Abstract
Solvation is a ubiquitous phenomenon in the natural sciences. At the macroscopic level, it is well understood through thermodynamics and chemical reaction kinetics1,2. At the atomic level, the primary steps of solvation are the attraction and binding of individual molecules or atoms of a solvent to molecules or ions of a solute1. These steps have, however, never been observed in real time. Here we instantly create a single sodium ion at the surface of a liquid helium nanodroplet3,4, and measure the number of solvent atoms that successively attach to the ion as a function of time. We found that the binding dynamics of the first five helium atoms is well described by a Poissonian process with a binding rate of 2.0 atoms per picosecond. This rate is consistent with time-dependent density-functional-theory simulations of the solvation process. Furthermore, our measurements enable an estimate of the energy removed from the region around the sodium ion as a function of time, revealing that half of the total solvation energy is dissipated after four picoseconds. Our experimental method opens possibilities for benchmarking theoretical models of ion solvation and for time-resolved measurements of cation–molecule complex formation.
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Data availability
The data supporting the findings of this study are available within the paper and its Supplementary Information. Should any raw data files be needed in another format, they are available from the corresponding author upon reasonable request. Source data are provided with this paper.
Code availability
The computing code used for the TDDFT simulations (M. Pi et al. 4He-DFT BCN-TLS: A Computer Package for Simulating Structural Properties and Dynamics of Doped Liquid Helium-4 Systems) is freely available at https://github.com/bcntls2016/. The code for the molecular dynamics simulations can be obtained upon request.
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Acknowledgements
We thank F. Stienkemeier, N. Halberstadt, F. Jensen, H. Birkedal, P. R. Ogilby and K. Mølmer for discussions and comments, and J. Thøgersen for help in the laboratory. H.S. acknowledges, in particular, S. Keiding, who sadly passed away earlier this year, for his constructive criticism of, advice on and genuine support of this work. H.S. acknowledges support from the Independent Research Fund Denmark (project number 8021-00232B) and from V. Fonden through a Villum Investigator Grant number 25886. M.B. and M.P. have been supported by grant number PID2020-114626GB-I00 from the MICIN/AEI/10.13039/501100011033. The molecular dynamics simulations were obtained at the Centre for Scientific Computing, Aarhus (https://phys.au.dk/forskning/faciliteter/cscaa/).
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S.H.A., C.A.S., J.K.C. and A.V.M. designed and built the experimental set-ups, maintained the experimental apparatus and carried out the experiments. S.H.A., C.A.S., J.K.C., A.V.M. and H.S. analysed the experimental data. C.E.P. and J.K.C. designed, wrote the code for and carried out the molecular dynamics simulations. M.P. and M.B performed the numerical TDDFT simulations. All authors discussed and interpreted the data. H.S. wrote the paper with input from all authors.
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Extended data figures and tables
Extended Data Fig. 1 Schematic of the experimental setup.
The key elements described in Methods are shown including the formation of the He droplets by expansion of high-purity 4He gas, the two doping cells, the pump and probe laser pulses, the velocity map imaging spectrometer consisting of three electrodes (repeller, R; extractor, E; and ground, G), and the imaging detector backed by the TPX3CAM. The figure is for illustration purposes only and is not drawn to scale.
Extended Data Fig. 2 Overview of the data analysis: from raw data to the Na+Hen ion yields.
a, Mass spectrum in the m/q range from 20 to 65 u/e, obtained when the pump and probe pulses interact with the doped He droplets. The peaks corresponding to the masses of Na+Hen ions are highlighted by red bars. The origin of the other peaks are discussed in Methods. b1–b6, 2D velocity images corresponding to some of the Na+Hen ions highlighted in the mass spectrum, integrated over all measured pump-probe delays. c1–c4, 2D velocity images of Na+He3 ions at four selected delays, t = 0.2, 1.0, 2.0, 3.0 ps, d, The speed distribution of Na+He3 ions for delays between 0 and 20 ps, found by Abel inversion of the 2D velocity images. The dashed lines indicate the radial range used for the determination of the ion yield plotted in panel e. e, The time-dependent yield of the Na+He3 ions obtained by integrating the speed distributions in panel d.
Extended Data Fig. 3 Helium density profile and Na+-He pair potential.
Top: helium density profile of Na+-4He2000 at equilibrium (black solid line) and of pure 4He2000 (red dashed line). Bottom: Na+-He pair potential used in this work.
Extended Data Fig. 4 MD simulation of the post-ejection dissociation process.
a, Schematic showing the simulation method for a Na+HeN complex. The minimized complex is heated, and then it gradually dissipates its internal energy by shedding He atoms through dissociation. b, MD simulation results for Na+He6 showing the number of helium atoms, averaging over 1000 simulations, <N>, attached to the complex as a function of time, for three average total kinetic energies. c, The same as b, but for Na+He14.
Extended Data Fig. 5 Time-dependent Na+Hen ion yields and sum of all ion yields.
a0–a25, Black dots: time-dependent Na+Hen ion yield, Yn(t) for n = 0 to 25. The blue curves represent the Poisson probability, Pn(t), that n He atoms have bound to the ion in the interval [0,t], scaled such that the peak of P2(t) matches the peak of the Na+(He2). b, Black dots: the sum of the ions yields shown in a0–a25, that is, \({{\rm{S}}{\rm{U}}{\rm{M}}}_{{\rm{i}}{\rm{o}}{\rm{n}}{\rm{s}}}(t\,)={\sum }_{n=0}^{25}{Y}_{n}(t\,)\).
Supplementary information
Supplementary Video 1
TDDFT simulation of the Na+ ion solvation process. Left video: time evolution of the He density in a symmetry plane. The red dot represents the Na+ ion. Right video: the solid black line shows the spherically averaged droplet density profile around the ion (left vertical axis). The dashed red line shows the number of He atoms as a function of the distance to the ion (right vertical axis).
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Albrechtsen, S.H., Schouder, C.A., Viñas Muñoz, A. et al. Observing the primary steps of ion solvation in helium droplets. Nature 623, 319–323 (2023). https://doi.org/10.1038/s41586-023-06593-5
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DOI: https://doi.org/10.1038/s41586-023-06593-5
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