Ozone and nitrogen oxides

As reported in Sec. 3.2.3, we suggested that the solvation of highly hygroscopic HNO₃ into water droplets can efficiently stabilize the laser generated particles, allowing them to survive even at low relative humidities. HNO3 naturally forms via subsequent chemical reactions involving water, nitrogen oxides and ozone [6].

Field measurements showed that filaments produce clearly detectable amounts of these species, but the experimental setup was not conceived to provide quantitative

Figure 3.16: Experimental setup for trace gas sampling.

measurements of the respective production rates, which are essential for predict-ing the chemical reaction rate constants, and hence the amount of generated nitric acid.

Therefore, we performed laboratory experiments in order to fill this gap and state if we can expect an efficient chemistry of O₃and NOx, leading to the formation of HNO₃in such large amounts that it could influence droplets stability.

Experimental setup and data acquisition

The experiments were conducted on the Helvetera platform at GAP Biopho-tonics department of the University of Geneva. This platform consists of a Ti:Sa femtosecond TW laser, delivering pulses of energy up to 12 mJ and 80 fs Fourier-limited pulse duration. Energy was varied by rotating a half-wave plate located before the compressor, while inducing a chirp by detuning the compressor allowed for increasing the pulse duration. The beam was focused by a f =2.8 m lens to generate one to two filaments inside a 2 m long Plexiglass cell of 2 cm diame-ter, with 250µm thick fused silica windows (see Fig. 3.16). Before entering the cell, the laser beam polarization could be switched between linear and circular by means of a quarter-wave plate.

Two equal 4 mm diameter apertures were made at the ends of the cell: fresh am-bient air from the laboratory environment entered the cell at one of them, while the other one was connected through polyethylene tubes to trace gas analyzers.

Air was continuously pumped, in parallel, by an ozone analyzer (Horiba APOA-350E) at a flow rate of 2.2 l/min, and a NO_x analyzer (Monitor Labs 8840) at a flow rate of 0.5 l/min.

The laser operated at 100 Hz, but a chopper reduced this rate by a factor of 40 in most of the experiments (i.e. 2.5 pulses/s) in order to limit the gas concentrations

3.3 Complementary laboratory tests: trace gases and ion species

Figure 3.17: Typical temporal evolution of trace gas concentration (O₂and NO₂) during 2 subsequent runs of laser firing.

in the cell so as to avoid saturation of measurement devices and reduce chemical reactions between generated species. We checked that all the measurements were linear with the number of laser shots per unit time.

A typical output signal from trace gases analyzers as a function of time is plot-ted in Fig. 3.17. The time interval covers two laser runs at different energies. O₃ and NO₂concentrations started to increase a few seconds after the laser was fired into the cell, and decreased exponentially once the laser was blocked. The sub-sequent run was begun when the cell returned to previous background concen-trations. Data points of all measurements were recorded once a steady state was reached in the cell, which corresponds to the plateau in the curves of Fig. 3.17.

Around the stationary conditions visible in the previous graph, the variation of the trace gas content in the cell arises from two opposite contributions: a laser source termS_i and a dilution term driven by sampling air flowF. Neglecting the losses due to chemical reactions between O₃and NOxduring the transit to the analyzers, one can express the variation of trace gas concentration by the following:

V×dC_i

dt =S_i−C_i×F, (3.3)

whereV is the volume of the cell andC_iis the number concentration of the species i, expressed in cm⁻³. In the steady state, the source term can therefore be easily calculated:

S_i=C_i×F. (3.4)

Volumic generation rates are then evaluated by dividing S_i by the total filament volume, corresponding to two filaments of 0.5 m length and 100µm diameter, i.e.

Figure 3.18: Generation of O₃, NO, and NO₂ in laser filaments as a function of (a) incident energy for an 80 fs pulse duration, and (b) the pulse duration for a pulse of 11.2 mJ energy. The polarization of the beam is linear. [21]

a total volume of 8 mm³. Dividing this quantity by laser repetition rate gives trace gas number concentration generated per pulse, expressed in molecules per cm³. Results and discussion

Figure 3.18 displays the generation rate per unit filament volume of O₃, NO, and NO₂ in the filament as a function of the incident pulse energy and dura-tion. The filaments produced considerable amounts of these trace gases. For 2.5 shots/s, the concentrations averaged over the cell volume reached 200 ppb of O₃ and 50 ppb of NO₂, one order of magnitude above the typical atmospheric values and even higher than the alert level in most countries [119]. They corre-spond to the generation per laser shot of extremely high concentrations within the 8 mm³filaments volume: 400 ppm of ozone and 100 ppm of NO₂.

The production of O₃, NO, and NO₂ increased linearly with pulse energy, with a threshold around 1−2 mJ, which corresponds to the filamentation threshold in our experimental conditions. It was proportional to that of electrons for various pulse durations and energies; the electrons released by filaments were measured with the setup described in Sec. 1.3.2.

The impact of beam polarization has also been assessed, showing that linearly po-larized pulses yielded 19% more ozone, 33% more NO, and 68% more NO₂than circularly polarized ones. Unlike the field measurements (Sec.3.2.4), the two po-larizations are not equivalent. This can be explained by considering the fact that, in these experimental conditions, the reduction of the number and intensity of the filaments, generated by circularly polarized pulses [116], was not compensated

3.3 Complementary laboratory tests: trace gases and ion species

by their increased length [21], because of the quite strong focusing applied to the beam. Also the charge release by filaments was twice as large as with linearly polarized incident pulses. These observations demonstrated that, at the average beam intensities at play, and for the considered focusing geometry, the contribu-tion of the filaments to the produccontribu-tion of trace gases was dominant with respect to that of the photon bath. This scenario will not hold for extremely high pulse energies, where trace gases are produced mainly in the photon bath, as it will be showed in Sec. 5.3.3.

The pathways leading to ozone and nitrogen oxides may be activated by photodis-sociation, ionization, or electron impact onto O₂ and N₂ molecules. The very complex chemistry of air plasmas [120, 121] prevent us from isolating one single scheme.

It is beyond the scope of this work to give a comprehensive view of all the pos-sible chemical reactions occurring in air plasmas under the excitation of laser filaments. However, it is possible to identify some mechanisms which are more likely to contribute significantly to the formation of O₃, NO, and NO₂, since they can be considered more efficient, relying on rate constants values known from lit-erature.

N⁺ ions are highly reactive with oxygen, with a rate constant as high as 5× 10⁻¹⁰ cm³/s at 300 K [122]. Filaments are known to negligibly heat the heavy species of the plasma [1,38], hence we make use of rate constants at room temper-ature for all the reactions considered. N⁺ ions combine with oxygen as follows:

N⁺+ O2 → NO⁺+ O^•, (3.5)

N⁺+ O₂ → N+ O⁺₂, (3.6)

N⁺+ O₂ → NO+ O⁺. (3.7)

The branching ratios between the previous reactions are, respectively, 43%, 51%

and 9%. Alternatively, NO can result from:

N^∗+ O₂→ NO+ O^•. (3.8)

The excited nitrogen atom required for the previous reaction can be generated by the recombination of electrons with N⁺₂, where the N-N bond is broken:

N⁺₂ +e→ N^∗+ N, (3.9)

or by the following:

N^∗₂+O^•→ NO+ N^∗, (3.10)

which also represents a potential source of NO.

Besides Reactions (3.5) and (3.8), O^•is also produced by the following:

e+ O2→ O^•+ O^•. (3.11)

The oxygen radicals immediately react with oxygen molecules, thus leading to ozone formation:

O^•+O₂+M→ O₃+M. (3.12)

Ozone will then oxidize NO into NO₂according to the following reaction [6]:

NO+ O₃→ NO₂+ O₂. (3.13)

It is currently impossible to perform quantitative simulations based on rate equa-tions of the measured concentraequa-tions of trace gases, in order to isolate the most rel-evant pathways among Reactions ( 3.5) - (3.10). This is due to two main reasons:

the lack of data on initial N^∗₂, N^∗, N⁺₂ and N⁺ concentrations and, on the other hand, the very rich chemical dynamics at play, for which we can’t exclude other contributing mechanisms not cited here. However, since the concentrations of O₃, NO, and NO₂ are closely related to the free electrons amount (see Fig. 3.18), a process initiation by Reactions (3.5) - (3.7) and (3.9) is more likely than a process initiated by excited nitrogen molecules (Reaction (3.10)).

The resulting very high O₃and NO₂concentrations in the filament volume allow for an efficient chemistry. In particular, the equilibrium:

NO₂+ NO₃+M N₂O₅+M (3.14)

is governed by K14= ([N₂O₅]/[NO₂][NO₃]) =3×10⁻¹¹cm³/s at 298 K.

NO₃results from a reaction between O₃ and NO₂(see Reac. (3.17)), whose rate constant isk₁₇=3×10⁻¹⁷cm³/s. Di-nitrogen pentoxide immediately reacts with water, as follows:

N₂O₅+ H₂O(s)→ 2HNO₃. (3.15) Given the rate constantk₁₅, the extremely high concentrations of O₃and NO₂ in the filaments could generate up to 6×10¹⁴ molecules/cm³/s of NO₃, a produc-tion rate comparable with that of NO2 in our experiments. Considering the equi-librium constantK₁₂ and the reaction ratek₁₅ =3×10⁻⁴s⁻¹, Reactions (3.17), (3.14) and (3.15) clearly result in the generation of N₂O₅, hence HNO₃, in the ppm range. Binary HNO3−H2O clusters then form [83], which are known to grow into condensation nuclei and allow macroscopic droplets formation by net uptake of water from the surrounding atmosphere.

The trace gas production rates determined in laboratory were compatible with the measured mean concentrations in the field experiment (see Sec. 3.2.3), tak-ing into account the uncertainties due to the difficulty to quantify the rate of air exchange in the latter case. It is thus justified to assume that multi-ppm levels of HNO₃ were present in the filaments core in the outdoor experiments as well.

Thus, condensing molecules provided by Reactions (3.5) - (3.15) were in large excess as compared with observed particle densities of at most some 10³cm⁻³in

3.3 Complementary laboratory tests: trace gases and ion species

the field measurements. These results allowed the identification of this pathway as a plausible explanation for the observed laser-induced condensation in subsat-urated atmosphere, where the relevant species are generated in sufficient amounts sufficient to explain this effect.

The contribution of the extremely large HNO₃amounts has been thus incorporated into a standard droplets stabilization and growth model, the outcome of which will be showed in Sec. 3.4.

Estimation of error sources: reactions amongO₃andNO₂

In Eq. (3.3) the contribution of chemical reactions that occurred during the transit towards the sampling devices was neglected. A quantitative estimation of this contribution provides an evaluation of the associated error in the measurement.

NO and NO₂undergo oxidation by ozone following the reactions [6]:

NO+ O₃ → NO₂+ O₂ (3.16)

NO2+ O3 → NO3+ O2 (3.17)

Ozone can also degrade into oxygen by diluting in the sampling tubes or at the wall surface, as follows:

2O₃→ 3O₂ (3.18)

All these reactions imply ozone as well as NO consumption; as a consequence, the quantities measured for these species represented a lower limit of their real laser-generated amounts. The same trivial conclusion could not be drawn for NO₂, since Reactions (3.16) et (3.17) have opposite effects.

The estimation of the discrepancy between generated and measured trace gas amounts relies on the assumption that the rates of reactions, involving ozone and nitrogen oxides, depend on the square of their concentrations. This is jus-tified by the fact that such concentrations are roughly proportional, as displayed in Fig. 3.19. Under this assumption, for each speciesieq. (3.3) rewrites as follows:

V×dC_i

dt =S_i−k_iC_i²−C_i×F, (3.19) which brings, in the steady state:

C_i= (−F+p

F²+4k_iS_i)/2k_i. (3.20) Comparing results in two conditions with identical source term but different sam-pling rates yields:

k_i= (C_i,1F₁−C_i,2F₂)/(C_i,2² −C_i,1² ). (3.21)

Figure 3.19: Trace gases concentration (NO and NO₂) as a function of ozone concentration. Markers: experimental points. Solid lines: calculated linear fit.

Coefficients of determination of the fit are, respectively,R²=0.99 for NO₂ and R²=0.75 for NO.

In the case of ozone, we measured [O₃]₁ = 314 ppb for F₁ = 2.2 l/min and [O₃]₂ =385 ppb for F₂ =2.7 l/min, which yields k_O3 =4.5 l/min/ppm. Im-plementing this correction in the source term increases it at most by 10%: it can be concluded then that losses due to ozone depletion via chemical processes in the flow cell are a minor source of error, considering that our goal was to estimate the order of magnitude of HNO₃production.

Furthermore, [NO₂]₁ =124 ppb for F₁= 0.5 l/min and [NO₂]₂ = 32 ppb for F₂=2.7 l/min, result ink_NO2=1.7 l/min/ppm; the correction is limited to 1.3%, showing that for NO₂source and sink, respectively, Reactions ( 3.16) and ( 3.17) approximately balance each other.

The depletion of NO was estimated by considering the ratek₁₄=1.9×10⁻¹⁴cm³/s for Reaction 3.16 and the concentration retrieved in the filaments. We find a de-pletion rated[NO]/[NO]dt=k₁₄[O₃] =200 s⁻¹. As a consequence, the NO pro-duced is almost completely oxidized into NO2within 50 ms due to the extremely high ozone concentration. This confirms that Reaction (3.16) is far from being the limiting factor in the generation of HNO₃.

Therefore, the concentrations measured at the output of the cell, and hence pro-duction rates of O₃and NO₂, can be trusted within typically 10%. Moreover, the molecule concentrations in the filament volume (left scale in Fig. 3.18) rely on the estimation of typical filament diameters, which may be trusted within a fac-tor of 2. However, the excess of HNO₃ by orders of magnitudes as compared to the amounts required to explain the observed laser-induced water condensation ensures the validity of our conclusion in spite of this relatively large quantitative

3.3 Complementary laboratory tests: trace gases and ion species

Figure 3.20: Anionic content of laser-induced particles by ionic chromatography of aerosols impacted on filters with a pore of 15 nm (a), 50 nm (b) and 1µm (c).

In each panel filament-affected (signal) and background (reference) aerosols are compared [19]

.

uncertainty.