Room Temperature Measurements
Typical concentration–time profiles of the singlet and triplet species of NCN are shown in Fig. 1. Note that the intense photolysis laser pulse causes a small background signal in the absorption profiles, which can be attributed to thermal effects. It is already discernible in the first μs before the actual initial rise of the signals takes place and causes an absorption plateau at longer reaction times. This interfering signal has also been observed, if to a lesser extent, in experiments in pure argon and was dependent on the adjustment of the optical setup. On the timescale of the kinetic experiments, it could be treated as a constant offset of the baseline. Following the photolysis of NCN3, the singlet signal exhibits a fast rise and subsequently a slower decay. The 3NCN profile is a little bit more complex. As can be seen in the inset of Fig. 1, a pronounced induction period on the order of 10 μs is followed by a steep rise of absorption, which then continues with a slower rate. At long reaction times, the signal starts to decay slowly.
Figure 1. Comparison of 1NCN and 3NCN concentration–time profiles and the corresponding fits at room temperature and p=56 mbar. t=0 corresponds to the excimer laser photolysis pulse. Note the pronounced offset (dashed line), which affects both singlet and triplet signals. The inset shows a magnification of the first 100 μs of the same signals.
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A simple model describes the singlet measurements: Vibrationally and electronically excited 1NCN radicals, denoted 1NCN*, are generated by the laser photolysis of NCN3. According to Bise et al. 41, a rich variety of six 1NCN electronic states is accessible following the 193-nm photolysis of NCN3. This excited 1NCN* is collisionally deactivated to its lowest electronic singlet state (1Δg), in which 1NCN is detected. This deactivation process is reflected by the fast increase in the signal. The slower decay of the signal can be attributed to several processes. Next to singlet–triplet relaxation via CIISC, 1NCN may also disappear through fast bimolecular reactions. Next to a self-reaction, 1NCN + 1NCN, the reactions with CN radicals and N atoms, which are also formed in the photolysis, are conceivable. Also radiative contributions cannot be completely ruled out. In contrast, diffusional loss can be assumed to be of minor importance since the decay of the 3NCN signal is much slower than that of the 1NCN signal and diffusion rates can be supposed to be similar for both species.
Apart from the instrumental offset, the 3NCN signal indicates three phases: The first phase comprises the initial induction time followed by the steep increase of the signal. We attribute this first phase to the direct relaxation of initially formed highly excited NCN radicals. For example, according to Baumgärtel et al. 42, even vibrationally excited 3NCN* can be directly generated in the spin-allowed photolysis process
The reported threshold energy of 190 nm is close to the used photolysis wavelength of 193 nm, thus a direct formation of 3NCN in the 193 nm photolysis via the spin-allowed reaction (2b) cannot be ruled out. It is also feasible that fast ISC processes of electronically and/or vibrationally highly excited 1NCN* radicals yield significant amounts of 3NCN*.
The second phase of the triplet signal comprises the slower rise taking place on the same timescale as the 1NCN decay. This part of the signal can be attributed to the formation of 3NCN following the CIISC process of vibrationally thermalized 1NCN radicals in their lowest electronic singlet state. From this point of view, the corresponding 3NCN formation should approximately match the 1NCN decay rate; in accordance with the signals shown in Fig. 1.
Finally, the third phase comprises the slow decay of the 3NCN signal at longer reaction times. It subsumes all NCN consuming processes such as self-reactions, reactions with other photodissociation or secondary products, and diffusion.
In the light of the limited experimental insight into the mechanistic details of the ongoing vibrational relaxation processes, 1NCN concentration–time profiles have been evaluated by a simple model of consecutive first-order processes capturing the main features of the reaction system. An analytical function was fitted to the measured profiles, and the measured instrumental offset was added as a constant.
The appearance rate constant kapp reflects k3b, and the consumption rate constant kcon corresponds to the sum of k3c and k4. Here, [1NCN*]0 denotes the initial concentration of vibrationally excited 1NCN* that is formed in the photolysis and is thermalized to 1NCN(1Δg) through reaction (3b). Note that an additional fraction of 1NCN* that may have been directly transformed to 3NCN* escapes from our 1NCN detection scheme. t0 has been introduced to account for the small pressure-dependent induction times on the order of 1–10 μs. More sophisticated models intended to extract an additional rate constant to fit these induction times turned out to be numerically unstable.
A plot of the determined 1NCN formation rate constants kapp is shown in Fig. 2. The experimental conditions and results are listed in the Supporting Information. The fact that the rate linearly depends on the total pressure and does not show any dependence on the initial NCN3 concentration reveals a simple collisional deactivation process. The slope of the regression line yields a bimolecular room temperature rate constant of
Actually, this rate constant value is untypically low for a simple vibrational relaxation process, which often proceeds close to the collisional limit. As already outlined above, several electronic states are involved in the 193-nm photolysis of NCN3. Consequently, it is feasible that rather slow electronic deactivation steps are subsumed in the measured overall relaxation rate constant.
Figure 2. Pressure dependence of the 1NCN formation rate constants following the 193-nm photolysis of NCN3 at room temperature.
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The decay of the 1NCN signal is assumed to reflect the sum of the 1NCN consuming processes, presumably dominated by CIISC. The corresponding rate constants kcon are shown in Fig. 3 and will be discussed below together with the results from the triplet measurements.
Figure 3. Pressure dependences of the rate constants associated with the CIISC process. The data represent the room temperature singlet decay rates as well as the slow component of the 3NCN formation following the 193-nm photolysis of NCN3. The solid line corresponds to a linear fit of the 3NCN data at p>20 mbar, and the dashed curve indicates the falloff-like low-pressure behavior.
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For fitting the triplet signals, the fast and slow components were treated as two independent processes with the rate constants kfastapp and kslowapp. According to the presented reaction scheme, the triplet species concentration–time profile is given by
Here, [1,3NCN*]0 refers to the fraction of initially formed highly excited singlet and triplet NCN* that directly forms 3NCN through reactions (2b), (3a), and (3d). Hence, it does not include initial 1NCN* that is thermalized within the singlet system. This latter fraction is termed [1NCN]0 and is further deactivated to the triplet ground state via CIISC. Although the experimental induction times are not necessarily equal for the fast and the slow processes, only one t0 value was used in the fits. Again, kcon subsumes secondary NCN reactions and diffusion.
The extracted rate constants of the slow component of the 3NCN appearance are summarized together with the 1NCN decay rate constants in Fig. 3. Data of the experimental conditions and results are listed in the Supporting Information. Overall, the singlet and triplet data show reasonable agreement with respect to absolute rate constant values as well as the observed pressure dependence. Thus, both rate constants can be assumed to represent the same process, namely CIISC. A simple linear fit of the 3NCN experiments at p>20 mbar roughly represents the overall pressure dependence of all data. It yields a high intercept value of k=4.5 × 103 s−1 at p=0 mbar. However, this intercept cannot be attributed to radiative processes in terms of a simple Stern–Volmer plot. Instead, as it is discernible from the 3NCN data at pressures p<20 mbar, the rate constants indicate a downward trend, which is not reflected by the simple linear fit. To guide the eye, the dashed curve in Fig. 3 represents this low-pressure behavior of the triplet data (circles). Unfortunately, due to experimental constraints, we were not able to perform measurements at even lower pressures to further verify this low-pressure trend. However, the depicted dashed curve is in agreement with the expected pressure dependence of a CIISC process. As outlined in the Introduction, the pressure dependence often changes its nature from a Stern–Volmer like behavior at low pressures to a weaker pressure dependence or pressure saturation at higher pressures. For example, a more detailed analysis of similar data has been presented by Strickler and Rudolph for the quenching of the 3B1 state of SO2 26. In their work, radiative and nonradiative pressure independent relaxation processes as well as the pressure dependent CIISC have been analyzed. For SO2 diluted in CO2 or N2, the CIISC process has been found to govern the relaxation and could be rationalized with a simple kinetic model similar to the well-established models for unimolecular reactions. Low-pressure and high-pressure regimes were identified, resulting in a pressure saturation effect of the relaxation rate constants toward higher pressures. Qualitatively spoken, the triplet data shown in Fig. 3 are consistent with such a model. Of course, the details of the “falloff”-like behavior strongly depend on the nature of the collider gas and the particular system under study 20,27.
Note that the overall pressure dependence of the data extracted from the 1NCN concentration–time profiles does not satisfy the discussed falloff-like trend. As already mentioned above, high electronic states are involved in NCN3 photodissociation at 193 nm. Relaxation processes of these states may have interfered with our simplified data analysis, and therefore the 1NCN data are less reliable. More sophisticated experiments with variable photolysis wavelengths and state resolved detection schemes would have been needed to gain further insight into the complicated dynamics of the initially formed highly excited species. Clearly, such measurements would have been beyond the scope of this study.
High -Temperature Measurements
1NCN High-Temperature Cross Section. 1NCN has been detected at high temperatures behind shock waves for the first time. The thermal decomposition of NCN3 behind shock waves was used as a source of 1NCN. Since the high-temperature detection of 1NCN is new and absorption cross sections are unknown, a part of the high-temperature spectrum of 1NCN has been measured behind incident shock waves at a temperature of T≈ 740 K and a pressure of p≈ 390 mbar, beforehand. The resulting spectrum is shown in Fig. 4. Each single data point is based on a separate shock tube experiment with the detection laser tuned to the respective wavelength. The spectrum is dominated by the band head of the 1Πu−1Δg transition of the (000)−(000) vibrational ground state. Compared to the room temperature spectrum 33,19, the band head is slightly shifted by ≈ 0.1 cm−1 toward lower wave numbers. All high-temperature kinetic measurements have been performed in the region of the absorption plateau at a wave number of 30,045.46 cm−1. Based on absolute 1NCN concentrations derived from the kinetic simulations outlined in the next section, temperature-dependent 1NCN absorption cross sections could be determined in the temperature range 618 K <T< 1231 K. A plot of the absorption cross sections versus temperature is shown in Fig. 5. Experiments have been performed at two different total densities. Although the lower density data points seem to be systematically higher by approximately 25%, in the light of the uncertainties of the mechanistic model, this pressure dependence is not significant. The data can be best represented by
A ±50% error results from uncertainties in the initial NCN3 concentrations, the modeled intermediate 1NCN concentrations, and the statistical error of the fit.
Figure 4. Part of the high-temperature spectrum of 1NCN. Shown is the band head of the 1Πu(000)-1Δg(000) transition.
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Owing to the broad absorption feature stemming from the overlap of many rovibrational lines, 1NCN absorption cross sections exhibit a rather weak temperature dependence. Both the absorption cross sections of 1NCN and of 3NCN are on the same order of magnitude. At T=1000 K, σ(3NCN)=1 × 108 cm2/mol, and σ(1NCN)=3 × 107 cm2/mol. Therefore, the unusual situation arises that both the electronic ground state and the excited state of a radical can be detected behind shock waves with comparable sensitivities. Performing kinetic measurements at similar experimental conditions simplifies the data evaluation and enhances the reliability of the derived models.
1NCN Measurements. A typical 1NCN concentration–time profile is shown in Fig. 6. Time zero is set by the Schlieren signal, which indicates the arrival of the incident shock wave. The width of the Schlieren signal roughly defines the time resolution of the experiments, in this work Δ t≈ 4 μ s. The formation of 1NCN is determined by the thermal decomposition of the precursor molecule NCN3. In contrast to the room temperature photolysis experiments, the thermal generation of 1NCN does not require relaxation of highly excited 1NCN* species. Within the time resolution of the experiments, no induction times have been observed. The 1NCN decay can be directly attributed to the CIISC process. Alternative loss processes such as secondary chemistry should not play a role due to the low concentration levels present in the experiments. For example, a simulation assuming a very high rate constant of k=1 × 1014 for the potential reaction 1NCN + 1NCN resulted in an only 10% lower value for the CIISC rate coefficient. Furthermore, the single exponential decays revealed a dominating (pseudo)–first-order process such that there is only little room for a significant contribution of any second-order reaction.
At longer reaction times, a small background absorption signal remains, which can be attributed to interfering 3NCN absorption. A slow decay of this weak background signal observed in validation experiments with much higher NCN3 mole fractions is consistent with NCN loss from the bimolecular reaction 3NCN + 3NCN. The concentration–time profiles were analyzed based on a simple consecutive first-order kinetics scheme according to
was fitted to the profiles by adjusting the rate constants of reactions (2), NCN3 → NCN + N2, reaction (3), 1NCN → 3NCN, and the amplitude of the function, which is determined by [NCN3]0. The second term the equation takes into account the interfering background absorption of the formed 3NCN, where f≈ σ(3NCN)/σ(1NCN).
A complication arose from the strong correlation between the two rate constants k2 and k3, which precluded their reliable determination at temperatures of T<770 K. Therefore, k3 has been extracted only from experiments at temperatures T>770 K, where the two processes were clearly separable. Then, by using extrapolated k3 values at lower temperatures, it was possible to extract reliable values for k2 at T<770 K, as well.
An Arrhenius plot of the obtained rate constants is shown in Fig. 7. Experiments have been performed in the temperature range 617 K <T< 1239 K at two different total densities: ρlow ≈ 3 × 10−6 mol/cm3 and ρhigh ≈ 6 × 10−6 mol/cm3. Data of the experimental conditions and results are listed in the Supporting Information. The rate constants are best represented by the following expressions (solid lines):
An error estimate of ± 30% holds for all expressions. It is based on a combination of statistical errors and a consideration of systematic errors of temperature, total density, and initial NCN3 concentration. The errors of the Arrhenius activation energies are ± 14 kJ/mol for reaction (2) and ± 7 kJ/mol for reaction (3). The rate constants k2 of the thermal decomposition of NCN3 have been determined up to temperatures of T=867 K. At higher temperatures, the too fast increase of the signal could not be resolved. With an activation energy of Ea=71 kJ/mol, the temperature dependence of the unimolecular decomposition of NCN3 is much stronger than the temperature dependence of the CIISC process. Consequently, at a temperature of T ≈ 650 K, the dominant reaction for the 3NCN formation switches from the NCN3 decomposition at low to CIISC at high temperatures. Regarding the density dependence, with 1.5 times higher rate constants at a doubled total density, the unimolecular decomposition process takes place in the falloff region. With a factor of 1.4, the CIISC process exhibits a similar pressure dependence. Keeping in mind the elevated pressures behind shock waves, this is in agreement with the pressure saturation effect already discussed in connection with the room temperature experiments.
Figure 7. Arrhenius plot of the rate constants of the NCN3 decomposition and the CIISC process at two different total densities ρ. The dashed lines denote the extrapolation of the rate constants to lower temperatures.
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In our recent paper 15, we reported an activation energy of Ea=93 kJ/mol for the thermal decomposition of NCN3. This value was based on a combination of quantum-chemical (G3) and statistical (RRKM) calculations. Although with 22 kJ/mol the difference between our previous value and the value reported in this work is not extensive, the reason for this deviation remains unclear. We suspect inaccuracies in our calculated threshold energy E0, which had been determined by the composite method G3. This method includes empirical scaling factors that might not be perfectly matched for the molecules NCN3 and NCN. Therefore, we recommend the experimentally based expressions reported in this work for future use.
3NCN Measurements. 3NCN concentration–time profiles have been measured behind incident shock waves in the temperature range 582 K <T< 1257 K at three different total densities. Some of these measurements have already been discussed in our recent publication 15. In this work, we further extended the database and reevaluated all data by taking into account the newly determined decomposition rates of NCN3 from the 1NCN experiments. A typical 3NCN signal together with a numerical simulation and the corresponding sensitivity analysis is shown in Fig. 8. In addition to the two reactions shown in the sensitivity analysis, our recent NCN mechanism 16 comprising many potentially interfering reactions and the GRI-Mech. 3.0 43 natural gas mechanism have been used as a background chemistry. After a short induction period, which can be attributed to the pyrolysis of the precursor molecule, the signal increases until it reaches a constant plateau value. The fact that a stable 3NCN concentration plateau is reached reveals that interfering secondary chemistry does not play a role for the experiment shown in Fig. 8. The sensitivity analysis illustrates that both the assumed rate constants for the NCN3 decomposition (2) and the CIISC process (3) are important at short reaction times. However, being able to keep k2 fixed as determined from the 1NCN measurements, k3 values could be reliably extracted by fitting the overall 3NCN formation rate. Data of the experimental conditions and results are listed in the Supporting Information. In Fig. 9, determined rate constant data are compared to the results of the singlet experiments. The singlet results have been adopted from Fig. 7 and are shown as dashed lines. The solid lines represent the Arrhenius expressions (701 K <T< 1256 K) of the triplet data measured at three different total densities of ρ1 ≈ 1.8 × 10−6 mol/cm3, ρ2 ≈ 3.5 × 10−6 mol/cm3, and ρ3 ≈ 7.0 × 10−6 /cm3:
An error estimate of ± 20% holds for all expressions. It is based on combined uncertainties of k2 and statistical errors. The Arrhenius activation energies are accurate to ± 10 kJ/mol. This rather large error results from the fact that only the low-temperature data points are systematically affected by the uncertainty of k3. At higher temperatures, the NCN3 decomposition becomes very fast, and the signal directly reflects the CIISC relaxation rate constant.
Figure 8. Top: Typical 3NCN signal at experimental conditions similar to the conditions of the 1NCN experiment shown in Fig. 6. The NCN3 decomposition process is discernible as a short induction time. The solid curve represents the numerical simulation of the reaction system. Bottom: Corresponding sensitivity analysis.
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Figure 9. Arrhenius plot of CIISC rate constants extracted from the triplet concentration-time profiles. Solid lines: Arrhenius fit of the measured data points. Dashed lines depict the results from the 1NCN measurements as shown in Fig. 7.
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In contrast to the 1NCN data, the activation energies seem to depend on the total density ρ. However, given the rather large error margin of the Arrhenius activation energies, all data can be assumed to yield essentially the same temperature dependence with an average activation energy of Ea=30 kJ/mol. Although there seems to be a significant offset between the 1NCN and the 3NCN data, especially at ρ=3.5 mol/cm3, the remaining discrepancies are <35% and thus within the combined error limits of the two measurements. As outlined above, a significant influence of 1NCN secondary chemistry that might have caused an overestimation of the relaxation rate in the 1NCN measurements is unlikely. Instead, we ascribe the offset to a numerical effect stemming from the fitting procedures used to separate the strongly correlated k2 and k3 values. Overall, the good agreement between the singlet and triplet data sets underlines our initial assumption that both the decay of the 1NCN and the increase in the 3NCN profiles directly reflect the CIISC process.