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

Abstract

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.

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“…AFM allows users to image surfaces down to 10 –9 m (1 nm) resolution, which provides precise information about the surface texture itself. Using this data, more information can be extracted that can improve understanding of the descriptive properties of the polymer, such as Young’s modulus, surface roughness, etc. , Thus, Zhukov et al analyzed atomic force microscopy scans of brass samples to study surface properties and have followed up with this approach to analyze the roughness of polyelectrolyte samples using machine learning methods to define possible correlations between surface roughness with the number of layers of polyelectrolytes . A handful of related works describe the usage of ML and deep learning in various scenarios, including several exemplar applications of using image analysis in combination with advanced computing methodologies to generate results.…”

“…For example, Bolshakova et al described the basis of using AFM as a tool to explore the properties of bacterial surfaces, while Aldritt et al used AFM to discover the organic structure of camphor molecules via a deep learning approach. Several works report analysis during and after the scanning process ,,− that focus on investigating specific compounds using selective methods. When investigating surfaces, minor changes to the chemical composition can lead to significantly different outcomes of the sample’s surface characteristics, therefore altering properties such as friction, adhesion, biocompatibility, etc. − …”

“… 16 , 17 Thus, Zhukov et al 18 analyzed atomic force microscopy scans of brass samples to study surface properties and have followed up with this approach to analyze the roughness of polyelectrolyte samples using machine learning methods to define possible correlations between surface roughness with the number of layers of polyelectrolytes. 19 A handful of related works describe the usage of ML and deep learning in various scenarios, 20 including several exemplar applications of using image analysis in combination with advanced computing methodologies to generate results. For example, Bolshakova et al 21 described the basis of using AFM as a tool to explore the properties of bacterial surfaces, while Aldritt et al 22 used AFM to discover the organic structure of camphor molecules via a deep learning approach.…”