SM3 Modeling and Calibration of Instrument Effects

Absolute Photoionization Cross Sections of ClO and ClOOCl

2.9. SM3 Modeling and Calibration of Instrument Effects

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61 and evaluating at the interval midpoint. To simulate the concentration profile of each species 𝑖 arising from the chemistry in the model (𝑁_𝑖^chem), the system of differential rate equations was integrated in steps. For 𝑡 < 0, each 𝑁_𝑖^chem(𝑡) was set to its pre-photolysis concentration. For the 0-1 ms interval, the model was integrated over 0-1 ms, and the result appended to 𝑁_𝑖^chem(𝑡). For the 1-2 ms interval, the model was integrated over 0-2 ms, and the 1-2 ms portion was appended to 𝑁_𝑖^chem(𝑡). For the 2-3 ms interval, the model was integrated over 0-3 ms, and the 2-3 ms portion was appended to 𝑁_𝑖^chem(𝑡). This process was repeated out to 60 ms.

One consequence of this approach is that discontinuities are created at the edges of each time interval. However, because the photolysis gradient is small, the initial radical concentration is similar between adjacent intervals and the discontinuities are imperceptible after convolution with the temporal instrument response function described in the next subsection.

2.9.SM3.2 Temporal Instrument Response

Species sampled from the molecular beam have a distribution of velocities that has been shown to approximate a Maxwell-Boltzmann distribution.⁷ The distribution is mass- dependent, with species of greater mass having a broader velocity distribution than those of smaller mass. Due to the finite transit time between exiting the pinhole and detection, ion signal recorded at time 𝑡 arises from neutrals sampled from the reactor at a distribution of times less than 𝑡. In practical terms, changes in the ion signal intensity measured for a species appear slower than true concentration changes of that species within the reactor.

This effect must be integrated into our model in order to accurately compare concentration profiles to time-resolved ion signals and determine cross sections. For a species exiting the reactor at time 0, its distribution of arrival times (𝑡^′) at the detector is proportional to ℎ_𝑖(𝑡^′):⁵

ℎ_𝑖(𝑡^′) =exp(𝐴_𝑚𝑖⁄𝑡^′2)

𝑡^′4 (5)

where 𝑡^′ > 0 (species cannot be detected before they exit the reactor) and 𝐴_𝑚𝑖 = 𝐴 ∙ 𝑚_𝑖. 𝐴 is a negative, mass-independent instrument constant describing the temporal response.

Larger absolute values of 𝐴 indicate a broader distribution of detection times (slower

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response) than smaller absolute values of 𝐴. After integrating the chemical kinetic model to determine 𝑁_𝑖^chem(𝑡), we convolve each profile with the instrument response according to:

𝑁_𝑖(𝑡) =∫_−∞^𝑡 𝑁_𝑖^chem(𝑠)ℎ_𝑖(𝑡 − 𝑠)𝑑𝑠

∫_−∞^𝑡 ℎ_𝑖(𝑡 − 𝑠)𝑑𝑠 (6)

where 𝑁_𝑖(𝑡) is the simulated concentration profile for comparison to the time-resolved ion signal. The denominator in Eqn. 6 acts as a normalization factor. 𝑁_𝑖(𝑡) is effectively a weighted average of the concentration within the reactor across all times less than 𝑡, with the weighting set by the distribution of arrival times.

2.9.SM3.3 Photolysis Offset

This effect is a simple offset (𝑡₀) between the predicted and actual firing of the photolysis laser. Concentration profiles are simulated assuming photolysis occurs at 𝑡 = 0.

After these profiles are convolved with the temporal instrument response (Eqn. 3), the model time axis is shifted by 𝑡₀ such that photolysis occurs at 𝑡 = 𝑡₀, in proper correspondence with the data time axis.

2.9.SM3.4 Calibration Experiments

The instrument parameters 𝐴, 𝐵, and 𝑡₀ require calibration in order to simulate 𝑁_𝑖(𝑡) for ClO and ClOOCl. We determined these instrument constants at 300 and 210 K by 351 nm photolysis of a sample of NO2 diluted in He:

NO2 + hv → NO + O (R1)

The O atoms react with the excess NO2 precursor according to:

O + NO2 → NO + O2 (R2)

O + NO2 + M → NO3 + M (R3)

At the total pressure of 50 Torr and both temperatures, R2 substantially dominates over R3. The total rate constant for the O + NO2 reaction is 1.0 x 10^-11 and 1.5 x 10^-11 cm³ molc^-

1 s^-1 at 300 and 210 K, respectively.⁸ With the [NO2] used in these experiments, this leads to an O atom lifetime of 𝜏 < 90 µs. Since the data points are binned to 200 µs spacing, the concentration profile of the NO produced from R1 and R2 should appear as a step-function in the absence of any instrument effects, with the step occurring at 𝑡 = 0. Deviations of the

+

63 The NO⁺ signals measured at 300 and 210 K are presented in Figure S3. As expected, the signal rises gradually after photolysis, rather than exhibiting a discrete step, due to the temporal instrument response. After the initial fast rise, the signal has a slower, linear rise due to the photolysis gradient. We first determined 𝐵 from a linear regression over 20–60 ms. By the definition given in Eqn. 3, 𝐵 is equal to the fitted slope divided by the fitted intercept. We neglected the first 20 ms to avoid any bias from the initial rise of signal. Over 20–60 ms, the change in signal due to the photolysis gradient is much slower than the instrument response.

We next determined 𝐴 and 𝑡₀. A simple kinetic model was constructed describing the [NO] as a step function. 𝐵 was fixed at the value determined from the linear regression.

Initially, we performed three-parameter fits, simultaneously floating 𝐴, 𝑡₀, and the NO signal after the step (𝑆_NO,∞). However, due to the strong correlation between 𝐴 and 𝑡₀, fits would typically terminate at a local minimum close to the initial guess. In order to find the global minimum across this parameter space, we performed a series of two-parameter fits, in which 𝑡₀ was fixed and stepped through an array with 0.01 ms spacing, while 𝐴 and 𝑆_NO,∞ were floated. The 𝐴 and 𝑡₀ that led to a global minimum in the residual sum of squares were taken as the instrument parameters. Overlaid on the traces in Figure S3 are the simulated signals from the step-function model implementing the optimized values of 𝐴, 𝐵, and 𝑡₀.

The values of 𝐴 and 𝑡₀ determined at the two temperatures were similar. However, the value of 𝐵 at 210 K was found to be ~4 times greater than the value at 300 K. This is not due to a difference in the photolysis gradient at the two temperatures, but rather an artifact that arises from the dimerization of NO2 at cold temperatures. While the rate constant for NO2 dimerization is not known at 210 K, extrapolation of available data suggests that dimerization has a half-life of order ~100 ms at our conditions.⁹ This is sufficiently long that fresh NO2 dimerizes as it flows through the reactor, leading to a spatial gradient in [NO2]. Since the [NO] produced upon photolysis is proportional to [NO2], this yields an additional gradient in initial radical concentration on top of that generated by divergence of the photolysis beam. To explore this effect, we conducted experiments by flowing different [NO2] through the reactor. Because the dimerization is pseudo bimolecular, changing [NO2] should result in a different dimerization half-life, and

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thus different kinetics. The NO⁺ signals measured in these experiments are presented in Figure S4. Despite having approximately the same signal level immediately after photolysis, the shapes of the traces diverge at longer times, reflecting the different rates of NO2 dimerization.

This effect does not impact our experiments studying ClO and ClOOCl because the radical precursor, Cl2, is stable at 210 K. The gradient in initial radical concentration in those experiments arises solely from divergence of the photolysis beam. The studies at 300 and 210 K were conducted using the same alignment of the beam through the reactor tube and the rate of divergence does not depend on temperature. We therefore assumed in our 210 K model of ClO and ClOOCl kinetics that the value of 𝐵 was the same as the value determined from 300 K NO2 photolysis. We note that the values of 𝐴 and 𝑡₀ determined from 210 K NO2 photolysis were not impacted by NO2 dimerization since the value of 𝐵 used in those fits encompassed both gradients (Figure S3b).

The final values of 𝐴, 𝐵, and 𝑡₀ determined from the NO2 photolysis experiments and used to model ClO and ClOOCl kinetics are presented in Table SII. The instrument response was slightly slower at 210 K than at 300 K, although only to a minor extent.

Table SII: Values of temporal response (𝐴), photolysis gradient (𝐵), and photolysis offset (𝑡₀) instrument parameters used to model ClO and ClOOCl concentration profiles.

T (K) 𝑨 (ms² amu^-1) 𝑩 (ms^-1) 𝒕_𝟎 (ms)

300.6 ± 0.9 -0.0306 0.00271 -0.60

210 ± 3 -0.0377 0.00271 -0.63

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Figure S3: NO⁺ signals (blue) recorded in experiments photolyzing NO2. The step- function model implementing optimized values of the instrument parameters is overlaid (black). (a) 300 K, 10.0 eV, and [NO2] = 3.74 x 10¹⁵ molc cm^-3. The fitted value of 𝐵 = 0.00271 ms^-1 corresponds to an initial radical concentration gradient arising from solely divergence of the photolysis beam. (b) 210 K, 10.1 eV, and [NO2] = 7.67 x 10¹⁴ molc cm^-3. The fitted value of 𝐵 = 0.0103 ms^-1 corresponds to an initial radical concentration gradient arising from divergence of the photolysis beam and a gradient in the NO2 precursor concentration.

Figure S4: NO⁺ signals recorded at 210 K and 10.1 eV in experiments photolyzing different concentrations of NO2.

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