Spatial Distribution of the Alkyl Radical

Both the phase and longitudinal relaxations for the alkyl radical in polyethylene are caused by the radical spin-spin interactions and are dependent on the radical concentration. This concentration dependence was examined in detail by changing the concentration with radiation dose and with thermal treatment [28]. The radiation dose was limited up to 30 kGy, where the G value of the alkyl radical is constant at 3.3. 

An example of the phase relaxation curve observed for the alkyl radical in irradiated polyethylene has already been shown in Fig. 5. Regardless of the radiation dose, the relaxation kinetics monitored at the center of the ESR spectrum can be expressed empirically by the following equation  

The rate constant for the first-order term, a, is dependent on the radiation dose (therefore, on the radical concentraion), while the rate constant for the second-order term, m, is independent of radiation dose. The dose-independent term is attributed to the hyperfine interaction with the surrounding protons. 

The dose-dependent term of the phase relaxation is attributed to the electron spin-spin interaction as described in the preceding section. By taking the dose-yield curve shown in Fig. 3 into account, the dose-dependent rate constant can be empirically expressed as 

The longitudinal relaxation of the alkyl radical in polyethylene as demonstrated in Fig. 7 can be expressed by the following equation  

---

The recombination between two alkyl radicals is believed to be the main source of radiation-induced crosslinks in polyethylene [21], so that it is important to study the mechanism for formation and reaction of the alkyl radical. We have applied the ESE method to elucidate the paramagnetic relaxation mechanism and the spatial distribution of the alkyl radical, in order to get further insight into the radiation-chemical reactions of polyethylene resulting in the formation of crosslinks. 

---