Ion Neutralization Times in the Gamma or Electron Radiolysis of

22

Ion N e u t r a l i z a t i o n T i m e s i n the G a m m a o r E l e c t r o n Radiolysis o f Several Dielectric L i q u i d s w i t h Different Dielectric Constants

Downloaded by UNIV LAVAL on July 14, 2016 | http://pubs.acs.org Publication Date: January 1, 1968 | doi: 10.1021/ba-1968-0082.ch022

GORDON R. FREEMAN University of Alberta, Edmonton, Alberta, Canada

The recently developed nonhomogeneous kinetics model for the reaction of ions produced during radiolysis of di electric liquids is applied to the estimation of the lifetimes of these ions in water, ethyl alcohol, acetone, and cyclohexane. Calculated lifetime spectra are given. The use of the complex dielectric constant in the calculations is dis cussed and found to be necessary for alcohols, but not for water, acetone, or hydrocarbons. The model predicts that the yield of ions observed at time t after an instantaneous pulse of radiation would be about 10% greater than G at 0.3 nsec. in water, 2 nsec. in ethyl alcohol, 3 nsec. in acetone and 400 nsec. in cyclohexane. The calculated results are consistent with the limited measurements that have been published. fi

^ recently proposed nonhomogeneous kinetics model (5) has been moderately successful in the interpretation of the rates of reactions of ions produced during the γ-radiolysis of dielectric liquids. A wide range of dielectric liquids has been tested, from hydrocarbons (5,14,20) to alcohols (16,17) and water (18). The same model explains the varia tion in the yield of free ions—i.e., ions that have escaped geminate neutralization—from one liquid to another (6). The model is still in a rather crude form and has many shortcomings. Its only strength is the degree to which it provides a quantitative interpretation of experimental results. The crudest part of the model is the discontinuous (step) function N(y) used to describe the initial distribution of separation distances between the positive ions and thermalized electrons (5, 6). When enough 339 Hart; Radiation Chemistry Advances in Chemistry; American Chemical Society: Washington, DC, 1968.

340

RADIATION CHEMISTRY

II

experience has been gained with the model in its present form and with the types of experiment required to test it, a suitable continuous function w i l l be sought to replace the function now in use. In fact, a start has already been made i n that direction (23).


W i t h the continuing improvement in the time resolution of pulsed radiation equipment, it should soon be possible to measure the lifetimes of a significant portion of the ions that undergo geminate neutralization. This information w i l l be valuable in determining the distribution of ion separation distances. In view of the moderate success of the kinetics model in its present form, it might be useful to present the radiolytic ion lifetime spectra that are predicted by the model for several different dielectric liquids. In anticipation of what follows, the very limited results of the few experiments that have attempted to measure these lifetimes [in cyclohexane (11) and in water (9)] are consistent with the present calculations. More extensive experiments are needed. Theory The System. Consider the ions produced in a dielectric liquid by an instantaneous pulse of radiation: A — — » [B + C"] M

(1)

+

(square brackets around reactants or products indicate that the species are inside a spur). The majority of ionizations in an irradiated system occur by the ejection of relatively low energy ( < 10 e.v.) electrons from molecules (12). These electrons lose their excess energy by exciting and ionizing the medium through which they pass. In a molecular dielectric liquid, when the electrons have been sufficiently de-energized they apparently become localized either by attachment to a single molecule, as probably occurs in acetone, or by interacting more or less equally with several molecules, as apparently occurs in water, ethyl alcohol, and cyclohexane, among others. This article is concerned only with the physical process of ion neutralization, so the possible occurrence of ionmolecule reactions and the precise nature of the ions B and C " are only of secondary importance (they are unimportant except insofar as they affect the charge mobilities). 3

+

The ions formed in Reaction 1 can follow two quite different paths to neutralization. The electron initially becomes localized—i.e., the species C " is formed—at a distance y from the ion B . The coulombic attraction between the pair of charges tends to draw them back together: +

[B + C~] —> [geminate neutralization] +

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

(2)

22.

FREEMAN

Ion Recombination Times

341

O n the other hand, random diffusive forces tend to drive them apart: [B + C"] - » B + C" (free ions) +

+

(3)

Thus, some pairs of ions undergo geminate neutralization and others become free ions. The free ions diffuse at random i n the liquid and ultimately meet other free ions from other spurs and undergo neutrali zation: B + C" —» random neutralization


+

(4)

In the calculation of the ion lifetime spectrum, Reactions 2 and 4 are considered separately. Reaction 4 is assumed to obey simple second order kinetics, so it presents no problem if the fraction of the total ions that becomes free ions can be determined. The nonhomogeneous kinetics model allows one to estimate this fraction (6) as well as the lifetimes of the ions that undergo Reaction 2 ( 5 ) . The model contains many approximations which can be criticized and discussed at length. In this article, however, the approximations are simply stated and briefly commented upon. The Approximations. First, there is only one ion pair per spur. This assumption is probably wrong for about half of the spurs. However, the error introduced by this approximation may be partly cancelled by that introduced by the next one. Second, the N(y) vs. y distribution—i.e., the initial distribution of B - C " separation distances—can be estimated by the simple method previ ously described (5). The method is very rough. However, no refined method yet exists to determine this distribution, because too little is known about such things as electron energy degradation spectra and the ranges of low energy electrons i n liquids. The experimental measurement of radiolytic ion lifetimes in liquids may help to determine more accurate N(y) vs. y distributions. Third, the static dielectric constant of the liquid can be used. This assumption w i l l be discussed later in this paper. Fourth, the mobilities of the ions depend on their identities, but it is assumed that in a pure solvent the mobilities do not change after the first 10" sec. of the charge lifetimes. This assumption becomes pro gressively less important with increasing ion lifetime. Ion Lifetime Calculations. The yield G of the radiolytic ions that become free ions is given by +

12

n

G

> * — m a r

'

(

)

where G„ is the total initial ionization yield and r = WAT


(Π)

342

RADIATION CHEMISTRY

Π

where ξ is the charge on the electron, c is the dielectric constant of the liquid, k is Boltzmanns constant and Τ is the absolute temperature. Equation I is solved numerically, using the appropriate N(y) vs. y distri bution (6). The yield G given b y

gn

of the ions that undergo geminate neutralization is G


(III)

= G -G

gn

0

fi

Consider the decrease of the number of ions i n a liquid as a function of time after an instantaneous pulse of radiation. T h e ions that undergo geminate neutralization move together under the influence of their mutual electric field. The relative velocity ν of a pair of ions with respect to each other is negative and is given by the negative product of the electric field strength between them and the sum of their mobilities: ν = -1.44 X 10-7 (

u+

+ u.)/(T , cm./sec.

(IV)

2

where u and u. are the mobilities (sq. cm./volt sec.) of the positive and negative ions, respectively, and r is the distance (cm.) between the ions of a pair. The time t required for a pair of ions to move together from their initial separation distance y is +

gn

= c(t/ -r )/4.32 X 10-7

*ιη =

3

0

3

+ _), u

s e c

.

(V)

where the value of r depends on the nature of the final charge transfer step that results i n neutralization. The value of r can be appreciably greater than zero if the final charge transfer step occurs by electron tunnelling, but i n the present work it w i l l be assumed that r < < t/ . 0

0

0

3

3

Equation V is used to convert values of y to corresponding values of t . Thus, SLnN(y) vs. y spectrum is transformed into an N(t ) vs. t spectrum. Since a step function was used for N(y) i n the present work, N(t ) is also à step function and it is too coarse for present purposes. It is transformed into a continuous function as follows. The total number N(t) of ions that survive at time t after an instantaneous pulse of radiation is given by gn

gn

gn

gn

00

N(t)=

N(t )(l-e-») gn

t

gn

+ J^N(y)e-'"

< > VI

= t

Equation V I takes into account the formation of free ions, which have relatively long lifetimes. However, it neglects the neutralization of the free ions, which w i l l be considered separately. By drawing a smooth curve through a plot oiN(t) function n(t) is obtained.

vs.t,a. continuous


22.

343

Ion Re combination Times

FREEMAN

The yield of C " ions, G ' ( C " ) , that would be observed spectroscopically at time t can be approximately calculated from n(t) according to Equation V I I . f

G'(C-) = ^ x n(0) t

G(C-)

(VII)

0

where n ( 0 ) is the number of C " ions at t = 0 and G ( C " ) is the corre sponding 100 e.v. yield.


0

The effect of neutralization of the free ions must be superimposed on Equation V I I . Since the lifetimes of the free ions are greater than those of the ions that undergo geminate neutralization, this can be done as follows. Reaction 4 obeys simple second order kinetics, so the fraction Ffi(t) of the free ions that survive at time t is given by

"'· fi

.

/ T V N

< >

m o l a r

IX

If the value of fc has not been measured directly, it can be estimated to within a factor of about two from Equation X : 4

fc = 2 Χ ΙΟ /*/, liter/mole sec.

(X)

10

4

where η is the viscosity, i n poise, of the liquid. Equation X was deduced from data i n Ref. 2, and from theoretical considerations of diffusion con trolled reactions between oppositely charged ions (3, 4, 5 ) . The over-all lifetime spectrum of the C~ ions, based upon Reactions 1, 2, 3, and 4, is calculated from the product of Equations V I I and V I I I : G ( C - ) , = G ' ( C - ) , · F (t)

(XI)

fi

The value of F (t) depends upon the initial free ion concentration (see Equation V I I I ) , which in turn depends on the irradiation dose delivered i n the instantaneous pulse (see Equation I X ) . If such a large dose were used that F (t) became appreciably less than unity before geminate neutralization had been completed, this would indicate the occurrence of spur overlap and would alter the calculation somewhat. fi

fi

It can be shown that in the liquids of interest the factor F (t) is within one percent of unity under the following conditions: for times up to 1 X 10" sec, doses up to 200 rad; for times only up to 1 X 10 sec, doses up to 2000 rad; for times up to 1 Χ 10" sec, doses up to 2 Χ 10 rad; and so on. The curves hx Figure 1 extend from 10" to 3 Χ 10" sec fi

e

7

8

4

12


6

344

RADIATION C H E M I S T R Y

II

and it has been assumed that F (t) is unity throughout, so for a pre cision of one percent, the right ends of the curves apply to pulse doses less than about 100 rads. fi

1.0

l>

0.8 0.6


I

U O

"si

•

H 0 2

-

\

V

-

0.4 -

C H OΗ 2

•

s

I

CH COCH^ 3

Q2 -

0,

2

•

11

10

Β 7 «? •LOG t (sec)

6

5

Figure 1. Calculated spectra of lifetimes of solvated electrons after an instantaneous pulse of high energy electrons or x-rays in pure water, ethyl alcohol and cy clohexane. The calculated spectrum of lifetimes of ions in acetone is also included. Liquid temperature, 20°C; pulse dose < 100 rads. The dashed curves on the left side of the figure were drawn arbitrarily. The dashed line on the right end of the ethyl alcohol spectrum indi cates the sum of (e~ + C H 0~) 80lv

2

5

Figure 1 shows calculated plots of G ( C " ) / G ( C ~ ) against t for the pure liquids water, ethyl alcohol, acetone, and cyclohexane. Other rele vant information is listed i n Table I. In pure water and pure cyclohexane the C " ions are probably solvated electrons throughout the times shown in Figure 1. In acetone, C " is assumed to be a negative molecular ion. In ethyl alcohol, the decomposition reaction f

éT

8 0 l v

-> H + C H 0 2

5

0

(5)

s o l v

has a half-life of 5 ± 2 /xsec. at room temperature (15), sofc->« 1.4 X 10* sec." . The pure ethyl alcohol curve i n Figure 1 has been drawn to account for this decay of the free ion solvated electrons; free ions continue to exist for a longer period, but their identities change from solvated electrons to ethoxide ions. To obtain the solvated electron curve, the factor Ffi(t) i n Equation X I was replaced by F -(t), which is given by 1

e

F At)

=e-V

(XII)

The upper end of each calculated curve contains a sharp angle because the N(y) vs. y spectra are very crude i n this region. The real life-


22.

FREEMAN

Table I. Liquid water ethyl alcohol acetone cyclohexane a b c

d


e

345


Data Relevant to the Ion Lifetime Spectra

Κ + u.) (sq. cm./volt sec.)

c

p

80 25 21 2.0

1.00 1.19 1.22 1.22

a

5.4 3 3 3

G /G » fl

0

0.68 0.37 0.33 0.027

Χ 10" Χ ΙΟ" Χ ΙΟ" X 10-3'·' 3d

3 r

3 c

Multiplication factor used to adjust the y values from those in water; see Ref. 6. Calculated from the model. Assumed. See Ref. 19. See Ref. 5.

time curves would probably be rounded, as indicated qualitatively b y the dashed lines. Lifetime spectra of specific types of ions in irradiated solutions could readily be calculated by the method used in the present work. Reactions that occur at times greater than about 10" sec. after the instantaneous pulse occur mainly by homogeneous kinetics. A t times shorter than 10" or 10" sec, the nonhomogeneous kinetics become progressively more important (see Figure 1 ) . If the radiolytic ion is neutralized by an ionic scavenger, e.g., 8

8

9

e" iv + H 0 -> H 0 —> Η + H 0 80

3

+

3

(6)

2

this reaction can readily be included in the kinetic treatment. The Value of the Dielectric Constant Used in Equations II, IV, and V. The curves in Figure 1 were calculated by using the static value of the dielectric constant for each liquid. However, the dielectric constant of a medium is time dependent, because it requires a certain amount of time for the medium to attain its new polarization equilibrium after the sudden application of an electric field. In a polar liquid the permanent molecular dipoles require a certain time to rotate to line up with the electric field. When the value of t is i n the vicinity of or smaller than that of the dielectric relaxation time τ of the liquid—i.e., when t 5 1 0 τ , — then a time-averaged complex dielectric constant should be used i n Equations II, IV, and V . A t a time t after the instantaneous application of a d.c electric field, the dielectric constant of the medium in the field is given approximately by gn

gn

constant. The equation for the real part of the complex dielectric constant in an oscillating electric field of frequency ν is c'(v)=Co

+

C » - € o

1 + (&n0

V


(XIV)

346

RADIATION

CHEMISTRY

II

To convert this equation for use at time t after the instantaneous applica tion of a constant electric surface charge, the angular velocity 2πν of the oscillating field has been equated to 1/t; hence, Equation XIII. (For discussions of complex dielectric constants see Refs. 1, 7, and 2 2 ) . The time averaged value of the dielectric constant, c e, during the period from t = 0 to t = t , is aV

gn


(XV)

It is difficult to know what value of τ to use in Equation X V . The dielectric relaxation time of a liquid is commonly determined from its microwave absorption spectrum. The energy of a microwave photon in the region of the absorption maximum, which is usually at greater than 1 cm. wavelength, is less than 1 X 10 e.v. This is much smaller than ifcT, which is 2.6 X 10~ e.v. at 2 5 ° C . The microwaves therefore do not appreciably perturb the normal thermal agitation of the system during the measurement. However, the sudden creation of a charged species i n a liquid would significantly alter the normal thermal motion of the neigh boring molecules. The ion-dipole interactions would increase the speed with which the nearest-neighbor dipoles would line up with the field of the ion. This means that the ion-dipole interactions would decrease the dielectric relaxation time in the immediate vicinity of the ion. 4

2

Ethyl alcohol w i l l be used as an example. The present discussion is especially pertinent to the radiolysis of alcohols because they have rela tively long relaxation times (8, 10, 21). From a plot of dielectric relaxation data in Ref. 21 it was determined that molecular rotation in liquid ethyl alcohol has an activation energy of 4.6 kcal./mole. In ethyl alcohol at 2 0 ° C , τ = 1.4 Χ 10" sec. ( 2 1 ) , so one can write for the unperturbed relaxation time 10

TC2H5OH

5.4 Χ 1 0

1 4

e*™

0/RT

(XVI)

The ion-dipole interaction exerts a torque on the dipole, which reduces the activation energy of the rotation. For randomly oriented molecules, the average torque U exerted on a molecule with dipole moment μ by a singly charged ion at a distance r through a medium of dielectric constant c is roughly

= 0.64

fr/er

2


(XVII)

22.

FREEMAN

347


where £ = 4.80 Χ 10" e.s.u. It is difficult to make meaningful calcula tions concerning dielectrics on a molecular level, but by treating each layer of molecules around the ion separately, it appears that the rotational relaxation time of the ethyl alcohol molecules between an ion and a localized electron that are separated by 20 A . would be reduced b y about an order of magnitude. In addition to the perturbation caused by U, for the molecular layers outside the first the enhanced rate of reorien tation of an inner layer would collisionally increase the "effective tem perature" of the adjacent outer layer. Furthermore, the effect of the field of the positive ion would enhance that of the localized electron on dipoles situated between them. Downloaded by UNIV LAVAL on July 14, 2016 | http://pubs.acs.org Publication Date: January 1, 1968 | doi: 10.1021/ba-1968-0082.ch022

10

-LOG

t(sec)

Figure 2. Effect of the assumed value of the dielectric relaxation time on the calculated spectrum of lifetimes of solvated electrons in ethyl alcohol. For Curve 1, as in Figure 1, e = c was used for all values of y; time-aver aged complex dielectric constants were used for Curves 2, 3, and 4. For Curve 2, = 1 Χ 10 sec; Curve 3, τ = 3 X 10 sec; Curve 4, = 1.4 X 10~ sec was used at all y x

11

T n

u

Ό

10

TllD

The value of U, and hence the perturbation of the relaxation time, rapidly becomes negligible with increasing r. To simplify the calculations involving Equation X V , the unperturbed value of τ, designated τ , was used for all values of y > 31 A . F o r y ^ 31 Α., a value for the perturbed τ, designated τ , was used. Although the appropriate value of τ may be an order of magnitude smaller than that of τ , the former is uncertain. Therefore, three sets of calculations were done, using different values of T . Values of e were thereby calculated from Equation X V , and electron lifetime curves were calculated from Equations V I , X I , and X I I . In Figure 2, Curves 2, 3, and 4 correspond to the use of τ /τ = 0.07, 0.2, and 1.0, respectively. C u r v ^ j ^ n ^ ^ u r e ^ ^ i s ^ ^ y ^ i y l alcohol curve Μ ρ

ρ

ρ

Μ Ρ

p

a v e

ρ

ηρ

Library 1155 16th S t . M L

WMtiington. D.a


348

RADIATION CHEMISTRY

II

taken from Figure 1, for which the static dielectric constant was used at all values of y. Curves 1 and 4 in Figure 2 correspond to the upper and lower limits, respectively, of the electron lifetime spectrum in y-irradiated ethyl alco hol, according to the present model. The true spectrum probably lies between Curves 2 and 3. A test of the relative appropriateness of the curves i n Figure 2 is the value of G that each predicts. It appears that G ( e " i ) « 4.0 in ethyl alcohol (16), so the predicted values of G are 1.5 for Curve 1, 1.4 for Curve 2, 0.9 for 3 and 0.5 for 4. M a n y workers have experimentally estimated G = 1.0 in ethyl alcohol, and the results of a recent, more complete, scavenger study are consistent with a value of G = 1.5 (16). It may therefore be concluded that the lifetime spectrum lies above Curve 3, and may be in the vicinity of Curve 2. The behavior of radiolytic ions i n other liquids such as water, acetone, and cyclohexane, can be similarly treated. Equation X V I can be generalized to 8 0

fi

v

0

fi

fi


fi

RUP

(XVIII)

= A eBr/RT r

Values of the constants in Equations XIII, X V I I , and X V I I I for water, acetone and cyclohexane at 2 0 ° C , are listed with those for ethyl alcohol in Table II. Table II.

Dielectric Data for Liquids at 2 0 ° C . CH COCH C H OH H0 2

2

^

ο

14

T

a

T

d

s e c > )

up

4.3 25.1 5.4 4.6 1.69 14.

5.2 80.4 0.26 4.8 1.84 0.95

A ( 1 0 " sec.)" E (kcal./mole) μ(άebye) r (ΙΟ"" >

s

3

s

c-C H

1.90 21.2 22. 1.9 2.75 0.33

6

}

2.02 2.02

— —

0

—

rup = Α β*τ/ . The listed values refer to temperatures between 0° and 40°C. and were derived from data in Ref. 21. Tup = \ /2irc, where \ is the critical wavelength and c is the velocity of light; values of \ taken from Ref. 21. See Ref. 21. See Ref. 13. β

κτ

τ

b

c

e

e

e

d

For cyclohexane, e = c , so the dielectric constant is independent of time. The cyclohexane curve in Figure 1 is therefore not altered by using the complex dielectric constant. It turns out that the water and acetone curves in Figure 1 are also not appreciably altered by the use of their respective complex dielectric constants, even if one uses r for all ion separation distances. This is because the dielectric relaxation times of these liquids are so short that a negligible amount of ion neutralization occurs during an interval equal to T . 0

x

up

UP


22.

FREEMAN


349

1

Since t varies as (M + w.)" , the upper limit of the dielectric relaxation time, Ti , for which it is permissible to use c» at all values of y is proportional to (u + u.)' . To sum up, when (u + « . ) = 5 X 10" sq. cm./volt sec, one may use € at all values of y in liquids that have dielectric relaxation times 1 χ 10" sec, and Ti a(u + «-) · When tg < 10T, the time-averaged complex dielectric constant is required; the perturbed relaxation time τ should be used for τ in Equation XV. The estimation of ion lifetimes in the radiolysis of ethyl alcohol, and of all alcohols, appears to require the use of the complex dielectric constant, but € may be used in the calculations for water, acetone, and hydro carbons. Comparison of Measured and Calculated Ion Lifetimes. The yield of biphenyl or anthracene ions in cyclohexane, observed by pulseradiolysis-absorption-spectroscopy, was 10%-20% greater at a few tenths of a microsecond than it was at 2-3 microseconds (11). Each of these solutes captures both positive and negative charges, so in each case the observed neutralization reaction was S + S" -» product (7) where S represents the solute. Thus, (u + u.) « 7 Χ 10" cm. /volt sec. (5). Using the present model, the calculated value of G(S + S") at 2 χ 10" sec. is 20% higher than that at 2 X 10" sec, in agreement with experiment. More recently it was observed that there was no significant decay in the yield of solvated electrons in water between 5 Χ 10" and 5 Χ 10" sec. (9). Time was measured from the beginning of the 3 Χ 10" sec. pulse of 3 m.e.v. electrons (pulse dose « 1 X 10 rad). Within experi mental error, there was no decay at times greater than 5 Χ 10" sec. (9). The present model predicts that there would be only one percent decay of solvated electrons in water between 5 Χ 10" and 5 Χ 10" sec, and six percent decay between 5 Χ 10" and 5 Χ 10" sec. These values are consistent with the observations. gn

+

im

1

3

+

+

χ

11

1

im

+

n

ρ


x

+

4

2

+

+

7

e

9

8

9

3

10

9

10

8

8

Literature Cited (1) Brown, W. F., "Handbuch der Physik," Vol. 17, pp. 119-121, SpringerVerlag, Berlin, 1956. (2) Dorfman, L. M., Matheson, M. S., Progr. Reaction Kinetics 3, 237 (1965). (3) Freeman, G. R.,J.Chem. Phys. 39, 988 (1963). (4) Ibid., 41, 901 (1964). (5) Freeman, G. R., J. Chem. Phys. 46, 2822 (1967). (6) Freeman, G. R., Fayadh, J. M.,J.Chem. Phys. 43, 86 (1965). (7) Frohlich, H., "Theory of Dielectrics," p. 73, Clarendon Press, Oxford, 1949. (8) Garg, S. K., Smyth, C. P.,J.Phys. Chem. 69, 1294 (1965). (9) Hunt, J. W., Thomas, J. K., Radiation Res. 32, 149 (1967).



350

RADIATION CHEMISTRY II

(10) Imanov, L. M., Mirzoev, F. G, Zul'fugarzade, Κ. E., Russ. J. Phys. Chem. 39, 1518 (1965). (11) Keene, J. P., Land, E. J., Swallow, A. J., J. Am. Chem. Soc. 87, 5284 (1965). (12) Lea, D. E., "Actions of Radiations on Living Cells," 2nd ed., Chap. 1, Cambridge University Press, 1955. (13) Partington, J. R., "An Advanced Treatise on Physical Chemistry," Vol. 5, pp. 507, 522, Longmans, Green & Co., London, 1962. (14) Robinson, M. G, Freeman, G. R.,J.Chem. Phys. 48, 983 (1968). (15). Russell, J.C.,Freeman, G. R.,J.Phys. Chem. 71, 755 (1967). (16) Ibid., 72,808(1968). (17) Ibid., 72, 816 (1968). (18) Russell, J.C.,Freeman, G. R., J. Chem. Phys. 48, 90 (1968). (19) Schmidt, K., Buck, W., Science 151, 70 (1966). (20) Stover, E. D., Freeman, G. R.,J.Chem. Phys. (in press). (21) "Tables of Dielectric Dispersion Data," Nat. Bur. Std. Circ. 589 (1958). (22) von Hipple, A. R., "Dielectric Materials and Applications," Chap. 1, John Wiley & Sons, New York, 1954. (23) Walker, L. G., Ph.D. Thesis, University of Alberta, 1967. RECEIVED December 5, 1967.


Ion Neutralization Times in the Gamma or Electron Radiolysis of

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