Title: Monte Carlo simulation of indirect damage to biomolecules irradiated in aqueous solution--the radiolysis of glycylglycine /
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Permanent Link: http://ufdc.ufl.edu/UF00098256/00001
 Material Information
Title: Monte Carlo simulation of indirect damage to biomolecules irradiated in aqueous solution--the radiolysis of glycylglycine /
Physical Description: vii, 178 leaves : ill. ; 28 cm.
Language: English
Creator: Bolch, Wesley Emmett, 1961-
Publication Date: 1988
Copyright Date: 1988
Subject: Glycylglycine   ( lcsh )
Glycine   ( lcsh )
Microdosimetry   ( lcsh )
Monte Carlo method -- Computer programs   ( lcsh )
Environmental Engineering Sciences thesis Ph. D
Dissertations, Academic -- Environmental Engineering Sciences -- UF
Genre: bibliography   ( marcgt )
non-fiction   ( marcgt )
Thesis: Thesis (Ph. D.)--University of Florida, 1988.
Bibliography: Includes bibliographical references.
Statement of Responsibility: by Wesley Emmett Bolch.
General Note: Typescript.
General Note: Vita.
 Record Information
Bibliographic ID: UF00098256
Volume ID: VID00001
Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
Resource Identifier: alephbibnum - 001125858
oclc - 20117707
notis - AFM2981


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This research was performed at the Health and Safety Research

Division of the Oak Ridge National Laboratory (ORNL), Oak Ridge,

Tennessee. During his graduate studies, the author was under

appointment to the Nuclear Engineering and Health Physics Fellowship

Program administered by Oak Ridge Associated Universities for the U.S.

Department of Energy.

The author wishes to acknowledge the principal developers of the

Monte Carlo computer codes OREC, SPCS, and RADLYS. These individuals

are Dr. Robert Hamm, Dr. Harvel Wright, Dr. Rufus Ritchie, Dr. James

Turner, and Dr. Cornelius Klots of the Oak Ridge National Laboratory,

and Dr. John Magee and Dr. Aloke Chatterjee of the Lawrence Berkeley

Laboratory. These three computer programs formed the foundation upon

which the simulation codes of this dissertation were constructed.

The author wishes to thank Dr. James Turner for serving as his

research advisor during the past three years. The author found it a

privilege to work for such a distinguished and understanding individual.

The author would also like to thank Dr. Harvel Wright, Dr. Robert Hamm,

and Dr. K. Bruce Jacobson for their useful discussions during this

research. The author would like to thank both Dr. Rufus Ritchie for

developing the electron thermalization scheme used in this dissertation

and Dr. Hiroko Yoshida for her experimental data which supported the

computer simulations of this research. In addition, the author

expresses his appreciation to Dr. Warren M. Garrison for his comments

and suggestions.

Finally, the author wishes thank his wife, parents, and family for

their continued and steadfast support.


ACKNOWLEDGMENTS ..................................................... ii

ABSTRACT ................... ... ........ ...... ................. .... vi


1 INTRODUCTION ................ .. ................................1

Radiolysis of Pure Liquid Water ..................................4
Research Objective .............................................. 10

2 OAK RIDGE MODEL FOR WATER RADIOLYSIS............................17

Physical Stage.................................................. 18
Prechemical Stage .............................................. 28
Early Chemical Stage ............................................30

3 MODIFICATIONS TO THE OAK RIDGE MODEL ............................41

Thermalization of Subexcitation Electrons.......................41
Time Decay of Hydrated Electrons and OH Radicals ................50
Additional Chemical Reactions ...................................52
Location of Reaction Sites ..................................... 63
Precision of Reported Product Yields ............................64
Critique of Model............................................... 65

GLYCYLGLYCINE RADIOLYSIS................... .................. 70

Glycylglycine Structure........................................ 74
Initiating Reactions ............................................76
Chemistry in Deoxygenated Solution ..............................80
Chemistry in Oxygenated Solution ............................... 88


Calculations for X Irradiation............. ...... ..............99
Calculations for 6"Co Gamma Irradiation ........................105

FOR MONOENERGETIC ELECTRONS..................................111

Free Ammonia.................................................. 113
Other Products.................................... ...............123

IN IRRADIATED SAMPLES....................................... 132

Free Ammonia.................... ............................... 133
Other Products................................................. 144


Summary ....................... ......... ..................... 158
Conclusions ....................... ........... .................161
Recommendations ................................................ 164

REFERENCES ........................................................... 171

BIOGRAPHICAL SKETCH ..................................................178

Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy





Chairman: Charles E. Roessler
Major Department: Environmental Engineering Sciences

The objective of this dissertation is to determine the feasibility

of studying indirect damage to biological molecules irradiated in

aqueous solution using detailed Monte Carlo computer simulations. The

molecule glycylglycine is chosen for this study primarily because its

radiation chemistry is reasonably well characterized, thus limiting the

number of unknowns in the modeling effort. Good agreement between

calculated and measured yields of radiolysis products supports this

calculational technique and its usefulness in investigating more complex

molecules, such as DNA.

The study involves three major tasks. First, a Monte Carlo

computer code is developed for simulating the radiolysis of

glycylglycine in both oxygenated and deoxygenated aqueous solution.

Second, this model is used to calculate the yields of various products

in solutions irradiated either by 250-kVp X-rays or by 6OCo gamma rays.

Third, calculated product yields are compared to measured yields where


The Monte Carlo computer codes used in this study are modified and

extended versions of three existing simulation codes, written at the Oak

Ridge National Laboratory (ORNL), which simulate irradiations of pure

liquid water. The ORNL codes calculate the formation, diffusion, and

reaction of free radicals and other species along charged-particle

tracks in liquid water. As part of this research, these codes are

extended to simulate irradiation of pure oxygenated water, oxygenated

glycylglycine solutions, and deoxygenated glycylglycine solutions.

Ammonia is released from the reaction between glycylglycine and

hydrated electrons within the track. In simulated irradiations of

deoxygenated glycylglycine solutions by 250-kVp X-rays. calculated

yields of ammonia are in statistically significant agreement with

measured yields. In addition, calculated yields of ammonia produced

during 6OCo gamma irradiation are shown to be greater than calculated

yields of ammonia produced during X irradiation. The Monte Carlo code

readily shows that this difference is attributable to track-structure

effects. This study concludes that Monte Carlo simulations represent a

unique and feasible method of understanding indirect radiation damage at

the molecular level.




Since the release of the International Commission on Radiological

Protection's Publication 26, recommended limits of exposure to ionizing

radiation have been based upon the risk of stochastic and nonstochastic

effects (ICRP 1977). Central to this system of radiation protection are

risk estimates for human cancer induction and germ cell mutation at low

doses and at low dose rates. Current risk estimates are primarily

obtained through extrapolation of human and animal data at high doses

and dose rates using an assumed shape of the dose-response function at

lower dose levels. Since actual risks of stochastic effects are small

and these effects occur naturally, any epidemiological study seeking to

statistically verify risk estimates at low doses would require a

prohibitive number of subjects. Consequently, efforts to quantify the

dose-response function cannot rely solely upon empirical observation,

but must include research into the mechanisms and supporting theory

behind carcinogenesis and mutagenesis (Upton 1982; Sinclair and Fry


Deoxyribonucleic acid (DNA) has long been recognized as a critical

molecular target for radiation-induced stochastic effects (Sonntag.

1987). The ultimate expression of these effects can be attributed to

three fundamental processes: (1) the creation of damage sites in

cellular DNA by ionizing radiation; (2) the enzymatic repair of damage

sites by the cell; and (3) the propagation of unrepaired damage and its

subsequent effects on cellular growth and function. Studies have

revealed many details of the latter two processes (Sinclair and Fry

1987). From investigations into the first process, it is known that

irradiation of DNA produces strand breaks, base damage, base deletions,

DNA-DNA crosslinks, and DNA-protein crosslinks. What is poorly

understood, however, are the physical and chemical mechanisms by which

radiation produces these types of damage. All three processes, however.

must be understood to some degree of detail before a theoretical

derivation of the risk of stochastic effects is feasible.

In an attempt to identify the fundamental mechanisms of

radiation-induced damage to DNA. a collaborative investigation was

initiated between researchers in the Health and Safety Research Division

and the Biology Division of the Oak Ridge National Laboratory (ORNL)

during the summer of 1986. This effort proposes investigating various

molecular systems of increasing complexity. These systems would begin

with simple amino acid polymers and would then be extended stepwise

through artificially-synthesized DNA subunits of increasing complexity,

ultimately to DNA itself.

For each molecular system, two coordinated investigations would be

carried out--one experimental and one calculational. In the

experimental effort, aqueous solutions of the molecule would be

irradiated and the chemical yields of radiation products measured.

In the calculational effort, the radiation experiment would be

simulated in complete detail by a Monte Carlo computer model. This

computer model would incorporate specific reaction mechanisms that lead

to the observable quantitative chemical yields. Comparison of

calculated and experimental yields could thus be used to develop a

detailed understanding of the mechanisms and pathways by which radiation

produces damage at the molecular level. In many instances, this

modeling effort would be a first attempt at linking the detailed physics

of radiation energy deposition to the detailed chemical damage

subsequently produced within biomolecules.

This dissertation presents simulations of the first molecular

system to be studied under this new technique. The first system chosen

is glycylglycine (a dimer of the amino acid glycine) in aqueous

solution. This system has three characteristics which make it a

suitable candidate for initial investigation. First, mechanisms of

glycylglycine radiolysis have been proposed by past researchers (Makada

and Garrison 1972; Garrison et at. 1973); thus a framework for model

development already exists. Second, the reactions exhibit very little

feedback, a fact that, while non-essential, simplifies the simulations.

Third, glycylglycine is a relatively small molecule. Consequently, at

concentrations 1.2 M, radiation damage is mostly caused by attack of

free radicals produced during irradiation of surrounding water (indirect

effects), and not by direct interaction with the incident radiation or

its secondary charged particles (direct effects).

Radiolysis of Pure Liquid Water

Radiolysis is defined as chemical decomposition by the action of

radiation. By considering a small volume within an irradiated medium,

the events which precipitate chemical change can be described in stages.

If the volume has dimensions no larger than a few tens of nanometers,

these stages begin, at a reference time zero, with the traversal of a

charged particle produced directly or indirectly by the radiation

source. Only in the case of very high dose rates would this volume be

traversed by a second charged particle at a time prior to the completion

of these stages. Table 1-1 summarizes the events which characterize

these stages and their associated time periods.

Physical Stage

A charged-particle traversing a water volume transfers its energy

through inelastic collisions resulting in ionization or excitation of

water molecules. Elastic collisions result in a change in trajectory of

the primary particle with negligible energy transferred to the water

medium. Secondary electrons produced in ionizations may have sufficient

energy to ionize and excite water molecules, yet are eventually degraded

in energy below the threshold for producing further electronic

transitions. The primary particle thus leaves in its wake a track of

ionized water molecules (H20O), excited water molecules (H20 ), and
subexcitation electrons (esub). These events are complete by 10- s

since the passage of the primary particle.

Table 1-1

Stages of Radiolysis for Low-Dose-Rate Irradiations

Stage Time Period (s) Events

Physical 0 10-15 Production of H20 H,20, and eub

Prechemical 10-15 1012 Production of H, OH, H2, H202,
H.30, and e

-12 -6
Early Chemical 101 10 Diffusion of track species

Chemical reactions within
individual charged-particle

Late Chemical > 10-6 Diffusion of track species

Chemical reactions between
neighboring charged-particle

When the water medium is in the liquid state, the creation of H20+

and H20 are not always localized at the site of initial energy transfer

(Heller et at. 1974; Ritchie et at. 1978). Inelastic collisions in

liquid water can result in energy transfers involving ~10 electrons.

These collective excitations eventually produce an HO+ or H20 at a

site which can be located up to nanometers from the trajectory of the

primary particle. This delocalization of energy transfer can play an

important role in the subsequent chemistry of the charged-particle


The mean rate of energy loss by a charged particle per unit

pathlength x in a given medium is called the stopping power of the

medium, (-dE/dx). The stopping power of liquid water for electrons, as

given by theoretical calculations, is shown in Fig. 1-1. Above 1 MeV,

-dE/dx gradually increases due to radiative losses and a relativistic

rise in collision losses. The stopping power of liquid water for a

charged particle is also referred to as that particle's unrestricted

linear energy transfer, or LET.

Prechemical Stage
-15 -12
During the time period from ~101 s to ~101 s, the medium

responds to initial changes produced during the physical stage, yet

there is not time enough for appreciable diffusion and chemical reaction

to take place. An ionized water molecule is thought to react quickly

with a neighbor water molecule forming a hydronium ion and a hydroxyl




-o U

-- a




0 0 0

- 1 0 I n

OA -o XP/3

(wuo/A8) xp/3p- m

H20, + H2O --- H30 + OH (1-1)

There is experimental evidence (Ogura and Hamill 1973; Hamill 1969) that

the H20 may first migrate (via charge transfer) several tenths of a

nanometer before undergoing reaction (1-1). Depending upon the

particular molecular transition involved, excitations are thought to

either dissociate according to

H2 { H + (1-2OH
H2-- +0 (1-2)

or autoionize with the resulting H20+ undergoing reaction (1-1). The

oxygen atom in reaction (1-2) reacts with a neighboring water molecule

to form hydrogen peroxide. Also during this time, subexcitation

electrons continue to lose energy through vibrational and rotational

excitations of the surrounding medium, eventually reaching thermal
energies. They become hydrated by ~101 s and are denoted by the

symbol e

Early Chemical Stage
At ~1012 s, a charged-particle track consists of a spatial

distribution of OH, H, H2, H202, HoO+, and e These species
subsequently undergo diffusion and chemical reaction within the track,

resulting in a net decrease of OH, H, e and H30 and a net increase

of H2, H202, and OH After ~10- s, the track species have diffused to

such an extent that further intratrack reactions are very unlikely and

all details of track structure are lost.

Two factors which can provide additional reactions during the early

chemical stage are the presence of a radical-scavenging solute and track

overlap during irradiations at high dose rates. Radical scavengers

compete with intratrack reactions at times dependent upon their
concentration. Scavenging reactions are appreciable at -10 s at one

millimolar scavenger concentrations and at 1010 s at one molar

scavenger concentrations (Wright et at. 1985a). In addition, the degree

to which scavenging reactions compete for species within the track

lessens with increases in particle LET.

For systems irradiated at very high dose rates, charged-particle

tracks can be produced in both temporal and spatial proximity. Under
these conditions, intertrack reactions occur at times prior to 10- s.

Examples include systems irradiated by pulses of accelerated electrons,

as in pulse radiolysis experiments.

Late Chemistry Stage

With the completion of intratrack reactions, all remaining species

continue to diffuse and react with species from neighboring tracks. At

high dose rates, this late chemistry stage is characterized primarily by

inhomogeneous reactions occurring within track overlap. At lower dose

rates, little overlap occurs before the remaining species have diffused

far apart and the chemistry of the system quickly becomes one of

homogeneous, steady-state reactions. The time at which the number of

intertrack reactions exceeds the number of intratrack reactions is thus

dose-rate dependent. At low dose rates, this time is ~10- s.

Research Objective

The objective of this dissertation is to determine the feasibility

of studying indirect radiation damage to glycylglycine through detailed

Monte Carlo computer simulations. This task is accomplished in three

stages. First, a computer model is developed for single-track

simulations of glycylglycine radiolysis, through the early chemical

stage, in both oxygenated and deoxygenated solutions. Second, this code

is used to calculate microsecond yields of various radiation products.

Third, these calculated yields are compared to experimental values where

available. If reasonable agreement is shown, the calculational approach

and its usefulness in investigating more complex molecular systems will

be supported.

Table 1-2 summarizes the modeling effort of this and previous

studies, along with experimental data currently available with which to

make comparisons. The left-hand column lists the four stages of

radiolysis, while the remaining columns correspond to three model

systems of interest: pure water, deoxygenated glycylglycine solutions,

and oxygenated glycylglycine solutions. For the pure water system, a

computer model simulating the first three stages was developed at ORNL.

Time-dependent yields of OH and eaq calculated by this code for the



SW b

0N "







4 1) 4 U
*0 0
) 0 0 A 0
b- d 0 d o-

o0 *



4)L C4 -4) -
OC -C 0o 0)o4o

Wi u ) ajW Z W 4) a4)
S EQ. =A > 2. a .a
cil in- r x r S T

0> l l )

4 )
o ow


early chemical stage can be compared to pulse radiolysis measurements in

the open literature (Jonah et at. 1976; Jonah and Miller 1977; Sumiyoshi

and Katayama 1982). In addition, analytical techniques exist for

calculating product yields at late times (Chatterjee et at. 1983; Boyd

et at. 1980). Experimental data also exist for this late chemistry

stage (Hochanadel 1952).

At glycylglycine concentrations 1.2 M, indirect radiation effects

dominate and the Oak Ridge model can therefore be used, as is, to

simulate the physical and prechemical stage of glycylglycine radiolysis

(see Table 1-2). Thus, this dissertation primarily involves the

development of a simulation code for the early chemical stage of

glycylglycine radiolysis in both oxygenated and deoxygenated solutions.

Future efforts will include modeling the late chemistry stage of

glycylglycine radiolysis by applying the techniques of Chatterjee et at.

(1983) to the microsecond yields calculated in this dissertation.

Several end products are formed as a result of glycylglycine

radiolysis. Experimental efforts at ORNL currently provide yields of

both free ammonia and glycylamide as functions of glycylglycine

concentration. These yields are determined under irradiation by 250-kVp

X-rays for both deoxygenated and oxygenated systems (Yoshida et at.

1988). In addition, previous studies provide yields of free ammonia and

several other radiolysis products created in both oxygenated and

deoxygenated systems under 6"Co irradiation (Makada and Garrison 1972;

Garrison et at. 1973).

Free ammonia in deoxygenated solution is the only radiolysis

product whose creation is complete within the early chemical stage.

Consequently. experimental support for the simulations performed in this

research is limited to comparing calculated and experimental yields of

free ammonia in deoxygenated solution. Although no direct comparisons

can be made, microsecond yields of additional intermediate products are

also calculated for this system.

Product yields are commonly reported as G-values, the number of

molecules produced per 100 eV of energy deposited in the system, and are

determined as functions of solute concentration. In order to make

comparisons with measured G-values of free ammonia produced in

photon-irradiated systems, calculated yields are determined as follows.

By definition,

S (100) Nt(C)
G(NH,.C) = E (1-3)

where G(NH3,C) is the G-value of free ammonia at glycylglycine

concentration C, Nt(C) is the total number of NH3 molecules produced at

concentration C, and Et is the total energy deposited in eV. Since a

distribution of electron energies is produced during irradiation,

(100) N(NHLC,E) t(E)dE
G(NH3,C) = (1-4)

E t(E)dE

where N(NH3,C,E) is the mean number of NH, molecules produced at

concentration C by electrons with initial energy E, t(E)dE is the total

number of electrons produced with initial energies between E and E + dE,

and E is the maximum initial energy of electrons produced by the
f f
incident radiation. Furthermore, N(NH..C.E) can be expressed as

S(NH3,C,E) E
N(NH3,C.E) = (1-5)

where G(NHfC,E) is the mean C-value for free ammonia production at

glycylglycine concentration C produced by electrons with initial energy

E. By substituting Eq. (1-5) into Eq. (1-4),

x (NH,C.E) E t(E)dE
G(NH IC) = 0 (1-6)
f max
SE t(E)dE

( max
G(NH,.C) = J G(NH3,C,E) W(E)dE (1-7)

where W(E)dE represents the fraction of total energy deposition

contributed by electrons of initial energy E per energy interval. By

this method, G-values calculated for comparison with experiment require

separate determinations of W(E)dE and G(NH3,C,E). Microsecond yields of

additional intermediate products are calculated in a similar manner:

G(X,C,s) = J (X,C,ps.E) W(E) dE (1-8)

where G(X,C,.s,E) is the mean microsecond G-value of product X produced

by electrons of initial energy E in a solution of glycylglycine at

concentration C.

The development of a complete track model for glycylglycine

radiolysis is presented in Chapters 2 through 4. Chapter 2 details the

existing ORNL model for the physical, prechemical, and early chemical

stages of liquid water radiolysis. Chapter 3 describes various

modifications and improvements which were made to the ORNL model during

this research, yet were still within the context of pure water

irradiation. Chapter 4 details the development of a model for the early

chemical stage of glycylglycine radiolysis in both oxygenated and

deoxygenated systems.

Calculated yields of free ammonia in deoxygenated solution are then

presented in Chapters 5 through 7. Chapter 5 gives calculations of


electron spectra for both X-ray and 60Co irradiations, while Chapter 6

presents microsecond yields of free ammonia and additional intermediate

products calculated for monoenergetic electrons. The results of

Chapters 5 and 6 are then used in Chapter 7 to calculate free ammonia

yields in systems irradiated either by both X-rays or by 60Co gamma

rays, followed by comparison with measured values. Conclusions drawn

from this modeling effort and recommendations for future investigations

are presented in Chapter 8.



The Oak Ridge model for water radiolysis was developed at the

Health and Safety Research Division (formerly the Health Physics

Division) of the Oak Ridge National Laboratory (Hamm et at. 1976;

Ritchie et al. 1978; Turner et al. 1981; Wright et al. 1983; Turner et

al. 1983; Hamm et al. 1985: Wright et at. 1985a; Wright et al. 1985b;

Turner et at. 1988a; Turner et al. 1988b). The model is incorporated

into three Monte Carlo computer codes, OREC, SPCS, and RADLYS. These

codes correspondingly simulate the physical, prechemical, and early

chemical stages of charged-particle track development in liquid water.

The late chemistry stage, if needed, can be treated in a separate set of


Furthermore, two versions of OREC exist--one for transporting

electrons and one for transporting protons or alpha particles. Since

all experiments in the ORNL project have been limited thus far to photon

irradiations, only the electron transport version of OREC will be

discussed in this and in other chapters. It is important to note,

however, that simulation codes for the other stages of radiolysis are

applicable for any charged-particle track. This is true for both the

pure water codes presented in this chapter and also the simulation code

for glycylglycine radiolysis presented in Chapter 4.

Physical Stage

The Oak Ridge model for the physical stage was formulated in two

phases. First, inverse mean free paths macroscopicc cross sections) for

inelastic and elastic electron-liquid water interactions were compiled

from experimental data in all three phases and from theoretical

calculations. Second, an electron transport code based upon these cross

sections was developed; the code follows a primary electron and all of

its secondary electrons through liquid water until their energies fall

below the threshold for further electronic excitation. The transport

code records the spatial location of all inelastic events and

subexcitation electrons for subsequent development of the track during

the prechemical stage.

Inverse Mean Free Paths for Inelastic Scattering

The cross sections for inelastic scattering are obtained from

dielectric theory in which liquid water is assumed to respond to the

passage of charged particles as any dielectric medium responds to an

electromagnetic disturbance (Heller et at. 1974; Ritchie et at. 1978).

This response is quantitatively characterized by the medium's complex

dielectric function e(w,q), where o and q are, respectively, the energy

and magnitude of the momentum transferred to the medium by the

disturbance. Cross sections derived from E(w,q) include the a prior

collective effects characteristic of the condensed phase.

The principal cross section derived from dielectric theory is the

total differential inverse mean free path (total DIMFP), dp/du, and is

the probability an electron of energy E will have an energy loss between

w and w + du per unit length traveled per unit energy lost. The total

macroscopic cross section of the medium at energy E is obtained by

integrating dp/du over all possible energy losses. For non-relativistic

electrons, the total DIMFP is given by

d_ 1 2 (.q) _d6 (2-1)
d = E Jq- el2(,q) + 2(w.q) q

where E is the electron energy, al and e2 are the real and imaginary

parts of the dielectric function, and q are the kinematic limits of

momentum transfer. All quantities are in atomic units such that

energies are given in multiples of 27.2 eV and lengths are given in

multiples of 0.0529 nm. Modifications to Eq. (2-1) are used for

electrons of relativistic energies. The fraction involving e1 and 62 in

the integrand is the energy-loss function Im(-l/e), the imaginary part

of the complex function (-1/e). A plot of this quantity for liquid

water, which forms a three-dimensional surface as a function of W and q,

is shown in Fig. 2-1. The regions corresponding to excitation and

o O-


Fig. 2-1. Energy-loss function Im[-1/e(w,q)] for liquid water above
the plane Im(-1/e) = 10-'5, with w in eV and q in atomic
units (Turner et at. 1988b).

ionization, which merge in the q = 0 plane, separate at higher values of

q. The ridge on the right at relatively large o is due to K-shell

ionization of oxygen, which has a threshold of 540 eV.

The energy-loss function in Fig. 2-1 is based on experimental data

for water in all three phases and on theoretical principles. At values

of q much larger than the mean momentum of electrons in the ground state

of the medium, it is expected that target electrons will respond as if

free and initially at rest. Values of o and q thus become uniquely

related and the energy-loss function corresponding to ionization

approaches a sharp structure referred to as the Bethe ridge.

Values for the energy-loss function in the q = 0 plane are obtained

directly from the optical data for liquid water. In this system,

photons transfer energy but not momentum to the media surface, and

e1(w.0) and a2(w,0) are inferred from measured values of surface

reflectance at photon energy E = w (Heller et at. 1974). The values of

a2(wO) and el(w,0) are then fit using the functional forms

62(,O) = p 2 2 n2n 22 (2-2)
(E [(E u )2 + 22
n n n

2 2 2 2 2 2 2
e1(w,0) = 1 + u 2 n n 2 2 n2 2 (2-3)
In2 22 222,(2-3)
n [(E w ) +r2
n L-n n -

where pu = 4rN N is the density of water molecules, E are resonance
p m m n
energies, n are damping constants, and f are oscillator strengths, all

taken to be fitting parameters.

Values of the energy-loss function in the q X 0 portion of the q-W

plane are extrapolated by allowing the fitting parameters En and -n to

become q-dependent. Constraints on fitting parameters are dictated by

certain quantum-mechanical sum rules such as

Se2(q) d = Z 2 (2-4)

f Im do = --Z 2 (2-5)
o E(,q) J 2 p

where Z is the number of electrons per water molecule.

To account for different modes of energy absorption in liquid

water, the total DIMFP is partitioned into 11 partial DIMFP's, each

associated with a particular excitation or ionization transition of the

water molecule. These transitions are listed in Table 2-1 along with

their classification type used in the transport code. The partitioning

of cross sections is accomplished by associating e2 (w,q) with the jth

mode of energy absorption such that e2(w,q) = j e2 ()w,q). The

partial DIMFP for the jth mode of energy absorption, d j/dw, is then


Modes of Electronic


Energy Absorption

Interaction Type Presumed Transition

Excitations: 1 A1B1

2 BgA1

3 Rydberg A+B

4 Rydberg C+D

5 Diffuse Band

6 Dissociative Excitation

Ionizations: 7 K-Shell

8 lb1

9 3al

10 lb2

11 2a

Note: Notation for excitations from Green and Rio (1982)
and ionizations from Tan et al. (1978).

defined by replacing e2(Pq) in the numerator of the integrand of Eq.

(2-1) by e2 ()(q).

Inverse Mean Free Paths for Elastic Scattering

Data on the elastic scattering of electrons in liquid water do not

exist. Therefore, total and differential scattering cross sections for

atomic hydrogen and oxygen are used under the assumption that electrons

scatter incoherently in liquid water. For electron energies up to 1000

eV, scattering probabilities are obtained from phase shift calculations.

Cross sections at higher energies are obtained by using the Thomas-Fermi

model in the first Born approximation. In this model, the total elastic

cross section as a function of velocity v and atomic number Z is

approximated by

,rZ 1
S= 4 2 1 (2-6)
v a2(1 + a2)

0.565 Z1/3s
a = (2-7)

and s is an adjustable parameter of the order of 0.66. The angular

distribution is approximated by

d _____Z2_______
d9 4 2 2 (2-8)
d 4v4(a2 + sin 2 (2-8)

where 8 is the polar angle of scatter.

Electron Transport

The electron transport code OREC models the physical process of

energy deposition by electrons in liquid water. The code begins by

considering a primary electron in a liquid-water medium with a given

initial energy and trajectory. A flight distance is selected for the

primary electron based upon the total inverse mean free path for all

elastic and inelastic collisions at that electron energy. The electron

is then moved to this collision site. Next, a type of interaction is

selected based on the partial IMFP's at that same energy.

If a collision is elastic, an angle of scatter is selected from Eq.

(2-8) and the flight distance to the next interaction is chosen. If a

collision is inelastic, an energy loss is selected based upon the

partial DIMFP for that event type and at that electron energy. If the

energy loss is less than 50 eV, a delocalization of the energy transfer

is allowed to occur. This delocalization is a consequence of collective

effects in the condensed phase and is modeled by displacing the

interaction site through a lateral distance r in a random direction

azimuthal to the incident particle's path. The distance r is chosen

from the distribution

P(r)dr = 2 2 (2-8)
r + b

where w is the energy loss, v is the particle's velocity, and b and -

are constants (taken to be 0.2 nm and 5, respectively, for liquid


If an inelastic collision is an excitation, the electron's energy

is reduced by the energy loss selected and the electron is allowed to

continue in its precollision direction. If an inelastic collision is an

ionization, the electron's energy is also reduced by the energy loss

selected, but is allowed to scatter as though it collided with a free

electron. The secondary electron produced is scattered as though

initially free and is given an energy equal to the energy lost by the

primary electron minus the binding energy of the target electron.

Each time a secondary electron is produced, the code continues by

transporting the electron with the lowest kinetic energy. When that

electron's energy falls below 7.4 eV, the assumed threshold for further

electronic excitation of liquid water, the code proceeds by transporting

the higher-energy electron. This process is continued until all of the

original electron's energy is expended in the creation of H0* H20 ,

and subexcitation electrons. The output of OREC is then the spatial

location of these three species.

As an example of these calculations, Fig. 2-2 shows the complete

tracks of six 800-keV electrons all starting at the same location and

traveling horizontally to the right. The plots were made by marking a

0 *



0 0)
0 *


z > >

o Ll
0 i

C ,)











dot at the projected location of every fifth inelastic event experienced

by the primary electron or one of its secondaries. Several physical

aspects of electron tracks are evident. Elastic scattering becomes more

pronounced as the electron losses energy, resulting in an increasingly

wandering track. Delta rays produced at sites of high energy loss are

also shown. Finally, the increase in stopping power at lower electron

energies (Fig. 1-1, p. 7) is evident as each track plot becomes

increasingly darker along its length.

Prechemical Stage

This stage of track development is characterized by the conversion

of the species H20 H20. and esub into chemical reactants. In the

simulations, this process is associated with the time period 10-5 s to
101 s with respect to local regions of a charged-particle track. The

prechemical stage is modeled by the code SPCS whose input is the spatial

location of all H20 H20 and eub 's computed by the transport code


When an H20 is formed, it is first allowed to migrate in a random

direction through a distance selected from a Gaussian distribution with

a mean displacement 0.75 nm. It then reacts with a neighboring water

molecule according to

HO+ + H20 --* H30 + OH. (2-9)

At 10-12 s, the products on the right replace the original H20 and are

separated by a distance chosen from a Gaussian distribution with a mean

value of 0.29 nm, the diameter of a water molecule. Since it is not

known in which direction the hydrogen atom transfer occurs, the position

of the H,0+ is taken to be that of the original H20+ in 50% of the

reactions, with the OH radical placed about it in a randomly selected

direction. The positions of the two species are reversed in the other

50% of the reactions.

When an H20 is formed, one of several subsequent pathways is

chosen, depending on which of the six specific excited states is

involved (see Table 2-1, p. 23). The A1B1 and B1A transitions (event

types 1 and 2) result, respectively, in the following two dissociations:

H20 --{ H+H (2-10)

The oxygen radical produced in the second dissociation is assumed to

react quickly with a neighboring water molecule to form H202. In the

other excitations (event types 3 through 6), which include high Rydberg

states seen in water vapor, it is assumed that an electron can be lost

to surrounding water molecules, leading to the formation of H20 and

reaction (2-9).

The subexcitation electrons formed in the physical stage thermalize
and become hydrated by 101 s. A hydration distance is randomly

selected for each subexcitation electron from a Gaussian distribution

with a mean displacement of 3 nm. Each subexcitation electron is thus

displaced by this distance in a random direction after which it is

designated a hydrated electron, eaq. A mean hydration distance of 3 nm

is used so as to obtain agreement between calculated and measured yields

of OH and e during the early chemical stage.
As an example of the calculations made at this stage of electron

track development. Fig. 2-3 shows the spatial location of reactive

species produced in the first 32 nm of a 4-keV electron track. The

electron was started at the origin in an initial trajectory along the

horizontal axis. A clustering of species is evident with hydrated

electrons spread over a somewhat greater volume than the other


Early Chemical Stage

The early chemical stage of track development is modeled by the

computer code RADLYS and is associated with the time period 101 s to
10- s with respect to local regions of the track. During this

interval, reactive species produced within the track undergo diffusion



I I a
OI or






.- ,


4) P


.- 4)


,- *




and chemical reaction. These processes are simulated using

relationships drawn from diffusion and collision theory.

Theory of partially diffusion-controlled reactions

The thermal motion of chemical reactants can be viewed on a

molecular level as discrete displacements, or "jumps," between molecules

of the surrounding medium. Starting with Fick's first law of diffusion,

one can ascribe a root-mean-square jump distance A traveled by a

reactant during a jump time T according to the relation

D (2-11)

where D is the experimentally determined diffusion coefficient for that

reactant (Chang 1981). By assuming that diffusive jumps are on the

order of 0.29 nm, the diameter of a water molecule, experimental

diffusion coefficients for radiogenic free radicals correspond to jump
times on the order of 3 x 10 s. Table 2-2 gives diffusion

coefficients and root-mean-square jump distances for various species
during a 3 x 101 s jump time.

The contribution of diffusion to the rate of a chemical reaction

was originally worked out by Smoluchowski (Smoluchowski 1916; Mozumder

1978). In his model, a reactant A was considered a sink towards which

another reactant B diffuses. Solving Fick's law of diffusion and using

Table 2-2

Reactant Species. Diffusion Coefficients D,
and RMS Jump Distances X

Species D (10-5 cm2 s-) (runm)

OH 2.5 0.21

H3O+ 9.5 0.41

e 5.0 0.30
H 8.0 0.38

OH 5.3 0.31

H202 1.4 0.16

Source: Wright et al. (1985b).

the boundary condition that the concentration of reactant B is zero at a

distance R from reactant A, he showed that

kd = 4rDR (2-12)

where kd is the reaction rate constant assuming the reaction is

completely diffusion-controlled, D is the sum of the diffusion constants

for reactants A and B, and R is the reaction radius. Mozumder (1978)

used this model to show that the probability of two species reacting in

time t, that were originally separated by distance B, is given by

P(t) -- erfc B ,R) (2-13)

where erfc is the error function complement.

The boundary condition proposed by Smoluchowski is no longer valid,

however, when the mean jump distance of a reactant is comparable to the

reaction radius or there exist energetic or geometric restrictions which

must be met before a reaction can proceed. Noyes solved Fick's

diffusion equation by using instead a radiative boundary condition

(Noyes 1961; Mozumder 1978), and obtained the expression

__ __

kd k
k d a (2-14)
obs kd + k

where kobs is the reaction rate constant expected to be observed, kd is

the rate constant if the reaction were diffusion-controlled, and k is
the rate constant if the reaction were not diffusion-controlled. The

activation-controlled rate constant k is given by k = ovP, where a is
a a
the collision cross section of the reaction, v is the approach velocity

of reactant B relative to A, and P is the probability of reaction during

a single collision (Wright et al. 1988). Thus

k = rR2 -- P (2-15)
a T

where X, the mean jump distance, is given by

2= h 3 (2-16)

The mean square jump distance, X is given as the sum of the squares of

the jump distances for reactants A and B:

X2 = A2 + 2 (2-17)

Using Eqs. (2-11) and (2-15) in Eq. (2-14), one obtains

kb = 4rDR [ 3RPP ] (2-18)
3RPX + 2 A J

The solution to Fick's diffusion equation under a radiative boundary

condition yields a zero concentration of reactant B. not at the reaction

radius R, but at a reduced radius a given by

a = R 3RPA (2-19)
3RPX + 2 A2

The reduced radius is related to the observed reaction rate constant by

kobs = 4rDa. Mozumder's expression for the probability of reaction in

time t then becomes

P(t) = erfc .( (2-20)

Table 2-3 lists the primary reactions occurring in the water

radiolysis along with their observed rate constants, reaction radii, and

reduced radii. Two of the reactions occur with a collision probability

of 1/7 and 1/3, respectively.

Table 2-3

Chemical Reactions. Rate Constants k. Reaction Radii

R, Reduced Radii a

Reaction k (1010 M s ) R (nm) a (nm)

H + H --H20 3.2 0.61 0.40

e + OH --OH 3.0 0.73 0.53
eaq + H + H2 H2 +OH 2.4 0.43 0.25

eaq + H3O H + H20 2.3 0.40 0.21

H+H --H2 2.1 0.25 0.10

OH + OH H202 (P=1/7) 0.6 0.60 0.16

2eaq + 2H20 -- H2 + 20H 0.6 0.20 0.08

H3+ + OH- 2H20 12.0 1.08 1.08

ea + H0 --2 OH + OH (P=1/3) 1.2 0.60 0.25
a~q 22j

Source: Wright et at. (1985b).

Simulation of Track Chemistry

As an example of the calculations performed during the chemical

stage, the upper left panel of Fig. 2-4 shows the entire track of the

4-keV electron shown previously in Fig. 2-3, each dot representing a

reactive species at 1012 s. The calculations of the chemical stage

begin with such a track. The code RADLYS checks pairs of species to see

if they are able to react with one another according to Table 2-3, and

if they are within the required reaction radius R. The order in which

the species are checked follows the same order in which their precursor

species at 10- s were formed. If a pair does react with collision

probability P. the reactants are removed from further consideration and

their products are created at the reaction site separated by a

root-mean-square distance of two molecular diameters. If the pair does

not react, a new pair is considered, one member taken from the previous

pair, and this checking continues throughout the track.

After permitting all possible reactions to proceed, the code allows

all unreacted species to undergo an elementary diffusive jump

corresponding to a time interval of 3 x 101 s. Specifically, each

species is moved in a random direction through a distance selected from

a Gaussian distribution with a mean displacement X calculated by Eq.

(2-11) (p. 32). After all species are jumped, the pairwise checking is

repeated. The chemical development of the track proceeds by alternating

simulations of chemical reaction and diffusion.

The above process, referred to as Reaction Scheme I, becomes

increasingly inefficient after 30 elementary jumps such that very few

ORNL-DWG 87-13030

N = 920

10-12 s

N = 474


N = 773


N =392

10- 7s

Fig. 2-4. Chemical evolution of a 4-keV electron track in liquid water
from 10-12 s to 10-7 s. Each dot marks the location of a
reactive chemical species (Turner et at. 1988b).


additional reactions occur between jumps. During the time 10- s to

10-6 s. Reaction Scheme II is implemented in which jump intervals larger

than three picoseconds are considered. During jump intervals in Scheme

II, pairs of species are allowed to react with a probability given by

Eq. (2-20) (p. 36). For each reaction, the products are placed at a

reaction site midway between the positions of the reactants at the

beginning of the jump interval. Unreacted species are allowed to

diffuse over this jump interval to the next time point.

The remaining panels of Fig. 2-4 show the result of these

calculations. Of the 920 reactive species originally present at 1012
s, only 392 remain at 10 s. This decrease is expected since the

primary result of the reactions in Table 2-3 is the conversion of

reactive free radicals (H, OH, e ) to unreactive molecular products
(H2, H202, H20). By 10- s the remaining species have diffused to the

extent that most evidence of track structure is gone and few remaining

intratrack reactions are possible. After a microsecond, the remaining

species continue to diffuse away from the track center and will begin to

react with species produced from neighboring tracks.



Prior to development of a simulation code for the early chemical

stage of glycylglycine radiolysis, several modifications were made to

the Oak Ridge model for pure water radiolysis. Thermalization of

subexcitation electrons was made an explicit function of electron

energy. Agreement was reached between calculated and experimental

yields of OH and e as a function of time by making assumptions as to
the fate of H20 and H20 during the prechemical stage. Other changes

included incorporating reactions with dissolved oxygen, improving the

scheme for locating reaction sites during the early chemical stage, and

adding calculations of standard deviations for all product yields. At

the close of this chapter, a critique of the modified codes is given.

Thermalization of Subexcitation Electrons

In the transport code OREC, the threshold for electronic excitation

of liquid water is 7.4 eV. Electrons which fall below that threshold

after an energy loss event are designated subexcitation electrons and

are not transported further. Subsequently, the code SPCS simulates

their thermalization by assuming each undergoes hydration during a

root-mean-square displacement of 3 nm.

A more realistic treatment would allow electrons to thermalize

through a distance dependent upon their subexcitation energy. From

Fermi age theory (Bethe et at. 1938, Fermi 1949, Weinberg and Wigner

1958), the root-mean-square distance traveled by an electron that is

liberated into a medium at velocity v and slows down to thermal

velocity vth is given as

r(v) = 2f v dv (3-1)


where 2et(v) is the elastic transport inverse mean free path, S(v) is

the stopping power of the medium, and atomic units are used throughout.

Both these quantities and the subsequent evaluation of Eq. (3-1) are

discussed separately.

Stopping Power for Low-Energy Electrons

From dielectric theory (Ritchie 1959, Ritchie et al. 1975), one can

formulate the stopping power for low-energy electrons of velocity v as


S(v) = 2 2 In -- 2(w,) (3-2)
rv2 J12 E (,0) + 62 (W.0)

where w is the energy lost to vibrational and rotational excitations and

D is the intermolecular distance of the medium, taken to be 0.3 nm for

water. In addition, 1E(,0) and e2(6,0) are the real and imaginary

parts of the dielectric constant at zero momentum transfer. Values of w

are restricted so that only positive values of the logarithm term of the

integrand are used.; Since there is negligible momentum transfer

accompanying energy losses by electrons at low velocities, the water

responds as if a photon of energy w is absorbed. Therefore, e1 and 2

can be obtained from optical properties of liquid water. Specifically,

2 2
e1(,O) = nr ni (3-3)


e2(',O) = 2nrni (3-4)

where n and n. are the real and imaginary parts of the index of

refraction and are obtained from surface reflectance measurements at

photon energy w (Heller et at. 1974). Tabulated values of n and n.
exist for photons inthe energy ranges 2 to 0.62 eV (Zoloratev and
exist for photons in the energy ranges 0.00002 to 0.62 eV (Zoloratev and

Demin 1977), 0.47 to 3.44 eV (Palmer and Williams 1974), and 2.0 to 25.6

eV (Heller et at. 1974). By using Eqs. (3-3) and (3-4), the energy-loss

function Im(-l/E) is computed and is shown in Fig. 3-1. Equation (3-2)

is then evaluated to give the stopping power for low-energy electrons

shown in Fig. 3-2.

Elastic Transport IMFP for Low-Energy Electrons

For an electron of velocity v, the elastic scattering inverse mean

free path, e(v), is defined by the expression

2vT NaP o
e(v) = A oa(v,.) sin9 dO (3-5)

where N is Avogadro's number, p and A are the density and atomic number
of the medium, 0 is the polar angle of scatter, and a is the elastic

scattering cross section, differential in angle 0. To measure the

importance of elastic scattering on electron transport, a is weighted by

the factor (1-cosS) to obtain the elastic transport inverse mean free

path, 2 (v). Thus,

2ir Nap
2e (v) = Nap o(v,9) (1-cosO) sinG d (3-6)

Experimental values of a are reported for electrons in water vapor

at energies of 0.01 to 10 eV (Itikawa 1978) and 4 to 10 eV (Danjo and




o t-

on oon

-0) ,-0

o o
I I_____ I I____ \i______ o .

o d d d d o d d0
I (3/1-)LA

o 2


z o




I I o -

\ laO~~~

(UO/A^y) xp/3p-

Nishimura 1985). A recent study has suggested that elastic cross

sections may be an order of magnitude smaller in solid media (Bader et

al. 1988). A comparison of calculated and measured time decay of e
(discussed in the following section) suggest a scaling of vapor elastic

cross sections by 0.6 to obtain values for liquid water. Values of a

for water vapor are thus scaled by 0.6 and Eq. (3-6) is evaluated to

give et as a function of electron energy as shown in Fig. 3-3.

Thermalization Distances for Low-Energy Electrons

Using S(v) and et(v) for electrons in the energy range 0.01 to

10.0 eV, Eq. (3-1) is evaluated to give the rms thermalization distance

r(E) for low-energy electrons shown in Fig. 3-4. A modified version of

the code SPCS includes the function r(E) in its treatment of electron

thermalization and hydration during the prechemical stage of radiolysis.

Specifically, the energy E of each subexcitation electron followed in

OREC is passed to the code SPCS. SPCS then creates a hydrated electron

in a random direction at an rms distance r(E) from its prethermalized

position. Electrons produced through autoionization of type 3-6

excitations are also thermalized through an rms distance r(E), where

their energy E is assumed to equal the energy of their parent excited

state minus an average binding energy of 8 eV.



II 1 -

/ o a

Z a

II wc

w o
/ /

/ 0 .a

I I I dSNV~ S,
O 0 0 O



Z '-
\ w




- In 10 0 -14


L __ ___

Time Decay of Hydrated Electrons and OH Radicals

There is limited experimental data on yields of radiolytic products
in pure water for times earlier than 10- s. Such data provide a means

of supporting the calculated yields given by the Oak Ridge model. Three

studies exist which report the G-value for hydrated electrons from 100

ps to 3 ns (Jonah et at. 1976), the G-value for hydrated electrons at 30

ps (Sumiyoshi and Katayama 1982), and the G-value for the OH radicals

from 200 ps to 3 ns (Jonah and Miller 1977). In these studies, sample

cells are irradiated by a pulse of high-energy electrons. At the same

time, a portion of the electron beam is intercepted by a cell containing

1 atm of xenon in which Cerenkov radiation is generated for use as an

analyzing light. By delaying the Cerenkov light, absorbance by ea or
OH radicals is measured as a function of time relative to the arrival of

the electron pulse.

In the Jonah studies, 20- to 22-MeV electrons were used, while in

the Sumlyoshi and Kaltayama study, 45-MeV electrons were used. Both

secondary-electron spectra and collision stopping powers are fairly

energy independent for electrons in the energy range 1 MeV to 50 MeV;

therefore, chemical yields within track segments of electrons at these

energies are not expected to differ greatly.

Figure 3-5 shows time-dependent yields of OH radicals and e for
1-MeV electron track segments as calculated by the unmodified ORNL model

described in Chapter 2. Experimental data is also shown. The initial

yield and decay rate of hydrated electrons is not in accordance with



N I I4 -
10 --
00 ru

= o -'

. ) .
:oo I o 2 8/
: o / : '8

- *

/ -

0 0


I -
/ / "^3

0 -4 o a
tIo /
0 0


3N VA-9I


.1 1.1.1 1.13 42o
3mt~h*0 2

experiment. So as to achieve better agreement, modifications are made

to the code SPCS.

The decay rates of hydrated electrons and OH radicals within a

track are greatly dependent upon their spatial distribution at 10 s.

In addition, these decay rates are not independent due to reactions such

as eaq + OH -- OH Using the thermalization scheme described in the
previous section and by increasing the migration distance of H20 from

0.75 nm to 1.25 nm, the calculated decay rate of hydrated electrons is

brought into agreement with experiment.

To match the experimentally suggested initial yield of eaq, the

scheme shown in Table 3-1 for partitioning of H20 into dissociations

and autoionizations is adopted. In this scheme, 25% of type 1

excitations and 23% of type 3-6 excitations are allowed to relax, where

AE represents thermal energy transferred locally to the medium. The

results of revised calculations of OH and e yields as functions of
time are shown in Fig. 3-6. By making these modifications to the Oak

Ridge model, excellent agreement between calculated and measured values

is achieved.

Additional Chemical Reactions

The reactions listed in Table 2-3 (p. 37) represent the primary

ones occurring within charged-particle tracks in liquid water. These

reactions are virtually diffusion controlled with rate constants on the

Table 3-1

Assumed Partitioning of Excitations

TYPE 1 H2 ---- H + OH 75%

H20 + AE 25%

TYPE 2 H20 H2 + 0 100%

TYPE 3-6 H2 -- HO + esub 57%

H + OH 20%

H20 + AE 23%



V I 0
S- I.

. a

0 o


a c an co I i C14
S3n V 0i
0 z 4 ) Q
I -

- I 0 L J

- o 43 0'

I *r

I I) -)0 0

O - ao 4 2

_~ / / It L** I
-_Or I 4-
I Is

3Il A-I
I a. -
0 IaI
(I) OV
4) .- c
.4) 4)-
Q,~~~44 N-~ U N
3m~h4) -b
i4t 4

order of 110 M s Reactions between free radicals and molecules of

biological interest occur with rate constants in the range 105 M-s-1 to
9 1-1
10 M s Therefore, pure water reactions which occur at comparable

rates must also be considered in a complete simulation of the chemical

stage. In addition, molecular oxygen reacts with e to form the
superoxide radical (02 ), while reaction with H radicals form its

conjugate acid, the hydroperoxyl radical (H02). Subsequent reactions

between 0 H02, and the pure water species virtually double the number

of reactions possible during the chemical stage.

Additional reactions are thus incorporated into RADLYS, five

occurring in pure water radiolysis and fifteen occurring in the presence

of molecular oxygen. Four of the oxygen reactions are considered to

follow pseudo-first-order kinetics and are treated separately from the

remaining second-order reactions.

Second-Order Reactions

An extensive list of reactions occurring in pure water and in the

presence of dissolved oxygen was compiled as part of the computer

program MACKSIM developed at Canada's Chalk River Nuclear Laboratories

(Boyd et al. 1980). MACKSIM calculates steady-state concentrations of

species produced during continuous low-dose-rate irradiation of water

systems, thus simulating the late chemistry stage of radiolysis. These

reactions are incorporated into RADLYS and are listed in Table 3-2.

Rate constants for the first ten reactions are fairly consistent with

ones previously used in RADLYS since they were both taken from the same

Table 3-2

Revised Reactions, Rate Constants k, Reaction

Radii R, Reduced Radii a

Reaction k (1010 M14 s -)a R (nm) a (nm)

H + OH -- H20 2.0 0.43 0.25

e + OH -- OH 3.0 0.72 0.53
eaq+H + H20 -- H + OH 2.5 0.45 0.25

eaq +H -- H + H2 2.2 0.39 0.20

H + H -- H2 1.0 0.23 0.083

OH + OH -- H202 (P=1/7) 0.55 0.55 0.15

2eq + 2H20 --*H + 20H 0.50 0.18 0.066
aq 2 2
H30+ + OH --- 2H20 14.3 1.58 1.28
eaq + H02 -- OH + OH (P=1/3) 1.2 0.57 0.25

OH + OH H20 + O 1.2 0.36 0.20

OH + H202 H20 + HO2 0.0033 0.015 0.0011

H + H202 -- H20 + OH 0.0090 0.020 0.0013

OH + H -- H20+H 0.0036 0.013 0.00063

H + OH H20 + eaq 0.0021 0.0087 0.00021
2 aq

aRate constants from Boyd et at. (1980).

National Bureau of Standards compilations (Anbar et al. 1973, Ross 1975,

Anbar et at. 1975, Farhataziz and Ross 1977). The last four reactions

listed are secondary reactions with rate constants on the order of 107
M-ls. Table 3-3 lists reactions in the presence of molecular oxygen.

A revised list of diffusion constants for all chemical species is given

in Table 3-4.

Pseudo-First-Order Reactions

Bimolecular reactions in which there is negligible consumption of

one reactant demonstrate first-order kinetics and are referred to as

pseudo-first-order reactions. The last two reactions listed in Table

3-3 are good examples, since one of the reactants is the aqueous

solvent. The first two reactions in that table, ones representing

scavenging by molecular oxygen, approach the pseudo-first-order limit

under two conditions. First, only a small fraction of the total oxygen

supply should be consumed during the irradiation, thus implying limits

on total absorbed dose for closed systems. Second, the concentration of

dissolved oxygen must be large relative to concentrations of e and H
radicals within individual electron tracks. These radicals are

initially produced in local concentrations of ~10 mM, yet are diluted

several orders of magnitude as the track diffuses outward within one

microsecond. Concentrations of dissolved oxygen appear large in

comparison, even for air-saturated systems.

The four pseudo-first-order reactions listed in Table 3-3 are

simulated in the code RADLYS as follows. Each species (e H, HO,, or

Table 3-3

Oxygen Reactions, Rate Constants k, Reaction Radii

R, Reduced Radii a

Reaction k (1010 M-1 s )a R (nm) a (nm)

eaq + 02 --02 1.9
H + 02 HO2 1.8b

H30 + 02 --0 HO2 + H20 4.5 0.74 0.51

H + H2 -- H202 2.0 0.45 0.26

OH + 02 OH +02 0.90 0.39 0.26

HO2 + OH --H20 +02 1.2 0.50 0.35

H + 02 HO2 2.0 0.44 0.26

eaq + 02 + H20 --HO2 + OH 1.3 0.40 0.24

eaq + HO2 O + OH 0.35 0.17 0.066

H30+ + H2- H20 + H202 2.0 0.41 0.23

HO2 + HO2 H202 + 02 0.00020 0.0036 0.000066

HO2 + 0 -- HO2 + 02 0.0089 0.025 0.0029
HO2 + H 20 H30+ + 02 0.000080b

0 + H20 -- OH + OH- 0.00017b

aRate constants from Boyd et at. (1980).

bModeled as pseudo-first-order reactions.

Table 3-4

Reactant Species and Diffusion Coefficients D

-5 2 -1
Species D (10 cm s ) Reference

OH 2.5 Wright et at. (1985b)

H30t 9.5
e 5.0
H 8.0

OH 5.3

H202 1.4

H2 5.0 Burns et at. (1981)

02 2.1

HO2 2.0

02 2.1

HO2 2.0 Estimated

O 2.0

0) is allowed to react with probability P1 over a time interval At

according to

P1 =1 ekCAt (3-7)

where k is the reaction's second-order rate constant and C is the

concentration of either 02 or H20, the latter assumed to be 55.5 M. If

a reaction did not occur, the species is allowed to diffuse over the

full At. If a reaction did occur, the species is first allowed to

diffuse over the time interval fAt, followed by diffusion of the

products over the the remaining interval (l-f)At, where O
fraction f is determined with probability P2 according to

1 e
P = -kCAt (3-8)
1 e

The scavenging capability of 02 is demonstrated in Fig. 3-7 and

3-8. Yields of e as functions of time for 500-eV electrons at several
values of the oxygen pressure are shown in Fig. 3-7. Oxygen gas above

the water and at these pressures is assumed to be in equilibrium with

dissolved oxygen. The pressure of 0.209 atm corresponds to that of

oxygen in atmospheric air. Figure 3-8 gives yields at 10-7 s for OH,

e and H as functions of oxygen pressure.













- 4)

2.0 --rr--L-u-v. ---


< 1.0




0.0 0.5 1.0 1.5

Fig. 3-8. Yields of OH, H, and hydrated electrons at 10-7 s calculated
for 500-eV electrons as functions of oxygen partial pressure
(Turner et at. 1988b).

Location of Reaction Sites

When a second-order reaction occurs between a pair of species

located at positions (xl y1,zl) and (x2y2,z2), the reaction site is

placed midway along the line segment connecting their positions. This

is a reasonable assumption when elementary diffusive jumps are employed

during Reaction Scheme I, yet becomes less realistic when longer time

intervals are simulated during Reaction Scheme II. A location scheme is

thus implemented which takes into account the relative diffusion of the

two species. Specifically, the coordinates of the reactants are

weighted inversely by their diffusion distances X. The x-coordinate of

the reaction site, for example, is given by

(xl I) + (x2 2)
x = (3-9)
(1/1) + (1/?2)
which reduces to

2 1
xr = x1 hi. +2 + x2 x lx2 (3-10)

Since NA=v' Dr

x = x1 + x2 (3-11)
1 2 1 2

These same weighting factors are also used 'determine the y- and

z-coordinates of the reaction site. This me od still assumes that the

most probable location for the reaction is along the line segment

connecting the species at the beginning of the time interval. More

sophisticated methods would select a reaction site according to a

predetermined spatial probability distribution.

Precision of Reported Product Yields

Product yields are reported by the code RADLYS as G-values, the

total number of molecules produced per 100 eV of energy deposition.

Thus for a series of simulated electron tracks,

(100)Nt (100)N
G =- -- (3-12)
Et E

where Nt is the total number of molecules produced, Et is the total

energy deposited in eV, N is the average number of molecules produced

per track, and E is the average energy deposited per track. It is

instructive to know the precision of reported yields and therefore

calculations giving the variance of product yields are added to the code

RADLYS. Since N and E are highly correlated.

2 2 2 2

[;G = [0 + -- 2N (3-13)

where a 2 is the covariance between N and E (Bevington 1969). For a

series of monoenergetic electrons of energy E, both a__ and a are zero
and Eq. (3-13) reduces to

100 a
CG (3-14)

Critique of Model

In attempting to formulate a model linking the physics and

chemistry of irradiated water, many uncertainties necessarily exist. It

is instructive to review these limitations for each stage in the


Physical Stage

Cross sections used by the transport code OREC are derived from a

theory in which compliance with quantum-mechanical restrictions is met,

collective effects of the liquid state are included, and experimental

data in all three phases are incorporated. Thus, the program is

believed to provide a representative simulation of electron transport in

liquid water.

In a recent study (Turner et at. 1988a), OREC's liquid-water cross

sections were scaled for plastic media. Subsequently, a version of OREC

using these modified cross sections was used to simulate the beta

response of a scintillator probe to both point and plaque sources.

Calculated depth-dose curves were in good agreement with measured

pulse-height spectra, thus providing an indirect check with experiment.

Since Monte Carlo techniques are used in the simulation code, new

experimental and theoretical data can be readily incorporated into the

program. Currently, a reassessment of the code's cross sections for

elastic scattering is planned in light of recent experiments in water

vapor (Danjo and Nishimura 1985).

Prechemical Stage

Of the three stages of the radiolysis simulated in the Oak Ridge

model, the prechemical stage is based least upon experimental data.

Physical limitations of pulse radiolysis techniques prohibit

investigating events occurring prior to 1012 s (Spinks and Woods 1976).

Subsequently, various assumptions are made in the model as to the

mechanisms linking the physical and chemical stages.

A much needed improvement to the model is the prescription of

electron thermalization presented in this chapter. It is not complete,

however, since the scaling of elastic scattering cross sections from the

vapor to the liquid was somewhat arbitrary. A method which will be

implemented in the near future proposes to use both optical data and

dielectric theory in an independent derivation of these cross sections

for liquid water. This would leave the migration distance of H20 and

the partitioning of excitations as the only adjustable parameters

available to fit the pulse radiolysis data shown in Figure 3-6. It is

hoped that all parameters used would eventually be firmly based upon

theory, experiment, or both.

An additional phenomenon not considered at present is that of

geminate recombination. Geminate pairs of radicals (i.e., produced from

the same H20 ) are currently allowed to recombine as early as 10-1 s,

the beginning of the early chemical stage. However, during an

ionization produced by the primary electron or an autoionization of an

H20 the subexcitation electron is always thermalized and hydrated. It

is conceivable that a fraction of these electrons are recaptured by

their parent H20 forming a H2O If recapture is possible, it remains

to be seen whether these electrons would produce further ionization or

excitation in the medium prior to recombination. As an alternative to

the partitioning of HO2 geminate recombination could be an explanation

for the high initial yields eq shown in Fig. 3-5 (p. 51).

Early Chemical Stage

Parameters used in simulating the early chemical stage are almost

exclusively taken from experimental data. However, limitations on

computer run-time permit only an approximate treatment of diffusion and

chemical reaction. If calculational limitations did not exist,

diffusive jump distances would be limited to molecular diameters

throughout track development. Between jumps, the total number of

reactant pairs whose separation is within their reaction radii would be

tabulated. If a species is capable of undergoing more than one

reaction, the reaction allowed to proceed would be selected at random.

To understand the number of calculations required in this more

realistic approach, consider the calculation of G-values for 100-keV

electrons. Each track might contain ~23,000 species at 101 s. For

diffusive jumps corresponding to 3 ps, some 333,333 time points would be

needed in order to simulate track development out to a microsecond. At

early time points, ~260,000,000 reactant pairs would be checked for

possible reactions and at latter times, assuming half the number of

reactants remain in the track, ~66,000,000 pairs would be checked.

These calculations would then be performed for -100 tracks to achieve

good statistics on product yields.

The number of required calculations is reduced in RADLYS by

allowing reactions to proceed as soon as they are found, thus avoiding

having to choose among several possible reactions for each species at

any given time. In addition, longer jump times are simulated during the

time interval 10-10 s to 10-6 s and Eq. (2-20) (p. 36) is used to

determine reaction probabilities for reactant pairs within the track.

This equation, however, is only strictly valid for isolated reactant

pairs and is thus applicable only as the track becomes very diffuse.

Regardless of its uncertainties, the modified Oak Ridge model

demonstrates excellent agreement with experimental data on

time-dependent yields for e and OH radicals, the primary initiators of
biological damage. Its extension to systems such as aqueous solutions

of glycylglycine is therefore made with some degree of confidence.



In the late 1960's and early 1970's, the radiation chemistry of

glycylglycine in aqueous solution was investigated at the Lawrence

Berkeley Laboratory as part of a continuing effort to understand

radiation effects on amino acids, peptides, and proteins. Under the

direction of Warren M. Garrison, several investigations sought to

measure yields of radiolytic chemical products. Reaction schemes were

proposed to account stoichiometrically for all products analyzed.

Studies were made in both oxygenated systems (Makada and Garrison 1972)

and deoxygenated systems (Garrison et at. 1973); measured product yields

from these studies are shown in Tables 4-1 and 4-2. Many of the

reactions outlined in these two investigations were confirmed during the

late 1970's and early 1980's through experimental techniques of spin

trapping, pulse radiolysis, and electron spin resonance (ESR)

spectroscopy (Garrison 1987).

This chapter presents a model for the early chemical stage of

glycylglycine radiolysis. Its foundation is the Oak Ridge model for

deoxygenated and oxygenated water radiolysis presented in Chapters 2 and

3. The reactions proposed in Garrison et at. (1973) for deoxygenated

Table 4-1

Product G-Values in the 6Co Irradiation of Glycylglycine
in Deoxygenated Aqueous Solution

Product 0.05 M 1.0 M Solid

Total Ammonia 3.3 5.2 5.4

Free Ammonia 2.8 3.8 3.5

Acetylglycine 0.9 2.9 3.3

Glyoxylic Acid 0.52 0.76 1.0

Formaldehyde <0.10 0.22 0.30

Aspartic Acid 1.1 0.30 0.1

Diaminosuccinic Acid 0.8 1.7 Present

Succinic Acid < 0.1 < 0.1 < 0.1

Source: Table I of Garrison et at. (1973).

Table 4-2

Product G-Values in the 6aCo Irradiation of 0.05
in Oxygenated Aqueous Solution


M Glycylglycine

0.05 M

Total Ammonia

Free Ammonia


Glyoxylic Acid

Formic Acid

Hydrogen Peroxide

Source: Table II of Makada and Garrison (1972).

solutions of glycylglycine and the reactions proposed in Makada and

Garrison (1972) for oxygenated solutions of glycylglycine are thus added

to the existing pure water reactions in the code. All second-order

reactions added to the code are modeled according to the techniques

presented in Early Chemical Stage of Chapter 2; all pseudo-first-order

reactions added are modeled according to the techniques presented in

Additional Chemical Reactions of Chapter 3.

There are seventeen reactions describing glycylglycine radiolysis

in oxygenated and deoxygenated solutions. However, the rate constant

for only one of these reactions is given in the two Garrison references.

Consequently, an extensive literature search was made for all values.

In cases where rate constants are unavailable, estimates are made from

analogous reactions or they are inferred from measured yields of final


After a brief review of glycylglycine structure and notation, the

model is presented in three sections: (1) the initiating reactions

between glycylglycine and radiogenic free radicals; (2) the subsequent

reactions in deoxygenated systems; and (3) the subsequent reactions in

oxygenated systems. For each section, the reactions as proposed in

Garrison et at. (1973) or Makada and Garrison (1972) are presented,

followed by estimates of rate constants and schemes for reaction

modeling. Makada and Garrison (1972) studied only the chemistry of 0.05

M glycylglycine; thus, the reactions proposed here for oxygenated

systems may not be valid for concentrated solutions of glycylglycine.

Glvcvlglycine Structure

The amino acid glycine, NH3CHCOO has the structure

\ I 1-0
H-N---C- .
H 0


where NH3- is the amino group, -COO is the carboxyl group, and the

central carbon atom is referred to as the a-carbon. Glycylglycine is

formed when the amino group of one glycine reacts with the carboxyl

group of another:

H I H\

\ + H 0 1 0


H H 0 H
\ I II I s0
Sx II I -
H--~-C-C--N--G-C + H20

The resulting bond between the two glycine a-carbons, -C-N-, is

called the peptide bond and thus glycylglycine is termed a dipeptide.

The two a-carbons of the glycylglycine molecule are notationally

distinguished by their adjacent functional groups; thus the two carbons

are respectively the N-terminal (amino end) and C-terminal carboxyll

end) a-carbon. When catalyzed by the addition of a strong acid or base,

a hydrolysis reaction splits the peptide bond through the addition of

the elements of water, thus reversing the above reaction. The

glycylglycine molecule is denoted in this chapter using the conventional

notation NH3CHCONHCHC0-.

Glycylglycine can exist in three protonated forms,

pK 3.1 pK = 8.1

where the pK values correspond to the pH at which two of the forms exist

in equal concentrations. The radiation chemistry of glycylglycine

depends greatly upon the protonated form of the molecule. For

simplicity, all experimental and calculational investigations of

glycylglycine are limited to a pH of -5.9, where the molecule is

predominantly in the zwitterion form.

Initiating Reactions

Reactions During Irradiation

The radiolysis of glycylglycine begins with three reactions between

the solute and radicals produced within charged-particle tracks. Two

reactions involve abstraction of a hydrogen atom from the C-terminal





Hydrogen abstraction is not energetically favorable at other locations

along the molecule as long as it is in its zwitterion form (Simic 1983).

The dot shown above the C-terminal a-carbon indicates the presence of an

unpaired electron and the resulting secondary free radical is hereafter

referred to as the H-abstraction radical.

The third initiating reaction involves interaction of a hydrated
electron with the carbonyl group (-C-) of the peptide bond forming an

electron adduct:

e + NHfCHCONHCHoo00 --- NH3CH-C-N--CHCOO (4-3)

The double bond character of the C = 0 within the carboxylic group is

considerably less than that of the C = 0 within the peptide bond; thus

electron attachment to the former is negligible (Willix and Garrison

1967). Following reaction (4-3), the electron is transferred

intramolecularly toward the positive amino group, resulting in reductive

deamination of the molecule:

0 H

NHCH+-- --CH -H -NH+ CHONHCH20 (4-4)

In order to be consistent with the terminology of Garrison et at.

(1973), the ammonium ion produced in reaction (4-4) will be referred to

as free ammonia, thus distinguishing it from other bound sources of

ammonia. At a pH of 5.9. ammonia remains in solution predominantly as

NH4. In this dissertation, the second product of reaction (4-4) will be

referred to as the deamination radical.

Reductive deamination of glycylglycine in reaction (4-4) is not

always 100% efficient (Simic et at. 1970). If the electron adduct

encounters an H-abstraction radical before it completes the electron

transfer, a reconstitution reaction may follow via



--- 2 NHoCH2CONHCH2COO + OH (4-5)


Such a reaction is thought to be important only in systems irradiated at

high dose rates, such as during pulse radiolysis, or possibly within

individual high-LET tracks.

Rate Constants and Modeling Scheme

Since the protonation state of glycylglycine changes with pH, rate

constants for the initiating reactions (4-1), (4-2), and (4-3) are pH

dependent. A list of experimentally determined rate constants for these

reactions is given in Table 4-3. Since both the experiments and

calculations of this research were performed at a pH of 5.9, the rate

6 -1 -1
constants selected from Table 4-3 are k4.i = 5.2 x 10 M s for

8 -1 -1
reaction (4-1) (Neta and Schuler 1971), k4-2 = 2.2 x 108 M s for

8 -1 -1
reaction (4-2) (Scholes et at. 1965), and k4_3 = 2.2 x 108 MI s for

reaction (4-3) (Tal and Faraggi 1975).

These three initiating reactions are modeled as pseudo-first-order

reactions such that each H. OH, and e is allowed to react with the
solute with a probability P = 1 e where k is the second-order

rate constants listed above, C is the concentration of glycylglycine,

Table 4-3

Rate Constants for Initiating Reactions

-1 -1 a
Reaction k (M s ) pH Reference

H + glygly 2.6 x 106 1 Neta and Schuler (1971)

5.2 x 106 ~7 Neta and Schuler (1971)b

OH + glygly 2.6 x 108 6 7 Adams et at. (1965)

2.2 x 108 5.5 6 Scholes et at. (1965)

4.4 x 108 4.2 Simic et al. (1970)

2.4 x 108 6.2 Masuda et at. (1976)

e + glygly 3.4 x 108 Davies et at. (1965)
2.5 x 108 6.38 Braams (1967)

3.7 x 108 6.4 Simic and Hayon (1971)

2.2 x 108 5.9 Tal and Faraggi (1975)

aMost references obtained from Dr. Alberta B. Ross. Radiation
Chemistry Data Center, Radiation Laboratory. University of Notre

bValue at neutral pH was estimated from measured value at pH 1.

and At is the time interval modeled. This assumption is thought to be
reasonable even at times of ~101 s (before the track species have

diffused appreciably), and at glycylglycine concentrations as low as

0.025 M.

Chemistry in Deoxygenated Solution

Reactions During Irradiation

During the irradiation of deoxygenated solutions of glycylglycine,

the initiating reactions with radiogenic free radicals can be summarized

as follows:



H+ + C O

In presenting the result of hydrated electron attack as that shown in

reaction (4-6), two assumptions are made: first, the electron adduct

intermediate of reactions (4-3) and (4-4) is very short-lived and need

not be modeled explicitly; and second, the yield of the reconstitution

reaction (4-5) is negligible. The latter assumption is generally a

valid one, especially during low-dose-rate photon irradiations. In

addition, it is implied that k4-, equals k4-3 given earlier.

The secondary free radicals formed in reactions (4-1), (4-2), and

(4-6) are removed through the following interradical reactions:

+ I -





In these reactions, a covalent bond is formed between two species at the

site of their original unpaired electron. The products of reactions

(4-7a), (4-8), and (4-9) are precursors to diaminosuccinic acid,

succinic acid, and aspartic acid, respectively.

An alternative pathway for reaction (4-7a) during irradiation is

the disproportionation reaction




The subsequent chemistry of the latter product, a dehydropeptide, yields

glycylamide, glyoxylic acid, and formaldehyde via



followed by

(glycylamide) (glyoxylic acid)

H+ +
(glycylamide) (formaldehyde)



An additional

the reaction

source of glycylamide, glyoxylic acid, and formaldehyde is

H202 + NHCH2~, NHCHCOO -- NH3CH20ONHCH(OH)COO + OH (4-12)

followed by reactions (4-11a) and (4-llb).

Another reaction occurring in irradiated, deoxygenated solutions of

glycylglycine is the scavenging of deamination radicals by the solute:



This reaction occurs in competition with reactions (4-8) and (4-9). The

result of reaction (4-13) is a conversion of deamination radicals to

H-abstraction radicals and acetylglycine.

Chemically-Induced Reactions

Several products are thus formed by irradiating deoxygenated

solutions of glycylglycine. Products which can be assayed directly from

the irradiated solution include free ammonia from reaction (4-6),

glyoxylic acid from reaction (4-11a), formaldehyde and carbon dioxide

from reaction (4-llb), and acetylglycine from reaction (4-13). Other

products are indirectly assayed by adding strong acid or base to

aliquots of the irradiated solution and then measuring various

hydrolysis products (Garrison et al. 1973). Irradiation products which

are indirectly assayed through this technique include those formed in

reactions (4-7a), (4-8), and (4-9), and also glycylamide formed in

reactions (4-11a) and (4-llb).

In Garrison et at. (1973), aliquots of the irradiation solution are

made acidic through the addition of 2N HC1, whereby the products of

reactions (4-7a), (4-8), and (4-9) undergo the following hydrolysis


+ +1

(diaminosuccinc acid)

2 HaO+ + CH2CONHCH2aOOH -- 2 NH+CH2COOH + CH2030H
succinicc acid)

(aspartic acid)

The yields of the acid precursors formed in reactions (4-7a), (4-8), and

(4-9) during irradiation are therefore equal to the yields of the

corresponding acids measured within the acidified solution.

The yield of glycylamide formed in reactions (4-11a) and (4-llb) is

inferred in Garrison et al. (1973) by measuring ammonia released during

its hydrolysis at high pH. When 2N NaOH is added to aliquots of the

irradiated sample, bound ammonia is released through the reaction:

(glycylamide) (glycine)

In Garrison et at. (1973), this source of ammonia is termed amide

ammonia so as to distinguish it from free ammonia produced in reaction

(4-6). The term total ammonia refers to the sum of free and amide


Rate Constants and Modeling Scheme

The chemistry of secondary radicals produced in deoxygenated

solutions is thus described in reactions (4-7) through (4-13). In the

simulation code, only the resulting stoichiometry of reactions (4-10),

(4-11a), and (4-11b) is considered. In this way, the code scores one

glycylamide and also one glyoxylic acid or formaldehyde for every

NH3CH2CN=CHCOO produced from reaction (4-7b) and for every

NH3CH2CONHCH(OH)OO- produced in reaction (4-12). Consequently, the

simulation code requires rate constants only for reactions (4-7), (4-8).

(4-9), (4-12), and (4-13). In addition, the simulation code requires

the branching ratio for reactions (4-7a) and (4-7b) and the branching

ratio for reactions (4-11a) and (4-11b). Rate constants for the

initiating reactions (4-1), (4-2), and (4-6) were discussed previously.

Literature values for secondary radical reactions are limited to

only reactions (4-7) and (4-8). In a pulse radiolysis study by Simic et

at. (1970), k4-7 was measured as 3.2 x 10 M s (pH -6.0) and k4,_ was

measured as 9 x 10 M s- (pH 7.0), respectively. Estimates are made

for the remaining parameters.

By assuming the rate at which secondary free radicals recombine is

fairly uniform, k4-9 is estimated at 6 x 10 M-ls the average of

k4-7 and k4-. given above. In estimating k4-12, one can make a crude

assumption that the relative reactivity of the H-abstraction radical

(HAR) with H202 and 02 is comparable to that of H radicals with H202 and

02. Thus,

k(H202 + HAR) k(H20 + H)

k(02 + HAR) k(0 + H)

7 -1 -1
where k(H202 + HAR) is k4-12, k(H202 + H) is 9.0 x 10 M s k(O2 + H)
10 -1 -1
is 1.8 x 10 M s and k(02 + HAR)O as estimated in the following
8 -1 -1
section, is 5.5 x 10 M s The rate constant k4-12 is thus estimated
6 -1 -1
at 2.8 x 106 M s1

Little information exists as to the value of k4-1, other than the

statement by Simic that reactions between secondary radicals and solute

molecules are "rather slow" (Simic 1983). A value of 1 x 10 M s is

arbitrarily chosen for k4.,- in the simulation code.

By using experimental yields shown in Table 4-1 (p. 71), an

estimate of the fraction of reactions (4-7) which result in dimerization

[reaction (4-7a)] is obtained by the expression

G(diaminosuccinic acid)
G(daminosuccinic acid) + G(glyoxylic acid) + G(formaldehyde)
G(diaminosuccinic acid) + G(glyoxylic acid) + G(formaldehyde)

This formulation assumes that the contribution of glyoxylic acid and

formaldehyde via reaction (4-12) is small compared to that produced via

reaction (4-7b). From the yields in Table 4-1 at 0.05 M and 1 M

glycylglycine, the equation above gives f4-7 as 0.56 and 0.63,

respectively. An average value of 0.60 is used in the simulation model.

Similarly, an estimate of the fraction of reactions (4-11) which

produce glyoxylic acid [reaction (4-11a)], as opposed to forming

formaldehyde and 002 [reaction (4-11b)], is made from the product yields

listed in Table 4-1. This fraction is estimated by the expression

G(glyoxylic acid)
f4-1 -
G(glyoxylic acid) + G(formaldehyde)

From the yields in Table 4-1 at 0.05 M and 1 M glycylglycine, the

equation above gives f4-11 as 0.84 and 0.78, respectively. An average

value of 0.81 is used in the simulation model.

As stated in the previous section, the three initiating reactions

are treated by pseudo-first-order kinetics in the simulation model.

Rate constants used in the model for reactions (4-7), (4-8), (4-9),

(4-12), and (4-13) are

8 -1 -1
k4-7 = 3.2 x 10 M s
8 -1 -1
k4-8 = 9 x 10 M s1

k4-9 = 6 x 108 M s1

k4-12 = 2.8 x 106 M s-1
7 -1 -1
and k4-13 = 1 x 107 M--

Branching ratios for reactions (4-7) and (4-11) are 0.60 and 0.81,

respectively. Each of the five reactions above is modeled explicitly at

various time points by considering the spatial separation of reactants

and their reaction radii. As a first approximation, diffusion

coefficients for all secondary free radicals are assumed to equal 1.06 x
-5 2 -1
105 cm2 s1, the diffusion coefficient of glycine (Weast 1976).

Chemistry in Oxygenated Solution

Reactions During Irradiation

The reactions presented in the previous section continue to occur

within irradiated solutions of glycylglycine even in the presence of low

concentrations of dissolved oxygen. However, in the presence of 02 at

sufficiently high concentrations, H radicals and hydrated electrons are

removed according to the reactions


H + 02 ---* HO

and e + 02 --- O0

The dominant reaction initiating glycylglycine radiolysis thus becomes

H-abstraction by OH radicals:



The subsequent chemistry begins with a scavenging of H-abstraction

radicals by molecular oxygen via

(peroxy radical)


The resulting peroxy radicals react with one another producing alkoxy


2 NHCH2CONHCH(02)00 --- 2 NH3CH2,0NHCH(O)00- + 02 (4-15)
(alkoxy radical)

which subsequently react with molecular oxygen according to

02 + NH3CH20CNHCH(O)O00 -- NH3CH2OONHCHO + 02 + 002 (4-16)

In competition with reaction (4-16), the (-CH-) site of the alkoxy

radical can react intramolecularly with the C-H bond of the N-terminal

a-carbon. The planar structure of the peptide bond forms a "6-member

ring" thus enabling an intramolecular hydrogen abstraction to occur:

+ H '- + H-0
NH---C C--COO --> NH---C C-00 (4-17)

The resulting product can then react with molecular oxygen via


followed by a hydrolysis reaction giving free ammonium ion,

glyoxylamide, and glyoxylic acid:

H20 + NH2=CHCONHCH(OH)COO --* (4-19)

(glyoxylamide) (glyoxylic acid)

Chemically-Induced Reactions

The terminating reactions for secondary peptide radicals in

irradiated, oxygenated solutions of glycylglycine are reactions (4-16)

and (4-19). Reaction (4-16) produces 02 002, and the species

NHCHICO2NHCHO. Upon the addition of strong base to the irradiated

solution, this latter product is hydrolyzed to give glycine, ammonia,

and formic acid:

(glycine) (formic acid)

As before, Makada and Garrison (1972) refer to this source of ammonia as

amide ammonia so as to distinguish it from the free or unbound ammonia

produced in reaction (4-19).

In addition to producing free ammonia, reaction (4-19) also yields

glyoxylamide and glyoxylic acid. At high pH, glyoxylamide is hydrolyzed

to give additional glyoxylic acid and amide ammonia through the reaction

(glyoxylamide) (glyoxylic acid)

Rate Constants and Modeling Scheme

The primary chemistry of secondary radicals produced in oxygenated

solution is thus described in reactions (4-14) through (4-19). In the

simulation code, only the resulting stoichiometry of reactions (4-18)

and (4-19) is considered. In this manner, the code scores the

production of one free ammonia, one amide ammonia, and two glyoxylic

acids (as measured after basic hydrolysis) for every intramolecular

reaction (4-17). Thus, only the rate constants for reactions (4-14),

(4-15), (4-16), and (4-17) are needed in the simulation code.

A literature search of rate constants was conducted which revealed

a range of values useful in estimating k4._4 and k4-,5. Table 4-4 gives

rate constants for the general reaction between molecular oxygen and

secondary free radicals. Of the species listed, the one which most

closely resembles the glycylglycine radical is the acetylglycylglycine

radical as measured by Hayon and Simic (1973). Thus, k4-4 is estimated

at 5.5 x 10 M- s-1

Table 4-5 gives rate constants for the general bimolecular reaction

between two peroxy radicals. Of the species listed in this table, the

one which most closely represents the peroxyglycylglycine radical is the

peroxyacetate radical, -02CH2COO as measured by Abramovitch and Rabani

(1976). The other listings are for hydroxyl radicals, one is for a

cyclic hydrocarbon radical, and the remaining listings are

generalizations. Thus, k4-1i is estimated at 6.5 x 108 M-1s-1

The two remaining reactions, (4-16) and (4-17), represent competing

reactions for the alkoxy glycylglycine radical, NH2CH2OONHCH(O)COO.

One can make the assumption that the reaction between 02 and the alkoxy

radical in (4-16) is similar to that between 02 and the H-abstraction

radical in reaction (4-14); thus k4-.1, k4-i4 5.5 x 10 M-1s-1

Given this approximate value for k4-.6, one can estimate the value of

k4-i. using the measured product yields listed in Table 4-2 (p. 72).

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