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

TL;DR

This paper provides exact analytical results for the effective interaction between surfaces mediated by a one-dimensional gas of particles, revealing two minima in the potential related to depletion and adsorption effects, with implications for surface adhesion.

Contribution

It introduces an exact solution for a lattice model of particle-mediated surface interactions, extending the Tonks gas framework to include attractive boundaries and adsorption phenomena.

Findings

Two minima in the interaction potential: depletion and adsorption-induced crosslinking.

The global minimum occurs at high binding energies and specific particle concentrations.

Maximum adhesion energy is achieved at intermediate particle concentrations.

Abstract

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.