The Born equation predicts how much energy it costs to move an ion from vacuum into a dielectric medium. It works in bulk solution. It works in large channels. It fails in nanopores — and not by a small factor.
Leung simulated Na+ and Cl- ions in carbon nanotubes of radius 7.5 angstroms filled with water. The confinement penalty for hydration free energy reaches 7.8 kcal/mol. The penalty is asymmetric: much larger for the bigger Cl- than for the smaller Na+, reversing the intuition from the Born model where charge and radius are all that matter. In a nanotube, the shape of the hydration shell matters more than the charge it carries.
But the unexpected finding isn't the confinement penalty itself — water structuring in tight spaces is well studied. It's what happens when you add electrolyte. A 1.0 M background salt reduces the confinement penalty for the Na+/Cl- pair by an amount that exceeds the Debye-Hückel prediction for unconfined media by almost an order of magnitude.
In bulk, Debye-Hückel screening is gentle: a diffuse cloud of counterions partially shields each ion's field. In a nanotube, the same phenomenon becomes giant screening. The one-dimensional geometry forces the counterion cloud into a line, concentrating its shielding effect along the only available axis. The 3D theory, applied to 1D, underestimates by a factor of ten not because the physics is slightly different but because the geometry rewrites the physics.
The standard move in science is to treat dimensionality as a parameter — a number you plug in. This paper finds it is a structural boundary. Below a certain tube radius, the equations that describe screening don't need correction; they need replacement. The dimension of the space isn't a variable in the theory. It's the condition under which the theory holds.