Juan Olives
email: olives@cinam.univ-mrs.fr

Zoubida Hammadi

Roger Morin

Laurent Lapena

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local electric field and based on the electron tunneling through the double layer of water molecules at the surface of a nanoelectrode. Depending on the experimental conditions, we can nanolocalize at a single point (the apex of the nanoelectrode) either the electrolysis oxidation reaction, the reduction reaction, or the production of bubbles.

We define "nanoelectrolysis" as the nanolocalization at a single point of any electrolysis phenomenon, such as an electrolysis reaction (of oxidation or reduction) or a bubble production. In this paper, we present a general model of water nanoelectrolysis based on (i) the high value of the electric field at the apex of a nanoelectrode (i.e., a tip-shaped Pt electrode, with micrometric to nanometric curvature radius at its apex) and (ii) the electron tunneling assisted by the electric field through the thin dielectric film (double layer of water molecules, 0.3 nm thick) at the surface of the nanoelectrode. Maxwell's equations give the discontinuities of the normal components of the electric field and the electric current at the dielectric-solution interface

E 2n -E 1n = ρ s ε , j 2n -j 1n = - ∂ρ s ∂t
(the subscript 1 is for the dielectric film and the subscript 2 for the solution; ρ s is the surface charge density and ε the permittivity) and a relation between E 1n , E 2n , V (the electric potential applied between the nanoelectrode and the counter electrode), and the 1 local mean curvature of the nanoelectrode surface. In the solution, j 2n = γ E 2n (Ohm's law)

and, in the dielectric film, j 1n is the tunneling current which depends non-linearly on E 1n and is modeled using a threshold value E 0 of the electric field. These equations lead to a For example, if we apply, from some initial time, a constant positive potential (between the nanoelectrode and the other electrode), the electric field (at some point of the nanoelectrode) will increase with time, but it always remains higher at the apex of the nanoelectrode (at each time). A tunneling current will occur when the electric field reaches the threshold value E 0 . The electric field will thus reach this threshold value at the apex of the nanoelectrode (at some time t ′ ; see Fig. 1), while it is still below this value on the rest of the electrode. If we turn the electric potential off (i.e., apply a zero potential, at some time t 1 , before the electric field reaches the threshold value on the rest of the electrode), the electrol-ysis reaction due to the tunneling current (in this case, the oxidation reaction, the electrode being at a positive potential) will then occur at a single point, the apex of the nanoelectrode.

differential
The electrolysis reaction is thus nanolocalized at a single point of the electrode.

The electrolysis reaction produces O 2 or H 2 molecules which diffuse in the solution. In our model, a bubble will appear when the concentration of these molecules in the solution reaches some supersaturation value.

If we apply a constant electric potential V 1 during a finite time t 1 , and then the opposite potential -V 1 during the same time t 1 , we show that there are three distinct regions in the plane (t 1 , V 1 ): one for the nanolocalization (at the apex of the nanoelectrode) of the electrolysis oxidation reaction, the second one for the nanolocalization of the reduction reaction, and the third one for the nanolocalization of the production of bubbles (see Fig. 2).

These parameters t 1 and V 1 completely control the time at which the electrolysis reaction (of FIG.

2. In the plane (t 1 , V 1 ), according to the model: nanolocalization of the oxidation reaction (between the two red curves), nanolocalization of the reduction reaction (between the two dashed blue curves), and nanolocalization of the production of bubbles (between the two green curves).

According to the experiments: the nanolocalization of the production of bubbles occurs between the series of black points and the series of white points. Solution with 10 -4 mol/L of H 2 SO 4 .

Logarithmic scale on both axes.

oxidation or reduction) begins, the duration of this reaction, the electrolysis current intensity

  equation of evolution of the electric field E = E 1n close to the surface of the nanoelectrode. If a given arbitrary electric potential V (t) is applied between the electrodes, the model then determines the electric field at any point of the surface of the nanoelectrode and at any time. Consequently, it determines at what point of the nanoelectrode and at what time a tunneling current-i.e., an electrolysis reaction-will occur. It is therefore the local electric field-and not the potential of the electrode-which controls the electrolysis reactions.

FIG. 1 .

 1 FIG.1. Evolution of the electric field E at the apex of the nanoelectrode. The tunneling currenti.e., the electrolysis reaction-occurs above the threshold value E 0 , i.e., between t ′ and t 1 (red part of the curve).

(i.e., the tunneling current), the number of produced O 2 or H 2 molecules, and the radius of the nanolocalized bubbles. The model is in good agreement with our experimental results, concerning the current intensity, the region for the nanolocalization of the production of bubbles (see Fig. 2), and the radii of the nanolocalized bubbles.