Sonochemical synthesis is becoming a popular method of preparing various nanomaterials, including metals, carbons, oxides, and chalcogenides. This method is relatively cheap and responds to the challenges of green chemistry as it typically does not involve high temperatures, high pressures, inert atmospheres, or long reaction times in comparison to other conventional methods. The utilization of ultrasound in synthesis makes the elimination of toxic solvents possible, as well as the execution of the synthesis without the use of reducing and stabilizing agents, while receiving products with the same or even better properties. The application of ultrasound allows for the synthesis of various nanomaterials with different properties for use in fields such as catalysis, electrochemistry, medicine, and biosensors. The final product is influenced by multiple variables such as temperature, pH, reagents, capping agents, time of reaction, and the addition of dopants.

Nanomaterials, including quantum dots, have gained more and more attention in the past few decades due to their extraordinary properties that make them useful for many applications, ranging from catalysis, energy generation and storage, biotechnology, and medicine to quantum informatics. Mathematical descriptions of the phenomena in which nanostructures are involved are of great demand because they may be utilized for the purpose of controlling these phenomena (e.g., the growth of nanostructures with certain sizes, shapes, and other properties). Such models may be of distinct nature, including calculations from first principles, ordinary and partial differential equations, and machine learning models (including artificial intelligence) as well. The aim of this article is to review the most important and useful computational and mathematical approaches for the description and control of processes involving nanostructures.

The objective of the study was to modify the surface of the silicone rubber, using dielectric barrier discharge (DBD) to improve its hydrophilic properties. The influence of the exposure time, discharge power, and gas composition—in which the dielectric barrier discharge was generated—on the properties of the silicone surface layer were examined. After the modification, the wetting angles of the surface were measured. Then, the value of surface free energy (SFE) and changes in the polar components of the modified silicone over time were determined using the Owens–Wendt method. The surfaces and morphology of the selected samples before and after plasma modification were examined by Fourier-transform infrared spectroscopy with attenuated total reflectance (FTIR–ATR), atomic force microscopy AFM, and X-ray photoelectron spectroscopy (XPS). Based on the research, it can be concluded that the silicone surface can be modified using a dielectric barrier discharge. Surface modification, regardless of the chosen method, is not permanent. The AFM and XPS study show that the structure’s ratio of oxygen to carbon increases. However, after less than four weeks, it decreases and reaches the value of the unmodified silicone. It was found that the cause of the changes in the parameters of the modified silicone rubber is the disappearance of oxygen-containing groups on the surface and a decrease in the molar ratio of oxygen to carbon, causing the RMS surface roughness and the roughness factor to return to the initial values.

Nanomaterials are interesting due to their unexpected and unique properties arising from phenomena occurring at the so-called mesoscale (that is, between single atoms and bulk solids). Among nanomaterials, one may distinguish quantum dots, which are highly crystalline nanocrystals with sizes up to c.a. 10 nm. Due to the quantum confinement effect, quantum dots exhibit extraordinary electronic and optical properties and may be utilized in photocatalysis. Semiconducting quantum dots may absorb photons, which results in the excitation of electrons from valence to conducting bands. Excited electrons in the conducting band and positive holes in the valence band may interact with chemical molecules (e.g., with water molecules), forming highly reactive radicals. Consequently, quantum dots may be utilized in advanced oxidation processes based on the action of light (i.e., photo-based advanced oxidation processes). Furthermore, quantum dots have advantages, such as having a tunable energy band gap and relative cost-effectiveness. Advanced oxidation processes are very important in the context of the constantly increasing pollution of the natural environment. Contaminants of emerging concern, such as pesticides, endocrine-disrupting compounds, and flame retardants, are still being detected in naturally present water. Such compounds may be degraded using advanced oxidation processes, utilizing quantum dots as photocatalysts. However, many operational parameters (such as quantum dots’ properties, including the means of their preparation) influence the efficiency of such processes; thus, detailed studies are being conducted.

The commercially available activated carbon was modified using barrier and spark discharge low-temperature nitrogen plasma treatment. The samples were investigated using nitrogen sorption at a temperature of −196 °C, XRD, SEM, and FTIR methods, and elemental analysis. The nitrogen content on the surface was increased, but other properties, such as specific surface area, total pore volume, pseudocrystallite height, and pseudocrystallite width, remained unchanged. The activated carbons after nitrogen plasma treatment indicated higher CO₂ adsorption than the pristine ones. Since the investigated materials only differed in their nitrogen content, it has been unequivocally demonstrated that the increased presence of nitrogen is responsible for the enhanced adsorption of CO₂. The low-temperature nitrogen plasma treatment of activated carbon is a promising method for enhancing CO₂ capture.

The aim of this study was to investigate the crystal structure and bandgap of the emerging material Cu₄TiSe₄ using both theoretical and experimental methods. We synthesized the title compound via solid-state synthesis from elements. The occurrence of the single crystals of the Cu₄TiSe₄ compound was proven by X-ray diffraction and EDX investigations. The resolved crystal structure proves the one recently reported for this compound. Additionally, we utilized the Uspex evolutionary algorithm for the prediction of the crystal structure of the Cu₄TiSe₄ compound and to check for the presence of potential polymorphs. It turns out that Cu₄TiSe₄ may theoretically occur in three different crystal structures (space groups: I-42m (no. 121), R3m (no. 160), and P-43m (no. 215)), in which the rhombohedral phase has the lowest energy. The ab initio study of the bandgap of Cu₄TiSe₄ showed that it is indirect for each polymorphic structure and varies in the range of 1.23–1.26 eV, while experimental investigation revealed a direct transition of energy of 1.35 eV, thus showing the potential of this compound for solar cell applications. Theoretical calculations suggested that the rhombohedral phase of Cu₄TiSe₄ should exhibit a negative or relatively low (0.64 eV) bandgap.