Higher-valence ions coagulate colloids more effectively according to the Hardy-Schulze law
Multiple studies and classical colloid chemistry models confirm the Hardy-Schulze law, demonstrating that ions with higher valency are increasingly effective at coagulating colloidal suspensions.
The retrieved papers consistently support the Hardy-Schulze rule (Schulze-Hardy rule), confirming that higher-valence counterions more effectively reduce critical coagulation concentrations and destabilize colloids.
Jiahui Gao, T. Sugimoto, Motoyoshi Kobayashi. Effects of ionic valence on aggregation kinetics of colloidal particles with and without a mixing flow.. 2023. https://doi.org/10.1016/j.jcis.2023.02.019
The study discusses the classical Schulze-Hardy rule regarding how counter-ionic valence inversely relates to critical coagulation concentration.
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Hegedűs T, Takács D, Vásárhelyi L, Szilágyi I, Kónya Z. Specific Ion Effects on Aggregation and Charging Properties of Boron Nitride Nanospheres.. 2021. https://doi.org/10.1021/acs.langmuir.0c03533
Findings confirm that critical coagulation concentrations decrease with increasing counterion valence in line with the direct Schulze-Hardy rule.
Chang YC, Jin Z, Li K, Zhou J, Yim W, Yeung J, Cheng Y, Retout M, Creyer MN, Fajtová P, He T, Chen X, O'Donoghue AJ, Jokerst JV. Peptide valence-induced breaks in plasmonic coupling.. 2023. https://doi.org/10.1039/d2sc05837e
The research demonstrates that nanoparticle coagulation tendencies follow the six-power relationship of the Schulze-Hardy rule with higher valency counterions.
Péter T, Takács D, Viczián D, Katana B, Alsharif NB, Szilagyi I. Correlations Between Colloidal Stability and Peroxidase Activity of Prussian Blue Nanozymes in Salt Solutions.. 2025. https://doi.org/10.1021/acs.jpcb.5c01256
Results show that multivalent ions significantly alter colloidal stability by compressing the electric double layer according to classical principles.
Gao X, Kou Q, Ren K, Zuo Y, Xu Y, Zhang Y, Lal R, Wang J. Quantitative characterization of non-DLVO factors in the aggregation of black soil colloids.. 2022. https://doi.org/10.1038/s41598-022-09067-2
Aggregation kinetics in different cation valence systems follow the classical Derjaguin-Landau-Verwey-Overbeek model aligned with these concepts.
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