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J. Phys. Chem. 1996, 100, 2900-2906
Thermal Energy Reactions of Size-Selected Hydrated Electron Clusters (H2O)nSusan T. Arnold,† Robert A. Morris, and A. A. Viggiano* Phillips Laboratory, Geophysics Directorate, Ionospheric Effects DiVision (GPID), Hanscom AFB, Massachusetts 01731-3010
Mark A. Johnson Sterling Chemistry Laboratory, Yale UniVersity, New HaVen, Connecticut 06511-8118 ReceiVed: September 5, 1995; In Final Form: NoVember 7, 1995X
The reactions of hydrated electron clusters (H2O)n-, n ∼ 15-30, with several neutral electron scavengers were studied in a selected ion flow tube apparatus at 100 K. The reactions with CO2, O2, and NO primarily produced the solvated charge transfer ions CO2-(H2O)n-1, O2-(H2O)n-5, and NO-(H2O)n-3,n-4, respectively. The reactions with N2O produced both O-(H2O)n-4 and OH-(H2O)n-3,n-4 product ion distributions. The number of neutral water molecules lost from the water clusters during these reactions is strongly correlated to the overall reaction exothermicities. The present measurements yield a value of 0.37 eV for the average effective monomer dissociation energy, D[(H2O)n‚‚‚(H2O)]. The CO2 reactions proceed at the collision rate, while the NO, N2O, and O2 reaction rates are significantly less than the corresponding collision rates. The reaction efficiencies for the CO2, NO, and O2 reactions can be rationalized on the basis of spin considerations. A proposed electron transfer mechanism is discussed that considers the diabatic free energy curves which correspond to the electron being predominantly associated with either the water cluster or the scavenger molecule. A comparison of the present results with a previous molecular beam reactivity study illustrates the competition between two cluster cooling mechanisms: evaporation and collisional quenching.
Introduction When a free electron is injected into a polar liquid, it can polarize the solvent and form a cavity so that the electron is surrounded by oriented solvent molecules. In water, this species is referred to as the hydrated electron, eaq-. The physical and chemical properties of eaq-, including its reactivity with hundreds of organic and inorganic compounds, have been studied extensively over the past several decades.1,2 In general, eaq- has served as a chemical reactant in investigating electron transfer processes in solution; it reacts by undergoing dissociative or nondissociative capture by a molecule or an ion in solution, by combining with other radical species, or by being converted into a hydrogen atom by reaction with proton donors. More recently, the gas-phase analogs of the hydrated electron, the (H2O)n- cluster anions, have been the focus of numerous experimental3-14 and theoretical studies.15-19 Interest in these clusters has centered around their possible use as probes into the microscopic nature of the condensed-phase eaq-. With regard to the chemical properties of these clusters, Johnson et al. have investigated the reactions of hydrated electron clusters with several neutral electron scavengers.9 In a molecular beam experiment, they found the overall cluster reactions to involve more than a simple charge transfer. Both dissociative and nondissociative charge transfer type reactions were accompanied by partial solvation of the resulting ion, yielding products of the form X-(H2O)n-m. A new ion source has recently been added to the variable temperature selected ion flow tube at Phillips Laboratory, providing the capability of studying reactions of large massselected cluster ions at a well-defined temperature. We have † Air Force Geophysics Scholar. Permanent address: 2133 Rayburn, House Office Building, Washington, DC 20515. * To whom correspondence should be addressed. X Abstract published in AdVance ACS Abstracts, January 15, 1996.
0022-3654/96/20100-2900$12.00/0
therefore undertaken a study to examine the kinetics of hydrated electron clusters reacting with several neutral electron scavengers under truly thermal conditions. Specifically, we have determined rate constants and primary product distributions for the reactions of (H2O)n-, n ∼ 15-30, with CO2, NO, N2O, and O2 at 100 K. The nature of the excess charge distribution in the reaction product ions was further investigated using the negative ion photoelectron spectrometer at Yale University. The reaction efficiencies and the overall reaction energetics, which govern the degree of product ion solvation, are discussed, along with a proposed electron transfer mechanism. The present results are also compared with the previous molecular beam study of these reactions. Experiment The reactivity measurements were made at Phillips Laboratory, using the variable temperature selected ion flow tube (SIFT). The SIFT apparatus has been described previously in detail,20-21 and only details pertinent to this study are discussed here. The hydrated electron clusters (H2O)n- were produced in a supersonic expansion cluster ion source which was recently added to the apparatus. The ion source, which is similar to those used by Bowen22 and by Haberland,3 is discussed in more detail in a separate publication.23 Hydrated electron clusters in the size regime n ) 13-35 were observed by expanding 4 atm of ∼5% H2O in Ar through a 25 µm nozzle. Numerous studies on hydrated electron clusters have previously demonstrated that there is a threshold for the formation of these clusters beginning at n ) 11, with an abrupt increase in the ion intensity occurring at n ) 15.3-7,10 (In some studies,3,4,10 several magic number species were also observed at sizes n ) 2, 6, 7, although they were not observed in the present flow tube experiments, presumably because they are unstable in the buffer at 100 K.) The temperature of the flow tube was maintained at 100 K since the hydrated electron clusters are not thermally stable much © 1996 American Chemical Society
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above this temperature, as evidenced by the ion signal growing in at temperatures below 140 K. Water cluster anions in the threshold regime, n ) 11-14, were seen in higher abundance when the flow tube was cooled to 90 K rather than 100 K. The ions were transported along the flow tube by a fast flow (∼4 × 104 cm s-1) of hydrogen buffer gas (99.999% research grade H2). The buffer gas was further purified by passing it through a molecular sieve trap cooled by liquid nitrogen which eliminated nearly all the reactive impurity species, mainly O2 and CO2. The use of hydrogen as the buffer gas rather than helium resulted in less dissociation of the cluster ions after their initial collisions with the buffer gas.24 The buffer gas pressure was typically ∼0.13 Torr. Neutral reactant gases were obtained commercially and were used without further purification. The CO2 and N2O reactants were added to the flow tube through a heated finger inlet to prevent freezing. This technique has been described previously.24 Turning on the heat had no effect on the ion distribution. At most the reactant neutral flow is 10-4 that of the buffer flow so that the added gas is thermalized before encountering reactant ions. The reactivity of (H2O)n- clusters with N2O was studied at only a few cluster sizes, due to the single amu mass resolution required to separate the OH-(H2O)n and O-(H2O)n products from the primary ions. Rate constants were determined by the standard technique of recording the pseudo-first-order attenuation of the primary ion count rate as a function of reactant neutral flow rate. The reported rate constants are averages of between 2 and 6 runs. The reaction time, typically 6-7 ms, was measured directly by time-of-flight techniques. A typical maximum concentration of the reactant neutral is 1 × 1012 molecules cm-3. Because the weakly bound hydrated electron clusters would partially break up upon injection, it was not possible to inject a single mass-selected cluster ion into the flow tube and follow the kinetics. Rate constants were measured by monitoring the decay of several primary ions all injected into the flow tube at once, while the reaction products were determined by injecting only a narrow distribution of cluster sizes into the flow tube and then monitoring the main product ion formation. Estimated uncertainties in the reported rate constants are (30%. Some of the product ions were further characterized using the negative ion photoelectron spectrometer at Yale. This apparatus has been described previously in detail.25 The product ions were prepared by reacting a distribution of hydrated electron clusters with a neutral reactant gas introduced into the source chamber. Results -
Reaction Rates. Bimolecular rate constants for (H2O)n reacting with CO2, NO, N2O, and O2 are shown in Figure 1 as a function of cluster size. For all the reactant neutrals studied here, there are no apparent changes in the total rate constant over the entire cluster range studied. Thus, average values for the rate constant, kavg, were determined and are represented as the dashed lines in Figure 1. Collision rate constants, kc, were calculated using the parametrized trajectory calculations of Su and Chesnavich.26 These are indicated by the solid line in Figure 1. The measured rates for the CO2 reactions are nearly equal to the calculated collision rates, while the measured rates for the other neutrals, NO, N2O, and O2, are somewhat smaller than the collision rate. The average efficiencies of the CO2, NO, N2O, and O2 reactions are 94%, 80%, 63%, and 35%, respectively, as shown in Table 1. Products of the CO2, NO, and O2 Reactions. The reaction products were determined by injecting only a narrow distribution of hydrated electron cluster sizes into the flow tube and then
Figure 1. Rate constants for the reactions of (H2O)n- with CO2, NO, N2O, and O2 shown as a function of cluster size. The dashed line represents the average cluster reaction rate constant, kavg, and the solid curve is the collision rate constant, kc, calculated using the parametrized trajectory method of Su and Chesnavich.26
TABLE 1: Average Rate Constants, Reaction Efficiencies, and Number of Water Monomers Lost from the Cluster for the Reactions of CO2, NO, N2O, and O2 with Hydrated Electron Clusters, (H2O)n-, Measured at 100 Ka CO2 NO (10-10
avg reaction rate constant efficiency of reaction (%) avg H2O loss, flow tube exp avg H2O loss, beam expc
cm3 s-1)
7.6 94 1.3 3
6.6 80 3.5 5
N2O
O2
5.7 63 4.1/3.5b 6/5
2.5 35 5.0 7
a The number of water monomers lost from the cluster when the reactions are carried out in a molecular beam is also included.9 The estimated accuracy of the reported rate constants is (30%. b Values for O-/OH- products. c Reference 9.
monitoring the main product ion formation. The products of the CO2, NO, and O2 reactions are essentially solvated charge transfer products and neutral water molecules.
CO2 + (H2O)n- f CO2-(H2O)n-m + m(H2O), 〈m〉 ) 1.3 (1) NO + (H2O)n- f NO-(H2O)n-m + m(H2O), 〈m〉 ) 3.5 (2) O2 + (H2O)n- f O2-(H2O)n-m + m(H2O), 〈m〉 ) 5.0 (3) In general, one or two products were observed for each cluster reaction, although they differ only in the number of water molecules solvating the charge transfer product ion. Small amounts of less abundant product ions would be masked by the primary products of adjacent-sized water cluster ions. The average number of water monomers lost from the cluster, 〈m〉,
2902 J. Phys. Chem., Vol. 100, No. 8, 1996
Figure 2. Photoelectron spectrum of [CO2‚(H2O)6]- indicates that, upon incorporation of the CO2 molecule, the binding energy of the cluster is stabilized over 3 eV relative to that of (H2O)6-.
varies between the reaction systems, as indicated in eqs 1-3 and as shown in Table 1. To demonstrate that the product ion charge distribution has fundamentally changed from that of (H2O)n- to that of a solvated molecular anion complex, X-(H2O)n, the ionic products of reaction 1 were further characterized by photoelectron spectroscopy. If a neutral CO2 molecule were adsorbed onto the (H2O)n- ion, the electron binding energy of the resulting cluster ion would increase only slightly relative to that of (H2O)n-, and the photoelectron spectra of the two species would be very similar. In contrast, if CO2- were solvated by water molecules, the electron binding energy of the ion-molecule complex would increase significantly relative to that of the unsolvated ion. The [CO2‚(H2O)n]- product ions were prepared as discussed in section II, and the photoelectron spectrum of n ) 6 is shown in Figure 2 along with the spectrum of (H2O)6-. The spectra illustrate that the electron binding energy of the product cluster has increased over 3 eV compared to the primary hydrated electron cluster ion, which indicates the charge center in the product ion is not a (H2O)n- moiety. The larger clusters ions, [CO2‚(H2O)n>6]-, are even more strongly bound and do not photodetach at the photon energy used in these experiments. The only ionic products of reactions 1-3 which underwent further secondary reactions were the NO-(H2O)n products:
NO-(H2O)n + NO f NO-(NO)(H2O)n-1 + H2O (4a) NO-(NO)(H2O)n + NO f NO-(NO)2(H2O)n-1 + H2O (4b) The NO-(H2O)n ions reacted with NO, rapidly switching up to two additional H2O molecules from the cluster ion. It is possible that minor channels involving clustering or loss of two waters could have been missed. The rate constants for the switching reactions are on the same order as the primary reaction, as evidenced by the increase in the NO-(NO)1,2(H2O)n signals at low NO flows. Further incorporation of NO could not be followed definitively because of mass coincidences, although a mass spectrum of the product ions at large NO flows appears to show (NO)3- as the core ion with the largest number of NO’s. The fact that more than one NO is incorporated into the cluster anion is not surprising in light of recent work on the stability
Arnold et al.
Figure 3. Primary and product ion distributions resulting from the reaction of N2O with a narrow distribution of water cluster anions peaked at (H2O)22-. The solid curve represents the primary ion distribution. Large dashed and small dashed curves represent the two major products: 75% O-(H2O)n-m, 〈m〉 ) 4.1 and 25% OH-(H2O)n-m, 〈m〉 ) 3.5, respectively, under conditions of ∼100% conversion to products.
of NO- clusters.27 Posey and Johnson found that the NO-‚NO dissociation energy is probably large, possibly as great as 1.19 eV. This is substantially larger than the energy to remove a H2O molecule from the present clusters, which would make ligand switching considerably exothermic. Carman found that the ion (NO)3- is particularly stable, probably reflecting the fact that, since NO- is a triplet and NO is a doublet, the smallest singlet configuration of (NO)n- is the trimer anion. Products of the N2O Reactions. Unlike the previously discussed reactions, the reaction of (H2O)n- with N2O produced two distinct product ion distributions:
(H2O)n- + N2O f O-(H2O)n-m + N2 + m(H2O), 〈m〉 ) 4.1 (75%) (5a) f OH-(H2O)n-m + N2 + OH + (m - 1)(H2O), 〈m〉 ) 3.5 (25%) (5b) As shown in Figure 3, where only a narrow distribution of hydrated electron cluster sizes was injected into the flow tube and allowed to react with N2O, the major products of these reactions were the solvated dissociative charge transfer product ions O-(H2O)n-m. Smaller amounts of OH-(H2O)n-m cluster ions were also produced. It should be noted that the two product channels are associated with slightly different average water monomer loss. No solvated charge transfer product ions, N2O-(H2O)n, were observed. Also, no further secondary reactions with the O-(H2O)n or OH-(H2O)n products were observed. It has been shown previously that a single H2O clustered to O- shuts off the reaction with N2O.28 Discussion Reaction Efficiencies. All four of the neutral reactants discussed here are efficient solution-phase hydrated electron scavengers, yielding ionic products which are similar to those observed in the cluster reactions.1,2,29 The reactions of O2 and CO2 with eaq- proceed at the diffusion-controlled limit, while the reaction with NO is reported to be somewhat faster than this limit.30 These reactions produce the solvated charge transfer product ions O2-, CO2-, and NO-, respectively. The reaction of eaq- with N2O also proceeds at near the diffusion-controlled limit, and solvated N2O- is the primary ion formed, although it
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rapidly undergoes reaction with the surrounding water molecules to form O- and OH-. Unlike the solution-phase hydrated electron reactions discussed here which proceed at or near the diffusion-controlled limit, the rates for the gas-phase hydrated electron cluster reactions are generally lower than the corresponding collision rate. However, the efficiencies of the cluster reactions can be largely rationalized by spin considerations. The hydrated electron clusters each have one unpaired electron and are therefore doublets, while the neutral reactants, CO2, NO, and O2, have ground state configurations which are a singlet, a doublet, and a triplet, respectively. Because some spin-allowed product species will be energetically inaccessible, the observed rate constant should be compared to the collision rate constant, kc, multiplied by a fractional statistical weight, f, which is applicable to the allowed product species.31 For example, the (H2O)n- doublet and O2 triplet reactants allow for either doublet or quartet state products. The only energetically accessible product is the ground state doublet state with a statistical weight of f ) 1/3, and therefore the expected rate constant should be 1/ k . The average efficiency of the O reaction was found to 3 c 2 be ∼35%, which is consistent with this explanation. Similarly, the expected rate constants for production of ground state products for the CO2 and NO reactions are kc and 3/4 kc, respectively, while the average efficiencies measured for these reactions corresponded to 94% and 80%, respectively, demonstrating a general correlation between the measured rates and the rates expected from spin considerations. The inefficiency of the N2O reactions is not explained in this manner. Other factors governing the dissociative charge transfer, including possible steric effects, i.e., the site of (H2O)n- attack on N2O,32 may account for the observed reaction rates being only 3/5 kc. Degree of Product Ion Solvation. Previously, Johnson et al. demonstrated that the number of neutral waters lost from the cluster was strongly correlated to the overall reaction exothermicity.9 In the case of CO2, NO, and O2 the net reaction can be described as follows: -
-
(H2O)n + X f X (H2O)n-m + m(H2O)
(6)
The overall exothermicity of the reaction can be estimated by breaking the process down into the following individual steps:
(H2O)n- f (H2O)n + e-
(7)
X + e- f X-
(8)
X- + (H2O)n f X-(H2O)n
(9)
For the dissociative charge transfer reaction channel with N2O that produces solvated O- ions (reaction 5a), the reaction also includes the neutral bond dissociation step. The reaction exothermicity is related to the number of water molecules lost during the reaction through the following expression:
∆H ) EA[(H2O)n] - EA(X) - Esolv[X-(H2O)n] + D0[N2‚‚‚O] ) -〈m〉D0[(H2O)n‚‚‚(H2O)]
(10)
where EA(X) is the electron affinity of the neutral reagent, EA[(H2O)n] is the electron affinity of the water cluster (estimated as ∼0.4 eV for ) 15),5,7 Esolv [X-(H2O)n] is the solvation energy of the product ion, D0[N2‚‚‚O] is the N2O bond dissociation energy (if applicable), 〈m〉 is the average number of neutral water monomers lost during the reaction, and D0[(H2O)n‚‚‚(H2O)] is
Figure 4. Plot of the overall reaction exothermicity, -∆H, calculated using eqs 10 and 14 vs the average number of neutral water molecules lost in the reaction of (H2O)n- with CO2, NO, N2O, and O2. The reaction with N2O produces two distinct product ion distributions, O-(H2O)n-m and OH-(H2O)n-m, which are associated with different 〈m〉. The slope represents the energy required to eject a single water monomer from the cluster ion, D[(H2O)n‚‚‚(H2O)] ∼ 0.37 eV.
the energy required to dissociate a water monomer from the larger cluster. At large cluster sizes, like those studied in the present experiment, the ion solvation energy is expected to approach the Born solvation energy:
Esolv )
( )
e2 1 12Ri e0
(11)
where e is the fundamental charge, Ri is the radius of the ion, and e0 is the static dielectric constant of the solvent. Calculating the exothermicity for the N2O reaction channel that produces solvated OH- cluster ions (reaction 5b) is somewhat more involved because the overall reaction scheme should also include the following individual steps:
(H2O)n f (H2O)n-1 + H2O O- + H2O f OH- + OH
∆H ) 0.35 eV
(12) (13)
The exothermicity of reaction 5b is estimated by including these two additional terms into eq 10:
∆H ) EA[(H2O)n] - EA(O) - Esolv[OH-(H2O)n-1] + D0[N2‚‚‚O] + D0[(H2O)n‚‚‚(H2O)] + ∆Hrxn 13 (14) The exothermicities for the reactions of (H2O)n- with CO2, NO, O2, and the N2O reaction which produces solvated Ocluster ions were estimated using eq 10, while the exothermicity for the other N2O reaction channel was estimated using eq. 14. These values are plotted in Figure 4 as a function of 〈m〉. Note that the number of neutral water monomers ejected from the cluster for reaction 5b is represented by 〈m〉 - 1 since one of the water molecules undergoes further reaction. A linear leastsquares fit to the data implies that roughly 0.37 eV is required to eject each water monomer from the cluster, which is close to the value of 0.42 eV (for n ) 15) calculated using the evaporative cooling model of Klots.33 Free Energy Reaction Paths. The primary force driving the evaporative charge transfer reactions can be understood on the basis of the changes in the physical dimensions of the excess electron in the reactants and the products and by a consideration of the associated Born solvation energies. Because the excess electron in (H2O)n- is delocalized, it has a small solvation energy [Esolv(e-) ∼ 0.4 eV] compared to the product solute anions,
2904 J. Phys. Chem., Vol. 100, No. 8, 1996
Figure 5. Diabatic free energy schematic for CO2 + (H2O)n-. The reaction coordinate, R, is the distance between CO2 and the center of mass of the water cluster ion.
which localize the excess electron in their orbitals and generally command hydration energies in the range of 2 eV. In discussing a detailed mechanism of how the electron is localized, it is useful to consider diabatic free energy diagrams such as those shown schematically in Figure 5 for the case of [CO2 + (H2O)n]-. These curves are meant to display the free energy of the system at a constant temperature, therefore describing the relative probabilities of finding the system in different configurations. The energy is parametrized along the reaction coordinate, R, which is the distance between the scavenger and the center of mass of the water cluster. To calculate the free energy, one might force the water molecules to assume a constant center of mass so that the cluster remains intact until the projectile hits. Otherwise, the water molecules would migrate toward the anion in the ion-cluster path. Within this constraint, individual water molecules would be allowed to rotate in response to an incoming molecule or ion. Since the solvent molecules in this case are allowed to rearrange, they find the most energetically favorable arrangement at a given distance R. This R-dependent free energy function describes an alternative three-dimensional well trapping the ion without the usual hard repulsive wall in the potential curves for diatomic encounters. This free energy surface may possess a minimum at the center or possibly a trough around the edge, depending on whether the ion is bulkor surface-solvated. The two curves of importance in simple evaporative charge transfer reactions pertain to whether the electron is associated with the (H2O)n- cluster or with the scavenger, in this case CO2. The reaction with CO2 presents a particularly interesting case in that the isolated CO2- monomer anion is metastable, lying 0.6 eV above the neutral CO2 and a free electron. Therefore, the asymptotic charge transfer reaction
CO2 + (H2O)n- f CO2- + (H2O)n ∆H ) EA[(H2O)n - EA(CO2)] (15) is quite endothermic (∆H ∼ 1 eV), which implies some interaction with the solvent is required for the cluster charge transfer reaction to occur. [Note that a long-range charge transfer reaction leading to unsolvated CO2- would require vertical transitions on both the water cluster and the CO2 molecule, making this pathway very endothermic: ∆E ) VDE(H2O)n- + EAv(CO2) ≈ 3.5 eV. It is therefore not
Arnold et al. surprising that the unsolvated charge transfer ions are not observed as products for any of the systems studied in these experiments.] At large distances, CO2- is very quickly stabilized on approaching the cluster due to the large polarizability of the water cluster. In contrast, the interaction energy of neutral CO2, bound by van der Waals forces onto an essentially neutral water surface, is much weaker. This implies there is a curve crossing at some distance, Rc, below which the solute anion is the most stable form of the system. The curve crossing shown in Figure 5 for CO5 is a general property of all the systems studied in this work since EA[(H2O)n] > EA[X] for clusters n g 16 and X ) O2, NO, N2O, and CO2. Photoelectron spectra of the CO2 + (H2O)n- reaction product ions, such as shown in Figure 2, indicated that the binding energy is greatly increased upon incorporation of CO2, showing that the observed product is indeed a CO2- core ion and that charge transfer has therefore taken place. While it is clear that charge transfer occurs in these reactions, it is not obvious actually how or where this process occurs relative to the cluster “surface”. For example, recent calculations have indicated that a significant portion of the anion stabilization can be achieved before the anion actually encounters the cluster.34 It appears the central issue controlling when the transfer occurs is the proximity of the excess electron orbital in the cluster relative to the molecular orbitals of the scavenger which will accept the electron. Using spectral moment analysis of the cluster absorption spectra, Johnson et al. have recently placed a lower bound on the mean-square radius of the excess electron in the (H2O)n- clusters.35 Those results indicated that in the cluster range n ∼ 20 the excess electron orbital is approximately the same size as the water cluster, so it is likely that the π* electron accepting orbital of CO2 will overlap a small piece of the electron wave function regardless of where it encounters the water cluster. Since the π* orbital of CO2 is solvent-stabilized in the vicinity of the water cluster, the electron can “pour” into this orbital so long as the solvation energy of the nascent ion is larger than the reorganization energy demanded by the loss of electron density around the water molecules. The inference that this process is initiated with the neutral reactant molecule accommodated on the surface of the water cluster is consistent with the fact that bulk solvation is expected to be higher in free energy than the surface-solvated molecule due to the disruption of the hydrogen-bonded network required in the bulk.36 The electron transfer can therefore be regarded as a dynamic process in which the water molecules participate in the reaction by following the changing charge density. The relaxation time of hydrated electrons in bulk water is known to be fast (240 fs),37,38 and it is reasonable that such a system could respond adiabatically to the electron transfer. This overall process is reminiscent of spontaneous reduction of molecules such as O2 at metal surfaces, where an image potential stabilizes the anion near the surface, and an electron is removed from the conduction band to form a surface-bound anion.39 However, in the case of water clusters, the solvent molecules can rearrange so that the final state will be an ion at least partially surrounded by water molecules. Comments on the Occurrence of the Endothermic O- + H2O f OH- + OH Reaction in Small Water Clusters. The observation of OH-(H2O)n products in addition to those with O-(H2O)n stoichiometry demonstrates that reaction 13, which is endothermic, has occurred within the clusters and that the neutral OH product has escaped from the cluster in competition with the more numerous water monomers. This raises the issue of whether the clusters with nominal O-(H2O)n stoichiometry
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might also exist as separated OH and OH- moieties where the cluster ensemble is representative of reaction 13 at equilibrium. In aqueous solution at room temperature, the lifetime of O- is only ∼10 ns; i.e., the forward reaction 13 proceeds with a pseudo-first-order rate constant of 108 s-1. Therefore, most of the initially injected O- appears as hydroxyl radical:
[O-] [OH-] -1 ) K ≈ 10-5 [OH] [H2O] eq
(16)
where Keq ) 1.8 × 10-4 and [OH-] ) 10-7 M.40 This is in marked contrast to the behavior displayed in small O-(H2O)n clusters, where ab initio calculations41 and a recent photoelectron spectroscopic study42 indicate that the binary system is essentially charge-localized, hydrogen-bonded O-H2O. Therefore, it is not straightforward to establish a priori the cluster size dependence of the equilibrium [O-]/[OH] ratio. We can shed some light on the situation by considering the results of a related experiment carried out at Yale.43 Reaction 13 was photoinitiated within water clusters in a scheme where O- was generated by photodissociation of O2- in size-selected O2-(H2O)n. These studies again displayed OH-(H2O)n products, with an onset at O- + (H2O)n collision energies in the range of ∼0.5 eV. However, in contrast to the persistence of OH- products over the entire cluster distribution observed in the bimolecular N2O + (H2O)n- reaction, the OH--based products from the photoinitiated reaction were observed to be strongly size dependent and disappeared above n ) 4 or 5 in favor of those with O-(H2O)n stoichiometry. These disparate features of the reaction can be readily understood in the context of the hypothesis presented above in which the bimolecular reactions are assumed to occur at the surface of the cluster. In the case of the H2O reactions, this implies dissociative electron attachment and hence O- formation at the surface of the cluster, while photoinitiation creates O- already embedded within the cluster. In the surface reaction, O- would impact the cluster with a large kinetic energy, given by the difference in the neutral and ioncluster interaction energies as shown in Figure 5, providing the energy to drive the endothermic reaction. A surface collision also naturally explains the absence of N2O- and the propensity to eject OH neutrals before they are trapped in the cluster (e.g., product caged), which surely occurs in the case of the intracluster, photoinitiated reaction. In summary, we suggest that the endothermic ion-molecule reaction 13 is driven by the nascent energy which is necessarily injected into the system in the model where the primary charge-transfer event occurs at the surface of the cluster. Comparison with the Molecular Beam Study: Competition between Evaporative and Collisional Cooling. The reactions reported here were previously studied using a “supersonic entrainment” reactor.9 In that molecular beam experiment, hydrated electron clusters were first formed in the high-density region of a supersonic expansion. The clusters then interacted with reactant molecules which were allowed to diffuse through the walls of the jet, i.e., through the shock boundary. Reactions occurred 50-100 nozzle diameters downstream of the expansion, where there are relatively few collisions occurring between the primary molecules. Thus, compared to the flow tube, where many collisions occur with the hydrogen buffer for each reactive encounter, the reaction environment of the jet is more like a very low-energy (e100 K) single-collision scattering cell. Although the molecular beam and the flow tube reactions of hydrated electron clusters both produced solvated charge transfer product ions, the average number of neutral water monomers ejected from the cluster in reactions 1-3 and 5 differs between
the two experiments. In general, the beam experiments are systematically associated with more water evaporation events. As shown in Table 1, the free jet reactions lose an average of 1.5-2 more water molecules (depending upon the reaction) compared to the flow tube reactions. One main difference between these experiments which accounts for this effect is that the nascent product distributions in the flow tube are affected by collisional cooling, while the jet reactions are kinetically controlled. Two cooling mechanisms exist for the initially formed excited product ions, collisional quenching and evaporation: kr[H2]
kevap(Eint)
X-(H2O)n + H2 79 X-(H2O)n* 98 X-(H2O)n-1 + H2O (17) where kr[H2] is the collisional quenching rate with the hydrogen buffer gas and kevap(Eint) is the rate of evaporation at an internal energy, Eint. A reactive encounter injects the nascent X-(H2O)n cluster with an energy ∆H given by eq 10. It is clear from all models that a cluster initially injected with several electronvolts of internal energy will evaporate the first few molecules very quickly, faster than the internal clocks of both experiments. In the jet, the evaporations will continue until kevap[Eint] ) 1/τ, where τ is the observation time determined by the spectrometer. Typically, the time from reaction to extraction is 50-100 ms. When the evaporation rate is this slow, the hot cluster can be collisionally quenched in the SIFT experiments when kr[H2] ≈ kevap(Eint). We can estimate the net rate of collisional cooling (eV/s) as the collision rate times the energy, ξ, removed per collision. The collision rate in the flow tube is on the order 108 s-1 at 0.1 Torr, and ξ, estimated from cooling studies of large molecules, is approximately 0.02 eV/collision, so the collisional quenching rate kr[H2] is about 2 × 106 eV/s. The evaporation rate observed in the jet is on the order of 106 s-1 for the last evaporation observed, which removes energy D0 ∼ 0.4 eV. This implies an evaporation cooling rate of approximately 4 × 105 eV/s. This indicates the cooling rate operative in the jet experiment during the last evaporation is indeed less than the collisional quenching rate in the flow tube. Thus, at least the last evaporation will be arrested in the flow tube, accounting for one of the approximately two fewer evaporations observed in the flow tube experiment compared to the beam experiment. The above argument assumes that both (H2O)n- cluster ensembles are initially at the same temperature, which may not be the case. The flow tube is quite cold (100 K), while clusters in an evaporative ensemble are estimated to be nearly 200 K.13 Because the colder clusters are not balanced on the verge of evaporation, as often occurs in isolated clusters, they can absorb more energy before falling apart. At most, this accounts for one fewer evaporation. Thus, the combination of these two effects, initial cluster temperature and collisional quenching, explains the differences between the flow tube and the beam experiments. Conclusion The reactions of hydrated electron clusters (H2O)n- with several neutral electron scavengers were studied in a selected ion flow tube apparatus at 100 K. The reactions with CO2, O2, and NO primarily produced the solvated charge transfer ions CO2-(H2O)n-1, O2-(H2O)n-5, and NO-(H2O)n-3,n-4, respectively. The reactions with N2O produced both O-(H2O)n-4 and OH-(H2O)n-3,n-4 product ion distributions. The number of neutral water molecules lost from the water clusters during these
2906 J. Phys. Chem., Vol. 100, No. 8, 1996 reactions is strongly correlated (R ) 0.95) to the overall reaction exothermicities. The overall reaction rates do not vary with cluster size. On average, the CO2 reactions proceed at the collision rate, while the average NO, N2O, and O2 reaction rates are significantly less than the corresponding collision rates. The reaction efficiencies for the CO2, NO, and O2 reactions are understood on the basis of spin considerations. A proposed electron transfer mechanism considers the diabatic free energy curves which correspond to the electron being predominantly associated with either the water cluster or the scavenger molecule. Because the excess electron in (H2O)nis delocalized and has a small solvation energy compared to the product solute anions, there is a critical distance as the scavenger approaches the cluster, where the excess charge is stabilized more by residing with the solute anion rather than with the water cluster. This represents a crossing in the diabatic free energy curves, and at this point, the electron distribution can “pour” into the electron-accepting orbital of the scavenger. The water molecules participate in the reaction by following the changing charge density. A comparison of the present results with a previous molecular beam reactivity study illustrates the competition between two cluster cooling mechanisms. In general, the free jet reactions, which are kinetically controlled, lose an average of 1.5-2 more water molecules compared to the flow tube reactions, where the nascent product distributions are affected by collisional cooling. The difference in water monomer loss is partly attributed to the evaporative cooling rate being significantly smaller than the collisional quenching rate and partly due to differing initial cluster temperatures. Acknowledgment. The PL authors thank John Williamson and Paul Mundis for technical support. The research at PL was supported by the Air Force Office of Scientific Research. M.A.J. acknowledges the support of the National Science Foundation and thanks M. G. Scarton, D. H. Lavrich, and C. G. Bailey for their help with the preparation of Yale’s contribution to this manuscript. References and Notes (1) Hart, E. J.; Anbar, M. The Hydrated Electron; Wiley-Interscience: New York, 1970. (2) Dainton, F. S. In Fast Reactions and Primary Processes in Chemical Kinetics; Claesson, S., Ed.; Wiley-Interscience: New York, 1967; p 185. (3) Haberland, H.; Schindler, H. G.; Worsnop, D. R. Ber. BunsenGes. Phys. Chem. 1984, 88, 270. (4) Haberland, H.; Langosch, H.; Schindler, H. G.; Worsnop, D. R. J. Phys. Chem. 1984, 88, 3903; J. Chem. Phys. 1984, 81, 3742. (5) Knapp, M.; Echt, O.; Kreisle, D.; Recknagel, E. J. Phys. Chem. 1987, 91, 2601. (6) Kondow, T. J. Phys. Chem. 1987, 91, 1307. (7) Posey, L. A.; Johnson, M. A. J. Chem. Phys. 1988, 89, 4807. (8) Posey, L. A.; Campagnola, P. J.; Johnson, M. A.; Lee, G. H.; Eaton, J. G.; Bowen, K. H. J. Chem. Phys. 1989, 91, 6536.
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