Geminate ion recombination

Williams (1964) derived the relation T = kBTrQV3De2, where T is the recombination time for a geminate e-ion pair at an initial separation of rg, is the dielectric constant of the medium, and the other symbols have their usual meanings. This r-cubed rule is based on the use of the Nernst-Einstein relation in a coulom-bic field with the assumption of instantaneous limiting velocity. Mozumder (1968) criticized the rule, as it connects initial distance and recombination time uniquely without allowance for diffusional broadening and without allowing for an escape probability. Nevertheless, the r-cubed rule was used extensively in earlier studies of geminate ion recombination kinetics. 

With the advent of picosecond-pulse radiolysis and laser technologies, it has been possible to study geminate-ion recombination (Jonah et al, 1979 Sauer and Jonah, 1980 Tagawa et al 1982a, b) and subsequently electron-ion recombination (Katsumura et al, 1982 Tagawa et al, 1983 Jonah, 1983) in hydrocarbon liquids. Using cyclohexane solutions of 9,10-diphenylanthracene (DPA) and p-terphenyl (PT), Jonah et al. (1979) observed light emission from the first excited state of the solutes, interpreted in terms of solute cation-anion recombination. In the early work of Sauer and Jonah (1980), the kinetics of solute excited state formation was studied in cyclohexane solutions of DPA and PT, and some inconsistency with respect to the solution of the diffusion equation was noted.1... 

Onsager s (1938) formula for the probability of escaping geminate-ion recombination in the presence of an external field E may be written as... 

The central problem in the theory of geminate ion recombination is to describe the relative motion and reaction with each other of two oppositely charged particles initially separated by a distance ro- If we assume that the particles perform an ideal diffusive motion, the time evolution of the probability density, w(r,t), that the two species are separated by r at time t, may be described by the Smoluchowski equation [1,2]... 

By solving Eq. (9) subject to boundary conditions (10) and (11b), the escape probability for the totally diffusion-controlled geminate ion recombination is calculated as... 

This expression characterizes the escape probability for the partially diffusion-controlled geminate ion recombination. 

When the motion of electrons and positive ions in a particular system may be described as ideal diffusion, the process of bulk recombination of these particles is described by the diffusion equation. The mathematical formalism of the bulk recombination theory is very similar to that used in the theory of geminate electron-ion recombination, which was described in Sec. 10.1.2 ( Diffusion-Controlled Geminate Ion Recombination ). Geminate recombination is described by the Smoluchowski equation for the probability density w(r,i) [cf. Eq. (2)], while the bulk recombination is described by the diffusion equation for the space and time-dependent concentration of electrons around a cation (or vice versa), c(r,i). 

PICOSECOND AND SUBPICOSECOND PULSE-RADIOLYSIS STUDIES OF GEMINATE ION RECOMBINATION IN LIQUID HYDROCARBONS... 

Here the progress in the picosecond and subpicosecond pulse radiolysis is described first and then the experimental studies on the kinetics of the geminate ion recombination is explained in connection with their application to advanced technology such as the next generation nanolithography and nanotechnology. 

With the development of the picosecond pulse radiolysis, the kinetics data of the geminate ion recombination have been directly obtained. The history of picosecond and subpicosecond pulse radiolysis is shown in Fig. 7. Very recently, the first construction of the femtosecond pulse radiolysis and the improvement of the subpicosecond pulse radiolysis started in Osaka University. 

The stroboscopic pulse radiolysis with the single bunch electron pulse instead of pulse trains started in Argonne National Laboratory in 1975 [54]. The research fields have been extended by the stroboscopic pulse radiolysis with the picosecond single electron bunch, although most of researches had been limited to hydrated and solvated electrons in the aqueous and alcoholic solutions. This system was unable to study the kinetics of the geminate ion recombination in liquid hydrocarbons until the modification of the Argonne linac in 1983, which made possible the quality measurements of the weak absorption. 

The combination of the picosecond single electron bunch with streak cameras, independently developed in 1979 at Argonne National Laboratory [55] and at University of Tokyo by us [56], enabled the very high time resolution for emission spectroscopy. The research fields have been extended to organic materials such as liquid scintillators [55-57], polymer systems [58], and pure organic solvents [59]. The kinetics of the geminate ion recombination were studied [55,57,59]. 

Subpicosecond Pulse-Radiolysis Studies of Geminate Ion Recombination... 

The kinetics data of the geminate ion recombination in irradiated liquid hydrocarbons obtained by the subpicosecond pulse radiolysis was analyzed by Monte Carlo simulation based on the diffusion in an electric field [77,81,82], The simulation data were convoluted by the response function and fitted to the experimental data. By transforming the time-dependent behavior of cation radicals to the distribution function of cation radical-electron distance, the time-dependent distribution was obtained. Subsequently, the relationship between the space resolution and the space distribution of ionic species was discussed. The space distribution of reactive intermediates produced by radiation is very important for advanced science and technology using ionizing radiation such as nanolithography and nanotechnology [77,82]. 

This occurs because the initial separation length between the cation radical and the electron is smaller than the Onsager length (/ (.) at which the thermal energy of an electron corresponds to the Coulomb field. This reaction is called the geminate ion recombination and has been investigated by many researchers globally. 

The experimental method and apparatus, and a procedure of the Monte Carlo method that simulates the geminate ion recombination are described, and the time-dependent distribution is elucidated. 

At the initial stage of reactions, the produced intermediate species such as the cation radical and the electron exist in a narrow space, the so-called spur. After the electron thermalization process, a pair of a cation radical and a thermalized electron remain in a spur. The geminate ion recombination of the cation radical and the electron occurs before these ionic species diffuse and spread uniformly in the media. Therefore the geminate ion recombination takes place in the spur. On the condition of a so-called single pair model,... 

On the other hand, the Monte Carlo method enables us to simultaneously obtain the time-dependent decay curve and the time-dependent distribution function. Therefore we adopted Monte Carlo simulation [18,21,84,85] for the analysis. The geminate ion recombination is also described as follows. 

Absorption due to main intermediates such as polymer cation radicals and excited states, electrons, and alkyl radicals of saturated hydrocarbon polymers had not been observed for a long time by pulse radiolysis [39]. In 1989, absorption due to the main intermediates was observed clearly in pulse radiolysis of saturated hydrocarbon polymer model compounds except for electrons [39,48]. In 1989, the broad absorption bands due to polymer excited states in the visible region and the tail parts of radical cation and electrons were observed in pulse radiolysis of ethylene-propylene copolymers and the decay of the polymer radical cations were clearly observed [49]. Recently, absorption band due to electrons in saturated hydrocarbon polymer model compounds was observed clearly by pulse radiolysis [49] as shown in Fig. 2. In addition, very broad absorption bands in the infrared region were observed clearly in the pulse radiolysis of ethylene-propylene copolymers [50] as shown in Fig. 3. Radiation protection effects [51] and detailed geminate ion recombination processes [52] of model compounds were studied by nano-, pico-, and subpicosecond pulse radiolyses. 

The last reaction should be very fast, because it represents geminate ion recombination. 

Saeki, A., Kobawa, T., Yoshida, Y., Tagawa, S. 2001. Study on geminate ion recombination in liquid dodecane using pico- and subpicosecond pulse radiolysis. Radiat. Phys. Chem. 60 319-322. 

Yoshida, Y., Ueda, T., Kobayashi, H., Tagawa, S. 1993. Studies of geminate ion recombination and formation of excited states in liquid n-dodecane by means of a new picosecond pulse radiolysis system. Nucl. Instr. Meth. Phys. Res. A 327 41 —43. 

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