The Experiments: summary of a simple model
Summary of a simple model describing macroscopically the LIAD by taking into account diffusion processes.

The LIAD effect is related to light induced desorption of atoms from the surface of a siloxane coating toward the volume of a gas-buffered cell. In this sense LIAD is a surface effect.

Nevertheless our results show a huge increase of atomic concentration in vapour: the density increase get its maximum in few seconds but it keeps very high during a time as long as many hours, though condensation to the metal source would push the density to the equilibrium value.

The condensation rate is quite fast, both according to the estimation of diffusion time inside the cell and to experimental observation which show the cell going back to equilibrium in few seconds when the desorbing light is switched off. This means that fresh atoms coming form the bulk of the siloxane layer replace those extracted by the light at its surface. In this sense the LIAD effect is also driven by diffusion processes in the coating volume.

So both surface and volume phenomena have to taken into account, like it' s sketched in next figure, where a 1-D description is drawn. Namely both surface adsorption/desorption and volume diffusion must be studied.

The scale-length of the coating and of the gas regions are quite different, nevertheless the diffusion constants may be different by order of magnitude, making it possible that the diffusion time in the coating is longer than the diffusion time in the gas.

The diffusion time in the gas phase (is in our conditions) of the order of few seconds, it has a weak dependence on the temperature, and increases proportionally to the buffer gas pressure. The diffusion in the gas can be neglected when studying dynamics over much longer time-scales.

On the other hand, the diffusion coefficient (and hence the diffusion time) in the coating dramatically depends on the temperature. Namely the diffusion coefficient in liquids can be assumed to follow an Arrhenius law:

Diffusion equations can be studied in the gas and coating regions, coupling them with border conditions which relate the fluxes to surface phenomena, as represented with arrows in the fig.2.

In particular, at the gas-siloxane interface (x=0), assuming that a continuity condition holds, equal fluxes must be requested:

Here S and B are spontaneous and induced desorption coefficients respectively, I is the intensity of desorbing light, and A is the adsorbtion coefficient. While D_gas and D_silox are the diffusion coefficients described above. A, B and S account for surface phenomena, while D_gas and D_silox account for bulk ones.

When a small intensity impinges on the coating, the flux is limited by the BI factor, but when strong intensity are used, even if BI>>S, the diffusion rate inside the coating becomes a limiting factor, and the system dynamics has a bottle-neck given by the diffusion in the coating. In other words, at high values of I, the coating is depleted close to its surface, and D_silox become the driving parameter of the LIAD effect.

As the depletion rate of the gas, due to condensation, is directly controlled by D_gas, that's to say the buffer gas pressure (which is a fixed parameter), the quasi-steady state value of Ngas strongly depends on D_silox, and hence on the temperature.

When the desorption light is powerful enough to make the siloxane diffusion be the bottle neck, large LIAD effect is achieved, provided that the temperature is large enough to allow the siloxane diffusion to prevail on the gas diffusion (see the results we report elsewhere).

If LIAD effect is studied as a function of the intensity of desorbing light, two regimes are expected to appear. As long as the siloxane diffusion can prevent the coating surface to be exhausted, the LIAD signal increases proportionally to the intensity, due to the linear term BI. Further increase of the intensity I will produce a saturated behaviour, where the alkali flux to the gas phase is limited by the diffusion in the siloxane.

As matter of fact, experimental results show a clear linear behaviour at lower intensities, which does not saturate to a definite value when higher intensity are achieved. In fact at higher intensities the LIAD effect shows as slower increase, which is proportional to the square root of the power.

This observation allows a simple explanation in terms of a linear increase of D_silox with the illumination power. As a consequence a microscopic description should relate both surface ejection and bulk mobility of alkali atoms interacting with the siloxane coating to the power of the desorbing light. Further details on this latter subject are available as a preprint, presently submitted for publication (see abstract).

Experiments presently in progress >