Mechanisms of chain adsorption on porous substrates and critical conditions of polymer chromatography.

Polymer adsorption is a ubiquitous phenomenon with numerous technological and healthcare applications. The mechanisms of polymer adsorption on surfaces and in pores are complex owing to a competition between various entropic and enthalpic factors. Due to adsorption of monomers to the surface, the chain gains in enthalpy yet loses in entropy because of confining effects. This competition leads to the existence of critical conditions of adsorption when enthalpy gain and entropy loss are in balance. The critical conditions are controlled by the confining geometry and effective adsorption energy, which depends on the solvent composition and temperature. This phenomenon has important implications in polymer chromatography, since the retention at the critical point of adsorption (CPA) is chain length independent. However, the mechanisms of polymer adsorption in pores are poorly understood and there is an ongoing discussion in the theoretical literature about the very existence of CPA for polymer adsorption on porous substrates. In this work, we examine the mechanisms of chain adsorption on a model porous substrate using Monte Carlo (MC) simulations. We distinguish three adsorption mechanisms depending on the chain location: on external surface, completely confined in pores, and also partially confined in pores in so-called "flower" conformations. The free energies of different conformations of adsorbed chains are calculated by the incremental gauge cell MC method that allows one to determine the partition coefficient as a function of the adsorption potential, pore size, and chain length. We confirm the existence of the CPA for chain length independent separation on porous substrates, which is explained by the dominant contributions of the chain adsorption at the external surface, in particular in flower conformations. Moreover, we show that the critical conditions for porous and nonporous substrates are identical and depend only on the surface chemistry. The theoretical results are confirmed by comparison with experimental data on chromatographic separation of a series of linear polystyrenes.