1. Introduction

Nowadays there are many concerns on the environmental and biochemical roles of combustion generated nanoparticles. Recently a strong interest has been directed towards very small (1–5 nm) particles [1–7], which show molecular-like properties due to their small size and large surface-to-volume ratio. Many of these particles are hardly detected with conventional techniques, because they are often out of the experimental limits. In particular, their absorption band typically lies in the UV spectral region, which makes them insensitive to visible radiation. Moreover, their high diffusivity prevents them from being captured by conventional filters.

In order to control and, possibly, reduce the nanoparticle emission by combustion sources, a major challenge for the current research is clarifying the whole process of soot production from unburned fuel/oxygen mixtures up to formation of large soot particles [7]. New non-intrusive measurement techniques are strongly required for the characterization of the various species involved in a combustion process. A particularly important role is played by in-situ methods that allow real-time monitoring directly within combustion regions, exhausts or atmosphere. Recently there have been several reports on the characterization of nanoparticles, formed or emitted from various combustion sources, with size ranging between 1 and 5 nm, [9,10]. The methods so far used were primarily based on ex-situ techniques, where samples are extracted from the flames and then analyzed with, e.g., differential mobility analyzers [5,11,12], thermophoretic sampling combined with atomic force microscopy (AFM) [12], time-resolved fluorescence polarization anisotropy (TRFPA) [13–16], and dynamic light scattering [17] on water diluted samples. However, the sampling procedure may strongly affect the chemical and physical structure of the probed species, which sometimes show a rather weak stability.

The number of non-intrusive in-situ techniques is very limited: The most widely used is based on combined laser light scattering/extinction and fluorescence (CLSEF) measurements, and has been used to characterize the size of particles within flames [1,18–20].

CLSEF measurements have been performed on various kinds of flame. The results suggest that the flames do generate small nanoparticles consisting of carbon-based species, usually named nano organic carbon (NOC), containing aliphatic and aromatic units, which bare great similarities with smaller polycyclic aromatic hydrocarbons (PAH) with up to 4 rings [1,18–20]. A problem arising with CLSEF techniques is that the optical properties of NOC particles, e.g., complex refractive index, absorption coefficients and fluorescence spectra, are not known with sufficient confidence to enable precise measurements of their size and structure. Moreover, due to the high temperatures occurring in flames, the spectral emission profiles broaden and become less structured with increasing temperatures, owing to strong vibrational mixing, internal redistribution and internal quenching. The loss of spectral details may become severe because of the highly temperature-sensitive rates of intersystem crossing and internal conversion. Finally, the effective fluorescence lifetimes of PAH have shown to strongly decrease with the temperature: At typical flame temperatures, they may range from a few nanoseconds down to hundreds or tens of picoseconds [21,22].

The investigation of the dynamics of fluorescence depolarization of complex organic compounds in the gas phase represents an effective way for gathering information on their physical and chemical properties.

In particular, the TRFPA technique seems to be a good candidate for measuring the average diameter of NOC particles directly within a flame, although some difficulties arise compared to the case of solvent-diluted and room temperature samples. In fact, the high flame temperatures reduce the lifetimes of excited states, whereas the gas-phase environment implies rather low friction forces. Consequently, depolarization times of tens of picoseconds are expected for nanometer sized NOC particles, and, thus, high time resolution is required for their measurement.

In the present work we propose the first application of TRFPA on combustion products directly within a flame, by exploiting ultrashort laser excitation and streak-camera detection of the fluorescence profiles for achieving the required time resolution.

2. Rotational correlation time

The phenomenon of fluorescence anisotropy has been analyzed in great detail in various textbooks (see [23]). In previous works [13–16] we illustrated its application to carbonaceous nanoparticles diluted in liquid solvents. Here we shall discuss the main aspects and differences with respect to previously reported studies.

The polarization state of the fluorescence radiation following an ultrashort, linearly polarized excitation pulse is characterized by the parameter r(t), the fluorescence polarization anisotropy or simply anisotropy, defined by the following relation:

where I _‖(t) and I _⊥(t) are, respectively, the signal intensities of parallel and perpendicular polarization components of the fluorescence light with respect to the polarization direction of the exciting radiation pulse.

It can be shown that the initial value of the anisotropy is r ₀=0.4 in the case of single photon absorption and parallel absorption and emission dipoles [23]. Subsequently, the rotational diffusion leads to a characteristic time behaviour of r(t), depending on both environmental conditions and size distribution of the ensemble of fluorescent particles. In simple situations, namely monodispersed samples of spherical particles in liquid solutions, the most widely used theoretical model for the description of rotational diffusion is based on the Stokes-Einstein-Debye (SED) theory [24–26]. The decay law is a single exponential with a time constant strictly related to the ensemble-averaged rotational properties of the particles, and, thus, to their average diameter. The characteristic time of fluorescence depolarization, τ_r, is often referred to as the rotational correlation time. In particular, it depends on particle volume, V, solvent macroscopic viscosity, η, and temperature, T[27,28]:

where k_B is the Boltzmann’s constant. The C factor depends on the boundary conditions at the particle surface, and ranges between 0 (slip boundary conditions) and 1 (stick boundary condition). The validity of Eq. (2) is typically limited to high viscosity environments (e.g., liquids) and nearly stick boundary conditions (1-C≪0). In fact, for C, η→0, the rotational correlation time is strongly affected by the free inertial rotation [28], which is not accounted for in Eq. (2).

Our interpretation of the experiment is that it consists of nanometric carbon particles immersed in a background gas (essentially air) at atmospheric pressure and temperature T≅900 K, with a shear viscosity η≅4×10^-5 Pa s. In these circumstances, collisions of the carbon particles with the gas molecules play an important role in determining the dynamic evolution of the system. Rotational reorientation in presence of collisions can be described by the Langevin friction model [29], the J-diffusion model [30,31] or the J-coherence model [32], depending on the collision frequency and efficiency. In order to work out and compare the relevant parameters determining the dynamic regime of our experiment, let us first assume that the sample consists of an ensemble of identical homogeneous spherical particles with mass density ρ≅10³ kg/m³ (typical of nanometric carbon particles) and radius R≅1.5 nm. This hypothesis will be verified later on. The moment of inertia, M, of such particles determines the classical free rotation period, τ_f:

The mean time between two consecutive collisions undergone by a background gas molecule (O₂ or N₂), τ_coll,g-g, is of the order of 90 ps, whereas the mean time between two successive collisions of the gas molecules with a given colloidal particle, τ_coll,g-p, is about 5 ps. Here we have used the approximation of a slow, heavy carbon particle in a bath of light (air) molecules. In fact, the ratio of O₂ or N₂ molecule mass and carbon particle mass is ~3.8×10^-3. Since τ_f≫τ_coll,g-p, the mean free rotation angle of the carbon particle between two successive collisions with the gas molecules is small (≅14°). Nevertheless, the efficiency of collisions in randomizing the angular momentum of the particle is rather low, because of the large particle mass compared to the mass of the collision partners. In this limit, the total torque due to collisions can be separated into the frictional torque, proportional to the angular velocity, ω⃗, and a random torque, F⃗, so that the angular dynamics is described by the Langevin friction model and is approximately governed by the equation [29]

where ξ is the reduced friction coefficient. The quantity τ_ω=1/ξ represents the decay time of the angular velocity autocorrelation function, that can be proven to be exponential as a consequence of the Markovian nature of the torque F⃗. An analytical expression of r(t) can be obtained [33–35]:

A simple estimate of τ_ω is found in the high density limit, namely at gas molecule number density approaching the liquid density. In such conditions the total friction coefficient, Mξ, is given by 8πη*R ³, leading to τ_ω=ρR ²/(15η*), where η* is the corresponding shear viscosity. The order of magnitude for τ_ω in liquid air (η*≅1.7×10^-4 Pa s) is 0.8 ps. On the other hand, Baskin et al. [29,32] studied the progressive effect of solvent friction on rotational motion for a well-defined solute in solvents from gas to liquid densities and observed a continuous transition from the free rotation regime occurring at low (atmospheric) gas pressure to the diffusive regime of supercritical solvent densities. Consequently, by exploiting the results of Evans et al. [36] (τ_ω is inversely proportional to the gas particle number density) we can assume that, in our experimental conditions (atmospheric pressure), τ_ω is of the order of hundreds of picoseconds.

From Eq. (5), we observe that for t≫τ_ω, the anisotropy r decays exponentially with a time constant τ_D=M/(6k_BTτ_ω). In the framework of the SED theory for rotational diffusion, Mξ=M/τ_ω=6ηV, with V the particle volume, so that:

namely, the (stick) diffusive limit of the rotational correlation time [see Eq. (2)]. Conversely, for t≪τ_ω, we obtain:

which is independent of τ_ω because at short time after the laser excitation, the particle motion has not yet been influenced by the surrounding gas. In such a case, the time profile of the anisotropy matches the early time (Gaussian) behaviour of free rotational motion.

From this qualitative analysis, we can conclude that the free rotation period of nanometric carbon particles, τ_f, is much smaller than the decay time of the angular velocity autocorrelation function, τ_ω, and, consequently, the particle reorientation occurs in the regime of coherent inertial motion. This is true in spite of the short collision time (τ_coll,g-p≪τ_f), because of the very low efficiency of collisions in randomizing the angular velocity. As a matter of fact, the coherent inertial motion is better described by the J-coherence model [29,32], that, at low gas densities, predicts a free-rotor anisotropy characterized by a coherent dip (approximately at t=τ_f/4) followed by a gradual return to the asymptotic value of 0.1. However, the anisotropy dip can hardly be observed when dealing with a polydispersed sample of particles, as in our case. In fact, the time profile of the experimentally measured ensemble-averaged anisotropy is the superposition of as many curves, each with its own dip position, width and depth, as the number of classes of particles with different diameters. In the resulting measured profile of r(t), the anisotropy dip is washed out by the intrinsic ensemble average performed by the measurement method (see Sec.3). Therefore, the Langevin model is a reasonable approximation for t≪τ_ω, although its monotonical decrease does not account for the coherence dip. Within this framework, the anisotropy ratio due to 1.5 nm carbon particles is expected to almost completely fall to the 0.1 asymptotic value in a time interval of about τ_f/4≅50 ps, which sets the upper limit of the required experimental time resolution.

3. Description of the experiment

Our experiment is the first attempt to measure the size of nanoparticles by means of TRFPA directly within a flame. As already mentioned before, the main difficulties arise from the short decay time (tens of picosecond) of the anisotropy ratio of small fluorescent nanoparticles. A suitable method for measuring such short times requires ultrafast excitation and high-time-resolution detection of the fluorescence intensities. To this end, we employed 100 fs lasers pulses to excite the sample and a streak-camera to capture the fluorescence signals.

 

Fig. 1. (a). Schematic view of the experimental apparatus: SHG: second harmonic crystal; HS: harmonic separator; CGF: colour glass filter; HWP: half-wave plate; GLP: Glan-laser polarizer; GTP: Glan-Thompson polarizer. (b) A photograph of Bunsen burner and propane flame.

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A schematic view of the optical layout is shown in Fig. 1. The laser system was an 82 MHz, mode-locked titanium-sapphire (Ti:Sa) laser (Spectra Physics, mod. Tsunami), pumped by a Nd:YVO laser (Spectra Physics, mod. Millennia V). The laser pulse length and energy were, respectively, 100 fs and 8 nJ at the fundamental wavelength (λ=770 nm). The radiation was then frequency-doubled to 385 nm in a β-barium-borate (BBO) crystal, cut for type-I phase matching, with approximately 15% conversion efficiency. A harmonic separator (highly reflecting at 400 nm and transmitting at 800 nm) and a low-pass colour-glass filter (with a cutoff wavelength of 480 nm) removed the residual infrared laser radiation. The combination of a half-wave plate and a UV Glan-laser polarizing cube achieved both continuous variation of the pulse energy and high-contrast vertical polarization of the exciting light pulse. The laser beam was then focused by a spherical UV-grade 200 mm focal-length lens into the center of a propane flame produced by a Bunsen-type burner at 25 mm height above the burner edge.

The fluorescence was collected at 90° with respect to both incoming laser beam and polarization direction of the exciting electric field. Two positive lenses imaged the fluorescent region of the flame onto the entrance slit of the streak-camera (Hamamatsu, mod. C5680), with a magnification close to 1. At the entrance of the detection system, a second polarizing cube (Glan-Thompson) selected either vertical or horizontal polarization component. Finally, the fluorescence light passed two spectral filters (450–650 nm bandpass) that reduced both scattering of the laser light and background flame radiation. The filters’ transmittances for the two polarization components of the fluorescence light were identical, as previously verified [14], so that the acquired time profiles of I _‖(t) and I _⊥ (t) in Eq. (1) did not need to be corrected.

The time profiles of the fluorescence radiation were thus recorded by the streak-camera, operating in synchronous mode with respect to the 82 MHz laser pulse train. The time gate for the streak-camera image intensifier was set at 56 ms, corresponding to a signal averaging over 4.6×10⁶ laser pulses. The streak images were further averaged over 3000 gate events. The streak-camera was controlled by a personal computer (PC) that also performed data acquisition and subsequent analysis. Streak images were also acquired in absence of the exciting pulse for subsequent background subtraction from the fluorescence signals.

 

Fig. 2. Background-corrected LIF spectrum of fluorescent species located in the propane flame at 25 mm height above the burner rim.

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The time resolution of the streak-camera was estimated as the width of the acquired intensity profile corresponding to a very short light event. It was experimentally measured by determining the time profile of the laser radiation scattered from air molecules and dust, after turning the flame off and removing the bandpass filters in front of the streak-camera. The 385 nm scattered light pulse, lasting as short as 100 fs, was detected with an acquisition time window set to 800 ps. Its time width, measured as full width at half maximum, was approximately 8 ps, that we assumed as the time resolution of our apparatus in typical operating conditions.

The flame was produced by a Bunsen-type burner operating in completely diffusion conditions. The burner had an internal diameter of 7 mm and an external one of 10 mm. It operated with an incoming pure propane flux of 500 ml/min. The radial temperature profile of the flame at 25 mm height was measured with a 300 µm thick thermocouple. The temperature of the central region of the flame was 700 K whereas close to the outer edge it was 1400 K. The average temperature of the excited flame region imaged onto the entrance slit of the streak camera was derived by integrating the temperature profile along the laser path, and resulted to be approximately 855 K.

In order to spectrally characterize the flame, we also determined its fluorescence spectrum. For these particular measurements, the laser system was operated in an amplified mode, using a Ti:Sa regenerative amplifier (Spectra Physics, mod. Spitfire) pumped by a Nd:YLF Q-switched laser (Spectra Physics, Merlin) at 1 kHz repetition rate. In the amplified configuration, the laser pulse energy was as high as 0.6 mJ at the fundamental frequency. The fluorescence light was, then, injected by a UV-grade, 100 mm focal-length lens into an UV-grade optical fibre positioned at 90° with respect to the laser beam. The other end of the fibre was coupled to the entrance slit of a spectrograph (Jobin-Yvon, mod. H.25), equipped with a 1200 grooves/mm diffraction grating and coupled to a CCD camera. With this configuration, the much larger fluorescence intensity due to the high laser pulse energy compensated the low fibre/spectrograph throughput, and allowed an easy and rapid detection of the fluorescence spectra. A background spectrum was first recorded in absence of the laser pulse and then subtracted from the one obtained with the laser pulse. This procedure allowed to remove steady-state contributions from the flame and to single out only the laser-induced fluorescence (LIF).

4. Results and discussion

Figure 2 shows a typical LIF spectrum of the flame. Besides the sharp peak at 385 nm, due to elastic scattering of the laser radiation, its overall shape closely resembles those obtained from similar flames. In particular, the maximum intensity at about 430 nm was also found in the spectra of ethylene/air premixed flames containing soot precursors, and obtained using an excitation wavelength of 266 nm [12]. In addition, there is a considerable agreement with ex-situ fluorescence spectra of combustion products collected in water and excited at 400 nm [13]. These fluorescence features are consistent with those found in other flames containing soot precursor nanoparticles, and suggest that nanometric aggregates are actually produced also in the propane flame.

 

Fig. 3. Signal intensities relative to I _‖(t) (black dots), I _⊥(t) (red triangles), and scattered laser radiation magnified by a factor of 100 (blue stars). Insert: Resulting anisotropy ratio (black dots).

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Figure 3 shows the two polarization components, I _‖(t) and I _⊥(t), of the fluorescence intensity as a function of time. In the same figure we also report the time profile (multiplied by a factor of 100) of the laser radiation scattered from air and recorded according to the procedure described in Sec. 3. The latter is assumed as the instrument response function of our apparatus. The anisotropy ratio derived from Eq. (1) is reported in the inset of Fig. 3, where the time origin has been shifted, so that t=0 corresponds to the maximum of r(t). The time profile of the anisotropy clearly presents two distinct regions: During the first 50 ps it follows a Gaussian behaviour, as expected in case of free coherent rotation, whereas at long times, a nearly exponential decay can be observed, although overlapped to a rather large noise.

An expanded view of the first 80 ps of the anisotropy ratio is reported in Fig. 4, where the red line is a Gaussian fit, according to Eq. (7). For NOC particles in the propane flame conditions (ρ=10³ kg/m³, T=885 K), we obtained an average particle diameter, D, of (3.3±0.3) nm. The uncertainty must not be interpreted as the particle size-distribution width, which cannot be determined with our present experimental setup and data analysis. It is the maximum deviation of the estimate of D and is related to the standard deviation of the Gaussian time width (≅3%) and to maximum deviations of T and ρ, both of about 15%.

 

Fig. 4. Time behaviour of the early time anisotropy ratio (black squares). The red line is the corresponding Gaussian fit.

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The above result confirms the initial assumption of carbon particles with linear dimensions of a few nanometres, although we cannot rule out that NOC particles have a non-spherical shape. However, besides particles’ shape and size distribution, our results unambiguously prove that the propane flame does produce small nanoparticles, showing a significant emission at wavelengths around 420 nm and linear dimensions shorter than 4 nm. As an additional relevant result, we have demonstrated that the TRFPA technique lends itself to the physical characterization of nanometric carbon particles directly within the flame, thus eliminating sampling and subsequent ex situ analysis. This feature allows a more direct characterization of the flame products, removing both the need of a collecting probe, that could alter the combustion process, and dilution of the collected particles in a solvent, that could modify the particles’ characteristics. Moreover, the method can be easily applied to flames and combustion systems where sampling is either difficult or unsuitable (e.g., counterflow diffusion flames).

In concluding this section, we discuss the initial value, r ₀, of the anisotropy ratio. As previously stated, in case of electric dipole single-photon absorption and collinear transitions (namely, when the absorption and emission transition moments are parallel), the expected value of r ₀ is 0.4 [23]. According to Eq. (1), this value corresponds to I _‖=3 I _⊥. However, as can be seen from Fig. 4, we measured r ₀≅0.75, corresponding to I _‖≅10 I _⊥. The reason of such a large value is not yet clear. A possible contribution may come from residual laser radiation scattered by the particles in the flame and passing the spectral filters in front of the streak-camera. This essentially would give rise to an overestimate of the correct value of I _‖. In our case, the measured contribution of the scattered laser light did not account for the very large value of r ₀. Larger values of r ₀ can also be produced by multiphoton absorption. In particular r ₀=0.571 and r ₀=0.667, respectively, for two- and three-photon absorption [37–39]. In our experiment, the laser intensity was as high as 4×10⁸ W/cm², which is not sufficiently large to give rise to a wealth of non-resonant, non-linear processes, but enough to produce resonant multiphoton absorption (MPA). However, additional investigations will be necessary in order to understand whether MPA is responsible of the large measured value of r ₀ or not.

In discussing our results, we have assumed that other phenomena affecting the fluorescence polarization anisotropy, such as internal vibrational redistribution or morphological changes of the particle causing internal rotations of the chromophores, occurred on a much shorter time scale compared to the characteristic times of rotational motion [23]. Therefore, they did not influence the measurement of the rotational correlation time.

5. Conclusions and perspectives

We have applied for the first time the TRFPA technique to in situ analysis of a laboratory flame. As a preliminary result, laser-induced fluorescence spectra of our propane flame exhibited a significant emission in the short wavelength part of the visible region. Such fluorescence can be ascribed to nanometric carbon particles produced within the flame. This statement was confirmed by TRFPA measurements of the average particle diameter. In fact, although the gas-phase environment surrounding the carbon nanoparticles and the high flame temperature entail a rather short rotational correlation time, detection of the fluorescence intensity profiles with a streak-camera achieved the required time resolution and led to particle diameters of approximately 3 nm.

Nevertheless, some aspects of the results specific of the propane flame in our experimental conditions remain unclear and need further theoretical and experimental studies. In particular, additional investigations are necessary to understand the reason of the large initial value of the anisotropy ratio that in our case exceeded the expected value of 0.4 by almost a factor of two.

The results reported in the present paper demonstrate the existence of nanoparticles generated within the propane flame, with average diameter of the order of a few nanometres. In addition, the applicability of the TRFPA technique to characterize nanoparticles in the gas phase of a laboratory flame encourages the extension of the method to different kinds of flames and other samples in the gas phase, where particle sampling and subsequent ex situ analysis is either unfeasible or inadequate.