Fractal and multifractal characteristics of swift heavy ion induced self-affine nanostructured BaF2 thin film surfaces

Evaluating the roughness dynamics of kefir biofilms grown on Amazon cupuaçu juice: a monofractal and multifractal approach

We conducted a comprehensive analysis of the surface microtexture of kefir biofilms grown on Theobroma grandiflorum Shum (cupuaçu) juice using atomic force microscopy. Our goal was to investigate the unique monofractal and multifractal spatial patterns of these biofilms to complement the existing limited literature. The biofilms were prepared dispersing four different concentrations of kefir grains in cupuaçu juice. Our morphological analysis showed that the surface of the obtained biofilms is essentially formed by the presence of cupuaçu fibers and microorganisms like lactobacilli and yeast. The topographic height-based parameter analysis reveals that there is a dependence between surface roughness and the concentration of kefir grains used. The strongly anisotropic well-centralized topographical height distribution of the biofilms also exhibited a quasi-symmetrical and platykurtic pattern. The biofilms exhibit comparable levels of spatial complexity, surface percolation and surface homogeneity, which can be attributed to their similar topographic uniformity. This aspect was further supported by the presence of similar multifractality in the biofilms, suggesting that despite their varying topographic roughness, their vertical growth dynamics follow a similar pattern. Our findings demonstrate that the surface roughness of kefir biofilms cultivated on cupuaçu juice is influenced by the concentration of kefir grains in the precursor solution. However, this dependence follows a consistent pattern across different concentrations. Graphical Abstract.

Three-Dimensional Surface Stereometric Analysis of Ni-Cu Films with Different Cu Contents

The purpose of this work is a stereometric analysis of Ni-Cu thin films to obtain the three-dimensional (3D) microtexture surface based on atomic force microscopy (AFM). Four Ni-Cu thin films on glass and silicon substrates were prepared by a capacitively coupled RF-PECVD system with a 13.56 MHz power supply. The AFM data of the samples were stereometrically analyzed, and the surface microtexture was determined according to the definition of relevant parameters in the standards ISO 25178-2:2012 and ASME B46.1-2009. All microtexture features can be implemented in numerical programs to simulate advanced microtexture models under specific microstructure and composition conditions. The results can be used to validate theoretical models for predicting or correlating the surface parameters of nanostructures. The Ni-Cu films with 40% Cu have a more irregular surface; hence, the maximum Sq value of the as-deposited Ni-Cu films is about 81.24 μm. The core roughness height Sk is calculated as a difference between two extreme levels (maximal and minimal) of the surface core, for which Ni-Cu films with 40% Cu have a maximum value of 183.4 μm. Since the surface kurtosis (Sku) of all sample films was lower than 7, there are very small peaks or valleys on the film surface and for Ni-Cu films with 5% Cu with a value of 3.568. With increasing Cu content, the height distribution histograms of films show more uniform distributions.

Fractal characterizations of MeV ion treated CaF2 thin films

We present the morphological evolution and fractal characterizations of CaF₂ thin-film surfaces modified by bombardment with 100 MeV Au⁺⁸ ions at various fluences. Atomic force microscopy (AFM) combined with line profile and two-dimensional power spectral density (2D-PSD) analysis was utilized to investigate the evolution of surface morphology as a function of fluence. The AFM images were utilized to investigate the relationship between fractal dimension, roughness exponent, lateral correlation length, and ion fluence. The surface erosion owing to sputtering was depicted using Rutherford backscattering spectrometry. The structural characteristics' dependency on fluence was explored with the help of glancing angle x-ray diffraction measurements on virgin and irradiated samples. Tensile stress calculated using a peak shift in the glancing angle x-ray diffractogram showed an increase in tensile stress with fluence that caused the surface to crack after the fracture strength of the surface was crossed. 2D-PSD analysis signified the role of sputtering over surface diffusion for the observed surface modifications. Fractal dimensions first increased and then decreased with ion fluence. The lateral correlation length decreased, while the roughness exponent increased with fluence after the threshold value.

Nanoscale surface dynamics of spatial patterns of polymeric bilayered particles loaded with essential oil

Gelatin/PCL bilayered particles loaded with Piper nigrum essential oil was synthesized aiming to access their morphological and surface dynamic patterns. Atomic force microscopy (AFM) was applied to investigate the 3D morphology and multifractal aspects of the particles surface. The AFM maps revealed spherical surfaces and well dispersed particles, besides a rougher surface on the loaded system. Minkowski functionals showed that shape of the rough peaks was similar in the unloaded and loaded systems; however, the presence of deep valleys on the loaded particles revealed their rougher pattern. Multifractal analysis revealed that unloaded and loaded particles presented multifractal behavior with different surface dynamics. The loaded surface presented a greater width of the multifractal spectrum and smaller difference of fractal dimensions, confirming their more vertically growing. These results can be useful in the development of novel polymeric-based particles loaded with essential oil. Their unique surface dynamics can provide enhanced physical properties and performance in emerging biotechnological applications.

Vapor Barrier Properties of Cold Plasma Treated Corn Starch Films

The development and efficient production of effective bioplastics is a hot topic, required to face up to the issue of the difficult disposal of plastics derived from oil. Among the different natural sources of bioplastics, starch is one of the most promising. However, for most applications, the proper mastering of the surface properties of bioplastic is necessary. We report about the surface modification of extruded corn starch films by means of cold plasma based on helium (He) and hexamethyldisiloxane (HMDSO). The differently treated surfaces were functionally characterized in wettability and water absorption. The nanoscale morphology was assessed by scanning electron microscopy and atomic force microscopy. The obtained images were analyzed by advanced figures describing both texture and amplitude parameters, including fractal behavior. The combined treatment (He/HMDSO) resulted in more homogeneous films with smaller, better-distributed grains compared to the case wherein He was not used. Despite the different morphologies observed, starch coated by HMDSO alone and by He/HMDSO presented similar hydrophobic character, with contact angles higher than 110°. Plasma treatment with HMDSO and He/HMDSO resulted in a significant reduction of absorbed water content without reduction of water vapor permeability. The nanotexture of the films did not present statistically significant differences, in terms of spatial complexities, dominant spatial frequencies, homogeneous void distribution, and surface percolation.

Fractal Analysis on Surface Topography of Thin Films: A Review

The topographies of various surfaces have been studied in many fields due to the significant influence that surfaces have on the practical performance of a given sample. A comprehensive evaluation requires the assistance of fractal analysis, which is of significant importance for modern science and technology. Due to the deep insights of fractal theory, fractal analysis on surface topographies has been widely applied and recommended. In this paper, the remarkable uprising in recent decades of fractal analysis on the surfaces of thin films, an essential domain of surface engineering, is reviewed. By summarizing the methods used to calculate fractal dimension and the deposition techniques of thin films, the results and trends of fractal analysis are associated with the microstructure, deposition parameters, etc. and this contributes profoundly to exploring the mechanism of film growth under different conditions. Choosing appropriate methods of surface characterization and calculation methods to study diverse surfaces is the main challenge of current research on thin film surface topography by using fractal theory. Prospective developing trends are proposed based on the data extraction and statistics of the published literature in this field.

The effect of deposition times in DC-magnetron sputtering on micromorphology of TiO2 thin films

TiO₂ thin films have been prepared by DC-magnetron sputtering process with various deposition times (8, 14, 16, and 20 min) and the micromorphology of their surface has been investigated by means of multifractal analysis. As the main purpose of the manuscript, the topography of all samples are examined by atomic force microscopy (AFM) through the Mountains Map® Premium software which characterizes motifs of significant peaks and pits through stereometric data by the watershed segmentation algorithm. In addition, multifractal features of samples provide deeper insight into texture characteristics and used as the supplementary of the results.

Robustness of Surface Roughness against Low Number of Picture Elements and Its Benefit for Scaling Analysis

Surface roughness is widely used in the research of topography, and the scaling characteristics of roughness have been noticed in many fields. To rapidly obtain the relationship between root-mean-squared roughness (Rq) and measurement scale (L) could be helpful to achieve more understandings of the surface property, particularly the Rq-L curve could be fitted to calculate the fractal dimension (D). In this study, the robustness of Rq against low number of picture elements was investigated. Artificial surfaces and the surfaces of two actual samples (a silver thin film and a milled workpiece) were selected. When the number of picture elements was lowered, Rq was found to be stable within a large portion of the concerned scope. Such a robustness property could validate the feasibility of Rq-L curve obtained by segmenting a single morphological picture with roughness scaling extraction (RSE) method, which was proposed in our previous study. Since the traditional roughness (TR) method to obtain Rq-L curves was based on multiple pictures, which used a fixed number of picture elements at various L, RSE method could be significantly more rapid than TR method. Moreover, a direct comparison was carried out between RSE method and TR method in calculating the Rq-L curve and D, and the credibility and accuracy of RSE method with flatten order 1 and 2 was verified.

Stereometric analysis of Ta2O5 thin films

The purpose of this work is the study of the correlation between the thickness of tantalum pentoxide thin films and their three-dimensional (3D) micromorphology. The samples were prepared on silicon substrates by electron beam evaporation. The differences in surface structure of the processed and reference samples were investigated. Compositional studies were performed by energy-dispersive X-ray spectroscopy. Stereometric analysis was carried out on the basis of atomic force microscopy (AFM) data, for tantalum pentoxide samples with 20 nm, 40 nm, 60 nm, 80 nm and 100 nm thicknesses. These methods are frequently used in describing experimental data of surface nanomorphology of Ta2O5. The results can be used to validate theoretical models for prediction or correlation of nanotexture surface parameters.

The effect of dental LED light-curing unit photoactivation mode on 3D surface morphology of dental nanocomposites evaluated by two-dimensional multifractal detrended fluctuation analysis

The objective of this study was to evaluate the effect of two photoactivation modes of dental LED light-curing unit (LCUs) (conventional and "Soft Start" mode) on surface texture parameters of two dental resin-based nanocomposites. LED LCUs were considered as standard light-curing devices in contemporary dental practice. Atomic force microscopy (AFM) was applied to investigate surface morphology on 90 × 90 μm² scanning area through 2D multifractal detrended fluctuation analysis with computational algorithms basis. In order to compare 3D surface roughness at nanometer scale, singularity spectrum f[α] was used which characterize local scale properties of multifractal nature of samples. The results confirmed that larger spectrum width Δα (Δα = α_max - α_min ) of f(α) is associated with non-uniform surface morphology. Moreover, materials whose polymerization was photoactivated by the "soft start" polymerization mode, showed better quality of the surface microstructure with lower values of AFM surface texture parameters.

Role of Fractals in Perovskite Solar Cells

The interface engineering plays important role in fabrication of the tandem and perovskite based solar cells. Recent experiments show that the interface effects caused by the coupling of the electron bands and the pairing of geometry of contacting surfaces. In particular, it has been experimentally revealed that the transition from planar to the rough interface improves many photoelectric parameters of the<br />device. It means that the value of the fractal dimension of the interface may be key factor in device performance. It is possible to formulate two problems: firstly, the understanding on simple models why the electrical properties at fractal interfaces are improved, and, secondly, to discuss one of the most promising approaches in modern electronics, namely technology of radiation applications in the creation of rough interfaces. Thirdly, the problem of photodegradation is analyzed in detail in the structures containing the fractal interfaces. On the basis of the constructed models, it was found: i) increase of roughness (fractal) of interface structure can enhance the role of total internal light reflection effect, thereby increasing the effective light path, and therefore, the number of generated e-h-pairs; ii) the curvature of the surface leads to the shift of Tamm levels both to the borders of allowed bands, and to the middle of the band gap; it opens the way of the control of carrier recombination on the interface; iii) surface Tamm orbitals interact differently each with other on the convex and concave areas; it leads to the different probability of defect formation and, consequently, reduces the fractal interface, inhibiting the effect of increasing of the photocurrent associated with the fractal interface (new channel of photodegradation).

Multifractal methods for rapeseed nitrogen nutrition qualitative diagnosis modeling

Nutrition diagnosis plays a key role in the crop’s growth, which has mainly been carried out in the field by agricultural workers. Currently, automatic nutrition recognition technologies have been widely used in this field. A procedure is proposed in this paper to diagnose nitrogen nutrition non-destructively for rapeseed qualitatively based on the multifractal theory. Twelve texture parameters are given by the method of multifractal detrended fluctuation (MF-DFA), which contains six generalized Hurst exponents and six relative multifractal parameters that are used as features of the rapeseed leaf images for identifying the two nitrogen levels, namely, the [Formula: see text]-mezzo and the [Formula: see text]-wane. For the base leaves, central leaves and top leaves of the rapeseed plant and the three-section mixed samples, three parameters combinations are selected to conduct the work. Five classifiers of Fisher’s linear discriminant algorithm (LDA), extreme learning machine (ELM), support vector machine and kernel method (SVMKM), random decision forests (RF) and [Formula: see text]-nearest neighbor algorithm (KNN) are employed to calculate the diagnosis accuracy. An interesting finding is that the best diagnose accuracy is from the base leaves of the rapeseed plant. It is explained that the base leaf is the most sensitive to the nitrogen deficiency. The diagnose effect by the base leaves samples is outshining the existing result significantly for the same leaves samples. For the mixed samples, the averaged discriminant accuracy reaches 97.12% and 97.56% by SVMKM and RF methods with the [Formula: see text]-fold cross-validation respectively. The resulting high accuracy on [Formula: see text]-levels identification shows the feasibility and efficiency of our method.