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GGA (PW91) + U is applied to the calculation of the structure (lattice parameters) and the electronic structure of the V 2 O 5 bulk and its (001) surface for different values of U eff used in the literature (0.0, 3.0 and 6.6 eV). Similar surface lattice parameters are calculated for the (001) surface and for the bulk, as well as similar electronic structures. The calculated lattice parameters (a and b for the surface and a, b and c for the bulk) are in good agreement with experimental results. It seems that there is no strong correlation between the calculated lattice parameters and the value of U eff. The calculated width of the valence band keeps the value of »5 eV for the three studied U eff. However, the energy gap between the valence and the conduction bands increases with the value of U eff. U eff =3.0 eV seems to be the most adequate value to describe the energy gap after comparison with experimental results. Electronic density contour plots indicate that for a larger (smaller) U eff the accumulated charge in the V-O(1) bond is overestimated (underestimated). The contour plots (in the a direction) show that the charge distribution V-O(3) is less correlated with U eff than the charge distribution V-O(1), whereas charge distribution V-O(2) seems not to be corretaled with U eff. The energy gap between the valence and the conduction bands seems to be strongly related with the charge distribution in the V-O(1) bond. The V-O(1) bond stability seems to be correlated with U eff. However, the stability of the V-O(2) and V-O (3) bonds seems not to be strongly affected by U eff .

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In the present paper, the discharge avalanche model, initially proposed by Dissado and co-workers, is modified to explore (by correlating its results with experimental information) the role of the space-charge characteristics in the fractal nature of electric trees. Stochastic fluctuations of the local electrical field in each site of the polymer sample (E(loc)) around the Laplacian field (E(lap)) are allowed and limited to intermediate values of E(lap). The major achievements of the modified model are the prediction of a nonmonotonic behavior in both the average time to failure and the average fractal dimension of the electrical trees, and the prediction of a transition from branched to runaway trees as the applied voltage is increased.

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h i g h l i g h t s• A new expression for the entropy of adsorbed dipoles improves current predictions.• The entropy of long molecules shows a non-monotonic dependence on the coverage.• The calculation of the entropy of diatomic molecules for any coverage is improved.• New formula to calculate the entropy of adsorbed dipoles as a function of coverage.