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Molecular Weight Heavy Medium Light ρb (C/m3) lc/lB lc (Å) L (nm) εp/ε0 937.31 1.7080 11.576 815.01 82.697 959.87 1.6530 11.307 795.86 81.936 1241.5 1.2804 9.1558 615.32 78.382 Table 5.1: Parameters for KCl with PLL and the dielectric constant in the polymer layer (εp/ε0, where ε0 is the permittivity of free space). We made the assumption that the polyelectrolyte dominates the dielec- tric constant in domain I and kept it a constant as a function of simple electrolyte concentration. The dielectric constant in domain II is varied with concentration as follows [125]: εw εo = 1 + α x (5.44) iii where εw is the dielectric constant of pure water (78.46), αi is an ion-dependent parameter, and xi is the mole fraction. The relevant values for αi are 2.43 for K+, 6.69 for Mg2+, 6.80 for Cl−, and 6.75 for NO−3 [125]. Furthermore, we made the assumption that the correlation length is a constant multiple of the Bjerrum length. In addition, we allowed the background charge density (ρb) for the heavy chains to vary. We did this to be able to first calculate the effective background charge density per area (ρbL), which was then kept constant for all other curves (including those in the following section), since we assumed that the effective background charge density would be roughly constant. Table 5.1 shows the parameters that were used for the curves in Figure 5-4. In contrast to the parameters for the traditional mean-field model, overall the trends we see in Table 5.1 and Figure 5-4 make sense. The thickness of the PLL layer decreases as the polymer chain molecular weight decreases (i.e. shorter chains), which causes the charge density to increase. The correlation length (on the order of the Bjerrum length) also decreases with decreasing molecular weight, maybe due to the tighter packing of the polymer chains in a smaller amount of space (i.e. higher concentration). Lastly, the dielectric constant remains largely constant and has a value that is reasonable for polyelectrolytes. Furthermore, we note that the absolute 127PDF Image | Shock Electrodialysis for Water Purification and Electrostatic Correlations
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