Random flight simulation

While many of the important reactions in radiation and photochemistry are fast, not all are diffusion-limited. The random flight simulation methodology has been extended to include systems where reaction is only partially diffusion-controlled or is spin-controlled [54,55]. The technique for calculating the positions of the particles following a reflecting encounter has been described in detail, but (thus far) this improvement has not been incorporated in realistic diffusion kinetic simulations. Random flight techniques have been successfully used to model the radiation chemistry of aqueous solutions [50] and to investigate ion kinetics in hydrocarbons [48,50,56-58]. 

The IRT model has been developed in detail in a series of papers of Green, Pimblott and coworkers and has been validated by comparison with full random flight simulations [47,49,51]. The IRT treatment of the radiation chemistry relies upon the generation of random reaction times from initial coordinate positions from pair reaction time distribution functions. A simulation, such as a random flight calculation, starts with the initial spatial distribution of the reactants. The separations between all the pairs of particles are evaluated... 

It has been reported in the literature [48] that Smoluchowski s rate constant overestimates the rate of scavenging for a single target that can be hit multiple times (for example DNA). In their work, the authors found that Smoluchowski s rate constant overestimated the scavenging yield in comparison to Monte Carlo random flights simulation (which makes no assumptions on the rate of scavenging as they are explicitly treated). The authors have found that a modiflcation to Smoluchowski s rate constant is required in order to properly take the correlation of reaction times into account however, the independent pairs approximation is still made. 

Monte Carlo Random Flights Simulation 4.3.1 Introduction... 

In random flights simulations the single most important parameter is the time step bt, which if not properly converged leads to incorrect results. If the drift remains effectively constant throughout the time step, then the separation between the pair behaves as a one dimensional Wiener process with constant drift. The relative drift... 

The IRT model [1,2, 12, 15] is essentially a Monte Carlo algorithm which assumes the independence of reaction times (i.e. each reaction is independent of other such reactions and that the covariance of these reaction times is zero). Unlike the random flights simulation, the diffusive trajectories are not tracked but instead encounter times are generated by sampling from an appropriate probability density function conditioned on the initial separation of the pair. The first encounter takes place at the minimum of the key times generated min(h t2, fs...) and all subsequent reactions occur based on the minimum of surviving reaction times. Unlike random flights... 

Fig. 43 Recombination yield for a single ion pair using an encounter radius of 5 A, D = 2 ps and Tc = 290 A. a = (6r/7) and b cr = (6r/7) exp(—with x = fc/fo- (Line) and open circle) correspond to random flights simulation and analytical expression respectively...

This chapter has presented the foundations of the IRT and random flights simulation techniques and how they have been extended to widen their application in the field of radiation chemistry. In Chap. 8 it will be shown how the IRT can be further extended... 

Although the IRT algorithm is sufficiently developed to completely simulate the system under study, the results are nevertheless compared with full Monte Carlo random flights simulation to make sure the correct kinetics and spin dynamics are obtained with no source of bias introduced by the IRT approximation. 

In the random flights simulation, at time (t+St) arandom number 17(0, 1] is generated from a uniform distribution and is compared to (l-e / ), where Tju is the relaxation time of the radical i. If U (0, 1] < (1 ), then spin relaxation takes... 

The exact computation time required for Slice depends on the number of slices used. As the number of slices increases, the computation time also increases as essentially the simulation is performing a Monte Carlo random flights simulation on a lattice. 

Fig. 5.9 Yield of H2O2, P and R2 obtained using the Hybrid and Slice simulation packages and compared with random flights simulation using a spin relaxation time of 100 ps on the hydroxyl radical. 12 M scavenger concentration was used in aU cases. Number of realisations used 5 x 10. Full simulation parameters are detailed in Tables 5.3 and 5.4. Here MC refers to random flights simulation...

Fig. 5.10 Spin polarisation (P — P ) on radicals M and M2 as a function of the number of slices and compared against fuU random flights simulations. The g-factors and the hyperfine constant on Ml and M2 were 2.025, 2.02 and 2.64 x 10" T respectively, a An exchange range and strength respectively of 1.07 A and 16 T were used, b An exchange range and strength of 2.14 A and 8 T respectively were used. Polarisation is per remaining radical...

Fig. 6.8 Reactive product H / OH placed at a e position b H+ZCj position c e q/ OH position dH+/ OH position. Abbreviation used free diffusion (FD) and first passage (FP). A spur width of a(7.5 A) was used for OH, H and ct(40 A) for Here MC refers to random flights simulation.

In order to extract the correlation between the e, H+ and OH distances, a set of random flights simulations were done in which at the point of the first reaction, the simulation carried on as normal as if the first reaction had not occurred (the type of the first reaction was however recorded). At the end of the simulation, a series of histograms were obtained which showed the probability of undergoing 0, 1 or 2 reactions and the type of reactions that had occurred. The results presented in Figs. 6.9 and 6.10 highlight the following ... 

In the random flights simulation, scavengers were treated explicitly, such that the e has to diffuse towards a stationary S to react. The IRT algorithm made use of Smoluchowski s time dependent rate constant, in which reaction times were generated from the probability distribution... 

Fig. 7.2 Scavenging yield of eS using an initial ion-pair separation of a 40 A b 60 A c 80 A and d 100 A. A Scavenger concentration of 0.5 M was used in both simulations. Here MC refers to random flights simulation...

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