Recent advances in nanoscience and nanotechnology radically changed the way we diagnose, treat, and prevent various diseases in all aspects of human life. Silver nanoparticles (AgNPs) are one of the most vital and fascinating nanomaterials among several metallic nanoparticles that are involved in biomedical applications. AgNPs play an important role in nanoscience and nanotechnology, particularly in nanomedicine. Although several noble metals have been used for various purposes, AgNPs have been focused on potential applications in cancer diagnosis and therapy. In this review, we discuss the synthesis of AgNPs using physical, chemical, and biological methods. We also discuss the properties of AgNPs and methods for their characterization. More importantly, we extensively discuss the multifunctional bio-applications of AgNPs; for example, as antibacterial, antifungal, antiviral, anti-inflammatory, anti-angiogenic, and anti-cancer agents, and the mechanism of the anti-cancer activity of AgNPs. In addition, we discuss therapeutic approaches and challenges for cancer therapy using AgNPs. Finally, we conclude by discussing the future perspective of AgNPs.

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We derive an identity connecting a theta function and a sum of Lambert series. As a consequence of this identity, we deduce a number of results of Jacobi, Dirichlet, Lorenz, Ramanujan and Rademacher.

BaTiO3 (BT) nanoparticles were prepared by the hydrothermal technique using different starting materials and the microstructure examined by XRD, SEM, TEM and HRTEM. X-ray diffraction and electron diffraction patterns showed that the nanoparticles were the cubic BaTiO3 phase. The BT nanoparticles prepared from the starting materials of as-prepared titanium hydroxide and barium hydroxide have spherical grain morphology, an average size of 65 nm and a fairly narrow size distribution. A uniform diffraction contrast across each single grain is observed in the TEM images, and the clear lattice fringes (with d110 = 0.28 nm) observed in HRTEM images reveal that well-crystallized BT nanoparticles are synthesized by the hydrothermal method. The edges of the particles are very smooth, with no surface steps. BT nanoparticles with average grain size of 90 nm, synthesized using barium hydroxide and titanium dioxide as the starting materials, show surface facets. In this case a bimodal size distribution of large faceted and smaller particles is observed. Diffraction contrast variation across the particles caused by high strains within the particles is clearly observed. The high strains obviously stem from structural defects formed during hydrothermal synthesis, presumable in the form of lattice OH− ions and their compensation by cation vacancies. HRTEM images demonstrate that surface facets parallel to the (100) and (110) planes and small islands with 3 ~ 4 atomic layer thickness are frequently observed around the edge of the particles.

Perovskite epitaxial multiferroic BiFeO3 nanoislands were grown on SrTiO3 (100) and Nb-doped SrTiO3 (100) single crystal substrates by chemical self-assembled method. Their phase structure and morphology were characterized by X-ray diffraction, scanning electron microscopy, and atomic force microscopy, respectively. The results showed that epitaxial multiferroic BiFeO3 nanoislands were obtained via post-annealing process in the temperature range of 650 - 800°C, and their lateral sizes were in the range of 50 - 160 nm and height of 6 -12 nm. With increasing the post-annealing temperature, the morphology of BiFeO3 nanoisland in the (100) growth plane evolved from tri-angled to squared, and then to plated shapes. By using piezo-force microscopy, ferroelectric characteristics of a single epitaxial BiFeO3 nanoisland (with lateral size of ~ 50 nm and height of 12 nm) grown on Nb-doped SrTiO3 (100) single crystal substrate, was characterized. The results demonstrated that fractal ferroelectric domains existed in the single BiFeO3 nanoisland, and self-biased polarization was also observed within this multiferroic nanoisland. This phenomenon can be ascribed to the interfacial stress caused by the lattice misfit between the BiFeO3 nanoisland and the SrTiO3 single crystal substrate.