Water Vapor Dependence of the β-Hydroxyethyl Peroxy Self Reaction
4.3 Results & Discussion
4.3.4 Branching Fraction
As discussed in the introduction, the true magnitude of the self reaction rate enhancement may be stronger or weaker than that predicted by the trend in 𝑘𝑜𝑏𝑠 since α (the branching fraction to the radical propagating channel) may also depend on humidity.
Larger values of α result in additional HO2 production and faster secondary loss of β-HEP through R7 rather than through the self reaction. Since we observed a strong dependence of 𝑘𝑜𝑏𝑠 on water vapor concentration at 3.6 °C, we conducted additional studies at this temperature to measure α as a function of [H2O].
To determine α, we measured the ion signals of ethylene glycol (detected at 𝑚/𝑧 = 62, 10.75 eV) and HO2 (detected at 𝑚/𝑧 = 33, 11.75 eV). Ethylene glycol is a unique product of the radical terminating channel of the self reaction (R3a). HO2 is a unique product of the radical propagating channel (R3b) and is generated regardless of whether the alkoxy radical decomposes (R4 / R5) or reacts with O2 (R6). (Formaldehyde is also unique to the radical propagating channel but would be unsuitable for this analysis since it is only generated by decomposition and, as discussed in the next section, the fate of the alkoxy radical changes with humidity.) From the stoichiometry, the ratio of HO2
and ethylene glycol yielded by the self reaction is related to α through:
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[HO2]𝑦𝑖𝑒𝑙𝑑
[HOCH2CH2OH]𝑦𝑖𝑒𝑙𝑑 = 2α
1 −α (Eqn. 4)
where the subscript 𝑦𝑖𝑒𝑙𝑑 is used to denote the total concentration of this species generated by the β-HEP self reaction after the completion of chemistry.
Unfortunately, it is not possible to simply average the ion signals of HO2 and ethylene glycol at long reaction times to determine their yields. HO2 is reactive and has a variety of chemical loss processes (R7 and R8). Ethylene glycol is chemically stable, but exhibits considerable loss at the walls of the reactor. To determine the yields of these species, we empirically modeled their time-dependencies through a rate law composed of bimolecular production and first order loss. The production of neither species is truly bimolecular since the decay of β-HEP arises from both R3 and R7. Furthermore, in the case of HO2, the decay is not truly first order due to its participation in R7 and R8. (We note that production of HO2 is indeed rate-limited by the β-HEP self reaction due to the high [O2] and short lifetime of the alkoxy radical.) Despite these limitations, the time- dependencies of HO2 and ethylene glycol could still be reasonably approximated by this empirical model. The rate law is given by:
𝑑[𝑖]
𝑑𝑡 = 𝑘𝑖,𝑏𝑖[𝑋]02
(1 + 2𝑘𝑡𝑜𝑡𝑎𝑙,𝑏𝑖[𝑋]0𝑡)2− 𝑘𝑖,𝑙𝑜𝑠𝑠[𝑖] (Eqn. 5) where 𝑖 represents the target species, 𝑋 represents the species that is self reacting to produce 𝑖, 𝑘𝑖,𝑏𝑖 is the rate constant of the 𝑋 self reaction channel that yields 𝑖, 𝑘𝑡𝑜𝑡,𝑏𝑖 is the total 𝑋 self reaction rate constant, and 𝑘𝑖,𝑙𝑜𝑠𝑠 is the first order loss rate of 𝑖. If we define 𝐶𝑖 as a scale factor between ion signal and concentration, then the ion signal is 𝑆𝑖 = [𝑖] ∙ 𝐶𝑖 and the rate law can be rewritten as a differential equation that describes the time-dependence of the ion signal:
𝑑𝑆𝑖
𝑑𝑡 = 𝐶𝑖𝑘𝑖,𝑏𝑖[𝑋]02
(1 + 2𝑘𝑡𝑜𝑡𝑎𝑙,𝑏𝑖[𝑋]0𝑡)2− 𝑘𝑖,𝑙𝑜𝑠𝑠𝑆𝑖 (Eqn. 6) There is no straightforward analytical solution to Eqn. 6. We therefore modeled the product ion signals by numerically integrating Eqn. 6 with 𝑆𝑖(0) = 0 as the initial condition.
Three-parameter fits were performed to each signal to optimize the values 𝐶𝑖𝑘𝑖,𝑏𝑖[𝑋]02, 2𝑘 [𝑋] , and 𝑘 . Division of the first parameter by the second parameter gives
155 𝐶𝑖∙ (𝑘𝑖,𝑏𝑖⁄𝑘𝑡𝑜𝑡,𝑏𝑖) ∙ ([𝑋]0⁄ ), which is equal to the yield of 𝑖 generated by the self reaction 2 expressed in ion signal units. This analysis was performed on kinetic traces of HO2 and ethylene glycol to approximate their yields generated by the β-HEP self reaction; example time-resolved ion signals and fits are presented in Figure 8ab.
The ion signal yields of HO2 and ethylene glycol were determined at each [H2O].
Their ratio, which is proportional to [HO2]𝑦𝑖𝑒𝑙𝑑⁄[HOCH2CH2OH]𝑦𝑖𝑒𝑙𝑑, is plotted in Figure 9a relative to the [H2O] = 0 case. We see that this ratio decreases by ~90% across the range of [H2O] utilized (up to RH = 18%), implying that the radical terminating channel of the β-HEP self reaction is being enhanced relative to the radical propagating channel.
However, while the ratio of the ion signal yields provides a qualitative trend, the ratio of the concentration yields is necessary to use Eqn. 4 and calculate α. We determined the proportionality constant between concentration and ion signal ratios by assuming our data at [H2O] = 0 is consistent with a prior measurement of α = 0.5 for the dry self reaction.25 (While the prior study was conducted at 22 °C and this data was collected at 3.6 °C, we measured little difference in 𝑘𝑜𝑏𝑠 between 3.6 and 26.6 °C when [H2O] = 0, suggesting that dry α = 0.5 is also valid at 3.6 °C.) This enabled calculation of α when [H2O] > 0, effectively relative to the dry case. The resulting values of α are plotted as a function of water vapor concentration in Figure 9b.
The value of the branching fraction decreases from α = 0.5 under dry conditions to α ≈ 0.1 at the maximum [H2O] = 3.7 x 1016 molc cm-3 (RH = 18%) used in experiments conducted at T = 3.6 °C. The radical terminating channel (R3b) is therefore significantly enhanced relative to the radical propagating channel (R3a) when β-HEP is complexed with water. This is consistent with enhancement of the inorganic HO2 self reaction by water vapor,4,9,10 which has only a radical terminating channel. Because the relative yield of secondary HO2 decreases with increasing humidity, the true enhancement of the self reaction rate constant is even greater than the enhancement implied by the trend in 𝑘𝑜𝑏𝑠, since a greater fraction of the β-HEP decay is now explained by the self reaction rather than secondary chemistry.
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