Impact of the inner solute structure on the electrostatic mean-field and strong-coupling regimes of macromolecular interactions

Systematic Incorporation of Ionic Hard-Core Size into the Debye-Hückel Theory via the Cumulant Expansion of the Schwinger-Dyson Equations

The Debye-Hückel (DH) formalism of bulk electrolytes equivalent to the Gaussian-level closure of the electrostatic Schwinger-Dyson identities without the interionic hard-core (HC) coupling is extended via the cumulant treatment of these equations augmented by HC interactions. By comparing the monovalent ion activity and pressure predictions of our cumulant-corrected DH (CCDH) theory with hypernetted-chain results and Monte Carlo simulations from the literature, we show that this rectification extends the accuracy of the DH formalism from submolar to molar salt concentrations. In the case of internal energies or the general case of divalent electrolytes mainly governed by charge correlations, the improved accuracy of the CCDH theory is limited to submolar ion concentrations. Comparison with experimental data from the literature shows that, via the adjustment of the hydrated ion radii, CCDH formalism can equally reproduce the nonuniform effect of salt increment on the ionic activity coefficients up to molar concentrations. The inequality satisfied by these HC sizes coincides with the cationic branch of the Hofmeister series.

On the nature of screening in charge-regulated macroion solutions

We present a derivation of the screening length for a solution containing a charge-regulated macroion, e.g. protein, with its counterions. We show that it can be obtained directly from the second derivatives of the total free energy by taking recourse to the "uncertainty relation" of the Legendre transform, which connects the Hessians or the local curvatures of the free energy as a function of density and its Legendre transform, i.e., osmotic pressure, as a function of chemical potentials. Based on the Fowler-Guggenheim-Frumkin model of charge regulation, we then analyze the "screening resonance" and the "overscreening" of the screening properties of the charge-regulated macroion solution.