Dynamical scaling properties of nanoporous undoped and Sb-doped Sn O2 supported thin films during tri- and bidimensional structure coarsening

Abstract

The coarsening of the nanoporous structure developed in undoped and 3% Sb-doped Sn O2 sol-gel dip-coated films deposited on a mica substrate was studied by time-resolved small-angle x-ray scattering (SAXS) during in situ isothermal treatments at 450 and 650°C. The time dependence of the structure function derived from the experimental SAXS data is in reasonable agreement with the predictions of the statistical theory of dynamical scaling, thus suggesting that the coarsening process in the studied nanoporous structures exhibits dynamical self-similar properties. The kinetic exponents of the power time dependence of the characteristic scaling length of undoped Sn O2 and 3% Sb-doped Sn O2 films are similar (α≈0.09), this value being invariant with respect to the firing temperature. In the case of undoped Sn O2 films, another kinetic exponent, α′, corresponding to the maximum of the structure function was determined to be approximately equal to three times the value of the exponent α, as expected for the random tridimensional coarsening process in the dynamical scaling regime. Instead, for 3% Sb-doped Sn O2 films fired at 650°C, we have determined that α′ ≈2α, thus suggesting a bidimensional coarsening of the porous structure. The analyses of the dynamical scaling functions and their asymptotic behavior at high q (q being the modulus of the scattering vector) provided additional evidence for the two-dimensional features of the pore structure of 3% Sb-doped Sn O2 films. The presented experimental results support the hypotheses of the validity of the dynamic scaling concept to describe the coarsening process in anisotropic nanoporous systems. © 2007 The American Physical Society.