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J. Phys. Chem. A 2010, 114, 11100–11108
Variable Electron and Neutral Density Attachment Mass Spectrometry: Temperature-Dependent Kinetics of Electron Attachment to PSCl3 and PSCl2 and Mutual Neutralization of PSCl2- and PSCl- with Ar+† Nicholas S. Shuman, Thomas M. Miller, Connor M. Caples, and A. A. Viggiano* Space Vehicles Directorate, Air Force Research Laboratory, Hanscom Air Force Base, Massachusetts 01731-3010 ReceiVed: March 4, 2010; ReVised Manuscript ReceiVed: May 27, 2010
We describe the VENDAMS (variable electron and neutral density attachment mass spectrometry) technique to measure the rate constants of various processes occurring as primary, secondary, and higher order chemistry in a flowing afterglow at high charge densities over a temperature range of 300 to 550 K. In particular, we report measurements of rate constants of ion-ion mutual neutralization and electron attachment to radical species, processes which have proven difficult to study through other means. The product negative ion abundances from the addition of PSCl3 to an Ar+/e- plasma have been measured as a function of initial electron densities between 1 × 108 and 4 × 1010 cm-3. Data at lower electron densities yield branching ratios of the primary electron attachment to PSCl3; determination of the reactions and rate constants occurring at low electron densities then allows for determination of the greater number of reactions and rate constants contributing at higher electron densities. Reaction rate constants and branching ratios of electron attachment to PSCl2 are reported; this is the first measurement of electron attachment to a radical as a function of temperature. The data show an unusual negative temperature dependence; however, a zero or even slightly positive dependence is within the uncertainty. Measured electron attachment rate constants are 1.4 × 10-7, 1.1 × 10-7, and 9.1 × 10-8 ( 40% cm3 s-1 at 300, 400, and 550 K, respectively; the dominant product channel is PSCl + Cl- (95, 87, and 77% at 300, 400, and 550 K), and the minor channel is PSCl- + Cl. Ion-ion mutual neutralization rate constants of both PSCl- and PSCl2- with Ar+ are reported over the investigated temperature range; rate constants at 300 K are 4.9 × 10-8 ( 20% cm3 s-1 and 4.5 × 10-8 ( 15% cm3 s-1 and show temperature dependences of T-0.5(0.3 and T-0.9(0.3, respectively. Introduction Flowing afterglow-Langmuir probe (FALP) apparatuses have been used to great effect during the past four decades to measure reaction rate constants of processes occurring in weak plasmas at thermal energies.1-3 The method is general in that any vapor may be introduced to the plasma flow (well downstream of the energetic plasma source) and resulting reactions are observed through monitoring of product ions (via a mass spectrometer at the end of the flow) and the time dependence of charge densities (via a movable Langmuir probe). Traditionally, the FALP technique is used to determine reaction rate constants by varying either reaction time or reactant concentration in such a way that a single process dominates the kinetics, and data analysis is therefore straightforward. However, doing so limits what can be studied to those situations for which such conditions can be established. This has resulted in a significant discrepancy in the amount of kinetics literature between data for “difficult” reactions and those processes that are amenable to the traditional measurements. For instance, electron attachment to stable molecules is well studied; however, only a handful of electron attachment rate constants to radical species have been reported.4,5 If conditions are such that the addition of a neutral species to the FA does not entirely deplete the electron concentration, remnant electrons may attach to neutral products, both initiating secondary and higher order chemistry and acting as a chemical †
Part of the “Klaus Mu¨ller-Dethlefs Festschrift”. * Corresponding author.
ionization agent for monitoring neutral reaction products. If multiple negative species are produced, then the relative abundance of those ions is a function of the rates of the reactions occurring; by measuring the relative ion abundances as a function of the starting electron density of the plasma, we may determine those reaction kinetics. Our group first attempted this approach to measure ion-ion mutual neutralization reaction rate constants and their product branching fractions.5,6 It became clear from those studies that in addition to the product information on neutralization, radical attachment kinetics were accessible by this method. Here we expand on the approach, which we now term variable electron and neutral density attachment mass spectrometry (VENDAMS). We present data obtained when PSCl3 is added to an Ar+/e- plasma in the afterglow. This has allowed for determination of the electron attachment rate constants and products to PSCl3 and PSCl2 as well as the ion-ion mutual neutralization rate constants for PSCl2- and PSCl- with Ar+. All processes were studied at 300, 400, and 550 K. The appeal of studying plasmas at the high electron densities where this novel chemistry happens has an unfortunate flipside: at high electron densities, numerous reactions are occurring in parallel, the rate constants of many of which are likely unknown. An analysis of the data requires simultaneously solving for all unknown rate constants and, importantly, convoluting the uncertainties in each of those determinations. As in any analysis involving many unknown parameters, there is concern that the data are underspecified. In general, by using
10.1021/jp101975a 2010 American Chemical Society Published on Web 06/17/2010
VENDAMS: Electron Attachment and Neutralization
Figure 1. Schematic of the flowing afterglow instrument.
a large range of initial electron densities (Ne(0)), the analysis becomes more tractable. For example, at low electron densities, attachment to PSCl3 is the only distinguishable process taking place (along with ambipolar diffusion). With increasing electron density, attachment to PSCl2, a product of attachment to PSCl3, becomes more important, but the contribution from PSCl3 attachment has already been established. Finally, at the highest densities, mutual neutralization becomes important. Determining rate constants and product branching ratios to within useful precision may require knowledge obtained by other means (e.g., ion-molecule kinetics) or VENDAMS measurements at a range of neutral densities. For instance, the study of mutual neutralization is aided by addition of a second attaching gas that produces an atomic ion that does not neutralize with Ar+. We present a general approach to analyzing VENDAMS data along with a detailed error analysis that accounts for this multiple unknown nature of the technique, which suggests that the technique may be successfully applied to a wide range of other systems. Experimental Methods Kinetics data were obtained with a FALP apparatus (Figure 1). Both the VENDAMS technique (although it was not termed as such) and the particular apparatus used here have been previously described.6 In brief, helium is continuously flowed at ∼100 m s-1 through a 7 cm diameter, 1 m long, stainless steel lined glass tube and maintained at constant number density of 3.2 × 1016 cm-3 (1 Torr at 300 K), although that parameter could be varied over narrow ranges. An electron-ion plasma is produced at the upstream end of the flow tube by a microwave discharge, with a small flow of argon (∼2%) added downstream of the discharge to convert He2+ and He metastables to Ar+. Charged particles in the resulting plasma are ∼10-1000 parts per billion in the He buffer gas, with the positive charge consisting of ∼95% Ar+ with the remainder He+. Electron density along the center axis of the flow tube is measured by a movable, cylindrical Langmuir probe, a 7 mm length of 25 µm diameter tungsten wire protruding from a glass sheath.7 Relative ion abundances are monitored using a quadrupole mass spectrometer at the downstream end of the flow. Reactant gases are added through a glass ring inlet comprising four needles 45 cm upstream of the mass spectrometer sampling aperture. Reactant concentrations were typically on the order of 109 cm-3, achieved by premixing the reactant with He in concentrations on the order of 1% and using flow controllers to measure the flow of the mixture into the flow tube at typically 1-10 std cm3 min-1. The plasma density at the reactant inlet may be varied by (a) moving the microwave discharge cavity further upstream or downstream and (b) varying the fraction of helium passing through the discharge yielding electron densities between the minimum reliably measured with the Langmuir probe (∼108 cm-3) and 5 × 1010 cm-3. The plasma velocity was measured by pulsing the microwave discharge and noting the arrival time of the pulse with the Langmuir probe as a function of distance along the flow tube.
J. Phys. Chem. A, Vol. 114, No. 42, 2010 11101 The ambipolar diffusion rate was determined by measuring the decrease in electron density with the Langmuir probe as a function of distance along the flow tube at a known plasma velocity in the absence of any electron attaching gas. Electron loss to diffusion was typically 300 s-1 at 300 K and increased roughly linearly with temperature. The primary data in VENDAMS are the fractional abundances of product anions as a function of Ne(0). Negative ion mass spectra were collected at discrete values of Ne(0) to determine those abundances. The mass spectrometer was tuned such that isotope peaks of a common ion were unresolved (spectra were also viewed at higher resolution in order to identify accurately all species present). The height of each peak was taken as proportional to the ion concentration, and the heights of each different ion peak were corrected for mass discrimination in the detection efficiency. Because our results depend on accurately measuring the relative concentrations of different ions, we have spent considerable effort to measure mass discrimination factors. We measured the discrimination in two ways: (a) Via ion-molecule reactions: an attaching gas was introduced through a port located upstream in the flow so that the electron density of the plasma was reduced to zero, and only a single primary anion was produced, for example, Cl- from CCl4. A second neutral species was introduced further downstream, reacting with the primary anion to produce a single product anion; for example, SO2 produced SO2Cl-. The peak heights for each negative species were measured for a range of concentrations of the downstream neutral species; the ratio of the changes in the two peak heights as a function of the neutral concentration indicates the relative discrimination between the two negative ions. (b) Via monitoring electron depletion: an attaching gas was added to deplete roughly half of the electron density at a fixed distance from the inlet and the resulting ion signal measured. Separately, a second attaching gas was introduced to yield the same electron depletion and its ion signal measured, with the ratio of the ion signals indicating the relative discrimination. Again, it was preferred that each attaching gas produced a single ion. Where it was possible to measure the discrimination using both techniques, excellent agreement between the methods was found. Light, monatomic ions tended to be discriminated against relative to heavier polyatomic ions. In the present work, Cl- was discriminated against relative to both PSCl2- and PSCl-. Because the mass discrimination factors are important, they were measured multiple times throughout the course of the study and were generally found to be constant to within 10% absent significant adjustments to the mass spectrometer. Both methods measure the mass discrimination occurring in the complete detection system, including quadrupole, detector, and lenses. The temperature of the buffer gas was varied between room temperature and 550 K by heating the entirety of the flow tube, which was wrapped by heating tapes and insulation. The temperature of the gas was monitored by three resistance temperature detector (RTD) elements located along the inner flow tube wall; in a previous experiment, the readings on the RTDs were correlated to the temperature along the center axis of the flow tube measured with a movable thermocouple in order to determine settings that result in a constant temperature along the center axis of the flow tube. Experiments were conducted at 300, 400, and 550 K. Reactant gases pass through ∼30 cm of a glass feedline located inside of the flow tube (i.e., at the flow tube temperature) prior to entering the main buffer gas flow and enter the flow tube at the wall temperature.
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J. Phys. Chem. A, Vol. 114, No. 42, 2010
Shuman et al.
PSCl3 + e- f PSCl2- + Cl f PSCl2 + Cl-
Figure 2. Experimental (b) and modeled best-fit (s) negative ion abundances as a function of initial electron density at the addition of 5 × 109 cm-3 PSCl3 to the flowing afterglow at the indicated temperatures.
PSCl3 was selected for this study partially because electron attachment produces multiple negative ions including a monatomic anion, and the neutral products of this primary attachment have exothermic attachment channels.8 If only a single anion were produced, no information would be accessible through a single gas experiment in VENDAMS. The technique is dependent on differentiating between reaction channels by mass spectrometric observation of their different product ions, either by attachment to secondary products or differing rates of mutual neutralization. Monatomic anions are desirable for the latter because they serve as an anchor to convert relative rate measurements (inherently what the technique yields) to absolute rates via the fact that monatomic ion pairs usually neutralize at a negligible rate.9 In the present case, Cl- and Ar+ are known to recombine with a rate constant below 1 × 10-9 cm3 s-1.6 In the absence of a monatomic product anion in the primary attachment, absolute reaction rates may still be determined by introducing a second neutral species that (1) produces a monatomic anion (e.g., Cl- from CCl4) or (2) produces an ion with a well-known neutralization rate constant. The data may also be supplemented by measurements of primary attachment in the historical manner of monitoring electron density as a function of reaction time using the Langmuir probe. Results and Analysis Figure 2a-c shows relative abundances of negative ions as a function of Ne(0) between 2 × 108 and 4 × 1010 cm-3 at 300, 400, and 550 K, respectively. In each case, the reaction time was 4.4 ms and had 4.8 × 109 cm-3 PSCl3 added to an Ar+/eplasma. Under all conditions, three negative ion species were observed: PSCl2-, PSCl-, and Cl-. Electron attachment to PSCl3 is known to occur dissociatively with a temperature-independent (298-550 K) rate constant equal to 5.1 × 10-8 cm3 s-1
(∆Hr,298K ) - 0.08 eV)
k1a (1a)
(∆Hr,298K ) - 0.17 eV)
k1b (1b)
(Reaction enthalpies are those calculated by the G3 model chemistry10 using the Gaussian-03 quantum chemical package.11).We refer to reactions 1a and 1b as primary attachment. Nondissociative electron attachment is exothermic but not observed at low pressure, whereas dissociative attachment to produce PSCl- is endothermic by ∼1 eV. The observation of PSCl- along with the strong dependence of the relative ion abundances on the initial charge density of the plasma are clear evidence that chemistry beyond the primary electron attachment process is occurring. Understanding this secondary chemistry requires identifying all candidate processes that may be occurring, evaluating which of those processes have non-negligible effects on the negative ion abundances, and finally deriving rate constants by modeling the system to fit the experimental abundances. In the present work, the ion abundances expected from a given set of reactions and rates were calculated and then compared with the experimental data. The calculation assumed a 1D model of the flow tube, and the set of coupled differential equations describing the kinetics was iteratively solved by the Euler method in time steps of 1 µs. Time steps were initially varied, and we found that 10 µs time steps were not quite adequate; that is, shorter time steps made small differences in the derived concentrations. No such effect occurred at times shorter than 1 µs. Ambipolar diffusion of positive ions and electrons was accounted for using an empirically determined rate. The model assumed no diffusive loss of negative ions until the electron population was depleted, at which point both negative and positive ions were treated as diffusing at half the rate12 empirically determined for the Ar+/ electron plasma. A large set of reactions was considered, composed of all exothermic processes possible among species observed (ions) or inferred (corresponding neutrals) to be present in the flow tube. In addition to attachment to PSCl3, reactions 1a and 1b, after accounting for known upper limits to various rate constants, the following reactions were found to have a non-negligible effect on the negative ion abundances PSCl2 + e- f PSCl- + Cl k2a (∆Hr,298K ) -0.05 eV)
(2a) f PSCl + ClPSCl + e- f PS + Cl-
k2b k3
(Hr,298K ) -1.87 eV) (2b)
(Hr,298K ) -0.41 eV)
(3) PSCl2- + Ar+ f PSCl2 + Ar
f PSCl + Cl + Ar PSCl- + Ar+ f PS + Cl + Ar
(4a)
k4a k4b k5
(4b) (5)
Reactions 2 and 3 are referred to as secondary and tertiary attachment, respectively. Other processes (ion-molecule reactions, mutual neutralization of Cl- and Ar+, and mutual neutralization of polyatomic anions with cations other than Ar+)
VENDAMS: Electron Attachment and Neutralization considered in the analysis have known upper limit rates that were found to be too small to effect the negative ion abundances in competition with reactions 1a-5. Additionally, we assume that nondissociative attachment to PSCl2 and PSCl, while exothermic, does not occur, based on the known behavior of PSCl3 under identical conditions. Both the dissociation and autodetachment rate constants of excited anions initially produced in electron capture by the smaller species will be increased,13 whereas the rate of stabilization of the parent anions by collision with the buffer gas will be similar. This suggests that nondissociative attachment to either species is very unlikely to occur. Even this subset of reactions still provides eight adjustable parameters and raises concern that the data may not provide sufficient constraint to determine accurately the unknown rate constants. The excellent fits to the data in Figure 2 are somewhat deceptive in that whereas they clearly represent a set of parameters that describe the data, the more important question is what range of values for each parameter precludes an accurate description of the data. Initial constraints on some rate constants are provided by previously reported measurements. Measurements of the primary attachment rates to PSCl3, k1a and k1b, have previously been reported by our group.8 However, since that publication we have discovered that the experiment suffered from mass discrimination in the ion detection efficiencies. As a result, the previously reported branching ratios for electron attachment to PSCl3 significantly underestimated the contribution of Cl- production. This issue did not affect the reported total attachment rate constant to PSCl3. An additional constraint is that the maximum rate constant of electron attachment to a given species is equal to its collision rate constant with an electron under the specified conditions; the collision rate constant may be calculated with knowledge of the species polarizability and dipole moment.14 Accurate determination of the other reaction rate constants to varying levels of precision is possible, even with the large number of adjustable parameters because ion abundances at different initial electron densities are more and less sensitive to each reaction rate. At very low Ne(0), attachment to PSCl3 is by far the dominant process; the ion abundances are essentially independent of all other rate constants, and determination of the relevant rate constants is straightforward. As Ne(0) is increased, secondary, tertiary, and higher order processes become important. In the present case, first attachment to PSCl2 becomes significant, then attachment to PSCl, and finally mutual neutralization. Because these more complicated conditions inherently build upon the lower density conditions, the relevant rate constants for which have been determined, the data contain sufficiently few unknowns that the rate constants may be determined. We emphasize that this progression of relatively simple systems at low plasma densities to more complex systems at high plasma densities is a general one, and the approach of interpreting primary chemistry in the simple system as a foundation for interpreting higher order chemistry in the complex system is illustrated by, but not unique to, the PSCl3/ e-/Ar+ system investigated here. Although the particulars of extracting each rate constant from the data are unique to a given system, we provide a detailed example by stepping through the analysis of the present case. (The data at each temperature are independently analyzed, and the analyses are qualitatively identical.) At Ne(0) below 109 cm-3, electron attachment to PSCl3 dominates yielding Cl- and PSCl2-. The relative abundances of Cl- and PSCl2- are essentially constant for Ne(0)
