Adhesion of surfaces via particle adsorption: exact results for a lattice of fluidcolumns

Abstract

We present here exact results for a one-dimensional gas, or fluid, of hard-sphere particleswith attractive boundaries. The particles, which can exchange with a bulk reservoir,mediate an interaction between the boundaries. A two-dimensional lattice of suchone-dimensional gas columns represents a discrete approximation of a three-dimensionalgas of particles between two surfaces. The effective particle-mediated interaction potentialof the boundaries, or surfaces, is calculated from the grand-canonical partition function ofthe one-dimensional gas of particles, which is an extension of the well-studied Tonks gas(Tonks (1936 Phys. Rev. 50 955)). The effective interaction potential exhibits two minima.The first minimum at boundary contact reflects depletion interactions, while the secondminimum at separations close to the particle diameter results from a single adsorbedparticle that crosslinks the two boundaries. The second minimum is the global minimumfor sufficiently large binding energies of the particles. Interestingly, the effective adhesionenergy corresponding to this minimum is maximal at intermediate concentrations of theparticles.