Mercury Bonding to Xerogel: The Interface Fractal Dynamics of the Interaction between Two Complex Systems

Abstract

This study describes novel solid substances founded on chitosan and TEGylated phenothiazine that have a high ability for hydrargyrum recovery from watery liquid solutions. These compounds were taken into account, consisting of two distinct entity interactions inside of the classic fractal dynamics conjecture of an “interface”. They were assimilated through fractal-type mathematical objects and judged as such. The bi-stable behavior of two fractally connected objects was demonstrated both numerically and graphically. The fractal character was demonstrated by the fractal analysis made using SEM images of the xerogel compounds with interstitial fixed hydrargyrum. For the first time, SEM helped to verify such samples from two distinct bodies, with the multifractal parameter values being listed in continuation. The fractal dimension of the rectangular mask is D1 = 1.604 ± 0.2798, the fractal dimension of the square mask is D2 = 1.596 ± 0.0460, and the lacunarity is 0.0402.

Analysis on the Morphology and Interface of the Phosphate Coating Prepared on X39Cr13 and S355J2 Steels

“…At lower magnification, however, these bumps are found to agglomerate into clusters almost two orders of magnitude wider (600 μm in horizontal diameter). The fractal dimension was also determined by Paun et al [ 24 ] and Kong et al [ 25 ] using SEM images. Results for X39Cr13 steel presented in Table 3 exhibit significantly different scaling behavior, in which both corner frequencies and fractal dimensions appear similar regardless of the magnification: the corner frequency τ 1 explaining small bumps approaches ca.…”

“…SEM images are composed of grayscale pixels corresponding to pseudo-heights that can be processed in order to derive various characteristics of the surface geometry. In the present paper, the two following approaches were used: (1) fractal analysis that makes use of scaling invariance between samples of averaged surface profiles [ 24 , 25 , 26 , 27 , 28 , 29 , 30 ] and (2) statistical approach working on the separated segments of original images. In the first method, original SEM images (example shown in Figure 1 A) were averaged along the rows of the slow scan axis in order to obtain roughness profiles ( Figure 1 B), which were then processed into discrete structure functions according to the formula [ 31 ]: where τ is the discrete shift between original profile and its copy, m = τ /Δ is the integer number, Δ—the scan step, z k —the k-th sample of the mean profile and N —the number of samples in each profile.…”