The fractal geometry of polymeric materials surfaces: surface area and fractal length scales

Using three common polymeric materials (polypropylene (PP), polytetrafluoroethylene (PTFE) and polycaprolactone (PCL)), a standard oxygen-plasma treatment and atomic force microscopy (AFM), we performed a scaling analysis of the modified surfaces yielding effective Hurst exponents (H ≃ 0.77 ± 0.02 (PP), ≃0.75 ± 0.02 (PTFE), and ≃0.83 ± 0.02 (PCL)), for the one-dimensional profiles, corresponding to the transversal sections of the surface, by averaging over all possible profiles. The surface fractal dimensions are given by d_s = 3 - H, corresponding to d_s ≃ 2.23, 2.25, and 2.17, respectively. We present a simple method to obtain the surface area from the AFM images stored in a matrix of 512 × 512 pixels. We show that the considerable increase found in the surface areas of the treated samples w.r.t. to the non-treated ones (43% for PP, 85% for PTFE, and 25% for PCL, with errors of about 2.5% on samples of 2 µm × 2 µm) is consistent with the observed increase in the length scales of the fractal regime to determine H, typically by a factor of about 2, extending from a few to hundreds of nanometres. We stipulate that the intrinsic roughness already present in the original non-treated material surfaces may serve as 'fractal' seeds undergoing significant height fluctuations during plasma treatment, suggesting a pathway for the future development of advanced material interfaces with large surface areas at the nanoscale.