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

Adhesion of surfaces via particle adsorption: Exact results for a lattice of fluid columns