Concentration Effects in Partitioning of Macromolecules into Pores with Attractive Walls

Abstract

The influence of polymer concentration on the partitioning of flexible macromolecules into adsorptive pores was examined by simulations in an open system under good solvent conditions. In dilute solutions, the partition coefficient K(ε , φ) is sensitive to small variations of both polymer−pore attraction strength ε and concentration φ, whereas in semidilute solutions both influences level off. At weak attraction below critical adsorption energy ε c, the coefficient K increases with φ in a fashion that resembles the weak-to-strong penetration transition found for purely steric exclusion (ε = 0) but modified as if the width of pores effectively increased. At moderate attraction above the critical condition the increasing concentration brings about a dramatic drop in the value of K. Additionally, the K(φ) dependences in attractive pores were calculated by an approximate method based on expressions for chemical potentials, and the results were in good agreement with the simulation data. The critical adsorption energy ε c for excluded volume chains was found to depend on concentration; the compensation point K = 1 was located at about φ = 0.012 irrespective of the pore width. The energy and entropy contributions to the free energy of confinement were calculated and the compensation of their values at the critical condition was demonstrated. Furthermore, it was shown that the effect of concentration in polymer partitioning with adsorptive pores can alternatively be regarded as a confined adsorption and two alternatives of the adsorbed amount Γ were calculated. The adsorption and depletion concentration profiles φ I(x) in the pore in equilibrium with the bulk solution were presented and their variation with concentration φ and attraction ε was analyzed.

Simulations of sieving characteristics of macromolecules in porous membranes at high concentrations

“…Thermodynamic quality of solvents for a given polymer can vary from "theta" solvents, characterized by a compensation of attractive and repulsive polymer-solvent interactions that results in "pseudo-ideal" chain dimensions, to "good" solvents, where polymer coils are highly expanded by favorable solvation. Enhancement of polymer partitioning with concentration observed in simulations in good solvents [10][11][12] is fully supported by the theory and by the static and gel-chromatography measurements [13][14][15][16][17]. On the other hand, simulations in theta solvents predict, at first, nearly the concentration-independent coefficient Φ in a broad concentration range, and then, an increase in the coefficient Φ at higher concentrations [10].…”

“…The simulation procedure is similar to the one employed in our preceding works [10][11][12]. Cubic-lattice Monte Carlo (MC) simulations were conducted for chains of the length N between 100 and 500 in a broad concentration range in two types of the solvent quality; previous results for slits and channels [10][11][12] were supplemented by additional data.…”

“…Cubic-lattice Monte Carlo (MC) simulations were conducted for chains of the length N between 100 and 500 in a broad concentration range in two types of the solvent quality; previous results for slits and channels [10][11][12] were supplemented by additional data. Chains in good solvents are represented by an athermal model where the segment-segment contact energy ε s = 0.…”

“…A twin-box model consisting of an interior (I) pore space and an exterior bulk space adjoining to pore [10][11][12] was used to obtain the partition coefficient Φ. Two pore geometries, a slit and a channel with a square cross-section (modeling a cylindrical pore), were assumed.…”

“…In other words, this formula suggests that the lag factor G = 1 in Eq. (12). We have tentatively applied Eq.…”