  We present here exact results for a one-dimensional gas, or fluid, of
hard-sphere particles with attractive boundaries. The particles, which can
exchange with a bulk reservoir, mediate an interaction between the boundaries.
A two-dimensional lattice of such one-dimensional gas `columns' represents a
discrete approximation of a three-dimensional gas of particles between two
surfaces. The effective particle-mediated interaction potential of the
boundaries, or surfaces, is calculated from the grand-canonical partition
function of the one-dimensional gas of particles, which is an extension of the
well-studied Tonks gas. The effective interaction potential exhibits two
minima. The first minimum at boundary contact reflects depletion interactions,
while the second minimum at separations close to the particle diameter results
from a single adsorbed particle that crosslinks the two boundaries. The second
minimum is the global minimum for sufficiently large binding energies of the
particles. Interestingly, the effective adhesion energy corresponding to this
minimum is maximal at intermediate concentrations of the particles.
