Schematic of changing percolation paths of unpressed (upper) and pressed (lower) porous electrodes due to decrease of porosity.
Electronic conductivity of a set of nanoparticulate electrodes compressed at different pressures as indicated. The starting thickness of the films is similar in all cases, and all films were sintered after pressing. The conductivity is determined from the current between parallel contacts (Ref. 9), normalizing to the length, width, and thickness of the layer. The original thickness before pressure is taken in all the cases, since there is no change in the amount of present on the electrode.
Overview of the thicknesses and pressures of the investigated samples.
Izyumov-Kirkpatrick (Refs. 26 and 28) and Bernasconi-Wiesmann (Ref. 29) analytical models of percolation conductivity for a 3D cubic lattice, in terms of (a) fractional occupation and (b) porosity of the lattice. The straight line indicates the dependence .
Dependence of on the layer thickness of unpressed electrodes. The solid line gives the dependence for .
Photocurrent transients of pressed porous electrodes with initial layer thickness of .
Dependence of on the layer thickness for pressed electrodes with different initial thicknesses. The pressures were 0.2, 0.4, 0.6, and . The dotted line gives the dependence for .
Dependence of the charge integrated over the diffusion peak on (a) and (b) .
Dependence of on the porosity of the pressed porous electrodes for the different initial thicknesses. is the critical porosity (0.76). The solid line shows the slope of 2.3.
Plot of the numerical results obtained by random walk simulation in Ref. 15 as a function of lattice occupancy. The fit to Eq. (7) gives , , and . The diffusion coefficient has been normalized to the value at obtained from the fit.
Representation of normalized diffusion coefficient as a function of fractional occupation of the lattice. Shown are the Izyumov-Kirkpatrick (Refs. 26 and 28) and Bernasconi-Wiesmann (Ref. 29) percolation theories, the data of Fig. 8 for (except those of ), the numerical data obtained by random walk simulation in Ref. 15, and parabollic fits to the two sets of data following Eq. (15). The diffusion coefficient has been normalized in all cases to the value at obtained from the fits.
Assumed relationship between porosity, packing fraction, and occupancy according to parameters in Table I.
Diffusion coefficient in Monte Carlo simulation (Ref. 15) as a function of porosity converted into a fractional occupancy .
Parameters selected for relating porosity with a lattice occupancy.
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