Electrostatic effects in nanosystems are understood via a physical picture built on their multiscale character and the distinct behavior of mobile ions versus charge groups fixed to the nanostructure. The Poisson–Boltzmann equation is nondimensionalized to introduce a factor λ that measures the density of mobile ion charge versus that due to fixed charges; the diffusive smearing and volume exclusion effects of the former tend to diminish its value relative to that from the fixed charges. We introduce the ratio σ of the average nearest-neighbor atom distance to the characteristic size of the features of the nanostructure of interest (e.g., a viral capsomer). We show that a unified treatment (i.e., λ∝σ) and a perturbation expansion around σ=0 yields, through analytic continuation, an approximation to the electrostatic potential of high accuracy and computational efficiency. The approach was analyzed via Padé approximants and demonstrated on viral system electrostatics; it can be generalized to accommodate extended Poisson-Boltzmann models, and has wider applicability to nonequilibrium electrodiffusion and many-particle quantum systems.
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