Adsorption is an important process
used in many industrial unit
operations. However, due to the heterogeneity of surfaces studied
experimentally, it is not a simple task to evaluate the validity of
theories for adsorption. Here, we present a thorough investigation
of density functional theory and density gradient theory based on
molecular simulation. While comparisons between these theories have
been made in the literature, only our recently developed equation
of state (EOS), the Perturbed Truncated and Shifted (PeTS) equation
of state and the according functional version, allow a thorough validation
of both theories, because the EOS separates repulsive and attractive
free energy contributions consistently with the inhomogeneous theory.
The PeTS EOS represents the thermodynamics of the Lennard-Jones truncated
and shifted fluid with a cutoff radius of 2.5 times the fluid diameter
very accurately and is valid in the metastable range, too. To check
the validity of both density gradient and density functional theory
in adsorption scenarios, molecular dynamics simulations are performed
for several wall potentials common in adsorption calculations at various
states and solid–fluid interaction energies. A new parametrization
for the density functional theory is proposed that relies on bulk
data for the pressure only. Adsorption is predicted well from this
new theory in both gaseous and liquid states. In contrast, density
gradient theory turns out to be valid only in the dilute gaseous regime
if the parameters are not fitted to adsorption.