Concentration of counterions

RPM model, but theories for the SPM model electrolyte inside a nanopore have not been reported. It is noticed that everywhere in the pore, the concentration of counterion is higher than the bulk concentration, also predicted by the PB solution. However, neutrality is assumed in the PB solution but is violated in the single-ion GCMC simulation, since the simulation result of the counterion in the RPM model is everywhere below the PB result. There is exclusion of coion, for its concentration is below the bulk value throughout the pore. Only the solvent profile in the SPM model has the bulk value in the center of the pore. 

Conformation depends on the degree of ionization and concentration of the polyion, the type and concentration of the counterion and the interaction between counterion and polyion. Extension is favoured by low concentrations of counterion and polyion. Conformational change is also affected by the extent of the charge on the polyion. As the charge on a polyion increases, the chain uncoils and expands under the influence of repulsive forces. Thus, the neutralization of a polyacid is accompanied by... 

Osmotic pressure results from the difference in concentration between the boimd but mobile coimterions within the polyion and the free counterions outside it. The concentration of counterions is greater within the polyion so that solvent molecules tend to enter this region. The osmotic force is proportional to the difference n—n where n equals the total number of counterions or the number of ionizable groups on the polyion. 

Concentration of counterion Increasing concentration Increases retention up to a limit. 

Micellization depends upon a balance of forces and the cmc decreases with increasing hydrophobicity of the apolar groups, and for ionic amphiphiles also depends on the nature and concentration of counterions in solution. Added electrolytes decrease the cmc, and the effect increases with decreasing charge density of the counterion. Divalent counterions, however, lead to... 

Unlike charges attract and like charges repel each other, so there is a high concentration of counterions attracted to the particle surface whilst co-ions (those with the same sign charge as that of the surface) are repelled. Thermal motion, i.e. diffusion, opposes this local concentration gradient so that the counterions are in a diffuse cloud around the particle. Of course particles which have a like charge will also repel each other but the interaction of the particle surfaces will be screened by the counterion clouds between the particles. The interaction potential is a function of the surface potential, i]/o, and the permittivity of the fluid phase, e = r80, where r is the relative permittivity.12,27... 

The presence of a net charge at the particle surface produces an asymmetric distribution of ions in the surrounding region. This means that the concentration of counterions close to the surface are higher than the ions with the same charge as the particle. Thus, an electrical double layer is measured around such a particle placed in water. 

There are several possibilities for the determination of the critical micellar concentration. If the micelles are formed from charged surfactants, a plot of the electrophoretic current at constant high voltage against the surfactant concentration shows an inflection point at the ccmc. It should be noted that the critical micellar concentration changes with temperature, the kind and concentration of counterions, and other buffer ingredients. 

Literature on reactions involving micellar counterions is particularly rich and for good reasons. The local concentration of counterions in the micellar Stern region is extremely high compared to typical aqueous solutions. As a result, bimolecular reactions involving bases such as hydroxide and acetate or oxidants such as perchlorate can be accelerated significantly by using these as a counterion for cationic surfactants. Discussion here will be restricted to a selected number of relatively recent examples of particular interest. This should not, however, distract from the merit of many of the other publications in this field. 

Nature of counterions counterions of higher valence are more strongly attracted to the gel phase in ionic hydrogels. These ions are preferred by the gel because the concentration of counterions needed inside the gel decreases. 

The solvent is supposed to be continuous and we took the permittivity of the medium to be constant. This is certainly a rough approximation because polar molecules are hindered from rotating freely in the strong electric field at the surface. In addition, the high concentration of counterions in the proximity of the surface can change the permittivity drastically. 

Let us start by considering a liquid on a planar, charged surface. If we apply an electric field parallel to the surface the liquid begins to move (Fig. 5.12). This phenomenon is called electro-osmosis. Why does the liquid start to move The charged surface causes an increase in the concentration of counterions in the liquid close to the surface. This surplus of counterions is moved by the electric field towards the corresponding electrode. The counterions drag the surrounding liquid with them and the liquid starts to flow. 

A bit of explanation is required here for those readers unfamiliar with the condensation concept, a key notion to describe polyelectrolytes. Consider as here a polyanion. If the charges are brought closer to one another, on the average, below a critical distance their mutual repulsion is such that — in order to continue to obey first principles electrostatics such as the Poisson equation — they screen themselves with an atmosphere of counterions. This atmospheric condensation, which can coexist with ionic binding at the individual sites, boosts the local concentration of counterions in the space surrounding the polyelectrolyte by as much as three orders of magnitude. The nmr measurements analyzed here focus on these water hydration molecules coordinated to condensed sodium counterions, next to the surface of the tactoids (see Fripiat s chapter). 

When an open tube with fixed charges at the tube wall is filled with an electrolyte solution, the ionic atmosphere forms an electrical double layer [31-33]. Since the double layer has a higher concentration of counterions than the bulk solution, electroneutrality requires that the bulk electrolyte outside the double layer has the same amount of excessive coions. 

At higher temperatures, higher concentrations of counterions are needed to induce folding in nucleic acids. This is so because thermal fluctuations resist the propensity of counterions to condense in the vicinity of the polyelectrolyte [108, 109]. This is in agreement with experiments [31, 108-110]. In fact,... 

From eqn.(3.84) and figures 3.22a, b and c we conclude that the concentration of counterions in IEC is a primary parameter which may be used to vary retention, i.e. to bring the capacity factor into the optimum range. Only the selectivity between solutes of different valencies will be affected considerably by changes in the concentration of the counterion. 

IEC Concentration of counterion pH Nature of modifier(s), counterion or buffer... 

This behavior may also be rationalized by observing that as id -> 0 the volume of the intervening solution per unit area of plate is decreasing, so that in order to hold the same number of counterions per unit area, the average concentration of counterions in the solution between the... 

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