8306
J. Phys. Chem. 1991, 95, 8306-8309
Evaporative Dlrwoclation of Ammonia Cluster Ions: Quantification of Decay Fractlons and Isotope Effects S. Wei, K. Kilgore, W. B. Tzeng,and A. W. Castleman, Jr.* Department of Chemistry, The Pennsylvania State University, University Park, Pennsylvania 16802 (Received: February 5, 1991) A modified version of the evaporative ensemble model is employed to deduce relative binding energies for protonated cluster ions using previously measured metastable dissociation fractions of ammonia cluster ions, (NH3),,H+,n = 4-22, obtained by using a laser-based time-of-flight mass spectrometer equipped with a reflectron. The newly derived values are found to be in good agreement with those reported earlier based on high-pressuremass spectrometry (HPMS) and several other methods employing data on dissociation dynamics. The various methods are found to be complementary. New measurements are reported for the metastable decay of deuterated cluster ions to investigate the influence of mass effects on the dissociation rate. The decay fractions of the cluster ions (ND3),,D+are found to be consistently higher than those of the corresponding (NH3),,H+by 15%. The isotope effect can be well accounted for by considering the differences of their bulk heat capacities, and such studies are found to be a promising method for measuring the heat capacities of small, unsupported cluster systems.
Introduction Studies of the dynamics of formation and dissociation and the changing properties of clusters at successively higher degrees of aggregation enable an investigation of the basic mechanisms of nucleation and the continuous transformation of matter from the gas to condensed phase to be probed at the molecular level.' In this context, the progressive clustering of a molecule involves energy transfer and redistribution within the molecular system, with attendant proccssa of unimolecular dissociation taking place between growth steps? Related of energy transfer and dissociation are also operative during the reorientation of molecules about ions following the primary ionization event employed in detecting clusters via mass spectrometry? providing further motivation for studies of the dissociation dynamics of clusters.@ At the praent time, attention is being focused on various classes of systems to clarify the mechanisms contributing to the various trends of energy release and their dependence on cluster size being reported.J*6Recently we have directed our efforts to investigations of hydrogen-bonded systems, many of which, following ionization, undergo facile internal ion-molecule reactions and concomitant protonated cluster ionw formation. There is also interest in these with regard to elucidating similar processes that are operative in solvated complexes in the condensed state. Recent advances in the field of molecular beam research, coupled with lasers and time-of-flight (TOF) mass spectrometry, enable the details of these various processes to be investigated. A major advance in the study of dissociation processes has become available through the use of a reflecting electric field (reflectron) placed in the field-free region of a TOF mass spectrometer which permits parent and progeny ions to be easily separated6V8and thereby enables detailed investigation of cluster dissociation dynamics to be made.8 During the course of an early systematic study of the dissociation of ammonia clusters following their ionization by multiphoton laser technique, we obtained direct proof (1) Castkman, A. W., Jr.; Keesee. R. G. Ace. Chem. Res. 1986.19.413. Castleman, A. W., Jr.; Keesee, R. G. Science 1988, 241, 36. (2) Kay, E. D.; Castleman, A. W., Jr. J. Chem. Phys. 1983, 78, 4297. (3) Castleman, A. W., Jr.; Kcesee, R. G. Chem. Reu. 1986, 86, 589. (4) Stace. A. J.; Moore, C. Chem. Phys. Left. 1983, 96,80. (5) (a) Caatlaman, A. W., Jt.; Ke9ee. R. G. In Srrucrun/Reacriuity and Thermoehemisrry of Ions;NATO AS1 Series, Ausloos, P., Lias, S. G., Eds.; D. Reidel Publishing Co.: Dordrecht, 1987; pp 185-217. (b) Miirk, T. D.; Castleman, A. W., Jr. A h . At. Mol. Phys. 1984.20.65. (c) M&k, T. D. Inr. J . Mass Spectrom. Ion Proc. 1!387, 79, 1. (6) (a) Echt, 0.;Dao, P. D.; Morgan, S.;Castleman, A. W., Jr. J . Chem. 82,4076. (b) Morgan, S.;Castleman, A. W., Jr. J . Phys. Chem. Phys. 1W, 1989,93,4544. (7) (a) Lifshitz, C.; Louage, F. 1. Phys. Chem. 1989. 93, 5633. (b)
Lifshitz, C.; Louage, F. Int. J. Mass Spectrom. Ion Proc., submitted. (8) Wei, S.;Tzeng, W. E.; Castleman, A. W., Jr. J . Chem. Phys. 1990, 92,332; 1990,93.2506. (9) Levinc. R. D.; Bernstein, R. E. Molecular Reacfion Dynamics and Chemical Reacfiuify;Oxford University Press: Oxford, 1987.
0022-3654/91/2095-8306$02.50/0
of the importance of the metastability of the cluster ions and of the extensive dissociation processes that influence the resulting cluster distributiona6 In particular, a combination of collisioninduced and unimolecular (evaporative) loss processes was observed for a range of cluster sizes ranging up to the 16-mer. Dimt evidence was found for the loss of as many as five monomer units from the protonated 8-mer following its production; both evaporative as well as collision-induced dissociation processes may be operative in the multiple loss steps. More recently, we demonstrated the use of the reflectron techniques in obtaining a precise measurement of the average kinetic energy release (KER), as well as the decay fractions of metastable cluster ions (NH3),,H+. In combination with several theoretical models, we demonstrated that binding energies for (NH3),H+, n = 4-17, are readily obtaineds from the measured values of KER. As the body of knowledge on cluster dissociation continues to increase, the complex issue of interpreting the processes arises. Several model^^^^^ have been presented in order to account for these unimolecular evaporative processes. Kl0ts'2'~in particular has elucidated various important factors regarding the formation and energetics of dissociating clusters or, as they are now termed, evaporative ensembles. He asserts that the cluster ion production methods utilized in these experiments do not lead to microcannonical ensembles; i.e., the clusters formed are not of uniform energy nor do they have a true Boltzmann energy distribution. This reasoning suggests that cluster dissociation should exhibit a broad range of measurable unimolecular rate coefficients, the magnitude of which will depend on the time domain in which metastability is studied. Furthermore, it follows that the metastable decay fractions should increase with cluster size. This qualitative trend is a useful signature of the evaporative ensemble and has been found in the trends of dissociation rates for many cluster systems, e.g., copper,14 argon,15 ammonia? etc. More recently, a quantitative method was reported13that could be used to calculate the decay fractions of evaporative dissociating cluster ions by considering the cluster ions of various sizes have different activation energies. The method was applied to copper and carbon cluster systems. An odd/even alternation of dissociation energies is in accordance with a similar alternation in electron affinities. By fitting the measured dissociation fractions of carbon cluster ions, thermodynamic properties of Cn+,n = 50-80, were deduced. (IO) Engelking. P. C. J . Chem. Phys. 1986.85, 3103.
(1 1) Stace, A. J. J . Chem. Phys. 1986,85, 5774. (12) Klots, C. E. J. Chem. Phys. 1985,83, 5854; Z . Phys. D 1987,5,83. (13) Klots, C. E. Kinetic Methods for Quantifying Magic. Preprint. (14) Begemann, W.; Meiwes-Broer, K. H.; Lutz, H. 0.Phys. Reu. Lett. 1986.56, 2248. (15) Mgrk, T. D.; Scheier, P.; kiter, K.; Ritter, W.; Stephan, K.; Stamatovic, A. Int. J . Mass Spectrom. Ion Proc. 1986, 74, 281.
0 1991 American Chemical Society
Evaporative Dissociation of Ammonia Cluster Ions
The Journal of Physical Chemistry, Vol. 95, No. 21, 1991 8307
In the present paper, we use previous data from our laboratory on the metastable decay of ammonia cluster ions as a test system for this new method for the reason that binding energies of (NH3),,H+, n = 4-17, are available from other approaches. Additionally, the metastable dissociation processes of (ND3),,D+ are investigated in the present work to determine whether isotope effects influence evaporative dissociations.
Experimental Section The apparatus used in the studies has been described in detail else~here,'~.''and only a brief description of the features relevant to the present study is given here. Neutral ammonia clusters are formed in a supersonic expansion of gaseous ammonia from a pulsed nozzle (diameter = 150 pm). Experiments are performed by subjecting the cluster beam to multiphoton ionization and analyzing the resulting cluster ions in a time-of-flight mass spectrometer. In the present study, the clusters are ionized via nonresonant multiphoton absorption at the focus of a pulsed 355-nm light from a frequency-tripled Nd:YAG laser. The laser system typically produces pulses of approximately 6 4 s duration with fluxes of 1OI6 photons/pulse. Ions formed by multiphoton ionization process are accelerated in a double electrostatic field to about 2 keV and directed through a 130-cm (1,) long field-free region toward a reflectron. Ions are then reflected at an overall angle of about 3O and thereafter travel 80 cm (I,) through another field-free region toward a chevron microchannel plate detector. The signal received by the detector is fed into a 100-MHz transient recorder coupled to an IBM PC/AT computer. The experiments operate at 10 Hz, and typically TOF spectra are accumulated for 2000 laser shots. A reflectron is employed to separate daughter and parent ions in order to measure decay fractions of unimolecular dissociation in the field-free region of our apparatus. This device is composed of a homogeneous reflecting electric field that serves to decelerate and reflect the ions to the ion detector. In this case, ions that do not dissociate between the last TOF lens and the reflectron unit give rise to a "normal" TOF spectrum. However, product ions that arise due to dissociation processes occurring between the last TOF lens and the reflectron form an additional spectrum that becomes displaced to earlier times from the arrival spectrum of the original parent ions. In the present experiments, the initial parent ion energy (Uo), established by potentials applied to the TOF lens elements, was measured to be 1900 f 10 V. A "hard reflection" TOF spectrum can be obtained when the voltage applied to the middle plate of the reflectron unit (Ut) is set higher than the initial parent ion energy. When a metastable parent ion decomposes to a daughter ion and a neutral species, the daughter ion has an energy of u d = (Md/M&, where Mdand M are the masses of daughter and parent ions, respectively. A TOFPspectrum containing a complete set of daughter ion peaks can be obtained when ud < Ut< U,. To identify the dissociation process, we apply an ion cutoff methodIs that involves observing the presence/absence of daughter ion peaks upon changing the voltage settings on the middle plate of the reflectron unit. In measurements of the decay fractions of the metastable cluster ions, corrections concerning instrumental artifacts and ion trajectory of parent and daughters are made to improve the precision.* ND3 (anhydrous, minimum purity 99.5%) used in these experiments was obtained from Cambridge Isotope Laboratories and was used without further purification. Results and Discussion Qundfication of Decay Fractions of (NH3),,H+,n = 4-22. A precise method for measuring decay fractions was reported earlier;* the earlier measured values (denoted by A) are replotted in Figure (16) Breen, J. J.; Tzeng, W. B.; Kilgore, K.;Wei, W.; Keesee, R. G.; Castleman, A. W., Jr. J. Chem. Phys. 1989, 90,19. (17) Tzeng, W.B.;Wei, S.;Castleman, A. W.,Jr. J . Am. Chcm. Soc. 1989,111,6035.
1
,
0.9
4
0.8
e 0.5
c
0.3
d
":LA /d
-
,
10 1
,
14
I
,
18
I
,
22
Number of Ammonia. n
Figure 1. Decay fractions of (NHa),,H+, n = 4-22, as a function of cluster size, n; the experimental values (denoted as A) are taken from ref 8. The solid line is from eq 2 with y = 25 and C,, = 6(n - 1). 1. The qualitative trend that decay fractions increase with cluster size is in good agreement with the predictions of Klots' evaporative ensemble model. The model assumes that each cluster ion has suffered at least one evaporation before entering the field-free region where the metastable dissociation process takes place. The distribution in energies that a cluster containing n evaporative units may possess at time to is then given', by
- exP(-kn(E + Wn)fo) (1) where W,,is the width of the ensemble. As an approximation that Pn(E) a exP(-kn(E)rd
the activation energies of all cluster ions are identical, the daughter ion population at later time t , when the parent ion is normalized to unity at to, is given', by D = (Cn/Y2)In [ t / ( t o
+ (2 - to) exp(-~'~/Cn))I
(2)
where C,, is the heat capacity of cluster size n (in units of Boltzmann constant), y'* = y2/(1 - (y/2C,J2), and y is the Gspann parameter. Since C,,increases with the cluster size, the decay fractions should increase accordingly. To apply eq 2 to the ammonia cluster system, the parameters C,,and y are simply chosen as 6(n - 1) and 25, respectively8 The calculated values are shown in Figure 1 (solid line). Even though the qualitative trend follows well the measured values, it is evident that the predictions from eq 2 display some discrepancy with respect to the experimental values for small cluster sizes. As discussed in the following section, this discrepancy results from different binding energies of ammonia cluster ions at various sizes; it should be noted that the possibility of varying bond energies with cluster size was neglected in deriving eq 2. When one considers that the cluster ions of sizes n and n 1 have different binding energies as denoted by AE,, and Me',the daughter ion population can be calculated from the following equation:"
+
D = 1 - (aW,,)-' In [l
+ (exp(aW,,) - l)to/t]
(3)
where awn =
Wn =
r2(Wn/mn)/tCn(l - 7/2Cn + (y/CJ2/12*-*121 (4)
+ [(dE/dmn)k
- 1 I ( m n - m+,)/bE,l
(5)
(dE/dUn)k = ( C n / y ) ( 1 + y / 2 C n + ( y / C J 2 / 1 2 * * * )( 6 ) In application of the above equations, y is found', to be -25 and independent of the nature of the system, C,,is estimated from the total number of the cluster modes, and to/t is calculated from the experimental conditions. By fitting the calculated decay fractions - U ~ J / A E are , , readily to the measured ones, the values of (U,, obtained. The deduced values of (AI?,, - M,,+,)/AE,,for ammonia cluster ions (NH3),,H+,n = 4-22, are shown in Figure 2. The points
8308 The Journal of Physical Chemistry, Vol. 95, No. 21, 1991 I
I
09
-
08
-
:
07
-
,"
0 6 1 05
-02
I
+
I
4 4
-0 3
I 10
Figure 2. Values of (AE,
I8
14
Number of Ammonia
100
22
n
- AE,,+J/AE,, from eqs
B
7
1
I
0 ; 10
14
18
40
50
60
70
Flight Time (microsecond)
IL i
30
Figure 4. Time-of-flight spectrum of photoionized (ND,),. P,, (ND,),D+; Un, (NDI),I+; An, (NDd,iND2+; I,, isotope p~akof
3-6 plotted as a function of n. Error bars are shown when y is varied from 24 to 25; C,, is assumed to be- 6(n - I). Data points denoted as X are calculated from binding energies in ref 8 .
500 100
I
20
-0 4
8oo 700
Wei et al.
22
Number of Ammonia. n
Figure 3. Plot of binding energies of (NH3),,H+versus n as determined from different method. 0 , thermochemical measurements taken from ref 18. X, Klots' evaporative ensemble model using KERs from ref 8. A, Klots' model from decay fractions, present work.
designated as A are obtained by assuming C, = 6(n - 1 ) and y = 24.5. The influence of the deduced trend in bond energies to the choice of y is evident from the figure; when y is varied from 24 to 25, the variation of (AE,- AE,,+J/AE,, corresponds to the range shown by the vertical lines; note that the vertical lines become equivalent to the size of the symbols for large cluster sizes. It can be easily seen that the values of (AE,, - AE,+I)/M,, are very sensitive to the choice of y for small cluster sizes; however, they become insensitive to y for larger ones. In the case where the binding energies of ammonia cluster ions (NH3),,H+, n = 4-17, were determined* from the measured KERs, the values of ((A& - AE,+I)/AE, are labeled as X in Figure 2 for comparison. Clearly, the difference of the values deduced from the two independent approaches is within fl5%. By using the literature value of binding energy of (NH3)5H+ deduced via HPMS as a reference point,I8 binding energies of (NH3),H+, n = 4-22, are calculated and shown in Figure 3 (labelled as A) with y = 24.5 and C, = 6(n - 1). The values determined from Klots' model by using the KERs measured in our laboratory are designated as X, and the reported thermochemical values are labelled as 0 . It should be noted that due to the sequential process involved in the analysis, errors in selecting the values of C, and y in analyzing the measurements could result in a drift away from the true values of the energy as the analysis proceeds. However, the fact that in the present case the values (18) Keesee, R.G.;Castleman, A. W., Jr. J . fhys. Chem. Ref. Dara 1986, IS, 101I . Castleman, A. W., Jr.; Tang, I. N. J. Chem. fhys. 1975,62,4576.
(ISND3),D+;D,, daughter ions of (ND3),ID+ from (ND,),D+; U,,1900
A 10 V; U,= 1995 V; Uk = 0 V.
from different approaches are in general agreement indicates that the parameters are properly chosen. It should be noted, however, that for small cluster sizes the binding energies deduced from decay fractions are very sensitive to the choices of y and C,. As seen from Figure 3, a 2%variation in y results in about 20%variation of binding energy for (NH3)4H+. Nevertheless, the relative binding energies determined from decay fractions become insensitive to the choices of y and C, for n > 10. Observation of Cluster Ions (ND3),D+, (ND3),IND2+, and (ND,),'. Following ionization of the neutral ammonia clusters, protonated cluster ions (ND3),D+ which are formed via rapid hydrogen atom or proton-transfer reactions are the most abundant species in the spectrum; see Figure 4. An intensity drop between n = 5 and n = 6, which has been reported in other is evident, indicating (ND3)4ND4+is a stable cluster ion that can be pictured as a complete solvation shell formed by four ND, molecules bound to an ammonium core ion. An expanded spectrum is also presented and the peaks are labeled. It should be noted that the peaks labelled D, ( n = 6 and 7) are the daughter ions coming from the metastable decompositions of their corresponding parent ions. The (small) time separation from their parent ions (labelled as P,, n = 6 and 7) is due to their different trajectories in the reflectron.8 The cluster ions (ND,),,ND2+ (labeled as A,, n = 6 and 7) are in general 2-5% of those of (ND,),D+. The unprotonated species (ND3),+ (labeled as U,, n = 6 and 7) are seen in trace amounts. The observations are consistent with the following proposed mechanisms:
--
+
+
(ND3),,,+ nhv (ND3),D+ ND2 ( m- n)ND3 + e- (7) (ND3)n_2N2D5+ + D + ( m- n)ND3 + e- (8) (ND3),+ (m - n)ND, e(9) In the gas phase, the ammonium ion is known to be formed via the reaction of NH3+ with NH,; the reaction is exothermic by 0.74 eV.22 This same reaction is expected to occur via an "internal" ion-molecule reaction within a cluster6 as expressed in mechanism 7. The observation of the cluster ion NH3.NH2+ with an appearance potential of 15.7 eV was reported previously in the electron impact ionization of ammonia clusters.23 More recently, Peifer et al.24reported finding (NH3),,NH2+ and (NH3),H2+, (19)
RR , 78 --
+
+
Hogg, A. M.; Haynes, R.M.; Kebarle, P. J . Am. Chem. Soc. 1966,
(20) Echt, 0.;Morgan, S.;Dao, P. D.; Stanley, R. J.; Castleman, A. W., Jr. Bunsen-Ges. fhys. Chem. 1984,88, 217. (21) Hirao, K.; Fujikawa, T.;Konishi, H.; Yamabe, S.Chem. fhys. k r r .
1984, 104, 184. (22) Castleman, A. W., Jr.; Tzeng, W. B.; Wei, S.;Morgan, S.J . Chem. Soc., Faraday Trans. 1990.86, 2411. (23) Stephan, K.; Futrell, J. H.; Peterson, K. I.; Castleman, A. W., Jr.; Wagner. H. E.: . Diuric. - . N.:. Mark. T. D. Inr. J . Mass Soecrrom. Ion fhvs. 1985,44, 167. (24) Peifer, W. R.;Coolbaugh, M. T.; Garvey, J. F. J . Chem. fhys. 1989, 91, 6684.
The Journal of Physical Chemistry, Vol. 95, No. 21, 1991 8309
Evaporative Dissociation of Ammonia Cluster Ions
20
26
32
38 44 50 56 62 Flight Time (microsecond)
68
74
80
Figure 5. Daughter ion spectrum of (ND,),,D+. U,= 1885 V; Uk= 0 V. n 5 25, in studies made by electron impact ionization of ammonia clusters with electrons ranging in energies from 40 to 100 eV. In addition, they observed a "magic number" (maximum intensity) at n = 7 in the ion intensity distribution of (NH3)n-1NH2+and at n = 8 in the distribution of (NH3)PZ'. Our present observation of (NDJWIND2+is in agreement with theirs, and a weak feature is also observed at n = 7 (not shown here). However, our studies clearly show that no cluster ions (ND3),,NDs+ are present as demonstrated in Figure 4. One possible reason for the discrepancy could be due to the different ionization methods between the two experiments. Metastable Dissociation of (ND3)@+, R = 4-22. In our observable time window between 1 I.CS and a few tens of microseconds, the dominant dissociation process of an ammonia cluster ion can be expressed as (ND3),,D+ -m (ND,),ID+
+ ND3
(10)
A typical daughter ion spectrum is shown in Figure 5 . It has been shown that the decay fractions following the metastable dissociation can be measured by using a reflectron TOF mass spectrometer. By separating the parent and daughter ions and forcing them to follow the same trajectory in the reflectron: we can determine decay fractions with high precision. The measured values of (ND3),,D+,along with resultss of (NH,),,H+, are plotted in Figure 6. On the basis of respective experiments, we estimate an error less than 5% for each point. It is clear that the values of (ND,),D+ are constantly higher than those of (NH3),,H+. To explain the difference between the decay fractions of (ND3),,D+ and those of (NH3),,H+,we consider the Klots' evaporative ensemble model in further detail as follows. From eq 3-6, it is seen that the parameters that influence the observed decay fractions are the following: (1) observation time window ratio to/?;(2) heat capacity term C,,; (3) Gspann parameter y; (4) binding energies AE,,and AEHI, or more precisely the values of ( ( A E n - AE,,+l)/AE,,. For cluster ions (ND3),,D+and (NH,),,H+, the time ratio to/t is kept the same for the measurements. The values of ((AE,, - AE,,+,)/AE,, for (ND3),,D+and (NH3),,H+are approximately the same since the contribution of the zero-point energy is negligible with respect to the magnitude of the binding energies. From the fact that Gspann parameter y is found to be -25 and independent of the cluster systems,I2it is plausible to assume y is the same for (ND3),,D+ and (NH3),,H+. Therefore, the only term that will result in different decay fractions for (ND3),,D+compared to (NH3),,H+ is the heat capacity, C,. In the temperature range 100-1 50 K, which is considered to be the reasonable temperature range of the metastable dissociating ammonia cluster ions, thermochemical measurementsZ5indicate that
(25) Manzhelii, V. G.; Tolkachev, A. M.; Krupskii. I. N.; Voitovich, E. I.; Popov, V. A.; Koloskova, L. A. J . Low Temp. Phys. 1974, 7, 169.
