The aqueous chemistry of water films confined between clay mineral surfaces remains an important unknown in predictions of radioelement migration from radioactive waste repositories. This issue is particularly important in the case of long-lived anionic radioisotopes (129I-, 99TcO4-, 36Cl-) which interact with clay minerals primarily by anion exclusion. For example, models of ion migration in clayey media do not agree as to whether anions are completely or partially excluded from clay interlayer nanopores. In the present study, this key issue was addressed for Cl- using MD simulations for a range of nanopore widths (6 to 15 Å) overlapping the range of average pore widths that exists in engineered clay barriers. The MD simulation results were compared with the predictions of a thermodynamic model (Donnan Equilibrium model) and two pore-scale models based on the Poisson-Boltzmann equation under the assumption that interlayer water behaves as bulk liquid water. The simulations confirmed that anion exclusion from clay interlayers is greater than predicted by the pore-scale models, particularly at the smallest pore size examined. This greater anion exclusion stems from Cl- being more weakly solvated in nano-confined water than it is in bulk liquid water. Anion exclusion predictions based on the Poisson-Boltzmann equation were consistent with the MD simulation results, however, if the predictions included an ion closest approach distance to the clay mineral surface on the order of 2.0 ± 0.8 Å. These findings suggest that clay interlayers approach a state of complete anion exclusion (hence, ideal semi-permeable membrane properties) at a pore width of 4.2 ± 1.5 Å.

In this work, we analyse a broad class of generalized Poisson–Boltzmann equations and reveal a common mathematical structure. In the limit of a wide electrode, we show that a broad class of generalized Poisson–Boltzmann equations admits a reduction that affords an explicit connection between the functional form of the corresponding free energy and the associated differential capacitance data. We exploit the relation to we show that differential capacitance curves generically undergo an inflection transition with increasing salt concentration, shifting from a local minimum near the point of zero charge for dilute solutions to a local maximum point near the point of zero charge for concentrated solutions. In addition, we develop a robust numerical method for solving generalized Poisson–Boltzmann equations which is easily applicable to the broad class of generalized Poisson–Boltzmann equations with very few code adjustments required for each model

We present a solver for the Poisson-Boltzmann equation and demonstrate its applicability for biomolecular electrostatics computation. The solver uses a level set framework to represent sharp, complex interfaces in a simple and robust manner. It also uses non-graded, adaptive octree grids which, in comparison to uniform grids, drastically decrease memory usage and runtime without sacrificing accuracy. The basic solver was introduced in earlier works [16,27], and here is extended to address biomolecular systems. First, a novel approach of calculating the solvent excluded and the solvent accessible surfaces is explained; this allows to accurately represent the location of the molecule’s surface. Next, a hybrid finite difference/finite volume approach is presented for discretizing the nonlinear Poisson-Boltzmann equation and enforcing the jump boundary conditions at the interface. Since the interface is implicitly represented by a level set function, imposing the jump boundary conditions is straightforward and efficient.

The definition of a molecular surface which is physically sound and computationally efficient is a very interesting and long standing problem in the implicit solvent continuum modeling of biomolecular systems as well as in the molecular graphics field. In this work, two molecular surfaces are evaluated with respect to their suitability for electrostatic computation as alternatives to the widely used Connolly-Richards surface: the blobby surface, an implicit Gaussian atom centered surface, and the skin surface. As figures of merit, we considered surface differentiability and surface area continuity with respect to atom positions, and the agreement with explicit solvent simulations. Geometric analysis seems to privilege the skin to the blobby surface, and points to an unexpected relationship between the non connectedness of the surface, caused by interstices in the solute volume, and the surface area dependence on atomic centers. In order to assess the ability to reproduce explicit solvent results, specific software tools have been developed to enable the use of the skin surface in Poisson-Boltzmann calculations with the DelPhi solver. The results indicate that the skin and Connolly surfaces have a comparable performance from this last point of view.