Concentration Dependence

As more solvent diffuses into a polymer the structure opens up, making it even easier for solvent to diffuse - in other words the diffusion coefficient is concentration dependent. This app is almost idential to the Fickian one except for the extra input which defines the diffusion coefficient at a high concentration, chosen in this app to be 30 Vol %. The diffusion coefficient is calculated as varying log-linearly between the zero-concentration value and this value and is then assumed to remain constant at higher values. A typical choice might be a 3 orders of magnitude increase in D between 0% and 30 vol%. The app accommodates these large changes to give reasonably accurate results. For simplicity in this app, the stated diffusion coefficients are log-linear between 0% and 30% and assumed constant after 30%. If your actual concentration range is less than this, then D at that concentration can be readily estimated.

It is obvious and proven that diffusion coefficients are concentration dependent. It is therefore rather sad that most models do not take this into account - giving rise to all sorts of ad-hoc explanations for why the diffusion doesn't fit a "simple" Fickian curve. Concentration-dependence is simple to understand and not much more difficult to model so there is no good excuse for not taking it into account. The other inputs and outputs have already been explained.

Concentration Diffusion

L (μm)
C (Vol Fraction)
D (cm²/s) @0%
D (cm²/s) @30%
t (min)
TimeOut in:
F (g/cm²/s)
t½ (min)
Breakthrough (min)

Enjoy playing with different concentration dependencies. If the 30% value is accidentally entered as being lower than the 0% value, the app assumes a constant coefficient at the 0% value. Note that for numerical reasons, if there is a big difference between the diffusion coefficients and if the sample is thin (L is small) then calculations take much longer

The official site of Hansen Solubility Parameters and HSPiP software.