The research matters because combustion synthesis is one of the workhorses of the nanomaterials industry, a sector valued at roughly 16.3 billion US dollars in 2025 and projected to grow at about 15 percent annually over the next six years. Titanium dioxide and silicon dioxide, the two oxides examined in this study, are produced at enormous scale for paints, catalysts, solar cells, carbon-based products, and drug delivery systems. Because nanoparticles form within milliseconds in the coupled heat and flow fields of a flame, their quality is exquisitely sensitive to flame instability and incomplete combustion. Plasma-assisted combustion, or PAC, has been promoted as a fix for exactly those problems, injecting clouds of ions, electrons, and reactive radicals that stabilize and energize the flame while cutting emissions.

Yet, as the authors point out, almost no one had directly measured what PAC does to the very earliest stages of inorganic particle formation. Previous work had shown that plasmas suppress soot, and a 1995 study by Vemury and Pratsinis found that a DC corona discharge shrank titania particles, apparently by shortening their residence time in the hot zone through ionic wind effects. But no in situ diagnostic study had ever tracked aerosol formation during plasma-assisted combustion at the sub-10-nanometer scale where particles are truly born. That gap is what the Miami and Missouri S&T team set out to close.

The experimental setup was elegantly simple in concept. The researchers burned a stoichiometric methane-oxygen mixture above a concentric tube burner, seeding the flame with vapors of titanium isopropoxide (TTIP) or tetraethyl orthosilicate (TEOS), two common precursors for making titania and silica. Two sharpened tungsten electrodes, placed 6 millimeters apart just above the burner, generated a high-frequency alternating current corona discharge at roughly 21 kilohertz, powered at either 56 or 125 watts. Choosing high-frequency AC was deliberate: at these frequencies the ionic wind that dominates DC discharges is minimized, so charged species enter the flame mainly by diffusion, letting the team isolate the chemistry of the plasma itself.

To watch particles at their birth, the team sampled the flame through a dilution probe that instantly quenched further reactions, then measured particle sizes with a high-resolution differential mobility analyzer paired with an electrometer, covering the 1-to-10-nanometer range. A dilution ratio of 152, combining flow mixing and thermal expansion, froze the aerosol dynamics so that what was measured reflected the flame, not the sampling line. Thermocouple measurements confirmed that the precursors barely disturbed the flame chemistry; even at the highest feed rates, oxidation of TTIP or TEOS shifted the flame only about 0.7 to 1.3 percent toward fuel-rich conditions, leaving temperature essentially unchanged.

The first surprise came from the ions themselves. Without precursors, the flame alone produces positive ions peaking near 1.2 nanometers and negative ions with bimodal peaks at 0.6 and 0.8 nanometers. When the corona discharge was switched on, the positive-ion size distribution barely moved, but its concentration jumped by 45 percent at 56 watts and 62 percent at 125 watts. The negative ions told a richer story: the 0.8-nanometer peak grew, and a new peak emerged at 1.0 nanometer, suggesting the plasma promotes distinct negative-ion chemistry rather than simply amplifying what the flame already makes. In short, the discharge does not create fundamentally new ionic species so much as supercharge the existing population, with negative ions drifting toward larger sizes.

Then came the central finding. At low precursor feed rates, up to about 19.2 milligrams per hour for TTIP and 60 milligrams per hour for TEOS, the plasma promoted particle formation and growth. Positively charged titanium-containing particle concentrations rose by 86 to 150 percent under the 125-watt discharge, and negatively charged clusters surged by up to 265 percent, with mode diameters growing by as much as 42 percent. The likely explanation is that plasma-generated ions, present at concentrations comparable to or exceeding the nascent particles, coagulate with them and even trigger ion-induced nucleation, a phenomenon in which charged seeds dramatically accelerate the formation of new particles from supersaturated vapors. An electron-rich environment can also promote nuclei formation at lower supersaturation, compounding the effect.

At high precursor feed rates, above roughly 29 milligrams per hour for TTIP and 80 for TEOS, the picture flipped. Particle sizes shrank, with mobility diameters suppressed by up to 12 percent for titanium-containing particles and up to 20 percent for silicon-containing ones. To explain the reversal, the team modeled how particles accumulate charge through diffusion charging and field charging. The calculations showed that electrons, with their extraordinary mobility of about 4000 square centimeters per volt-second and vanishingly small mass, dominate diffusion charging by orders of magnitude, and field charging by electrons under the plasma’s electric field was roughly 69 times stronger than in a flame alone. Because negative charge carriers, electrons and fast, light negative ions, outpace the heavier positive ions, particles become preferentially negatively charged. Like charges repel, and that electrostatic repulsion suppresses coagulation, the main growth pathway when particle concentrations are high. The suppression effect, it turns out, simply overwhelms the nucleation promotion once enough particles crowd the flame.

The implications stretch from the factory floor to pollution control. Industrial nanoparticle synthesis operates in heavily loaded regimes with high precursor concentrations, precisely the conditions where the team found suppression. The results suggest that dialing ion concentration to match precursor loading could give operators a practical knob for tuning particle size in real time, and the same physics could help strip unwanted particulates from combustion exhausts. The authors caution that mobility analysis alone cannot fully resolve the mechanism; imaging and chemical analysis of particles below 5 nanometers remain notoriously difficult because the particles are so highly diffusive, and complementary offline characterization will be needed to complete the picture. They also note an unexpected temperature rise in the plasma-assisted flame, attributed to elongation of the reaction zone, which may itself influence downstream growth. Still, the study delivers something the field has lacked: a mechanistic, size-resolved demonstration that a flick of electrical power can flip nanoparticle formation between promotion and suppression, turning the flame into a switchable nanomaterials reactor.

Subject of Research: Plasma-assisted combustion and the formation of sub-10 nm titanium- and silicon-containing nanoparticles

Article Title: Nascent titanium-/silicon-containing particle formation in corona-discharge-assisted combustion

Article References: Bagya Ramesh, C., Han, F. D., & Wang, Y. (2026). Nascent titanium-/silicon-containing particle formation in corona-discharge-assisted combustion. Aerosol Research, 4(1), 265-277. https://doi.org/10.5194/ar-4-265-2026

Image Credits: AI Generated

DOI: 10.5194/ar-4-265-2026

Keywords: plasma-assisted combustion, corona discharge, nanoparticle synthesis, combustion synthesis, titanium dioxide, silicon dioxide, ion-induced nucleation, aerosol science, differential mobility analyzer, electrostatic repulsion, particle charging, flame chemistry

The research, carried out by Chia-Ching Li, Sih-Yuan Wang, Sheng-Chun Weng, Qi-Lin Yang and Ting-Han Pei, focuses on a structure that is deliberately simple to fabricate: a silicon dioxide substrate perforated with a hexagonal array of holes, each filled with silicon. Photonic crystals of this kind control light the way semiconductor crystals control electrons, using periodic modulation of refractive index to open forbidden frequency ranges, called photonic band gaps, where light simply cannot propagate. The hexagonal lattice was chosen over a square one because its higher structural symmetry consistently supports wider band gaps and offers greater design flexibility, a conclusion the authors confirmed through direct comparison. The material pairing matters too. Pure silicon dioxide photonic crystals, whether square or hexagonal, struggle to produce clear band gaps at all, so embedding high-index silicon into the low-index silica background provides the dielectric contrast needed to trap and steer light while remaining fully compatible with chip manufacturing.

What distinguishes this work from earlier thermal studies is the rigor of the optical input data. Rather than treating refractive index as a constant or assuming it varies linearly with temperature, the team coupled experimentally based, wavelength- and temperature-dependent refractive-index models directly into their band-structure calculations. For silicon dioxide, they employed two independent descriptions: the semi-empirical Ghosh model, which explicitly accounts for thermal expansion and the temperature-induced shift of the material’s excitonic band gap, and a modified Sellmeier equation whose fitting parameters vary with temperature. The two models agreed closely, predicting a silica refractive index of about 1.44415 at 314 kelvin rising to 1.44873 at 754 kelvin at the telecommunications wavelength of 1.55 micrometers, with differences between the models so small they are practically negligible. For silicon, the researchers adopted the classic experimentally grounded model published by H. H. Li in 1980, valid from 1.2 to 14 micrometers and from 100 to 750 kelvin, which captures the distinctly nonlinear behavior of silicon’s refractive index with temperature.

The computational engine behind the study is the plane wave expansion method, a workhorse technique more than three decades old that exploits the periodicity of photonic crystals by expanding the electromagnetic fields and the inverse dielectric function into Fourier series. Substituting these expansions into Maxwell’s equations converts the problem of finding allowed light frequencies into a matrix eigenvalue problem in reciprocal space. The authors built their own MATLAB implementation, verified it against worked examples in Kazuaki Sakoda’s standard textbook, and pushed convergence hard, testing truncation sizes from 41 by 41 up to 91 by 91 plane waves. The Bloch wave vector was scanned along the high-symmetry path from M through Gamma to K in the first Brillouin zone, and band gaps were confirmed wherever the minimum frequency of an upper band exceeded the maximum frequency of the band below it. All calculations were performed in the transverse-electric polarization mode at the 1.55 micrometer telecommunications wavelength, deep within silicon’s transparency window, where band-to-band absorption is absent and free-carrier absorption remains negligible even at 600 kelvin.

The results reveal a photonic crystal with a rich thermal personality. Eight band gaps initially emerged below a normalized frequency of 1.1, though one of them, Gap 6, proved so vanishingly narrow that it was excluded from quantitative analysis as a likely numerical artifact. Of the seven reliable gaps that remained, the lower-order ones behaved like thermal bedrock. The first gap, between the first and second bands, held a normalized width of roughly 0.022 with almost no change from 200 to 600 kelvin. The second, the widest of all at a normalized width near 0.035, was similarly indifferent to heating. In stark contrast, the higher-order gaps widened noticeably as temperature climbed. The seventh gap grew by more than 50 percent, from a normalized width of 0.006 to 0.0095, while the eighth expanded by more than 25 percent, from about 0.018 to 0.023. The third, fourth and fifth gaps showed gentler but measurable widening. This split behavior arises because different photonic bands distribute their electric fields differently between the silicon and silica regions, so each gap responds uniquely to the changing refractive-index contrast.

Perhaps the most practically valuable finding concerns the mid-gap positions. Across the entire 400-kelvin temperature span, the centers of all identified gaps shifted only slightly and gradually, meaning the frequencies at which the crystal blocks light stay roughly put even as the gaps themselves breathe. That stability is a gift for engineers, but the study also quantifies how much tolerance designers actually have. For the eighth gap, the team found that its lower edge at 200 kelvin nearly coincides with its upper edge at 600 kelvin, a warning that devices targeting this gap must be designed with care. Operating at the gap center at 250 kelvin, corresponding to a normalized frequency of about 1.007, yields a lattice constant of 1.5609 micrometers at 1.55 micrometers, with a fabrication tolerance of only plus or minus 9.3 nanometers. The second gap is far more forgiving: centered at a normalized frequency of 0.37, it permits a lattice constant of 0.5735 micrometers with a tolerance of plus or minus 27.1 nanometers, roughly three times looser.

The authors also confronted the physical effects they chose to set aside, and the reasoning holds up under scrutiny. Thermal expansion of the silica substrate changes the hole radius by only about 0.02 percent over the full 200-to-600-kelvin range, a variation too small to matter. Differential expansion between silicon and silica does generate compressive stress in the silicon-filled holes, and strain is known to alter silicon’s refractive index by as much as 1.4 percent under extreme conditions, but the estimated internal stress in this geometry falls far below the gigapascal-scale strains required for such shifts, especially compared with the 1.8 percent refractive-index change silicon undergoes purely from heating across 300 kelvin. The photoelastic contribution is therefore safely negligible. The main limitations the authors acknowledge are the boundaries of their material models, which exclude wavelengths shorter than 1.2 micrometers or longer than 14 micrometers, temperatures below 200 or above 600 kelvin, and the absence of direct experimental verification, though every refractive-index input rests on experimentally fitted data.

Placed alongside recent literature, the study carves out a clear niche. Earlier work on diamond-lattice silicon photonic crystals used linearized refractive-index formulas and reported a temperature sensitivity of about 0.0518 nanometers per kelvin at the first band-gap center, hinting at applications in optical temperature sensing and biosensing chips. Other groups have demonstrated thermally tunable silicon valley photonic crystal rings, mapped heat spread from thermo-optic devices, and built photonic crystal temperature sensors from defect-mode resonance shifts. By contrast, this work spans a broader temperature range, covers multiple band gaps simultaneously, and applies nonlinear, experimentally validated refractive-index functions to a structure directly relevant to silicon photonic waveguides. The practical upshot is a design map: lower-order gaps for thermally robust passive components such as filters and waveguides that must survive harsh environments unchanged, and higher-order gaps for thermally tunable or temperature-sensing applications where deliberate sensitivity is the point. As silicon photonics pushes into hotter, harsher and more ambitious territory, knowing exactly where the light is allowed to travel, and how much that map shifts with heat, may prove as important as the circuits themselves.

Subject of Research: Thermal effects on the photonic band gaps of a two-dimensional SiO2-Si hexagonal photonic crystal for silicon photonics

Article Title: The thermal effects on the photonic band gaps of the two-dimensional SiO 2 -Si hexagonal photonic crystal

Article References: Li, C.-C., Wang, S.-Y., Weng, S.-C., Yang, Q.-L., & Pei, T.-H. (2026). The thermal effects on the photonic band gaps of the two-dimensional SiO2-Si hexagonal photonic crystal. Results in Optics, 25, Article 101146. https://doi.org/10.1016/j.rio.2026.101146

Image Credits: AI Generated

DOI: 10.1016/j.rio.2026.101146

Keywords: silicon photonics, photonic crystals, photonic band gaps, thermo-optic effect, plane wave expansion method, silicon dioxide, refractive index, hexagonal lattice, telecommunication wavelength, thermal stability, waveguide design, high-temperature applications