Level index was introduced in 2017 for rooted trees which is a component of Gini index. In the origin, Gini index is a tool for economical investigations but Balaji and Mahmoud defined the graph theoretical applications of this index for statistical analysis of graphs. Level index is an important component of Gini index. In this paper we define a new graph polynomial which is called level polynomial and calculate the level polynomial of some classes of trees. We obtain some interesting relations between the level polynomials and some integer sequences.

In the study of QSAR/QSPR, due to high degree of predictability of pharmaceutical properties, the eccentric-connectivity index has very important place among the other topological descriptors, In this paper, we compute the exact formulas of eccentric-connectivity index and its corresponding polynomial, total eccentric-connectivity index and its corresponding polynomial, first Zagreb eccentricity index, augmented eccentric-connectivity index, modified eccentric-connectivity index and its corresponding polynomial for a class of phosphorus containing dendrimers.

As the field of nanoscience is rapidly evolving, interest for novel, upgraded nanomaterials with combinatory features is also inevitably increasing. Hybrid composites, offer simple, budget-conscious and environmental-friendly solutions that can cater multiple needs at the same time and be applicable in many nanotechnology-related and interdisciplinary studies. The physicochemical idiocrasies of dendritic polymers have inspired their implementation as sorbents, active ingredient carriers and templates for complex composites. Ceramics are distinguished for their mechanical superiority and absorption potential that render them ideal substrates for separation and catalysis technologies. The integration of dendritic compounds to these inorganic hosts can be achieved through chemical attachment of the organic moiety onto functionalized surfaces, impregnation and absorption inside the pores, conventional sol-gel reactions or via biomimetic mediation of dendritic matrices, inducing the formation of usually spherical hybrid nanoparticles. Alternatively, dendritic polymers can propagate from ceramic scaffolds. All these variants are covered in detail. Optimization techniques as well as established and prospected applications are also presented.

Novel TFN membranes were examined for the removal of heavy metals (Cu and Pb) from synthetic wastewater in forward osmosis (FO) experiments using MgCl2 as a draw solute. The TFN membranes were fabricated on top of a commercial PS35 ultrafiltration membrane by in-situ interfacial polymerization of piperazine (PIP) and 1,3,5-benzenetricarbonyl trichloride (TMC) containing different amounts of dispersed functionalized halloysite nanotubes (HNTs) nanoparticles. The HNTs nanoparticles were functionalized with the first generation of poly(amidoamine) (PAMAM) dendrimers. The TFN and the control TFC membranes showed rejections of Cu2+ and Pb2+, ranging from 94.5% to 98.1%. The presence of heavy metal in the feed solution enhanced the FO performance of all membranes. In particular, the reverse flux of MgCl2 decreased at least 2.5 times compared to the experiments with pure water as a feed. Simultaneously, the water flux also increased. The improved FO performance of the membranes in the presence of heavy metal ions is attributed to their adsorption by the membranes. The adsorption of heavy metals was confirmed by a decrease in the negativity of zeta potential and the results from inductively coupled plasma mass spectrometry (ICP-MS) of the membranes after the FO experiments.

Two different silica conformations (Xerogels and Nanoparticles) both formed by the mediation of dendritic poly (ethylene imine) were tested at low pHs on the problematic uranyl cation sorption. The effect of crucial factors i.e., temperature, electrostatic forces, adsorbent composition, accessibility of the pollutant to the dendritic cavities and MW of the organic matrix was investigated to conclude the optimum formulation for water purification under these conditions. This was attained with the aid of UV-Visible and FTIR spectroscopy, dynamic light scattering (DLS), ζ-potential; Brunauer–Emmett–Teller (BET) porosimetry, Thermo Gravimetric Analysis (TG) and Scanning Electron Microscopy (SEM) Results highlighted that both adsorbents have extraordinary sorp-tion capacity. Xerogels are cost-effective since they approximate the performance of na-noparticles with much lesser organic content. Furthermore, they are more practicable materials since they may penetrate the pores of a metal or ceramic solid substrate in the form of a precursor, gel-forming solution.

Radially polymerized dendritic compounds are nowadays an established polymer category next to their linear, branched and cross-linked counterparts. Their uncommon tree-like architecture is characterized by adjustable internal cavities and external groups. They are therefore exceptional absorbents and this attainment of high concentrations into their interior renders them ideal reac-tion media. In this framework they are applied in many environmentally benign implementa-tions. One of the most important among them is water purification though pollutant decomposi-tion. Simple and composite catalysts and photo-catalysts containing dendritic polymers and ap-plied in water remediation will be discussed jointly with some unconventional solutions and fu-ture prospects.

Methicillin-resistant Staphylococcus aureus (MRSA) exerts a considerable concern in healthcare and the community. Globally MRSA strains cause numerous infections with high morbidity and mortality rates. The success of MRSA is a result of the extensive production of virulence factors. With the limited treatment options for the MRSA infection and growing resistance problem, an urgent call is needed to search for an alternative to antibiotics. One of the promising strategies is targeting the quorum sensing (QS) system, of the MRSA, by using a dendrimer loaded with kinase inhibitor peptide. This study formulates a poly-amidoamine dendrimers (PAMAM) G4 dendrimers loaded with Quorum Quencher (QQ), QQ3 peptide which is a Histidine Kinase inhibitor. The physicochemical properties of the formula were characterized using different in-vitro analysis method such as Zetasizer and transmission electron microscope (TEM). The antibacterial activity and anti-virulence effect of the formula was tested against MRSA and different mutant stains using growth assay, haemolysis assay and biofilm assay. Overall, QQ3-G4 complex showed antibacterial and anti-virulence activity and it can be a potential alternative treatment to overcome antimicrobial resistance and treat MRSA infection.

Four leather substrates from different animals were treated by dispersions containing hydrophilic composite silica-hyperbranched poly(ethylene imine) xerogels. Antimicrobial activity was introduced by incorporating silver nanoparticles and /or benzalkonium chloride. The gel precursor solutions were also infused before gelation to titanium oxide powders typically employed for induction of self-cleaning properties. The dispersions from these biomimetically premade xerogels integrate environmentally friendly materials with short coating times. Scanning electron microscopy (SEM) provided information on the powder distribution onto the leathers. Substrate and coating composition were estimated by infrared spectroscopy (IR) and ener-gy-dispersive X-ray spectroscopy (EDS). Surface hydrophilicity and water permeability were assessed by water-contact angle experiments. The diffusion of the leather's initial components and xerogel additives into the water were measured by Ultraviolet-Visible (UV-Vis) spectroscopy. Protection against GRAM- bacteria was tested for Escherichia coli, Pseudomonas aeruginosa, and Klebsiella Pneumoniae against GRAM+ bacteria for Staphylococcus aureus, and Enterococcus faecalis and against fungi for Candida albicans. Antibiofilm capacity experiments were performed against Staphylococcus aureus, Klebsiella Pneumoniae, Enterococcus faecalis, and Candida albicans. The application of xerogel dispersions proved an adequate and economically feasible alternative to the direct gel formation into the substrate’s pores for the preparation of leathers intended for medical uses

Hybrid organic-inorganic (dendritic polymer-silica) xerogels containing silver nanoparticles (Ag-Nps) were developed as antibacterial leather coatings. The preparation method is environmentally friendly, based on two biomimetic reactions. Silica gelation and spontaneous (Ag-Np) formation were both mediated by hyperbranched poly (ethylene imine) (PEI) scaffolds of variable Mw (2000-750000). The formation of precursor hydrogels was monitored by dynamic light scattering (DLS). The chemical composition of the xerogels was assessed by Infra-Red Spectroscopy (IR) and Energy-dispersive X-ray spectroscopy (EDS) while the uniformity of the coatings was established by scanning electron microscopy (SEM). Release properties of coated leather samples and overall behaviour in water in comparison to untreated analogs were investigated by UV-Vis spectroscopy. Antibacterial activity was tested towards Escherichia coli, Pseudomonas aeruginosa, and Staphylococcus aureus, and antibiofilm properties against Staphylococcus aureus, Staphylococcus epidermidis, Escherichia coli, Acinetobacter baumannii, Enterococcus faecalis while SARS-Cov-2 clinical isolate was employed for the first estimation of their antiviral potential. Toxicity was evaluated using the Jurkat E6.1-cell line. Finally, water contact angle measurements were implemented to determine the enhancement of the leather surface hydrophilicity caused by these composite layers. The final advanced products are intended for use in medical applications.

The binding of actinide ions (Am(III) and U(VI)) in aqueous solutions by hybrid silica-hyperbranched poly(ethylene imine) nanoparticles (NP) and xerogels (XG) has been studied by means of batch experiments at different pH values (4, 7 and 9) under ambient atmospheric conditions. Both materials present relatively high removal efficiency at pH 4 and pH 7 (> 70%) for Am(III) and U(VI). The lower removal efficiency for the nanoparticles is basically associated with the compact structure of the nanoparticles and the lower permeability and access to active amine groups compared to xerogels, and the negative charge of the radionuclide species formed under alkaline conditions (e.g. UO2(CO3)34- and Am(CO3)2-). Generally, the adsorption process is relatively slow due to the very low radionuclide concentrations used in the study and is basically governed by the actinide diffusion from the aqueous phase to the solid surface. On the other hand, the adsorption is favored with increasing temperature assuming that the reaction is endothermic and entropy-driven, which is associated with increasing randomness at the solid-liquid interphase upon actinide adsorption. To the best of our knowledge, this is the first study on hybrid silica-hyperbranched poly(ethylene imine) nanoparticle and xerogel materials used as adsorbents for americium and uranium at ultra-trace levels. Compared to other adsorbent materials used for binding americium and uranium ions, both materials show far higher binding efficiency. Xerogels could remove both actinides even from seawater by almost 90%, whereas nanoparticles could remove uranium by 80% and americium by 70%. The above, along with their simple derivatization to increase the selectivity towards a specific radionuclide and their easy processing to be included in separation technologies, could make these materials attractive candidates for the treatment of radionuclide/actinide contaminated water.