# AFM Characterization of Track-Etched Membranes:
## 6 Conclusions  
In this paper, a technique for the structural characterization of porous polymer films (track-etched membranes) was implemented by using atomic force microscopy (AFM) and subsequent computer analysis of the data. The technique allows obtaining the distribution of the diameters of the pores (and identifying defective pores), the minimum distances between the nearest pores, and their average spatial density. We suggested a method for the characterization of surface anisotropy in pores distribution by analyzing the orientation of the nearest pores pairs. The main criteria for defective pores selection were their anomalous large diameters and the distance between the nearest pores.  
Three model pore distributions in TM were realized and investigated by numerical simulation (uniform distribution, random distribution, and spatially oriented distribution). In all cases, the distributions of the minimal distances between the nearest pores were analyzed, as well as ring histograms which demonstrated the distribution of the orientation of the nearest pores pairs. In the case of a random distribution with a preferred direction, the orientation ring histogram had peaks that demonstrated the formation of some \"chains\" and \"agglomerates\" of pores. It means that this way of statistical processing of AFM data allows establishing the presence (or absence) of the preferred direction of pores distribution in a sample.  
The analysis of the images of the three types of TM (based on PP, PETP, and PC) made it possible to conclude that there was no surface anisotropy (a preferred direction of pores orientation) in all studied samples.  
From the analysis of the experimental data, it can be concluded that the average value of pore density in the PETP sample markedly differed from that of the other two samples by more than an order of magnitude. Apparently, this was because the minimum distance between the nearest pores in this sample was \(\sim\)2 \(\upmu\)m, which was three times greater than that in the other two samples; in addition, the average pores diameter (1430 nm) was very large (183 and 375 nm). The developed method allows a more complete description of the parameters of porous membranes, including the coordinates of the centers, the diameters, the minimum distance, the density, and the direction of pore distributions.  
Conceptualization, A.V.G. and I.Y.E.; Data curation, A.I.A. and A.V.N.; Formal analysis, A.V.G.; Investigation, A.V.G., M.A.D. and A.I.A.; Methodology, A.I.A.; Project administration, A.V.N.; Resources, I.Y.E.; Software, A.V.G.; Supervision, A.V.N.; Validation, I.Y.E.; Visualization, A.V.G. and K.R.K.; Writing--original draft, A.V.G., M.A.D. and A.I.A.; Writing--review & editing, K.R.K., I.Y.E. and A.V.N. All authors have read and agreed to the published version of the manuscript.  
The work was supported by the Russian Foundation for Basic Research (project No. 20-02-00871 realized at the Institute of spectroscopy RAS) and the Ministry of Education of Russia (State Contract at MPGU AAAA-A20-120061890084-9 for Laboratory of Physics of Advanced Materials and Nanostructures). The authors are members of the leading scientific school of Russia \"Optical-spectral nanoscopy of quantum objects and diagnostics of promising materials\" (project NSh-776.2022.1.2).  
Not applicable.  
The authors acknowledge [PERSON] (JINR, Dubna) for the samples of etched tracking membranes [2,15].  
The authors declare that they have no conflict of interest.