Trivalent counterion

The theory of counterion condensation is implicit in Oosawa (1957) but the term was coined later (Imai, 1961). The phenomenon was demonstrated by Ikegami (1964), using refractive index measurements of the interaction between sodium and polyacrylate ions. It has since been confirmed for many mono-, di- and trivalent counterions and polyionic species (Manning, 1979). 

Figure 4.10 The effect of monovalent, divalent and trivalent counterions on the hydration state of neutralized poly(acrylic acid). Based on Ikegami (1964).

Evidently, more work has to be done for a comprehensive comparison of theory and experiment. Theory and simulations reveal clearly that the PB-cell model should be a poor approximation for divalent counterions and breaks down totally for trivalent counterions [29]. A comprehensive experimental test of these very important conclusions is still missing. 

Hribar, B., and Vlachy, V. Monte Carlo study of micellar solutions with a mixture of mono- and trivalent counterions. Langmuir, 2001, 17, No. 6, p. 2043-2046. 

Spohr, E., Hribar, B., and Vlachy, V. Mechanism of macroion-macroion clustering induced by the presence of trivalent counterions. Journal of Physical chemistry B, 2002, 106, No. 9, p. 2343-2348. 

FIG. 26 Three-dimensional g(r) for the generic system with trivalent counterions at a density of 0.04247a- 3. Clearly visible is a structure pointing to local arrangements of the ions, for which the position of the first maximum is taken as a characteristic length. 

The collapse of the PMETAI stars by the multivalent counterions can be used to tune the size and morphology of the stars by counterions which change their valency by an external stimulus. Hence, trivalent counterion [Co (CN)6]3 can undergo... 

Fig. 10). The UCST-type cloud points shift to higher temperatures with the increased concentration of added trivalent counterions, whereas the LCST-type cloud points hardly change. Thus, the LCST-type transition can be adjusted by pH, while the UCST-type cloud points can be adjusted by the concentration of trivalent counterions. It is also possible to switch the UCST behavior of the PDMAEMA by using the light-sensitivity of hexacyanocobaltate(III) as the trivalent counterions. Under UV illumination, the trivalent counterions are turned into a mixture of divalent and monovalent counterions and the UCST-behavior disappears [81].

When the monovalent counterions are replaced by divalent or trivalent counterions, the osmotic pressure within the polyelectrolyte architecture will decrease dramatically due to the exchange of a considerable amount of entrapped, monovalent... 

The same phenomenon was observed with trivalent counterions at Z j, = 1. Figure 16 shows the typical AFM image of the brushes with added trivalent counterions and enlarged portions. Clear helical structures are observed. Since there is no... 

Trivalent counterions added to ChSO -Ca solutions were also shown to condense (l ) so that which is initially equal to 1/2 =2), is lowerta to i =1/3... 

Calculate the expected critical coagulation concentrations (ccc) for a charged colloidal system in water with a Hamaker constant = 2.0 x 10 ° J in the presence of mono-, di- and trivalent counterions. 

Critical Coagulation Concentration (in mol/L) for Mono, Di, and Trivalent Counterions at Positively and Negatively Charged Colloidal Particles... 

So, in the case of trivalent counterions the electrostatic interactions are so strong that the ion aggregation proceeds even in such polar media like water. The same behavior was observed in the less polar solvent methanol. Similar to the hydrophobic aggregates in polyelectrolyte gels, the ion aggregates (multiplets) begin to form when the gel still occurs in the swollen state (and remain in the gel upon collapse). 

Ionic polymers can be cross-linked by the addiction of di- or trivalent counterions. This method is based on the principle of gelling a polyelectrolyte solution (eg, Na" "alginate") by using a multivalent ion with an opposite charges (eg, Ca + + 2C1") (Fig. 10.10). Alginate is a type of polysaccharide that occurs naturally in aU brown algae as a skeletal component of their cell walls. 

Figure 4.7 Rg for N=100. (a) Freely jointed polyelectrolyte chain with monovalent counterions in comparison with an athermal uncharged chain, (b) Comparison of electrostatic swelling for monovalent, divalent, and trivalent counterions. (From Liu, S. and Muthukumar, M., J. Chem. Phys., 116, 9975, 2002. With permission.)...

Some surfactants, such as SLS, are affected by hard water. What this means is that the di- and trivalent counterions (Ca, Mg, Fe, etc.) replace the sodium ion of... 

Accordingly, the results are presented as follows Firstly, we analyze the case of a salt with divalent counterions. Secondly, the case of trivalent counterions is studied. Finally, we will focus on the case of electrolyte mixtures made of mono- and multivalent electrolytes. 

Recently, other authors have also reported this phenomenon with trivalent counterions [38-40]. In our case, the reversal is observed for a salt concentration of about 15 mM (to which we will refer as the reversal concentration). It should be stressed that values of the same order of magnitude have also been found for other polymeric latexes with strong acid groups (sulfate [38] and sulfonate [40]). In contrast, much lower reversal concentrations (of the order of 10 M) have been found for carboxylic latexes [37], This seems to suggest that the chemical nature of the surface groups has certain influence on mobility reversal in 3 1 electrolytes. There also exist differences in the magnitude of mobility for electrolyte concentrations under or above the reversal concentration. In our work, the electrophoretic mobility values are smaller than those reported by Ottewill, but resemble the results reported for similar sulfonated latexes [40],... 

It has been known for more than 100 years that many aqueous dispersions precipitate upon addition of salt [438]. Schulze and Hardy observed that most dispersions precipitate at concentrations of 25-150 mM of monovalent counterions [439, 440]. For divalent ions, they found far smaller precipitation concentrations of 0.5-2 mM. Trivalent counterions lead to precipitation at even lower concentrations of 0.01-0.1 mM. For example, gold colloids are stable in NaCl solution, as long as the NaCl concentration does not exceed 24 mM. If the solution contains more NaCl, then the gold particles aggregate and precipitate. The appropriate concentrations for KNO3, CaCl2, and BaCl2 are 23, 0.41, and 0.35 mM [441], respectively. 

This hydrophobization, linked to a decrease in the negative value of the -potential by the admixture of small amounts of plurivalent counter ions, has been shown to cause flocculation of a variety of initially stable particle suspensions, e.g., calcite powder, montmorillonite (SWy-1) particles (Wu, 1994 Wu et al, 1994a,b). The flocculated particles could be reconverted to a stable suspension by complexation of the di- and trivalent counterions with, e.g., EDTA or hexameta phosphate (Wu, 1994). Upon standing for about 16 hours, the flocculated suspensions repeptized spontaneously, as a result of intercalation of the counterions into the clay particle structure (Wu, 1994). 

In principle, multivalent counterions can physically crosslink polyelectrolytes, which cause a further complication in the description of the joint conformational distribution of the polymer chain and spatial distribution of the counterions. While FS with its two spatially close charges may not be well suited to study this phenomenon, the larger trivalent counterion TAM (Figure 15) does crosslink PDADMAC." Unlike the nitroxide FS, the triphenylmethyl radical TAM is not amenable to DEER experiments, as its ESR spectmm is too narrow. On the other hand, the narrow spectmm opens up the possibility to estimate distance distributions from dipolar line broadening, in analogy to the related analysis of nitroxide spectra described in Sertion 2.08.2.4. To avoid distortions by electron-proton spin flip transitions, the experiments were performed at W-band frequencies. 

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