Electrostatic free energy for a confined nanoscale object in a fluid

We present numerical calculations of electrostatic free energies, based on the nonlinear Poisson-Boltzmann (PB) equation, for the case of an isolated spherical nano-object in an aqueous suspension, interacting with charged bounding walls. We focus on systems with a low concentration of monovalent ions (≲10(-4) M), where the range of electrostatic interactions is long (~30 nm) and comparable to the system and object dimensions (~100 nm). Locally tailoring the geometry of the boundaries creates a modulation in the object-wall interaction, which for appropriately chosen system dimensions can be strong enough to result in stable spatial trapping of a nanoscale entity. A detailed view of the underlying mechanism of the trap shows that the physics depends predominantly on counterion entropy and the depth of the potential well is effectively independent of the object's dielectric function; we further note an appreciable trap depth even for an uncharged object in the fluid. These calculations not only provide a quantitative framework for understanding geometry-driven electrostatic effects at the nanoscale, but will also aid in identifying contributions from phenomena beyond mean field PB electrostatics, e.g., Casimir and other fluctuation-driven forces.