i z a tions, etc., as w e l l as the t o t a l y i e l d of a l l p r i m a r y o p t i c a l transitions :

g

=

100M RZ°

2

where M : 2

J Ε dE spectrum

d t

(6)

-

A n a l o g o u s g e n e r a l p r o c e d u r e f o r the r e m a i n i n g p a r t g

s

( caused b y

collisions of s l o w electrons ) of the t o t a l y i e l d g is not a v a i l a b l e present.

at

W e m u s t therefore content ourselves w i t h a rather c r u d e esti

m a t i o n of g f r o m a n energy b a l a n c e u s i n g a p p r o p r i a t e average values of s


530

RADIATION CHEMISTRY

1

energies of s e c o n d a r y excitations a n d i o n i z a t i o n s b y s l o w electrons

to

gether w i t h a n estimate of shape of the e n e r g y s p e c t r u m of these electrons. Results of o u r c a l c u l a t i o n s (20) T a b l e III.

f o r several m o l e c u l e s are s h o w n i n

F o r calculations of o p t i c a l y i e l d s , d a t a o n o p t i c a l spectra of

molecules c a n be u s e d , a b o v e a l l . Besides that, the t o t a l o p t i c a l y i e l d g ° , w h i c h is a n i n t e g r a l over the entire s p e c t r u m , is c o n n e c t e d w i t h a n u m b e r of o p t i c a l p r o p e r t i e s of m o l e c u l e s .


m a t i v e f o r m u l a , d e r i v e d b y us (20),

T h u s , for e x a m p l e , a n a p p r o x i

c a n b e u s e d f o r its e s t i m a t i o n :

T h i s f o r m u l a connects the t o t a l o p t i c a l y i e l d w i t h the m o l a r p o l a r i z a t i o n Ρ ε ( i n ce. ) of the m o l e c u l e . Table III. Molecule

Survey of Calculated Yields for Certain Molecules

CH

H0

h

2

2 n

3

6.9-6.4 7.6-5.5 10.0-7.4 - g 4.8 3.7 4.5 4.7 3.3 2.1-1.6 3.9-1.8 5.5-2.9 3.5 3.3-2.8 4.3-2.2 6.2-3.6 1.0 1.2 0.7 1.7 1.6-1.1 3.3-1.2 5.0-2.4 2.8 3.6 3.3 3.8 4.5 3.1 2.7 3.3 4.0 0.6 0.5 0.5 0.5 0.9-0.8 1.3-0.7 1.6-1.2 0.8 0.52 0.39 0.35 0.2 3.3-2.0 4.8-1.7 10.6-5.3 5.6

g g° g*

ëian

y yO

r

The yield g °

i o n

o

(CH )

NH

2

He

Ne

9.2-6.5 —3.7 1.7 2.8 2.0 6.4-3.7 1.0 6.0-3.3 0.2 0.4 0.8 5.6-2.9 3.2 2.7 2.4 1.5 1.2 0.8 0.4 1.8-1.0 0.11 0.18 6.5-3.4 0.7

H

2

—3.4 2.8 0.6 1.0 1.0 0.1 2.4 1.8 0.6 0.4 0.53 0.2

—6.2 5.8 0.4 3.4 3.1 0.2 2.8 2.6

5 5

5

O.I5 1.2 1.19 2.0

c a n b e d e t e r m i n e d f r o m the spectra of p h o t o i o n i z a -

t i o n o r f r o m measurements of m o l e c u l a r i o n i z a t i o n cross sections for fast electrons.

F o r a n u m b e r of c o m p o u n d s the d a t a o n W, the m e a n energy

e x p e n d i t u r e p e r i o n p a i r , are f u r t h e r a v a i l a b l e . T h e y are r e l a t e d to the t o t a l y i e l d of i o n i z a t i o n b y a s i m p l e f o r m u l a g

i o n

=100/W.

(8)

T h e m a i n u n c e r t a i n t y i n the values of g i n T a b l e I I I is i n t r o d u c e d b y the less accurate e s t i m a t i o n of g

s

e x c

f r o m the energy b a l a n c e .

T h e m a i n c o n c l u s i o n w h i c h c a n b e d r a w n f r o m T a b l e I I I is that b o t h the o p t i c a l a n d the t o t a l y i e l d s , as w e l l as the ratios y = excitations

to i o n i z a t i o n s , are m a r k e d l y i n f l u e n c e d b y the

g / g i o n of exc

molecular


36.

SANTAR AND BEDNÂR


n a t u r e of the m e d i u m {20).

Particle

C h a r a c t e r i s t i c values v a r y f r o m 3 to 6 f o r

g ° , f r o m 6 u p to 10 f o r g, f r o m 0.2 to 0.6 for y°, u p to 1.5 f o r y.

531

a n d f r o m 0.5 p o s s i b l y

T h e o p t i c a l y i e l d g ° is d e t e r m i n e d essentially b y

the

o v e r a l l shape of the o p t i c a l s p e c t r u m of a m o l e c u l e , whereas the y i e l d g

s

a n d c o n s e q u e n t l y also the t o t a l p r i m a r y y i e l d g are p r e s u m a b l y m o r e

strongly d e p e n d e n t o n the i n d i v i d u a l m o l e c u l a r nature a n d o n details of the l o w - e n e r g e t i c p a r t of the o p t i c a l s p e c t r u m . b e t w e e n y°

T h e differences

found

a n d y illustrate the necessary c a u t i o n w h i c h s h o u l d b e t a k e n

w h e n a p p l y i n g the o p t i c a l a p p r o x i m a t i o n to p r e d i c t observable

overall

effects i n r a d i o l y s i s .


O n e i m p o r t a n t p o i n t remains to be r e s o l v e d , h o w e v e r . P l a t z m a n has r e c e n t l y (14)

s u m m a r i z e d his efforts for i n t r o d u c i n g the o p t i c a l a p p r o x i

m a t i o n i n t o the t h e o r y of r a d i a t i o n c h e m i s t r y a n d suggested a f o r m u l a f o r the o v e r a l l y i e l d goA of p r i m a r y activations :

oAE) E=™

g

( R / E

d

^{

T h i s f o r m u l a c o m b i n e s o p t i c a l d a t a s u c h as df/dE an i n t e g r a l over a l l i o n i z e d states analogous to M e m p i r i c a l r a d i a t i o n - c h e m i c a l d a t a o n W. the f o r m g =

const X

(9)

dE.

/ d E )

and M 2

2

i o n

, w h i c h is

i n E q u a t i o n 6, w i t h

E q u a t i o n 9 is essentially

of

g ° a n d thus represents a n alternative to, a n d

s h o u l d b e c o m p a r e d w i t h our v i e w , g = the o p t i c a l a p p r o x i m a t i o n expressed

g ° + g . It does, i n fact, extend s

b y E q u a t i o n 1 to the t o t a l i t y

of

p r i m a r y activations i n the p h y s i c a l stage a n d y i e l d s , i n p a r t i c u l a r , the approximative conclusion y =

y°.

W i t h o u t g o i n g i n t o details to b e discussed elsewhere W h i l e o u r a p p r o a c h tends to e m p h a s i z e secondary

as f o l l o w s :

the c o n t r i b u t i o n g

electrons to the p r i m a r y y i e l d s , P l a t z m a n ' s

we may

(20),

p o i n t out the m a i n difference b e t w e e n the t w o approaches

of

slow

treatment

puts

s

g e n e r a l l y m o r e emphasis o n the i n t e r n a l energy of the i o n i z e d species t h a n w e d o . C o n s e q u e n t l y , his absolute values of p r i m a r y y i e l d s are, i n general, l o w e r t h a n ours, a n d a significant p a r t of the o b s e r v e d d e c o m p o s i t i o n is i m p l i c i t l y expected to o c c u r i n s u b s e q u e n t p h y s i c o c h e m i c a l a n d c h e m i c a l stages of r a d i o l y s i s . I n contrast, o u r a p p r o a c h explains most of the o b s e r v e d d e c o m p o s i t i o n b y the p r i m a r y processes of the p h y s i c a l stage. A n y d e c i s i v e conclusions a b o u t the p r o b l e m i n the f u t u r e w i l l neces s a r i l y d e v o l v e u p o n a d e t a i l e d k n o w l e d g e of energy d i s t r i b u t i o n of i o n i z a t i o n processes a n d secondary electrons, a n d p o s s i b l y also u p o n a better understanding

of

the

physicochemical

and

chemical

processes

radiolysis.


of

532

RADIATION CHEMISTRY

Initial Structure

of the Track

of an Ionizing

1

Particle

I n c o n d e n s e d m e d i a the e l e m e n t a r y acts a c q u i r e m u c h m o r e c o m p l i c a t e d character

(see

Table I)

since the c o n c e p t

o f c o l l i s i o n of a n

e l e c t r o n w i t h a n i s o l a t e d m o l e c u l e loses its m e a n i n g . T h e i o n i z i n g p a r t i cles interact i n a dense m e d i u m m o r e o r less w i t h t h e field

electromagnetic

of a p l a s m a of m o l e c u l a r electrons n o t necessarily b e l o n g i n g t o a

single m o l e c u l e .

C o n s e q u e n t l y , the r e s u l t i n g a c t i v a t i o n m a y b e d e l o c a l -

i z e d at t h e v e r y b e g i n n i n g .

Fano's t h e o r y (2, 3, 4)

of

electromagnetic

interactions i n dense m e d i a suggests that the o p t i c a l s p e c t r u m c a n b e


a p p r e c i a b l y m o d i f i e d i n c o m p a r i s o n w i t h that of a n isolated m o l e c u l e . O u r k n o w l e d g e of the s p e c t r a l properties of c o n d e n s e d matter is v e r y p o o r at present,

b u t estimations

of P l a t z m a n (14)

i n d i c a t e that t h e

p i c t u r e d e v e l o p e d f o r the gaseous phase m a y serve as a first a p p r o x i m a t i o n e v e n f o r t h e c o n d e n s e d phase. I n v i e w of the possible d e r e a l i z a t i o n of t h e p r i m a r y activations the space element a l r e a d y enters t h e c o n s i d e r a tions o n the p r i m a r y act. O n t h e m a c r o s c o p i c scale, h o w e v e r , the p i c t u r e remains analogous to t h e d i l u t e gas so that f o r t h e d e s c r i p t i o n of the energetic d i s t r i b u t i o n of p r i m a r y activations t h e homogeneous

statistic

picture could again be used. H o w e v e r , t h e d e n s i t y of t h e m e d i u m affects t h e course of r a d i o l y s i s i n another w e l l - k n o w n , a n d v e r y i m p o r t a n t w a y . L o n g - l i v i n g

reactive

intermediates s u c h as free atoms a n d r a d i c a l s r e m a i n l o c a l i z e d f o r a n a p p r e c i a b l e p e r i o d of t i m e i n t h e close n e i g h b o r h o o d of the p a r e n t a c t i v a tions b e c a u s e of their l i m i t e d m o b i l i t y i n c o n d e n s e d phase.

Hitherto

n e g l e c t e d space a n d t i m e correlations b e t w e e n the i n d i v i d u a l e l e m e n t a r y acts thus b e g i n to influence c o n s i d e r a b l y t h e subsequent processes.

This

f a c t has to b e t a k e n i n t o a c c o u n t i n t h e t h e o r y of p r i m a r y processes. A t u s u a l intensities of i r r a d i a t i o n , t h e tracks of i n d i v i d u a l p r i m a r y electrons

are w e l l isolated.

O n t h e other h a n d , t h e average

distance

b e t w e e n subsequent collisions a l o n g t h e track of a p a r t i c u l a r electron is m u c h r e d u c e d i n the c o n d e n s e d m e d i u m . T h i s enhances t h e p r o b a b i l i t y of m u t u a l i n t e r a c t i o n of the intermediates w i t h i n t h e track.

T h i s fact

has l e d to t h e i d e a of a n i s o l a t e d track o f a n i o n i z i n g p a r t i c l e as a w e b a l o n g w h i c h t h e p h y s i c o c h e m i c a l a n d c h e m i c a l events d e v e l o p i n space a n d time. T h e u s u a l e x t r a p o l a t i o n of e x p e r i m e n t a l k n o w l e d g e b a c k a l o n g t h e t i m e sequence of r a d i o l y t i c processes has p r o v i d e d us w i t h t h e p i c t u r e of a r a d i c a l track w h i c h is f o r m e d at t h e b e g i n n i n g of the c h e m i c a l stage. W h i l e the f u r t h e r d e v e l o p m e n t of this track b y d i f f u s i o n a n d c h e m i c a l reactions

h a d b e e n successfully treated i n great d e t a i l b y the t h e o r y

of d i f f u s i o n k i n e t i c s , t h e i n i t i a l structure of the t r a c k w a s p i c t u r e d o n l y


36.

SANTAR AND BEDNÂR


b y very crude a n d approximate models. p r i n c i p a l i n c a p a b i l i t y of t h e c h e m i c a l

Particle

533

T h e reason f o r this w a s the experience

to y i e l d ,

by

back

extrapolation, physical information. T h e o r i g i n a l i d e a ( 1 5 ) w a s that of a s t r i n g o f i s o l a t e d centers ( s p u r s ) a l o n g t h e track, i n e a c h of w h i c h a n energy of the order of tens of e.v. h a d b e e n d e p o s i t e d i n t h e p r i m a r y act. H o w e v e r , the p h y s i c a l nature of spur f o r m a t i o n r e m a i n e d rather u n i d e n t i f i e d a n d u n e x p l a i n e d i n d e t a i l (6).

O n t h e other h a n d , i t is seen f r o m t h e f o r e g o i n g that t h e track

formation involves a number of both qualitatively a n d quantitatively different processes w h i c h t e n d to c o m p l i c a t e t h e i n i t i a l structure of t h e Downloaded by UNIV LAVAL on July 11, 2016 | http://pubs.acs.org Publication Date: January 1, 1968 | doi: 10.1021/ba-1968-0081.ch036

track. Q u i t e r e c e n t l y M a g e e a n d his co-workers (7, 9, J O ) e n d e a v o r i n g t o stimulate f u r t h e r d e v e l o p m e n t of t h e t h e o r y of track took u p a m o r e d e t a i l e d analysis of these p r i m a r y processes o f track f o r m a t i o n

(see

T a b l e I V ) . D e p e n d i n g o n the energy loss Ε of t h e p r i m a r y p a r t i c l e Mozumder and Magee

( 9 ) d i v i d e d t h e c o l l i s i o n a l processes a l o n g t h e

track i n t o the f o l l o w i n g g r o u p s : 1. spurs, 2. b l o b s , 3. short tracks, a n d 4. b r a n c h tracks. T h e b y f a r most f r e q u e n t spurs c o r r e s p o n d i n g to l o w energy losses b e l o w 100 e.v. c a n b e i d e n t i f i e d w i t h t h e o p t i c a l c o l l i s i o n of fast electrons T a b l e I V ) . It is i m p o r t a n t here that t h e secondary electron f r o m

(see

a n o p t i c a l i o n i z a t i o n is so s l o w that it loses its energy v e r y near t o the p o i n t of t h e p r i m a r y c o l l i s i o n . B e c a u s e of this, a l l secondary

excitations

a n d i o n i z a t i o n s i n d u c e d b y this electron o c c u r w i t h i n t h e same single spur.

T h e a c t i o n of s l o w electrons is thus c o m p l e t e l y i n c l u d e d i n t h e

spurs, a n d o n l y fast electrons are c o n s i d e r e d as i o n i z i n g particles f o r m i n g the characteristic entities i n t h e track. T h i s s i t u a t i o n is exactly analogous to t h e s p l i t t i n g of the d e g r a d a t i o n s p e c t r u m i n t o s l o w a n d fast electrons i n t h e t h e o r y of P R C Y : T o t a l y i e l d of spurs is e q u a l to t h e y i e l d g ° of o p t i c a l collisions. I n t h e case of d i l u t e gases there w a s n o n e e d f o r a n y f u r t h e r sub d i v i s i o n of fast electrons since t h e m e a n free p a t h of a l l of t h e m w a s a l w a y s so large that a l l p r i m a r y activations w e r e w e l l separated.

O n the

other h a n d , i n c o n d e n s e d m e d i a t h e free p a t h of electrons h a v i n g a n energy close to the l o w e r l i m i t of the fast r e g i o n is r e d u c e d to t h e extent that t h e spurs f o r m e d b y t h e m t e n d to o v e r l a p f r o m the v e r y b e g i n n i n g . S e c o n d a r y electrons w i t h energies of 100 to 500 e.v. f o r m p e a r - l i k e w i t h a h i g h l o c a l c o n c e n t r a t i o n of o v e r l a p p i n g spurs.

blobs

S t i l l faster δ-elec-

trons w i t h Τ b e t w e e n 500 a n d 5000 e.v. f o r m c y l i n d r i c a l short tracks

with

h i g h L E T , i n w h i c h t h e extent of t h e o v e r l a p o f spurs is s t i l l a p p r e c i a b l e . O n l y t h e electrons of energies h i g h e r t h a n 5000 e.v. are a c t u a l l y c o n s i d e r e d as p r o d u c i n g the b r a n c h tracks c o m p o s e d of isolated spurs, b l o b s ,


534

RADIATION CHEMISTRY

Table I V .

1

Survey 100

E,T:


SPURS P R O C E S S

optical excitations of valence electrons

C a n be induced by electrons

all fast

Properties of the secondary electron

(

T

slow < 100 e.v.)

Integration limits over Τ - i n theory of P R C Y

-*

g

s

^

- i n track theory etc.

T h e t o t a l y i e l d of a l l b l o b s , short tracks, a n d b r a n c h tracks corre

sponds, of course, to the s m a l l y i e l d s g * of δ-electrons f r o m h a r d c o l l i s i o n s and g

K

of A u g e r electrons f r o m the i n n e r - s h e l l i o n i z a t i o n s .

M a g e e does not r e g a r d the b r a n c h tracks as p a r t i c u l a r entities b u t he develops t h e m i n the same w a y as the track of the p r i m a r y fast electron. T o c o m p a r e his results w i t h the t h e o r y of P R C Y it is, h o w e v e r , necessary (20)

to d e v e l o p e v e n the b l o b s a n d t h e short tracks i n t o t h e i r c o n s t i t u t i n g

spurs. F o r the c o r r e s p o n d i n g p a r t i t i o n of the t o t a l y i e l d of spurs w e t h e n obtain g° = g(spur) + g ( s p u r )

51

+ g(spur) .

T h e results of M a g e e ' s c a l c u l a t i o n s (7, 10)

st

(10)

of t r a c k structure repre

sent either the t e r m g ( s p u r ) for i s o l a t e d spurs o n l y or the s u m g ( s p u r ) +

g (spur)

s t

if the short tracks h a d f u r t h e r b e e n d e v e l o p e d i n t o spurs.

S i m p l y , it matters w h e r e the l i m i t of energy is p u t above w h i c h

the

e l e c t r o n is s t i l l a s c r i b e d the a b i l i t y to generate isolated activations. I n the l a n g u a g e of d e g r a d a t i o n s p e c t r u m this statement

is e q u i v a l e n t to

the

s h i f t i n g of the b o r d e r l i n e b e t w e e n fast a n d s l o w electrons, the latter as if d i s s i p a t i n g t h e i r energy "at the spot"—i.e., w i t h i n a single entity. T h u s ,


36,

SANTAR AND BEDNÂR


535

Particle

of T r a c k E n t i t i e s 500

5000

T MAIN

BLOBS

SHORT

TRACKS

h a r d

TRACK +

BRANCH a)

0

c o l l i s i o n s

TRACKS

(δ-electrons)

b) optical excitations of inner electrons (Auger electrons) K-el. : C Ν Ο


t

t

Î

part

of

fast

fast range < 200 A .

T

_ "~g(spur)

b l

100 e.v.)

range > 200 A .

M

"*

( >

(Τ > E)

>-

g 0

g(spur)

-*

mean free path > 100 A .

*·

st

*

g(spur)

>

again, w e meet the necessity of a r e s o l u t i o n i n t o parts of the d e g r a d a t i o n s p e c t r u m , a n d of separate e v a l u a t i o n of c o n t r i b u t i o n s of these parts to the t o t a l y i e l d . A n a p p r o x i m a t e s o l u t i o n of this p r o b l e m ( I I )

is g i v e n i n F i g u r e 1,

w h e r e the r e l a t i v e c o n t r i b u t i o n s of electrons of different energies to t h e t o t a l y i e l d g are s h o w n . T h e p a r t of the c u r v e f o r g ° is b a s e d o n theo r e t i c a l c a l c u l a t i o n s of the d e g r a d a t i o n s p e c t r u m ( 8 ) , the c o n t r i b u t i o n g is extrapolated s c h e m a t i c a l l y .

s

F r o m this F i g u r e w e get as a r o u g h first

a p p r o x i m a t i o n the ratios 6 5 : 2 2 : 1 3 f o r the percentage of the terms o n the r i g h t - h a n d side of E q u a t i o n 10. Since the o p t i c a l a p p r o x i m a t i o n is v a l i d f o r a l l fast electrons,

and

since the latter are a l l able to i n d u c e the entire s p e c t r u m of o p t i c a l transitions, the energy d i s t r i b u t i o n of spurs is the same f o r i s o l a t e d spurs a n d f o r the spurs i n b l o b s or short tracks. T h e average energy p e r s p u r is thus e q u a l i n a l l entities a n d the p a r t i t i o n of energy b e t w e e n

spurs,

b l o b s , a n d short tracks is a p p r o x i m a t e l y g i v e n b y the above ratios, too. T h i s is one of the reasons w h y the y i e l d g

s

c a u s e d b y s l o w electrons is

u n i f o r m l y a d d e d to the w h o l e area of the y i e l d g ° of spurs i n F i g u r e 1.



536

RADIATION CHEMISTRY

1

Figure 1. Subdivision of the degradation spectrum and contributions of its various regions to the total yield of primary activations O u r conclusions are c o r r o b o r a t e d b y a n analysis of M a g e e ' s results. H i s a p p r o a c h (10)

is to s i m u l a t e the t r a c k b y a M o n t e C a r l o m e t h o d .

T h e c o m p u t e r generates pairs of r a n d o m n u m b e r s w i t h w h i c h the free paths of the electrons before p a r t i c u l a r collisions, a n d the energy losses i n these collisions, are u n i v o c a l l y associated o n t h e basis of a p a r t i c u l a r f o r m of the cross sections. T h e result of this a l g o r i t h m is the d i s t r i b u t i o n of n u m b e r s a n d ener gies of i s o l a t e d spurs, b l o b s , a n d short tracks f o r m e d d u r i n g the c o m p l e t e a b s o r p t i o n of a p r i m a r y 1 M e v . electron. that the histograms (JO)

It c a n b e seen f r o m F i g u r e 2

f o r w a t e r agree i n shape v e r y w e l l w i t h the

s p e c t r u m of oscillator strength a n d w i t h the d e r i v e d excitation s p e c t r u m ( 1 / E ) ( df/dE

), w h i c h M a g e e u s e d . T h i s is i n f u l l agreement w i t h o u r

c o n c e p t i o n of the o p t i c a l a p p r o x i m a t i o n (see

Equations 3 and 5).

On

the other h a n d , the absolute values are different since M a g e e u s e d a sub s t a n t i a l l y different o p t i c a l s p e c t r u m for w a t e r t h a n w e p r e v i o u s l y d i d (16). W e m a d e a n u m b e r of calculations (20) of the track structure b y o u r m e t h o d , w h i c h has b e e n b r i e f l y m e n t i o n e d above. T a b l e V a g a i n shows a p r o n o u n c e d effect of the c h e m i c a l nature of molecules o n the


36.

SANTAR AND BEDNAR


Particle

537

f u n d a m e n t a l r a d i a t i o n - c h e m i c a l properties. W h i l e t h e y i e l d s of b l o b s a n d short tracks r e m a i n r o u g h l y u n c h a n g e d , t h e y i e l d s of spurs v a r y w i t h i n a factor of t w o . T h i s m a y b e i m p o r t a n t i n d e e d i n considerations of t r a c k


effects i n different l i q u i d s .

Figure 2. Comparison between the optical spectra used and the spurdistribution histograms obtained for a 1 Mev. primary electron absorbed in water spectra df/dE, (R/EXdf/dE) used by Magee ( 1 0 ) , - - - - - resulting histograms of number and energy distribution of spurs, by Monte Carlo method, spectrum df/dE for an isolated water molecule (16)


538

RADIATION CHEMISTRY

Table V . g° H CH

Effect of Chemical Composition of the Medium on the T r a c k Structure g(spur)

5.8 4.8

2

4

m

1.5 1.2

g(spur)

st

0.8 0.7

3.5 2.9

3.7 2.8

2

o

2

1.0 0.7

0.5 0.4

2.2 1.7

g(s.t.)

g(blob)

g(spur)

) )~0.1

H 0

1

I

;

)

() —0.01

(

I n c o n c l u s i o n , i t m a y b e s a i d that, at present, t h e o r y appears to b e a b l e t o p r o v i d e a u s e f u l a priori

information o n primary radiolytic proc


esses a n d y i e l d s .

Literature Cited (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) (16) (17) (18) (19) (20)

Durup, J., Platzman, R. L., Discussions Faraday Soc. 31, 156 (1961). Fano, U., Phys. Rev. 103, 1202 (1956). Ibid.,118,451(1960). Fano, U., Ann. Rev. Nucl. Science 13, 1 (1963). Hart, E. J., Platzman, R. L., "Mechanisms in Radiobiology," Vol. I, p. 93, A. Forssberg, M. Errera, eds., Academic Press, New York, 1961. Magee, J. L., Ann. Rev. Phys. Chem. 12, 389 (1961). Magee, J. L., Funabashi, K., Mozumder, Α., Proc. 6th Japan Conf. Radio isotopes, Tokyo, p. 755, 1965. McGinnies, R. T., U. S. Natl. Bur. Stds. Circ. No. 597 (1959). Mozumder, Α., Magee, J. L., Radiation Res. 28, 203 (1966). Mozumder, Α., Magee, J. L.,J.Chem. Phys. 45, 3332 (1966). Ore, Α., "Radiation Research," p. 54, G. Silini, ed., Proc. Intern. Congr. of Radiation Res., 3rd, North-Holland Publ. Co., Amsterdam, 1967. Platzman, R. L., Intern. J. Appl. Radiation Isotopes 10, 116 (1961). Platzman, R. L., The Vortex 23, 372 (1962). Platzman, R. L., "Radiation Research," p. 20, G. Silini, ed., Proc. Intern. Congr. Radiation Research, 3rd, North-Holland Publ. Co., Amsterdam, 1967. Samuel, A. H., Magee, J. L.,J.Chem. Phys. 21, 1080 (1953). Santar, I., Bednář, J., Coll. Czech. Chem. Commun. 32, 953 (1967). Ibid., 33, 1 (1968). Santar. I., Bednář, J., "The Chemistry of Excitation and Ionization," p. 217, G. R. A. Johnson, G. Scholes, eds., Taylor & Francis, London, 1967. Santar, I., "To the Theory of Primary Radiation—Chemical Yield" (in Czech), Dissertation, The Nuclear Research Institute, Czechoslovak Academy of Sciences,Rež(1967). Santar, I.,Bednář,J. (to be published).

RECEIVED January 2,

1968.


The Optical Approximation, Primary Radiation Chemical Yields, and

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