TR MFE Decay Curves

8 Correlation Between Spin Entanglement and the Spin Relaxation Time 

6 Senulogarithmic plot of the ratio of fluorescence intensity using 2 pairs (black) 4 pairs (red) 6 pairs (green) 8 pairs (blue) 10 pairs (cyan) 15 pairs (magenta) 20 pairs (yellow) and 40 pairs (dark yellow) of [e + Solv ]. A mutual diffusion coefficient (D ) of 0.5 h ps was used for S / C-RH+. Cations were arranged on a line 20 A apart, with anions Gaussian distributed from their respective cations with a standard deviation of 80 A. Shortest T was calculated to be 50ns (dark yellow). Smooth line corresponds to Eq. (8.3) with T2 = 3 ns and T = 50 ns (9 = 0.22) 

Zero field spin relaxation time (Tq) was set to 9 ns. Cations were arranged on a fine 20 A apart, with anions Gaussian distributed from its respective cation with a standard deviation of 80 A 

In this section the effect of (i) treating spin relaxation phenomenologically and (ii) the spatial distribution of the cations is explored to analyse how the TR MFE curve changes. All high field simulations were done using a relaxation time of T = 350 and 130 ns and T2 = 15 and 9 ns for Sj and c-RH+ respectively. These parameters are the experimentally determined spin relaxation time for Sj and c-RH+ as shown in Table 8.2, apart from the T value for c-RH+, which was calculated from Eq. (8.9). Eor all zero field simulations it was assumed Tq = 72. In the TR MFE decay curves where line is indicated, the cations were distributed on a straight line 20 A apart and where sphere is indicated, the cations were distributed on a sphere of radius 20 A. 

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The complexity of simulating an entire track structure from the IRT framework has been highlighted in this chapter. Although in the TR MFE decay curves the contribution of cross-recombination may have been overestimated, the results nonetheless highlight a distinctive correlation between cross-recombination and the spin-lattice relaxation time. Further work is now required to (1) incorporate a more realistic description of the magnetic interactions (in particular the exchange and dipole interactions) (2) use a realistic description for the track structure to describe the radiolysis of hydrocarbons, where the ERP effect can be properly understood in terms of the spatial distribution of the primary and secondary ion-pairs. 

In the first simulation (Fig. 8.18a), the effects of spin-exchange reactions (15), (16) and (17) were taken into consideration indirectly by using the experimentally determined T and T2 values. The purpose of this simulation was to isolate the effect of cross-recombination without complicating the decay of the TR MFE curve by other random processes which can cause relaxation as well. 

From the analysis of the TR MFE curves, a number of distinctive conclusions can be made. First of all, when a high field relaxation rate is phenomenologically treated using a value of Ti = 220 ns, the decay in the TR MFE curve is not accelerated by... 

In agreement with the findings of Borovkov [34, 35], the source of the spin-lattice relaxation in TMPD+ remains unclear as typical relaxation mechanisms cannot provide the observed relaxation time. From the kinetics, it is also clear that the decay of the TR MFE curve cannot be explained by an increase in the fraction of magnetic-field-insensitive emission due to reaction (8), since its frequency decreases after several nanoseconds after the formation of the secondary ion pairs. Borovkov [34, 35] has also highlighted that long-range spin-spin dipole interactions cannot resolve the problem either. 

Linear spur structure To investigate the effect of the spatial distribution of the cations on the overall decay of the TR MFE curves, a second simulation was done in which the cations were placed along a line (with a mean spacing of 60 A found to produce the correct magnitude of the magnetic field effect). No high field spin relaxation mechanism was assumed to take place but reactions (15), (16) and (17)... 

By modelling the TR MFE fluorescence decay curves in low-permittivity solvents using new simulation techniques, it has been shown that the spin-lattice relaxation time can be significantly decreased by this cross-combination effect, depending on the number of radical pairs in the spur. It is hypothesised that this effect acts as an extra source of spin relaxation in hydrocarbons where the recombination fluorescence is slowed down by an electron scavenger, such as hexafluorobenzene. It has also been hypothesised that different spin-lattice relaxation times are to be expected for photolytic and radiolytic pairs. 

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