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Fractal Fract
Special Issues
Fractal Analysis and Fractal Dimension in Materials Chemistry
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Fractal Analysis and Fractal Dimension in Materials Chemistry

A special issue of Fractal and Fractional (ISSN 2504-3110). This special issue belongs to the section "Mathematical Physics".

Deadline for manuscript submissions: closed (15 April 2024) | Viewed by 15075

Special Issue Editors

Dr. Gianina Dobrescu

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Guest Editor
Romanian Academy, “Ilie Murgulescu” Physical Chemistry Institute, Bucharest, Romania
Interests: fractal theory; surface science; adsorption mechanism; modeling gases adsorption and desorption from metal-supported catalysts; Applying fractal theory for the characterization of surfaces; modeling adsorption on fractal surfaces; computing fractal dimension from micrographs (TEM, SEM, AFM, STM); growth surfaces and the computation of time and spatial scaling exponents.
Special Issues, Collections and Topics in MDPI journals
Dr. Florica Papa

E-Mail Website
Guest Editor
Romanian Academy, “Ilie Murgulescu” Physical Chemistry Institute, Bucharest, Romania
Interests: fractal theory; catalytic and photocatalytic reaction; mono and bimetallic nanoparticles synthesis by alkaline polyol method; oxidation of C1-C4 aliphatic hydrocarbons on simple and doped oxides; oxidative coupling of methane on rare earth oxides; Selective catalytic reduction of nitrates and nitrites in the liquid phase; catalytic oxidation of ammonia nitrogen with ozone in water; modified catalysts and their fractal properties
Special Issues, Collections and Topics in MDPI journals
Dr. Razvan State

E-Mail Website
Guest Editor
Institute of Physical Chemistry “Ilie Murgulescu”, Romanian Academy, 060021 Bucharest, Romania
Interests: fractal theory; catalysis, catalytic synthesis, catalytic pyrolysis processes; synthesis of well-defined mono/bimetallic nanoparticles; photocatalytic degradation of organic compounds in water; nitrate and nitrite abatement; photocatalysis/light harvesting—water and air depollution
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

After B.B.Mandelbrot published his works regarding fractals, defining them as objects with a peculiar geometry and characterized by fractional exponents, a lot of studies have emerged in the scientific literature. Applications were developed in engineering (fractal antennas), physics and chemistry (heterogeneous catalysis, adsorption, chemical reactions and light scattering on fractal surfaces), computer science (iterative algorithms for image compression) and even in literature or geography.

The aim of this Special Issue is to present the state-of-the-art applications of the fractal theory in materials chemistry. Topics invited for submission include, but are not limited to, the following:

  • The fractal dimension determination of materials (the micrograph analysis, adsorption isotherms methods and SAXS method);
  • The relation between the physical and chemical properties of materials and the fractal dimension;
  • Adsorption on fractal surfaces;
  • Fractal adsorption isotherms;
  • Applications of the fractal theory on chemical reactions;
  • Catalysts and applications of the fractal theory on catalysis;
  • Dynamics on fractals;
  • Fractons in diffusion-limited reactions.

Dr. Gianina Dobrescu
Dr. Florica Papa
Dr. Razvan State
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Fractal and Fractional is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2700 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • fractal dimension
  • fractal adsorption isotherms
  • catalysis
  • diffusion-limited reactions
  • fractons

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Related Special Issue

Published Papers (8 papers)

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Editorial

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4 pages, 181 KiB  
Editorial
Fractal Analysis and Fractal Dimension in Materials Chemistry
by Gianina Dobrescu, Florica Papa and Razvan State
Fractal Fract. 2024, 8(10), 583; https://doi.org/10.3390/fractalfract8100583 - 3 Oct 2024
Viewed by 767
Abstract
Using fractal analysis and computing fractal dimension to understand materials chemistry and solve problems such as catalysis, chemical reactions, fuel storage, and material design is an important scientific research domain [...] Full article
(This article belongs to the Special Issue Fractal Analysis and Fractal Dimension in Materials Chemistry)

Research

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16 pages, 3554 KiB  
Article
A Novel Contact Stiffness Model for Grinding Joint Surface Based on the Generalized Ubiquitiformal Sierpinski Carpet Theory
by Qi An, Yue Liu, Min Huang and Shuangfu Suo
Fractal Fract. 2024, 8(6), 351; https://doi.org/10.3390/fractalfract8060351 - 12 Jun 2024
Cited by 1 | Viewed by 1066
Abstract
A novel analytical model based on the generalized ubiquitiformal Sierpinski carpet is proposed which can more accurately obtain the normal contact stiffness of the grinding joint surface. Firstly, the profile and the distribution of asperities on the grinding surface are characterized. Then, based [...] Read more.
A novel analytical model based on the generalized ubiquitiformal Sierpinski carpet is proposed which can more accurately obtain the normal contact stiffness of the grinding joint surface. Firstly, the profile and the distribution of asperities on the grinding surface are characterized. Then, based on the generalized ubiquitiformal Sierpinski carpet, the contact characterization of the grinding joint surface is realized. Secondly, a contact mechanics analysis of the asperities on the grinding surface is carried out. The analytical expressions for contact stiffness in various deformation stages are derived, culminating in the establishment of a comprehensive analytical model for the grinding joint surface. Subsequently, a comparative analysis is conducted between the outcomes of the presented model, the KE model, and experimental data. The findings reveal that, under identical contact pressure conditions, the results obtained from the presented model exhibit a closer alignment with experimental observations compared to the KE model. With an increase in contact pressure, the relative error of the presented model shows a trend of first increasing and then decreasing, while the KE model has a trend of increasing. For the relative error values of the four surfaces under different contact pressures, the maximum relative error of the presented model is 5.44%, while the KE model is 22.99%. The presented model can lay a solid theoretical foundation for the optimization design of high-precision machine tools and provide a scientific theoretical basis for the performance analysis of machine tool systems. Full article
(This article belongs to the Special Issue Fractal Analysis and Fractal Dimension in Materials Chemistry)
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17 pages, 5190 KiB  
Article
Multivariate Analysis on a Complex, Rare-Earth Doped Alumina Database with Fractal Dimension as a Microstructural Quantifier
by Zeno Dorian Ghizdavet, Adrian Volceanov and Enikő Volceanov
Fractal Fract. 2023, 7(4), 286; https://doi.org/10.3390/fractalfract7040286 - 26 Mar 2023
Cited by 1 | Viewed by 1420
Abstract
Alumina ceramics were obtained from three different alumina sources, A1–A3, with various rare-earth dopants (La2O3–La, Nd2O3–Nd, and Y2O3–Y), concentration levels (500 and 1000 ppm) and synthesizing routes (1500 °C, 1815 °C [...] Read more.
Alumina ceramics were obtained from three different alumina sources, A1–A3, with various rare-earth dopants (La2O3–La, Nd2O3–Nd, and Y2O3–Y), concentration levels (500 and 1000 ppm) and synthesizing routes (1500 °C, 1815 °C and cold plasma-P). Absorption (A) and density (ρ in text, rho in images) were measured, resulting in a complex, multivariate database. Principal Component Analysis (PCA) was run with the aim of deducing relationships between variables (alumina source, dopant level, thermal processing route, A and ρ), observations, and between variables and observations. A total of 206 Scanning Electron Microscopy (SEM) micrographs were recorded at various scales and the corresponding images were processed to quantify the microstructural features. Two techniques of edge detection were used; Fractal Dimension (FD) was calculated for each micrograph and results were compared. Various scales of the micrographs prevented us from using any other approach, such as simply measuring the grains or obtaining shape parameters. The initial database was extended by including FDs and PCA was run again. We found that plasma processing is positively correlated to A and negatively correlated to both temperature (T) and ρ; La ceramics have an opposite behavior to Y and Nd ceramics. FD successfully explained observations being correlated, mainly, to Y, Nd and, to a lesser extent, to La. FD proved that it is a reliable and simple approach to quantifying microstructural features when comparing highly different, noisy micrographs. Full article
(This article belongs to the Special Issue Fractal Analysis and Fractal Dimension in Materials Chemistry)
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12 pages, 2121 KiB  
Article
Cerofolini’s Model and the Fractal Adsorption Isotherms
by Gianina Dobrescu, Florica Papa, Daniela Culita, Ioan Balint and Niculae I. Ionescu
Fractal Fract. 2023, 7(3), 262; https://doi.org/10.3390/fractalfract7030262 - 14 Mar 2023
Cited by 1 | Viewed by 1364
Abstract
The close link between the roughness of a surface and its adsorptive properties in Cerofolini’s model yields, with an adequate choice of adsorption energy, the well-known Dubinin-Radushkevich or Freundlich adsorption isotherms. Assuming fractal behavior concerning both energetic and geometric surface heterogeneities described by [...] Read more.
The close link between the roughness of a surface and its adsorptive properties in Cerofolini’s model yields, with an adequate choice of adsorption energy, the well-known Dubinin-Radushkevich or Freundlich adsorption isotherms. Assuming fractal behavior concerning both energetic and geometric surface heterogeneities described by the power-law expressions and fractal dimensions, the paper will develop some fractal adsorption isotherms. Using our theoretical approach, fractal isotherms will provide insights not only into the fractal behavior of the surface geometry but also into the fractal energetic heterogeneities, implying that a sorbent does not need to be porous to apply a fractal isotherm: adsorption on “flat” surfaces can also be described by fractal isotherms and fractal dimensions related to energetic disorders. For example, the theory will be applied to computing the energetic fractal dimensions of some nanoparticle catalysts, Rh/Al2O3, Rh/TiO2, and Rh/WO3. Full article
(This article belongs to the Special Issue Fractal Analysis and Fractal Dimension in Materials Chemistry)
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12 pages, 3918 KiB  
Article
Pore Microstructure and Multifractal Characterization of Lacustrine Oil-Prone Shale Using High-Resolution SEM: A Case Sample from Natural Qingshankou Shale
by Shansi Tian, Yuanling Guo, Zhentao Dong and Zhaolong Li
Fractal Fract. 2022, 6(11), 675; https://doi.org/10.3390/fractalfract6110675 - 15 Nov 2022
Cited by 6 | Viewed by 1623
Abstract
Pore structure is one of the important parameters for evaluating reservoirs, critical in controlling the storage capacity and transportation properties of hydrocarbons. The conventional pore characterization method cannot fully reflect the pore network morphology. The edge-threshold automatic processing method is applied to extract [...] Read more.
Pore structure is one of the important parameters for evaluating reservoirs, critical in controlling the storage capacity and transportation properties of hydrocarbons. The conventional pore characterization method cannot fully reflect the pore network morphology. The edge-threshold automatic processing method is applied to extract and quantify pore structures in shale scanning electron microscope (SEM) images. In this manuscript, a natural lacustrine oil-prone shale in the Qingshankou Formation of Songliao Basin is used as the research object. Based on FE-SEM, a high-resolution cross-section of shale was obtained to analyze the microstructure of pores and characterize the heterogeneity of pores by multifractal theory. The stringent representative elementary area (REA) of the SEM cross-section was determined to be 35 × 35. Four pore types were found and analyzed in the stringent REA: organic pores, organic cracks, inorganic pores, inorganic cracks. The results showed that inorganic pores and cracks were the main pore types and accounted for 87.8% of the total pore area, and organic cracks were of the least importance in the Qingshankou shale. Inorganic pores were characterized as the simplest pore morphologies, with the largest average MinFeret diameter, and the least heterogeneity. Moreover, the inorganic cracks had a long extension distance and stronger homogeneity, which could effectively connect the inorganic pores. Organic pores were found to be the most complex for pore structure, with the least average MinFeret diameter, but the largest heterogeneity. In addition, the extension distance of the organic cracks was short and could not effectively connect the organic pore. We concluded that inorganic pores and cracks are a key factor in the storage and seepage capacity of the Qingshankou shale. Organic pores and cracks provide limited storage space. Full article
(This article belongs to the Special Issue Fractal Analysis and Fractal Dimension in Materials Chemistry)
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12 pages, 2302 KiB  
Article
Evolution of Morphology, Fractal Dimensions, and Structure of (Titanium) Aluminosilicate Gel during Synthesis of Zeolites Y and Ti-Y
by Gabriela Petcu, Gianina Dobrescu, Irina Atkinson, Madalina Ciobanu, Jean-Luc Blin and Viorica Parvulescu
Fractal Fract. 2022, 6(11), 663; https://doi.org/10.3390/fractalfract6110663 - 10 Nov 2022
Cited by 5 | Viewed by 1814
Abstract
Zeolite Y and Ti-containing zeolite Y (1%, 2% and 5% TiO2) were synthesized by a hydrothermal seed-assisted method. In order to evidence the evolution of morphology, structure, and fractal dimensions during the zeolitization process at certain time intervals, a small volume [...] Read more.
Zeolite Y and Ti-containing zeolite Y (1%, 2% and 5% TiO2) were synthesized by a hydrothermal seed-assisted method. In order to evidence the evolution of morphology, structure, and fractal dimensions during the zeolitization process at certain time intervals, a small volume from the reaction medium was isolated and frozen by lyophilization. The obtained samples were characterized by scanning electron microscopy (SEM), wide-angle X-ray diffraction (XRD), and small-angle X-ray scattering (SAXS). The fractal dimension values of the isolated samples, calculated from SAXS data, evidenced a transition from small particles with a smooth surface (2.021) to compact structures represented by zeolite crystallites with rough surfaces (2.498) and specific organization for zeolite Y. The formation of new structures during hydrothermal treatment, the increase in crystallite size and roughness due to the continuous growth were suggested by variation of fractal dimensions values, SEM microscopy images and X-ray diffractograms. The incorporation of titanium in low concentration into the zeolite Y framework led to the obtaining of low fractal dimensions of 2.034–2.275 (smooth surfaces and compact structures). On the other hand, higher titanium concentration (2%) led to an increase in fractal dimensions indicating structures with rougher surfaces and well-defined self-similarity properties. A mechanism for zeolite synthesis was proposed by correlation of the results obtained through morphological, structural, and fractal analysis. Full article
(This article belongs to the Special Issue Fractal Analysis and Fractal Dimension in Materials Chemistry)
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11 pages, 14335 KiB  
Article
Fractal Analysis on the Mapping Relationship of Conductivity Properties in Porous Material
by Cheng Li, Yao Xu, Zhouting Jiang, Boming Yu and Peng Xu
Fractal Fract. 2022, 6(9), 527; https://doi.org/10.3390/fractalfract6090527 - 17 Sep 2022
Cited by 4 | Viewed by 1833
Abstract
The mapping relationships between the conductivity properties are not only of great importance for understanding the transport phenomenon in porous material, but also benefit the prediction of transport parameters. Therefore, a fractal pore-scale model with capillary bundle is applied to study the fluid [...] Read more.
The mapping relationships between the conductivity properties are not only of great importance for understanding the transport phenomenon in porous material, but also benefit the prediction of transport parameters. Therefore, a fractal pore-scale model with capillary bundle is applied to study the fluid flow and heat conduction as well as gas diffusion through saturated porous material, and calculate the conductivity properties including effective permeability, thermal conductivity and diffusion coefficient. The results clearly show that the correlations between the conductivity properties of saturated porous material are prominent and depend on the way the pore structure changes. By comparing with available experimental results and 2D numerical simulation on Sierpinski carpet models, the proposed mapping relationships among transport properties are validated. The present mapping method provides a new window for understanding the transport processes through porous material, and sheds light on oil and gas resources, energy storage, carbon dioxide sequestration and storage as well as fuel cell etc. Full article
(This article belongs to the Special Issue Fractal Analysis and Fractal Dimension in Materials Chemistry)
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Review

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24 pages, 5660 KiB  
Review
Fractal Theory in Thin Films: Literature Review and Bibliometric Evidence on Applications and Trends
by Fredrick M. Mwema, Tien-Chien Jen and Pavel Kaspar
Fractal Fract. 2022, 6(9), 489; https://doi.org/10.3390/fractalfract6090489 - 31 Aug 2022
Cited by 8 | Viewed by 3133
Abstract
A bibliometric analysis of publications on fractal theory and thin films is presented in this article. Bibliographic information is extracted from the Web of Science digital database and the bibliographic mapping undertaken using VOSviewer software. Based on the analysis, there is a growing [...] Read more.
A bibliometric analysis of publications on fractal theory and thin films is presented in this article. Bibliographic information is extracted from the Web of Science digital database and the bibliographic mapping undertaken using VOSviewer software. Based on the analysis, there is a growing trend in research on the applications of fractal theory in thin film technology. The factors driving this trend are discussed in the article. The co-citation, co-authorship and bibliographic coupling among authors, institutions and regions are presented. The applications of fractal theory in thin film technology are clarified based on the bibliometric study and the directions for future research provided. Full article
(This article belongs to the Special Issue Fractal Analysis and Fractal Dimension in Materials Chemistry)
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