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5.4 Conclusions In conclusion, in this work, we presented a simple analytical model based on the 4th order Poisson-Boltzmann equation that can explain apparent charge inversion data. We find that including the Born energy and an estimate for how the polymer layer behaves as a function of concentration allows us to use physically reasonable parameters for the polymer layer thickness, the background charge density, and the correlation length. The correlation length here scaled in the same manner as the Bjerrum length, indicating that correlation effects are confined to length scales below which electrostatic forces dominate over thermal energies. Furthermore the dielec- tric constants that we found to fit the data well are generally in the correct range for polyelectrolytes; however, it is not clear whether the exact values for the various electrolytes and how they relate to each other is correct. To further validate this model, more experiments like the ones used here should be done, especially to vali- date whether the minimum observed at high concentrations is actually observed in experiment as well. Upon further validation, this simple model could prove useful in scenarios in which estimates of the underlying surface potentials/charges of surfaces upon which polymers have been deposited are necessary and in which the traditional Debye-Huckel theory does not provide satisfactory results. 139PDF Image | Shock Electrodialysis for Water Purification and Electrostatic Correlations
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