Poisson–Boltzmann description of interaction forces and aggregation rates involving charged colloidal particles in asymmetric electrolytes

Trefalt, Gregor; Szilágyi, István; Borkovec, Michal

doi:10.1016/j.jcis.2013.05.071

Cited by 97 publications

(165 citation statements)

References 49 publications

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“…This model interprets the overall interparticle forces acting between the particles in the presence of dissolved ions as the superposition of the repulsive electrical double layer forces and the attractive van der Waals forces. The first ones weaken with increasing the ionic strength, while the latter ones are always present independently of the solution composition [36]. Therefore, stable dispersions are predicted at low ionic strengths and rapid aggregation of the particles leading to unstable systems occurs at high electrolyte concentrations.…”

Section: General Considerationsmentioning

confidence: 94%

Effect of Ionic Compounds of Different Valences on the Stability of Titanium Oxide Colloids

Muráth

Sáringer

Somosi

et al. 2018

Colloids and Interfaces

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Titanium oxide particles of various morphologies have been prepared for applications of scientific or industrial interest in recent decades. Besides development of novel synthetic routes and solid-state characterization of the obtained particles, colloidal stability of titanium oxide dispersions was the focus of numerous research groups due to the high importance of this topic in applications in heterogeneous systems. The influence of dissolved ionic compounds, including monovalent salts, multivalent ions and polyelectrolytes, on the charging and aggregation behaviour of titanium oxide materials of spherical and elongated structures will be discussed in the present review.

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Section: General Considerationsmentioning

confidence: 94%

Effect of Ionic Compounds of Different Valences on the Stability of Titanium Oxide Colloids

Muráth

Sáringer

Somosi

et al. 2018

Colloids and Interfaces

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“…In this case, no ioncorrelations effects are expected [19]. The PB equation is solved numerically for two charged plates immersed in an asymmetric electrolyte solution, for details see [8,26]. The characteristic shape of the pressure curve is the consequence of expulsion of multivalent coions from the gap between the surfaces, which in the presented case happens at about 60 nm, see Fig.…”

mentioning

confidence: 85%

“…Note that in the case of the coions the dependence on valence is much weaker. * E-mail: gregor.trefalt@unige.chInterestingly, in the low particle charge limit, where the DL forces can be described by the Debye-Hückel (DH) approximation, the samedependence for both counterions and coions is reached [8,9]. The latter low charge limit (3) lies between the Schulze-Hardy (1) and inverse Schulze-Hardy (2) dependences.…”

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confidence: 99%

Derivation of the inverse Schulze-Hardy rule

Trefalt

2016

Phys. Rev. E

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The inverse Schulze-Hardy rule was recently proposed based on experimental observations. This rule describes an interesting situation of the aggregation of charged colloidal particles in the presence of the multivalent coions. Specifically, it can be shown that the critical coagulation concentration is inversely proportional to the coion valence. Here the derivation of the inverse Schulze-Hardy rule based on purely theoretical grounds is presented. This derivation complements the classical Schulze-Hardy rule which describes the multivalent counterion systems.The aggregation of charged colloids is a long-studied phenomenon. More than 100 years ago Schulze and Hardy showed that the aggregation power of salts depends strongly on the ion valence [1,2]. More precisely, the critical coagulation concentration (CCC) (i.e., concentration of salt at which particles start to aggregate fast) [3] decreases very rapidly by increasing counterion valence. This discovery was later confirmed theoretically by Derjaguin, Landau, Verwey and Overbeek and is known as the DLVO theory [4,5]. They have shown that by assuming the interaction between particles as a sum of van der Walls (vdW) and double layer forces (DL) in the symmetric z:z electrolyte the CCC is inversely proportional to the sixth power of the valence,The above relation, also named Schulze-Hardy rule, is valid for highly charged particles. This explanation confirmed the DLVO theory and made it widely accepted. The symmetric z:z electrolytes are usually practically insoluble, therefore in experiments one typically uses asymmetric 1:z or z:1 multivalent electrolytes. In the case of asymmetric electrolytes, multivalent ions can either play a role of the counterions or the coions, where they have the opposite or the same charge as the colloidal particle, respectively. It was shown experimentally as well as theoretically that for highly charged particles the SchulzeHardy rule (1) is a good approximation also for asymmetric electrolytes where z is the counterion valence [6][7][8]. Recently Cao et al.[9] investigated a complementary problem, namely the influence of multivalent coions on the aggregation. In this situation experimental data could be reasoned with the inverse Schulze-Hardy rule, namelywhere z is the valence of the coion. Note that in the case of the coions the dependence on valence is much weaker. * E-mail: gregor.trefalt@unige.chInterestingly, in the low particle charge limit, where the DL forces can be described by the Debye-Hückel (DH) approximation, the samedependence for both counterions and coions is reached [8,9]. The latter low charge limit (3) lies between the Schulze-Hardy (1) and inverse Schulze-Hardy (2) dependences. This proposed inverse Schulze-Hardy rule therefore elegantly completes the understanding the aggregation in experimentally relevant asymmetric multivalent electrolytes. The Schulze-Hardy rule (1) and the low charge DH limit (3) were both derived theoretically. On the other hand, the inverse Schulze-Hardy rule was only given as an empirical ...

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“…20. K + is adsorbed to -SO 3 − of membrane of Selemion CMV at the interface between the KCl solution and membrane by obeying the Langmuir isotherm, and all the ions distribute according to the Boltzmann distribution [1,2,6,[9][10][11][12][13][14][18][19][20][21][22][23][24][25][26].…”

Section: Reconsideration Of Potential Across the Ion Exchange Membranementioning

confidence: 99%

Membrane potential generation without ion transport

Tamagawa

2014

Ionics

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Current view about cell is that the cell is a watery solution coated with semi-permeable membrane and there exists nonzero potential, so-called membrane potential, across the semi-permeable cell membrane. Goldman-Hodgkin-Katz equation and Donnan theory are the fundamental existing theories for explaining the cause of membrane potential generation. However, the observations of membrane potential inexplicable by these existing theories have been repeatedly reported by a small number of researchers for more than the past half century. Hence, it is needless to say important to reconsider the membrane potential generation mechanism. Based on the experimental result shown in this paper, it was concluded that the existing theories were not genuinely right for the explanation of membrane potential generation. Adsorption theory is only a genuinely right theory instead. The adsorption theory describes that the adsorption of the mobile ions on the adsorption sites on the membrane generates the membrane potential. This work introduces the experimental observation inexplicable by Goldman-Hodgkin-Katz equation or Donnan theory but is in harmony with the adsorption theory.

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Poisson–Boltzmann description of interaction forces and aggregation rates involving charged colloidal particles in asymmetric electrolytes

Cited by 97 publications

References 49 publications

Effect of Ionic Compounds of Different Valences on the Stability of Titanium Oxide Colloids

Effect of Ionic Compounds of Different Valences on the Stability of Titanium Oxide Colloids

Derivation of the inverse Schulze-Hardy rule

Membrane potential generation without ion transport

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