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Figure 5-1: Left: Experimental Configuration. Upper Right: Deposition of poly L- lysine (PLL) layers. Lower Right: Data showing charge inversion of positive PLL layers on a negative silica surface with increasing concentration of KCl in water. [83] 5.2 Mathematical Model To tackle this problem, we construct a simple one-dimensional model to describe the behavior of the measured interfacial charge. Our model consists of two domains. In the domain right next to the surface (domain I) containing polyelectrolyte, we have used the simple theory of electrostatic correlations in RTILs published by Bazant et al [8] to describe the behavior, while for the domain outside of the polymer region (domain II), we have used traditional models. In each of these models we use the Debye-Huckel approximation for the ionic charge density. The model in the polymer region is based on a 4th order modified Poisson-Boltzmann equation with a permittiv- ity operator, where we have made the assumption that the permittivity is independent of location within the polymer region: εˆ∇2φp = −ρeq(φp) (5.2) εˆ = εp 1 − lc2∇2 (5.3) 117PDF Image | Shock Electrodialysis for Water Purification and Electrostatic Correlations
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