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Electrolyte/MW ρ c−1/3 (C/m3) l /l l (Å) Lc1/3 (nm) ε /ε b0cBc0p0 KCl/heavy 4747.2 KCl/medium 4931.2 KCl/light 6310.1 KNO3 /heavy 10419 MgCl2 /heavy 4015.6 1.7041 11.627 1.6251 11.199 1.2591 9.0744 1.5500 6.2451 4.7131 25.557 176.38 82.148 169.80 81.332 132.69 77.770 78.663 139.11 208.52 103.36 Table 5.4: Parameters for various electrolytes and molecular weights of PLL using the Pincus relation and incorporating the Born solvation energy at the interface. centration (Figure 5-13), his model suffers from the same problem of extremely high potentials that the tradition Debye-Huckel model suffers from. This problem is not one that we attempted to rectify in this model, since we were more interested in see- ing how it would change at high concentration and how the potential profile behaves. Interestingly, even at this low concentration, we already observe some oscillation of the potential profile, which may be indicative of some overscreening, though the dis- tances are quite large, and hence, due to the limitations mentioned, this profile at low concentration may not be entirely reliable. However, if we look at more concentrated solutions we see a much better picture. For 1 M KCl (Figure 5-14) with only the Pincus relation taken in account, we see some oscillation (overscreening) close to the surface and relatively quick decay. However, if we incorporate the Born solvation en- ergy (Figures 5-15 & 5-16) into the model, we can see that there is a jump in potential at x = L, which is required to push ions into the polymer layer. This jump is positive in both figures, because the dielectric constant in the polymer layer is larger than in the bulk electrolyte. Furthermore, we also see an oscillation near the interface at x = L for MgCl2, which indicates that we have an accumulation of ions near the interface. The overall large positive potential in the polymer region for this case indicates that the large Born energy required for MgCl2 makes it harder for ions to penetrate the polymer and hence that we don’t have as much screening of the polymer charges by ions. 136PDF Image | Shock Electrodialysis for Water Purification and Electrostatic Correlations
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