Counterion deviation from ideality

Before presenting numerical results, it is worth summarizing the main characteristics of the experimental results for the osmotic pressure of polyelectrolyte solutions [9, 17, 18, 57, 107], The measured osmotic coefficients most often exhibit strong negative deviations from ideality. The measured values are a) lower than it was predicted by the cylindrical cell model theory, b) rather (but not completely) insensitive to the nature of the counterions, and c) also insensitive to the polyelectrolyte concentration in a dilute regime and/or for... 

With the IRC-50-NaPSS system, the rigid matrix of the resin is resistant to the entry of solvent so that at equilibrium the concentration of counterions increases from 0.46 to 4.08M over the a range examined. At these resin-phase molarities it has been shown that the contribution of ion-solvent interaction to the deviation from ideal behavior of the counterions (II), while negligible at low concentration, is a factor to... 

Figure 8 is similar to Fig. 6, but it illustrates deviations from the ideal behavior in the case of transfer to counterion. Because the rate of transfer... 

Tertiary oxonium ions that are active species in CROP of cyclic ethers are inherently stable (trialkyloxonium salts with stable counterions are commercially available and may be stored without special precautions for prolonged periods of time). Thus, if basic impurities are avoided in CROP of cyclic ethers, there is essentially no irreversible termination. Those polymerization are, however, not classified as living because reversibility of propagation and reversible chain transfer to polymer cause deviations from the ideal situation observed for, for example, anionic vinyl polymerization in which DP = [M]o/[I]o/ molecular weight distribution is close to Poisson distribution and the nature of end-groups may be strictly controlled. As will be discussed in subsequent sections, conditions of living polymerization may be more closely approached if polymerization proceeds by the AM mechanism. 

Subdivision of counterions into condensed and uncondensed populations according to the Manning/Oosawa depiction is not unique. For example, a hypothetical thermodynamically bound counterion population can be defined to account for the deviations of polyelectrolyte solutions from thermodynamic ideality (35) this population is not equal to the condensed population. One can also use different definitions of condensed. The inflection point in the radial ion distribution, the Bjerrum length, and the radial distance over which the electrostatic interaction energy decays to kT have all been employed as alternative criteria for defining a condensed fraction (50). 

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