Apparent linear charge density

In Figure 27 the apparent linear charge density as a function of the actual linear charge density is shown for the NLDH (Eq. [263]) and PGC (Eq. [365])... 

Figure 27 The apparent linear charge density as a function of actual linear charge density for a cylinder of radius 10 A in a mixed 1 1-2 1 electrolyte with concentration 0.1-0.02 M within the NLDH (dashed lines Eq. [263] with the exact ( or approximate (a values) and PGC (solid lines Eq. [365] with exact and approximate Sdgc values) approximations. The NEDH low and high charge density approximations (Eqs. [264]) are shown by dotted lines the infinite-charge density limit is shown by the horizontal dotted-dashed line.

The fact that the apparent linear charge density is lower than the actual charge density can be seen as confirmation that PB theory does predict some sort of counterion condensation. We mention that because the ADH method results from a (linear) DH interpretation of the (nonlinear) PB equation, it also has a (rather tenuous) mathematical connection to Manning s coimterion condensation theory, which also makes use of the DH solution. " From either Eq. [192] or Eq. [263], the fraction of linear charge density neutralized can be written as (ignoring a contribution from Q... 

To obtain the apparent DH potential within the PGC approximation that asymptotically matches the cylindrical PB profile, we simply replace in Eq. [259] with an apparent linear charge density adh obtained from Eq. [322] ... 

Reed WF, Ghosh S, Medjahdi G, Francois J. Dependence of polyelectrolyte apparent persistence lengths, viscosity, and diffusion on ionic strength and linear charge density. Macromolecules 1991 24 6189-5198. 

Bulk Model Apparent DH Linear Charge Density and... 

The simultaneous negative frequency shift of the EQCM (Fig. 12.1(a)) indicates mass increase in agreement with Takahashi s results [44]. The apparent molar mass of deposited film, M was evaluated from the average initial slope of a linear plot—A/ vs. the anodic charge density, q in Fig. 12.2 and use of the Sauerbrey equation and Faraday s law of electrolysis. 

The corrected Linear Response approach (cLR) consists in the use the TDDFT relaxed density and the corresponding apparent charges (7-38) into Eqs. (7-36) and (7-37) to obtain the first-order approximation to the state specific free energy of the excited state. The details of the implementation are described in Ref. [17], This corrected Linear Response computational scheme can be applied to the analogous of the Time Dependent Hartree-Fock approach either in the complete (Random Phase Approximation) or approximated (Tamm-Dancoff approximation or Cl singles, CIS) version. 

---