Critical conditions of polymer chromatography: an insight from SCFT modeling

In polymer chromatography, chain molecules are separated by molecular weight, size, and chemical composition due to adsorption and exclusion in nanoporous substrates. Three regimes of separation are distinguished depending on the adsorption strength and the pore size. In the regime of size exclusion chromatography, the adsorption energy is weak and the separation is entropy-driven with larger molecules having shorter retention times. On the opposite, in the regime of adsorption chromatography, enthalpy gain due to strong adsorption energy prevails over entropy loss, and the retention time of smaller molecules is shorter. We study the intermediate regime of so-called critical conditions, at which the entropic and enthalpic effects are mutually compensated, and the partition coefficient does not depend on the polymer molecular weight. Using the self-consistent field theory of tethered polymer chains, we confirm that for ideal chains the critical conditions are justified, albeit they depend on the pore size. However, for real chains with the excluded volume effect, the critical conditions hold only approximately, and the discrepancy increases as the pore size decreases. We show that it is important to consider three characteristic adsorption states: chains adsorbed at the external surface, chains adsorbed completely inside the pores, and partially translocated chains or "flowers" with a "root" adsorbed inside the pore and a "stem" hanging outside. The interplay of different adsorption mechanisms and the pore size distribution inherent to real substrates may lead to the manifestation of apparent critical adsorption conditions within the inherent deviation of experimental data.