Communication: Thermodynamic analysis of critical conditions of polymer adsorption

Polymer adsorption to solid surfaces is a ubiquitous phenomenon, which has attracted long-lasting attention. Dependent on the competition between the polymer-solid adsorption and polymer-solvent solvation interactions, a chain may assume either 3d solvated conformation when adsorption is weak or 2d adsorbed conformation when adsorption is strong. The transition between these conformations occurring upon variation of adsorption strength is quite sharp, and in the limit of "infinite" chain length, can be treated as a critical phenomenon. We suggest a novel thermodynamic definition of the critical conditions of polymer adsorption from the equality of incremental chemical potentials of adsorbed and free chains. We show with the example of freely jointed Lennard-Jones chains tethered to an adsorbing surface that this new definition provides a link between thermodynamic and geometrical features of adsorbed chains and is in line with classical scaling relationships for the fraction of adsorbed monomers, chain radii of gyration, and free energy.