Complexity of micro- and nanostructured surfaces

The aim of this work is the elaboration of a methodology for the quantitative characterization of the complexity of nanostructured surfaces in order to provide novel means to link nanostructure morphology to surface properties and functionalities. The key point is the distinction of complexity from randomness contrary to the usual approaches in nanometrology. The inspiration is based on the work of R. Alamino [1] where the notion of the average symmetry is proposed to put on the same footing full order and full randomness. According to this approach, the complexity is defined with an entropy-based metric quantifying the “distance” of a system morphology from average symmetry. Here, we propose and apply an alternative of this measure properly adapted to the specific characteristics of nanorough surfaces.
Firstly, the method is tested to synthesized nanostructured surfaces with controlled mixture of randomness and order to validate its results. Three series of synthesized surfaces are used. In the first case, the full order is represented by a homogeneous flat surface and noise is added by gradually and randomly replacing the surfaces points. In the second case, the full order is represented by an almost homogeneous surface with very large correlation length and the randomness is introduced through a reduction of correlations (smaller correlation length) resulting in the random morphology of almost zero correlation length. In the last case, we generate mounded periodic surfaces which are ordered. Randomness is induced by affecting positions, widths and heights of the surface peaks. The gradual increase of noise amplitude in these dimensions degrades periodicity and leads to fully randomization of surfaces.
In all cases, the proposed metric of complexity exhibits a bell-like curve with a maximum in between full order and randomness at the point where the morphological heterogeneity of surfaces seems to maximize. Besides the applications in synthesized surfaces, the complexity measure has been calculated in real surfaces of polymer materials after their treatment in plasma reactors measured with Atomic Force Microscope. The polymer morphology presents an increased complexity in the course of etching time which cannot be described with the conventional math tools. Also, we applied our methodology in surfaces of Aluminium which are etched with a solution of FeCl3 or CuCl2 and then with boiling water to create micro- and nanostructuring respectively. The surfaces are depicted with top-down SEM images which are analyzed to calculate the complexity of their morphologies. The proposed complexity metric seems to capture our intuition and quantify the change of complexity with etchant (FeCl3 or CuCl2) in accordance with the variation of the surface heat transfer.
Acknowledgements
This work has received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement No 801229 (project Harmonic: HierARchical Multiscale NanoInterfaces for enhanced Condensation processes)
References
[1] R. Alamino, J. Phys. A, 48(27):275101 (2015)