Topological Data Analysis of Nanoscale Roughness of Layer-by-Layer Polyelectrolyte Samples Using Machine Learning

The surface roughness of layer-by-layer (LbL) polyelectrolytes is studied by atomic force microscopy (AFM) and analyzed with novel methods including topological data analysis (TDA) and machine learning (ML) to correlate multiscale roughness with the number of bilayers and to recognize the types of polyelectrolytes (PEs). LbL PEs composed of one to four bilayers of (1) polyethylenimine (PEI)/poly(sodium 4-styrenesulfonate) (PSS), (2) PEI/poly(acrylic acid) (PAA), and (3) PEI/MXene rigid flakes are deposited on a smooth silicon wafer. With a growing number of bilayers, the roughness changes from a smooth surface to an equilibrium rough profile. The AFM study of the surface morphology demonstrates that surface roughness is multiscale, with smaller features imposed on larger ones. Roughness data is filtered from measurement resolution artifacts, and several methods are applied: correlation length, statistics of the distribution of extremes in trimmed images, and TDA barcodes and persistence diagrams of simplexes in 8D data space. An ML algorithm is used to determine the number of bilayers in a PE. Roughness analysis indicates a gradual transition from a smooth to a rough surface with saturation at three to four bilayers and the existence of multiscale roughness invariance.