The Born equation predicts that smaller ions pay a larger penalty for confinement. In bulk water, each ion sits inside a solvation shell scaled to its radius — the smaller the ion, the more tightly organized the shell, the more energy it costs to compress. Squeeze ions into a nanopore, and you expect sodium (smaller) to suffer more than chloride (larger).
Leung's molecular dynamics simulations in carbon nanotubes show the opposite. Chloride pays a larger confinement penalty than sodium in tubes with 7.5 Å radius — up to 7.8 kcal/mol. The Born equation fails because it treats the ion as a charged sphere in a continuum dielectric. In a nanopore, the ion's solvation shell doesn't simply compress; it restructures. Chloride's larger, more diffuse hydration geometry is more disrupted by the geometric constraint than sodium's compact shell. The penalty tracks disruption of solvation structure, not ionic radius.
A second violation: adding background electrolyte reduces the confinement penalty by amounts nearly ten times greater than Debye-Hückel theory predicts. In bulk solution, screening weakens interactions over the Debye length. In a nanopore, the confined geometry amplifies screening because ions in the tube interior see a disproportionate fraction of their counterions — the cylindrical geometry concentrates the screening effect that the spherical theory underestimates.
Both violations arise from the same error: applying bulk-derived theories to systems where the boundary dominates the physics. The Born equation and Debye-Hückel theory describe ions far from walls. In a nanopore, every ion is near a wall. The approximation that worked in open water breaks exactly where the application matters most.