Debye-Hiickel parameter effective

Plotting ixbase VS. pH gives a sigmoidal curve, whose inflection point reflects the apparent base-pAi, which may be corrected for ionic strength, I, using Equation 6.11 in order to obtain the thermodynamic pATa value in the respective solvent composition. Parameters A and B are Debye-Hiickel parameters, which are functions of temperature (T) and dielectric constant (e) of the solvent medium. For the buffers used, z = 1 for all ions ao expresses the distance of closest approach of the ions, that is, the sum of their effective radii in solution (solvated radii). Examples of the plots are shown in Figure 6.12. 

We again see that in the limit of small Ka, the effective Debye-Hiickel parameter is given by Eq. (3.52) and that in the limit of large Ka, rod-like zwitterions behave like monovalent electrolytes of concentration nJ2 and the effective Debye-Hiickel parameter is given by Eq. (3.55). 

At moderate ionic strengths a considerable improvement is effected by subtracting a term bl from the Debye-Hiickel expression b is an adjustable parameter which is 0.2 for water at 25°C. Table 8.4 gives the values of the ionic activity coefficients (for Zi from 1 to 6) with d taken to be 4.6A. 

In the above two equations, the former value is valid for basic SI units and the latter value for / in moles per cubic decimetre and a in nanometres. The parameter a represents one of the difficulties connected with the Debye-Hiickel approach as its direct determination is not possible and is, in most cases, found as an adjustable parameter for the best fit of experimental data in the Eq. (1.3.29). For common ions the values of effective ion radii vary from 0.3 to 0.5. Analogous to the limiting law, the mean activity coefficient can be expressed by the equation... 

The GB model is a modification of the Coulomb equation to include the Born radius of the particle or atom which estimates the degree of the particle s burial within the molecule. Equation 5 relates AGdec to the solvent/solute dielectric (e), the separation between the partial atomic charges r, the effective Born radii R(i and /), and the smoothing function fGR. A Debye-Hiickel screening parameter (k) similar to that used in the PB equation is used to account for the monovalent ions. 

Evidently there are factors at work in an electrolytic solution that have not yet been reckoned with, and the ion size parameter is being asked to include the effects of all these factors simultaneously, even though these other factors probably have little to do with the size of the ions and may vary with concentration. If this were so, the ion size parameter a, calculated back from experiment, would indeed have to vary with concentration. The problem therefore is What factors, forces, and interactions were neglected in the Debye-Hiickel theory of ionic clouds ... 

With the help of the condensation criterion from Sec. IV.B, the extent of the correlation-enhanced condensation can be further quantified. The Manning fraction from the molecular dynamics simulation increases only by a fairly small amount. It is at most 4% larger than the PB value. This translates to an effective Manning parameter eff = 1/(1 — fe) being 5-10% larger than the bare one. This increase is very accurately captured by the Debye-Hiickel hole-cavity theory. Its prediction for fe is at most 1% smaller than the value obtained in the simulation. Interestingly, it is even independent of density. This, however, is not a feature to be generally expected and should therefore not be overinterpreted. 

As explained in section 3.6.1, many modifications have been proposed for the Debye-Hiickel relationship for estimating the mean ionic activity coefficient 7 of an electrolyte in solution and the Davies equation (equation 3.35) was identified as one of the most reliable for concentrations up to about 0.2 molar. More complex modifications of the Debye-Huckel equation (Robinson and Stokes, 1970) can greatly extend the range of 7 estimation, and the Bromley (1973) equation appears to be effective up to about 6 molar. The difficulty with all these extended equations, however, is the need for a large number of interacting parameters to be taken into account for which reliable data are not always available. 

Figure 12. Salt effect on the relative R 0H/R 0 quantum yield in two different solvents Water (left panel) and a 50/50% (by volume) mixture of met Hanoi/water [11c]. Circles are experimental data obtained from the relative height ratio of the two peaks in the steady-state fluorescence spectrum e.g., Figure 10. Dashed and full curves correspond to the Debye-Hiickel expression (with finite ion-size correction) [21] and the Naive Approximation [17, 11c], respectively. Both models employ the zero-salt kinetic parameters.

Reliable theories that accurately correlate or predict polyelectrolyte phase diagrams are lacking. Letting electrostatic excluded volume between chain segments be modeled at the level of the Debye-Hiickel approximation, a modified or effective Flory-Huggins parameter Xeff can be determined via the random phase approximation (141) ... 

The ionic diameters used in the Debye— Hiickel theory have been described as, ... the effective diameter of the ion in solution. Since no independent method is available for evaluating aj this quantity is an empirical parameter, but the aj s obtained are of a magnitude for ion sizes. [26]. Values for these effective ionic diameters have been experimentally evaluated and can be found in the literature [26, 27]. 

Netz and co-workers treat electrolyte systems within a field-theoretic framework that reduces to the Debye-Hiickel description at the Gaussian level of approximation.Of particular interest is the application of the model to ions of valence Zo (with no added salt) near a planar surface of charge density where the size of correlation effects can be described by a single parameter ... 

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