  Adsorption is the accumulation of a solute at an interface that is formed
between a solution and an additional gas, liquid, or solid phase. The
macroscopic theory of adsorption dates back more than a century and is now
well-established. Yet, despite recent advancements, a detailed and
self-contained theory of single-particle adsorption is still lacking. Here, we
bridge this gap by developing a microscopic theory of adsorption kinetics, from
which the macroscopic properties follow directly. One of our central
achievements is the derivation of the microsopic version of the seminal
Ward-Tordai relation which connects the surface and subsurface adsorbate
concentrations via a universal equation that holds for arbitrary adsorption
dynamics. Furthermore, we present a microscopic interpretation of the
Ward-Tordai relation which, in turn, allows us to generalize it to arbitrary
dimension, geometry and initial conditions. The power of our approach is
showcased on a set of hitherto unsolved adsorption problems to which we present
exact analytical solutions. The framework developed herein sheds fresh light on
the fundamentals of adsorption kinetics, which opens new research avenues in
surface science with applications to artificial and biological sensing and to
the design of nano-scale devices.
