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Description
It is challenging to measure the real time bond formation between two atoms or molecules because of the difficulty in preparing such a system in a well-defined starting geometry. A second challenge is to measure when the reactants meet since this is determined by diffusion, a process which is not easily controlled. Previous work have overcome these difficulties by preparing the system as a weakly bonded van der Waals complex, and then initialising the reaction by photoionisation [1].
In this work, we show real-time measurements of diffusion limited formation of Li$^+$-benzene complexes. The initial system is prepared using a helium nanodroplet housing a benzene molecule at its centre and and lithium atom on its surface. The atom-molecule separation is determined by the radius of the droplet which, in our experiments, can be controlled to be in the range 35-55 Å. We initialise the diffusion process at a well-defined time by ionising the lithium atom through a multi-photon ionisation process using a 800 nm, 50 fs laser pump pulse. Following the ionisation, the newly formed lithium ion is pulled into the droplet, and a subsequent ionisation of the benzene molecule would lead to measurement of the solvation rate of the ion as found in [2,3].
However, not ionising the benzene molecule will allow the lithium ion to meet benzene at the centre of the droplet and form a complex. We terminate the diffusion of the lithium ion – whether it has reached the benzene molecule or not – at a well-defined time by ionising benzene with a 400 nm, 70 fs laser probe pulse. This triggers a strong Coulomb repulsion between the two positively charged ions, and they will be ejected from the droplet.
Using a VMI spectrometer, we detect a 180 degree coincidence angle between benzene and lithium ions only after the complex has formed. This allows us to determine at which time the complex has formed by varying the delay of the probe pulse with respect to the pump pulse. In extension, this allows us to determine the diffusion rate, i.e. the speed at which the lithium ion moves through the droplet, by varying the size of the helium droplets. We found the diffusion rate of Li$^+$ through the droplets to be 22 $\pm$ 3 m/s.
[1] Kyung Hwan Kim et. al., Nature 518, 385–389 (2015)
[2] Simon H. Albrechtsen et. al., Nature 623, 319–323 (2023)
[3] Simon H. Albrechtsen et. al., arXiv:2502.11783
