Charge Distribution of Incipient Flame-Generated Particles

Abstract

We report the size and electrical charge distributions of incipient nanoparticles generated in atmospheric pressure hydrocarbon/air premixed flames in conditions prior to the onset of soot particles. The particle size and charge distributions are measured by Differential Mobility Analysis (DMA) and compared to theoretical charge distributions predicted for flame conditions. The results show that the charge distribution attained in flames is well predicted by Boltzmann theory for all particles, including even the smallest incipient particles with diameters in the 1–3 nm size range. In flame conditions that produce only particles smaller than 3 nm, the charge fraction of particles agrees with that predicted by Boltzmann theory near the flame temperature (1700 K). In flame conditions with ‘bimodal’ particle size distributions, the charge fraction of the smallest particles agrees with the Boltzmann prediction at maximum flame temperature, while the charge fractions of larger particles agree with Boltzmann theory at temperatures that coincide with the local temperature near the probe surface (1000–1200 K). The results of this paper show that the temperature of the Boltzmann charge fraction that best agrees with the measured charge fraction for each particle size gives the local temperature of their last coagulation event. The smaller particles, which retain their charge fraction predicted by Boltzmann at the maximum flame temperature, do not thermalize by coagulation in the cool region near the probe evidencing low probability for charge transfer as well as for coagulation.

1. INTRODUCTION

A relevant fraction of particles produced in combustion is charged, and thermal ionization and diffusion charging are generally considered the main charging processes (Balthasar et al. 2002; Fialkov 1997; Kim et al. 2005; Maricq 2006). Most studies measuring flame generated charged species (molecules, macromolecules and incipient particles) examined low pressure high temperature (> 2000 K) flames with mass spectrometry (Calcote and Keil 1990, Fialkov 1997; Homann 1998; Howard 1969). Relatively few works have studied flame charging processes in atmospheric pressure flames (Balthasar et al. 2002; Maricq 2006; Starik et al. 2008) and the relevance of the two mechanisms, thermal ionization and diffusion charging. As a result particle charge distribution in these conditions are not yet fully known. It is of particular interest to know the size and charge distribution of nanoparticles produced in flames since this information could be exploited in their study, manufacture, and control. Also, if the charge of flame generated particles were well-understood and predictable, it would be possible to derive information on the size distribution of the total aerosol population from accurate measurements of the size (or mass) distribution of charged nanoparticles present, without using a particle charger, which introduces measurement uncertainties in many instruments (Mass Spectrometers, Differential Mobility Analysers or Electrical Low Pressure Impactors).

Thermal ionization depends on the size and work function of the particles and their temperature. While it is well-accepted that larger particles undergo thermal ionization at flame temperatures, it is not as clear if flame-generated particles smaller than 10 nm are charged by thermal ionization (Balthasar, et al. 2002), especially in atmospheric hydrocarbon flames with flame temperatures lower than 1800 K. Diffusion charging is instead determined by collisions between particles and molecular ions and electrons, that are produced in the flame front by chemiionization reactions (Fialkov 1997), which change the charge state of particles by charge transfer or ion attachment. Particles reduce their charge state if they collide with an ion of opposite polarity, and vice versa, they gain charge if the particle is neutral or of the same charge as the ion. If the concentration of ions is high enough in the environment where particles are formed, the aerosol comes to a steady-state charge distribution, and the charge distribution becomes a predictable function of particle size.

Several works examined the charge distribution attained by ultrafine aerosols when mixed with a bath of bipolar ions at room temperature in order to accurately determine the charging efficiency of commercial diffusion chargers (Adachi, et al. 1985; Alonso et al. 1997; Hoppel and Frick 1986; Reischl et al. 1996; Wiedensohler 1988; Wiedensohler and Fissan 1988). Ion-particle combination coefficients for diffusion charging are calculated differently in three regimes according to the Knudsen number (Kn = 2λ _i /d _p , where d _p is the particle diameter and λ _i the ion mean free path) (Pui et al. 1988). For small Kn (d _p ≫ λ _i ), ion transport is described using the diffusion-mobility equation. The kinetic theory of gasses may be used in the free molecule approximation for large Kn (d _p ≪ λ _i ), and the charge distribution is described by Boltzmann's law (Equation (2)) (Liu and Pui 1974). In the transition regime (Kn ∼ 1 or d ∼ λ _i ), a semi-phenomenological approach is often employed: the continuum theory, described by the diffusion-mobility equations, describe ion transport outside a limiting sphere surrounding the particles at a distance on the order of λ _i , the free molecule transport equation is considered inside the sphere, and the two fluxes are matched at the surface of the limiting sphere (Fuchs 1963; Hoppel and Frick 1986). The last theory, first developed by Fuchs, seems to reproduce experimental results at atmospheric conditions for particles as small as 2.5 nm (Adachi et al. 1985; Alonso et al. 1997; Hoppel and Frick 1986; Reischl et al. 1996; Wiedensohler 1988; Wiedensohler and Fissan 1988), even though such small particles are in the free molecular regime (Kn ∼ 30). Following these studies, the charging efficiency of commercial particle bipolar diffusion chargers is calculated assuming the Fuchs' steady-state charge distribution. Nevertheless, whether particles (or macromolecules) smaller than 2.5 nm are fully charged to the Fuchs' charge distribution is still controversial. One study examining WO _x particles found good agreement with Fuchs' theory at the smallest size measured (2 nm) (Reischl et al. 1996), but another study examining NaCl particles measured a charge fraction that was significantly lower than Fuchs' one for particles smaller than 2.5 nm (Alonso et al. 1997). Obviously, if the actual charging efficiency is significantly lower than the assumed one, measurements using a commercial charger would be underestimating the number of particles.

In atmospheric pressure premixed flames recent studies show that particles larger than 13 nm attain a symmetric charge distribution that agrees well with the Boltzmann equilibrium charge distribution calculated at flame temperatures (Maricq 2006; Maricq 2008; Maricq 2005). This result was explained as a consequence of diffusion charging followed by particle coagulation, which ‘equilibrate’ the charge fraction to the surrounding gas temperature (Maricq 2005). Furthermore, these works report that particles smaller than 13 nm had a lower than Boltzmann charge distribution and were entirely neutral late in the flame. These results at high temperature are quite different than what is found at room temperature since the Fuchs' charge distribution is significantly higher than the Boltzmann one for d < 20 nm particles. Also, the Fuchs' distribution predicts a slightly higher fraction of negatively charged particles compared to the fraction of positively charged particles while the Boltzmann' charge distribution is instead symmetric at all temperatures. The two theories (Boltzmann and Fuchs') predict nearly the same charge distribution for d > 20 nm at room temperature.

In this work, we use electrical mobility measurements to derive the charge distribution of flame-generated aerosols as a function of particle size in the size range of 1–20 nm. These measurements extend the study of charged particles in premixed flames to include the inception particles smaller than 2 nm. Thermal and diffusion charging mechanisms are explored to explain the measured charge distributions, and we discuss the implications of the results for particle coagulation at high temperature. The particles are produced in atmospheric pressure premixed flames, which have been previously examined with many complementary particle diagnostics with sensitivity to particles/macromolecules as small as 1 nm, including multiwavelength optical, microscopy and mobility measurements (D'Alessio et al. 2005, D'Alessio et al. 1998, D'Alessio et al. 2009; Minutolo et al. 1999; Sgro et al. 2008). While the various measurement techniques are in excellent agreement in flame conditions that eventually produce particles larger than 3–5 nm, the DMA measurements are significantly lower than in situ optical measurements in flame conditions where the size distribution is unimodal with a modal diameter, d_modal∼ 2 nm (Sgro et al. 2009). The reason for this discrepancy, which cannot be explained simply as losses in the sample lines, is not yet well understood because of the inherent uncertainties of the measurement techniques (Minutolo et al. 2007; Sgro et al. 2009). A side objective of this work is also to verify if the assumed charging efficiency of the particle charger used in the DMA data analysis could be inaccurate for the smallest inception particles resulting in a source of experimental error.

2. EXPERIMENTAL METHODS

The size distribution (SD) of flame-generated particles was measured by Differential Mobility Analyser, (DMA). Figure 1 shows the experimental set up. Particles were formed in flat atmospheric pressure laminar premixed flames stabilized on a McKenna (Holthius & Associates) or capillary tube burner. The cold gas flow velocity to the burner for all flames in this study was 10 cm/s, and flow rates were controlled with mass flow controllers (Brooks Instruments) with an accuracy of +/– 0.7%. The mixtures of fuel, oxidant, and diluent were varied in the range C/O = 0.61–0.67. Most of the flames burned mixtures of ethylene and air, but one hotter flame was also studied that utilized Ar as the oxygen diluent rather than N₂. Previous works showed that these flames, which produce significant amounts of particles with diameters of just a few nanometers, are below the onset of soot particles since they have undetectable amounts of absorption in the visible or incandescence (D'Alessio et al. 2009; Minutolo et al. 1998; Sgro et al. 2009). The sampling probe is a tube (ID = 8 mm) positioned horizontally over the flame. 30 l/min of Nitrogen flows through the probe, and the sample is drawn into this flow through a 0.3 mm orifice in the tube wall (wall thickness = 0.5 mm) oriented towards the burner surface. The fast cooling and dilution of the sampled flow prevent particle coagulation and losses. Earlier works describing this sampling system noted that probe cooling lowers the local flame temperature several hundred degrees near its surface (Zhao et al. 2003).

FIG. 1 Sketch of sampling probe used to quickly and highly dilute flame generated incipient nanoparticles and measure their size distributions. Components in the figure with a dotted line were sometimes used in the set up. Temperature profiles for the hottest (C/O = 0.61) and coolest (0.67) C₂H₄-Air flame with and without the probe located at H = 15 mm show the cooling effect of the probe on the flame.

Figure 1 also shows the temperature profiles measured in the hottest (C/O = 0.61) and coolest (C/O = 0.67) flames burning air. Temperature was measured using an uncoated type R thermocouple, with a spherical junction bead, d = 250 μ m. Radiation corrections were made following Shaddix (1999).

A fraction of the sample flow containing diluted flame products was analyzed either by a single DMA (TapCon 3/150) or by two separate DMAs (TapCon 3/150 and TSI SMPS 3936-nano). Particle distributions measured with a DMA are usually reported in terms of “mobility diameter,” which is calculated from the measured electrical mobility by equating the drag force on the particle, given by Stokes' law, to the electrical force acting on the particle (by the well known Stokes-Millikan equation). Recent works have shown that, for particles smaller than 10 nm, Stokes' law cannot be considered valid because of the effective diameter of the carrier gas molecule, the charge induced dipole interaction, van der Waals interactions between particle and gas molecules, and the transition from specular scattering, or elastic collisions between small molecules, to diffuse scattering, or inelastic gas-particle collisions (Li and Wang 2003; Tammet 1995). Various correction expressions have been reported to obtain particle diameters from mobility measurements (Fernández de la Mora et al. 2003; Reischl et al. 1996; Tammet 1995). In the following work, SDs were calculated in terms of the mass equivalent diameter, d, from the electrical mobility, Z, measured in a sheath flow of a carrier gas with molecular mass, m, temperature, T and pressure, p, using the semi-empirical equation reported by Fernández de la Mora et al. 2003:

where d _o is an effective diameter of the gas in which the aerosol is immersed (d _o = 0.5 nm for air at 273 K). Equation (1) is valid also for particles smaller than 10 nm and consistent with experimental data for molecular clusters with known masses as small as a few hundred amu, and d determined from Equation (1) essentially coincides with the mobility diameter calculated by the Stokes-Millikan equation for particles larger than about 3 nm. The SD of the total aerosol population (including both charged and neutral particles) was measured by placing a laminar flow bipolar diffusion charger of Am-241 120 MBq prior to the two DMAs. The total particle number concentration, N, is obtained by dividing the measurements made with the charger by the Fuchs' steady-state charge distribution. Flame-generated charged particles were instead measured without using any particle charger. Since the flames examined in this paper produce only particles smaller than 20 nm, it is reasonable to assume that the particles had only a single charge (Balthasar et al. 2002; Fialkov 1997; Kim et al. 2005; Maricq 2004; Maricq 2005; Reischl et al. 1996).

We used two different DMAs to simultaneously measure the SD of positively charged particles (with the TSI DMA) and negatively charged particles (using the TapCon DMA). The aerosol and sheath flow rates through the DMA systems were q_aerosol (TapCon) = 5 l/min, q_sheath (TapCon) = 50 l/min, q_aerosol (TSI) = 1.5 l/min, q_sheath (TSI) = 15 l/min. The TSI DMA has an impactor prior to its aerosol inlet that is regulated in the control system. Flows through the TapCon DMA are instead controlled with critical orifices, and it was operated without an impactor. The TapCon DMA employs a Faraday Cup Electrometer (FCE) detector, which has a lowest detection limit of 1fA. The FCE counts charge carried by the particles and independently of particle size (Reischl et al. 1997). The Condensation Particle Counter, CPC model 3025A, used by the TSI DMA as the detector has a 50% detection efficiency at 3 nm that decreases strongly with decreasing diameter (Stolzenburg and McMurry 1991). The particle losses in the TSI DMA are well known (Chen et al. 1998; Stolzenburg 1988), and TSI provides loss corrections for this DMA which have been used in this work. We extended the measurement range of the TSI SMPS down to 1.8 nm by correcting the raw data for losses and CPC detection efficiency following earlier work (Minutolo et al. 2007). Loss corrections for the TapCon DMA, have never been measured, but this instrument was designed to be operated with high flow rates to have negligible losses. We verified that losses are negligible by comparing the size distribution function measured with the TapCon DMA without loss correction to the one measured with the TSI instrument with loss correction. Since the TapCon DMA measured comparable or higher values, we did not correct measurements made with the TapCon DMA for particle losses within the DMA itself as in earlier works (De Filippo et al. 2009; Sgro et al. 2009; Sgro et al. 2007).

Because of the high dilution ratio used to prevent particle coagulation (dilution ratio = 10³-10⁴) and the relatively large flow rates in the probe, particle diffusion losses are negligible in the sampling line. Losses are only significant in the orifice prior to dilution and only for d < 4 nm particles (De Filippo et al. 2009; Sgro et al. 2009). Previous works investigating the impact of flame-generated inception particles with surfaces at flame temperatures concluded that d < 5 nm particles may experience thermal rebound, and there is no currently accepted theory to calculate size-dependent losses of particles in tubes at the temperature of the orifice (800–1000 K) in the size range of interest in this study (1–5 nm) (D'Alessio et al. 2005; De Filippo et al. 2009; Sgro et al. 2009). Losses in the orifice are significantly different depending on whether or not thermal rebound occurs, but in both cases they only affect d < 4 nm particles (see Figure 5 in De Filippo et al. 2009). The degree to which thermal rebound occurs is not accurately known, and, therefore, both correcting and not correcting for particle losses in the orifice could be a source of systematic error leading to inaccuracies in the reported size distributions. Since, in this work, our main points, discussion and conclusions are limited to observations of relative changes of particle size distributions and of the absolute values of charge fraction distributions, which are both independent of particle losses, we decided to report size distributions without correcting for particle losses in the orifice. Random errors, estimated from repeated measurements, are within 20% of the measured values of N and N_{+/− 1} in the size distribution measurements, which gives an estimated error of less than 40% for the charge distribution measurements.

The fraction of singly charged particles, f _{+ 1/−1}, for each size bin was determined by dividing the number concentration of the singly charged flame products, N_{+ 1/–1} (measured without the charger), by the total particle number concentration, N (measured with the charger). Electrophoretic losses were minimized using conductive and grounded sampling lines, and we assume that they are negligible. As a consequence of the higher flow rates through the instrument, the absence of an impactor at its inlet, and the use of the electrometer as detector, the TapCon DMA is more sensitive to smaller particles, and has a lower size detection limit, less than 1 nm. We, therefore, used the TapCon DMA to measure the onset of inception particles in a range of flame conditions that produced no signal using the TSI DMA.

Throughout the paper, measured charged fraction distributions are compared to charge fraction curves calculated by the Boltzmann law (Liu and Pui 1974):

where f _+/−n B(d, T) is the fraction of particles carrying n elementary units of charge, e (4,8e–10 stC) is the elementary unit charge, d is the particle diameter in cm, k is Boltzmann's constant, and T (K) is the absolute temperature.

For some measurements, an electrostatic precipitator (ESP) was used to remove flame-generated charged species prior to the measurements. In the ESP, particles were subjected to the electric field generated between a central tungsten wire (10 cm long, 1 mm thick) and the outer stainless steel walls (ID = 8 mm) of the ESP by applying a potential of about 800 V, which removed charged particles from the aerosol flow.

3. RESULTS

Figure 2 plots the size distribution measured by the TapCon DMA with and without the charger at the inlet in terms of raw signal, the FCE current. Signals measured with the flame off are also reported in order to show interference signals superimposed over signals that are definitely due to flame-generated nanoparticles. The lower detection limit of the FCE is about 10^–15 Amperes, and for the flame conditions reported in the figure, all of the signal for diameters larger than 3 nm is background noise of the electrometer. Without the charger and the flame off (thin line in Figure 2), a background signal is measured below 1 nm. This signal was subtracted from all measurements taken without the charger, thus obtaining the signal of flame-generated negatively charged particles, N_-1.

FIG. 2 Current measured by the electrometer detector for negative ions exiting the TapCon-DMA as function of particle diameter with and without the ²⁴¹Am charger with the flame on or off in the ethylene-air flame C/O = 0.61, H = 15 mm.

In measurements with the charger and the flame off (thin dotted line) the relevant subnanometer signal is mostly due to charged molecular clusters formed by ion-induced nucleation in the particle charger itself at ambient temperature (Sgro et al. 2007; Winklmayr et al. 1990). It confounds the measurement of flame-generated species smaller than about 1 nm (Sgro et al. 2007), and it cannot be simply subtracted since its shape and intensity depend on the unknown concentrations of ion pairs in the charger as well as gasses and particles sampled from the flame. The interference of the subnanometer peak is more severe for low concentration of flame generated particles, and Figure 2 shows the worst-case scenario for a flame condition near the on-set of particle inception. In data analysis, we therefore, only considered size bins where the particle signal was larger than the interfering signal due to “charger clusters.” For example, for the measurements shown in Figure 2, only data to the right of the vertical dotted line were considered, and the signal showing a peak at diameter of about 2 nm can be certainly attributed to flame-generated particles. For the incipient flame-generated particles, the FCE current measured with and without the charger is the same within experimental noise (Figure 2), so that the number of particles ionized by the flame is roughly the same as the number of ionized particles exiting the bipolar diffusion charger. Since the charging efficiency of the bipolar charger employed in this study was never measured for particles smaller than 2 nm, we first needed to verify if the charger was effectively changing the charge state of these particles to the Fuchs' steady state value to exclude the possibility that the DMA instead measures only those particles already charged by the flame. To this aim, we used an electrostatic precipitator, ESP, upstream of the charger to remove the flame-generated charged species, and verified the effect of the bipolar charger on neutral particles by measuring the amount of ions arriving to the DMA with and without the charger given by the FCE Current.

Figure 3 shows that in measurements without the charger, when the ESP was turned on the FCE current was significantly reduced since a relevant part of flame generated particles were effectively removed from the gas stream even though some of them still penetrated the ESP. On the other hand, when the particle charger was installed downstream of the ESP, there was no significant difference between the FCE current measured with the ESP turned on or off. This result shows that removing most of flame-charged particles had a negligible impact on the amount of charged particles exiting the ²⁴¹Am charger. These results remove doubts concerning the inability of the charger to change the charge state of particles smaller than 2 nm. They indicate that the charger is effectively changing the charge state of the measured aerosol, even in conditions of very small particles for which the charger efficiency has not yet been tested. The similarity between the with and without charger curves must be due to a similar charging efficiency for 1–3 nm particles inside the flame and inside the ²⁴¹Am charger.

FIG. 3 Current measured by the electrometer detector for negative ions exiting the TapCon-DMA as function of particle diameter with the electrostatic precipitator, ESP, off or on and with and without the ²⁴¹Am charger in the ethylene-air flame C/O = 0.71, H = 5 mm.

Figure 4 shows the SDs of the positively and negatively charged and total particles measured at H = 12 and 15 mm in the C/O = 0.65 ethylene-air flame. The two different DMA systems used to measure positive and negative ions measured roughly similar size distributions for the total particles and the charged fraction, indicating that a comparable amount of positive and negative particles are produced in the flame.

FIG. 4 Size distribution of the total aerosol population (with charger) and the negatively (measured with the TapCon DMA) and positively (measured with the TSI DMA) charged particles in diluted flame products from an ethylene-air C/O = 0.65 flame H = 12 mm and H = 15 mm. Data to the left of the dotted line are affected by confounding signal due to “charger clusters.”

The fraction of negatively (f _{− 1}) and positively (f _{+ 1}) charged nanoparticles determined from these measurements are reported in Figure 5.

FIG. 5 Fraction of positive (open symbols) and negative (filled symbols) singly charged particles, f_{+/− 1}, measured at two different heights above the burner, H, in an ethylene-air C/O = 0.65 flame. Lines show the Boltzmann charge fraction distributions calculated at high flame temperatures, B(T). The charge fraction distributions calculated at 300 K by Fuchs', F ₊(300K) and F ₋(300K), and Boltzmann theory, B(300K), are also shown.

Since both DMA systems give the same charge fraction for every particle size bin, the charge distribution seems to be symmetric. Furthermore, the result that the measured charge fractions from two different DMA systems with different diffusion losses is equal without correcting for diffusion losses in the TapCon DMA validates our assumption that losses in the sampling lines do not depend significantly on the particle charge state (see discussion in Experimental Methods). Figure 5 also plots the fraction of singly charged particles calculated by the Boltzmann law (Equation (2)), B(T), at three high temperatures. These curves are in good agreement with the measurement. The three temperatures chosen for the calculation are: T = 1700 K, which is the maximum flame temperature that remains relatively constant until probe cooling becomes significant, i.e., up to a distance of 4 mm from the probe position, T = 1200 K, which is the measured temperature at a distance of about 1 mm from the probe inlet and T = 800 K, the approximate temperature at the probe inlet, extrapolated from the measurements (Figure 1). The charge fraction distributions measured with the probe at H = 12 mm, where the flame-generated particles were all smaller than 5 nm (Figure 4), lie between the Boltzmann curves calculated at T = 1700 K and T = 1200 K. Positioning the probe at slightly higher H (H = 15 mm), larger flame-generated particles were measured with sizes extending up to 8 nm (Figure 4), and the charge fraction of the larger particles of the distribution agree with the Boltzmann distribution at the probe inlet temperature, f _{+/− 1} B(800K) (Figure 5).

Figure 5a also shows the fraction of singly charged particles, F ₋(300 K) and F ₊(300 K), predicted at room temperature by Fuchs' theory and following Boltzmann theory B(T) calculated with Equation (2). The measured fraction of singly charged particles clearly agree best with Boltzmann curves at high temperature, and they are significantly different than charge distributions at 300 K, the temperature inside the probe. This result verifies that the dilution probe effectively minimizes particle coagulation within the probe. The analysis of the curves reported in Figure 5 explains the reason for the similar amount of ions measured without or with the ²⁴¹Am source in the flame condition reported in Figure 2. The raw signals measured without the charger are proportional to the fraction of charged particles present in flame, given by the Boltzmann high temperature curve. Instead, the raw signals measured with the charger are proportional to the fraction of charged particles in the bipolar radioactive source charger at ambient temperature given by the Fuchs' distribution. As a consequence, these two signals are equal for the diameter at which the F ₋(300 K) and F ₊(300 K) curves cross the high temperature Boltzmann curve (Figure 5). For particle diameters smaller than this crossing point, the charger increases the flame-charged fraction of particles since the Fuchs F ₋(300 K) and F ₊(300 K) curves are higher than the Boltzmann one at high temperature. Vice versa, the charger reduces the charged fraction for particles that are larger than this crossing point. The crossing point is at about d = 5, 2.8, and 1.8 nm for temperatures of 800, 1200, and 1700 K, respectively.

The observation that particles sampled from the flame have a f _{+ 1/−1} described by the Boltzmann distribution at high temperature, B(T), is reasonable since this is the distribution function describing diffusion charging in the free molecule regime, and all of the sampled particles are in the free molecular regime in flame (Kn ≫ 1). Nevertheless, this observation is apparently in contrast to the works which report that nanoparticles as small as 2 nm attain the Fuchs' charge distribution in the bipolar charger at room temperature, even though such small particles are in the free molecule regime. Fuchs' theory was derived for particles in the transitional regime, and its validity for particles significantly smaller than the mean free path of gases, d < 20 nm at room temperature, appears to be suspicious (Reischl et al. 1996). The anomalous behaviour of small particles at room temperature can be explained considering that charged particles in an ion rich environment, like near a bipolar radioactive source or in a flame, can be considered to be in the free molecular regime if Kn ≫ 1 and if the electrostatic energy of a particle can be neglected with respect to its thermal energy (Lushnikov and Kulmala 2005). To account for this, Lushnikov and Kulmala (Lushnikov and Kulmala 2005) proposed that another parameter, in addition to Kn, should also be considered for determining the collisional regime, the Coulomb length: lc = qQe²/KT where q and Q are the ion and particle charge numbers, e is the unit charge, T the temperature and K the Boltzmann constant. lc represents the length in which electrostatic interactions are relevant for particle-ion interactions. They consequently consider particle-ion interactions in the free molecule regime if lc ≪ λ _i and Kn ≫ 1. At ambient temperature lc ∼ λ _i = 60 nm, which could explain why Fuchs' theory, valid for particles in the transition regime, correctly predicts the charging efficiency of small particles even as small as 2 nm. Instead, at flame temperature (1700 K), lc ≪ λ _i since lc ∼ 10 nm and λ i ∼ 350 nm, and free molecule regime can be expected for particles satisfying Kn ≫ 1, d ≪ 350 nm.

Thermal ionization is often considered in addition to diffusion charging in flames. In premixed flames with temperatures of 2000K Balthasar et al. (2002) verified that the equilibrium between thermal emission of electrons by particles and recombination is reached and found an asymmetric charge distribution. These results cannot be directly extended to our flames since this effect is strongly dependent on temperature. So, to estimate the relevance of thermal ionization in our flames, we solved the Saha equation at the temperature of 1700 K following the procedure described by Balthasar et al. (2002). This equilibrium calculation predicts a particle charge fraction at 1700 K that is symmetric and essentially the same as the one predicted by the Boltzmann charge fraction. As a result, the shape of the charge fraction distribution can not shed light on which of the two mechanisms, thermal or diffusion charging, is prevailing. Furthermore, the assumption of equilibrium can be appropriate in our flame conditions. So, to verify if particles in our flame conditions can be charged by thermal ionization we considered as a timescale for the thermal emission of one electron by a particle, the reciprocal of the rate constant, k _f , for the process: °P→⁺P + e whose expression was reported by Balthasar et al. (2002)

where m _e is the mass of electron, K the Boltzmann constant, h the plank constant, e the elementary charge, C the capacity of a particle C = 2π ϵ ₀ d for a sphere of diameter d and ϵ ₀ is the permittivity of vacuum, Φ is the ionization potential of particles, Φ = V+e ²/2C with V the work function of material making up the particles, which is assumed to be that of graphite V = 4.6 eV.

In Figure 6, τ (d) is reported as a function of the temperature. The timescale for the emission of one electron by a particle increases by several orders of magnitude when the particle temperature decreases from 2000 K to 1700 K. Compared to the typical residence time in flames, which is of the order of twenty ms from the flame front to the probed volume, the high values of τ for particles smaller than 3 nm are consistent with the generally reported observation that thermal ionization is not a reasonable process for particles with masses smaller than 10⁴ amu (d < 3 nm) (Fialkov 1997). Furthermore, for flame temperatures less than 1600 K thermal ionization seems to be unrealistic for particles of every size. Increasing particle size thermal ionization becomes more efficient because of a decreasing ionization potential, Φ. Our analysis cannot determine the exact particle size for which thermal ionization becomes relevant in our flames since electron-particle recombination is not considered, and therefore our analysis would overestimate the true charge rate by thermal ionization. In addition, in the evaluation of τ we used the work function of graphite as often done for soot (Fialkov 1997), whereas earlier works showed that particles produced in our conditions have a low degree of graphitization and are quite different than particles produced in richer fully sooting flames (D'Alessio et al. 1998; D'Alessio et al. 2009; Minutolo et al. 1999) so that a higher work function can be expected which would result in an even lower ion emission rate.

FIG. 6 Timescale for the thermal emission of one electron by a particle versus particle diameter for various particle temperatures.

On the basis of these considerations, it seems that the particles produced in our flame conditions are not charged by thermal ionization. Instead, the observed agreement between the measured charge fraction and the Boltzmann expression calculated at high temperature is thought to be a consequence of a diffusion charging mechanism in the flame involving molecular ions, electrons and particles, followed by particle coagulation, which operates as a sort of “thermalization” process reducing the charge fraction of the aerosol to the Boltzmann one at the local temperature (Maricq 2008). The charge fraction distributions in Figure 5 seem to show a size-dependent thermalization by coagulation behaviour. The smaller particles have a charge fraction in agreement with Boltzmann curves near the maximum flame temperature while the f_{+ 1/− 1} of larger particles in the distribution are in better agreement with B(T) at the cooler temperatures near the probe inlet.

In order to analyze in more detail the smallest inception particles, we performed measurements as a function of height above the burner, H, thus varying flame residence time, in two flames, where the coagulation process is quite different (D'Alessio et al. 2005; Minutolo et al. 1999). Figure 7A and Figure 7B shows the measured size distributions of negatively charged particles and total particles at various H for two ethylene-air flames (C/O = 0.61 and 0.65). The size distributions of particles in the C/O = 0.61 flame are relatively unchanging with H compared to the slightly richer C/O = 0.65 flame. The C/O = 0.61 flame is the flame with the lowest C/O that gives a significant particle signal, and the SD in this flame presents a single mode that shows little particle growth throughout the entire post-flame region. A similar size distribution is measured at low H in the C/O = 0.65 flame where only an inception mode is detected. Later in the C/O = 0.65 flame, the SD increases in number concentration and widens toward larger diameters, until it becomes evidently bimodal, with an inception mode with a modal diameter of about 2 nm and a second larger mode with a modal diameter of about 4 nm. Late in the flame at H > 10 mm, the number concentration, N, of the smaller mode begins to decrease while it continues to increase for larger particles in the distribution. Figure 7C and Figure 7D reports the charge fractions evaluated from data reported in Figure 7A and Figure 7B and compares the measurements to Boltzmann curves calculated at the maximum flame temperature and at 1200 and 800 K.

FIG. 7 Size distributions measured with and without the particle charger of diluted flame products (A and B) and charge fraction distributions f _{− 1} (C and D) for ethylene-air flames with C/O = 0.61 (A and C) and C/O = 0.65 (B and D) varying height above the burner, H. Measurements are compared with Boltzmann charge distributions, B(T). Error bars estimated from repeated measurements are plotted for the measurements at H = 10 mm. Data to the left of the dotted line are affected by confounding signal due to “charger clusters.”

For all flame heights in the C/O = 0.61 flame and early in the C/O = 0.65 flame, when the size distributions show only the inception particles smaller than 3 nm, the charge fraction of the smallest particles in the distribution agrees best with the one calculated using the Boltzmann equation at the maximum flame temperature. With increasing H in the C/O = 0.65 flame, the charge distribution of the smallest particles in the distribution are still best described by the Boltzmann distribution at the maximum flame temperature, but the charge distribution of the larger particle mode is in good agreement with that predicted by Boltzmann theory at 1200K, the temperature about 1 mm prior to the probe surface. The fact that the charged fraction of the d < 2 nm mode particles agrees with B(1700 K) means not only that these particles do not thermalize by coagulation in the cooler region within 2–4 mm from the probe, but also that they could not have been formed in this cooler region in these flames. If it were the case, their charge fraction would be lower than B(1700 K) or eventually they would be entirely neutral, depending on the amount of ion pairs available to charge freshly nucleated particles, which decreases with H (Starik et al. 2008). In other words, the observation that the d < 2 nm particles retain their charge fraction predicted by B(1700 K) indicates that in such flames, which are just slightly rich, there is no evidence of particles nucleation at high H or nucleation due to condensation in the cooled region near the probe.

To examine in more detail the thermalization of smaller particles, we examined a range of flames with different C/O and temperature, Figure 8 plots the fraction of negatively singly charged particles sampled from C/O = 0.61–0.67 ethylene flames with the probe positioned in the post-flame region, at H = 15 or 17 mm. Similar to the results in Figure 5 and Figure 7, the charge fraction of all particles (d = 1-18 nm) measured in these flames lies between the Boltzmann curve calculated at the maximum flame temperature f ₋₁ B(T max flame) and that calculated at the estimated inlet orifice temperature of the probe, f ₋₁ B(800K) (Figure 8).

FIG. 8 Fraction of singly negatively charged particles in various flame conditions. The probe was positioned at H = 15 mm for the flames burning C₂H₄ air mixtures (open symbols and gray diamonds) and at H = 17 mm for the flame burning C₂H₄-Ar-O₂(full circle). The Boltzmann charge distribution curves, B(T_{max flame}), were calculated for the maximum flame temperatures measured in the C₂H₄-Ar-O₂ flame (T_{max flame} = 1820 K +/–50K, black solid lines) and the C/O = 0.61 flame burning air (T_{max flame} = 1770 +/–50K, grey dashed lines).

In flame conditions with bimodal size distributions (C/O = 0.65 and 0.67, H = 15 mm reported in Figure 8) the charge fraction of the smallest particles agree better with the Boltzmann prediction at the maximum flame temperature while the charge fractions of larger particles agree with Boltzmann theory at a lower temperature (1200 or 800 K), which coincides with the temperatures measured about 1 mm upstream and just at the probe inlet (Figure 1). The low temperature describing the charge status of larger particles is consistent with “thermalization” produced by coagulation as reported by Maricq (2004, 2005, 2009); the larger particles do coagulate in the cool region near the probe, thus reducing their charge distribution to the one calculated at the lower temperatures near the probe surface. The same thermalization is not observed for the smaller particles.

Earlier works, based on optical measurements, reported a size-dependent coagulation efficiency for particles formed in similar flames (D'Alessio et al. 2005) which was interpreted as due to thermal rebound of colliding particles. For decreasing particle size, the interaction potential well becomes less deep and the time spent by colliding particles within a capture distance becomes very low. Because of this, particles with a high kinetic energy can rebound and coagulation efficiency becomes very low. One possible explanation for the anomalous absence of “thermalization by coagulation” observed for small particles in Figure 5, Figure 7, and Figure 8 can be that the same reasoning applies also to interacting ions so that during the interaction there is not enough time for charge transfer and ion neutralization. Since the interaction potential well depends on the particle composition through the Hamaker constant, the recombination probability should also be dependent on particle composition in agreement with the experiments. In fact, the measurements in Figure 8 also seem to indicate that the anomalous thermalization behaviour is not only dependent on particle size. For example, the charge fraction of 3–5 nm particles in the C/O = 0.65 flame agrees well with the Boltzmann charge distribution at 1200 K, B(1200 K), but the same size range in the C/O = 0.67 agrees better with B(1000 K). Since the number concentration of 3–5 nm particles is significantly higher in the C/O = 0.65 flame than in the C/O = 0.67 flame, the 3–5 nm particles in the C/O = 0.65 flame should have a higher coagulation rate than those in the C/O = 0.67 flame and they should continue coagulating until they enter the probe giving a Boltzmann charge distribution equal to the temperature near the probe (∼ 800 K), in contrast with the experimental evidence. It is worth noting that variations in the measured temperature profiles for all of the flames studied are small (within 70 degrees) and cannot account for the evidences discussed here (Figure 1). Particle coagulation in the probe cannot determine the observed phenomena. Also, the observation that all charge distributions were in agreement with Boltzmann theory for temperatures higher than 800 K indicates that coagulation in the probe was effectively supressed, and could not account for the observed phenomena. We verified that a reduction in the dilution ratio to allow particle coagulation in the probe caused the charge distribution to reduce to the Boltzman prediction for 300 K, the temperature of the bulk flow in the probe, in agreement with the experiments performed by Maricq (2008, 2009).

It is worth discussing other possible effects, which may explain the size-dependent thermalization trends observed in Figure 7, and Figure 8. We can identify four possible confounding factors: (1) the possibility that particles in flame do not attain the equilibrium Boltzmann charge distribution by diffusion charging, (2) the possibility that the interfering signal of the ‘charger ions’ previously discussed and reported in Figure 2 significantly affects the size distribution measured with the charger, (3) the possibility that there are some electrophoretic effects in the sampling lines so that the assumption that charged and neutral particles experience the same size-dependent losses to the walls is incorrect, and (4) the possibility that the charger is unable to fully charge the measured aerosol to the steady-state Fuchs' distribution (at 300 K). If the particles in the flame do not attain the equilibrium (Boltzmann) charge distribution by diffusion charging their charge distribution would be lower than Boltzmann. The higher value observed for the smaller particles could only result from a super-equilibrium charging process in the flame, but the presence of super-equilibrium charged particles high in the flame, H > 10 mm, where the concentration of chemiions should be very low (Starik et al. 2008), seems to be highly improbable. Regarding point 2, if the ‘charger ions’ produced in the ²⁴¹Am source were significantly augmenting the signal attributed to total particles the estimated charge fraction would be lowered, which, again, is opposite to the trend observed in Figure 7, and Figure 8. If electrophoretic losses were significant, this would affect the results by lowering the measured charged fraction of the smaller particles, which, again, is opposite to the trend observed in Figure 7, and Figure 8.

4. DISCUSSION AND CONCLUSIONS

All of the measurements in this study have shown that the charge fraction of particles in flame can be well described by Boltzmann theory. This result is based on the assumption that the particles reach the Fuchs' steady state distribution in the ²⁴¹Am charger. This assumption has not been demonstrated for particles smaller than 2 nm, but the results of experiment done with the ESP demonstrate that the ²⁴¹Am charger is able to change the charge state of incoming particles. In addition, all of the measured charge distributions lie within the predicted values of Boltzmann theory for T = 1700 K (flame temperature) to the coolest temperature determined just at the inlet of the probe (800 K), and none of the measured charge distributions were higher than that predicted for the maximum flame temperature even for the hottest flame studied, the C₃H₄-Ar-O₂ flame (Figure 8). The results strongly suggest that Boltzman theory predicts well the charge distribution of particles at high temperature in the flame and Fuchs' theory is accurate at ambient temperature for predicting the charge state of particles in the bipolar charger for all charged particles/macromolecules examined, even those with diameters as small as 1.5 nm. Further work is needed to directly measure it for flame-generated incipient nanoparticles.

The methodology described in this paper can be used to determine the temperature at which the measured particle undergoes the last coagulation event, and give information on particle nucleation throughout the flame.

In the flames examined here, the larger particles (d > 3 nm) undergo “thermalization by coagulation” as they travel through the cooler environment near the probe. As a result, their charge fraction is reduced to a Boltzmann charge fraction, B(T), corresponding to the temperature of the last coagulation event. The same behaviour is not observed for smaller particles (d < 3 nm), which instead retain a charge distribution corresponding to the maximum flame temperature. Previous observations based on optical measurements, suggested that the coagulation coefficient of the smallest particles formed in these flames was lower than the gas kinetic value; it was explained by a coagulation model, which showed that the smallest particles may escape collisions by thermal rebound when the thermal energy of the particle is larger than the interaction potential well and the time spent in the well is small enough (D'Alessio et al. 2005; Minutolo et al. 1999). The absence of “thermalization by coagulation” evidenced here for such small particles suggests that also for charged particles the interaction time is small enough to avoid charge transfer and consequently neutralization.

The results presented in Figure 8 furthermore evidence that particles with the same size produced in different flame conditions may have a different “thermalization by coagulation” behaviour. This result could imply that these nanoparticles have a different chemical nature with a presumably different Hamaker constant although their size is similar. However, this hypothesis cannot be verified until the number concentration of small particles in flames is evaluated with high confidence. It also requires that particle losses be estimated with greater certainty. Instead, the explanation that smaller particles undergo less thermalization by coagulation than larger particles holds since all particles of every size are travelling and colliding as they enter the dilution probe in the cool region near the probe.

The charge fraction of particles larger than 13 nm in slightly richer flames is in excellent agreement with Boltzmann theory, consistent with results reported by Maricq (2005). The main difference between our results and those of Maricq is that we measured a Boltzmann charge fraction for all conditions tested, even high in the flame and for all sizes down to 1 nm. Instead, Maricq found a lower than Boltzmann charge distribution for nanoparticles smaller than 10 nm, which eventually became completely neutral at higher H (Maricq 2005). This trend was attributed to persistent nucleation of particles, which are neutral because of the absence of flame ions high in the flame. This notable difference could imply that persistent nucleation does not occur significantly in the slightly rich flames examined here.

Numerical modeling studies that combine chemical kinetics and particle growth dynamics show that predictions of particle size distributions late in the flame depend strongly on the size of incipient nanoparticles considered in the model (Singh et al. 2006), and it is important to measure these particles with higher accuracy/resolution. If one could estimate the temperature at which the particles last coagulation event occurred, the total aerosol population could be easily estimated from a measurement of the charged fraction of particles without having to use a particle charger. As an example, Figure 7d shows that the charge distribution is relatively well-predicted by Boltzmann theory at the maximum flame temperature (1700 K) at H = 5 mm in the C/O = 0.65 flame. In this case, the SD of the total inception particles (charged and neutral) could be determined by dividing the measured SD without the charger in each size bin by the Boltzmann charge fraction at 1700 K calculated by Equation (2). This procedure eliminates uncertainties due the charger included the confounding signal of ion-induced clusters formed in the particle charger. Figure 9 shows that the calculated SD of the total aerosol population in the flame (x signs) based on the measurement without the charger (diamonds) is quite similar to that measured with the charger (line with square symbols). This result is obvious because of the close agreement with the Boltzmann charge distribution at 1700 K, but the technique could be useful in more sensitive high resolution measurement systems like on-line Time of Flight-Mass Spectrometry to get additional information on the inception mode particles in different flame conditions. Figure 9 shows clearly that the dip at 0.8 nm is due to the interfering signal of the charger ions and that there is not much error in simply cutting off the SD measured with the charger for d < 0.9, where the inflection is observed, which is what we did in this and past works to avoid the interfering “charger ions.”

FIG. 9 Size distribution of total nanoparticles (+) determined from the size distribution of negatively charged particles in the flame measured without the particle charger (diamonds) assuming the Boltzmann, T = 1700 K, charge distribution. Also shown in the figure is the SD of total particles measured with the charger (line without symbols). C/O = 0.65 flame H = 5 mm.