Understanding
the role of the counterion species in surfactant
solutions is a complicated task, made harder by the fact that, experimentally,
it is not possible to vary independently bulk and surface quantities.
Here, we perform molecular dynamics simulations at constant surface
coverage of the liquid/vapor interface of lithium, sodium, potassium,
rubidium, and cesium dodecyl sulfate aqueous solutions. We investigate
the effect of counterion type and charge sign on the surface tension
of the solution, analyzing the contribution of different species and
moieties to the lateral pressure profile. The observed trends are
qualitatively compatible with the Hofmeister series, with the notable
exception of sodium. We point out a possible shortcoming of what is
at the moment, in our experience, the most realistic nonpolarizable
force field (CHARMM36) that includes the parametrization for the whole
series of alkali counterions. In the artificial system where the counterion
and surfactant charges are inverted in sign, the counterions become
considerably harder. This charge inversion changes considerably the
surface tension contributions of the counterions, surfactant headgroups,
and water molecules, stressing the key role of the hardness of the
counterions in this respect. However, the hydration free energy gain
of the counterions, occurring upon charge inversion, is compensated
by the concomitant free energy loss of the headgroups and water molecules,
leading to a negligible change in the surface tension of the entire
system.