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.

The fractal properties of carbon paste electrodes (CPEs) and carbon paste electrodes modified with ionic liquid (IL), AuTiO₂/graphene oxide, and IL/AuTiO₂/graphene oxide were investigated using scanning electron microscopy (SEM), and cyclic voltammetry (CV). The impact of fractal dimensions and self-similarity ranges on electrochemical responses was underlined. It was proved that a higher fractal dimension and a broad self-similarity domain lead to a higher electrochemical response. Results indicated that IL/AuTiO₂/graphene oxide composite-modified CPEs are a great candidate to be used as electrochemical sensors, with a high fractal dimension and large self-similarity domain.

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