Counterion multivalent

Conditions Low water activity (65% sacharose) pH<3.5 Presence of multivalent counterions (Ca+2)... 

The critical value for Q is 1/z. There is a proportional increase in the number of free counterions, f/z, as Q increases from zero, reaching a plateau when Q = z. Also, below this value the degree of dissociation,) , increases as the concentration decreases, and tends to unity as v tends to zero. When Q> /z, p decreases with 0 and tends to /zQ as 0 tends to zero. The number of free ions caimot exceed njz Q. Note that this number is inversely proportional to the square of the valence. The condensation of ions is thus very sensitive to valence for multivalent counterions it takes place at a lower value of Q and the number of free ions is much smaller... 

Imai (1961) has observed that multivalent counterions are more strongly bound than are monovalent ones. This phenomenon can be demonstrated theoretically by considering equilibrium conditions for two counterions with valencies z and (Zj > z and degrees of dissociation and P -For a cylindrical model the equilibrium equations are... 

The precipitation of polyelectrolytes by the addition of multivalent counterions may be explained in these terms. When there are no multivalent ions in solution there is a strong repulsive force between polyions and the osmotic pressure is large. The solubility of polyions is a result of these repulsive forces. 

The binding of multivalent counterions decreases the repulsion and causes attraction between polyions. This attraction is the result of the fluctuation of the counterion distribution and is equivalent to a multivalent counterion bridge between polyions. 

The procedure used for testing the ideal Donnan theory is applicable to any model that decouples ionic effects from network elasticity and polymer/solvent interactions. Thus we require that nnet depend only on EWF and not C. While this assumption may seem natural, several models which include ionic effects do not make this assumption. For example, the state of ionization of a polymer chain in the gel and the ionic environment may affect the chain s persistence length, which in turn alters the network elasticity [26]. Similarly, a multivalent counterion can alter network elasticity by creating transient crosslinks. 

High concentration, however, is not the only means to obtain LC phases of DNA in aqueous solutions. DNA has been found to collapse upon adding in the solutions various condensing agents, which introduce effective attractive interhelical interactions. This is what happens with alcohols and other solvents, which reduce DNA solubility [40], or with multivalent cations like spermidine, spermine, and cobalt hexamine, which are thought to establish correlated counterion fluctuations with... 

Micellar solutions of anionic amphiphiles are usually not stable with respect to the addition of di- or multivalent cations since a precipitation occurs (hard water). In exceptional cases, where precipitation does not occur, the question arises as to how the uni-, di- and multivalent ions compete for binding to the micelles. Due to the high value of I l close to the micellar surface a counterion of high charge will be strongly favored and there is a discrimination between the different types of ions299. For example for SDS close to the CMC, -e(r[)/kT — 7 and if the presence of small amounts of calcium ions does not affect [Pg.74]

This short discussion shows that despite significant progress in the analytical theories, there are still many unsolved issues. The situation gets even more complicated if one allows for added salt and/or multivalent counterions [58] or varies the Manning ratio in the system. 

Compact structures are also induced by size, shape, and charge of multivalent counterions, such as spermidine3+ and [Co(NH3)6]3+ [31, 108, 109]. The concentrations of trivalent and divalent ions that are necessary to reach the intermediates states are much lower than the corresponding concentrations of monovalent ions [108,109]. To put it differently, the number of multivalent condensed cations that reduce the net charge of RNA is smaller than the number of condensed monovalent ions needed to reach the same charge reduction [31, 108, 109]. 

As y tends to decrease with z because multivalent ions compensate more charge In the Inner layer, and as this is a strong effect because of the fourth power dependence, the Schulze-Hardy rule remains explainable In fact, the precise dependence on z and the nature of the counterion now depends on the system, as Is experimentally found. This re-lnterpretatlon of classical knowledge followed from double layer studies with silver Iodide. 

The polyion domain volume can be computed by use of the acid-dissociation equilibria of weak-acid polyelectrolyte and the multivalent metal ion binding equilibria of strong-acid polyelectrolyte, both in the presence of an excess of Na salt. The volume computed is primarily related to the solvent uptake of tighdy cross-linked polyion gel. In contrast to the polyion gel systems, the boundary between the polyion domain and bulk solution is not directly accessible in the case of water-soluble linear polyelectrolyte systems. Electroneutrality is not achieved in the linear polyion systems. A fraction of the counterions trapped by the electrostatic potential formed in the vicinity of the polymer skeleton escapes at the interface due to thermal motion. The fraction of the counterion release to the bulk solution is equatable to the practical osmotic coefficient, and has been used to account for such loss in the evaluation of the Donnan phase volume in the case of linear polyion systems. 

Fig. 4 Principles of complex aqueous coaeervation (A) Oppositely charged polyelectrolytes (B) polyelectrolyte/ multivalent counterions.

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