Use of atomic force microscopy and fractal geometry to characterize the roughness of nano-, micro-, and ultrafiltration membranes

Membrane surface roughness alters the surface area accessible to foulants and may influence macroscopic properties, such as zeta potential. It is usually quantified by atomic force microscopy (AFM) at a single scan size. This would be appropriate if roughness is independent of scale. This study shows that the root-mean-square roughness, R_RMS, is scale (or scan size, L × L) dependent through the power law R_RMS = AL^3−D. The coefficient, A, is the roughness at a scan size of 1² μm². D is the fractal dimension that relates the increase in roughness to the increase in scan size. Values for A and D were determined for a range of micro- and ultrafiltration membranes using an AFM scan series covering at least three orders of magnitude in L. They were also determined for nanofiltration membranes by re-analysis of data in the literature. The results suggest that using the power law expression allows potentially greater discrimination among membrane types and provides a way to quantify membrane roughness over a range of scales. It was further observed that the coefficients A and D of PVDF membranes showed positive and negative correlations, respectively, with the molecular weight cut-off. Additionally, zeta potentials of PVDF membranes measured by the tangential streaming potential method became more negative with increasing A and more positive with increasing D, suggesting possible significant influence of roughness on hydrodynamic transport of ions.