IGC Diffusion Simulator

The simulation is based on the work of Munk at U Texas at Austin¹. Rather than real particles covered by a stationary phase (Munk called it "polymer", here we use the general word "sample"), a simple tube with a coating of the equivalent thickness (i.e. a capillary column) is assumed. In addition to the length of the column and the flow rate, a diffusion coefficient within the coating is needed, along with a partition coefficient between phases.

Via numerical integration, three processes are modelled in a stepwise manner:

1. Peak movement down the column. This simply follows the flow velocity and leaves the peak shape unchanged from the previous step. With no diffusion, it would emerge the same as the sharp injection peak.
2. Peak broadening via gaseous diffusion. Although we could add a gaseous diffusion coefficient, a fixed value of 0.1cm²/s is assumed.
3. Diffusion into (and out of) the stationary phase. This slows down and broadens the peak. Note that there(effectively) is no diffusion along the coating - the probe goes in and out driven by diffusion with gradients depending on the partition coefficient. The diffusion coefficient, D, varies from 1e-6 for a very liquid stationary phase to 1e-8 (and less) for a phase too solid to be worth investigating.

The graph shows the (relative) concentration of the probe in the gas phase along the column plus the concentrations at the sample surface and at the sample/support interface. As the diffusion coefficient decreases, the sample-related peaks increasingly lag behind the gas peak.

The t_max rel is the relative time compared to a non-interacting peak eluting at time t=length/velocity. With low values you see what happens to the peak within the column, and can gradually increase it till the peak starts to elute - at which point the simulation stops as there is no further significant useful information. The t_stop value gives you some idea of what the relative retention time would have been.

From your inputs a number of values are calculated that are used in the model and showed for reference. The Z values make the calculations cleaner and simpler and the graphs are normalized accordingly:

• V₀. The Void Volume.
• V_s. The Sample Volume.
• u. The Velocity of the gas flow.
• t₀. The Elution Time for a non-interacting probe.
• Z_p. A normalizing Partition coefficient: the real coefficient scaled by V_s/V₀.
• Z_L. A normalizing sample diffusion coefficient: the real coefficient scaled by scaled by length/(velocity*thickness²).
• Z_g. A normalizing gas diffusion coefficient: the real coefficient scaled by 1/(velocity*length) .

The default Z values on startup are Z_p=4, Z_L=1 and Z_g=0.002. These are considered by Munk to be "typical" for a reliable diffusion experiment. When Z_L is significantly below 0.2 then there is poor equilibration. When Z_p is less than 1 then the probe spends relatively little time in the sample.