Recombination on fractal networks: Photon and electron emission following fracture of materials

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We report measurements and analysis of fracture-induced photon and electron emissions from several polymeric and inorganic systems on time scales of 10~2 to 103 s following fracture. The dominant mechanism for postfracture emission involves the recombination of mobile free carriers (usually electrons) with immobile recombination centers. The emission decays were modeled as (pseudo)unimolecular and bimolecular recombination on fractal lattices as described by Zutnofen, Blumen, and Klafter.1 Although the decay kinetics shows a great deal of variability from material to material, this random walk description of the recombination process provides an excellent description of the emissions over long time scales. This analysis shows a strong correlation between the local structure at the fracture surface and the resulting decays.

I. INTRODUCTION The transport of molecular excitations has proved to be a useful probe of the local environment in materials where the transport is limited by the local geometry.2 For instance, the nm-scale porous structure of vycor glass is reflected in the decay kinetics of excited naphthalene molecules within the pores.3 Similarly, the structure of polymer coiling has been probed by observing the diffusion of optical excitations along the polymer chain.4 These studies typically employ specially introduced chromophores to ensure efficient optical excitation and experimentally useful excitation lifetimes. In many cases, the effects of transport on the decay can be studied only in dilute solutions of the material of interest. Long-lived excitations are produced during the fracture of many materials.5'6 In vacuum, photon and electron emissions (two components of what is known as fracto-emissiori) are readily observed from many materials. On sub-;U,s time scales, the emission intensities often reflect the erratic behavior of rapidly propagating cracks.7'8 Following fracture, these emissions frequently persist at reduced intensities for many seconds and sometimes hours. As noted below, the kinetics of the emission decays has much in common with the decay of excitations in restricted geometries and shows considerable potential as probes of the local geometry of the material along the fracture surface. Fracture induced excitations are easily produced in a wide variety of solid materials without the introduction of chromophores, and are thus applicable to a wide range of materials. Fracture also localizes the excitations in the near-surface region, where the detection geometry is ideal. The photon and electron emissions after fracture are readily sampled on a wide range of time scales (e.g., 10" 5 to 104 s). Although the details of the emission J. Mater. Res., Vol. 8, No. 11, Nov 1993

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mechanisms are not always known, a number of studies suggest that the dominant emission process involves the recombination of mobile electrons with immobile recombination centers.9'10 In unfilled polymers, these excitations can be produced by bond breaking during f