Thermodynamics of Charge Regulation near Surface Neutrality

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.

Electrostatic interactions between charge regulated spherical macroions

We study the interaction between two charge regulating spherical macroions with dielectric interior and dissociable surface groups immersed in a monovalent electrolyte solution. The charge dissociation is modelled via the Frumkin-Fowler-Guggenheim isotherm, which allows for multiple adsorption equilibrium states. The interactions are derived from the solutions of the mean-field Poisson-Boltzmann type theory with charge regulation boundary conditions. For a range of conditions we find symmetry breaking transitions from symmetric to asymmetric charge distribution exhibiting annealed charge patchiness, which results in like-charge attraction even in a univalent electrolyte-thus fundamentally modifying the nature of electrostatic interactions in charge-stabilized colloidal suspensions.

Charge regulation indicates water expulsion from silica surface by cesium cations

HYPOTHESIS

Since the discovery of the Hofmeister effect in 1888, the varied propensity of ions to proteins, DNA and other surfaces has motivated research aimed at deciphering the underlying ion specific adsorption mechanism. Experimental and numerical studies have shown that in agreement with Collins' heuristic law of matching water affinity, weakly hydrated (chaotropic) ions adsorb preferentially to hydrophobic surfaces. Here, we show that this preference is driven by expulsion of bound water molecules from the surface by the adsorbing ions.

EXPERIMENTS

Using AFM spectroscopy of the force acting between two silica surfaces, we characterize surface charge regulation by adsorbed Na⁺ and Cs⁺ ions at different salt concentrations, pH values and temperatures. These data are analyzed in the framework of a recent theory of charge regulation, relating it to change in surface entropy.

FINDINGS

Upon binding to the silica, cesium cations expel water molecules from the surface to create additional adsorption sites for more ions. Cs⁺ adsorption is thus driven by the release of hydrating water molecules and the resulting increased surface entropy. The model indicates that on average, the binding of three cesium cations releases enough water molecules to make room for two additional bound cations. Na⁺ does not exhibit such behavior.