^{1,2}, Pierre Labastie

^{1,2}and Jean-Marc L'Hermite

^{1,2}

### Abstract

We have measured fragmentation cross sections of protonated water cluster cations (H_{2}O)_{ n=30−50}H^{+} by collision with water molecules. The clusters have well-defined sizes and internal energies. The collisionenergy has been varied from 0.5 to 300 eV. We also performed the same measurements on deuterated water clusters (D_{2}O)_{ n=5−45}D^{+} colliding with deuterated water molecules. The main fragmentation channel is shown to be a sequential thermal evaporation of single molecules following an initial transfer of relative kinetic energy into internal energy of the cluster. Unexpectedly, that initial transfer is very low on average, of the order of 1% of collisionenergy. We evaluate that for direct collisions (i.e., within the hard sphere radius), the probability for observing no fragmentation at all is more than 35%, independently of cluster size and collisionenergy, over our range of study. Such an effect is well known at higher energies, where it is attributed to electronic effects, but has been reported only in a theoretical study of the collision of helium atoms with sodiumclusters in that energy range, where only vibrational excitation occurs.

I. INTRODUCTION

II. EXPERIMENTAL SETUP

III. COMPUTATION AND CALIBRATION OF FRAGMENTATION CROSS SECTIONS

IV. EXPERIMENTAL RESULTS

A. Fragmentation cross section

B. Thermal effect

C. Fragmentation patterns

V. DISCUSSION

VI. CONCLUSION

### Key Topics

- Energy transfer
- 36.0
- Atomic and molecular clusters
- 11.0
- Excitation energies
- 9.0
- Collision theories
- 8.0
- Charged clusters
- 5.0

##### B01D1/00

## Figures

Experimental relative intensities of fragments (H_{2}O)_{ n }H^{+} (black lines) from the collision of (H_{2}O)_{30}H^{+} with H_{2}O molecules at four center-of-mass collision energies *E* _{cm}. Continuous and dashed red lines are obtained from Monte Carlo simulations (continuous line: 3*n* − 6 degrees of freedom, *ν* _{0} = 5.5 THz, dashed line: 6*n* − 6 degrees of freedom, *ν* _{0} = 6.5 THz, see text).

Experimental relative intensities of fragments (H_{2}O)_{ n }H^{+} (black lines) from the collision of (H_{2}O)_{30}H^{+} with H_{2}O molecules at four center-of-mass collision energies *E* _{cm}. Continuous and dashed red lines are obtained from Monte Carlo simulations (continuous line: 3*n* − 6 degrees of freedom, *ν* _{0} = 5.5 THz, dashed line: 6*n* − 6 degrees of freedom, *ν* _{0} = 6.5 THz, see text).

Experimental data points for −ln(*I*/*I* _{0}) (see relation (1)) as a function of the product of water vapor density in the cell times the cell length. The continuous line is a linear fit through the data points. The fit yields a value of 125 Å^{2} for the fragmentation cross section. The data points are obtained for (H_{2}O)_{30}H^{+} clusters at a collision energy of 2.3 eV.

Experimental data points for −ln(*I*/*I* _{0}) (see relation (1)) as a function of the product of water vapor density in the cell times the cell length. The continuous line is a linear fit through the data points. The fit yields a value of 125 Å^{2} for the fragmentation cross section. The data points are obtained for (H_{2}O)_{30}H^{+} clusters at a collision energy of 2.3 eV.

Fragmentation cross section, relative to the geometrical cross section, plotted for various cluster sizes and collision energies. (a) Fragmentation of deuterated heavy water clusters induced by collisions with heavy water molecules. (b) Fragmentation of protonated water clusters induced by collisions with water molecules.

Fragmentation cross section, relative to the geometrical cross section, plotted for various cluster sizes and collision energies. (a) Fragmentation of deuterated heavy water clusters induced by collisions with heavy water molecules. (b) Fragmentation of protonated water clusters induced by collisions with water molecules.

Cross section of the fragmentation of (H_{2}O)_{30}H^{+} induced by collisions with H_{2}O molecules as a function of collision energy for two different initial temperatures of the cluster (25 K and 100 K). The continuous and dashed lines are obtained from a Monte Carlo simulation using the model described in the text. Continuous line: 3*n* − 6 degrees of freedom, *ν* _{0} = 5.5 THz, dashed line: 6*n* − 6 degrees of freedom, *ν* _{0} = 6.5 THz. The straight line (red online) at 210 Å^{2} is the geometrical cross section.

Cross section of the fragmentation of (H_{2}O)_{30}H^{+} induced by collisions with H_{2}O molecules as a function of collision energy for two different initial temperatures of the cluster (25 K and 100 K). The continuous and dashed lines are obtained from a Monte Carlo simulation using the model described in the text. Continuous line: 3*n* − 6 degrees of freedom, *ν* _{0} = 5.5 THz, dashed line: 6*n* − 6 degrees of freedom, *ν* _{0} = 6.5 THz. The straight line (red online) at 210 Å^{2} is the geometrical cross section.

The radial energy transfer: only the energy transferred along the radial component *v* _{ radial } is assumed to be transferred into internal energy.

The radial energy transfer: only the energy transferred along the radial component *v* _{ radial } is assumed to be transferred into internal energy.

Fragmentation cross section, relative to the geometrical cross section, plotted as a function of the duration of the collisions for different cluster sizes for D_{2}O (a) and H_{2}O (b) clusters. The vertical lines indicate the vibrational period deduced here from *ν* _{0} = 5.5 THz.

Fragmentation cross section, relative to the geometrical cross section, plotted as a function of the duration of the collisions for different cluster sizes for D_{2}O (a) and H_{2}O (b) clusters. The vertical lines indicate the vibrational period deduced here from *ν* _{0} = 5.5 THz.

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