Contact line pinning and the relationship between nanobubbles and substrates.

We report a theoretical study of nanobubble stabilization on a substrate by contact line pinning. In particular, we predict the magnitude of the pinning force required to stabilize a nanobubble and the threshold values of the pinning force that the substrate can provide. We show that the substrate chemistry and the local structures of substrate heterogeneity together determine whether or not surface nanobubbles are stable. We find that for stable nanobubbles, the contact angles are independent of substrate chemistry as its effects are cancelled out by the pinning effect. This prediction is in agreement with available experimental data.