Past exam of the MPhil in micro- and nanotechnology enterprise course of the University of Cambridge / 2022 / Paper 2 / Section B / 23 / v / b

At lower salt concentration, the longer Debye–Hückel screening length allows the two diffuse layers to interact at greater separation. For sufficiently charged surfaces, this produces a positive free-energy barrier between separated plates and the short-range primary attractive region. Crossing a barrier costs free energy, so it can kinetically stabilize a dispersion even though a more attractive state exists at close approach. The relevant barrier in a finite object must be compared with thermal energy using the appropriate geometry and interaction area.

Over the experimentally relevant range of several screening lengths, the low-salt interaction can be predominantly repulsive, as drawn in the illustrative model. Strictly, at asymptotically infinite separation, the supplied nonretarded DLVO model still approaches zero from the attractive side, because $e^{-{\kappa }_{D}d}$ decays faster than $d^{-2}$ for any finite salt concentration. A shallow secondary minimum can therefore occur beyond the barrier. Calling the entire far field repulsive without specifying the distance range would conceal this distinction.

Lower salt alone does not guarantee a barrier: surface potential, charge regulation and attraction strength still matter. Extremely dilute or salt-free systems also require counterion and finite-cell constraints beyond blindly holding $B$ fixed while sending ${\kappa }_D$ to zero.