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For the presently considered system, we expect that the Poisson - Boltzmann approach is accurate and effects of ion - ion correlations are negligible.
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A parallel shift in the log W vs log I (or log W vs pH) plots would also be caused by accounting for hydrodynamic retardation or for the hydrophobic effect, as discussed in ref 7.
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Hydrophobic interactions can be assumed to decay with distance in very much the same way as the dispersion forces and can thus be lumped into an effective Hamaker constant, see: Yoon, R.-H.; Flinn, D. H.; Rabinovich, Y. I. J. Colloid Interface Sci. 1997, 185, 363. From their findings, an even stronger modification of the theoretical Hamaker constant due to hydrophobicity could be expected.
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27 that suggests a regulation behavior close to the constant potential limit. A quantitative criterion within a linearized model is derived in: Carnie, S. L.; Chan, D. Y. C. J. Colloid Interface Sci. 1993, 161, 260. Based on: Chan, D. Y. C.; Mitchell, D. J. J. Colloid Interface Sci. 1983, 95, 193.
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27 that suggests a regulation behavior close to the constant potential limit. A quantitative criterion within a linearized model is derived in: Carnie, S. L.; Chan, D. Y. C. J. Colloid Interface Sci. 1993, 161, 260. Based on: Chan, D. Y. C.; Mitchell, D. J. J. Colloid Interface Sci. 1983, 95, 193.
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It must be mentioned that the same sort of description fails to describe correctly the low pH regime where the hematite is positively charged. However, we doubt that for this situation the requirements of cleanliness and surface homogeneity are fulfilled to the same degree as for the system of negatively charged hematite (Figure 4), because of the different role of negatively charged residual impurities. Experimental data for the whole pH range and the corresponding discussion are given in ref 27.
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