Fractal nature of electrical conductivity in ion-implanted polymers

Abstract

The electrical-conductivity and current-transient data for ion-implanted polymers are explained in terms of a percolative phase transition from an insulating state to trap-controlled hopping conduction on a backbone cluster. The value of the critical exponent s’ for electrical conductivity versus the fluence ranges from ∼4 to 5, consistent with the fractal behavior in the vicinity of the phase transition. The percolative stabilization of radicals is suggested as a reason for the sharp increase in the unpaired spin concentration within the damage structures, recorded by the ESR measurements. A scaling relation between the free spin concentration and ESR linewidth, including an exponent ${\mathit{d}}_{\min }$ [∼1.2±0.05 for poly(2,6-dimethylphenylene oxide)] is established. The change in s’, as a function of ion energy, is connected with the crossover between nuclear and electronic energy transfer. The one-dimensional character of the temperature dependence of the electrical conductivity is related to the links connecting the groups of traps. The contribution of dangling bonds is suggested as a reason for the lagging of the percolation threshold in the conductivity measurements, as compared to ESR. The fractal exponent α of the dielectric relaxation is measured versus fluence from the current transients (α between 0.22 and 0.85). A sharp increase in the real part of the dielectric constant at low frequencies is observed, as expected for fractals.