Spur model

The hydrated electron, if the major reducing species in water. A number of its properties are important either in understanding or measuring its kinetic behavior in radiolysis. Such properties are the molar extinction coefficient, the charge, the equilibrium constant for interconversion with H atoms, the hydration energy, the redox potential, the reaction radius, and the diffusion constant. Measured or estimated values for these quantities can be found in the literature. The rate constants for the reaction of Bag with other products of water radiolysis are in many cases diffusion controlled. These rate constants for reactions between the transient species in aqueous radiolysis are essential for testing the "diffusion from spurs" model of aqueous radiation chemistry. 

For glutamic acid (18) and glycine (10) the yield of ammonia varies approximately as the cube root of the concentration. This variation agrees with the diffusion of the spur model which derives from the hypothesis that at higher solute concentrations, water radicals are scavenged which would react with each other in more dilute solution. However, for the effect of cathode rays on the aromatic amino acids phenylalanine, tryptophan, and tyrosine and for cystine, this relationship is inverted, and amino acid destruction decreased with an increase in concentration (29). 

Another model of positronium formation, the so-called spur model, was originally developed by Mogensen (1974) to describe positronium formation in liquids, but it has found some applications to dense gases. The basic premise of this model is that when the positron loses its last few hundred eV of kinetic energy, it creates a track, or so-called spur, in which it resides along with atoms and molecules (excited or otherwise), ions and electrons. The size of the spur is governed by the density and nature of the medium since these, loosely speaking, control the thermalization distances of the positron and the secondary electrons. It is clear that electrostatic attraction between the positron and electron(s) in the spur can result in positronium formation, which will be in competition with other processes such as ion-electron recombination, diffusion out of the spur and annihilation. 

The spur model, proven to be valid in condensed media, proposes that Ps formation would occur through the reaction of a (nearly) thermalized positron with one of the electrons released by ionization of the medium, at the end of the e+ track, in a small region containing a number of reactive labile species (electrons, holes, excited molecules) [1],... 

The spur model in polar solvents (Strasbourg Group) [2]... 

Enhancement of Ps formation. As expected from the spur model, all solutes that are efficient hole scavengers, thus somehow preventing the recombination process and increasing the electron availability (see reactions I—IX) enhance Ps formation. In water, strong positive ion scavengers are essentially the halide and pseudo-halide ions, together with amines. A convenient empirical equation to describe the Ps intensity variation is as follows [2] ... 

There are two models which utilize this mechanism, the spur model [18, 16] and the blob model (diffusion-recombination model) [19, 20]. In spite of the fact that both models answer the question about the Ps precursor in the same way, they differ as to what constitutes the terminal part of the e+ track and how to calculate the probability of the Ps formation. 

Quantitative formulation of the spur model was given by Tao [2l]. It is based on the following assumptions ... 

Thus, in the framework of the spur model, Ps formation probability is written as ... 

An explanation for the lost polarization in water was first introduced as part of the spur model of Mu formation and reactions as shown in Fig. 11 [63]. 

Here Mu is assumed to be formed as a result of combination of and an excess electron. This view is the same as for the spur model of positronium (Ps) formation. While the spur model has received strong support for positronium yield in condensed phases, the validity of the same model for Mu formation is not clear. Figure 11 presents the original form of the spur model of Mu formation, since it helps to contrast the difference between the epithermal model (Fig. 2) and the spur model of Mu formation. Alternatively, the part of Mu formation, i.e., p and excess electron combination, in Fig. 11 may be replaced with the picture of Mu... 

Fig. 11. A proposed scheme of Mu formation and reactions in water. Mu is formed by reaction with nearly thermalized p and an excess electron formed by radiolysis (the spur model of Mu formation) with the probability h, and the rest (Iiq) is solvated ttecomeing diamagnetic muon. Mu thus formed can further react with aqueous electrons by spin exchange reaction it is depolarized and the polarization is lost (Pi. By chemical reactions, a fraction of Mu is incorporated into diamagnetic muon while another fraction becomes dephased and forms a part of depending on how fast the reactions proceed. Mu that has not reacted is observed as free Mu (P )...

A model which combines certain features of both models is Tao s "modified spur model" (37). In this model Tao considers both the possibility of combination of a positron with an electron created in the spur as well as the "direct" formation of a positronium, similar to the mechanism discussed in the Ore model, if the total kinetic energy of the resulting electron-positron pair is less than the potential energy between them. 

Four types of interaction between matter and radiation are under discussion - the photo effect, the Compton effect, the pair formation effect and the spurs model. In the following sections changes of the main food constituents (lipids, carbohydrates and proteins) will be summarized. 

The formation of positron states takes place in a much more complicated way in molecular solids and fluids. The structures of these materials are more complex than those of metals, and diverse radiation products are formed in the thermalization process. Consequently, any theory explaining the behavior of positrons in these materials needs the use of radiation chemistry. The so-called spur model (Mogenssen 1974) does exactly this and states that the thermalized positron reacts with the particles of its own radiation track. The spur contains ground-state (M) and excited molecules (M ), ions (M" ), free radicals (R ), and electrons (e ). These species react with the positron and, parallel, with each other. Some possible reactions are given inOEq. (27.1) ... 

The formation of positronium atoms is affected by many factors but first of all, asO Eqs. (27.1) and O (27.2) suggest, by the material itself. According to the mentioned spur model (Mogenssen 1974), thermalized positrons compete with molecules of the material and with radiation products for available electrons. Sometimes, these spedes are such effective inhibitors or scavengers that they prevent positronium formation totally. Even if the inhibition is negligible, not all of the positrons can form Ps. Positronium formation reactions given by O Eqs. (27.2b) and (27.2c) require positrons of some particular energies. 

Although the Ore model is more quantitative than the spur model, it works without serious errors only for gasses. In a condensed phase, conditions determining Ps formation are much more complicated. Usually, even some crucial parameters (e.g., ionization potential, solvating effect, etc.) are known with insufficient accuracy. Consequently, for condensed phases, one should use the spur model instead. Usually, it does not supply quantitative data, and its list of equations changes from material to material, hut, even so, its results are impressive. 

Independently of what one thinks of their formation mechanism, Ps atoms need space to be formed. In gasses, there is an enormous empty space between gas molecules, so space (or the shortage of it) is not a limiting factor of Ps formation. In fluids, however, Ps creates a small empty space, a bubble around itself. The bubble model was developed a long time ago (Ferrel 1957) and has been modified continually. Its present form tries to synthesize the results of the spur model and modern physical chemistry (Stepanov et al. 2000). In solids, structural free volumes might serve the empty space needed for positronium formation. 

The macroalkyl radicals are firstly trapped in solid polyethylene especially in crystalline phase. Then, allyl and polyenyl radicals are also partially screened toward subsequent reactions [99K2, 07B5]. The decay kinetics of radicals in irradiated polyethylene at room temperature and in vacuum follows the second order one, which is consistent with the spur model. 

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