Collisions of Fe‘ ions, clusters and hydroxides ligated by water molecules P. Pradel,a L. Poisson,a J. P. Visticot,a* J. M. Mestdagha and C. Rolandob a C.E.A., DSM/DRECAM/SPAM, Baü t.522, C.E. Saclay, F-91191 Gif-sur-Y vette Cedex, France b Ecole Normale Supe rieure, De partement de Chimie, F-75231 Paris Cedex 05, France

A laser evaporation source has been used to generate a beam of Fe`, FeOH`, Fe(OH) `, FeH`, Fe ` and Fe ` ions solvated by 2 2 3 up to 11 water molecules, with the major series of ions corresponding to Fe(H O) ` clusters. These ions were collided, prior to 2 n mass selection, with Ar, N , O or CH OH, and apparent scattering cross-sections were measured. Simple collision models, 2 2 3 coupled with a Monte Carlo simulation of the scattering experiment, were used to account quantitatively for the observations. The most striking result is that only methanol exchanges with a cluster water molecule, although this is a minor channel. There is inelastic scattering with argon but the other collisions are mainly elastic.

1 Introduction Clustering of metal ions by solvent molecules is relevant for an understanding of solvent e†ects in chemical reactions at a microscopic level. Such knowledge is useful for the development of reliable models to account for solvation phenomena in important Ðelds such as solution chemistry and atmospheric chemistry. Solvation by water molecules is of particular interest in view of their connection with atmospheric chemistry. For example, water clusters play an important role in the mechanism of chloroÑuorocarbon (CFC) induced polar ozone depletion.1 Moreover, Fe` ions solvated by up to six water molecules have been reported in noctilucent clouds at mesospheric altitudes (ca. 85 km).2 Most studies on metal ionÈwater clustering concern the solvation of alkali-metal3h5 and alkaline-earth metal ions.6h14 There have been fewer studies of the solvation of other ions. Notable exceptions concern the solvation, by up to four water molecules, of transition-metal ions.15h21 Solvation of Al` has also been studied.22 Essentially, two questions may be addressed when investigating metal-ion solvation : (i) what is the nature and strength of the bonding of the metal ions with the surrounding solvent molecules ? and (ii) how do the solvent molecules a†ect the ion reactivity ? Most of the work cited above attempted to answer the Ðrst question. The present work is a step toward answering the second question, by examining the e†ect of collisions on solvated metal ions. Iron ions Fe`, ligated iron ions FeOH`, Fe(OH) `, FeH` and small Fe ` clusters, solvated 2 n by water molecules, were collided with simple gases (Ar, N , 2 O and CH OH). The experiment was carried out using a 2 3 set-up that couples a laser evaporation source, which generates the cluster ions, with a time-of-Ñight mass spectrometer. The collision experiment consists of colliding these ions, prior to mass selection, and observing the e†ect of the collisions on the relative intensities of the mass peaks. Two questions are addressed in the present work. The Ðrst considers the elastic or inelastic character of the collisions. The question is whether the cluster behaves as a rigid body leading to elastic collisions, or if the numerous internal degrees of freedom of the cluster could actually be coupled to the collision coordinate, leading to an inelastic collision. We Ðnd that the answer depends on the nature of the target and not on the size and chemical nature of the cluster ion. The second question is closely connected to the existence of inelastic collisions,

and concerns whether the collision can attach the target to the cluster ions, either by a simple pick-up or by a waterÈtarget exchange reaction. Answers to these questions do not come directly from the raw experimental data in our present beam-gas scattering experiments, since these give only e†ective collision crosssections, but are obtained using simple collision models and a Monte Carlo simulation of the collision experiment.

2 Experimental The experimental set-up is essentially the same as that described in ref. 23. It is shown schematically in Fig. 1. Hydrates of iron ions are generated in a Smalley-type source that combines laser vaporisation and supersonic expansion.24 The second harmonic of an Nd : YAG laser (Quantel 585-10), with energy ca. 5 mJ per pulse, is used to vaporise metal atoms and metal ions from a rotating and translating iron rod (Johnson Matthey, purity 99.9985%). The cluster beam is generated by pushing the plasma, formed in the vaporisation zone, with a mixture of helium and water, through a piezoelectric valve,25 operating at 10 Hz with a 70 ls opening time. The backing pressure of the helium gas is 1 atm and it is mixed with water by bubbling through distilled water at room temperature before entering the source chamber. The pulsed supersonic expansion takes place after the gas mixtures have passed through the vaporisation zone. The expansion proceeds via a 2 mm diameter, 30 mm long channel. The neutral and ionic metal clusters, created by the laser vaporisation, are thermalised as the gas mixture Ñows through the channel

Fig. 1 Experimental set-up

J. Chem. Soc., Faraday T rans., 1997, 93(9), 1697È1703

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and then cooled further in the supersonic expansion that follows. The clusters are formed either during the thermalisation stage, or during the expansion, or both. No further means of ionization is used. The beam is deÐned by a 5 mm diameter pre-skimmer and a 3 mm diameter skimmer separated 257 mm apart. After the pre-skimmer, it crosses a region (diameter 15 and length 140 mm) where collisions with the scattering gas (Ar, N , O or 2 2 CH OH) take place. The scattering-gas pressure can be varied 3 between 0 and 3 ] 10~6 mbar. The beam then enters a deÑection region where the positive ions are extracted from the beam by a voltage pulse on three deÑection plates forming a Wiley and McLaren device.26 The entrance diaphragm into this region is the 3 mm diameter skimmer. This deÐnes the detector aperture used in Section 5. The timing between opening of the pulsed valve and application of the ion extraction voltage was used to ensure that ion velocities in the beam are 2300 ^ 200 m s~1. The ions are mass analysed in a high-resolution reÑectron time-of-Ñight mass spectrometer (Bruker, Franzen analytic)27 and detected using multi-channel plates. Finally, the spectra are recorded on a 200 MHz digitizer (Sony Tektronix RTD 710) and stored using a PC. The experiments are conducted by recording mass spectra as a function of the gas pressure in the scattering region. Since the clusters all have the same velocity in the beam, whatever their mass, the average collision energy depends on the cluster size. It varies from 0.5 eV in the Fe`ÈAr collision to 0.75 eV in the Fe(H O) `ÈAr collision. With N as perturber, instead of 2 10 2 Ar, the collision energies range from 0.4 to 0.55 eV. The results of the scattering experiments are presented in Section 4. Variations in peak intensities in the raw data as the scattering gas pressure is varied do not yield collision crosssections directly. The procedure used to extract cross-sections from the experimental data is described in Section 4.2.

3 Preparation of the cluster ions A typical mass spectrum is shown in the top panel of Fig. 2. As shown in the lower panels of the Ðgure, the full spectrum can be understood as the superposition of several series of peaks, corresponding to the solvation of bare iron ions (Fe`), iron cluster ions (Fe ` and Fe `) and ligated iron ions 2 3

[FeOH`, Fe(OH) `, FeH`] with up to 10 water molecules. 2 The shape of this spectrum is fairly insensitive to variation in the He backing pressure. Varying the energy of the evaporation laser pulses a†ects, essentially, the abundance and size of the iron clusters. Under extreme conditions (10 mJ pulse~1), up to Fe ` clusters have been observed. 8 The times between the gas pulse, the laser pulse and the pulse of the extraction voltage have also been varied systematically. Two times are considered : Ðrst, varying the delay between the gas pulse and the laser pulse changes the time spent by the carrier gas with the plasma formed in the laser evaporation ; roughly, a long interaction time (100 ls) stimulates formation of large complexes. Secondly, varying the delay between the gas pulse and the extraction pulse allows extraction of the ions at will, between the early and the late stage of the supersonic expansion. Late extraction stimulates the formation of large clusters. Under extreme conditions, solvation by up to 20 water molecules could be observed. The cluster distributions shown in Fig. 2 for each family of peaks are characteristic of those observed in laser vaporisation sources. They are adequately Ðtted by Poisson distributions [P(n) \ jn/n ! exp([j)]. One such Ðt is shown for the family of peaks Fe(H O) ` (dashed line). It corresponds to 2 n j \ 6 ^ 1. We recall that the Poisson distribution gives the probability P(n) of observing n events from zero-memory (i.e. independent of past events) stochastic phenomenon that yields an average of j events (collisions). Successive collisions of a projectile passing through a gas are adequately described by Poisson statistics. The Ðt shown in Fig. 2 thus indicates that ionic cores experience ca. six attaching collisions in order to form the observed cluster ions. A statistical model has been proposed to account for cluster distributions in laser evaporation experiments.28 A log-normal distribution was used to describe the size distribution of the cluster. Unfortunately, the paper does not discuss the physical meaning of the parameters k and p of the distribution, only the goodness of the Ðt is considered. We think that the Poisson distribution that has very much the same shape as a log-normal distribution is a better function for Ðtting cluster distributions since its unique parameter j has a clear interpretation in terms of a collision number for forming cluster ions. The experimental conditions used for the collision studies reported below correspond to an average mass of the cluster ions present in the beam of 180 ^ 10 u. This number will be useful, in the following, for normalisation purposes.

4 Experimental results 4.1 Raw data

Fig. 2 Typical mass spectra obtained with the laser evaporation source. Each “ family Ï is scaled by a factor indicated on the right-hand side. (É É É É É) shows a Poisson distribution for j \ 6.

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The main e†ect of collisions is to scatter the cluster ions out of the beam. The total ion current, measured as the integrated mass spectrum, thus decreases as the pressure of the scattering gas is increased in the collision cell. No attempt has been made to relate the gas pressure to an absolute scale. Therefore, the scattering data shown in Fig. 3 and 4 are plotted as a function of the total ion current. The horizontal scale of the plot, i.e. the total ion current, is given in arbitrary units. The value of one on this scale corresponds to the ion current measured when no scattering gas is added in the scattering volume. The total ion current decreases exponentially to zero, according to the BeerÈLambert law, when gas is added in the scattering volume. As we shall see later, the horizontal scale of the plot is thus related to the number of collisions experienced by the cluster ions. The right-hand side of the plot shows what happens when no collision is acting on the cluster ions and the left-hand side illustrates what happens when many collisions are present. Fig. 3 and 4 display the intensity of a number of peaks of the mass spectra as a function of the total ion current on

some other peaks seems fairly insensitive to the scattering gas pressure [e.g. Fe(H O)` ]. Finally, the family of 2 11 Fe(CH OH)(H O) ` ions, shown in Fig. 4 requires a speciÐc 3 2 n comment. It is not present at zero CH OH pressure and 3 appears gradually as methanol is introduced into the scattering region. It corresponds to the attachment of one methanol molecule by the cluster in a clusterÈmethanol collision or to a solvent molecule exchange, where one or more water molecules are replaced with one methanol molecule. Such behaviour has not been observed with argon. Experiments have also been performed with O and N as 2 2 scattering gas. The corresponding results are qualitatively similar to those reported in Fig. 3 and 4 for argon and methanol. As with argon, no attachment of O and N to the 2 2 cluster ions is observed. 4.2 Data analysis

Fig. 3 Contribution to the full mass spectrum of several mass peaks as a function of the total ion current when the pressure of the scattering gas (Ar) is varied. Large scattering-gas pressures correspond to small values of the total ion current. (…) Experimental data, (ÈÈ) Ðts of the experimental data by the Ðrst data analysis procedure (see text).

varying the scattering gas (argon and methanol, respectively) pressure. The peak intensities have been normalised with respect to the total ion current and therefore represent the contribution of the speciÐed peak to the full spectrum. Several di†erent e†ects are observed in Fig. 3 and 4. The contribution of Fe` to the total spectrum increases dramatically as the cluster beam is collided with argon, whereas the contribution of Fe(H O) ` decreases in the same experiment. 2 3 Increasing contributions may indicate either that the corresponding ion is being formed by collision in the scattering zone, or that it is less a†ected by collisions than other ions. Both types of behaviour are encountered. The contribution of

Observation of the raw data has revealed the existence of two categories of ions : those that exist prior to collisions and those that are created by collisions [namely Fe(CH OH)(H O) ` ions]. Each category requires a speciÐc 3 2 n treatment in order to extract e†ective cross-sections from the scattering data. 4.2.1 Ions existing prior to collisions. The main e†ect of collisions is to reduce the total ion current I by scattering cluster ions out of the beam. Let p be the cross-section for this process, and N L be the product of the number density of the s scattering gas and the length of the scattering region. The total ion current I is attenuated according to the standard BeerÈLambert law : I(L ) \ I(0)exp([pN L ) (1) s The cross-section p is the e†ective cross-section of the scattering process. The way in which it di†ers from the real crosssection is a†ected by the thermal motion of the scattering gas and by the relative geometry of the ion beam, the scattering volume and the ion detector. The relating of e†ective crosssections to real ones was investigated in detail in the 1960s by groups measuring total scattering cross-sections using the beam attenuation method29h32 and has been reviewed recently.33 In our case, the cross-section p is further averaged over the size distribution of the clusters present in the beam. The important problem of relating e†ective cross-sections to the real ones will be addressed in Section 5. Let p be the e†ective cross-section for scattering the ions m of mass m out of the beam, and let us assume the speciÐed ion is not being formed by any collision process and then scattered into the detector region. In this case, the attenuation of the partial ion current I due to the interaction of the ion m beam with the scattering gas is simply given by the BeerÈ Lambert law, as the total ion current : I (L ) \ I (0)exp([p N L ) (2) m m m s The contribution of the ion of mass m to the full mass spectrum is given by the ratio I /I. Eqn. (1) and (2) allow us to m derive

C D

I (L ) I (0) I(L ) (pm~p)@p m \ m I(0) I(0) I(L )

Fig. 4 As Fig. 3 but with CH OH as scattering gas ; (È È È) in the top 3 using the second data analysis profour panels corresponds to Ðts cedure (see text)

(3)

The ratio I(L )/I(0) in the right-hand side of eqn. (3) expresses the total ion current in arbitrary units, i.e. it directly represents the horizontal scale of each panel in Fig. 3 and 4. Therefore, eqn. (3) has been used to Ðt the scattering data. Fits are shown as solid lines in Fig. 3 and 4. The peak intensity variations are well Ðtted, except for ion masses that are populated by the collisions. This is the case for Fe`, where no Ðt is J. Chem. Soc., Faraday T rans., 1997, V ol. 93

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the parent ion of mass m at the point x of the scattering region are : dI (x) d \ [pN I (x) ] p N I (x) s d r, m s m dx dI (x) m \ [(p ] p )N I (x) r, m s m dx

(4)

After integration over the scattering region of length L , the ion current I (L ) is given by : d I(L ) pr,m@p I (L ) I (0) d \ m 1[ (5) I(0) I(0) I(L )

A C D B

Fig. 5 (p [ p)/p as a function of m, p and p are deduced from the m m Ðrst data analysis (see text). (L) Fe(OH) (H O) `, (|) Fe 2 2 n OH(H O) `, (]) Fe(H O) `, (]) FeH (H O) `, ()) Fe (H O) `, (5) 2 n 2 n 2 n 2 2 n Fe H (H O) ` and (=) Fe (H O) `. (ÈÈ) Predictions of the scat2 2 n 3 2 n tering model.

shown, and for the Fe(CH OH)(H O) ` family, that requires 3 2 n a separate treatment given below. The Ðt performed using eqn. (3) provides us with the value of the ratio (p [ p)/p. The corresponding values are shown in m Fig. 5. Each panel of the Ðgure corresponds to a di†erent scattering gas. The ratio (p [ p)/p is plotted as a function of the m ion mass m. A positive value of (p [ p)/p indicates that the m contribution of the ion of mass m to the full spectrum is enhanced by the collisions ; it is negative in the opposite case. 4.2.2 Ions being formed by the collisions. The second data treatment deals with ions that are populated by the collisions and that do not exist in the ion beam prior to collision. It, therefore, deals with the Fe(CH OH)(H O) ` family of ions 3 2 n that originates in the collisional addition of methanol to the parent cluster Fe(H O) ` or in the substitution of water by 2 p methanol in the same parent family. Let p be the crossr, m section of the addition (or substitution) process, m being the mass of the parent ion. As in the Ðrst model, let p be the average cross-section that describes the collisional decay of all the ions present in the beam. The rate equations describing the variation of the ion currents I (x) and I (x) of the daughter ion of mass d and of d m

Again, the cross-sections p and p that appear in eqn. (5) are r, m e†ective cross-sections. The data of Fig. 4 that concern the Fe(CH OH)(H O) ` ion family have been Ðtted using eqn. (5). 3 2 n This provides the ratio p /p as a function of n for n O 10 as r, m shown in Fig. 6. The Ðts are shown as dashed lines in Fig. 4 for n \ 1, 4, 7 and 9. The uncertainty in the value of 0.06 found for p /p at m \ 218 u is probably quite large, since the r, m population of the parent Fe(H O) ` is very small under the 2 10 experimental conditions.

5 Numerical analysis 5.1 Collision models Two collision models have been derived to account for cluster collisions. They correspond to two extreme assumptions. In the Ðrst, the collision is elastic : no collision energy is transferred to the cluster, which acts as a rigid body during the collision. In the second, 100% of the collision energy is transferred to the cluster as internal excitation. This model corresponds either to addition of the scattering gas to the cluster, or to a situation where solvent molecules are ejected from the cluster with negligible kinetic energy. The discussion in Section 6 examines the physical picture brought by these models and their validity with respect to cluster collisions. The present section deals with connecting the real cross-sections used in the collision model to the e†ective cross-sections provided by analysis of the experimental data. According to the Ðrst collision model, scattering of the cluster ion by a scattering gas molecule is well represented by two structureless particles moving in a 1/R4 potential (1/R4 is the well known potential for a point charge interacting with a polarizable particle). In this case, the scattering process is described by a forward-peaked di†erential cross-section of the form (see for example ref. 34) :

C A BD

h 2 dp dp (h) \ (0)exp [ h* dX dX

(6)

where h is the centre of mass scattering angle and h* the differential cross-section angular width. A value of 1 radian was chosen for h* in the calculation reported below. According to the second collision model, clusters have zero velocity in the centre-of-mass reference frame. No angular distribution has to be considered in this case since all the clusters are scattered in the direction of the cluster/target centre-ofmass. 5.2 Monte Carlo simulation of the scattering experiment Fig. 6 Data analysis of the Fe(CH OH)(H O) ` family using the 3 Predictions 2 n of the scattering second data analysis procedure. (ÈÈ) model.

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Monte Carlo calculations are used to simulate e†ective crosssections from the above two models. The simulation considers all the parameters that a†ect e†ective cross-sections : the posi-

tion and diameter of the diaphragms that deÐne the ion beam, spatial and velocity distributions of the scattering gas, angular and velocity distributions of the scattered ion in the laboratory after proper transformation of the centre-of-mass reference frame into the laboratory reference frame, e†ect of multicollisions, e†ect of the acceptance angle of the ion detector. The random generator of the MicroSoft fortran library was used to sample the following items : cluster ion trajectory before the collision, velocity (module and direction) of the target molecule, location of the collision, scattering angles of the ion in the centre-of-mass reference frame and iteration for the possibility of several collisions. 2 000 000 random events were sampled and, for each, the ion trajectory across the scattering region was calculated. The calculation was performed under the collision regime that is achieved experimentally : a cluster ion experiences an average of two collision events when crossing the scattering region. Knowing the detection geometry, we could simulate signals corresponding to both collision models. Calculations were performed for cluster ions of mass 56 ] 18n u [Fe(H O) `] with n \ 0 to 11 and for 2 n scattering gases of mass 40 (argon), 32 (oxygen and methanol) and 28 u (nitrogen). The data analysis distinguishes between whether the cluster ion that is to be detected is present in the mass spectrum prior to collisions or is populated by the collision. The same distinction has to be made here to derive e†ective cross-sections from the Monte Carlo simulations. In the Ðrst case, collisions scatter the ions without changing their mass. The Monte Carlo calculation thus simulates a beam attenuation experiment, and the e†ective cross-section p of the process is calculated for each value of m using eqn. m (2). The corresponding results are shown in Fig. 7(a) for scattering of the cluster ion by a gas of mass 32 u. The two curves correspond to the two collision models. The experiment was performed with 180 ^ 10 u average-size cluster ions. The calculated cross-section p is therefore plotted in Fig. 7 after norm malisation according to (p [ p )/p for easy comparison m 180 180 with the experiment in the next section.

Fig. 7 (a) p and (b) p , calculated according to the collision m r, m models of Section 5, for scattering of clusters of mass m by a gas of mass 32 u. (a) (È È È) Elastic scattering model, (ÈÈ) fully inelastic model. (b) (ÈÈ) Branching ratio, b \ 0.01, between solvent model addition (or substitution) and elastic scattering. The horizontal scale is the mass of the cluster ion ; it has been made continuous in the calculation although, in reality, the values are integers.

The second scattering situation is when collisions result in solvent molecule addition (or substitution). At Ðrst sight, the fully inelastic collision model is the only one that is relevant in this case, since no kinetic energy is available in the centre-ofmass reference frame after the collision. On this basis, the trajectories that are provided by the Monte Carlo simulation provide the following information : those that hit the detector when the scattering gas is absent are the Ñux U of the parent m ions of mass m, and those that hit the detector with the scattering gas present are the Ñux U of daughter ions. This means d that we assume that each collision results in solvent molecule addition. This is certainly not the case. Only a few trajectories lead to solvent molecule addition or substitution. We therefore assume that the collision is mainly elastic and that the branching ratio for solvent molecule addition or substitution is b, where b is much less than one. According to this, there are two steps in the simulation of a solvent molecule addition (or substitution). The Ðrst step is a fully elastic calculation that provides the e†ective elastic cross-section p using eqn. (3). m The second step involves a fully inelastic calculation and provides the e†ective reactive cross-section p through the r, m expression :

A

B

U 1 ln 1 [ d (7) p \[ r, m bU N L m s The corresponding results are shown in Fig. 7(b) for a 32 u gas and a branching ratio b \ 0.01. The cross-section is plotted as a function of m. Here, too, the e†ective cross-section p is r, m scaled with respect to the scattering cross-section p of the 180 ions of average mass 180 u present in the beam.

6 Discussion 6.1 Scattering of clusters by argon atoms We start the discussion by considering the calculated e†ective cross-section p shown in Fig. 7(a). This will help to discuss m the comparison between these calculations and the experimental observations. We shall then be in a position to obtain information about the inelastic character of cluster scattering and about collision-induced evaporation of solvent molecules from the cluster. The behaviour of the ratio (p [ p )/p that is shown in m 180 180 Fig. 7 can be understood very simply. Let us split the di†erential cross-section of the scattering process into three regions corresponding to forward, backward and sideways scattering. Considering that the angular aperture of the ion detector is not inÐnitely small, forward scattered clusters are detected, whatever their mass. Considering that the detector aperture is not 4n sr in the laboratory frame, backward scattered clusters never reach the detector, whatever their mass. In both cases, the value of (p [ p )/p is therefore zero. This ratio m 180 180 behaves di†erently when considering sideways scattering ; it is non-zero and its values depends on m. Heavier clusters, indeed, are scattered in the laboratory frame at a smaller angle than the light ones. They accordingly reach the detector in larger quantities and are associated with smaller e†ective scattering cross-sections than light clusters. This explains the general trend observed in Fig. 7 where the ratio (p m [ p )/p is negative above m \ 180 u, and positive below. 180 180 From the calculation we know that this e†ect is more pronounced when the amount of kinetic energy available in the centre-of-mass reference frame is smaller (the solid curve corresponding to inelastic scattering has a larger slope than the dashed curve that corresponds to fully elastic scattering). In contrast, the e†ect of varying the width of the di†erential cross-section [the h* parameter in eqn. (6)] is small. The more isotropic the cross-sections are, the smaller the variations in the ratio (p [ p )/p . m 180 180 J. Chem. Soc., Faraday T rans., 1997, V ol. 93

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We come now to the discussion of the e†ective crosssections derived from experiment (Fig. 5). We start the discussion with argon. The behaviour that has just been discussed, where p m decreases as m is increased, is exactly what is observed experimentally in Fig. 5 when the cluster mass is heavier than 120 u. The Ðgure shows that the variation of p is the same for the m various families of ions present in the beam. This certainly suggests that the trend in p variation is due to the mass of m the cluster ion rather than to its chemical nature. The calculated ratio (p [ p )/p was compared to the experimental m 180 180 ratio (p [ p)/p. The best agreement was found for the calcum lation assuming that the collision is fully inelastic, i.e. when argon atoms leave the cluster with negligible kinetic energy. The corresponding prediction is shown as a solid line in Fig. 5. It is in excellent agreement with the experimental crosssection, except for clusters with two and three water molecules. We shall return to this point later. The strongly inelastic character of the collision can be understood when considering that argon has a larger mass (40 u) than the water molecules forming the cluster ions (18 u). The collision energy (0.5 to 0.75 eV) has, indeed, the same order of magnitude as the binding energy of water molecules to the ionic core [expected to be O0.8 eV for clusters larger than Fe(H O) ` 21]. In this case, argon atoms that 2 4 collide with the cluster at impact parameters smaller than the capture radius of the cluster (3 to 4 Ó) enter fairly deeply into the cluster and are inelastically scattered within the cluster. The collision energy is thus transferred, as heat, into the cluster. Argon atoms could be trapped by the cluster in such a process but this is actually not observed for the following reasons : Ðrst, the binding energy of argon to the ionic core is expected to be about an order of magnitude smaller than that of water (the binding energy Fe`wAr is 0.175 eV35 whereas that of Fe`wH O is 1.33 ^ 0.05 eV21) ; secondly, the cluster 2 has insufficient degrees of freedom to accommodate the collision energy. It therefore evaporates particles after the collision. Since argon is the less strongly bound particle, it is likely to be the one to evaporate. Let us now return to the e†ective cross-sections that are smaller than calculated, for ions carrying two and three water molecules. This observation indicates that the corresponding ions are more populated than predicted by the calculation. A possible reason can be found in the evaporation process that has just been discussed. Collisions of large clusters may lead to fragmentation, as a minor channel, besides the evaporation of argon. As a result, small cluster ions are populated from the large one, thus decreasing the associated e†ective scattering cross-section. Similarly, the large increases in the iron peak intensity observed in Fig. 3 at high argon gas pressures should also be correlated with the evaporation process.

no tendency to fragment into smaller ones, as was discussed to be the case with argon. The fact that the collision with molecular targets is elastic is very intriguing. The mass of oxygen and methanol is indeed marginally smaller than that of argon and therefore should not a†ect the scattering of the target within the cluster. The qualitative di†erence between argon, and O and CH OH is 2 3 more likely related to the molecular character of the latter targets. The rotation of the molecules may indeed prevent their penetrating the cluster, thus resulting in little transfer of the collision energy to internal vibration of the cluster. The agreement between experiment and calculation for N 2 is poor. E†ective scattering cross-sections of clusters with less than Ðve or six water molecules are much smaller than calculated. It is hard to believe that this trend could be due exclusively to collisional fragmentation of heavier clusters, N 2 being the lightest of the four targets that have been investigated.

6.2 Scattering of clusters by molecular targets

7 Conclusion

The qualitative trend observed in the previous section with argon is used now as a guide line in discussing the molecular targets. The decrease in the e†ective cross-section p as m increases m is actually observed, when m is large enough, both for argon and the molecular targets. However, the e†ect is much smaller for the molecular targets, and appears only for those with 32 u. For these gases, the best agreement is found with the Ðrst collision model of Section 5, when assuming that the collision is fully elastic. The predictions of the elastic-scattering version of the model are shown as solid lines in Fig. 5. The agreement is quantitative for both methanol and oxygen targets, even for the smaller cluster ions. This makes a further di†erence from what is observed with argon, and must be related to the elastic character of the collision. No energy is transferred as heat to the cluster, and large clusters thus have

The laser evaporation of an iron rod coupled to the supersonic expansion of a gas containing water vapour was used to generate a beam of Fe`, FeOH`, Fe(OH) `, FeH`, Fe ` and 2 2 Fe ` ions solvated by up to 11 water molecules. The main 3 series of ions corresponds to Fe(H O) ` clusters. These ions 2 n were collided with Ar, N , O and CH OH, and apparent 2 2 3 scattering cross-sections were measured. Simple collision models, coupled to a Monte Carlo simulation of the scattering experiment, were used to account quantitatively for the observations. This provided us with information on the relative importance of elastic, inelastic and ligand exchange collisions. Only methanol exchanges with cluster water molecules. This is a minor channel representing only 1% of the scattering events that, surprisingly, does not depend on the size of the cluster. The major event in collisions with the three molecules was found to be elastic scattering. In contrast, collisions with

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6.3 Exchange reactions in cluster collisions The discussion of Sections 6.1 and 6.2 has stressed the possibility that the target may penetrate deep into the cluster before leaving it. We have just seen that the probability of such behaviour for methanol is small. However, with respect to the few events exhibiting this behaviour, we must also consider the following point. The interaction energy of methanol with the ionic cluster is expected to be comparable with, or larger than, that of water (the bond energy of Fe`wCH OH 3 is 1.4 eV36 whereas that of Fe`wH O is 1.33 ^ 0.05 eV21). In 2 this case, the particle that evaporates from the cluster is not necessarily methanol, but can be water. The second collision model described in Section 5 is appropriate for this process. The ratio p /p that is predicted by the model in the lower r, m 180 panel of Fig. 7 is compared to experiment in Fig. 6. The calculated curve was obtained assuming that 1% of the scattering events result in exchange between one methanol molecule of the scattering gas and one water molecule of the cluster. Good agreement is observed between experiment and calculation. Note that the increase in the e†ective exchange cross-section with m does not reÑect increasing efficiency of the exchange process as m increases (it is equal to 1% whatever the value of m), but simply that e†ective cross-sections are measured. The good agreement, observed in the Ðgure, between experiment and calculation, suggests that the exchange of solvent molecules is a minor channel that does not depend on the size of the cluster. A closer examination of Fig. 6 shows that the calculation slightly underestimates the increase in p /p as m r, m varies. This might be due to an increased exchange efficiency for large clusters. However, the discrepancy between experiment and calculations is too small compared with the experimental uncertainties to be conclusive on this point.

argon are strongly inelastic for clusters carrying more than three water molecules. There is also evidence that collisions with argon result in fragmentation of the clusters to smaller ones, a process that is apparently less important in collisions with oxygen and methanol.

17 18 19 20

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