Effective charge density

Drijvers and Goethals 52) have reported that excess sulphide functions (monomer and polymer) and diethyl ether have no detectable effect on the dissociation of two sulphonium tetrafluoroborate salts in methylene chloride and nitrobenzene, when present in similar proportions to those in corresponding polymerisation reactions. In contrast to this, however, Jones and Plesch 51) have shown that the dissociation constant of triethyloxonium hexafluorophos-phate in methylene chloride at 0°C increases by a factor of - 2 when small quantities of tetrahydrofuran are added. The latter molecule has a lower dielectric constant than methylene chloride and might therefore be expected to reduce dissociation. These workers have interpreted their results in terms of specific solvation of the cation by ether molecules, with subsequent reduction in the effective charge density of the positive ion and hence in the coulombic force favouring ion pairing, e.g. 

The present review deals mainly with two examples of polyelectrolyte phase behavior as discussed above. As an example for an H-type precipitation, the solution properties of polyvinylpyridinium chains are monitored as function of added inert salt. Here, we focus on the determination of the effective charge density and of the solvent quality parameter which are supposed to play a central role for the understanding of polyelectrolyte solution without specific counterion interactions. The second system under investigation comprises the interaction of polyacrylic acid with alkaline earth cations which exhibit very specific interactions, thus representing an example for type L-precipitation. Here the coil dimensions close to the phase boundary are compared to those close to type H-precipitation with inert added salt. 

Since several approaches exist to determine the effective charge density, we denote/determined from a fit of Rg as/, throughout the paper. 

It is most interesting to note that the fitted value for the effective charge density fa does significantly depend on the hydrophobicity of the chain and... 

Effective Charge Density at Low and High Salt Concentrations... 

Effective Charge Density Determined by the Osmotic Coefficient... 

Comparison of equations 19 and 20 shows that we can consider the product zO as an effective charge number zeff, hence O=zeffz. The osmotic coefficient is therefore a measure of the extent to which the dissociated counterions are not independent osmotic entities due to Coulombic interactions [61]. The effective charge density fos is then derived as... 

In close vicinity to the salting out phase transition, the effective charge density was determined by conductivity measurements in combination with the known and estimated electrophoretic mobilities of the counterions and the polyions, respectively. The procedure is based on the fact that, shortly before the precipitation of the polyion, the conductivity comprises contributions of polyions, free counterions and added salt. After precipitation of the polyion by reducing the temperature the conductivity is given solely by the supernatant aqueous salt solution, thus the difference Act is due to polyions and free counterions... 

For most samples investigated, the temperature interval during which precipitation occurs, is quite small, i.e. 2-5 °C, as shown in Fig. 10. The upper dotted curve in Fig. 10 represents the temperature dependence which would be expected for the polyion solution if no precipitation occurs and if the fraction of free counterions would not increase with temperature, i.e. the increase in conductivity is solely caused by the decrease of the viscosity of water. Act may be utilized to determine the effective charge density f by the equation... 

Fig. 14 Effective charge density close to the precipitation boundary as a function of Nal concentration ( ) MePVP1940I, Q=80% and ( ) BuPVP1940I, Q=70%...

In summary the discussion above appears to provide a crude and qualitative explanation of the experimental charge densities. For more detailed recent progress by computer simulations in this field the reader is referred to theoretical contributions in this volume. However, the determination of the effective charge densities remains a highly delicate issue and the discussion above may at most provide some qualitative trends which, however, are based on several assumptions. 

In the latter type of solvent there will be no hydrogen bonds to anions, and so there is no envelope of solvent molecules hindering the attack of the base on the proton. This also has the effect of increasing the effective charge density on the base, as it is not dissipated by a solvent shell. This in turn increases the effective hardness of the base, and so favours elimination over substitution. Furthermore, in a solvent that has a low polarity, the stability of any charged intermediate would be reduced, and so bimolecular reactions would be favoured over unimolecular alternatives, and this also favours elimination. 

In order to determine the effective charge density of the polyelectrolyte brushes conductivity measurements were performed under argon gas atmosphere on salt-free aqueous solutions. For evaluation of the effective charge density the mobility of the polyion and of the counter-ion have to be known according to ... 

Table 7 Fraction of free counterions, fc (normalized to the number of chemically quater-nized monomers), the effective charge density, / (normalized to the total number of monomers), the effective charge density per main chain monomer fma the cross sectional radius of gyration RgjC) the mean concentration of counterions cc and the mean inverse Debye screening length Xb l within the volume of a cylindrical brush molecule due to condensed counterions...

In summary, the light-scattering investigations support the results obtained by conductivity measurements that the effective charge density of cylindrical polyelectrolyte brushes is much smaller than for linear flexible polyions. 

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