To what extent of ion neutralization can multivalent ion distributions around RNA-like macroions be described by Poisson

To what extent of ion neutralization can multivalent ion distributions around RNA-like macroions be described by Poisson–Boltzmann theory?

Xiong Gui, Xi Kun, Zhang Xi^†, Tan Zhi-Jie^‡

(color online) “ritical”urface charge density σ_c for RNA-like spherical macroions with surface charge density of 0.0143e/Å² as a function of divalent salt concentration [2+] (a) and trivalent salt concentration [3+] (b), respectively; z is the valence of divalent ion (a) or trivalent ion (b). The symbols are obtained through extensive comparisons between PB theory and MC simulations, and the lines are from the empirical formula Eq. (4). Different colors denote macroions with different radii: 10 Å (red), 15 Å (green), 20 Å (blue), 25 Å (magenta), and 30 Å (cyan). σ_c for RNA-like spherical macroions with different surface charge densities σ around the typical value of 0.0143e/Å² can be found in Fig. S6 in the supplementary material.