Nanoparticles (NP) are defined as those particles with a size lower than 100 nm [1], which are featured with a spherical shape and a composition of natural or artificial polymers [2]. Among the entire group of elements that can compose a nanoparticle, carbon and metal-oxide (TiO₂, SiO₂, Fe_xO_y, Al_xO_y, etc.) molecules are most often found and studied, following their advantages in potential applications--their spherical shape and high surface area-to-volume ratio [2]. The following is a brief discussion of the abundance and applications of different NP, as well as the methods that yield them.

Carbon nanoparticles (CNP) are identified with unusual mechanical, electrical, and chemical properties [3,4,5]. The most notable of these nanostructures are carbon nanotubes (CNT) and carbon nano-onions (CNO) [4]. CNTs provide an alternative to use for composite materials reinforcement, fuel cells, Li-ion batteries, and hydrogen storage [3]. Because of their high specific surface area and electrical conductivity [6], CNOs have been considered for use in solar and fuel cells, solid lubricants, and catalytic materials. One concern regarding the synthesis of CNPs is their tendency to agglomerate [5]. Titanium-based nanomaterials have become essential in applications related to energy and water [7], because of their use as components for photovoltaic, photocatalytic, and electrochemical processes [7,8]. Synthesized TiO₂ materials have four different phases: anatase, rutile, srilankite (TiO₂-II) and brookite [8,9]. The most frequently used TiO₂ NP is the Degussa P25, which is composed of 20% rutile and 80% anatase phases [9]. The anatase phase is characterized by a low rate of charge recombination [9,10]; the rutile phase has strong thermodynamic stability [9], and it is one component of the white pigments [10]. The srilankite phase has been identified with an open crystal structure, metastable at high pressures [8]. Iron-based NPs offer functional magnetic properties and high chemical reactivity [11,12,13], including the possibility for use in magnetic resonance imaging, magnetorheological fluids, and microfluiding systems [12]. Their chemical reactivity also enables their use in lithium-ion batteries, and catalysis [12,13]. These NPs are commonly found in magnetite (Fe₃O₄), maghemite (γ-Fe₂O₃), and hematite phases (α-Fe₂O₃) [11,12,13]. The wustite phase (FeO) [12,13] has also been identified in these synthesized materials.

A flame provides thermal energy to evaporate particle precursors and initiate chemical reactions that allow particles to grow. Various burners have been used to accommodate engineering needs (e.g., production of particles of different properties, ease of modeling, ease of diagnostics, etc.).

In premixed Bunsen burner flames, gaseous fuel or a precursor mixes with an oxidizer and fuel before burning. Radial temperature profiles are uniform in premixed laminar flames. Varying the fuel stoichiometry in premixed flames can control the production of species in the post-flame region [29,47]. Premixed flames are subject to the risk of flashback, which occurs when the flame enters and propagates through the burner [48]. Flame arrestors and safety valves should be installed in the fuel lines to avoid flashback; pyrophoric fuels should be avoided to minimize the risk of flashback [30]. If pyrophoric fuels are studied, pressure should be reduced to minimize the formation and accumulation of particles within the burner tube [30]. However, in practical devices, mixers may be required for different degrees of premixing—increasing the complexity of the devices [48].

In non-premixed flames, the fuel/precursor and the oxidizer are fed separately into the reactor; this configuration eliminates the hazard of flashback in premixed flames and allows a wider range and operating conditions. However, unlike premixed flames, non-premixed flames possess rather complex geometries. Decoupling the flame properties—including temperature, equivalence ratio, products, and residence time—is challenging.

Arranging the distribution of the fuel/oxidizer streams enables different diffusion flames (namely normal diffusion flames, inverse diffusion flames, and counterflow flames).

A co-annular burner, consisting of an inner fuel tube and a concentric outer oxidizer tube, can produce a normal diffusion flame. As the fuel flows along the axis, it diffuses radially outward, while the oxidizer diffuses radially inward [48]. The fuel and oxidizer react stoichiometrically in the narrow regions, forming flame zones. The radial temperature profile is typically annular-shaped, with high temperatures on the sides and low temperatures in the center. The fuel flow rate primarily controls the flame length [49,50]. Soot—an undesirable product in flame synthesis—forms on the fuel side of the reaction zone of hydrocarbon flames due to high temperatures; it is oxidized and consumed as it travels downstream into an oxidation region. Soot can grow along the metal particle, forming a carbon layer; however, depending on the flame conditions, soot may break through the flame, forming a sooting or smoking flame. The flames, in general, have higher flame temperatures and produce nanoparticles with larger sizes [31,32]. For the same reason, this flame configuration is unsuitable for low melting temperature substrates, e.g., silicon substrates with anode aluminum oxide nanotemplates [33].

Inverse diffusion flames and normal diffusion flames can share the same burner geometry. Unlike the latter, the inner tube supplies the oxidizer of inverse diffusion flames into a fuel reservoir. In inverse diffusion flames, polycyclic aromatic hydrocarbon (PAH) and soot form outside the reaction zone [51]. The flames contain low soot concentration [34], which is beneficial for the production of carbonaceous particles (e.g., carbon nanotubes (CNT)), as the competition from soot formation is minimal. Unrau et al. [35] reported that using oxy-fuel inverse diffusion flames minimizes the contamination of amorphous carbon impurity. Carbonaceous particles form on the annular side of flames, avoiding the particle oxidation and thermal defects induced by the flame high-temperature region [36,47]. This formation also facilitates the external collection of the particles [35]. Due to lower flame temperatures, inverse diffusion flames may produce smaller nanoparticles than normal diffusion flames [31,32].

Counterflow diffusion flames employ two opposing jets of fuel and oxidizer. A stagnation plane formed when the axial velocity equals zero creates two distinctive regions, fuel-rich and fuel-lean, on the fuel and the oxidizer sides. The flame forms on the oxidizer side of the plane. The flames are used mainly in fundamental research because they approximate a one-dimensional character, making measurements and calculations much more practical [48,52]. The one-dimensionality of the flames also gives flexibility in adjusting the spatial gradient of temperature and reactant concentration [38], enabling a fundamental study of the effects of temperature, catalytic substrate positioning, and gas-phase composition on synthesis processes [47]. In addition, the flames allow minimum flame-substrate interaction, facilitating specific particle production processes. For example, Li et al. used silicon substrates with anode aluminum oxide nanotemplates, sensitive to temperature change, in a counterflow flame to produce well-aligned, size-controllable CNTs [33]. The synthesis zone of CNTs is on the fuel side near the flame edge due to the closer supply of carbon. Nanoparticle synthesis in counterflow flames is also affected by the strain rate, which affects the amount of carbon supply and residence time. A counterflow flame with a high strain rate would have more carbon sources but a shorter residence time. However, the availability of carbon sources explains the effect of strain rate on the growth of carbonaceous particles, as opposed to residence time [37]. Thus, although they have a shorter residence time, flames with higher strain rates produce more carbonaceous particles.

A multi-element diffusion flame burner (MEDB), commonly known as a Hencken Burner, generates multiple-diffusion flames [30,53]. The burner comprises an array of hypodermic needles within a honeycomb [30]. The fuel flows though the needles, and the oxidizer flows through the surrounding open cells, generating multiple small, tightly spaced diffusion flames. The flames share the advantages of both premixed and non-premixed flames, which are beneficial for the production of nanomaterials. First, uniform temperature and species profiles can be obtained downstream of the flames [39]. Second, as fuel and oxidizer are initially separated, flashback is avoided, as well as unwanted reactions before the flame [39], enabling a wider range of operation and allowing the use of pyrophoric fuels.

Flame spray pyrolysis (FSP), mainly used for synthesizing metal oxides [54], refers to a combustion process in which a precursor is in liquid form (a mixture of metal precursor, e.g., nitrates, and organic solvent, e.g., ethanol) and contributes more than 50% of the total energy of combustion [43]. The liquid is atomized and conveyed by the central nozzle, surrounded by a coflowing oxidizer. An external flame is required to provide a heat source to evaporate and ignite the liquid precursor [44,46]. Because the liquid precursor is highly exothermic, the resultant flame is self-sustaining [54] and has a high temperature [44]. Induced by the entrainment of the surrounding oxidizer, FSP is also characterized by short residence time and steep temperature gradients [45], with rapid cooling of several hundred K cm−1

[54]. These factors yield highly homogeneous and crystalline nanomaterials [46].

The composition of liquid precursors can control the morphology of nanoparticles. Karthikeyan et al. [42] showed that nitrate precursors produced crystalline and dense nanoparticles. The use of organometallic precursors can also improve the homogeneity and provide smaller grain size distribution [42]. The oxidizer flow rate is also influential in the morphology of nanoparticles. For small, non-agglomerated particles, the oxidizer flow rate should be high for sufficient mixing, whereas, for larger particles, a reduced oxidizer must be used for a flame with a longer length and residence time [40,41].

The equivalence ratio (φ) is defined as the ratio of the flow rates of fuel and oxidizer applied in the real process, divided by the same ratio at stoichiometric conditions [63,64]. This ratio helps to determine whether the fuel and the oxidizer supplied for the combustion process are under conditions of lean (excess of oxidizer, φ < 1), rich mixtures (excess of fuel, φ > 1), or under stoichiometric conditions (φ = 1). This ratio varies with the change in the flow rate of the oxygen and fuel streams [18].

For the determination of combustion performance, this factor is the most relevant in the many processes and devices that use it [48]. In combustion processes, the reactor releases heat, which can be expressed as the enthalpy of reaction (with the same magnitude as the enthalpy of combustion), which varies with the amount of fuel and oxidizer provided in the reaction—and consequently is a function of φ [48]. Furthermore, with the correct assumptions and applying the concept of the first law of thermodynamics, the enthalpy of the reactants at the initial state is equal to that of the products at the final state, featured with the adiabatic flame temperature [48]. Henceforth, the equivalence ratio exerts a remarkable effect over both the enthalpy of combustion and the flame temperature, as evidenced in previous studies on flame synthesis of nanoparticles [10,18,26].

It is possible to control the yield of produced nanoparticles with the variation of φ by considering a negative correlation since oxygen availability dominates the main chemical reaction [15]. The higher amount of oxygen in the synthesis increases the efficiency of the oxidation of precursors and solvents [13].

The oxygen availability is also a relevant feature in the phase composition of particles, demonstrated in iron-oxide NPs by the reduction of magnetite and the rise in hematite content in the materials produced by the decrease in φ [13]. Sorvali et al. [12] demonstrated the strong effect of φ on the maghemite content in synthesized iron-oxide NPs, regardless of the type of alcohol used as a solvent for the precursor solution.

The stoichiometric mixture fraction, Zst, represents the mass fractions of products from the combustion reaction, based on the fuel stream, at the location of complete theoretical combustion. The value of Zst increases at higher oxygen concentrations in the oxidizer stream of a diffusion flame configuration [56].

The flame temperature correlates positively with Zst; consequently, this parameter exerts influence over the flame structure, which associates the distribution of chemical species present in the combustion process with the temperature field in the flame. Therefore, Zst also rules the flame shape [56]. Another feature influenced by this fraction in a diffusion flame is the local atomic carbon-to-oxygen ratio (C/O), which indicates the potential of oxide formation in the combustion process. Metal oxides with more oxygen atoms are formed at smaller C/O ratios, while flames with larger C/O ratios synthesize more reduced oxides [56].

The relations described above explain the effects on the synthesis of nanoparticles. At first, higher values of Zst in the flame partially suppress the soot formation in hydrocarbon flames, which is convenient for synthesizing metal-oxide NPs [56]. Moreover, the Zst may influence the structural phase composition in NPs, as shown by the formation of iron-oxide NPs, where particles with higher magnetite content were obtained when Zst increased [56].

The flame temperature can be affected by the equivalence ratio (φ) in premixed flames and the stoichiometric mixture fraction (Zst) in diffusion flames, as discussed in Section 2.1 and Section 2.2, respectively. Moreover, the addition of diluent gases (e.g., Ar, N₂, CO₂) in a burner and the variation in their flow rates enables the control of the temperature field in the flame [65]. In normal diffusion flames, the reduction of flame temperature is demonstrated by the increase in the velocity of the oxidizer stream, raising the flow rate of cold gases [61], while the increase in the flow rate of the fuel stream supplies higher enthalpies, producing higher flame temperatures [61]. Moreover, the addition of metal-oxide NP precursors also influences this parameter [60] since these are involved in the combustion kinetics, acting as catalysts with OH and H radicals, demonstrated in the synthesis of iron-oxide NPs [60].

An increase in the flame temperature reduces the particle size of CNPs [57]. The particle formation of CNPs in flames explains this behavior. The nucleation mode takes place as a single mode from the base of the burner until a particular value of HAB, where the size growth mode (particle coagulation and aggregation) starts and converts the formation process as bimodal [57,58]. As the temperature increases, the HAB limit for the nucleation mode moves towards higher HABs, suppressing the size growth modes of CNPs [57,58]. Moreover, CNPs precursors, such as the PAHs, decompose at high flame temperatures [57,58]. The temperature effect is different for the metal-oxide NPs since this size correlates positively with the flame temperature [56,61]. The positive correlation of the crystal growth rates, particle sintering, and particle collision with the flame temperature justify this behavior [56,61]. Low temperatures increase the time required for sintering and decrease particle collision, leading to lower particle growth rates [61]. Enhanced sintering provides high yields of larger spherical particles [61]. The sintering process is different among the produced metal-based NPs, based on the temperature required for the total coalescence of particles in flame synthesis [61]. As a comparison, titanium-based NPs require lower temperatures for this coalescence, hence obtaining larger particle sizes than silica NPs [61].

High-temperature zones in the flame are responsible for the reduction in the mass concentration of flame-made NPs, [57,60] due to the oxidation of the formed particles at the initial stage [60] and the suppression of the surface growth mechanisms at high temperatures [57]. However, particle-particle coagulation dominates the number density of soot particles. This coagulation process faces thermodynamic reversibility at high temperatures. Therefore, the number density of soot particles is nearly constant. Instead, particle residence time mainly affects this number density [57].

In terms of the morphology of particles, higher temperatures increase the size of the undisturbed lattices [58] and decrease the atomic hydrogen content [57,58]. This last content (also expressed as the H/C ratio in the produced CNPs) leads to a lower susceptibility to oxidation [57]. These facts demonstrate fewer disordered structures in the CNPs synthesized at higher temperatures, which are noticed for particles with constant size [58]. Since the temperature variation dominates the sintering process, temperature also governs the surface area of the obtained particles, demonstrated by the reduced area from decreased temperature [18]. Because this is linked with the combustion enthalpy, it is crucial for forming homogeneous particles [26,62]. Lower values of temperature and enthalpy in the flame enhance a lower degree of sinter neck formation, producing more fused nanoparticles [14,18].

The stability of the structural phases of nanoparticles varies with the temperature in the flame synthesis process. Therefore, the phase transformations occur at high flame temperature increase [15,18]. Moreover, this stability is also ruled by the particle size in both phases, evident in titanium-oxide NPs since the anatase phase is more stable at smaller sizes [10,59], and rutile phase stability improves at larger sizes [59]. Temperature also plays a relevant role in the alumina-based NPs, with the increase of θ-alumina and the reduction of η-alumina phases caused by a temperature increase in the flame [18]. These two phases are related because at higher temperatures, the γ and η-alumina phases transformed into δ-alumina, which under long residence times consequently turned into θ-alumina [18].In iron-based NPs, Fe(III) is almost the unique component at relatively low flame temperatures [56]. This decrease as the temperature rise, leading to a higher content of Fe(II) in the produced material. The increase in the Fe (II) produces higher contents of the magnetite phase [56].

In a combustion process, the heat released also depends on the type of fuel supplied to the burner. Each fuel has a unique heating value, also known as the enthalpy of combustion [48]. Precursors must be added to the reaction to synthesize nanoparticles because they contain the metal components that are oxidized to form these materials--excluding the carbon nanostructures. These precursors can be added to the fuel stream as a solution, considering the main precursor as the solute (e.g., TMS for SiO₂ and TTIP for TiO₂) and the use of alcohols as solvents [18]. This solution plays a relevant role in the enthalpy of the reaction [18]. However, this effect is not present in the Hencken burner configuration since the contribution of the combustion heat from the solvents to the flame enthalpy is low [67].

A high solvent boiling point makes possible the formation of homogeneous particles [12,62]. The increase in the precursor feed rate also raises the total number concentration of flame-synthesized particles [13,18] and shifts their distribution to smaller sizes [18]. Low precursor flow rates produce fuel-lean combustion, leading to incomplete oxidation of the components caused by low temperatures [13].

Since the most common fuels applied in combustion devices are hydrocarbons (CxHy), these are used as precursors in synthesizing CNPs. The higher number of carbon atoms in the fuel, and the presence of C=C double bonds in the hydrocarbon molecule, accelerate soot formation [25], leading to a much higher amount of soot, as observed in the flame synthesis process using ethylene and compared with the yield obtained in methane flames [25].

Residence time is defined as the time that particles and molecules last in the reaction zone (bounded by the flame), and can be quantified as the mass of the entire mixture, which is the density of the mixture multiplied by the volume of the reaction zone, and divided by the overall mass flow rate passing through the reactor [48]. The mass flow rates of gases supplied to the burner determine this parameter, also modifying the gas velocity in the process. The residence time increases with the reduction in the carrier gas or oxidizer gas flow rates in the combustion process [13,18]. In the case of a premixed flame, the equivalence ratio plays a relevant role at this time, since a linear influence from φ over the flame height has been shown [12,18] which is more remarkable at low values of carrier gas flow velocity [26]. Additionally, at the same values of φ, the increase in the gas velocity increases the flame height and the particle residence time in the high-temperature zone [12]. The effect from the type of fuel has also been noted, since a higher amount of carbon atoms in the fuel molecules produces a higher residence time in the particles in the flame [10].

The particle size of flame-synthesized nanoparticles is inversely dependent on the velocity of the premixture issuing from the burner and, therefore, the residence time in the synthesis flow field [8,12]. This time is one of the factors governing the sintering process, thus affecting the surface area of the synthesized materials, described as an inverse correlation [10,18]. Furthermore, this time influences the yield of particles with homogeneous structures --with a positive correlation--as evidenced in the production of CNTs through the I_G/I_D ratio [26]. However, it is suggested that to effectively carry out precursor decomposition and solvent combustion, droplet size, and oxidant availability are more relevant than increased residence time [13].

Nevertheless, at short residence times in the flame high-temperature region (which can be caused by the use of low precursor flow rates), the phase transition in nanoparticles is a kinetically limited transformation process (as demonstrated in alumina NPs [18]) since the residence time to carry out a complete conversion of droplets is minimal [13]. This effect is also notable for titanium-based NPs. As the residence time decreases, the rutile yield shrinks, and the srilankite content grows [8]. The increase in anatase content can be explained by a longer residence time in the high-temperature region at a low precursor flow rate [10]; if this time increases, the anatase content mutates to the rutile phase [10].

Substrates are components in the flame synthesis setup where the nanoparticles are deposited after they are formed [25]. These substrates can also carry catalysts to improve the reaction performance [26]. The choice of material for the substrate may affect the synthesis process in terms of purity and crystallinity [3]. The effect of the substrate material arises from three factors linked to their properties [3]. One is the melting point because materials with a lower melting point enable an active state in the substrate, allowing the dissolution of the NPs formed in the substrate and improving their nucleation and growth [3]. Potential oxidation of the elements that compose the substrate is another relevant factor since an oxidizer is essential in the flame synthesis process, and this oxidation inhibits nucleation and growth of NPs [3]. Finally, the substrates with an open spatial configuration permit oxidation of the synthesized NPs, compared with those with a closed space—such as the foam; this is undesirable for some types of nanoparticles (e.g., CNPs [3]). The last factor also affects the morphology of the material obtained, since a closed space can cause disordered structures [3]. This spatial configuration also determines the yield of the synthesis, considering the deposition of NPs as a coating over the substrates. Evidence of deactivation of the catalysts was present in this substrate after its complete encapsulation by the formed NPs [11,25].

This configuration exerts a notable influence over particle size distribution in the obtained particles, regardless of the operation parameters in the combustion process. These intervals were obtained from the measured size distributions, using TEM [15,18,25,27,62] extracted through the full-width at half-maximum method (FWHM), which is applied to Gaussian peaks using several measurement techniques [6,13]. Note the larger flame sizes (obtained in laminar (premixed and diffusion)) than those measured in particles synthesized through flame spray pyrolysis (FSP). The gas-to-particle formation route governs the synthesis process in the FSP reactors, which leads to small particle sizes [18]. However, because the FSP configuration operates with short residence times [45], it enables the production of NPs with smaller particles than those obtained through laminar flames, confirming the effect of residence time over particle size.