Separation regions, simulated moving

Fig. 6.7. Simulated moving-bed operating region for complete separation.

The rationale of using hybrid simulation here is that a classic diffusion-adsorption type of model, Eq. (2), can efficiently handle large distances between steps by a finite difference coarse discretization in space. As often happens in hybrid simulations, an explicit, forward discretization in time was employed. On the other hand, KMC can properly handle thermal fluctuations at the steps, i.e., provide suitable boundary conditions to the continuum model. Initial simulations were done in (1 + 1) dimensions [a pseudo-2D KMC and a ID version of Eq. (2)] and subsequently extended to (2 + 1) dimensions [a pseudo-3D KMC and a 2D version of Eq. (2)] (Schulze, 2004 Schulze et al., 2003). Again, the term pseudo is used as above to imply the SOS approximation. Speedup up to a factor of 5 was reported in comparison with KMC (Schulze, 2004), which while important, is not as dramatic, at least for the conditions studied. As pointed out by Schulze, one would expect improved speedup, as the separation between steps increases while the KMC region remains relatively fixed in size. At the same time, implementation is definitely complex because it involves swapping a microscopic KMC cell with continuum model cells as the steps move on the surface of a growing film. 

At an effertive temperature z below the polyelectrolyte solutions are phase separated over some concentration range. The dependence of the spinodal line of the salt-free polyelectrolyte solution on the fraction of chared monomers/on the polymer backbone is shown in Figure 44. With increasing fraction of charged monomers /, the two-phase region moves toward lower effective temperatures and is located at lower temperatures than in solutions of neutral polymers (for neutral polymers Za -2/- /N) making polyelectrolyte solutions more stable. MC simulations of the phase separation in polyelectrolyte solutions have confirmed that is independent of the d ee of polymerization... 

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