Radical Yields as a Function of pH and Scavenger Concentration

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pH and Scavenger Concentration G I D E O N CZAPSKI Department of Physical Chemistry, Hebrew University, Jerusalem, Israel

G values of radicals and molecular products have been measured and have appeared in numerous publications. It has been generally assumed that at extreme acidity, alka linity, or at high concentrations of radical scavengers, the radical yields effectively increase. This behavior was sum marized in a recent review by Hayon, who generalized by assuming G radicals to depend solely on the product of kR+S · [ S ] . This approach is criticized on theoretical (the different models proposed) as well as experimental grounds. In many cases, where G values of radicals seem to depend on pH or scavenger concentrations, the effect observed was really an artifact caused by neglecting the effect of back reactions.

TVJumerous determinations of product yields have been measured i n irradiated aqueous systems. The assumption of a mechanism and the measuring of product yields in such systems led to the conclusion that several species are produced in the radiolytic decomposition of water. [Systems of this kind, up to 1960, have been summarized by Allen (7).] These studies showed that water decomposes, yielding radicals ( 69 ) and molecular entities (5). Later studies have shown that the two molecular products, H and H 0 , are formed with different yields (30), G < G o - The radical products were assumed to be H and O H radicals (69). Later, it was shown that the reducing radical may exist in two forms (12), one being a H atom (20) and the other a hydrated electron (19, 24). It was also shown that an e reacts with H to yield a H atom (23, 43), while the opposite reaction—the conversion of H atoms by O H " into e —has been demonstrated as well (50). 2

H 2

H 2

2

2

2

&q

aq

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

+

8.

czAPSKi

e

Allan and S choies have proved that in neutral solutions both H and are formed as products of the radiolysis of water (3, 57). These investigations may be summarized by the following equation:

m

107

Radical Yields

H 0 -> H , e , O H , H 0 , H , and H 0 2

+

3

m

2

2

2

The primary yields of these species have been determined in many systems. G and G o are lower in systems where high concentrations of e or O H scavengers are added (7). Recently, it has also been shown that G is decreased by both elec tron and H 0 scavengers (9, 38). The radical yields are increased by e and O H scavengers as well as by increased acidity or alkalinity. These results were summarized in a recent review by Hayon (47). The diffusion model drawn up by Samuel and Magee ( 59 ) and later modified in the light of the knowledge that the reducing radical is a hydrated electron rather than a H atom, tried to explain the yield of all entities in the following manner (53, 54, 55, 63). The basic assumption is that water is decomposed by radiation into e , O H , and H 0 , which are formed inhomogeneously in spurs. In these spurs, which are spherical, with a diameter of 10-40 Α., several pairs of these radicals are initially formed where their initial concentra tion is very high ( 0 . 1 - 1 M ) . The distance between spurs depends on the L E T of the radiation. For γ-, x-rays, or fast electrons most of the spurs are isolated, and only a small fraction overlaps and forms blobs or short tracks (56). A t high L E T radiation, the overlapping of the spurs pro duces cylindrical tracks. This model assumes that after the spur is formed, two simultaneous processes occur: diffusion of the radicals from the spur into the bulk, and during this process, several reactions between the radicals take place. These latter reactions are responsible for the H , H 0 , and Η formed. The success of this model is quite impressive as its calculations succeed in predicting quantitatively many effects found experimentally (53, 54, 55, 56, 63), namely: H 2

H 2

2

aq

H

3

+

m

m

3

+

2

2

2

( 1 ) The absolute value of G , G o , G , G , and G for γ-rays. (2) The dependence of the molecular and radical yields on the L E T . (3) The effect of scavengers on the radical and molecular yields. (4) The increase of G o from almost zero (0.02) (42), for γ-rays, to 0.25 (36) for α-rays (owing to the reaction of O H with H 0 in the tracks ). Little has been done in calculating the p H effect on yields according to the diffusion model. H 2

H

H 2

2

H

e a q

0 H

2

2

2

As mentioned above, the dependence of the molecular and radical yields on p H and scavenger concentration have been studied for γ-rays in many systems. There is some general agreement concerning this

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

108

RADIATION CHEMISTRY

1

dependence for molecular yields. However, the dependence of the reducing radical yield on the p H and scavenger concentrations have given rise to much controversy in the literature. Several theories explain the p H or scavenger effect on the G value. Hayon (47), i n a recent review, advanced a unique theory covering these effects and reviewed many publications connected with this hypothesis. In this paper, my aim is to review and discuss mainly two points: (1) The actual dependence of G values on p H and scavenger concentrations. (2) The various theories concerning the dependence of the yield on the p H and scavenger concentrations. The discussion w i l l be limited almost entirely to the dependence of the radical yield rather than that of the molecular yields; regarding the latter, theory and experiment agree reasonably well. Possible Errors in Determining G Values G values are generally determined from experimental yields of products i n an irradiated system. To obtain, from the actual G (product), the G values of the radicals, knowledge of the reaction mechanism is necessary. The value of G (product) is derived as the slope of a straight line when plotting the product concentration vs. dose. Possible errors i n evaluating G may be caused either by misinterpreting the reaction mechanism or by incorrect slopes of the product dose plots. To avoid ambiguity, we w i l l define the different symbols of G being used. A l l these G values are i n units of number of χ molecules or radicals per 100 e.v. absorbed. mûic&ïs

The symbol G ( x ) is used generally as the measured yield of an entity χ i n a given system. G is used as primary yields of x, where χ is one of the radical or molecular primary products, as H , H2O2, H , O H , and e . x

2

m

To estimate errors i n G values, let us take as an example the deter mination of G and see how this value has been measured i n numerous systems. €

G

e

an

The reactions which may occur and which may affect the measured are: e

aq

+

OH +

Si

-»· P

x

S

-» P

2

2


8.

czAPSKi

Radical Yields

109 h

H

+

S

s

-» P

3

e

+

P

x

-> P

4

aq

h e

aq

+ H 0 -> OH" + OH 2

2

H

+

Pi

-> P

H

h + OH" ->

e

e

aq

G is determined from the initial yield of Pi. (We deal only with systems where e reacts with one solute rather than competing for two or more solutes. ) e

aq

Let us divide these systems into the following groups. (I) The e competition with S , P , and H 0 ; the yield in this system is given by Equation I: aq

t

"ddose

—

2

2

2

, . M M+ Mëh2e1 *i[Si] *i[Si]

-— W

a

(l)

(II) The electron competing in reaction with S T? or H 0 ; the yield will be given by Equation II : u

ddose

•

2

u

fce[H Q ] 2

2

P

2

( III ) Should the competition be that of H for C and Pi, the yield will be given by Equation III: 3

ddose-^"

M

M

" "

(m)

7

*T[PI]

(IV) Should the atom be partially converted to an electron, the yield will be given by: Ί

d[Pi] _

r

,

r

.

_

MPi] fc [OH-] 8

( ) IV

+

r

fc [OH-] fc [OH"] 8

8


110

RADIATION CHEMISTRY

1

In Equations I - I V , as long as the terms of P i and H 0 can be set aside when comparing the other terms and provided the scavenger con centration does not change, the yield of P i w i l l be linear with dose, and (G ) observed can be obtained from the slopes of the line of P i vs. dose ' G plots. (In Equation IV, the slope would yield: G + fc j-g -j ·) 2

2

e

H

E < I Q

fc [OH-] The situation w i l l be different if this assumption is not valid; then, Equa tions 1 - I V would have to be used without cancelling out the terms competing with the reactions of the e with S i , or H with P i . In these cases, P i is not really linear with dose, and the curve bends over. 1 +

8

m

In Tables I - I V , the ratio of the observed G

e

7

r

to the real G

e

aq

aq

was

calculated. ( G ) observed is obtained from the slope of the best straight line of P i vs. dose dependence by the least-mean square method. ( P i vs. dose values were calculated by a computer, using Equations I - I V ) . e

^ Cjcβ

^ observed

The value of — — r — depends on the relative rate constants, V *-*e / real concentration, and total dose or, more explicitly, on the value of the denominator in Equations I and III or the fraction in Equations II and I V at the maximum dose used in the P i vs. dose plot. Values in Tables I - I V are given for Equations I - I V , with either of the two following assumptions: ( a ) P i vs. dose yields a straight line with zero intercept, ( b ) P i vs. dose yields a straight line with non-zero intercept. These tables are calculated assuming: aq

^ H ^ n ^ y need not be considered. It is assumed also that the concentraMSi] tions of S i , S , S are not depleted during irradiation, while P i , P , and P are computed by solving the differential Equations I - I V , taking G = 2.8, G = 0.6, G O H = 2.8. The values of α, β, y, and δ are thus functions of y rn -ι τ r'g , * [ J ^ , and the dose. (Should an KiLSiJ fci[Si]' k fc [OH ] ' fc [OH ] ' observable depletion in S i , S , or S occur during irradiation, the correc tion is even larger.) 2

3

2

3

CQ

H

Ί

?

3

S s 7

7

Γ

8

8

2

3

Tables I - I V can be used to estimate the error in different determina tions of G e , where the experimental details given in the published paper are sufficient to calculate the value of α, β, γ, or δ ( as defined in Equations I - I V ) at the highest dose used. The fact that in most of the publications from which G values were calculated the plot of product vs. dose yielded straight lines, does not in itself constitute proof that the slope is really the initial slope. aq


8.

CZAPSKI

Radical Yields

111 Table I.· aq

K

)observed

aq )real

k,5 [Pg] max

0.02 0.049 0.095 0.18 0.29 0.41 0.73 It is assumed that

l)max

a

Zero Intercept

Non-Zero Intercept

Intercept

0.98 0.95 0.91 0.84 0.78 0.71 0.58

0.993 0.982 0.965 0.934 0.899 0.861 0.777

0.991 0.976 0.954 0.916 0.871 0.825 0.725

640 260 136 72 46 34 20

,

f c i [ S i ]

«

.

Table II.' ( G ^ )ohserved e

(G

0.0196 0.0476 0.091 0.168 0.255 0.345 a

γ. .

)

r e a l

(PUmax

β

Zero Intercept

Non-Zero Intercept

Intercept

0.96 0.91 0.83 0.71 0.59 0.48

0.985 0.964 0.931 0.874 0.811 0.745

0.981 0.953 0.911 0.839 0.760 0.681

320 130 67 35 22 16

, ., . _fce[H2C>2j[

It is assumed that

eae

fci[Sl]

fc4[Pj2

«

.

Table III. (^-*e )observed aq

^7 [Pi] max 0.55 1.0 1.59 2.55 5.10

(P l)max

7

Zero Intercept

Non-Zero Intercept

Intercept

0.645 0.5 0.381 0.282 0.164

0.917 0.944 0.957 0.971 0.982

0.902 0.934 0.949 0.966 0.981

100 130 180 300 900

^3 [$3]


112

RADIATION

Table I V .

CHEMISTRY

a

observed

(Ge

^7 L^l] max k [OH"] 0.925 0.56 0.383 0.234 0.119 0.06

e

sfOH"]

c a n

oe

)real (Pl)max

8

Zero Intercept

Non-Zero Intercept

Intercept

0.039 0.282 0.446 0.62 0.787 0.888

1.097 1.14 1.16 1.18 1.196 1.205

1.07 1.12 1.14 1.17 1.19 1.20

52 86 115 175 322 610

neglected in comparison with ^ [QJJ8

Figure 1. F as function of dose calculated from Equation II with kj/k^. [S^] = 10 up to a maximum dose where F = 4.8 X 10~ t

4

l m a x

6

Initial slope Calculated by least mean squares Calculated by least mean squares assum ing zero intercept


1

8.

czAPSKi

113

Radical Yields

Figures 1 and 2 show a computed plot of yield vs. dose according to Equation II (taking ^ f f i f f i = 0, a

nd^4

reaching 0.048 and 0.168

at the maximum dose. ) The straight lines are calculated using the leastmean square method, having a slope which is lower b y 5 or 13-16%, respectively, than the initial one. ( Such a difference may lower G from an initial value of 2.8 to an "observed" value of 2.4. ) c q

As w i l l be shown, many determined G values were too low since the slopes measured were not the initial ones.

Figure 2. Ρ χ as function of dose calculated from Equation II with k^/k^. S = I 0 up to a maxi mum dose where P os — 1·68 X 10~ 4

1

5

lma

Initial slope Calculated by least mean squares Calculated by least mean squares, assuming zero intercept Dependence of

G dicais ra

On pH

Numerous determinations of G have been undertaken with various chemical systems, and a wide spectrum for the observed G values has resulted. The value of G hicinp lies generally i n the range of 2.8-3.5, where G is about 0.6, the balance being G ^ . R

re
it would seem that in the F e - 0 , F e - N 0 systems, most—if not all—of the p H effect is 2

H

ra

2 +

2

2 +

2


e

116

RADIATION

CHEMISTRY

1

caused by reactions of radicals with products, and quite possibly the same may be valid for the 0 - C H O H and f o r m a t e - 0 systems; i n the C O - 0 system the p H effect is probably not caused by reactions of the radicals with products, but the increase is sharp at low p H (1.4-2.2) and does not rise above p H 1.4. In pulse radiolysis studies of Br" solutions and i n the acetone-isopropyl alcohol system, no p H dependence was observed. These results seem to indicate that there is no real evidence i n favor of an appreciable increase in G with acidity, as there seemed to be and as was summarized by Hayon (47). 2

2

5

2

2

R

A L K A L I N E SOLUTIONS. Several systems have been irradiated i n alkaline solutions i n recent years. In most of these systems G increases with p H . However, although most determinations do agree on the trend of increase of G , the measured G values differed extensively. Hayon ( 47 ) reviewed the difficulties, pitfalls, and some of the possible reasons as to why G values disagree. R

R

The radiation chemistry of alkaline solutions is fraught with many complications. For instance, i n oxygenated solutions Of is formed from O " + 0 , and the product of the reaction of e + 0 has a lifetime of up to several minutes (25). Such facts as these are liable to render more intricate the reaction mechanism on which the evaluation of G values depends. In strong alkaline solutions at p H > 13 there exists the danger of impurities. (In 1 M N a O H , 0.01% of an impurity i n the reagent may yield up to 10" M impurities i n the solutions. ) 2

2

m

4

Another difficulty lies i n determining G o or G ( H 0 ) since H 0 is unstable i n alkaline solutions. In alkaline solutions both H and O H react with O H " to yield e and O " respectively; hence, one should account for the different reactivities of the neutral and alkaline forms of the radicals with various scavengers. H 2

2

2

2

2

2

m

In a number of instances G d increased between p H 10 and 14, but the mechanisms assumed the existence of only one reducing radical—the solvated electron. It is now known that both e and H atoms are formed by irradiation. W e should consider that i n these systems the H atom is converted, i n alkaline solution, into e , and that the reaction mechanism involving H and e are responsible for the apparent increase of G a* This would mean that what was really measured i n many of these determinations was G(e ), which at low p H equals G but increases, i n strong alkaline solutions, up to the value of G + G . Most irradiated systems containing N 0 belong to this group. The reactivity of e towards N 0 is assumed to be 2 X 10 -fold faster than that of H atoms. re

m

m

m

re

m

e&q

6 a q

H

2

4

2

m

N 0 + e 2

m

- » N + O2

N 0 + H —» N + O H 2

2


8.

czAPSKi

Radical Yields

117

ki is about 5.6 X 1 0 M sec. , while k> is much lower. [The value of 2 X 10 M sec." has been estimated ( 2 1 ) , but recent measurements indicate the value to be about one order of magnitude higher (29, 40).1 9

5

_ 1

_ 1

-1

1

The first and simplest systems to be irradiated were solutions of N 0 over the entire p H range (31). In this system, G ( N ) increased between p H 1 1 - 1 3 , by about one unit, while G ( 0 ) increased by only 0 . 3 5 units. In this same system, the net effect of radiation is that N 0 decomposes into 0 - f N , as H and H 0 descend to very low steady states owing to their decomposition by O H radicals which have no solute to react with. Thus, one expects G ( N ) = 2 G ( 0 ) . 2

2

2

2

2

2

2

2

2

2

2

The experimental value of ^/^? | is 2 . 5 below p H 1 1 and about 2 . 8 5 2

at p H 14, but neither of these values provides a material balance. Although quantitatively this system is open to question, the observed increase of G ( N ) and of G ( 0 ) is expected and should be equal to G H and to | G , respectively. The average value of G owing to the increase in G ( N ) and G ( 0 ) coincides with the known value of G = 0.6. 2

2

H

H

2

(AG(N ) 2

2

=

H

0.95, A G ( 0 ) 2

=

0.2.)

Another system that has been studied is the f e r r i - f e r r o c y a n i d e - N 0 system (32). Here, G increases from 2 . 7 5 to 3 . 8 5 between p H 6.5 and 13.5. This increase is attributed to H 0 * or ( H . . . O H ) which are scavenged by O H " . It was assumed in the analysis that only e was formed. A t low p H , the H atoms with G — 0.6 are more likely to reduce ferricyanide than to react with N 0 , while at a higher p H , the H atoms can be converted into e which reacts with N 0 . 2

R E D

2

m

H

2

2

m

Thus, G ( N ) should increase by 0.6 units between p H 9 to 14, and G ( F e ) w i l l increase in the same range by about 1.2 units. The experi2

m

mental results are in semiquantitative agreement with this prediction and mechanism. It has been shown recently ( 2 9 ) that G ( N ) in this system 2

is not p H dependent, but depends only on the ratio j^p^nj . This indicates that the increase in G ( N ) is caused by competition of H atoms in 2

the reactions: H + OH" -» e

(followed by e

m

m

+ N 0 -» N + OH 2

2

and O H + F e " - » O H " + Fe™) H + Fe " ->H + Fe" 1

+

Buxton and Dainton have investigated the N 0 - I " system (16). Here G ( N ) increases by about 0.7 units between p H 1 1 and 14; i n this same p H range, G ( I ) increases by about 1.4 units. This increase may 2

2

2


118

RADIATION

CHEMISTRY

1

again be caused by the competition of I reduction by H atoms or by the conversion of the H into e which oxidizes iodide. 2

m

The reactions are: H + OH" -» e

aq

(e

m

+ N 0 -> N + O", 2

2

ΟΗ + Γ - > Ο Η + Ι )

(I)

H + I - » HI + I 2

The average I concentration during radiation amounted to 50 μΜ. A t p H 13 when [I ] = 50 μΜ, Reactions I and II have comparable rates, so we expect G ( I ) and G ( N ) to increase by 0.7 or 0.35 units, respec tively, over their value at low p H . 2

2

2

2

This prediction is in full agreement with experimental evidence. It follows that this increase can be attributed to G and Reactions I and II. Buxton and Dainton (16) discussed this possibility but discarded it since they assumed G ( N ) reached too high a value for G ^ + G , which they assumed was about 2.9. H

2

H

e

To summarize this system, the increase of G (No) and G ( I ) with p H is in good agreement with the accepted value of G . The value this system gives for G is 3.2, which is higher than that usually assumed. 2

H

e

Other systems studied and showing G to increase between p H 10 and 14 were: the N 0 - T e l l u r i t e (34), P t - N 0 (35), and I r - N 0 (35) solutions. The behavior in these systems is identical to that in the Γ - Ν 0 system. The increase of G ( H ) + G ( N ) from 3.38 to 4.28 between p H 10.5 and p H 13.8 in the tellurite solutions can be accounted for by the competition of Η atoms with O H " and tellurite. The similar behavior in the Ir and Pt solutions can be caused by the reduction of P t or I r by Η atoms. It is not yet possible to check these observations quantitatively because the rate constants of the reactions of Η atoms with tellurite, P t , and I r are unknown. R

n

2

m

2

2

2

2

2

I V

I V

I V

I V

In the two systems ferricyanide-formate-0 and ferricyanide-ethan o l - 0 , Hayon (46) has shown that G increases from 2.85 to about 3.45 at p H 11.5-14. 2

2

r e d

In the ferrieyamde-formate-Oo solutions and ferricyanide-ethyl alcoh o l - 0 systems, G is derived by assuming that all the O H radicals react with the organic solute and that none react with the ferrocyanide. These systems are further complicated by the fact that O H radicals can convert into O " radicals, whose rate constants with the solutes are not known. 2

m

l

In these systems the initial ferricyanide was 800 μΜ, and the concen tration of ferrocyanide at the end of irradiation reached a concentration of 300 μΜ.


8.

czAPSKi

Radical Yields

119

At the end of radiation the following ratios would be obtained: fcoH+formate [formate] &OH+ferrocyanide [f erricyanide] ÔH ethyl alcohol [ethyl alcohol] &OH+ferrocyanide [ferrocyanide] +

—42 _

:

3

3

Thus, in the formate or ethyl alcohol cases (46), 1 0 - 1 5 % of O H (not O") would react with ferrocyanide formed. The increase with p H may be attributed to O H and O " reacting differently with the solutes. A t any rate, the G ed yields calculated by Hayon at p H < 1 1 appear to be too low r

by 1 0 - 1 5 % .

Another determination ( 1 5 ) of G values i n the formate-ferri-ferro cyanide system yielded results which suffer the same criticism. The values of ip +formate [formate] ^ j doses, were as low as 6, which fcOH + ferrocyanide J cannot vindicate the assumption that O H reacts with formate only. No p H dependence was reported in several systems studied i n alkaline solution. The B r O " ( 18 ) was studied by Cheek and Linnenbom who found that G was 2 . 8 5 for N a O H 0 . 0 1 - 1 . 0 M . Julien and Pucheault (45) arrived at a similar conclusion when studying the irradiation of hypochlorite. Haissinsky (38) demonstrated two features in the nitratephosphate system: G ^ increases and G decreases i n the p H range 8 . 2 13.9, but G has the value of 3 . 2 - 3 . 3 in this range. Two determinations of G as function of p H have been made using pulse radiolysis. Brown et al. (14) found that G increased by 5 0 % from p H 9 to 1 3 . (This increase includes the partial contribution of H atoms converted into solvated electrons.) Fielden and Hart (37) also observed an increase in G at p H 10—13. They found that all the increase is between p H 9 and 12, while at p H > 1 2 , i n contrast to other deter minations (34) no further increase was observed. Fielden and Hart (37) determined G(e ) i n this p H range i n three solutions: (a) 7 Χ 1 0 " M H , ( b ) 7 X 1 0 M H + 1 - 2 X 1 0 " M ethyl alcohol, ( c ) 1 M ethyl alcohol. They compared the value at p H 1 3 with G(e ) in neutral solution and reported the ratios 2.42, 1.35, and 1 . 1 5 for solutions a, b, and c, respectively. They assumed that at p H 1 3 i n 7 X 1 0 " M H G(e ) = G, + G + G O H , i n 1 M ethyl alcohol G ( e ) = G ^ and i n 7 X 1 0 " M H + 1 - 2 X 1 0 ~ M ethyl alcohol G(e ) = G -f- G . W i t h this assumption and the measured yield of G in neutral solution having the value of 2.7, they found at p H 1 3 : G — 3.10, G = 2.87, and G = 0.54. The authors suggest that G should fall at p H 1 3 compared with neutral solution but failed to get such an effect. A t p H ~ 1 3 i n 7 X 1 0 " M H + 1 - 2 χ 1 0 " ethyl alcohol solutions, O H is converted by O H " into O " before reacting 1

m

a

x

m

u

m

e

R E D

H

e

R E D

E < I Q

e

c

m

4

4

2

3

2

m

4

m

3

m

2

A Q

m

4

e

H

2

H

e

e

6 A Q

0

H

H

H

4

2


3

120

RADIATION

CHEMISTRY

1

with either H or ethyl alcohol, as &ΟΗ- + ΟΗ[ΟΗ~] > & O H + H [ H 2 ] (S) or & Ο Η + Ο Η 5 0 Η [ 0 Η Ο Η ] . However, O " can compete in the solution for H and C H O H . The rate of O" with ethyl alcohol is not known, but since it does not react faster than the rate of O H with C H O H (58), up to 10% of O " would react with H , yielding Η atoms which are converted into electrons. O n this assumption, the following G values are recalculated: 2

2

2

2

2

5

2

5

2

5

2

Ge

aq

= 3.10

G

O H

= 3.2

G = 0.21 H

These values are only approximate sincefco-+ c H oH is not known accurately. The interesting point is that G is about 3.4, almost un changed from the value i n neutral solution, while G is lower i n the alkaline solutions as Fielden and Hart expected (37). The second feature is the high value of G H which might exceed G ^. Similar behavior was observed i n alkaline oxygenated ferrocyanide solutions (44), where G ~ 3.16 and G O H = 3.2. In the pulse radiolysis of ferrocyanide it was shown (2) that G O H is p H independent over the range 4.4-13. The last point worth mentioning i n Fielden and Hart's (37) study, is the p H independ ence of the yield i n the range 12-13. 2

5

red

H

0

e&

Caq

Two main questions exist concerning the p H dependence of G : is there a p H dependence, and what are the radical yields? R

The increase observed for G when passing from neutral to either acid or alkaline soltuions is, i n most systems, an artifact resulting from several causes. R

In both acid and alkaline solutions, the two reducing entities, and H atoms, can be converted into each other in reactions:

e

m

H + O H " -> e

m

Since these two species have different reactivities towards various solutes and radiation product, they must be taken into account. The oxidizing O H radical exists i n two forms i n alkaline solutions, and these radicals may react in different ways with solutes or with radia tion products. Some of the radicals react with radiation products; therefore back reactions must also be considered. The relative contribution of these back reactions may also be p H dependent, either in their reaction with a solute, as i n the H + F e reaction i n acid solutions, or because of the competition of an intermediate radical with a solute or radiation product, and the conversion of this radical into its other form. 3 +

In m y opinion, i n most of the cases where p H dependence was observed, it is caused by neglect of the above-mentioned points. W h e n


8.

czAPSKi

Radical Yields

121

proper consideration is given to these effects, little or no p H effect on the yield is observed. As for the value of G , different systems lead to different values. This inconsistency w i l l be discussed below. R

Dependence of G ^

on Electron Scavenger Concentration

e

Numerous determinations of G ^ in many chemical systems resulted in a wide range of values—namely, 2.3-2.9. e

Hayon endeavored to prove that G ^ is equal to 2.3 at low concen trations of electron scavenger, where &e [S] < 10 , and at higher concentrations follows G(e J = 2.3 + f ( i t [ S ] ). The function (f(k [S] ) is given as an experimental curve (47). Hayon believes that the observed spread in G is caused only by the different values of & e [ S ] in the systems which were studied and proposes a theory (45). However, on checking his data, it can be shown that in these systems, an appreciable—if not the entire—effect of the decrease in Ge as the concentration of S decreases, is caused by e competition with the irradiation products formed. e

7

aQ+s

e q + s

&

enq+s

e&

aq+s

aq

m

In the N 0 3 ~ - 0 - C H O H system, he states that yields are linear up to 1.5 χ 10 e.v./ml. However, upon calculating his observed G values, at the maximum dose applied, in this solution the peroxide concentration reaches 60-80/xM. Since the e reacts 1.3 times faster with peroxide than with nitrate (8), an appreciable fraction of e does not react with nitrate at low nitrate concentrations. This would explain the lower G found by Hayon at nitrate concentration below 2 m M . 2

2

5

18

m

m

r e d

In the Ν 0 - Γ system (45), the dependence of G ^ on N 0 concen tration was studied in the range 0.53-16 m M N 0 . Iodine concentration, at maximum dose, is 20-30/xM, but since e reacts about 9 times faster with I than with N 0 in this system (8), at low N 0 concentrations, up to 20% of e competes for I and N 0 . 2

2

e

2

m

2

2

2

2

m

2

In the T 1 - N 0 system, the results are even stranger since the reac tion of e with T l is overlooked even though under Hayon's experi mental conditions a large fraction of e should react with T l rather than with N 0 (30-99% ). (The results hint at a possible decomposition of N 0 by Tl°.) +

2

+

aq

+

m

2

2

In the ferricyanide-ferrocyanide-N 0 and 0 2 - H - C H O H system (45), maximum doses are missing, but in the latter system, the p H effect can be attributed to the competition of electrons on the 0 and aldehyde formed, while at low p H , Η atoms would probably react with 0 only. 2

+

2

3

2

2

N e u t r a l Saturated N 2 O Solutions. Several determinations of G ( N ) were made in neutral solutions of N 0 (26, 31, 33, 48, 60), according to 2

2


122

RADIATION CHEMISTRY

1

which G ( N ) depends on N 0 concentration. In an earlier determination (31) it was found that in neutral solution G ( N ) = 3.1, G ( 0 ) = 1.23, G ( H ) = 0.2, G ( H 0 ) = 0.5. Since there are no O H scavengers in this system, H and H 0 are attacked by O H and should reach low steady-state values. Taking into account all possible reactions with their known rate constants and assuming the accepted G values of e , H , O H , H 0 , and H , we were able to solve all the differential equations for the radicals and molecular products N and 0 for the various dose rates used by using a computer. The results (26) showed that H and H 0 reach steady-state concentrations of the order of 10~ M or less when nitrogen is formed at a concentration of about 10" M or even less. These results contradict the experimental observations and suggest that the higher yields of H and H 0 ( 31 ) are caused by impurities which react with O H radicals. 2

2

2

2

2

2

2

2

2

2

2

aq

2

2

2

2

2

2

2

7

r>

2

2

2

Dainton and Walker (33) observed that G ( H ) and G ( H 0 ) de pend on dose and reach a steady state at a dose of 3 Χ 10 and 3 χ 10 e.v./liter, respectively. These authors observed that G ( N ) decreases at lower N 0 concentrations and higher total dose. The dose dependence is obvious as almost total decomposition of N 0 occurred at the higher doses used. Therefore, the oxygen produced competes with the N 0 for e . Again, the increase of G ( N ) with N 0 concentration is consistent with the competition of e for 0 and N 0 as, under the doses used, 0 reached concentrations comparable with and even larger than the N 0 present. 2

2

2

21

20

2

2

2

2

2

aq

2

2

aq

2

2

2

Head and Walker (48) restudied this N 0 system recently at p H 7 in 10" -2.5 X 10" M N 0 solutions. They report that in 2.5 X 10" M N 0 solutions, G ( 0 ) = 0.65, G ( H ) = 0.1, and G ( N ) == 3.2. These values are dose dependent. The authors explained the low 0 yield by the fact that H 0 had not yet reached a steady state. Their reasoning is not immediately obvious since H 0 should reach a steady state of about 10" M at doses of less than 1 % of the applied. This would seem to imply the presence of impurities; hence, the dependence of G ( N ) on N 0 concentration may well be caused by competition with these impurities. Furthermore, at the dose used, 0 reaches a concentration of 7 X 10~°M; thus, in solutions of 2.5 X 10" M N 0 , 10% of the electrons w i l l react with 0 . 2

5

2

2

2

2

2

2

2

2

2

2

2

2

7

2

2

2

4

2

2

Scholes and Simic studied the system (60) and observed that the N and 0 yields had negative intercepts. In 1.6 X 10" M N 0 at p H 6, G ( N ) = 3.2 ± 0.1 and G ( 0 ) = 1.68 ± 0.05, while H and H 0 reached steady-state values below 10~ M. In 2.10" M N 0 these authors found G values lower by about 30%, but in this solution, their plot extrapolates to very large negative intercepts which are nonlinear. 2

2

2

2

2

2

2

6

3

2


2

2

8.

czAPSKi

123

Radical Yields

The N 0 system, in the absence of O H scavengers, seems very sensi tive to impurities and therefore vulnerable to misinterpretations. The relatively high G ( H ) and G ( H 0 ) values required that this system be treated with caution, especially since computer calculations show that these products should reach values lower by more than one order of magnitude. ISOPROPYL A L C O H O L - N 0 . Allan and Beck (4) measured G ( N ) and G ( H ) in 10" M isopropyl alcohol at p H 5.90 as a function of N 0 in the range 3-22 χ 10" M. G ( N ) increased and G ( H ) decreased at higher N 0 concentrations. They observed A G ( N ) ^ 2 A G ( H ) , a result which they attributed to competition of N 0 in the spurs with the recombination of e in the spur. SOLUTIONS C O N T A I N I N G T N M . Henglein (49) introduced tetranitromethane ( T N M ) as a scavenger in radiation chemistry of aqueous sys tems and was able to show that both the reducing radical and the hydroperoxy radical react with T N M to yield N F " , ( C ( N 0 ) ~ ) , and N 0 . The O H radical is unreactive towards T N M . In the presence of an organic solute, such as alcohol, the O H reacts with the organic solute and yields a radical R, which reacts with T N M as does the reducing radical (49). This system is thus suitable for measuring G and G \ + G. In their study of G in the T N M system, Asmus and Henglein (JO) showed that G increases with increased T N M concentration. The G for 1.3 χ 10" and 6.4 X 10~ M T N M is 3.05 and 3.3, respectively. As N 0 " , N 0 ~ , and NF~ all react with e and H with comparable rate constants and as the G values were derived from initial slopes where ( N F ) > 1.5 Χ 10" Μ, it can be expected that at a low T N M concentra tion such as (1.3 χ 1 0 " M ) , up to 10% of the electrons w i l l be reacting with N F " , N 0 " , or N O " , and lower G values would be obtained. Bielski and Allen (13) restudied this system in presence of air. A t neutral p H , they found G = 3.37 ± 0.15, with T N M concentration ranging from 2.1 χ 10" to 3.82 X 10" M. They also showed that N F " reacts with 0 " or e . They were able to measure initial yields, in solu tions where ( N F " ) < 2 X 10" M. Under these conditions, back reactions could be ignored at T N M concentrations above 4 X 10" M. This seems to be one of the most successfully studied systems since true initial yields were measured, and an exact material balance of products was achieved. Pulse Radiolysis Studies. The effect of scavengers on G was also studied using the pulse radiolysis technique. In oxygenated bromide solutions in neutral p H G ( B r " ) is constant for 2 Χ 10" to 1 M Br" (67). Similar behavior was observed wtih thiocyanate, where in 10~ to 0.1M C N S " G ( C N S ) was constant ( I ) . 2

2

2

2

2

2

2

2

2

3

2

2

2

2

2

2

m

2

3

2

r e d

re(

ox

r e d

r e d

r e d

4

4

2

3

-

aq

Γ)

4

2

a

r e d

m

l

5

2

3

m

6

5

R

2

3

3


124

RADIATION CHEMISTRY

1

To summarize the effect of scavengers on the radical yields: in the majority of cases reviewed most, if not all, of the observed increase of radical yield at high alkalinity, acidity or, radical scavenger concentra tion is an artifact. There is no real experimental evidence in most systems studied, that G is affected to a large extent by adding high concentrations of solutes, although in a few systems the yield does increase with solute concentration. R

The Diffusion Model The diffusion model used in recent calculations accounted well for yields observed in y-radiolysis (53, 54, 55, 63). However, recent compu tations (55, 63) assumed that some of the G was formed in an inde pendent reaction and not by H - f m ~^ H . The calculations enabled other effects to be explained, such as the decrease of molecular yield with scavenger concentrations. As to the effect of electron and O H scav engers on radical yields, both calculations agree that the increase in G is. about eight times higher than the decrease of G when e scav engers are added (55, 63). H

+

e

e a q

H 2

m

Kuppermann has given plots of all the predicted yields (55): Ge , G , GOH, G and G o function of electron and O H scaven gers. Schwarz (63) noted that N 0 " and Γ should have, and do have, different effects on G o since the N 0 ~ reacts with either e or O H efficiently, while the I" reacts with O H only. Thus, in the first case, H 0 is protected against e by N 0 " . q

H

H 2

Hp

a s

2

a

2

H 2

2

2

m

2

2

2

aq

Accordingly, Kuppermann's curves of G , G , and G H as functions of electron or O H scavengers, respectively, are not always justified. H e reports the yield only as a function fc [S]. Let us take a simple case where S reacts with only one of the radicals, as in the iodide case. H

e

0

R+s

The calculations assumed that Reactions 1 to 12 occur in the spur while reactions of iodine atoms (Reactions 13 to 19) are neglected. âq

e

m

e

aq

-+H

âq

+ H

^ H

+OH

(1)

2

(2)

2

-> O H -

(3)

H

(4)

e

+H

H

+ H

->H

H

+ OH

-» H 0

(6)

OH + O H

^H 0

(7)

OH + H

-> H + H 0

aq

+

(5)

2

2

2

2

2

2

OH + H 0 -» H 0 + 2

2

2

ll.O


(8) (9)

czAPSKi

125

Radical Yields e

+ H 0

2

—> O H + O H

(10)

+ H 0

2

-» H 0 + OH 2

(11)

-> O H " + I

(12)

aq

H

2

2

O H + I" I + I I

+e

-» I

(13)

2

(14)

a q

(15)

I + H

—> I" + H

h + e

V

(16)

-> I - + H

(17)

aq

I + H 2

+

2

I + H 0 2

I + OH

2

- » H 0 + H + I-

(18)

-> HIO

(19)

+

2

If fc ^k — k , k ~ h, k , — h, ku^ho, kn.—-fcn and k H + O H + H or O H + H

+

+

H 0 * + O H " —> H + O H + O H " or O H + 2

H 0* + S

2

+

e

aq

—» Intermediate and free radicals

2

The lifetime of this H 0 * must be longer than 10~ sec. to account for the observed increase of yields. 8

2

Evidence for the existence of any excited water molecule with such a long lifetime is lacking since little if any fluorescence from T 0 solutions was observed (27). The very low G value for fluorescence observed could not be quenched by 1 M acid, base, and other solutes (27). These results rule out an excited singlet of H 0 and make an excited triplet very unprobable, or if it exists, its G value would be below 0.1. (There are indications that the water triplet is a repulsive state, hence of no chemical importance (51). 2

2

The alternative theory suggests pairs or cages of H and O H radicals ( H . . . O H ) rather than H 0 * (3, 32, 44). In this case the reactions would be similar to those of H 0 * , namely: 2

2

( H . ., .OH) - » H + OH

(I)

( H . .. OH) - > H 0

(Π)

2

( H . . .. OH) + H

+

-> H + O H + H or H +

2

+

( H . . . . OH) + O H " - » H + O H + O H " or e

aq

( H . ., .OH) + S

+ OH + OH

—» intermediates and radicals

(III) (IV) (V)

This hypothesis requires that in the absence of scavengers ( Reactions I I I - V ) Reaction II predominates over I since otherwise most of the pairs would form H and O H in the bulk by escaping out of this cage. This requirement limits the lifetime of this pair. One would require much higher concentrations of H , O H " , or S in order to compete in Reactions I I I - V with II than is experimentally observed (62). +

Similar behavior is observed in the photochemistry of water at 1849 Α., where water yields Η and O H radicals (65). The dependence of the


8,

czAPSKi

Radical Yields

127

quantum yield on scavenger concentration agrees well with the model of geminate recombination of the radicals. Stein (66) criticized this treatment and reports that although formally the system follows the geminate recombination model, unreasonable parameters are obtained since too-low concentrations of scavengers bring the quantum yield to its limiting value. It seems to me that Stein's self-criticism of this model rules out the model, and an alternative explanation to geminate recombination should be sought. A possible explanation is that in the photochemical studies, where geminate recombination was postulated, the lower quantum yields observed at low scavenger concentrations is caused by back reactions with products. In many of these systems, yields were not linear with dose at low scavenger concentrations, and possibly the initial yield was not obtained by the extrapolation used. [Czapski and Ottolenghi have shown recently that in these systems the cage effect is non-existent, and the back reactions can account for the system's behavior (28).] Hayon's theory (47) explains the dependence of G on scavenger concentration. H e assumes the diffusion model and explains the G dependence by reactions of solutes with the radicals in the spurs. R

The observed G values satisfactorily fix a general curve with only one parameter, fc [scavenger] (47). M y criticism of the theory is identical with that of the diffusion model. I do not expect a general behavior of e scavengers on the yield. The product of the reaction of the different scavengers with the electrons yield products which are not identical and thus have different reactivities with other radicals in the spur. Furthermore, it was demonstrated earlier that in many cases the observed yields at low scavenger concentrations are incorrect since initial yields were not always measured. R+s

m

G Values According to Theory and Experiment It is beyond the scope of this paper to analyze all determinations of G as functions of p H and scavenger concentrations. The systems reviewed are examples given to show that many of the p H and scavenger concentration effects are at least partially caused by indirect reasons— mainly by back reactions or competitions which were neglected. As to theories concerning the prediction of the p H and scavenger concentration effects, no general behavior is expected. N o adequate calculation of the diffusion model was carried out to study the p H effect. As to the radical scavengers concentration effect on radical yields, the calculations made with the diffusion model suffer from the assumed simplifications which neglected secondary spur reactions of radicals with products of r a d i c a l solute scavenging reactions. R


128

RADIATION CHEMISTRY

1

This simplification would indicate a general behavior, while one would expect each system to behave quantitatively different. There may be e scavengers which increase, decrease, or do not change the radical yields. (In the iodide system, as discussed earlier, no change is ex pected—a fact experimentally verified ( 6 7 ) . However, in oxygenated solution G is expected to increase, as was indeed observed, owing to the replacement of e by 0 ~ or H 0 — t h e latter radicals reacting slower than e with other radicals i n the spur. ) aq

R

m

2

2

m

Although i n many systems the dependence of G on p H or scaven gers, for a given system, is mainly an artifact, the G values i n some of the systems vary immensely. R

Most observations seem to lead to the value 3.4 to 3.6 for G . Never theless, there are some systems where the yield is lower by about 0.6 units ( 18, 52, 64 ). Similar results are obtained for G H R E D

0

Inconsistencies i n G values still exist, and while many are artifacts, others cannot be explained by any present theory. Acknowledgment The author thanks E . J. Hart, D . Mayerstein, J. Rabani, G . Stein, and E . Peled for reading and discussing the manuscript. Literature Cited (1) Adams, G. E., Boag, J. W., Currant, J., Michael, B. D., "Pulse Radiolysis," p. 117, Academic Press, New York, 1965. (2) Adams, G . E., Boag, J. W . , Michael, B. D . , Trans. Faraday Soc. 61, 492 (1965). (3) Allan, J. T., Scholes, G., Nature 187, 218 (1960). (4) Allan, J. T., Beck, C. M . , J. Am. Chem. Soc. 86, 1483 (1964). (5) Allen, A. O., J. Phys. Chem. 52, 479 (1948). (6) Allen, A. O., Rothschild, W . G., Radiation Res. 8, 101 (1958). (7) Allen, A. O., "The Radiation Chemistry of Water and Aqueous Solutions," Van Nostrand, New York, 1961. (8) Anbar, M . , Neta, P., Intern. J. Appl. Radiation Isotopes 18, 493 (1967). (9) Appleby, Α., "The Chemistry of Ionization and Excitation," p. 269, Taylor & Francis, London, 1967. (10) Asmus, K. D . , Henglein, Α., Ber. Bunsen Ges. Phys. Chem. 68, 348 (1967). (11) Balkas, T., Dainton, F. S., Dishman, J. K., Smithies, D . , Trans. Faraday Soc. 62, 81 (1966). (12) Barr, N . F., Allen, A. O., J. Phys. Chem. 63, 928 (1959). (13) Bielski, B. H. J., Allen, H . O., J. Phys. Chem., in press. (14) Brown, D . M., Dainton, F. S., Keene, J. P., Walker, D . C., Proc. Chem. Soc. (London) 1964, 266. (15) Burchill, G . E., Dainton, F. S., Smithies, D., Trans. Faraday Soc. 63, 432 (1967). (16) Buxton, G. V., Dainton, F. S., Proc. Roy. Soc. A287, 427 (1965).


8.

CZAPSKI

Radical Yields

129

(17) Cercek, B., Ebert, M . , Gilbert, C. W., Swallow, A. J., "Pulse Radiolysis," p. 83, Academic Press, New York, 1965. (18) Cheek, C. H., Linnenbom, U . J., J. Phys. Chem. 67, 1956 (1963). (19) Collinson, E., Dainton, F. S., Smith, D . R., Tazuke, S., Proc. Chem. Soc. (London) 1962, 140. (20) Czapski, G., Ph.D. Thesis, Hebrew University, Jerusalem, Israel. (21) Czapski, G., Jortner, J., Nature 188, 50 (1960). (22) Czapski, G., Stein, G., J. Phys. Chem. 63, 850 (1959). (23) Czapski, G., Allen, A. O., J. Phys. Chem. 66, 262 (1962). (24) Czapski, G., Schwarz, Η. Α., J. Phys. Chem. 66, 471 (1962). (25) Czapski, G., Dorfman, L .M.,J. Phys. Chem. 68, 1169 (1964). (26) Czapski, G., Israel J. Chem., in press. (27) Czapski, G., Katakis, D., J. Phys. Chem. 70, 637 (1966). (28) Czapski, G., Ottolenghi, M . , Israel J. Chem., in press. (29) Czapski, G., Peled, E., Israel J. Chem., in press. (30) Dainton, F. S., Sutton, H . C., Discussions Faraday Soc. 12, 121 (1952). (31) Dainton, F. S., Peterson, D . B., Proc. Roy. Soc. A267, 443 (1962). (32) Dainton, F. S., Watt, W. S., Proc. Roy. Soc. A275, 447 (1963). (33) Dainton, F. S., Walker, D. C., Proc. Roy. Soc. A285, 339 (1965). (34) Dainton, F. S., Rumfeldt, R., Proc. Roy. Soc. A287, 444 (1965). (35) Ibid., A298, 239 (1967). (36) Donaldson, D . M . , Miller, N . , Trans. Faraday Soc. 52, 652 (1956). (37) Fielden, Ε. M., Hart, E. J., in press. (38) Haissinsky, M . , J. Chim. Phys. 62, 1141, 1149 (1965). (39) Hart, E. J., J. Am. Chem. Soc. 76, 4198 (1954). (40) Hart, E. J., J. Chem. Phys. 56, 594 (1952). (41) Hart, E. J., J. Am. Chem. Soc. 76, 4312 (1954). (42) Hart, E. J., Radiation Res. 2, 33 (1955). (43) Hayon, Ε., Weiss, J., Proc. Intern. Conf. Peaceful Uses Atomic Energy, 2nd, Geneva, 1958, 29, 80. (44) Hayon, Ε., Trans. Faraday Soc. 60, 1059 (1964). (45) Ibid., 61, 723 (1965). (46) Ibid., p. 734. (47) Hayon, Ε., Farkas Symposium, Jerusalem, 1967. (48) Head, D. Α., Walker, D. C., Can. J. Chem. 45, 2051 (1967). (49) Henglein, Α., Jaspert, J., Z. Physik Chem. 12, 324 (1957). (50) Jortner, J., Rabani, J., J. Am. Chem. Soc. 83, 4868 (1961). (51) Jortner, J., private communication. (52) Julien, R., Pucheault, J., J. Chim. Phys. 64, 725 (1967). (53) Kuppermann, Α., Radiation Res. Suppl. 4, 69 (1964). (54) Kuppermann, Α., Radiation Res. 25, 101 (1965). (55) Kuppermann, Α., "Radiation Research," p. 212, North Holland Publish ing Co., Amsterdam, 1967. (56) Mozumder, Α., Magee, J. L., Radiation Res. 28, 215 (1966). (57) Rabani, J., Stein, G., J. Chem. Phys. 37, 1865 (1962). (58) Rabani, J., Farkas Symposium, Jerusalem, 1967. (59) Samuel, A. H . , Magee, J. L . , J. Chem. Phys. 21, 1080 (1953). (60) Scholes, G., Simic, M . , J. Phys. Chem. 68, 1731 (1964). (61) Schwarz, Η. Α., Radiation Res. Suppl. 4, 137 (1964). (62) Schwarz, Η. Α., Ann. Rev. Phys. Chem. 16, 347 (1965). (63) Schwarz, Η. Α., Proc. Informal Conf. Hc Radiation Chem. Water, 5th, Notre Dame, Ind., 1966, p. 51. (64) Seddon, W . Α., Allen, A. O., J. Phys. Chem. 71, 1914 (1967). (65) Sokolov, U . , Stein, G., J. Chem. Phys. 44, 2189, 3329 (1966). (66) Stein, G., "The Chemistry of Ionization and Excitation," p. 25, Taylor & Francis, London, 1967.


130

RADIATION CHEMISTRY

1

( 6 7 ) Sutton, H . C., Adams, G. E., Boag, J. W., Michael, B. D., "Pulse Radiolysis," p. 6 1 , Academic Press, New York, 1965. ( 6 8 ) Weiss, J., Nature 153, 7 4 8 ( 1 9 4 4 ) . RECEIVED January 12, 1 9 6 8 . Work partially supported by A E C contract AT(30-1)-3753.


Radical Yields as a Function of pH and Scavenger Concentration

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