Compound redistribution due to droplet evaporation on a thin polymeric film: Theory

Abstract

A thin polymeric film in contact with a fluid body may leach low-molecular-weight compounds into the fluid. If this fluid is a small droplet, the compound concentration within the liquid increases due to ongoing leaching in combination with the evaporation of the droplet. This may eventually lead to an inversion of the transport process and a redistribution of the compounds within the thin film. In order to gain an understanding of the compound redistribution, we apply a macroscopic model for the evaporation of a droplet and combine that with a diffusion model for the compound transport. In the model, material deposition and the resulting contact line pinning are associated with the precipitation of a fraction of the dissolved material. We find three power law regimes for the size of the deposit area as a function of the initial droplet size, dictated by the competition between evaporation, diffusion and the initial compound concentrations in the droplet and the thin film. The strength of the contact line pinning determines the deposition profile of the precipitate, characterised by a pronounced edge and a linearly decaying profile towards the centre of the stain. Our predictions for the concentration profile within the solid substrate resemble patterns found experimentally.The following article will be submitted to Journal of Applied Physics. After it is published, it will be found at https://aip.scitation.org/journal/jap.

Evaporation of water droplets on photoresist surfaces – An experimental study of contact line pinning and evaporation residues

“…It may cause increased leaching or, conversely, mass transfer from the wet residue into the top of the resist. 23 The smoothness of the thin film interference fringe pattern in Fig. 3(h), which has been recorded approximately 30-60 minutes after the evaporation process was apparently complete, indicates that a significant frac-tion of water might still be present in the deposit.…”

“…It is thus conceivable that within a submicron distance from the contact line the concentration of e.g. the leached quencher or PAG ions either exceed their solubility limit 23 or induce a significant localized viscosity increase. Both alternatives could induce a temporary pinning of the contact line, until the contact angle has dropped sufficiently, such that depinning occurs.…”

“…36 A detailed model for such a precipitation mechanism underlying the first pinning event is presented in Ref. [23]. The prediction for the case of slow leaching of material out of the PR layer compared to the evaporation timescale is that D 1 should scale as D 4/3 0 .…”

“…Our experimental results compare favourably with a recent theoretical model of residue formation. 23 200X) on Si-wafers with a spin speed between 2000 and 6000 rpm for 200 s, which gives a thickness h on order of 60 to 100 nm, respectively. Prediluted PR (1 part PR solution diluted further in 2 parts of pure solvent mixture, by volume) coated at 6000 rpm yields a film thickness of about 20 nm.…”