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The long-standing discrepancy between the kinetics of the hydrated electron measured in pulse radiolysis experiments and the time dependent decay inferred from the inverse Laplace transform of scavenger data is resolved by the incorporation of an improved measurement of the rate coefficient for the CH3Cl + eaq- reaction used in the inverse Laplace transform treatment. The revised analysis of both data types leads to the conclusion that the spatial distribution of secondary electrons produced in the energetic electron radiolysis of water is nearly twice as wide as suggested by previous studies.

A stochastic simulation method employing suitable experimentally based cross sections has been developed for probing the spatial distribution of energy loss and the trajectory of 100 eV to 1 MeV electrons in gaseous and liquid water. Elastic collisions and large-energy-loss inelastic collisions strongly influence the passage of electrons such that the separation between the initial and final (E = 25 eV) position is considerably smaller than the path length. At all energies, the mean axial and the mean radial penetrations are somewhat similar, however, the former is strongly influenced by inelastic collisions and the latter by elastic collisions. The effect of phase on the density-normalized range is small for energetic electrons, but differences are apparant at the lowest energies

The dipole oscillator strength distributions for solid and for gas phase cyclohexane, cyclohexene, 1,3-cyclohexadiene, 1,4-cyclohexadiene, and benzene were constructed from experimentally derived optical constants and from atomic X-ray absorption cross sections. Monte Carlo simulations of the energy loss by electrons of initial energy from 10 keV to 1 MeV in these media were performed using cumulative inelastic cross sections obtained from a formulation incorporating the constructed dipole oscillator strength distributions. In the solid phase, the energy loss distributions, the most probable energy losses, and the mean energy losses for electrons show little effect due to the conjugation of $pi bonds. However, there are large differences between the gases, and there is a considerable effect due to condensation. The most probable and the mean energy losses for 1 MeV incident electrons in solid cyclohexane, cyclohexene, 1,3-cyclohexadiene, 1,4-cyclohexadiene, and benzene are in the ranges 22-24 and 47-48 eV, respectively. Comparison with data for water suggests that the values for the solid phases of hydrocarbons are acceptable approximations for the liquid phase. Density normalized stopping powers, inelastic mean free paths, and ranges for electrons in the various hydrocarbons are also presented. 36 refs., 4 figs., 7 tabs.

Diffusion-kinetic methods are used to investigate the effects of incident particle linear energy transfer (LET) on the radiolysis of water and aqueous solutions. Chemically realistic deterministic diffusion-kinetic calculations examining the scavenging capacity dependences of the scavenged yield of e[sub aq][sup [minus]] and of OH demonstrate that the scavenged yields are related to the underlying time-dependent kinetics in the absence of the scavenger by a simple Laplace transform relationship. This relationship is also shown to link the effect of an e[sub eq][sup [minus]] scavenger on the formation of H[sub 2] with the time dependence of H[sub 2] production in the absence of the scavenger. The simple Laplace relationship does not work well when applied to H[sub 2]O[sub 2] formation in high-LET particle tracks even though such a relationship is valid with low-LET particles. It is found that while the secondary reaction of H[sub 2]O[sub 2] with e[sub aq][sup [minus]] can be neglected in low-LET particle radiolysis, it is of considerable significance in the tracks produced by high-LET particles. The increased importance of this reaction with increasing LET is the major reason for the failure of the Laplace relationship for H[sub 2]O[sub 2]. 55 refs., 9 figs., 2 tabs.

The temperature dependence of the chemistry in the track of a fast electron in water has been examined with a deterministic diffusion-kinetic model. The model calculations suggest that there is an increase in the yields of the hydrated electron and hydroxyl radical and a decrease in the yields of molecular hydrogen and hydrogen peroxide with increasing temperature. These results are consistent with most of the experimental data. It is found that the best fit to the experimental data occurs when the radius of the initial spatial distribution of the hydrated electron is dependent on a process which scales according to an Arrhenius-like equation with an activation energy similar to that for electron movement between potential traps in water. The radii of the initial spatial distributions of all the other species appear to be independent of the temperature. The predictions of the model suggest that the initial radiation chemical yields of the reactive species are independent of temperature. An additional thermally dependent reaction for the decomposition of water is not required for the model predictions to match the experimental data. 47 refs., 8 figs., 1 tab.

The Stern-Volmer analysis is an elementary method of photochemistry and is discussed in many standard physical chemistry texts. This relationship of photochemistry is generalized to describe systems in which the decay under investigation is nonexponential and systems in which the quenching or scavenging is inherently transient and must be described with a time-dependent rate constant. 39 refs.

Stochastic simulation techniques have been developed for modeling partially diffusion-controlled reactions in spur kinetics. These methods have been used to examine whether deviation from full diffusion control influences the overall spur chemistry. Studies of idealized two-species spurs suggest that the time dependence of the kinetics is not affected by the nature of the reaction; however, the overall chemistry of a spur can be influenced by a deviation from full diffusion control as whether the reaction is fully or merely partially diffusion controlled can have a significant effect on the initial overlap of the reactants. The reaction at time zero, which depletes the yield of reactants, is determined by the relative values of the width of the spur and of the encounter radius. This depletion is of particular importance in the radiation chemistry of water where the spatial distribution of the hydroxyl radical in a spur is believed to be significantly tighter that the distribution of the hydrated electron. 36 refs., 8 figs., 2 tabs.

An analytic description of the cooperative effects of scavengers on the radiation chemistry of the hydrated electron in aqueous solution is developed by using the available experimental data and the results of deterministic diffusion-kinetic calculations. The formulation has two components: the first corresponds to the effect of the primary (electron) scavenger in isolation and the second represents the suppression of the e{sub aq}{sup {minus}} + OH spur reaction by the secondary (hydroxyl radical) scavenger. The two aqueous systems that have been considered in detail are nitrate/formate and nitrous oxide/2-propanol. The agreement between the analytic treatment, the experimental data, and the kinetic modeling is good. 37 refs., 7 figs., 2 tabs.

Stochastic independent reaction times (IRT) simulations are used to model the fast reaction in spurs similar to those found following the high-energy electron radiolysis of water and aqueous solutions. The time dependence of the rate coefficient for the reaction of the hydrated electron or the hydroxyl radical with a scavenger is shown to be important in modeling scavenging reactions only when the steady-state rate is large, e.g. for the reactions e{sub aq}{sup {minus}} + O{sub 2} or OH + Br{sup {minus}}. The calculations are used to test the accuracy of the commonly used Laplace relationship between the time dependence of the radicals and the molecular product resulting from the high-energy electron radiolysis of water and the scavenger concentration dependence of the observed yields following the radiolysis of scavenger solutions. Agreement between modeled yields for the scavenger systems and predictions of the Laplace transforms of the decay and the formation kinetics in the absence of scavenger is excellent once the time dependence of the scavenging rate coefficient has been incorporated in the Laplace relationship. 47 refs., 7 figs., 4 tabs.

Analytic models are used to show that at low concentrations the effect of scavengers on radiation chemical yields should be expressed as a power series in the square root of the scavenger concentration. The coefficients of the different terms in the series are determined by the initial distribution of separations of the reactants and by the interparticle forces. Conventional empirical functions used to describe the scavenger concentration dependence of radiation chemical yields are shown to be equivalent to a power series in which all the coefficients are defined by a single fitting parameter. The importance of the terms of higher order than the square root of the scavenger concentration is emphasized, and the need for a second fitting parameter to account for the difference between the coefficients of these terms and the square root term is demonstrated. A new function to describe the scavenger dependence of radiation chemical yields is discussed, and it is shown to reproduce other existing empirical fitting functions, even those which do not have the correct square root of scavenger concentration asymptote, over the limited concentration range that is experimentally accessible. 57 refs., 5 figs.

An analytic treatment for the short-term recombination following the photolysis of water is presented. The technique is used to look at the way that the spatial distribution of the reactants resulting from the photoionization influences the escape probability and the time-dependent decay kinetics of the solvated electron. The predictions of the analytic method are compared with the experimentally observed decay of the solvated electron. Two different distributions are used to describe the initial separation of the hydrated electron from the hydroxyl radical and the hydrated proton with which it may react. To match model to experiment requires either a Gaussian of standard deviation 0.6 nm or an exponential with a characteristic width of 0.3 nm. The two distributions have the same root-mean-square separation, 1.0 nm, once the initial overlap of reactants is taken into account.

A procedure for the calculation of entity-specific ionization and excitation probabilities for water radiolysis at low linear energy transfer (LET) has been developed. The technique pays due attention to the effects of the ionization threshold and the energy dependence of the ionization efficiency. The numbers of primary ionizations and excitations are not directly proportional to the spur energy. At a given spur energy, ionization follows a binomial distribution subject to an energetically possible maximum. The excitation distribution for a spur of given energy and with a given number of ionizations is given by a geometric series. The occurrence probabilities depend upon the cross sections of ionization, excitation, and other inferior processes. Following the low-LET radiolysis of liquid water the most probable spurs contain one ionization, two ionizations, or one ionization and one excitation, while in water vapor they contain either one ionization or one excitation. In liquid water the most probable outcomes for spurs corresponding to the most probable energy loss (22 eV) and to the mean energy loss (38 eV) are one ionization and one excitation, and two ionizations and one excitation, respectively. In the vapor, the most probable energy loss is 14 eV which results in one ionizationmore » or one excitation and the mean energy loss is 34 eV for which the spur of maximum probability contains one ionization and two excitations. The total calculated primary yields for low-LET radiolysis are in approximate agreement with experiment in both phases.« less

The stopping powers, the inelastic mean free paths, the ranges, and the distributions of energy loss events for electrons in some gaseous alkanes have been calculated from experimentally based dipole oscillator strength distributions. The results show very little difference between the members of the homologous series of straight-chain hydrocarbons, C{sub n}H{sub 2n+2} where n = 2, 4, 6, and 8. For instance, the integrated path length of a 1-MeV electron in ethane of unit density is 0.38 cm and increases to 0.40 cm in octane of the same density. The stopping power of a 1-MeV electron in unit density hexane is 0.2 eV/nm, and the inelastic mean free path is 220 nm. The corresponding values for the other alkanes differ by less than 10%. The distribution of energy loss events along the track of a high-energy electron in these gaseous hydrocarbons is not significantly affected by the value of n, and it is insensitive to the incident electron energy from 10 keV to 1 MeV. The most probable energy loss along the track of a 1-MeV electron is 14 eV in ethane, 15 eV in butane and hexane, and 16 eV in octane. The mean energy loss is 25 eVmore » in butane, hexane, and octane and is 1 eV less in ethane.« less

A master equation formalism is presented which describes the evolution of the number of reactive particles in a multipair spur. This technique is particularly appropriate for modeling ion combination in low-permittivity solvents. For the simple case where all the cation-anion distances are identically distributed, the equations can be solved analytically in terms of the geminate survival probability. An analytic solution for the free-ion yield from an ensemble of isolated clusters also follows. Solutions are compared with simulation results and with other models of the same process.

The distributions of energy deposition events for electrons in gaseous and liquid water and in amorphous ice have been calculated. These calculations make use of an inelastic cross section that takes into account binding energy, exchange, and relativistic effects and that is based on experimentally determined dipole oscillator strength distributions. The most probable energy loss in a single event by a 1-MeV electron is 22.5 eV in the condensed phases and 13.5 eV in the gaseous phase, while the average energy loss is 34, 38, and 40 eV/event for gaseous and liquid water and amorphous ice, respectively. Very little dependence of the distributions on incident electron energy is found. At 1 MeV the differential or single event distribution is found to be the same as the integral or cumulative distribution. The fractions of the total energy lost in events that are less than 100 eV are 0.76, 0.75, and 0.69 for gaseous and liquid water and amorphous ice, respectively.

Deterministic diffusion-kinetic calculations show that the yields of the cationic and the anionic species, H 3 O + and e aq - +OH - , produced in the fast electron radiolysis of neutral water are significantly reduced by the addition of nitrous oxide as an electron scavenger. This reduction is demonstrated to be a direct consequence of the conversion of the hydrated electron to the hydroxide anion which undergoes more rapid intraspur reactions with H 3 O + than does e aq

The diffusion-controlled recombination of small clusters of ions in low-permittivity solvents is considered. A Monte Carlo simulation technique used previously for high-permittivity solvents is introduced and discussed briefly. The independent reaction times (IRT) simulation method is described, and its implementation for the kinetics of ion clusters is detailed. The IRT approximation is tested against the full Monte Carlo simulation for a variety of random and nonrandom initial configurations and against alternative analytic theories. We find the IRT method to be surprisingly accurate under these stringent conditions.

Alternative theories for the kinetics of diffusion-controlled reactions between ions in radiation-induced spurs are considered for solvents of high permittivity, such as water. A Monte-Carlo (MC) technique for simulating the paths of the diffusing ions and their encounters is developed and shown to provide an accurate description of the time-dependent reaction probability for the case of a single pair, by comparison with numerical solutions of the Debye-Smoluchowski equation. The MC simulations are then used to test the application of more approximate theories for the kinetics of multipair spurs. Two models are examined: (i) prescribed diffusion, which is conventionally applied in radiation chemistry, and (ii) the independent reaction times (IRT) model in which reaction times are associated independently with each ion pair. The IRT model is shown to describe the kinetics better than prescribed diffusion for a two-pair Gaussian, showing time-dependent reaction probabilities that are close to those obtained from the MS simulations. Good agreement is also found for the regular tetrahedron, where the effects of competition are maximized. The performance of both approximate models improves as the number of pairs in an initially Gaussian spur is increased and prescribed diffusion copes better with ionic reactions than it does with reactionsmore » between neutral species. Finally, a comparison between ionic and neutral spurs demonstrates that it is necessary to include charge in any model of spur kinetics involving ions, even in a high-permittivity solvent such as water.« less

A transformation is introduced and used to formulate a series of approximations for the time-dependent diffusion-controlled geminate reaction probability. Each approximation has the properties of a probability distribution function. The implications of the approximations are analyzed by use of established relationships to give corresponding approximations for the geminate reaction probability with a radiation boundary condition and for the time-dependent rate coefficient with a Boltzmann initial concentration profile. The first-order approximation, which holds when the interparticle forces are weak, is applied to the recombination of ions in an aqueous solution of a strong electrolyte; its accuracy is assessed by comparison with numerical results.