Topological characterization of antireflective and hydrophobic rough surfaces: are random process theory and fractal modeling applicable?

Abstract

The random process theory (RPT) has been widely applied to predict the joint probability distribution functions (PDFs) of asperity heights and curvatures of rough surfaces. A check of the predictions of RPT against the actual statistics of numerically generated random fractal surfaces and of real rough surfaces has been only partially undertaken. The present experimental and numerical study provides a deep critical comparison on this matter, providing some insight into the capabilities and limitations in applying RPT and fractal modeling to antireflective and hydrophobic rough surfaces, two important types of textured surfaces. A multi-resolution experimental campaign by using a confocal profilometer with different lenses is carried out and a comprehensive software for the statistical description of rough surfaces is developed. It is found that the topology of the analyzed textured surfaces cannot be fully described according to RPT and fractal modeling. The following complexities emerge: (i) the presence of cut-offs or bi-fractality in the power-law powerspectral density (PSD) functions; (ii) a more pronounced shift of the PSD by changing resolution as compared to what expected from fractal modeling; (iii) inaccuracy of the RPT in describing the joint PDFs of asperity heights and curvatures of textured surfaces; (iv) lack of resolution-invariance of joint PDFs of textured surfaces in case of special surface treatments, not accounted by fractal modeling.

Application of three-dimensional printing to pavement texture effects on rubber friction

“…In Figure 5, a shift on the power spectrum is also noticed between the measurements of the two optical instruments. Similar observations were found in the results of Borri and Paggi (2015); Lorenz, Persson, Dieluweit, and Tada (2011); Persson (2014a) and Yashchuk et al (2005), where different magnifications or resolutions of the optical instrument affected the resulting PSD curves. Any judgement on the cause and the nature of these differences requires more roughness examinations at different magnifications and with multiple profilometery techniques.…”

“…The PSD converged to a final wide-bandwidth spectrum as the surface size increased. The effect of the surface size on the PSD calculations was also addressed in the work of Borri and Paggi (2015). It is worth noting that the asphalt specimen that was examined exhibits a fractal nature on a smaller length scale.…”

Topology simulation and contact mechanics of bifractal rough surfaces*

“…19,20 The applicability of random process theory to randomly rough surfaces is, however, an important topic still debated, especially in relation to complex surfaces with artificial multiscale texturing or processing. 21 Natural rough surfaces often have fractal characteristics since every part of them can reproduce one another after suitable scaling. 22 This property has led to the possibility of using simulation methods such as the Weierstrass-Mandelbrot function, 23,24 the random midpoint displacement method (RMD), 25 and the spectral synthesis method (SSM) 26 to generate fractal surfaces with self-affine features to be used as input for micromechanical or numerical contact models.…”

A three‐dimensional multiphysics modeling of thin‐film amorphous silicon solar cells

“…Fortunately, there are different methods to achieve such enhancement. For instance, applying a randomly textured layer inside the device is a standard approach to gain more effective scattered rays inside the device [2][3][4][5]. Additionally, introducing a periodic structure as a reflector to enable the increase of light path inside the absorber [6][7][8]; thus enhancing light absorption.…”