F. Berthias, L. Feketeová, R. Della Negra, T. Dupasquier, R. Fillol, H. Abdoul-Carime, B. Farizon, M. Farizon, and T. D. Märk

Transcription

1 Correlated ion and neutral time of flight technique combined with velocity map imaging: Quantitative measurements for dissociation processes in excited molecular nano-systems F. Berthias, L. Feketeová, R. Della Negra, T. Dupasquier, R. Fillol, H. Abdoul-Carime, B. Farizon, M. Farizon, and T. D. Märk Citation: Review of Scientific Instruments 89, 0307 (208); View online: View Table of Contents: Published by the American Institute of Physics Articles you may be interested in A mini-photofragment translational spectrometer with ion velocity map imaging using low voltage acceleration Review of Scientific Instruments 89, 030 (208); 0.063/ Attosecond transient absorption instrumentation for thin film materials: Phase transitions, heat dissipation, signal stabilization, timing correction, and rapid sample rotation Review of Scientific Instruments 89, 0309 (208); 0.063/ Simultaneous 3D coincidence imaging of cationic, anionic, and neutral photo-fragments Review of Scientific Instruments 89, (208); 0.063/ A velocity map imaging mass spectrometer for photofragments of fast ion beams Review of Scientific Instruments 89, 0402 (208); 0.063/ Development of a low power miniature linear ion trap mass spectrometer with extended mass range Review of Scientific Instruments 88, 2308 (207); 0.063/ A low energy ion beam facility for mass spectrometer calibration: First results Review of Scientific Instruments 89, (208); 0.063/

2 REVIEW OF SCIENTIFIC INSTRUMENTS 89, 0307 (208) Correlated ion and neutral time of flight technique combined with velocity map imaging: Quantitative measurements for dissociation processes in excited molecular nano-systems F. Berthias, L. Feketeová, R. Della Negra, T. Dupasquier, R. Fillol, H. Abdoul-Carime, B. Farizon, M. Farizon, and T. D. Märk 2 Université de Lyon, F Lyon, France; Université Lyon, Lyon, Villeurbanne, France; and CNRS/IN2P3, UMR5822, Institut de Physique Nucléaire de Lyon, F Lyon, Villeurbanne, France 2 Institut für Ionenphysik und Angewandte Physik, Leopold Franzens Universität, Technikerstrasse 25, A-6020 Innsbruck, Austria (Received 22 August 207; accepted 29 December 207; published online 22 January 208) The combination of the Dispositif d Irradiation d Agrégats Moléculaire with the correlated ion and neutral time of flight velocity map imaging technique provides a new way to explore processes occurring subsequent to the excitation of charged nano-systems. The present contribution describes in detail the methods developed for the quantitative measurement of branching ratios and cross sections for collision-induced dissociation processes of water cluster nano-systems. These methods are based on measurements of the detection efficiency of neutral fragments produced in these dissociation reactions. Moreover, measured detection efficiencies are used here to extract the number of neutral fragments produced for a given charged fragment. Published by AIP Publishing. I. INTRODUCTION Collisions involving molecular systems play an important role in many gaseous and plasma environments where they contribute to both, plasma heating and cooling mechanisms. 3 The study of such collisions is thus not only of fundamental importance, but it is also essential for the understanding of large-scale systems such as astrophysical plasmas, planetary atmospheres, and fusion plasmas. Such collisions are also responsible for energy transfer in ion-matter and ionbiological molecule collisions. Complete knowledge of these elementary processes is thus of primary importance for ioninduced modification of materials as well as for radiolysis and biological damages due to radiation exposure. 4 7 We newly constructed rather versatile tandem Mass Spectrometer (MS/MS), the experimental setup DIAM (Dispositif d Irradiation d Agrégats Moléculaires). 8 The specificity of this apparatus is to produce a very intense beam of mass- and energy-selected molecular cluster ions by combining a high performance cluster source with a double focusing ExB mass spectrometer. A COINTOF (Correlated Ion and Neutral Time Of Flight) detection technique developed recently 9 allows us to detect ion and neutral fragments, from a single dissociation event, and more importantly, the correlation of the time of flights of the fragments is recorded and preserved for detailed analysis on an event by event basis. A Velocity Map Imaging (VMI) technique 0 added to the COINTOF detection technique allows us to record, in addition to the arrival times of the fragments, their impact positions onto the detector plate. Thanks to this experimental setup, we can deduce important information on the dynamics and energetics of the underlying fragmentation mechanism. Along this line, we present here a method developed to measure the detection efficiency of the detector and its electronics. This allows a quantitative measurement of cross sections and branching ratios for the collision-induced dissociation (CID) reactions under study. The method is described and applied here to collision-induced dissociation (CID) of protonated water clusters. Finally, we will show how the detection efficiency measurements are used to extract the number of neutral fragments produced for a given dissociation channel. II. EXPERIMENTAL SECTION The tandem MS/MS type experimental setup has been described thoroughly previously. 8 0 In brief, protonated molecular clusters are produced by electron impact following the supersonic nozzle expansion of an admixture of a vapor of the investigated molecular system and a seed gas (i.e., helium or argon). They are accelerated to a given kinetic energy that can be chosen in the range of 2 0 kev, before being energy- and mass-selected by a double focusing ExB sector field mass spectrometer. The selected protonated cluster beam is then crossed in a collision area at right angles by an effusive jet of argon atoms for which the density is controlled to insure single collision conditions. After the collision and dissociation of protonated precursors, the daughter fragments are detected by the COINTOF-VMI (Correlated Ion Neutral Time Of Flight Velocity Map Imaging) technique. 9,0 The COINTOF technique records the daughter ions as well as neutral species produced from the dissociation of a single parent ion, referred to as the dissociation event. After collision, the fragment ions and the neutral fragments leave the collision area and enter an acceleration zone where the charged fragments are accelerated by.7 kv before reaching the field free zone of the TOF. It has to be noted that in this field free zone, a pusher-electrode allows to spatially separate the impact /208/89()/0307/9/$ , Published by AIP Publishing.

3 Berthias et al. Rev. Sci. Instrum. 89, 0307 (208) FIG.. Correlation plots, y-impact position vs. T, for (a) the first fragment (i.e., ion species) and (b) the second fragment (i.e., neutral species) hitting the MCPs. Associated with the correlation plots, the y-position projection and the T projection are provided where T represents the arrival time difference between the two fragments. These CID results are obtained for 8 kev protonated water tetramer ions, H+ (H2 O)4, interacting with an Ar gas target. position of the charged fragments on the detector plate according to their mass to charge ratio. Neutral fragments emerging from the collision zone are not affected by any electric fields and keep almost the initial velocity of the parent ion (except for small changes due to the additional kinetic energy released in the dissociation process). All species reach a pair of multichannel chevron detector plates (MCPs F2225-2SX from Hamamatsu). Due to the additional velocity acquired in the acceleration field, the charged fragment arrives significantly earlier on the MCP than the corresponding neutral species and triggers the start of the recording window (e.g., between 200 ns and 4 µs). This typical time window allows the recording of all possible daughter fragments formed from a single dissociation event. Furthermore, the intensity of the precursor ions is sufficiently low (typically 500/s) to ensure that in general only fragments coming from a single parent ion reach the detector during the acquisition time window. As a consequence of this, the correlation between the arrival times of the charged and neutral fragments within a given fragmentation event can be deduced without interferences. The arrival times are recorded with a dual Analogic-Digital Converter (ADC, 8 GHz-0 bits, Acqiris ) and a multi-hit Time-Digital Converter (TDC, TDC8HP, Roentdek ) acquisition chain. In this acquisition chain, the dead time is of typically 0 ns. In addition, the (x, y) position of the fragment hitting the multichannel plates (MCPs) is localized using a delay-line anode (DLA). Therefore, any fragment produced from a single dissociation event that arrives at the detector is characterized by a set of three parameters: arrival time, x position, and y position. The data acquisition and the analysis of a large number of single dissociation events (typically 06 events) provide information such as the COINTOF mass spectrum,8 dissociation cross sections and branching ratios, and velocity distributions of the neutral water molecule evaporated from a water nanodroplet.2 As an example, Fig. presents a set of data recorded for a 8 kev-collision-induced dissociation (CID) of H+ (H2 O)4 interacting with an Ar target. The 2D correlation plot, y-position vs. T, exhibits the y-position of (a) the first fragment hitting the detector [i.e., the H+ (H2 O)4 m fragment ion], and (b) the second fragment (i.e., a neutral H2 O species) as a function of the arrival time difference T, i.e., the difference between the arrival time of the second and the first (the ion species in the dissociation) detected fragments, T = T2 T. The y-position projection of the 2D correlation plot provides the distribution of fragments hitting the detector on the y-axis, while the T-projection gives the COINTOF mass spectrum. As the neutral fragment keeps the velocity of the precursor ion, the flight time remains almost constant irrespective of the nature of the neutral species. On the contrary, the fragment ion is accelerated, and thus the flight time depends strongly on the mass to charge ratio m/z, i.e., the lighter the mass, the shorter the flight time is. Therefore, the light masses are associated with the larger T values. The identity of the ion fragments is then obtained from a comparison of the measured T to the one obtained from ion trajectory simulations. As the precursor beam has been initially centered to the middle of the MCPsDLA, referred as the (x = 0; y = 0) position, the y-position of the neutral H2 O fragments shown in Fig. (b) is distributed around y = 0 as these neutral fragments are not affected by the electric fields. In contrast, ion fragments are deflected by the pusher-electrode located in the field free flight zone, and the y-position of the ion fragments shown in Fig. (a) differs according to the mass of the species.0 Therefore in Fig. (a), the two main contributions observed at y = 2 mm and at y = 6 mm are associated with two different daughter ions,

4 Berthias et al. Rev. Sci. Instrum. 89, 0307 (208) H + (H 2 O) 3 and H + (H 2 O) 2, respectively. This is corroborated by the COINTOF mass spectrum, i.e., the two strongest peaks visible in the arrival time range of µs can be attributed to the H + (H 2 O) 3 and H + (H 2 O) 2 ion fragments. H + H 2 O and H + are not present in this example since these ions are deflected out of the MCPs-DLA detection window and thus cannot be detected here. Thus, by specifically selecting a given daughter ion in the COINTOF mass spectrum, i.e., T (within a given range), only the corresponding neutral fragments can be consequently selected. It is interesting to note an additional feature located at y = 0 mm in both Figs. (a) and (b). This is the signature of ion species with a mass heavier than those mentioned earlier. Moreover the y-position is not correlated with a specific T as shown by the horizontal stray region in the 2D correlation plot in Figs. (a) and (b). These events can be attributed to precursor H + (H 2 O) 4 ions that have not dissociated. This feature illustrates the (unwanted) presence of a second parent ion recorded accidental in the acquisition time window triggered by the first decaying parent ion. These false events are sorted out by further analysis including the selection of specific sorting parameters. 0 III. MEASUREMENT OF THE DETECTION EFFICIENCY As the particle, i.e., ion or neutral, hits the detector, its energy relying on the efficiency of the detection system is converted (or not) into a single recorded event possessing three characteristics, i.e., arrival time, and x and y impact positions. The detection efficiency depends on several factors: the nature and the energy of the incident particle that hits the MCPs surface, 3 the specificity of the MCPs given by the manufacturer as well as the applied voltage, 4 the gain of the preamplifiers to produce the electron pulse, and finally the ability to discriminate the pre-amplified signal from the electronic noise prior to recording by the acquisition device. 9,0 In our detection system, the highest level of noise reaches at most a value of 5-7 mv and thus appears to be negligible in the recorded data (see supplementary material of Ref. 0). The following results are obtained from measurements using always the same set of MCPs with an applied voltage of 400 V. The method of measurement of the detection efficiency of the neutral particles, ε 0, is illustrated, here, using as an example collision-induced dissociation (CID) of 8 kev protonated water tetramer ions, H + (H 2 O) 4, under single collision conditions with an argon gas target. We consider in this example the dissociation channel corresponding to the evaporation of one water molecule and use the pusher-electrode in order to spatially separate the impact position of the charged fragments. The detection efficiency can be deduced from the ratio between the number of H + (H 2 O) n ions detected in correlation with an evaporated water molecule and the total number of detected ions, H + (H 2 O) n, ε 0 = N(n) d = d,tot i σ n e i σ n e ε + ε +ε 0, () where d is the number of H + (H 2 O) n ions detected in correlation with a water molecule resulting from the loss of a single water molecule. The value n corresponds to the number of water molecules in the incident cluster, and the subscript d corresponds to the dissociation channel (one evaporated molecule). d,tot is the total number of detected ions H + (H 2 O) n. σ n is the dissociation cross section of the H + (H 2 O) n cluster ion and depends on the gas target and the incident beam energy. e is the target thickness. is the branching ratio associated with the loss of a single water molecule for the protonated water cluster H + (H 2 O) n. ε + is the detection efficiency of the H + (H 2 O) n ion fragment. The detection efficiency ε 0 is therefore calculated by simultaneously determining N n d and N n d,tot in a multiparametric data analysis involving the Object-Oriented Data Analysis Framework (ROOT). 5 This procedure involves spatial distinction between those ions resulting from the evaporation of a single molecule and all other ions. Figure 2 exhibits a close up view of the y-axis projection of the impact position distribution of the first detected fragment (i.e., ion) hitting the detector in the case of the protonated water tetramer. The black curve represents the number of events with a detected multiplicity, M d, larger or equal to, i.e., the number of events involving at least one impacting particle. The observed features have been discussed above in Fig., and they are attributed to H + (H 2 O) 4 (parent ions) and the daughter ions H + (H 2 O) 3 and H + (H 2 O) 2, located at 0 mm, 2 mm, and 6 mm, respectively. The red curve is obtained by additionally restricting M d to 2 and the specific T corresponding to the H + (H 2 O) 3 ion fragment (cf. the COINTOF mass spectrum in Fig. ). As can be seen, the only persisting structure in this case corresponds to the selected fragmentation channel associated with the production of the H + (H 2 O) 3 ions. The integrated yield provides the number of H + (H 2 O) 4 ions, N 4 d, detected in correlation with a water molecule resulting from FIG. 2. y-impact position projection for the first fragment hitting the MCPs after CID of a 8 kev protonated water tetramer ions, H + (H 2 O) 4, interacting with an Ar gas target. The black curve designates dissociation reactions with at least one fragment (M d ); the red curve designates dissociation reactions involving two fragments, i.e., one ion and one neutral fragment (M d = 2).

5 Berthias et al. Rev. Sci. Instrum. 89, 0307 (208) the loss of a single water molecule in this set of analyzed data. The total number of detected H + (H 2 O) 3 ions, N (4) d,tot, is deduced from all the events for which this ion is detected (with or without a neutral molecule associated), and it is extracted using Gaussian fits to the black curve of this set of analyzed data. From these numbers, it is possible to calculate the detection efficiency ε 0 for evaporated water molecules, i.e., for H + (H 2 O) 4 ions impacting with 8 kev, ε 0 is equal to ± The uncertainty given in this case is calculated by propagation of the N 4 d and N 4 d,tot statistical uncertainties. Figure 3 shows the dependence of ε 0 as a function of the velocity of the impacting particle. The obtained values (filled red circles) for the detection efficiency of neutral H 2 O are similar to those measured by Peko and Stephen using a different detection setup (MCPs and electronics) and analysis method and different neutral particles, i.e., H and D atoms. 6 With the present method, we were able to obtain the detection efficiency in general from the analysis of a few thousands of dissociation events, and the typical measurement time for such a data set was about 30 min. Thus, it is possible to carry out such a procedure whenever data are taken. It necessitates absolute calibration, thereby taking into account the status of the detector (e.g., ageing and damage) and improving the quality of the acquired data. In Fig. 3, we also show for comparison detection efficiency values for the ions O + in blue and Ar + in violet reported by Peko and Stephen. 6 The detection efficiency values vary from 3% at a velocity of m s up to about 34% at m s. From these values, we can deduce an empirical law (R 2 = ) of ε 0 as a function of the velocity, v i, for our apparatus valuable in the present velocity range and for the MCPs used in the form of ε 0 = v i v i v i , (2) where v i is the velocity of the incident cluster ion. FIG. 3. Efficiency for the detection of the neutral fragment (H 2 O) as a function of the velocity (red circles). The experimental measurements (red circles) are compared to the efficiencies reported by Peko and Stephen 6 for atoms H (yellow open circles) and D (orange open triangles), and the ions O + (blue open squares) and Ar + (violet open rhombuses). The presently measured detection efficiency is used to determine branching ratios and cross sections detailed in Secs. IV VI. IV. BRANCHING RATIO MEASUREMENT After a collisional excitation, the excited protonated water clusters H + (H 2 O) n will relax along different pathways accessible by the system via the evaporation of m water molecules, each of the dissociation channels being characterized by a branching ratio R m (n) with n m= m =. (3) The underlying mechanisms of the dissociation processes have been discussed elsewhere. Here we will present the method to determine the absolute values R m (n). For a given dissociation channel with m evaporated molecules, the number of ions H + (H 2 O) nm detected in correlation with at least one of these m water molecules, N m (n) d, can be expressed as follows: where m d = diss R(n) m ε + F(ε 0, n, m), (4) N m (n) d is the number of H + (H 2 O) nm ions detected in correlation with at least one of these m evaporated water molecules. is the number of dissociated incident clusters. diss ε + is the detection efficiency of the H + (H 2 O) nm ions. ε 0 is the detection efficiency of the water molecules. F(ε 0, n, m) is the probability to detect at least one of the water molecules among the m evaporated molecules of the incident cluster ion of size n. This can be expressed as F (ε 0, n, m) = m j= m! (m j)!j! (ε 0) j ( ε 0 ) j m. (5) Peko and Stephen 6 showed that the MCP detection efficiency for charged fragments reaches a saturation value between 0.8 and for an ion kinetic energy above kev. In our present setup, because incident-ion kinetic energies are way above kev and taking into account the results from Peko and Stephen, we consider ε + equal for all the charged ions and Eq. (5) can then be expressed as follows: n = + m=2 m. (6) From Eqs. (4) (6), we deduce a mathematical expression allowing to calculate the branching ratio of the dissociation channel corresponding to the evaporation of water molecule (m = ) depending on ε 0 and N m (n) d, = + n m=2 m,d,d mj= m! (m j)!j! (ε 0) j ( ε 0 ) j m. (7) Equation (7) provides the branching ratio for H + (H 2 O) n to dissociate into a H + (H 2 O) n ion and one neutral

6 Berthias et al. Rev. Sci. Instrum. 89, 0307 (208) FIG. 4. Branching ratio for the evaporation of m H 2 O molecule(s) from H + (H 2 O) n, with n = 2 (red), 3 (yellow), 4 (light green), 5 (dark green), 6 (light blue), 7 (dark blue), and 8 (purple). The evaporation is induced by a single collision of the protonated water cluster ions accelerated at 8 kev with an argon atom. FIG. 5. Branching ratios for the evaporation from H + (H 2 O) 4 of one water molecule (red), two water molecules (blue), three water molecules (green), and four water molecules (purple) at four different incident collision energies (3 kev, 4 kev, 6 kev, and 8 kev). H 2 O unit. More generally, we can write for other branching ratios (m > ) as R m (n) = R n m,d,d mj= m! (m j)!j! (ε 0) j ( ε 0 ) j m. (8) Figure 4 shows the branching ratios obtained for 8 kev-cid experiments involving various H + (H 2 O) n ions with n from 2 to 8. The general trend shows a decrease of with increasing m. This would be in line with the general understanding of a sequential evaporation process leading to this type of distribution of fragment ions. Moreover, we can observe an additional trend where R m (n) is larger for smaller the precursor size n. The value of R m (n) is especially large for very small precursor ions, n = 2 and 3, moderate for n = 4 and 5, and small for larger precursor sizes, indicating that the underlying mechanisms are quite dependent on the size of the decaying excited system. In addition to these general trends, the figure exhibits another interesting specific trend, that is, branching ratios for the case n-m = 0 are especially low, for instance, R (2) and R (2) 2 for the evaporation of one and two water unit(s) from the protonated water dimer with 97.5% and 2.5%, respectively (red bars), and R (3), R (3) 2, and R (3) 3 for the loss of one, two, and three water units from H + (H 2 O) 3 with 55.2%, 43.9%, and 0.9%, respectively (yellow bars). These values are comparable to those obtained in low energy (< kev) CID experiments (Ref. and references therein). 7,8 Figure 5 shows the branching ratios measured for the fragmentation of the H + (H 2 O) 4 precursor ions into the 4 possible dissociation channels related to the evaporation of one (red bars), two (blue bars), three (green bars), and four water molecules (purple bars) at four different incident kinetic energies (3, 4, 6, and 8 kev). It can be seen that within the given error bars these branching ratios are not changing much with increasing kinetic energy. m The out-of-equilibrium dynamics of protonated water clusters after an electronic excitation is not yet well known, specifically the influence of the proton mobility on the energy redistribution via the vibrational modes of the water molecules. However, the well-known Zundel- and Eigen-type structures of protonated water clusters 9 could explain the relative maxima leading to the production of H 3 O + and H + (H 2 O) 2 (see Fig. 4), in view of their rather high proton affinities compared to the water cluster ions of higher size. V. DISSOCIATION CROSS SECTION MEASUREMENT In scattering experiments, the number of particles arriving on the detector without fragmentation,, can be derived 0,d from the general attenuation law, 0,d = ε + ( i e σ n e ), (9) where i represents the number of incident particles [e.g., for a protonated water tetramer precursor, H + (H 2 O) 4, n = 4], e represents the gas target thickness, and σ n represents the dissociation cross section. Within single collision conditions, the number of detected undissociated parent ions,, can be 0,d approximated by 0,d = ε + i ( σ n e) (0) and the number of dissociated particles by m,d = ε + i m σ n e. () The ratio between the two numbers provides directly the value of the dissociation cross section σ n as follows: σ n = ). (2) ( + N(n) 0,d m e m,d Scattering processes are described by the interaction cross sections. The collision leads to the exchange of energy between

7 Berthias et al. Rev. Sci. Instrum. 89, 0307 (208) the colliding particles. It may also lead to charge transfer between the target and the projectile. The COINTOF VMI technique is able to provide information on both types of reaction but requiring different operating modes. 20 In the following, we will not include those events associated with charge exchange processes. The pusher-electrode located in the free field zone of the COINTOF VMI (see Fig. ) allows us to separate the fragment ions in the detection plane according to their m/z. Therefore the measured number of un-dissociated precursor ions together with the corresponding measured number of daughter ions for a given dissociation channel n into m provides via Eq. (2) directly the dissociation cross section for this specific dissociation process. Note that besides the ratio N(n) 0,d the gas target m,d thickness, e, must also be measured for the determination of such a cross section. The target thickness resulting from the effusive gas target is controlled via the measurement of the residual pressure in the collision chamber, P res. An absolute calibration is performed here by He + /Ar charge exchange experiments at 7 kev, for which the electron capture cross section is well known. 2 In the measured residual pressure range, mbar to mbar, the gas target thickness increases linearly with P res in agreement with Troitskii s model, 22 e ( 0 4 atoms cm 2) = P res ( 0 6 mbar ) (3) As an example, the total CID cross section (without including electron-capture processes) for 8 kev-h + (H 2 O) 4 ions has been determined to be cm 2. This value agrees well with those expected for such reactions (see Ref. ). VI. MEASUREMENT OF THE NUMBER OF NEUTRAL FRAGMENTS ASSOCIATED WITH A GIVEN DAUGHTER ION In collision experiments, usually information on fragmentation of molecular (and cluster) ions is being obtained via the detection and identification of the charged fragments by mass spectrometry techniques, including both positive and negative daughter ions. However, direct experimental evidence about neutral fragments that are associated with the production of a specific ion species have not been available to date. Theory can predict whether the energetics of the fragmentation can favor the production of certain neutral species along with the production of a specific daughter ion, but this is still far from a truly dynamical description. Based on the detection efficiency of neutral fragments determined in the frame of the present COINTOF technique, we have developed a method to extract the number of neutral fragments associated with the production of a given charged fragment. This is presented and validated, here, in the case of 8 kev H + (H 2 O) 4 CID experiments. Figure 6(a) shows the COINTOF mass spectrum measured for CID of 8 kev H + (H 2 O) 4 ions; the production of H + (H 2 O) 3, H + (H 2 O) 2, and H + (H 2 O) fragments is localized at T = 200 ns, T = 270 ns, and T = 450 ns, respectively. The first dissociation channel, R (4), located at T = 200 ns FIG. 6. COINTOF mass spectrum obtained by using different sorting conditions for 8 kev-cid of H + (H 2 O) 4 : (a) selection of events with strictly two fragments detected, i.e., one ion and one of the evaporated neutral species (M d = 2); (b) selection of events with strictly three detected species (i.e., one ion and two neutrals, detected multiplicity M d = 3). The arrival time difference T is calculated for the ion and the first detected neutral fragment (purple curve), for the ion and the second detected neutral fragment (pink curve), and for the ion and the average arrival time of the two neutral fragments (green curve); (c) the dashed curve is obtained by multiplying the black curve in (a) by a coefficient that depends on the detection efficiency, ε 0, and the probability ξ for the second molecule to fall within the dead-time of the discriminator (see text). Green curve as in (b). is associated with the loss of one neutral water unit while for the second and the third channels additional neutral water units have been evaporated from the precursor cluster ion. It should be noted that this mass spectrum is obtained by using a sorting condition that selects events with strictly two fragments detected, i.e., one ion and one of the evaporated species (M d = 2). Consequently, in the case of the dissociation channel of the evaporation of only one molecule (m = ), all the fragments are detected. In the two other cases, i.e., the evaporation of 2 (m = 2) or 3 water molecules (m = 3), only one neutral water molecule out of 2 or 3 evaporated molecules, respectively, is detected. In Fig. 6(b), the COINTOF mass spectrum is plotted with a different sorting condition involving the strict selection of events with three detected fragments (i.e., one ion and two neutral fragments, M d = 3). The violet line corresponds to these selected events sorted with respect to the (T 2 T ) value, the arrival time difference between the ion (T ) and the first detected neutral molecule (T 2 ). The pink line corresponds to the selected events sorted with respect to the (T 3 T ) value, T 3 being the arrival time of the second detected neutral molecule. The green line corresponds to the selected events (M d = 3) sorted with respect to the value of (T 3 + T 2 )/2 T, the arrival

8 Berthias et al. Rev. Sci. Instrum. 89, 0307 (208) time difference being calculated using the mean value of the arrival times of the two water molecules. When comparing Figs. 6(a) and 6(b), the main feature is the vanishing of the peak ( T = 200 ns, m = ) in Fig. 6(b) where the selected events correspond to the detection of one ion and two neutral molecules. This proves that the corresponding dissociation channel in Fig. 6(a) is associated only with the production of a daughter ion and one single neutral fragment. This kind of result, which is expected here in the test case of the evaporation of a single molecule from H + (H 2 O) 4 leading to a daughter ion H + (H 2 O) 3 will be of interest in the CID of more complex molecular ions. Considering the two peaks with m = 2 and 3, the position of the maxima of the green curve ( T = 270 ns for m = 2 and T = 450 ns for m = 3) involving the mean arrival times is identical to those observed in Fig. 6(a), while the purple curve and the pink curve are shifted with respect to the average position. The shift observed between the purple curve and the pink ones with respect to the green curve results from the arrivaltime order of the molecules on the detector. It implies slightly different T values for each of the molecules detected. Nevertheless, within the selection condition M d = 2, we select events for which we randomly detect the first evaporated neutral molecule or the second one. The good agreement between the green line in Fig. 6(b) and the black curve in Fig. 6(a) shows that in the case of M d = 2, we measure the average arrival time of both evaporated molecules. Moreover, it is interesting to discuss the difference observed in the abundance of the number of events for m = 2 when comparing Figs. 6(a) and 6(b). This difference is due to the detection efficiency of a water molecule [ 20.2% for 8 kev H + (H 2 O) 4 parent ions] since in Fig. 6(a) only one of the evaporated species (M d = 2) is detected and in Fig. 6(b) both of the evaporated species are detected. The dead time (0 ns) of the data acquisition device prevents the detection of two fragments for arrival time difference, T, smaller than this dead-time. Indeed, the detection of two successive particles relies on the capability of the electronics to be fully ready for the detection of the second particle. Therefore, the probability ξ for the second molecule to fall in the dead-time zone has to be taken into account when comparing the abundances in Figs. 6(a) and 6(b). This can be done in the following way. For the dissociation channel corresponding to the evaporation of two water molecules ( T = 270 ns), when the detected multiplicity is equal to 3 [green curve in Figs. 6(b) and 6(c)], the number of measured events can be expressed as When M d is equal to 2 [black curve in Fig. 6(a)], this number of events can be expressed as follows: N (4) 2,Md=2 = N4 diss R(4) 2 ε +ε 0 [ 2 ( ε0 ) + ε 0 ξ ]. (5) The ratio is then given by N (4) 2,Md=3 ε 0 ( ξ) N (4) = 2 ( ε 0 ) + ε 0 ξ. (6) 2,Md=2 As explained previously, the COINTOF method allows the simple measurement of the detection efficiency ε 0 for the water molecules [ε 0 = 20.2%, 8 kev-h + (H 2 O) 4 parent ions]. Thanks to the VMI technique, the probability ξ for the second molecule to arrive within the dead-time can be calculated from Monte Carlo trajectory simulations. Using the measured velocity distribution,2 as an input for the velocity of two molecules evaporated by 8 kev-h + (H 2 O) 4 parent ions in the simulation of the COINTOF setup, the time difference, T, between two successive neutral particles arriving on the MCP can be calculated. These calculated arrival-time differences are presented in Fig. 7 for the protonated water tetramer for various incident energies [8 kev (red), 6 kev (orange), 4 kev (green), and 3 kev (blue)]. The probability ξ for the second molecule to arrive within the dead time is deduced from the comparison between the area under the curve from 0 to 0 ns and the one under the total curve. The value of ξ obtained from these calculations is 34%, 27%, 9%, and 3% for the H + (H 2 O) 4 parent ion at a collision energy of 8 kev, 6 kev, 4 kev, and 3 kev, respectively. As expected, the width of the T distribution increases with higher collision energy and consequently ξ decreases with decreasing velocity of the parent ion. N (4) 2,Md=3 = N(4) diss R(4) 2 ε +ε 0 2 ( ξ), (4) where N (4) 2,Md=3 is the number of H+ (H 2 O) 2 ions detected in correlation with two water molecules. N (4) diss is the total number of dissociated H+ (H 2 O) 4. ε + is the detection efficiency of the H + (H 2 O) 2 ion. ε 0 is the detection efficiency of the water molecules. ξ is the probability for the second molecule to fall in the dead-time zone. FIG. 7. Monte Carlo trajectory simulations for the two water molecules evaporated from protonated water tetramer H + (H 2 O) 4 ions at 8 kev (red), 6 kev (orange), 4 kev (green), and 3 kev (blue) collision energies yielding the shown histograms of T, i.e., the difference between the arrival times of the two neutral water molecules. The shaded area represents the T range where the second water molecule cannot be detected due to the dead time (0 ns) of the discriminator. The distributions are normalized to the total number of trajectories, for each energy.

9 Berthias et al. Rev. Sci. Instrum. 89, 0307 (208) 3.3%, 5.9%, and 2.6% for H+ (H2 O)4 at 8, 6, 4, and 3 kev incident energy, respectively, we have then multiplied the curves obtained with the selection of events of detected multiplicity Md = 2 by the factor (4) N2,Md=3 (4) N2,Md=2 [Eq. (6)] [dashed black curves plotted in Figs. 8(a) 8(d)]. Also shown in Figs. 8(a) 8(d) are the results obtained with the selection of events of detected multiplicity Md = 3 (green line). It can be seen that there exists again very good agreement between the two peaks associated with the evaporation of two molecules at all energies, validating the method and demonstrating the consistency of the experimental data sets. Thus by combining different quantitative measurements in the same instrument, the COINTOF-VMI technique opens up a new perspective for the quantification of the number of neutral species produced in correlation with a fragment ion within a given dissociation channel. VII. CONCLUSION In this paper, we show the ability of the COINTOF VMI spectrometer combined with the event-by-event recording method to provide quantitative information on molecular ion fragmentation processes induced by a collision-induced dissociation. We demonstrate that dissociation cross sections and branching ratios for different fragmentation channels can be derived from measurements of the detection efficiency of neutral fragments. Finally, the method also allows us to measure the number of neutral fragments associated with a given daughter ion resulting from the fragmentation of a complex molecular ion. FIG. 8. COINTOF mass spectra obtained for events of detected multiplicity Md = 3 (green curve) for CID of H+ (H2 O)4 at incident energies of (a) 8 kev, (b) 6 kev, (c) 4 kev, and (d) 3 kev, respectively. The black dashed curves also shown are obtained by multiplying respective COINTOF mass spectra obtained for events of detected multiplicity Md = 2 by a coefficient that depends on the detection efficiency, ε0, and the probability ξ for the second molecule to fall within the dead-time of the discriminator (see text). The red rectangle is focusing on the very good agreement between the two peaks associated with the evaporation of two molecules at all energies, validating the method and demonstrating the consistency of the experimental data sets. ACKNOWLEDGMENTS This work was supported by the Agence Nationale de la Recherche Franc aise through Grant Nos. ANR-06-BLAN039 and ANR-0-BLAN-04. J. S. Brodbelt, Mass Spectrom. Rev. 6, 9 (997). G. Christophorou, in Atomic and Molecular Radiation Physics, edited by J. B. Birks and S. P. McGlynn (Wiley-Interscience John Wiley and Sons, 97). 3 N. F. Mott and H. S. W. Massey, in The Theory of Atomic Collision, 3rd ed., edited by M. F. Mott, E. C. Bullard, and D. H. Wilkinson (Oxford at the Clarendon Press, 965). 4 R. S. Mc Taylor and A. W. Castleman, Jr., J. Atmos. Chem. 36, 23 (2000). 5 G. Veronis, U. S. Inan, and V. P. Pasko, IEEE Trans. Plasma Sci. 28, 27 (2000). 6 D. Trbojevic, B. Parker, E. Keil, and A. M. Sessler, Phys. Rev. Spec. Top. Accel. Beams 0, (2007). 7 T. Schlatho lter, in Radiation Damage in Biomolecular System, Biological and Medical Physics, Biomedical Engineering, edited by G. Garcı a and M. Fuss (Springer, 202). 8 G. Bruny et al., Rev. Sci. Instrum. 83, (202). 9 C. Teyssier et al., Rev. Sci. Instrum. 85, 058 (204). 0 F. Berthias et al., Rev. Sci. Instrum. 88, 0830 (207). F. Berthias et al., Phys. Rev. A 89, (204). 2 H. Abdoul-Carime, F. Berthias, L. Feketeova, M. Marciante et al., Angew. Chem., Int. Ed. 54, 4685 (205). 3 G. A. Rochau et al., Rev. Sci. Instrum. 77, 0E323 (2006). 4 J. L. Wiza, Nucl. Instrum. Methods 62, 587 (979). 5 R. Brun and F. Rademakers, Nucl. Instrum. Methods Phys. Res., Sect. A 389, 8 86, (997). 2 L. Multiplying the black curve shown on Fig. 6(a) by the factor (4) N2,Md=3 (4) N2,Md=2 [Eq. (6)] calculated using ε 0 and ξ values deduced from measurements, we obtain the dashed black curve plotted in Fig. 6(c). This dashed black curve is compared in Fig. 6(c) with the green curve representing the arrival-time difference between the ion and the average arrival time difference of both water molecules with Md = 3, as in Fig. 6(b). It can be seen that there exists very good agreement between the two peaks associated with the evaporation of two molecules. This is clear evidence that two neutral fragments are associated with the production of the charged fragment ion corresponding to this dissociation channel. The method has been applied to different incident energies of the same dissociation channel of the protonated water tetramer, H+ (H2 O)4. Taking into account that the detection efficiency of the neutral molecules decreases from 20.2% to

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