  Surface nanobubbles emerging at solid-liquid interfaces of submerged
hydrophobic surfaces show extreme stability and very small (gas-side) contact
angles. In a recent study Ducker (W. A. Ducker, Langmuir 25, 8907 (2009).)
conjectured that these effects may arise from the presence of impurities at the
air-water interface of the nanobubbles. In this paper we present a quantitative
analysis of this hypothesis by estimating the dependence of the contact angle
and the Laplace pressure on the fraction of impurity coverage at the liquid-gas
interface. We first develop a general analytical framework to estimate the
effect of impurities (ionic or non-ionic) in lowering the surface tension of a
given air-water interface. We then employ this model to show that the
(gas-side) contact angle and the Laplace pressure across the nanobubbles indeed
decrease considerably with an increase in the fractional coverage of the
impurities, though still not sufficiently small to account for the observed
surface nanobubble stability. The proposed model also suggests the dependencies
of the Laplace pressure and the contact angle on the type of impurity.
