Determination by Small-angle X-ray Scattering of Pore Size Distribution in Nanoporous Track-etched Polycarbonate Membranes

Nanoporous track-etched membranes with narrow pore size distributions and average pore size diameters tunable from 100 to 1000 Åare produced by the chemical etching of latent tracks in polymer films after irradiation by a beam of accelerated heavy ions. Nanoporous membranes are used for highly demanding filtration purposes, or as templates to obtain metallic or polymeric nanowires (L. Piraux et al., Nucl. Instr. Meth. Phys. Res. 1997, B131, 357). Such applications call for developments in nanopore size characterization techniques. In this respect, we report on the characterization by small-angle X-ray scattering (SAXS) of nanopore size distribution (nPSD) in polycarbonate track-etched membranes. The obtention of nPSD requires inverting an ill-conditioned inhomogeneous equation. We present different numerical routes to overcome the amplification of experimental errors in the resulting solutions, including a regularization technique allowing to obtain the nPSD without a priori knowledge of its shape. The effect of deviations from cylindrical pore shape on the resulting distributions are analyzed. Finally, SAXS results are compared to results obtained by electron microscopy and conductometry.