Positron diffusion coefficient

The semi-classical random walk theory gives the following expression for the positron diffusion coefficient ... 

Positron diffusion coefficient at room temperature. For experimental values ... 

The sizes and concentration of the free-volume cells in a polyimide film can be measured by PALS. The positrons injected into polymeric material combine with electrons to form positroniums. The lifetime (nanoseconds) of the trapped positronium in the film is related to the free-volume radius (few angstroms) and the free-volume fraction in the polyimide can be calculated.136 This technique allows a calculation of the dielectric constant in good agreement with the experimental value.137 An interesting correlation was found between the lifetime of the positronium and the diffusion coefficient of gas in polyimide.138,139 High permeabilities are associated with high intensities and long lifetime for positron annihilation. 

In solids the free positron lifetime r lies in the approximate range 100-500 ps and is dependent upon the electron density. Following implantation, the positrons are able to diffuse in the solid by an average distance L+ = (D+t)1//2, where D+ is the diffusion coefficient. This quantity is usually expressed in cm2 s-1 and is of order unity for defect-free metallic moderators at 300 K (Schultz and Lynn, 1988). The requirement of very low defect concentration arises because the value of D+ is otherwise dramatically reduced owing to positron trapping at such sites. 

Here ct, ce and cp are the concentrations of the positive ions, electrons and the positron probability density at a point r measured from the center of the blob at time t. Dp is the diffusion coefficient of the positron, Di = De = Damb 0 is the ambipolar diffusion coefficient of the blob, a2 o2 ss a2 is the dispersion of the intrablob species, and a2 is the dispersion of the positron space distribution by the end of its thermalization. Decay rate Te-1 = 1/t + kescs is the sum of the electron solvation rate and possible capture by solute molecules t 2 = 1 /t2 + l/r + kpscs accounts for the free e+ annihilation, solvation and reaction with S. Similarly, t 1 = l/rjmr + hscs, where T r is the rate of the ion-molecule reaction. 

After losing their kinetic energy the penetrated positrons may either directly annihilate with surrounding electrons into two gamma rays, or combine with an electron to form a Ps atom. Although both positrons and Ps are known to localize within the free volumes, a certain fraction of them may diffuse back to the surface and escape to the vacuum. The probability of positrons and Ps annihilating in the polymer depends on their diffusion coefficients. 

Tanaka, K., Kawai, T., Kita, H., Okamoto, K., Ito, Y. (2000) Correlation between gas diffusion coefficient and positron annihilation lifetime in polymers with rigid polymer chains . Macromolecules, 33, 5513. 

In crystals, impurities can take simple configurations. But depending on their concentration, diffusion coefficient, or chemical properties and also on the presence of different kind of impurities or of lattice defects, more complex situations can be found. Apart from indirect information like electrical measurements or X-ray diffraction, methods such as optical spectroscopy under uniaxial stress, electron spin resonance, channelling, positron annihilation or Extended X-ray Absorption Fine Structure (EXAFS) can provide more detailed results on the location and atomic structure of impurities and defects in crystals. Here, we describe the simplest atomic structures more complicated structures are discussed in other chapters. To explain the locations of the impurities and defects whose optical properties are discussed in this book, an account of the most common crystal structures mentioned is given in Appendix B. 

E. J. M. Hensen, A. M. de Jong, and R. A. van Santen have written Chapter 7, which introduces the tracer exchange positron emission profiling (TEX-PEP) as an attractive technique for in-situ investigations, for example, in a stainless steel reactor, of the adsorption and diffusive properties of hydrocarbons in zeolites under chemical steady-state conditions. Self-diffusion coefficients of hydrocarbons, labeled by proton-emitting C at finite loadings and even in the presence of another imlabeled alkane, may be extracted. The method is illustrated by adsorption and diffusion measurements of linear (n-hexane) and branched (2-methylpentane) alkanes in Fl-ZSM-5 and silicalite-1. 

It is necessary to mention that the positron, entering into the solid matter, forms a pair with the electron (positronium Ps), which itself (Ps) migrates to the solid phase (about 10 -10 s). Meeting with defects of crystal structure, the electron and positron annihilate. This method can be used for the determination of defect and size distribution in solids. The diffusion coefficient of Ps is 0.1 cm /s. 

Positron scattering off phonons leads to the following temperature dependence of the diffusion coefficient ... 

The mean diffusion length L+ of the positron is defined as the mean distance from the point of thermalisation that the positron reaches by diffusion movement. This quantity is related to the diffusion coefficient by the relation [72]... 

Abstract Zeolites are of prime importance to the petrochemical industry as catalysts for hydrocarbon conversion. In their molecule-sized micropores, hydrocarbon diffusion plays a pivotal role in the flnal catalytic performance. Here, we present the results of Positron Emission Profiling experiments with labeled hydrocarbons in zeolites with the MFI morphology. Single-component self-diffnsion coefficients of hexanes in silicalite-1 and its acidic connterpart H-ZSM-5 are determined. For the first time, self-diffnsion co-... 

The effect of copolymer composition on free volume and gas permeability of PECT copolymers as well as PET and PCT homopolymers was studied by Hill et al. (97). The free volume was studied by positron annihilation lifetime spectroscopy (PALS) in order to determine the relative size and concentration of free volume cavities in the copolymers. The logarithm of the permeability to oxygen and carbon dioxide increased linearly with the %mol content of 1,4-CHDM units in the copolymer, which was in agreement with the free volume cavity size and relative concentration observed by PALS measurements. Light et al. (98) studied the effect of sub-T relaxations on the gas transport properties of PET, PCT and PECT polyesters. They observed that modification of PET with 1,4-CHDM increased the magnitude of the p-relaxation, as well as the diffusion and solubility coefficients for oxygen and CO. ... 

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