Nonhomogeneous kinetics

More sophisticated calculations (14,20), using either stochastic Monte Carlo or deterministic methods, are able to consider not only different Irradiating particles but also reactant diffusion and variations In the concentration of dissolved solutes, giving the evolution of both transient and stable products as a function of time. The distribution of species within the tracks necessitates the use of nonhomogeneous kinetics (21,22) or of time dependent kinetics (23). The results agree quite well with experimental data. 

The organization of this chapter is as follows. In the following section, Sec. 4.2, the elastic and inelastic interaction cross sections necessary for simulating track structure (geometry) will be discussed. In the next section, ionization and excitation phenomena and some related processes will be taken up. The concept of track structure, from historical idea to modern track simulation methods, will be considered in Sec. 4.4, and Sec. 4.5 deals with nonhomogeneous kinetics and its application to radiation chemistry. The next section (Sec. 4.7) describes some application to high temperature nuclear reactors, followed by special applications in low permittivity systems in Sec. 4.8. This chapter ends with a personal perspective. For reasons of convenience and interconnection, it is recommended that appropriate sections of this chapter be read along with Chapters 1 (Mozumder and Hatano), 2 (Mozumder), 3 (Toburen), 9 (Bass and Sanche), 12 (Buxton), 14 (LaVerne), 17 (Nikjoo), and 23 (Katsumura). 

The blob model describes reactions (16) in terms of nonhomogeneous kinetics via Eqs. (17-18) on concentrations of the particles. It is an adequate approach to the problem because the number of particles involved is large and local motion of the intrablob electrons and the positron is fast... 

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

A recently proposed nonhomogeneous kinetics model (5) has been moderately successful in the interpretation of the rates of reactions of ions produced during the y-radiolysis of dielectric liquids. A wide range of dielectric liquids has been tested, from hydrocarbons (5,14, 20) to alcohols (16,17) and water (18). The same model explains the variation in the yield of free ions—i.e., ions that have escaped geminate neutralization—from one liquid to another (6). The model is still in a rather crude form and has many shortcomings. Its only strength is the degree to which it provides a quantitative interpretation of experimental results. 

In the calculation of the ion lifetime spectrum, Reactions 2 and 4 are considered separately. Reaction 4 is assumed to obey simple second order kinetics, so it presents no problem if the fraction of the total ions that becomes free ions can be determined. The nonhomogeneous kinetics model allows one to estimate this fraction (6) as well as the lifetimes of the ions that undergo Reaction 2(5). 

Lifetime spectra of specific types of ions in irradiated solutions could readily be calculated by the method used in the present work. Reactions that occur at times greater than about 10"8 sec. after the instantaneous pulse occur mainly by homogeneous kinetics. At times shorter than 10 8 or 10 9 sec., the nonhomogeneous kinetics become progressively more important (see Figure 1). 

Freeman, G.R. Kinetics of Nonhomogeneous Processes Wiley New York, 1987. 

A successor to PESTANS has recently been developed which allows the user to vary transformation rate and with depth l.e.. It can describe nonhomogeneous (layered) systems (39,111). This successor actually consists of two models - one for transient water flow and one for solute transport. Consequently, much more Input data and CPU time are required to run this two-dimensional (vertical section), numerical solution. The model assumes Langmuir or Freundllch sorption and first-order kinetics referenced to liquid and/or solid phases, and has been evaluated with data from an aldlcarb-contamlnated site In Long Island. Additional verification Is In progress. Because of Its complexity, It would be more appropriate to use this model In a hl er level, rather than a screening level, of hazard assessment. 

A number of different techniques have been developed for studying nonhomogeneous radiolysis kinetics, and they can be broken down into two groups, deterministic and stochastic. The former used conventional macroscopic treatments of concentration, diffusion, and reaction to describe the chemistry of a typical cluster or track of reactants. In contrast, the latter approach considers the chemistry of simulated tracks of realistic clusters using probabilistic methods to model the kinetics. Each treatment has advantages and limitations, and at present, both treatments have a valuable role to play in modeling radiation chemistry. 

The irradiation of water is immediately followed by a period of fast chemistry, whose short-time kinetics reflects the competition between the relaxation of the nonhomogeneous spatial distributions of the radiation-induced reactants and their reactions. A variety of gamma and energetic electron experiments are available in the literature. Stochastic simulation methods have been used to model the observed short-time radiation chemical kinetics of water and the radiation chemistry of aqueous solutions of scavengers for the hydrated electron and the hydroxyl radical to provide fundamental information for use in the elucidation of more complex, complicated chemical, and biological systems found in real-world scenarios. 

Showalter, K. (1987). Chemical waves. In Kinetics of nonhomogeneous processes, (ed. G. R. Freeman). Wiley, New York. 

Mark F, Becker U, Herak.J.N., Schulte-Frohlinde D (1989) Radiolysis of DNA in aqueous solution in the presence of a scavenger A kinetic model based on a nonhomogeneous reaction of OH radicals with DNA molecules of spherical or cylindrical shape. Radiat Environ Biophys 28 81-99 Marquis RE, Sim J, Shin SY (1994) Molecular mechanisms of resistance to heat and oxidative damage. J Appl Bacteriol Symp Suppl 76 40S-48S... 

The trajectories of the major portion part of dipoles-rotators occupy in this case almost all the sphere (it is seen in Figs. 7 and 9). Consequently, a nonhomogeneity of the potential (94) could be neglected also in this case. Thus again we may consider free rotation of a dipole, but now in a zero potential, unlike the small-(3 case considered above. Hence, the kinetic energy of a dipole... 

The resistance term in Eq. (1), 2A, usually increases directly with the membrane thickness, so reducing thickness by some percentage generally increases flux by the same percentage. This generalization has some exceptions. For instance, reaction or complexation kinetics within the membrane or nonhomogeneous morphologies within the membrane can cause such exceptions in some cases (Crank, 1975). 

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