Modulation effects within the mean-field theory of electrolyte solutions

The consequences of source charge and surface modulation are studied within the framework of the Poisson-Boltzmann theory of electrolyte solutions. Through a consideration of various examples, it is found that inherent modulation can lead to both like-charge attraction and overcharging effects.

Figure 1

Portions of two long, identical polyelectrolytes are shown. At large distances they repel but at short distances they attract.

Figure 2

A plot of the approximate interaction energy versus separation for the model polyelectrolytes.

Figure 3

A plot of the one component fluid’s second order charge condensation versus $z$, the distance from the plane. Here, $G=2\gamma =2/l_D$. The condensation is particularly localized and then screened at larger distances. The localization increases exponentially with the magnitude of $G$. The total integrated charge from $z=0$ to $\infty$ is zero for each component, as expected.

Figure 4

A plot of the effective charge density versus modulation wavelength for the near cylinder. The thin line is the unmodulated charge density, the dashed line is the modulated effective charge valid to second order in $\beta$, and the thick line is the radii-averaged value discussed in the text. The parameter values were set to $\beta =0.1$, ${ϵ}_i=1$, ${ϵ}_0=5$, and $\gamma =5$.