Uncovering the dual role of dimensionless radius in buckling of spherical shells with random geometric imperfections.

Localized deformation and randomly shaped imperfections are salient features of buckling-type instabilities in thin-walled load-bearing structures. However, it is generally agreed that their complex interactions in response to mechanical loading are not yet sufficiently understood, as evidenced by buckling-induced catastrophic failures which continue to today. This study investigates how the intimate coupling between localization mechanisms and geometric imperfections combine to determine the statistics of the pressure required to buckle (the illustrative example of) a hemispherical shell. The geometric imperfections, in the form of a surface, are defined by a random field generated over the nominally hemispherical shell geometry, and the probability distribution of the buckling pressure is computed via stochastic finite element analysis. Monte-Carlo simulations are performed for a wide range of the shell's radius to thickness ratio, as well as the correlation length of the spatial distribution of the imperfection. The results show that over this range, the buckling pressure is captured by the Weibull distribution. In addition, the analyses of the deformation patterns observed during the simulations provide insights into the effects of certain characteristic lengths on the local buckling that triggers global instability. In light of the simulation results, a probabilistic model is developed for the statistics of the buckling load that reveals how the dimensionless radius plays a dual role which remained hidden in previous deterministic analyses. The implications of the present model for reliability-based design of shell structures are discussed.

Size Dependent Phase Transformation of Liquid Gallium.

As the most popular liquid metal (LM), gallium (Ga) and its alloys are emerging as functional materials due to their unique combination of fluidic and metallic properties near room temperature. As an important branch of utilizing LMs, micro- and submicron-particles of Ga-based LM are widely employed in wearable electronics, catalysis, energy, and biomedicine. Meanwhile, the phase transition is crucial not only for the applications based on this reversible transformation process, but also for the solidification temperature at which fluid properties are lost. While Ga has several solid phases and exhibits unusual size-dependent phase behavior. This complex process makes the phase transition and undercooling of Ga uncontrollable, which considerably affects the application performance. In this work, extensive (nano-)calorimetry experiments are performed to investigate the polymorph selection mechanism during liquid Ga crystallization. It is surprisingly found that the crystallization temperature and crystallization pathway to either α -Ga or ß -Ga can be effectively engineered by thermal treatment and droplet size. The polymorph selection process is suggested to be highly relevant to the capability of forming covalent bonds in the equilibrium supercooled liquid. The observation of two different crystallization pathways depending on the annealing temperature may indicate that there exist two different liquid phases in Ga.

Size Effect for Inhibiting Polysulfides Shuttle in Lithium-Sulfur Batteries.

It is undeniable that the dissolution of polysulfides is beneficial in speeding up the conversion rate of sulfur in electrochemical reactions. But it also brings the bothersome "shuttle effect". Therefore, if polysulfides can be retained on the cathode side, the efficient utilization of the polysulfides can be guaranteed to achieve the excellent performance of lithium-sulfur batteries. Based on this idea, considerable methods have been developed to inhibit the shuttling of polysulfides. It is necessary to emphasize that no matter which method is used, the solvation mechanism, and existence forms of polysulfides are essential to analyze. Especially, it is important to clarify the sizes of different forms of polysulfides when using the size effect to inhibit the shuttling of polysulfides. In this review, a comprehensive summary and in-depth discussion of the solvation mechanism, the existing forms of polysulfides, and the influencing factors affecting polysulfides species are presented. Meanwhile, the size of diverse polysulfide species is sorted out for the first time. Depending on the size of polysulfides, tactics of using size effect in cathode, separator, and interlayer parts are elaborated. Finally, a design idea of materials pore size is proposed to satisfy the use of size effect to inhibit polysulfides shuttle.

Efficient Photoelectrochemical Hydrogen Generation Based on Core Size Effect of Heterostructured Quantum Dots.

Colloidal quantum dots (QDs) are shown to be effective as light-harvesting sensitizers of metal oxide semiconductor (MOS) photoelectrodes for photoelectrochemical (PEC) hydrogen (H2) generation. The CdSe/CdS core/shell architecture is widely studied due to their tunable absorption range and band alignment via engineering the size of each composition, leading to efficient carrier separation/transfer with proper core/shell band types. However, until now the effect of core size on the PEC performance along with tailoring the core/shell band alignment is not well understood. Here, by regulating four types of CdSe/CdS core/shell QDs with different core sizes (diameter of 2.8, 3.1, 3.5, and 4.8 nm) while the thickness of CdS shell remains the same (thickness of 2.0 ± 0.1 nm), the Type II, Quasi-Type II, and Type I core/shell architecture are successfully formed. Among these, the optimized CdSe/CdS/TiO2 photoelectrode with core size of 3.5 nm can achieve the saturated photocurrent density (Jph) of 17.4 mA cm-2 under standard one sun irradiation. When such cores are further optimized by capping alloyed shells, the Jph can reach values of 22 mA cm2 which is among the best-performed electrodes based on colloidal QDs.

The Reactivity of Ptn + Clusters With N2O Facilitated by Dual Lewis-Acid Sites.

The size dependence of metal cluster reactions frequently reveals valuable information on the mechanism of nanometal catalysis. Here, the reactivity of the Ptn + (n = 1-40) clusters with N2O is studied and a significant dependence on the size of these clusters is noticed. Interestingly, the small Ptn + clusters like Pt3 + and Pt4 + are inclined to form N2O complexes; some larger clusters, such as Pt19 +, Pt21 +, and Pt23 +, appear to be unreactive; however, the others such as Pt3 , 9,15 + and Pt18 + are capable of decomposing N2O. While Pt9 + rapidly reacts with N2O to form a stable quasitetrahedron Pt9O+ product, Pt18 + experiences a series of N2O decompositions to produce Pt18O1-7 +. Utilizing high-precision theoretical calculations, it is shown how the atomic structures and active sites of Ptn + clusters play a vital role in determining their reactivity. Cooperative dual Lewis-acid sites (CDLAS) can be achieved on specific metal clusters like Pt18 +, rendering accelerated N2O decomposition via both N- and O-bonding on the neighboring Pt atoms. The influence of CDLAS on the size-dependent reaction of Pt clusters with N2O is illustrated, offering insights into cluster catalysis in reactions that include the donation of electron pairs.

CdSe nanostructured thin film by electrophoretic deposition for quantum dots sensitized solar cell.

Cadmium selenide (CdSe) quantum dots (QDs) with different size, 2.5 and 3.2 nm, were successfully deposited on mesoporous titanium dioxide (TiO2) (Degussa-P25) nanostructures by electrophoretic deposition method (EPD) at the applied voltage 100 V for 120 s deposition time. In this study, the morphology of CdSe films deposited by EPD and the performance of the film when assembled into a solar cell were investigated. From the field emission scanning electron microscopy cross-section, the thickness of the CdSe nanoparticles with size 2.5 nm films were 3.4 and 3.0µm for CdSe 3.2 nm nanoparticles film. The structure of 2.5 nm is denser than compare of 3.2 nm CdSe nanoparticles. From UV visible spectroscopy, the band gap calculated for 2.5 nm CdSe nanoparticles is 2.28 eV and for 3.2 nm is 2.12 eV. Photovoltaic characterization was performed under an illumination of 100 mW cm-2. A photovoltaic conversion efficiency of 1.81% was obtained for 2.5 nm CdSe and 2.1% was obtained for 3.2 nm CdSe nanoparticles. This result shows that the photovoltaic efficiency is dependent on CdSe nanoparticle size.

Sources and Health Risks of Heavy Metals in Kindergarten Dust: The Role of Particle Size.

Particle size effects significantly impact the concentration and toxicity of heavy metals (HMs) in dust. Nevertheless, the differences in concentrations, sources, and risks of HMs in dust with different particle sizes are unclear. Therefore, guided by the definition of atmospheric particulate matter, dust samples with particle sizes under 1000 µm (DT1000), 100 µm (DT100), and 63 µm (DT63) from Beijing kindergartens were collected. The concentrations of HMs (e.g., Cd, Pb, Zn, Ni, Cr, Ba, Cu, V, Mn, Co, and Ti) in dust samples with different particle sizes were measured. Besides, the differences in HM concentrations, contamination levels, sources, and source-oriented health risks in dust samples of different particle sizes were systematically explored. The results show that the concentrations of Mn, V, Zn, and Cd gradually increase with decreasing dust particle sizes, the concentrations of Ba and Pb show a decreasing trend, and the concentrations of Cr, Cu, Ni, and Co display an increasing and then decreasing trend. The degree of contamination of HMs in dust of different particle sizes varies, with Cd being the most dominant contaminant. Compared with DT1000 and DT63, DT100 is the most polluted. In addition, the sources of HMs in DT1000, DT100, and DT63 become more single with decreasing particle size, which may be mainly due to the particle-size effect inducing the redistribution of HMs in different sources. Notably, the potential health risk is higher in DT100 than in DT1000 and DT63. The highest contribution of industrial sources to the health risk is found in DT100, which is mainly caused by highly toxic chromium (Cr). This work emphasizes the importance of considering particle size in risk assessment and pollution control, which can provide a theoretical basis for precise management of HMs pollution in dust.

Improving the stability, foliar utilization and biological activity of imidacloprid delivery systems: Size effect of nanoparticles.

Nanotechnology could improve the effectiveness and functionality of pesticides, but the size effect of nanopesticides on formulation performance and the related mechanisms have yet to be explored, hindering the precise design and development of efficient and eco-friendly nanopesticides. In this study, two non-carrier-coated imidacloprid formulations (Nano-IMI and Micro-IMI) with identical composition but varying particle size characteristics were constructed to exclude other interferences in the size effect investigation. Nano-IMI and Micro-IMI both exhibited rod-like structures. Specifically, Nano-IMI had average vertical and horizontal axis sizes of 239.5 nm and 561.8 nm, while Micro-IMI exhibited 6.7 µm and 22.1 µm, respectively. Compared to Micro-IMI, the small size effect of Nano-IMI affected the arrangement of interfacial molecules, reduced surface tension and contact angle, thereby improving the stability, dispersibility, foliar wettability, deposition and retention of the nano-system. Nano-IMI exhibited 1.3 times higher toxicity to Aphis gossypii Glover compared to Micro-IMI, attributed to its enhanced foliar utilization efficiency. Importantly, the Nano-IMI did not intensify the toxicity to non-target organism Apis mellifera L. This study systematically elucidates the influence of size effect on key indicators related to the effectiveness and safety, providing a theoretical basis for efficient and safe application of nanopesticides and critical insights into sustainable agriculture and environmental development.

Exploring the origins of the indentation size effect at submicron scales.

The origin of the indentation size effect has been extensively researched over the last three decades, following the establishment of nanoindentation as a broadly used small-scale mechanical testing technique that enables hardness measurements at submicrometer scales. However, a mechanistic understanding of the indentation size effect based on direct experimental observations at the dislocation level remains limited due to difficulties in observing and quantifying the dislocation structures that form underneath indents using conventional microscopy techniques. Here, we employ precession electron beam diffraction microscopy to "look beneath the surface," revealing the dislocation characteristics (e.g., distribution and total length) as a function of indentation depth for a single crystal of nickel. At smaller depths, individual dislocation lines can be resolved, and the dislocation distribution is quite diffuse. The indentation size effect deviates from the Nix-Gao model and is controlled by dislocation source starvation, as the dislocations are very mobile and glide away from the indented zone, leaving behind a relatively low dislocation density in the plastically deformed volume. At larger depths, dislocations become highly entangled and self-arrange to form subgrain boundaries. In this depth range, the Nix-Gao model provides a rational description because the entanglements and subgrain boundaries effectively confine dislocation movement to a small hemispherical volume beneath the contact impression, leading to dislocation interaction hardening. The work highlights the critical role of dislocation structural development in the small-scale mechanistic transition in indentation size effect and its importance in understanding the plastic deformation of materials at the submicron scale.

Influence of silver doping on pro-inflammatory and pro-fibrogenic effects of nano-titanium dioxide in murine lung.

Silver is usually loaded on nano-titanium dioxide (TiO2 ) through photodeposition method to enhance visible-light catalytic functions for environment purification. However, little is known about how the toxicity changes after silver doping and how the physicochemical properties of loaded components affect nanocomposite toxicity. In this study, Ag-TiO2 with different sizes and contents of silver particles were obtained by controlling photodeposition time (PDT) and silver addition amount. Pro-inflammatory and pro-fibrogenic responses of these photocatalysts were evaluated in male C57BL/6J murine lung. As a result, silver was well assembled on TiO2 , promoting visible-light catalytic activity. Notably, the size of silver particles increased with PDT. Meanwhile, toxicity results showed that pure TiO2 (P25) mainly caused neutrophil infiltration, while 2 wt/wt% silver-loaded TiO2 recruited more types of inflammatory cells in the lung. Both of them caused the increase of proinflammatory cytokines while decreasing the anti-inflammatory cytokine in bronchoalveolar lavage fluid. However, 2 wt/wt% silver doping also accelerated the lung pro-fibrogenic response of photocatalysts in the subacute phase from evidence of collagen deposition and hydroxyproline concentrations. Mechanistically, the overactivation of TGFBR2 receptors in TGF-ß/smads pathways by silver-loaded TiO2 rather than pure TiO2 may be the reason why silver-loaded TiO2 can promote pro-fibrogenic effect response. Intriguingly, the increased toxicity caused by silver doping can be rescued by increasing the size of the loaded silver or decreasing the silver amount. These results may be important for the new understanding of the toxicity of TiO2 -based photocatalysts.

Graphene Nanoplatelets/Polydimethylsiloxane Flexible Strain Sensor with Improved Sandwich Structure.

In engineering measurements, metal foil strain gauges suffer from a limited range and low sensitivity, necessitating the development of flexible sensors to fill the gap. This paper presents a flexible, high-performance piezoresistive sensor using a composite consisting of graphene nanoplatelets (GNPs) and polydimethylsiloxane (PDMS). The proposed sensor demonstrated a significantly wider range (97%) and higher gauge factor (GF) (6.3), effectively addressing the shortcomings of traditional strain gauges. The microstructure of the GNPs/PDMS composite was observed using a scanning electron microscope, and the distribution of the conductive network was analyzed. The mechanical behavior of the sensor encapsulation was analyzed, leading to the determination of the mechanisms influencing encapsulation. Experiments based on a standard equal-strength beam were conducted to investigate the influence of the base and coating dimensions of the sensor. The results indicated that reducing the base thickness and increasing the coating length both contributed to the enhancement of the sensor's performance. These findings provide valuable guidance for future development and design of flexible sensors.

Role of Micelle Size in Cell Transcytosis-Based Tumor Extravasation, Infiltration, and Treatment Efficacy.

Transcytosis-based active transport of cancer nanomedicine has shown great promise for enhancing its tumor extravasation and infiltration and antitumor activity, but how the key nanoproperties of nanomedicine, particularly particle size, influence the transcytosis remains unknown. Herein, we used a transcytosis-inducing polymer, poly[2-(N-oxide-N,N-diethylamino)ethyl methacrylate] (OPDEA), and fabricated stable OPDEA-based micelles with different sizes (30, 70, and 140 nm in diameter) from its amphiphilic block copolymer, OPDEA-block-polystyrene (OPDEA-PS). The study of the micelle size effects on cell transcytosis, tumor extravasation, and infiltration showed that the smallest micelles (30 nm) had the fastest transcytosis and, thus, the most efficient tumor extravasation and infiltration. So, the 7-ethyl-10-hydroxyl camptothecin (SN38)-conjugated OPDEA micelles of 30 nm had much enhanced antitumor activity compared with the 140 nm micelles. These results are instructive for the design of active cancer nanomedicine.

The Effect of Monomer Size on Fusion and Coupling in Colloidal Quantum Dot Molecules.

The fusion step in the formation of colloidal quantum dot molecules, constructed from two core/shell quantum dots, dictates the coupling strength and hence their properties and enriched functionalities compared to monomers. Herein, studying the monomer size effect on fusion and coupling, we observe a linear relation of the fusion temperature with the inverse nanocrystal radius. This trend, similar to that in nanocrystal melting, emphasizes the role of the surface energy. The suggested fusion mechanism involves intraparticle ripening where atoms diffuse to the reactive connecting neck region. Moreover, the effect of monomer size and neck filling on the degree of electronic coupling is studied by combined atomistic-pseudopotential calculations and optical measurements, uncovering strong coupling effects in small QD dimers, leading to significant optical changes. Understanding and controlling the fusion and hence coupling effect allows tailoring the optical properties of these nanoscale structures, with potential applications in photonic and quantum technologies.

Computation of X-ray and Neutron Scattering Patterns to Benchmark Atomistic Simulations against Experiments.

Molecular Dynamics simulations study material structure and dynamics at the atomic level. X-ray and neutron scattering experiments probe exactly the same time- and length scales as the simulations. In order to benchmark simulations against measured scattering data, a program is required that computes scattering patterns from simulations with good single-core performance and support for parallelization. In this work, the existing program Sassena is used as a potent solution to this requirement for a range of scattering methods, covering pico- to nanosecond dynamics, as well as the structure from some Ångströms to hundreds of nanometers. In the case of nanometer-level structures, the finite size of the simulation box, which is referred to as the finite size effect, has to be factored into the computations for which a method is described and implemented into Sassena. Additionally, the single-core and parallelization performance of Sassena is investigated, and several improvements are introduced.

Characterization and Performance of Peanut Shells in Caffeine and Triclosan Removal in Batch and Fixed-Bed Column Tests.

Peanut shells' adsorption performance in caffeine and triclosan removal was studied. Peanut shells were analyzed for their chemical composition, morphology, and surface functional groups. Batch adsorption and fixed-bed column experiments were carried out with solutions containing 30 mg/L of caffeine and triclosan. The parameters examined included peanut shell particle size (120-150, 300-600, and 800-2000 µm), adsorbent dose (0.02-60 g/L), contact time (up to 180 min), bed height (4-8 cm), and hydraulic loading rate (2.0 and 4.0 m3/m2-day). After determining the optimal adsorption conditions, kinetics, isotherm, and breakthrough curve models were applied to analyze the experimental data. Peanut shells showed an irregular surface and consisted mainly of polysaccharides (around 70% lignin, cellulose, and hemicellulose), with a specific surface area of 1.7 m2/g and a pore volume of 0.005 cm3/g. The highest removal efficiencies for caffeine (85.6 ± 1.4%) and triclosan (89.3 ± 1.5%) were achieved using the smallest particles and 10.0 and 0.1 g/L doses over 180 and 45 min, respectively. Triclosan showed easier removal compared to caffeine due to its higher lipophilic character. The pseudo-second-order kinetics model provided the best fit with the experimental data, suggesting a chemisorption process between caffeine/triclosan and the adsorbent. Equilibrium data were well-described by the Sips model, with maximum adsorption capacities of 3.3 mg/g and 289.3 mg/g for caffeine and triclosan, respectively. In fixed-bed column adsorption tests, particle size significantly influenced efficiency and hydraulic behavior, with 120-150 µm particles exhibiting the highest adsorption capacity for caffeine (0.72 mg/g) and triclosan (143.44 mg/g), albeit with clogging issues. The experimental data also showed good agreement with the Bohart-Adams, Thomas, and Yoon-Nelson models. Therefore, the findings of this study highlight not only the effective capability of peanut shells to remove caffeine and triclosan but also their versatility as a promising option for water treatment and sanitation applications in different contexts.

One-Step Hydrothermal/Solvothermal Preparation of Pt/TiO2: An Efficient Catalyst for Biobutanol Oxidation at Room Temperature.

The selective oxidation of biobutanol to prepare butyric acid is an important conversion process, but the preparation of low-temperature and efficient catalysts for butanol oxidation is currently a bottleneck problem. In this work, we prepared Pt-TiO2 catalysts with different Pt particle sizes using a simple one-step hydrothermal/solvothermal method. Transmission electron microscopy and X-ray diffraction results showed that the average size of the Pt particles ranged from 1.1 nm to 8.7 nm. Among them, Pt-TiO2 with an average particle size of 3.6 nm exhibited the best catalytic performance for biobutanol. It was capable of almost completely converting butanol, even at room temperature (30 °C), with a 98.9% biobutanol conversion, 98.4% butyric acid selectivity, and a turnover frequency (TOF) of 36 h-1. Increasing the reaction temperature to 80 and 90 °C, the corresponding TOFs increased rapidly to 355 and 619 h-1. The relationship between the electronic structure of Pt and its oxidative performance suggests that the synergistic effect of the dual sites, Pt0 and Pt2+, could be the primary factor contributing to its elevated reactivity.

Bacillus species as tools for biocontrol of plant diseases: A meta-analysis of twenty-two years of research, 2000-2021.

The traditional way of dealing with plant diseases has been the use of chemical products, but these harm the environment and are incompatible with the global effort for sustainable development. The use of Bacillus and related species in the biological control of plant diseases is a trend in green agriculture. Many studies report the positive effect of these bacteria, but a synthesis is still necessary. So, the objective of this work is to perform a meta-analysis of Bacillus biocontrol potential and identify factors that drive its efficacy. Data were compiled from articles published in journals listed in two of the main scientific databases between 2000 and 2021. Among 6159 articles retrieved, 399 research papers met the inclusion criteria for a systematic review. Overall, Bacilli biocontrol agents reduced disease by 60% compared to control groups. Furthermore, experimental tests with higher concentrations show a strong protective effect, unlike low and single concentration essays. Biocontrol efficacy also increased when used as a protective inoculation rather than therapeutic inoculation. Inoculation directly in the fruit has a greater effect than soil drenching. The size of the effect of Bacillus-based commercial products is lower than the newly tested strains. The findings presented in this study confirm the power of Bacillus-based bioinoculants and provide valuable guidance for practitioners, researchers, and policymakers seeking effective and sustainable solutions in plant disease management.

Evaluation of Damage Stress Thresholds and Mechanical Properties of Granite: New Insights from Digital Image Correlation and GB-FDEM.

We employed a novel combination of digital image correlation (DIC) and grain-based hybrid finite-discrete element method (GB-FDEM) to improve the comprehension of the relationships between microstructural features and the mechanical properties of granitic rocks. DIC and numerical results showed that macrocracks initiated and propagated along grain boundaries among different minerals driven by the high stiffness contrast between the compliant biotite and the stiffer feldspar/quartz grains. Surface deformation analyses revealed that tensile-dominated macrocracks open at monotonically increased rates before the crack damage threshold, and the opening accelerated afterwards with the increased shear component. The onset of the acceleration of the opening rate of macrocracks can be used to infer the crack damage threshold. Both strain and acoustic emission were used to infer damage stress thresholds in the synthetic numerical samples. Numerical results showed that the damage stress thresholds and uniaxial compressive strength decrease with increasing grain size following log-linear relations. Coarse-grained samples tend to fail by axial splitting, while fine-grained samples fail by shear zone formation. Biotite and quartz contents significantly affect mechanical properties, while quartz to feldspar ratio is positively related to the mechanical properties. Our study demonstrates the capacities of DIC and GB-FDEM in inferring damage conditions in granitic rocks and clarifies the microstructural control of the macroscopic mechanical behaviors. Our results also provide a comprehensive understanding of the systematics of strain localization, crack development, and acoustic emission during the rock progressive failure process. Supplementary Information: The online version contains supplementary material available at 10.1007/s00603-024-03789-7.

Irradiation-Hardening Model of TiZrHfNbMo0.1 Refractory High-Entropy Alloys.

In order to find more excellent structural materials resistant to radiation damage, high-entropy alloys (HEAs) have been developed due to their characteristics of limited point defect diffusion such as lattice distortion and slow diffusion. Specially, refractory high-entropy alloys (RHEAs) that can adapt to a high-temperature environment are badly needed. In this study, TiZrHfNbMo0.1 RHEAs are selected for irradiation and nanoindentation experiments. We combined the mechanistic model for the depth-dependent hardness of ion-irradiated metals and the introduction of the scale factor f to modify the irradiation-hardening model in order to better describe the nanoindentation indentation process in the irradiated layer. Finally, it can be found that, with the increase in irradiation dose, a more serious lattice distortion caused by a higher defect density limits the expansion of the plastic zone.

(Nano)Granules-Involving Aggregation at a Passage to the Nanoscale as Viewed in Terms of a Diffusive Heisenberg Relation.

We are looking at an aggregation of matter into granules. Diffusion plays a pivotal role here. When going down to the nanometer scale (the so-called nanoscale quantum-size effect limit), quantum mechanics, and the Heisenberg uncertainty relation, may take over the role of classical diffusion, as viewed typically in the mesoscopic/stochastic limit. A d-dimensional entropy-production aggregation of the granules-involving matter in the granule-size space is considered in terms of a (sub)diffusive realization. It turns out that when taking a full d-dimensional pathway of the aggregation toward the nanoscale, one is capable of disclosing a Heisenberg-type (diffusional) relation, setting up an upper uncertainty bound for the (sub)diffusive, very slow granules-including environment that, within the granule-size analogy invoked, matches the quantum limit of h/2πµ (µ-average mass of a granule; h-the Planck's constant) for the diffusion coefficient of the aggregation, first proposed by Fürth in 1933 and qualitatively foreseen by Schrödinger some years before, with both in the context of a diffusing particle. The classical quantum passage uncovered here, also termed insightfully as the quantum-size effect (as borrowed from the quantum dots' parlance), works properly for the three-dimensional (d = 3) case, making use of a substantial physical fact that the (nano)granules interact readily via their surfaces with the also-granular surroundings in which they are immersed. This natural observation is embodied in the basic averaging construction of the diffusion coefficient of the entropy-productive (nano)aggregation of interest.