Drying front position as function of time

In figure 1 the hydrogen signal profiles of a solvent based alkyd sample are shown. About 10 minutes were needed to obtain each profile, because 512 averages were taken. From the figure two stages can clearly be identified. The first profiles show that the film shrinks, this process takes about one hour.

Figure 1: The measured profiles during drying of a alkyd sample
At a certain time, after the 7th profile in figure 2, a front forms which moves towards the lower part of the coating. In figure 2 is shown that if we plot the front position against the square root of time we obtain a linear curve. We can explain this behavior using an oxygen diffusion model

Figure 2: The front position as a function of time as measured by NMR.

We assume the reaction rate to be high compared to the diffusion of oxygen. Finally we obtain the following equation:
where f0is the front position at the moment t0the front forms and starts to move into the coating, D the diffusion constant for oxygen,r0 the oxygen density in the surface layer of the coating film andn the cross-linked volume per mole of oxygen. The difference in drying front speed of the two systems shown in figure 2, can be explained in more detail using this model. The front speed depends on the amount of double bonds (cross link density), oxygen diffusion constant and solubility density. In the solvent borne alkyd the amount of consumed double bonds was smaller, resulting in a higher value for n. In a system with higher polymer mobility the diffusion constant is expected to be higher. From the signal decay (not shown here) of the alkyds it can be concluded that the polymer mobility is indeed higher for the solvent borne alkyd. The oxygen solubility however is not expected to change drastically. The higher values of D and n are higher this explains the higher front speed of the solvent borne alkyd.

Figure 3. The front position as a function of time. For a certain amount of time the air was replaced by argon,
hence removing all the oxygen
If we remove the oxygen above the sample by putting the sample in an argon atmosphere the front stops, see fig 3.