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April 20th 2019

Researchers from the University of Amsterdam and FOM institute AMOLF have investigated how protons can oscillate in very small volumes of water. They did this by comparing the proton movements in a large quantity of water with that in miniscule water drops of different diameters – just billionths of a metre in size.

From small to large
The small water drops are inverse micelles: small groups of water molecules that are dissolved in a hydrophobic solvent creep together and form a tiny droplet to minimise the contact between the water and the solvent around it. The researchers made solutions in which such tiny drops all have the same size and they measured the oscillations of the protons dissolved in the water using an externally applied vibrating electric field.

In a large quantity of water, in which protons can move without limitations, the amplitude of the oscillation of the protons decreases the faster the external electric field oscillates (possesses a higher frequency). In the miniscule droplets of water, with diameters of several nanometres, the movement of the protons is, however, strongly limited. The proton movement has a specific resonance frequency at which the amplitude is maximal. This frequency is several gigahertz.

The resonance is caused by the moving protons accumulating at the wall of the water droplet. Were the external electric field to be switched on only briefly, the protons would move backwards and forwards with a characteristic resonance frequency. In the experiment the electric field remains on but continually changes direction. If the time between each change of direction agrees (is therefore resonant) with the reversal time of the spontaneous proton oscillation, the protons oscillate with a maximum amplitude. For smaller volumes the protons accumulate faster at the walls of the nanodroplet, which increases the resonance frequency.

The size of the resonance frequency also depends on how fast the protons can move in the water droplet. If the protons can scarcely move through the droplet, the resonance frequency is low. Measurements of the resonance frequency revealed that the rate of movement of protons in nanodrops is much lower than in a macroscopic quantity of water. Therefore for protons in the nanodrop the water is highly viscous. This result is important for our understanding of proton transport inside cell organelles and in the membranes of fuel cells.