Spur radii

In their deterministic modelling, Swiatla-Wojcik and Buxton [9] scaled the change in the initial spur radii r° with temperature t using Eq. (8) ... 

The required parameters for the spur diffusion model are the initial yields, G°, and the spur radii t e for eaq , and f for i = iT, H, OH, H2 and H2O2. In their treatment, Swiatla-Wojcik and Buxton [1,31] chose these parameters to fit the extensive data available for low LET radiation at ambient temperature. The values are hsted in Table 2. The values of G° were then assumed to be independent of temperature and the spur radii were scaled with temperature according to the density, with the result that t e and increased by no more than 11.5% up to 300 °C. The main factors determining the temperature dependence of the g-values, therefore, are the rate constants listed in Table 1. Thus, the significant increase in g(OH) compared with g(eaq ) reflects the fact that the spur reactions of OH (R2, R7 and R8 in Table 1) become significantly slower than the diffusion-controlled rate, whereas reactions Rl, R4, R5 and R9 are close to diffusion-controlled over the whole range of temperature. 

Initial yields and spur radii for modelling water radiolysis [1]°... 

Kevan (1974) has exhaustively reviewed ein organic glasses, to which the reader s attention is drawn. He points out that the effective spur radius r for trapped electrons may be operationally given in angstroms as... 

Here fi2 = 1/Lv(t + r), L is the mean free path of radicals at thermal velocity v, and the initial spur radius r0 and the fictitious time T are related by r2 = Lvr. On random scattering, the probability per unit time of any two radicals colliding in volume dv will be ov/dv, where <7 is the collision cross section. The probability of finding these radicals in dv at the same time t is N(N - 1 )p2 dv2, giving the rate of reaction in that volume as crvN(n - 1 )p2 dv. Thus,... 

Clifford et ah (1987a,b) considered acid spurs (primary radicals H and OH) and computed the evolution of radical and molecular products by the master equation (ME) and IRT methods. Reasonable values were assumed for initial yields, diffusion constants, and rate constants, and a distribution of spur size was included. To be consistent with experimental yields at 100 ns, however, they found it necessary that the spur radius be small—for example, the radius of H distribution (standard deviation in a gaussian distribution) for a spur of one dissociation was only in the 0.4—0.75 nm range. Since in acid spurs H atoms inherit the distribution of eh, this is considered too low. This preliminary finding has later been revised in favor of spurs of much greater radius. 

Defining the radius of the spur as the radius within which 99% of the radical is included, the spur radius rs is expressed as... 

The effective local concentration determined from the longitudinal relaxation as mentioned above is roughly equal to the value of the bulk concentration where the dose-yield curve begins to deviate from the linear relationship. Assuming that the dose-yield curve starts to saturate at the bulk concentration of 8.4 mmol/dm3 or the radical-pair concentration of 4.2 mmol/dm3 due to the overlap of the spurs, the radius of the spur is estimated to be 4.5 nm. This value is in good agreement with the spur radius of 4.1 nm obtained from the relaxation measurement. This coincidence seems to support the general view that the... 

The string of beads model has been proposed by Samuel and Magee [12] and has been widely used for the discussion of diffusion-controlled reactions in water. Radicals are supposed to be formed in spherical volumes called spurs . About 40 eV energy is deposited in each spur which are equidistant. The distance between spurs is about 3000 A for a 450 eV electron in water. The initial spur radius is 10—15 A. The picture of an electron track according to this model is given in Fig. 4(a). 

The main purpose of railroads is to provide an inexpensive means for obtaining raw materials and for shipping products. This means that they should be close to raw material and / or product storage. Buildings and loading docks should be set back 8 ft (2.4 m) from the center of the railroad track. Spurs and switches should be laid out with a 100 ft. (30 m) radius.3 Roads are used not only for these purposes, but... 

The Samuel-Magee model can be extended to a-particle tracks, considered as cylindrical columns formed by excessive spur overlap due to high LET. To a good approximation, the length I of the cylinder remains constant while its radius grows by diffusion. In this geometry, the normalized radical distribution is given by... 

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. 

In irradiated solutions of proteins, the reacting groups (the amino acid residues) are concentrated into small regions of the solution, and the water radicals are produced in small spurs (approximately 10 A. in radius). The kinetics of their interactions are therefore expected to be different from those of free amino acids which are distributed randomly throughout the solution. A brief treatment of this problem has been presented by Schwartz 32). 

A semi-quantitative picture of positronium formation in a spur in a dense gas was developed by Mogensen (1982) and Jacobsen (1984, 1986). If the separation of the positron from an electron is r, and there is assumed to be only one electron in the spur (a so-called single-pair spur), then the probability of positronium formation in the spur, in the absence of other competing processes, can be written as [1 — exp(—rc/r)] here rc is the critical, or Onsager, radius (Onsager, 1938), given for a medium of dielectric constant e by... 

When people consider confinement effects, they consider mainly an increase in the encounter probability inside a single pore and therefore, expect an acceleration of the reaction. Such in-pore acceleration has been quantified by Tachiya and co-workers for diffusion-limited reactions through the so-called confinement factor [see Eq. (11.58) in Ref. 40]. From this treatment, confinement effects are expected to disappear when the reaction radius is less than one tenth of the confinement radius. Considering the reaction radii of radiolytic species, no acceleration by confinement should be expected for pore diameter larger than 10 nm. For smaller pore size, acceleration of the recombination reactions within spurs would be critical in the determination of radiolytic yields in the nanosecond time range. However, the existence of such an acceleration of radiolytic reactions has not been suggested in the nanosecond pulse radiolysis of zeolites and has still to be assessed using picosecond pulse radiolysis. 

Interestingly, it has been shown that the recombination of the hydrated electron is greatly dominated by reaction with OH radical, because the reaction with HjO is not diffusion controlled despite the Coulombic attraction. Geminate ion recombination is usually considered to be negligible in water because the Onsager radius is small (0.7 nm) compared to the radius ofthe distribution of e, in the spur ( 2.3 nm) (Chapter 1). 

Permissible radius of curvature for spurs—consult local rail authorities... 

Any epiphysis or apophysis may develop from multiple centres and similarly the epiphysis of the distal radius or ulna may arise from two ossification centres appearing deft or bipartite (Fig. 7.21) (Harrison and Keats 1980). Separate ossification centres for the radial or ulna styloid processes may fuse with the main ossification centre or persist unfused as accessory ossicles into adulthood. In late adolescence or early adulthood remnants of the fusing or fused epiphysis can be mistaken for fractures. These include fine sclerotic or lucent lines and residual epiphyseal spurs (Fig. 7.22). 

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