Polymer membranes – Fractal characteristics and determination of roughness scaling exponents

Surface roughness is a parameter widely reported when characterising membrane surfaces, due to its effect on membrane properties, such as fouling / biofouling and wetting. However, a surface does not have a single roughness value, rather the magnitude of measured roughness is dependent on the length scales of measurement. Here, we report findings from roughness measurements of several commercial filtration membrane surfaces using atomic force microscopy. All membranes showed self-affine behaviour at scan sizes below approximately 10 µm, where the magnitude of root mean squared roughness, R_q, was described by both the scan length and an exponential factor, H. Furthermore, we show that values of H can be obtained from power spectra of AFM images using a relatively simple approach. Using values of H and R_q obtained at a single scan size from image power spectra allowed us to estimate, within reasonable error, R_q values at other scan size, below a cross-over length. Above this crossover length roughness scaling was linear, rather than exponential for the membranes studied.