Citation: Paun, M.-A.; Paun, V.-A.; Paun, V.-P. Mercury Bonding to Xerogel: The Interface Fractal Dynamics of the Interaction between Two Complex Systems. Gels 2023, 9, 670. https://doi.org/10.3390/ gels9080670 Academic Editors: Francesco Caridi, Giuseppe Paladini and Andrea Fiorati Received: 21 July 2023 Revised: 11 August 2023 Accepted: 16 August 2023 Published: 18 August 2023 Copyright: © 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). gels Article Mercury Bonding to Xerogel: The Interface Fractal Dynamics of the Interaction between Two Complex Systems Maria-Alexandra Paun 1, * , Vladimir-Alexandru Paun 2 and Viorel-Puiu Paun 3,4 1 Division Radio Monitoring and Equipment, Section Market Access and Conformity, Federal Office of Communications (OFCOM), 2501 Bienne, Switzerland 2 Five Rescue Research Laboratory, 75004 Paris, France; vladimir.alexandru.paun@ieee.org 3 Physics Department, Faculty of Applied Sciences, University Politehnica of Bucharest, 060042 Bucharest, Romania; viorel.paun@physics.pub.ro 4 Academy of Romanian Scientists, 50085 Bucharest, Romania * Correspondence: maria_paun2003@yahoo.com Abstract: This study describes novel solid substances founded on chitosan and TEGylated phe- nothiazine 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 hydrar- gyrum. 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 D 1 = 1.604 ± 0.2798, the fractal dimension of the square mask is D 2 = 1.596 ± 0.0460, and the lacunarity is 0.0402. Keywords: complex systems; fractal-type objects; bi-stable behaviors; SEM images; fractal parameters 1. Introduction The so-called heavy metals, which have intermediate properties between those of metals and nonmetals, are known as metal chemical elements themselves and have a comparatively large density in comparison to water density, which is what the appellative heavy refers to [1]. In the well-established hypothesis that toxicity and heaviness are capitally connected, the hard/heavy metals also cover the generic category of metalloids, such as silicon, polonium, and arsenic, that are capable of high toxicity and need to be reduced in terms of human exposure level [2]. In the same category of disadvantages, the so-called pure metals can also be introduced, as they are directly responsible for the damage they produce. In this article, we will only deal with one of them, namely mercury, which is fixed interstitially in compounds with xerogels. However, we remind you that the metals mentioned above do not have well-established biological functions and are, thus, taken into account as non-essential active metals from this point of view [3,4]. The important heavy metals exercise some biochemical, biophysical, and physiological major functions in vegetable and animal organisms. Thus, these substantial constituents of integrated basic enzymes have or manifest sig- nificant roles in various complex reactions, the most important being oxidation–reduction. Among the original metals, we mention Copper, which participates as a necessary cofactor in some oxidative stress-connected enzymes, such as ferroxidases, monoamine oxidase, catalase, and specific dopamine β-monooxygenase [5]. Thanks to the exponential growth in ecological awareness and the global public health correlated with the territory surrounding contamination concerning the mentioned metals, these problems have become among Gels 2023, 9, 670. https://doi.org/10.3390/gels9080670 https://www.mdpi.com/journal/gels