Aggregation of Colloidal Particles in the Presence of Multivalent Co-Ions: The Inverse Schulze–Hardy Rule

Cao, Tianchi; Szilágyi, István; Oncsik, Tamas; Borkovec, Michal; Trefalt, Gregor

doi:10.1021/acs.langmuir.5b01649

Cited by 55 publications

(73 citation statements)

References 28 publications

(72 reference statements)

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“…For a 1:2 electrolyte the effect is weaker, but noticeable, similarly to the difference between the Monte Carlo data and the DLVO curve in [14]. The greater reduction of the electrostatic repulsion with the rise of coion valence found in the present study is in qualitative agreement with the inverse Schulze-Hardy rule established in [37]. …”

Section: Materials Methods and Experimental Resultssupporting

confidence: 90%

Effect of Ionic Correlations on the Surface Forces in Thin Liquid Films: Influence of Multivalent Coions and Extended Theory

2016

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Experimental data for the disjoining pressure of foam films stabilized by anionic surfactant in the presence of 1:1, 1:2, 1:3, and 2:2 electrolytes: NaCl, Na2SO4, Na3Citrate, and MgSO4 are reported. The disjoining pressure predicted by the Derjaguin-Landau-Verwey-Overbeek (DLVO) theory coincides with the experimental data in the case of a 1:1 electrolyte, but it is considerably greater than the measured pressure in all other cases. The theory is extended to account for the effects of ionic correlations and finite ionic radii. Original analytical expressions are derived for the local activity coefficient, electrostatic disjoining pressure, and asymptotic screening parameter. With the same parameter of counterion binding as for a 1:1 electrolyte, the curves predicted by the extended theory are in perfect agreement with the experimental data for 1:2 and 1:3 electrolytes. In comparison with the DLVO theory, the effect of ionic correlations leads to more effective screening of electrostatic interactions, and lower electric potential and counterion concentrations in the film’s midplane, resulting in lower disjoining pressure, as experimentally observed. The developed theory is applicable to both multivalent coions and multivalent counterions. Its application could remove some discrepancies between theory and experiment observed in studies with liquid films from electrolyte solutions.

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Section: Materials Methods and Experimental Resultssupporting

confidence: 90%

Effect of Ionic Correlations on the Surface Forces in Thin Liquid Films: Influence of Multivalent Coions and Extended Theory

2016

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“…coagulating power of coions decreases with increasing valence. Due to this inversion, the phenomenon was given a name: inverse Schulze-Hardy rule [32][33][34].…”

Section: Introductionmentioning

confidence: 99%

Interactions between silica particles in the presence of multivalent coions

2017

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Forces between charged silica particles in solutions of multivalent coions are measured with colloidal probe technique based on atomic force microscopy. The concentration of 1:z electrolytes is systematically varied to understand the behavior of electrostatic interactions and double-layer properties in these systems. Although the coions are multivalent the Derjaguin, Landau, Verwey, and Overbeek (DLVO) theory perfectly describes the measured force profiles. The diffuse-layer potentials and regulation properties are extracted from the forces profiles by using the DLVO theory. The dependencies of the diffuse-layer potential and regulation parameter shift to lower concentration with increasing coion valence when plotted as a function of concentration of 1:z salt. Interestingly, these profiles collapse to a master curve if plotted as a function of monovalent counterion concentration.

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“…On the other hand, Trefalt et al [13][14][15][16][17][18][19] have recently investigated the critical coagulation concentration of charged colloids in electrolyte solutions with 1:Z ions (monovalent counterion and multivalent co-ion) and have reported that aggregation behavior depends on the co-ion valence, even though the ionic strengths are the same. Though a similar behavior, i.e., more effective aggregation with smaller co-ion valence, has been reported for the coil-globule transition of DNA [20,21], there have been only a few reports on colloidal aggregation in electrolyte solutions with 1:Z ions.…”

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confidence: 99%

Electrostatic double-layer interaction between stacked charged bilayers

et al. 2017

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The inapplicability of the DLVO theory to multilayered anionic bilayers is found in terms of the co-ion-valence dependence of the lamellar repeat distance. Most of the added salt is expelled from the interlamellar space to the bulk due to the Gibbs-Donnan effect on multiple bilayers with the bulk. The electrostatic double-layer interaction is well expressed by the formula recently proposed by Trefalt. The osmotic pressure due to the expelled ions, rather than the van der Waals interaction, is the main origin of the attractive force between the bilayers.

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Aggregation of Colloidal Particles in the Presence of Multivalent Co-Ions: The Inverse Schulze–Hardy Rule

Cited by 55 publications

References 28 publications

Effect of Ionic Correlations on the Surface Forces in Thin Liquid Films: Influence of Multivalent Coions and Extended Theory

Effect of Ionic Correlations on the Surface Forces in Thin Liquid Films: Influence of Multivalent Coions and Extended Theory

Interactions between silica particles in the presence of multivalent coions

Electrostatic double-layer interaction between stacked charged bilayers

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