The Joule regime at large electric fields in composites is presented in the context of a conduction phase diagram in the field-concentration plane. A sample suffers breakdown when the field is too large. The resistance up to breakdown is described by a universal curve as a function of field. It is found that the ratio of the breakdown resistance to the zero-field resistance assumes a fixed value Y at breakdown. Y is found to be 1.37 in carbon high-density polyethylene composites and is independent of carbon fraction and external conditions but depends on the nature of the conductor. A quantity which is independent of conducting material is defined. Results are compared with previous data.PACS numbers: 72.80.Ng, 05.70.Jk, 72.20.Ht Application of finite force (F, mechanical or electrical) in disordered systems usually results in a nonlinear response leading to some sort of catastrophic behavior in the extreme limit (e.g., fracture in mechanical systems and dielectric breakdown or burning in electrical systems). In recent years there has been a renewed interest in the problem of catastrophic phenomena [1] although the problem of non-Ohmic electrical conductivity in the precatastrophic regime in various disordered systems has been studied for a long time [2,3]. However, there have been very few attempts so far to describe the behavior of a system over the full range of the applied force. Such a study holds the promise of unraveling many important aspects such as precursor effects, predictability, and the effect of disorder on the nature of breakdown. Yagil et al.[4] carried out somewhat limited measurements of I-V curves in thin semicontinuous metallic films of Ag and Au. Focusing on breakdown events, it was concluded that breakdown currents I b in the films scale as I b ϳ B 2x , where B is the normalized third harmonic component (see below) generated as a result of Joule heating. Breakdown was assumed to occur when the sample resistance R exhibited the first irreversible discontinuity as a function of applied current I. The exponent x was measured to be 0.48 and 0.41 in films of Ag and Au, respectively. The authors also derived theoretical bounds for x, 0.5 $ x $ 0.5͓1 2 1͞t͑2 1 w J ͔͒ so that breakdown currents were expected to lie between two bounds. Here, t is the electrical conductivity exponent and w J k͞t, k being the noise exponent [5].In this Letter, we present systematic measurements of electrical resistance, particularly in the Joule regime of a composite system of carbon high-density polyethylene (HDPE) up to breakdown. The breakdown in a sample has the nature of a first-order transition: as soon as the current from a constant current source exceeds a certain value I b , the sample resistance R starts increasing uncontrollably and becomes unsteady. Let R o R͑0͒ be the linear or zero-field resistance, R b R͑I b ͒ be the breakdown resistance and Y R b ͞R o . It is found that for p . p J , where p is the (volume) fraction of conducting component (carbon) and p J is a fraction characteristic of the system ...

The I-V characteristics of a carbon-wax mixture slightly above the percolation threshold are found to be nonlinear. Generally for low (linear) -resistance samples, the I-V curves are smooth. The leading nonlinear term is quadratic, rather than cubic. For high-resistance samples, the onset of nonlinearity is marked by the appearance of resonance like structures in the R-V curves. The current I, at which nonlinearity starts scales with the linear conductance X& as I, -X&, with x =1.4 in both cases. The secondorder conductance, X2, in the case of smooth curves, also scales with X& as X2-X&, with y =0.59. Results are discussed within the framework of two previously suggested models. It is shown that none of these models can explain fully results obtained with the carbon-wax system.

The I-V characteristics of four conducting polymer systems like doped polypyrrole (PPy), poly 3,4 ethylene dioxythiophene (PEDOT), polydiacetylene (PDA) and polyaniline (PA) in as many physical forms have been investigated at different temperatures, quenched disorder and magnetic fields. Transport data clearly show the existence of a single electric field scale for all systems. Based upon this observation, a phenomenological scaling analysis is performed, leading to extraction of a numerical value for a nonlinearity exponent called xM which serves to characterize a set of I-V curves. The conductivity starts deviating from an Ohmic value σ0 above an onset electric field Fo which scales according to Fo ∼ σ x M 0 . The electric field-dependent data are shown to be described by Glatzman-Matveev multi-step tunneling model [JETP 67, 1276[JETP 67, (1988] in a near-perfect manner over nine orders of magnitude in conductivity and five order of magnitudes in electric field. Furthermore, xM is found to possess both positive and negative values lying between -1/2 and 3/4. There is no theory at present for this exponent. Some issues concerning applicability of the Glatzman-Matveev model are discussed.

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At a composition far above the percolation threshold, the resistance of a composite sample increases with time due to Joule heating as a constant current of a sufficiently large value is passed through the sample. If the current is less than a certain breakdown current (I(b)) the resistance eventually reaches a steady value with a characteristic relaxation time tau(h). The latter diverges with current I as tau(h) approximately (1-I(2)/I(2)(b))(-z). The value of the exponent z displays large fluctuations leading to unusual scaling of the relaxation time. It is shown that the results lead to important conclusions about the nature of breakdown phenomena.

a b s t r a c t Keywords:Zinc oxide thin film Sol-gel preparation Annealing X-ray diffraction Atomic force microscopy Optical properties This investigation deals with the effect of annealing temperature on the structural, topographical and optical properties of Zinc Oxide thin films prepared by sol-gel method. The structural properties were studied using X-ray diffraction and the recorded patterns indicated that all the films had a preferred orientation along (002) plane and the crystallinity along with the grain size were augmented with annealing temperature. The topographical modification of the films due to heat treatment was probed by atomic force microscopy which revealed that annealing roughened the surface of the film. The optical properties were examined by a UVvisible spectrophotometer which exhibited that maximum transmittance reached nearly 90% and it diminished with increasing annealing temperature.

The complex AC conductance of carbon-wax mixtures was measured as a function of angular frequency omega from 7 Hz to 100 kHz for different concentrations p of carbon near the percolation threshold pc. The scaling exponents x=0.72+or-0.01, y=0.23+or-0.05 were found to be remarkably close to the theoretical values expected from the intercluster polarization model. The characteristic frequency omega c at which the real part of the AC conductance deviates from its DC value scales with the DC conductance sigma DC as omega c approximately sigma DCz, where z approximately=1.1. The nature of the variation of loss tangent tan delta with frequency was studied in detail. It was found that tan delta went through a minimum at a frequency which increased with p. The increase of tan delta at higher frequencies cannot be explained by the usual RC model. The authors consider a modified version, the R-RC model in which a capacitor is always in series combination with a resistor, i.e. capacitors are lossy. This model is shown to reproduce the observed behaviour of tan delta and believed to be more realistic than the RC model hitherto considered in that series resistors may be a more effective representation of the dangling bonds in the system.

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