Morgan E.
Balabanoff
,
Mahmut
Ruzi
and
David T.
Anderson
*
Department of Chemistry, University of Wyoming, Laramie, WY 82071, USA. E-mail: danderso@uwyo.edu
First published on 30th November 2017
We are studying the details of hydrogen atom (H atom) quantum diffusion in highly enriched parahydrogen (pH2) quantum solids doped with chemical species in an effort to better understand H atom transport and reactivity under these conditions. In this work we present kinetic studies of the 193 nm photo-induced chemistry of methanol (CH3OH) isolated in solid pH2. Short-term irradiation of CH3OH at 1.8 K readily produces CH2O and CO which we detect using FTIR spectroscopy. The in situ photochemistry also produces CH3O and H atoms which we can infer from the post-photolysis reaction kinetics that display significant CH2OH growth. The CH2OH growth kinetics indicate at least three separate tunneling reactions contribute; (i) reactions of photoproduced CH3O with the pH2 host, (ii) H atom reactions with the CH2O photofragment, and (iii) long-range migration of H atoms and reaction with CH3OH. We assign the rapid CH2OH growth to the following CH3O + H2 → CH3OH + H → CH2OH + H2 two-step sequential tunneling mechanism by conducting analogous kinetic measurements using deuterated methanol (CD3OD). By performing photolysis experiments at 1.8 and 4.3 K, we show the post-photolysis reaction kinetics change qualitatively over this small temperature range. We use this qualitative change in the reaction kinetics with temperature to identify reactions that are quantum diffusion limited. While these results are specific to the conditions that exist in pH2 quantum solids, they have direct implications on the analogous low temperature H atom tunneling reactions that occur on metal surfaces and on interstellar grains.
It is believed10–19 that H atoms tunnel between adjacent lattice sites in solid pH2 by a chemical mechanism that is based on the simplest chemical reaction, H + H2 → H2 + H. Given that the activation barrier20 for this chemical reaction is 9.60 kcal mol−1 (3360 cm−1), at low temperature the only way the H atom can “quantum diffuse” is by repeated tunneling jumps through the reaction barrier. From a chemistry perspective, this means that H atom reactions with chemical dopants in solid pH2 can continue to occur even at the lowest achievable temperatures because the H atom retains its mobility through quantum effects (tunneling). Evidence of quantum diffusion in surface studies is usually provided by the observation of temperature independent diffusion rates.21 The transition at low temperature from classical thermally activated hopping (Arrhenius-type temperature dependence) to quantum tunneling (temperature independent) typically occurs in the range of 60–140 K for H atoms on metal surfaces.22 Observation over such a large temperature range is not possible in solid pH2 where the solid starts to rapidly sublime at temperatures above 5 K. Similarly, H atom reaction studies conducted in rare gas matrices can only be conducted over limited temperature ranges, but usually the H atoms only diffuse at appreciable rates in the classical thermal hopping range.9 The chemical physics in the quantum diffusion range should be distinct from the thermal hopping regime because the diffusion is governed by quantum mechanical phenomena. We therefore expect that quantum diffusion limited chemistry of H atoms with other chemical species in solid pH2 will show both interesting temperature effects and reaction products. Indeed, we have now documented a series of H atom reactions with N2O, HCOOH, and NO that show novel temperature effects and products.6–8,23
In this study we focus on investigating reactions of H atoms with methanol (CH3OH). The photochemistry and low temperature surface reactions of this chemical system (H + CO) have been well studied due the abundance of CH3OH in a variety of astronomical environments.4,24 To do this we rely on the 193 nm in situ photochemistry of methanol (CH3OH) in solid pH2 to generate H atoms. At this photon energy there are five open dissociation channels, namely,25,26
CH3OH + hν(193 nm) → CH3O + H | (1a) |
→ CH2OH + H | (1b) |
→ CH3 + OH | (1c) |
→ CH2 + H2O | (1d) |
→ CH2O + H2 | (1e) |
CH3O + H2 → CH3OH + H → CH2OH + H2 | (2) |
Our interest in the 193 nm in situ photochemistry of CH3OH in solid pH2 is motivated by our desire to study the H + CH3OH → CH2OH + H2 tunneling reaction.28,31 As discussed, if photochannel (1a) is dominant, along with the generation of CH3O is the production of H atoms. Further, because some of the primary photolysis products (CH3O and CH2OH) are also photolabile at 193 nm, there can be additional H atom production from secondary photolysis events. We can test for the presence of H atoms using the tunneling reaction of H atoms with CH3OH to produce CH2OH. By conducting these photolysis experiments such that CH3OH is the most concentrated species after photolysis, repeated FTIR scans after photolysis can be used to indirectly monitor the H atom concentration via the tunneling reaction with CH3OH. We can study the reaction kinetics as a function of temperature over the experimental range (1.7 to 4.3 K) to further explore the details of H atom quantum diffusion. That is, because the H + CH3OH reaction is a bimolecular reaction that requires both reactants to be in adjacent lattice sites to react, the reaction kinetics are likely controlled by how fast and to what extent the two reaction partners diffuse next to each other. As we will show, reactions that rely on H atom quantum diffusion to occur can display anomalous temperature effects. Specifically, this type of reaction may only occur at low temperature and not at high temperature over this small range. This can be the result of changes in the microscopic details of H atom quantum diffusion over this small temperature range. Specifically, non-resonant tunneling jumps can be accommodated by one- and two-phonon processes that might steer the H atom differently towards a potential reaction partner.32–34 This is still an active area of research and in these studies we will show evidence for H atom reactions with CH3OH that only occur at 1.8 K, and not 4.3 K.
(3) |
Photolysis is achieved using the 193 nm output of an ArF excimer laser (Gam Laser EX5) configured to pass through the sample at an angle of 45° with respect to substrate surface normal. This optical setup permits FTIR spectra to be recorded within the photolyzed region of the crystal either during or immediately after 193 nm irradiation. The typical experimental procedure is to photolyze a CH3OH/pH2 sample at a specified temperature for a short period of time and then record repeated FTIR spectra with short acquisition times to measure the ensuing low temperature kinetics. In this study we used two different FTIR configurations. To characterize the as-deposited sample we used a liquid nitrogen cooled InSb detector to record the spectrum from 1800–5000 cm−1 at 0.05 cm−1 resolution. To characterize the kinetics, we used a liquid nitrogen cooled HgCdTe detector for the range from 600 to 4900 cm−1 at a resolution of 0.05 cm−1 with a 5500 cm−1 low pass filter in the IR beam. In this study we did not explicitly check for the effects of the FTIR beam on the measured kinetics; however, previous studies have shown that the decay of CH3O is not induced by IR irradiation.30 The time resolution of the FTIR spectra used to map out the kinetics therefore is controlled by how many scans are averaged together and the resolution. For example, the methanol system required a time resolution of 41.3 s (4 co-added scans at 0.05 cm−1 resolution) for one of the fastest post-photolysis reactions measured in this study.
We employed the GAUSSIAN 09 program40 to perform geometry and harmonic vibrational calculations on CH2OH for all possible hydrogen and deuterium isotopomers. We conducted both MP2 and density functional calculations with Dunning's correlation-consistent polarized-valence triple-zeta (cc-pVTZ or aug-cc-pVTZ) basis sets.41,42 These data are presented in the ESI,† in Tables S2–S10.
Fig. 2 Kinetic plots for a 193 nm photolysis experiment (Expt. #4) conducted on a CH3OH/pH2 sample at 1.84(1) K. The photolysis exposure (3 min, 80 Hz, 19 mW cm−2) is indicated by the grey vertical bar. The data are represented by dotted circles, and the lines are the results of least-squares fits of the data to eqn (4) or (5), except the CH2OH data that is fit to the sum of three first-order processes (see text for details). |
We will first characterize the photolysis step. In the four photolysis experiments performed in this study the general findings are (1) the CH3OH photolysis follows first-order kinetics with a quantum yield of Φ = 0.14(1), (2) the major photolysis products are CO and CH2O in a concentration ratio of [CO]/[CH2O] = 1.1(1) and (3) there is a 13(9)% systematic overestimation in the concentration of the photoproducts (CO + CH2O) compared to the decay in the CH3OH precursor concentration. Using the published cross section50 for CH3OH at 193 nm and the measured UV fluence and exposure time, the determined quantum yield is consistent with the photolysis quantum yields of other small molecules measured by this lab27,51 (see Fig. S5, ESI† for analysis) and illustrates the weak cage effect of solid pH2. The photo-induced production of CO indicates a significant amount of secondary photolysis is occurring under these conditions as none of the primary photochannels produce CO (see eqn (1)). We note that in addition to CO and CH2O there is minor production (<10%) of CH4 which can arise from CH2 production (CH2 + H2 → CH4). Given the uncertainties in the measured concentrations of each species, getting the concentrations to agree to within ±20% is an adequate level of agreement. We point out that the CH3OH concentration is determined using the ν1 OH stretching vibration. This CH3OH feature has a complicated lineshape (see Fig. S3, ESI†) thereby making systematic errors in the CH3OH concentration likely larger. In the experiment shown in Fig. 2 we observe only minor photoproduction of H2O (<1 ppm), however, H2O is difficult to characterize because H2O is present in the vacuum gas surrounding the crystal. Examination of Fig. S4 (ESI†) shows that for most experiments there is zero-order growth in the H2O concentration due to continued deposition of gas phase H2O. However, we find no evidence of H2O satellite peaks52,53 or ortho-H2O immediately54 after the photolysis laser is stopped indicating that H2O is not produced at significant levels by the in situ photolysis of CH3OH. The negligible H2O production is consistent with the gas phase photochemistry that shows channel (1d) is a minor channel and experiments conducted on CD3OD (to be shown) which display only minor production of D2O.
What is striking about the kinetic traces in Fig. 2 is the amount of chemistry that occurs well after the photolysis laser is shut off. For example, the CH3OH concentration continues to decrease by 7.0(3)% over the full post-photolysis reaction period (approximately 500 minutes). This post-photolysis behavior in the CH3OH concentration can be quantified by fitting the data to a single exponential decay function,
[X] = [X]∞ + Aexp(−kt) | (4) |
For the two major photoproducts CO and CH2O, the kinetic behavior after photolysis is qualitatively different. Surprisingly, a clear decrease in the CO concentration after photolysis is not observed. The fitted line in Fig. 2 for the CO data is just the equation of a straight line (y = mx + b) and it shows almost no change in the CO concentration (a slight decrease). In contrast, the CH2O concentration decays immediately after photolysis with a first-order decay constant. The CH2O data are fit to eqn (4) and the extracted parameters are shown in Table S15 (ESI†). CH2O decays with a significantly greater average rate constant (kAVG = 1.8(4) × 10−2 min−1) than CH3OH. However, we believe the CH2O decays for the same reason as CH3OH, reactions with H atoms. We will discuss the CH2O decay in more detail, but we assert it is faster because it involves local migration of H atoms to photo-produced CH2O.
The two species that continue to grow after photolysis are CHO and CH2OH. The CHO growth after photolysis is fit to the following expression,
[X] = [X]0 + A[1 − exp(−kt)] | (5) |
H + CH2O → H2 + CHO | (6a) |
→ CH2OH | (6b) |
We will return to the discussion of why the rate constant for eqn (6) is significantly larger than the rate constant extracted from the CH3OH data in the Discussion section. We want to point out that comparing first-order rate constants is not affected by systematic errors in the concentration determinations. Clearly, we check the proposed mechanisms by verifying that the amount of products equals the loss in reactants, but these comparisons are only as good as the determined absolute concentrations. By “matching” rate constants we provide a more reliable way to infer the elementary tunneling reaction steps that are occurring under these conditions. The proposed mechanism reported in eqn (6) thereby suggests that we might also measure a contribution to the growth of CH2OH that has a first-order rate constant in the range measured for CH2O decay. Examination of Fig. 1b shows that this reaction can occur by H atom addition to CH2O (however with a higher reaction barrier).
By far the most complex kinetic behavior is displayed by the growth of the CH2OH species. As shown in Fig. 2, right after photolysis there is rapid growth in the CH2OH concentration that is right at the limit of the time resolution of the repeated FTIR spectra. Then the CH2OH growth transitions into a slower increase that continues for the full length of the experiment. The high quality of the CH2OH data allows us to fit the growth to an expression that contains three separate first-order rate expressions. The total fitted expression is shown as a blue line in Fig. 2 and the individual fitted components are shown in an expanded view in Fig. 3. There is a fast process with an average (excluding experiment #1 which was recorded with too slow a time resolution) rate constant k1 = 0.35(1) min−1 that happens right after the photolysis laser is stopped. The value of this extracted rate constant is very close to the rate constant determined by Lee and co-workers (k = 0.46(2) min−1) for the decay in the CH3O concentration after photolysis of CH3ONO at 3.2 K.30 Thus, we assign the fast component of the CH2OH growth to reactions of CH3O with the pH2 host. The medium rate growth process has an average rate constant of k2 = 1.7(6) × 10−2 min−1 and is assigned to reactions of H atoms with CH2O according to eqn (6b). Finally, the slowest process that accounts for 74.1% of the post photolysis growth of CH2OH occurs with an average rate constant k3 = 4.0(5) × 10−3 min−1. We assign this process to reactions of H atoms with CH3OH because the k3 rate constant is very close to the rate constant for the CH3OH decay (k = 6.1(10) × 10−3 min−1) as it must be if we are observing a single elementary step, i.e., H + CH3OH → H2 + CH2OH. This reaction continues to occur over the full 500 min reaction time. We assert that the H + CH3OH → H2 + CH2OH reaction is quantum diffusion limited. We point out that the extracted k3 rate constant is very similar to the average rate constant (k = 4.9(7) × 10−3 min−1) measured for the H + HCOOH → H2 + HOCO reaction studied previously7 in solid pH2 at 1.9 K that we also claim is quantum diffusion limited. As discussed previously, this slow process is the most interesting because we believe it occurs via long-range migration of H atoms.
Fig. 3 Expanded view of the early time growth kinetics of CH2OH for the experiment depicted in Fig. 2. A fit to the data consisting of three first-order processes is shown as a solid blue line, the three individual first-order components to the CH2OH growth are plotted as solid red lines (labeled by the rate constant and percent final concentration), and the residuals from the fit are plotted as a solid black line. See text for details. |
We want to explore the fast growth in the CH2OH concentration observed immediately after photolysis a little further. This reaction has been studied extensively theoretically due to its importance in methanol combustion chemistry.31,61,62 Shown in Fig. 1(a) is the best ab initio estimates28 for the reaction barriers (ΔV00) and enthalpy of reaction (ΔH00) at 0 K for the two reactions involved in the conversion of CH3O to CH2OH in solid pH2. In the proposed tunneling mechanism, CH3O reacts with a neighboring pH2 molecule to form CH3OH and an H atom. This reaction step involves tunneling through a 4440 cm−1 barrier and is almost thermo-neutral depositing about 280 cm−1 to the reaction products. Then because the two products are produced in adjacent lattice sites and solid pH2 can efficiently dissipate the reaction energy, they undergo a second tunneling reaction (ΔV00 = 2870 cm−1) to form CH2OH and H2. This two-step tunneling mechanism is relatively fast because the first tunneling reaction is for a dopant reacting with the pH2 host and therefore the reaction does not require diffusion of the reactants to occur.
CD3O + H2 → CD3OH + H → CD2OH + HD, | (7) |
To test our interpretations of the CH2OH kinetic data we conducted three additional photolysis experiments using fully deuterated methanol (CD3OD). First, we need to characterize the concentration of various deuterated methanol isotopomers to look for the possibility of isotopic scrambling prior to photolysis. We detect absorption features for the CD3OD/pH2 samples in both the O–D and O–H stretching regions, indicating that some scrambling has occurred for the hydroxyl deuterium atom. However, only minor scrambling (if any) of the methyl deuterium atoms was detected. Using Ar matrix infrared data63 for the various deuterium isotopomers of methanol, we expect medium to strong infrared absorptions in the 2800 to 3000 cm−1 region for various C–H stretching modes of CHD2OH, CHD2OD, CH2DOH and CH2DOD. As shown in Fig. S6 in the ESI,† if we examine this region for both the CH3OH/pH2 and CD3OD/pH2 samples, prominent C–H stretching peaks are only observed for the CH3OH/pH2 sample. For the CD3OD/pH2 sample, the only absorption in this region is due to the O–D stretching vibration of CD3OD near 2709.65 cm−1. Note that the absorption near 2612.76 cm−1 in Fig. S6 (ESI†) is due to the hydrogen bonded O–D stretch of the CD3OD dimer.64 Even at 10 times the magnification, only very small absorptions are measured in the expected C–H stretching region. We take this as evidence that the only methanol isotopomers at appreciable concentrations prior to photolysis are CD3OD and CD3OH. This scrambling likely occurs in the metal sample holder attached to the dopant vacuum manifold prior to deposition.
We performed the first CD3OD photolysis experiment in an analogous fashion as the CH3OH/pH2 photolysis experiments on a low temperature, as-deposited sample. We can monitor the growth of CD2OH and CD2OD separately using the corresponding CO stretch peaks near 1200 cm−1 that are shown in Fig. S7 in the ESI.† The kinetic behavior of the CD2OD and CD2OH isotopomers are qualitatively different and provide further support for the mechanistic interpretations of the CH2OH kinetic data. The full kinetic data for all species are shown in Fig. S8 in the ESI;† we present expanded views of the kinetic data after the first photolysis for CD2OD and CD2OH in Fig. 4. We fit both isotopomers to a sum of two first-order growth expressions and find clear differences between the two growth curves. For CD2OH, we observe 45% production via a fast process and 55% via a slow process. Thus, as predicted by mechanism (7) we observe fast growth in CD2OH after photolysis consistent with rapid tunneling reactions of CD3O with the pH2 host. In contrast, the importance of this fast growth process is much diminished in CD2OD, although not completely absent. For CD2OD, we observe 12% production via a fast process and 88% via a slow process. As we show in Fig. S8 (ESI†), in a second photolysis exposure of the same CD3OD/pH2 sample the amount of this fast process for CD2OD was even more diminished. Further, for both species the rate constant extracted from the slow growth process quantitatively matches the rate constant extracted for the slow growth of CH2OH. We take this as evidence that for all three hydroxymethyl isotopomers (CH2OH, CD2OH, CD2OD) the slow growth is caused by reactions of mobile H atoms with the corresponding methanol isotopomers (CH3OH, CD3OH, CD3OD). The reason the extracted rate constants are all approximately the same is because the rate is determined by the rate of H atom quantum diffusion to the reactive partner. We note that in these deuterated methanol experiments the photoproduction of CD2O is much less (about a factor of two less) suggesting that H atom reactions with CD2O should be less important to the CD2OH kinetics and that is why the CD2OH growth kinetics can be well fit with just two first-order rates.
We then lowered the temperature of the sample to 1.74 K and mark the first data point recorded at the lower temperature with an arrow in Fig. 5. We let the sample equilibrate and recorded four repeated FTIR spectra. We did not detect any significant changes in the concentration of any of the species implying that significant concentrations of H atoms are not present in the sample at this time. After the sample equilibrated at the lower temperature (1.74(1) K), we photolyzed the sample for a second time (photo #2) and recorded the ensuing kinetics. Consistent with our previous low temperature experiments, we observe the complicated CH2OH growth kinetics that can be fit to the sum of three single exponential growth expressions. We find similar fitted parameters showing significant contributions to the growth of CH2OH from the slow k3 process. We also detect growth in the CHO concentration and decay in the CH3OH and CH2O concentrations that support our interpretation of the kinetics. We point out that for the two photolysis exposures at different temperatures, the amount of fast CH2OH growth and the fitted k1 rate constants are equal to within the fitted uncertainties. This supports our assignment of the fast process to reactions of the CH3O with the pH2 host. The photolysis conditions of both exposures are the same and therefore we produce comparable amounts of CH3O during photolysis that then decay at the same rate. We expect the rate constant for reaction of the CH3O photofragment with the pH2 host to be independent of temperature over this range because it does not depend on H atom diffusion. Basically, this rate constant characterizes the pseudo first-order decay kinetics ([pH2] ≫ [CH3O]) of CH3O in the pH2 host; the two reactive species are in constant physical contact because the CH3O is produced in solid pH2. In contrast, a reaction of an H atom with CH3OH requires these two species to be in close proximity and therefore depends on the details of H atom quantum diffusion. These results verify that H atom quantum diffusion is qualitatively different at these two temperatures and implies that only at the lower temperature does the H atom undergo long-range migration and reaction with CH3OH.
We performed a similar temperature dependent photolysis experiment on a CD3OD/pH2 sample. The full kinetic data for this experiment is shown in Fig. S9 in the ESI† and in Fig. 6 we show the results for just CD2OH and CD2OD. We deposit the CD3OD/pH2 sample, raise the temperature to 4.36 K, and record four FTIR spectra prior to photolysis. As can be seen in Fig. 6, photolysis at 4.36 K produces around 0.35 ppm of CD2OH and almost no CD2OD as expected based on the high temperature CH3OH/pH2 photolysis results. That is, CD2OH can still be produced by reactions of the CD3O photofragment with the pH2 host, but CD2OD cannot be produced by this mechanism. These findings are also consistent with the work of Lee and co-workers who did not report30 observation of the CD2OD isotopomer in their photolysis experiments conducted at 3.2 K. This isotopomer can only be produced by H atom reactions with CD3OD and these quantum diffusion limited reactions do not occur at higher temperatures (only at 1.8 K). Then the sample temperature is lowered (as marked with an arrow in Fig. 6) and after the sample equilibrates it is photolyzed for a second time. Photolysis at 1.67(1) K clearly shows the qualitatively different kinetics for CD2OH and CD2OD. The CD2OH shows significant contributions from two first-order processes with rate constants that match the previously recorded k1 and k3 rate constants. Note the CD2OD kinetics only show a minor medium rate constant component (∼4%) with greater than 96% coming from the slow k3 component. In this case, the different post-photolysis kinetics for CD2OH and CD2OD is even more evident than in Fig. 4. Furthermore, the different temperature behaviors of the CD2OD/CD2OH kinetic traces are consistent with the temperature dependence measured in the 193 nm photolysis of CH3OH/pH2. We note for completeness, that we performed another experiment on a CD3OD/pH2 sample where we conducted the temperature dependent photolysis in the reverse order (e.g., low and high) and rigorously found the same behavior (see Fig. S10 and Tables S18 and S19, ESI†).
We can roughly estimate the timescale for the first tunneling reaction step as follows. If we model the reaction as tunneling through a square barrier, we can calculate the probability or rate constant (s−1) using the following expression,
(8) |
We assign both the medium (k2) and slow (k3) rate constants for CH2OH growth at low temperature to reactions with mobile H atoms. These H atom quantum diffusion reactions are different from reactions of a chemical species with the pH2 host because they require the H atoms to both quantum diffuse and react. The reason we can separate the fast growth of CH2OH from these other first-order growth processes is because the fast reaction is occurring by a different reaction mechanism than the H atom quantum diffusion reactions, i.e., reactions of CH3O with the pH2 host. However, why the medium and slow CH2OH growth processes can be separated into two different “types” of first-order H atom quantum diffusion reactions is not so immediately apparent. Assuming that all H atoms quantum diffuse at the same rate and react with different dopant species at different rates depending on the barrier to reaction, then you should only measure one effective rate constant that equals the sum of all the first-order rate constants. To better illustrate this idea examine Fig. 3. Only a small percentage (9.4%) of the H atoms react with a medium rate constant. The majority of H atoms (74.1%) react with a much slower rate constant. How can this be that the medium rate constant reaction does not use up all the H atom reactants? Clearly, H atom reactions with CH2O should continue to occur given that the CH2O concentration is still non-zero (see Fig. 2). But, indeed this is not what we observe. The ability to decompose these two CH2OH growth processes into two first-order reactions immediately suggests that there are different “types” of H atoms.
Another indication that quantum diffusion can be selective such that H atoms only diffuse next to certain species is given in the pseudo first-order rate constant plots shown in Fig. 7. For both the medium (k2) and slow rate (k3) coefficients that we have assigned to H atom reactions that involve quantum diffusion, we observe that the effective rate constant extracted from the fits does not scale linearly with the concentration of the H atom reaction partner. For example, take the reaction of H atoms with CH2O that produces CHO which are shown as green circles in Fig. 7(b). Given that this is an elementary step we can immediately write the rate law as Rate = k[CH2O][H]. Assuming that the CH2O concentration does not change much, we can rewrite the rate law as Rate = keff[H], where keff = k[CH2O]. This implies that the effective pseudo first-order rate constant keff should scale linearly with the CH2O concentration. Examination of Fig. 7(b) shows that this is not the case, instead, the measured k2 rate constant remains constant for changes in the initial CH2O concentration of more than a factor of 2 (e.g., 4 ppm to 10 ppm). We have now observed this behavior for a variety of H atom quantum diffusion reactions that we have studied to date.7,23 We observe the same behavior for the H + CH3OH → H2 + CH2OH reaction with the slowest rate constant where the measured rate constant does not scale linearly with the initial CH3OH concentration (see Fig. 7(c)). Further, we measure the same rate constant for the growth of CD2OD (brown circles) or CD2OH (cyan circles). We take this as evidence that the reaction is not “diffusion limited” in the normally defined sense. As we have shown previously for the H + NO reaction,23 because the H atom continues to be mobile due to quantum diffusion the bimolecular reaction kinetics are intrinsically first-order (the rate does not depend on the CH3OH concentration over the 75 to 120 ppm range) and the H atom decay kinetics reflect the H atom quantum diffusion rate, not the tunneling reaction rate of H atoms with CH3OH.
We speculate that the two different rates for the H atom quantum diffusion reactions are caused by both short- and long-range diffusion mechanisms. That is, the reactions that occur with a faster first-order time constant represent reactions of H atoms with other photofragment species that are nearby. Under these conditions where the CH3OH concentrations is the largest, but still rather dilute (<100 ppm), the dominant H atom decay channel is the reaction of H atoms with CH3OH. Only this reaction continues to occur over the full length of the experiment and constitutes proportionally the greatest amount of H atom decay. This implies that the H atom reactions with CH2O only occur for H atoms that are generated in near proximity to the CH2O photofragment. This explains why the amount of H atoms that decay via the medium rate (k2) tunneling reactions with CH2O is always small; only a subset of the generated H atoms is produced near another chemical impurity. In addition, these H atoms may be the result of secondary photolysis and be in regions of the crystal that are damaged or strained. One possible example is an H atom created in an interstitial site close to a CH2O photofragment. However, H atoms that quantum diffuse through the solid over longer distances only react with the CH3OH molecule. Thus, the two “types” of H atoms that are formed during the in situ CH3OH photolysis step are H atoms in close proximity to other photofragments, and well isolated H atoms. By well-isolated we mean H atoms produced in substitutional sites far removed from other chemical impurities. The smaller fraction of H atoms that react on a faster timescale do so because they have smaller distances to quantum diffuse and react. These short-range H atoms diffuse differently because the quantum diffusion is perturbed by the presence of a nearby chemical dopant or because the H atom is produced in a region that is strained. Once these H atoms are consumed, these reactions stop occurring and now the only H atom reactions possible involve long-range quantum diffusion through the pH2 solid and the reaction with CH3OH. Clearly this interpretation of the data is speculative and more experiments are needed to refine our understanding. However, two features measured in this study provide important clues as to the details of this chemistry. First, the H atom reactions do not obey pseudo first-order kinetics and second they can be separated into two different first-order processes.
Another important signature of H atom quantum diffusion limited chemistry is the strong temperature dependence these reactions show. The H atom decay channels and rates depend on the details of how an H atom diffuses next to a chemical impurity and this differs from the quantum diffusion rates in pure pH2. H atom quantum diffusion in a perfect pH2 crystal proceeds via a resonant tunneling mechanism H + H2 → H2 + H where the initial and final lattice positions of the H atom have exactly the same energy due to the translational symmetry of the crystal.16–18 The presence of crystal imperfections (e.g., chemical dopants) breaks this translational symmetry and causes a mismatch in the zero point energies of the H atom in for example second nearest and nearest neighbor lattice sites which greatly reduces the tunneling rate from the resonant value. This level mismatch can be compensated for by one- and two-phonon processes, which leads to a strong temperature dependence of the H atom quantum diffusion rate close to crystal imperfections.32 Not only is the rate changed, but the two different phonon assisted mechanisms lead to qualitatively different diffusion trajectories.32 For attraction between the reaction partners, diffusion towards the reaction partner is accompanied by spontaneous emission of phonons. The rate of spontaneous emission is proportional to ω3 (ω is the phonon emission frequency) and thus the most probable quantum diffusion jump is along the energy gradient (toward the chemical impurity).32 This mechanism would be operative only at the last stages of pairing when the intermolecular forces with the chemical dopant are the strongest. This mechanism is also independent of temperature. In contrast, the two-phonon mechanism where a thermal phonon inelastically scatters off the H atom–pH2 pair can either result in positive or negative energy mismatch jumps. Because it requires the presence of phonons, this mechanism becomes more important at higher temperatures. For the two-phonon mechanism, the most facile tunneling trajectory is along small energy mismatches.32 This mechanism therefore leads to H atom trajectories that avoid chemical dopants. This combination of resonant, one- and two-phonon mechanisms can lead to temperature dependent H atom quantum diffusion where the different diffusional mechanisms compete with each other. While the details of how H atom quantum diffusion towards chemical impurities still need to be worked out, this work and others from this laboratory6,7,23 show that H atom quantum diffusion reactions typically show a strong temperature dependence over the 1.7 to 4.3 K temperature range.
One of the major experimental observations of this study is that the H + CH3OH → H2 + CH2OH reaction continues to occur long after the photolysis laser is shut off when the sample is maintained at 1.8 K. In fact, detailed analysis of the CH2OH growth kinetics after photolysis indicate that at least three separate tunneling reactions are contributing to the CH2OH growth; (i) the fast initial growth is due to reactions of the photoproduced CH3O with the pH2 host, (ii) the medium rate growth is due to H atom reactions with the CH2O photofragment that are likely produced in close proximity, and (iii) the slowest and largest contribution to the growth is due to long-range migration of H atoms and reaction with CH3OH. The different mechanisms of CH2OH growth are confirmed via simultaneous kinetic measurements on CH3OH and CH2O. The reason the tunneling reaction of CH3O with the pH2 host represents the fastest CH2OH growth mechanism is because the two reagents are in constant physical contact. Tunneling reactions of a photogenerated species with the pH2 host can be relatively improbable (have large reaction barriers), but still represent the fastest decay channel because the two species do not need to diffuse to come in contact with each other to react. In contrast, reactions between an H atom and another dopant species require the two species to be in neighboring lattice sites, and this relies strongly on the basic transport mechanism of the H atom. Therefore, typically H atom reactions with other dopants are much slower than reactions with the pH2 host and can be said to be quantum diffusion limited.
The second major finding of this work is that the H + CH3OH reaction shows anomalous temperature dependence. Namely, this reaction readily occurs at 1.8 K while at 4.3 K it does not. This is the third example measured in this laboratory of an H atom reaction in solid pH2 that more readily occurs at low temperature.6–8 As we discuss in this paper, we believe the anomalous temperature dependence is related to the details of H atom quantum diffusion. We show in this paper that the expected dependence on reaction partner concentration for the pseudo first-order H atom reaction kinetics is not observed implying that the rate limiting step is not diffusion limited in the normal sense. H atom quantum diffusion limited reactions in solid pH2 is still not fully understood and deserves further investigation. For example, not all H atom reactions with chemical dopants show this same anomalous temperature dependence. We note that the H + NO → HNO/NOH association reaction has a rate constant that increases with temperature over the 1.7 K to 4.3 K temperature range in an Arrhenius-type fashion, but yet also does not show pseudo-first order kinetics.23
Footnote |
† Electronic supplementary information (ESI) available. See DOI: 10.1039/c7cp05064j |
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