Adhesion and Separation of Nanoparticles on Polymer-Grafted Porous Substrates.

This work explores interactions of functionalized nanoparticles (NP) with polymer brushes (PB) in a binary mixture of good and poor solvents. NP-PB systems are used in multiple applications, and we are particularly interested in the problem of chromatographic separation of NPs on polymer-grafted porous columns. This process involves NP flow through the pore channels with walls covered by PBs. NP-PB adhesion is governed by adsorption of polymer chains to NP surface and entropic repulsion caused by the polymer chain confinement between NP and the channel wall. Both factors depend on the solvent composition, variation of which causes contraction or expansion of PB. Using dissipative particle dynamics simulations in conjunction with the ghost tweezers free energy calculation technique, we examine the free energy landscapes of functionalized NPs within PB-grafted channels depending on the solvent composition at different PB grafting densities and polymer-solvent affinities. The free energy landscape determines the probability of NP location at a given distance to the surface, positions of equilibrium adhesion states, and the Henry constant that characterizes adsorption equilibrium and NP partitioning between the stationary phase of PB and mobile phase of flowing solvent. We analyze NP transport through a polymer-grafted channel and calculate the mean velocity and retention time of NP depending on the NP size and solvent composition. We find that, with the increase of the bad (poor) solvent fraction and respective PB contraction, NP separation exhibits a transition from the hydrodynamic size exclusion regime with larger NPs having shorter retention time to the adsorption regime with smaller NPs having shorter retention time. The observed reversal of the sequence of elution is reminiscent of the critical condition in polymer chromatography at which the retention time is molecular weight independent. This finding suggests the possibility of the existence of an analogous special regime in nanoparticle chromatography at which NPs with like surface properties elute together regardless of their size. The latter has important practical implications: NPs can be separated by surface chemistry rather than by their size employing the gradient mode of elution with controlled variation of solvent composition.

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.

Critical conditions of polymer adsorption and chromatography on non-porous substrates.

We present a novel thermodynamic theory and Monte Carlo simulation model for adsorption of macromolecules to solid surfaces that is applied for calculating the chain partition during separation on chromatographic columns packed with non-porous particles. We show that similarly to polymer separation on porous substrates, it is possible to attain three chromatographic modes: size exclusion chromatography at very weak or no adsorption, liquid adsorption chromatography when adsorption effects prevail, and liquid chromatography at critical conditions that occurs at the critical point of adsorption. The main attention is paid to the analysis of the critical conditions, at which the retention is chain length independent. The theoretical results are verified with specially designed experiments on isocratic separation of linear polystyrenes on a column packed with non-porous particles at various solvent compositions. Without invoking any adjustable parameters related to the column and particle geometry, we describe quantitatively the observed transition between the size exclusion and adsorption separation regimes upon the variation of solvent composition, with the intermediate mode occurring at a well-defined critical point of adsorption. A relationship is established between the experimental solvent composition and the effective adsorption potential used in model simulations.

Characterization of synthetic copolymers by interaction polymer chromatography: Separation by microstructure.

Gradient elution of synthetic polymers has been studied both theoretically and experimentally using normal and reversed-phase HPLC systems. An accurate equation describing the gradient elution of polymer-homologous series in the context of continuous random-flight model of a flexible polymer chain interacting with attractive surface of the porous material has been derived and experimentally verified against a series of narrow polystyrene standards. Both the theory and the experiment predict the existence of molar mass-independent gradient elution at critical point of adsorption (CPA). The extension of the theory to synthetic copolymers predicts the existence of the CPA for statistical copolymers and describes its dependence on chemical composition and microstructure (blockiness) of the polymer chains. One of the important theoretical conclusions is that blockiness always increases the retention, so that blockier polymer chains elute later than their more random counterparts with the same chemical composition. This prediction has been confirmed experimentally using block and statistical styrene-methylmethacrylate copolymers. Block copolymers do not have CPA and always elute between critical points of the corresponding homopolymers. The retention depends on the polymer molar mass and increases with the length of the blocks from a stronger absorbing monomer. These findings provide theoretical and experimental bases for separation of statistical and block copolymers by chemical composition and microstructure of polymer chains.