The work, carried out by Bijan Kumar Gangopadhyay, an independent researcher based in West Bengal, India, addresses a long-standing challenge in nanoscale thermodynamics. For decades, scientists have known that the properties of a material change dramatically when its dimensions shrink to the nanometer scale. The reason lies in simple arithmetic: as particles get smaller, an ever-larger fraction of their atoms sits on the surface rather than in the interior. Surface atoms are less tightly bound than their bulk counterparts because they have fewer neighbors, and this deficit of bonding partners destabilizes the crystal, allowing it to melt at lower temperatures and to contract under the pull of surface stress.

What has often been missing from earlier treatments, however, is a clean, explicit way to connect geometry to thermodynamics. Many existing models rely on average coordination numbers, empirical fitting parameters, or assumptions borrowed from macroscopic thermodynamics that become questionable at small sizes. The new model takes a different route. It begins with a direct, geometrical count of the fraction of atoms that reside on the surface of a nanoparticle of arbitrary shape, whether that particle is a sphere, a cube, a tetrahedron, or a thin film. From this surface-atom fraction, the model derives a relaxation factor that quantifies the effect of dangling bonds, the unsatisfied chemical bonds that terminate at any free surface.

The physical logic is straightforward. Every atom in the interior of a face-centered cubic metal such as gold or copper is surrounded by twelve nearest neighbors, giving it the full complement of bonding interactions that define the bulk cohesive energy. An atom on a flat surface, by contrast, may have only eight or nine neighbors, while an atom at a corner or edge of a faceted particle may have fewer still. These dangling bonds represent missing cohesive energy, and the more of them a particle has, relative to its total number of atoms, the more its average binding energy falls below the bulk value. Because melting occurs when thermal energy overcomes cohesive binding, a reduced average binding energy translates directly into a reduced melting temperature.

The same surface-atom fraction also governs the lattice parameter, the characteristic spacing between atoms in the crystal. Surface stress, arising from the imbalance of forces experienced by surface atoms, pulls the outer layers of the crystal inward, and this contraction propagates into the interior. Experimental measurements dating back to classic electron-diffraction studies of gold in the late 1960s and of copper and platinum in the early 1970s have confirmed that nanoscale metallic particles do indeed have smaller lattice constants than bulk crystals, with the deviation growing as particle size shrinks. The new analytical model reproduces this behavior by linking the relaxation factor, which describes how surface atoms adjust their positions and bonding, to the same geometric quantity that controls melting.

Applying the framework to gold and copper nanoparticles across a wide range of sizes, the study finds good agreement with available experimental measurements of both melting temperature and lattice parameter. The comparison covers spherical particles, cubes, tetrahedra, and nanofilms, demonstrating that a single set of analytical expressions can handle geometries that differ radically in their surface-to-volume ratios. A thin film, with two dominant surfaces and a thickness of only a few nanometers, has a far larger fraction of surface atoms than a sphere of comparable characteristic dimension, and the model captures the consequences: stronger melting-point depression and more pronounced lattice contraction.

One of the study’s clearest findings concerns what the author calls the shape factor. As the shape factor increases, reflecting a geometry with a larger surface-to-volume ratio, both melting-point depression and lattice contraction intensify. This provides a practical design rule for experimentalists: if you want to tune the thermal behavior of a metallic nanostructure, changing its shape can be as consequential as changing its size. A tetrahedral particle and a spherical particle containing the same number of atoms will not melt at the same temperature, because their surface atoms carry different weights in the overall energy balance.

The implications extend beyond gold and copper. The model is formulated for face-centered cubic metals in general, and its analytical simplicity means it can be evaluated with pencil and paper rather than computationally expensive simulations. Molecular dynamics and Monte Carlo approaches remain indispensable for capturing the full atomistic detail of nanoscale systems, including surface reconstructions, facet-specific chemistry, and thermal fluctuations, but they are costly and often difficult to interpret. An analytical expression that captures the leading-size and shape effects gives researchers a fast screening tool and a physical baseline against which simulations and experiments can be compared. The author suggests the framework could be extended to other thermodynamic properties of metallic nanomaterials, such as Debye temperature, specific heat, and thermal expansion, which previous studies have shown follow related size-dependent trends.

The scientific pedigree of the problem is long. Researchers have proposed liquid-drop models, coordination-number models, and various semi-empirical relations to explain melting-point depression since the phenomenon was first systematically studied. What distinguishes the present contribution is its explicit geometrical foundation: rather than treating the surface-atom fraction as an adjustable parameter, the model computes it directly from particle shape, and then ties it transparently to the physics of dangling bonds. This makes the model physically transparent in a way that purely fitted formulas are not, and it explains why different shapes produce different depressions of the melting point without requiring shape-specific calibration.

For technologists, the stakes are real. Gold nanoparticles are workhorses of catalysis, plasmonics, biomedical imaging, and drug delivery, and copper nanoparticles are increasingly important in electronics, antimicrobial coatings, and thermal interface materials. In all of these applications, the particles are processed, annealed, and operated at temperatures where their reduced melting points matter. Sintering, coalescence, and shape changes during manufacturing are governed by the same surface thermodynamics that the new model describes. A reliable analytical prediction of when a given nanoparticle will begin to soften and rearrange could help engineers choose processing windows that preserve the carefully engineered shapes on which device performance depends. Conversely, controlled melting could be exploited to fuse particles into desired architectures. As nanomaterials continue to move from laboratory curiosities to manufactured components, compact predictive tools of this kind are likely to become standard equipment in the nanoscale designer’s toolkit.

Subject of Research: Size- and shape-dependent melting temperature and lattice parameter behavior of gold and copper metallic nanoparticles

Article Title: Unified analytical model for size- and shape-dependent melting temperature and lattice parameter of gold and copper nanoparticles

Article References: Gangopadhyay, B. K. (2026). Unified analytical model for size- and shape-dependent melting temperature and lattice parameter of gold and copper nanoparticles. Journal of Nanoparticle Research, 28(10), Article 249. https://doi.org/10.1007/s11051-026-06770-3

Image Credits: AI Generated

DOI: 10.1007/s11051-026-06770-3

Keywords: metallic nanoparticles, melting-point depression, lattice contraction, surface-atom fraction, surface relaxation, gold nanoparticles, copper nanoparticles, nanoscale thermodynamics, analytical modeling, face-centered cubic metals, nanofilms, surface stress

The central mechanisms are surprisingly convergent. Nanoparticles can enter endocrine cells through circulation and lymphatic routes, bind to hormone receptors and either activate or inhibit downstream signaling pathways. Silver and zinc nanoparticles, for example, can bind estrogen receptors and display estrogenic activity, effectively mimicking natural hormones. Perhaps the most important pathway, however, is the generation of reactive oxygen species. These reactive molecules induce oxidative stress, damaging cellular structures and disrupting the signaling cascades that coordinate hormone synthesis and secretion. In parallel, nanoparticles activate innate immune responses, provoke the release of inflammatory cytokines, interfere with enzymes and transporters involved in endocrine regulation, and impair hormone metabolism. The end result of these disturbances can range from reproductive failure to metabolic syndrome, and the review stresses that the endocrine-disruptor effect of metallic nanoparticles depends heavily on their capacity to release metal ions that inhibit nuclear receptors and interfere with natural hormone action.

The thyroid gland emerges as one of the most intensively studied targets. Titanium dioxide nanoparticles administered to rats at 5 milligrams per kilogram for 21 days produced histopathological changes, including abnormal follicular cell morphology and epithelial damage, alongside a decrease in the sodium/iodide symporter, elevated caspase-3 apoptotic protein, and increased pro-inflammatory factors such as interleukin-1 beta and tumor necrosis factor alpha. In vitro, follicular cell viability declined. Silver nanoparticles affected the messenger RNA expression of thyroid hormone related genes in laying hens, raising serum triiodothyronine without altering thyroxine and prompting tissue-specific expression of genes involved in thyroid hormone metabolism, including deiodinases and the hormone transporter MCT10. Longer term exposure in female rats decreased thyroxine concentrations and caused degeneration of thyroid follicles. Intriguingly, the story is not uniformly negative: biogenic silver nanoparticles of 17 to 35 nanometers have been reported to raise triiodothyronine and thyroxine levels in experimentally hypothyroid rats, suggesting a potential therapeutic dimension.

Zinc oxide nanoparticles add another layer of complexity. Fed to albino rats at high doses for 30 days, they decreased thyroxine and thyroid stimulating hormone while producing histopathological damage. When combined with lead acetate over eight weeks, they lowered triiodothyronine and thyroxine, raised thyroid stimulating hormone and tumor necrosis factor alpha, and triggered significant overexpression of the nuclear factor erythroid 2 related factor, a master regulator of antioxidant response. The review also situates metallic nanoparticles within the broader landscape of thyroid-disrupting chemicals, noting that phthalates, bisphenol-A and polybrominated diphenyl ethers released by micro- and nanoplastics are established thyroid disruptors that enter through the gastrointestinal system and interfere with hormone secretion, transport and the hypothalamo-pituitary-thyroid axis. Transcriptomic studies further show disruption of thyroglobulin synthesis and interference with Pax8 and CERB gene expression, which are crucial for thyroid growth, differentiation and hormone secretion. By contrast, direct studies of the parathyroid gland remain scarce.

The thymus, a primary lymphoid organ where T cells mature, illustrates the overlap between endocrine and immune toxicity. Silver nanoparticles stimulate immune responses and promote cytokines such as interleukin-6, driving inflammation, while at higher concentrations they induce oxidative stress and DNA damage. Zinc oxide nanoparticles can activate human T cells and even preferentially kill cancerous T cells, with toxicity tracking the level of T cell activation, an effect attributed largely to reactive oxygen species. Orally administered zinc oxide caused degenerative changes in the thymus and spleen of rats, reduced thymus weight over three months of sub-chronic exposure, and shifted staining patterns consistent with decreased proliferation and increased p53-associated damage. Cadmium nanoparticles produce thymic atrophy, depletion of CD4-positive and CD8-positive T cells, and oxidative stress and apoptosis, with prenatal exposure producing persistent changes in immune cell repertoires. Cadmium oxide and lead oxide nanoparticles altered T cell populations in mice, while nickel nanoparticles stimulated pro-inflammatory cytokines that affect T cell activation, and titanium dioxide nanoparticles showed a striking dose dependence, provoking inflammation at low doses and cytotoxicity at high doses.

The pineal gland, source of the antioxidant hormone melatonin, faces a double-edged relationship with nanomaterials. Zinc oxide nanoparticles damage both brain and pineal tissue through reactive oxygen species, and in a counterintuitive finding, melatonin pretreatment actually enhanced zinc oxide toxicity in C6 glial cells rather than protecting them. Exposures to aluminum oxide and silver nanoparticles are associated with neurotoxicity and pineal dysfunction. Yet melatonin-loaded nanocarriers are now being deployed therapeutically, delivering the hormone with superior efficacy against disease than free melatonin alone. Melatonin complexed with nanometric gold offered testicular protection, a melatonin palladium complex induced apoptosis in human lung adenocarcinoma cells, and palladium nanoparticles served as platforms for detecting melatonin and related molecules electrochemically. This duality, harm and remedy coexisting in the same material class, runs throughout the review and underscores the difficulty of blanket risk assessments.

At the top of the hormonal hierarchy, the hypothalamo-pituitary axis is vulnerable in ways that ripple across the entire endocrine system. Copper nanoparticles inhibited pituitary gonadotropin secretion in male mice, suppressing luteinizing hormone and follicle stimulating hormone alongside degenerative changes in the anterior pituitary. Nanoparticles interfere with the ability of glial cells to regulate gonadotropin-releasing hormone, and trans-generational effects have been reported, with lithium carbonate nanoparticles affecting both the pituitary-gonadal and pituitary-thyroid axes in female rat progenies. The adrenal glands are similarly susceptible. Nanoparticles can activate the hypothalamic-pituitary-adrenal axis, surging adrenocorticotropic hormone and driving structural and functional changes, while also affecting key steroidogenic enzymes including aromatase, 5-alpha reductase, CYP11A1 and CYP11B1. Silver nanoparticles increased cortical functional activity and proved cytotoxic to adrenal pheochromocytoma cells through ATP depletion, cytoskeletal changes and oxidative stress, and in zebrafish they suppressed the cortisol response to acute stress by altering the hypothalamic-pituitary-interrenal axis at the transcriptomic level. Short-term oral titanium dioxide exposure impaired adrenal cortex and medulla structure in rats without apparent general toxicity, in vitro studies confirmed uptake of magnetic iron oxide nanoparticles by adrenal cortical cell lines, and nano-arsenic was reported to induce adrenal tumors through oxidative tissue damage and hormonal disturbance.

The pancreas and placenta complete the picture. Titanium dioxide nanoparticles caused histopathological and biochemical changes in the rat pancreas, with effects attributed to oxidative stress, inflammation and apoptosis of beta cells, decreased insulin secretion and disrupted carbohydrate metabolism, collectively raising diabetes risk. Yet low-dose zinc oxide nanoparticles normalized pancreatic function in diabetic rats by protecting beta cells through GLP-1 and oxidative stress pathways, and nanoselenium protected endocrine and exocrine pancreatic function in a rat model of acute pancreatitis through antioxidant and anti-inflammatory actions. Nanoparticles are also being pursued for targeted insulin delivery, with polymeric nanoparticles proposed for oral insulin administration and oligonucleotide-loaded particles explored for gene and cell therapy to stimulate insulin production. At the placenta, nanoparticles can cross the blood-placental barrier, disrupt placental function and the release of signaling factors needed for fetal development, and dysregulate the placental secretome with consequences for angiogenesis and vascularization. Ex vivo human placental perfusion studies have illuminated these risks, though the review notes that current regulatory guidelines do not sufficiently address placental toxicity, while smart nanoparticles engineered to target the placenta could eventually improve its function.

The review closes with a call for methodological renewal. Because nanoparticle toxicology involves multiple organs and interdependent molecular mechanisms, no single experimental model can simulate a realistic scenario; the author advocates microfluidic and organ-on-chip systems combined with single-cell culture, multi-omic approaches and in silico models to achieve accurate in vivo evaluation. Attention to biomarkers, mitochondrial versus cytoplasmic sources of reactive oxygen species, and the combined effects of multiple nanoparticles is warranted. A new generation of redox nanoparticles, including cerium oxide, boron cluster and silica-containing particles, offers promising antioxidant properties and the ability to cross the blood-brain barrier for treating endocrine disruption. The overarching conclusion is sobering but constructive: endocrine toxicity must remain central to risk assessment if nanotechnology is to be safely integrated into healthcare, theranostics, industry and the environment.

Subject of Research: Mechanisms of endocrine gland toxicity induced by metallic nanoparticles

Article Title: Endocrine gland specific mechanistic paradigms of toxicity induced by metallic nanoparticles

Article References: Rana, S. V. S. (2026). Endocrine gland specific mechanistic paradigms of toxicity induced by metallic nanoparticles. Discover Toxicology, 3(1), Article 20. https://doi.org/10.1007/s44339-026-00064-y

Image Credits: AI Generated

DOI: 10.1007/s44339-026-00064-y

Keywords: metallic nanoparticles, endocrine glands, oxidative stress, thyroid toxicity, hormone disruption, hypothalamo-pituitary axis, reactive oxygen species, adrenal glands, pancreas, placenta, nanotoxicology, antioxidants