(109f) Oligomer Adsorption in Cylindrical Pores: a Comparison of Density Functional Theory and Discontinuous Molecular Dynamics Simulation
We present here a new theoretical scheme for oligomers confined in a cylindrical pore based on the classical density functional theory (DFT) for polymers by Yu and Wu. Attractive interactions for the monomers are accounted for by employing the direct correlation functions obtained from the first-order mean-spherical approximation for the square-well fluid. The direct correlation function is calculated at the average pore density in the hard cylindrical pore and at the bulk density. This approach may be viewed as a variant of the reference fluid density functional approach of Gillespie et al, where the reference density functional is kept constant over the pore volume. All convolutions in our approach (for example, integration) are calculated in Fourier space using Fast Fourier Transform. This significantly increases the computing performance, allowing even the two-dimensional calculations to be performed on a single processor. By comparison, we also present discontinuous molecular dynamics (DMD) simulations of the adsorption of hard-sphere 4- and 8mers in a hard cylindrical pore. Equilibrium between the bulk reservoir and pore has been maintained by constant adjustment of the reservoir volume and the adsorption is studied over a broad range of bulk packing fractions. Results for DFT and DMD both show a direct correlation between bulk and pore packing fraction. Also, several trends are noted. At low packing fractions, monomers prefer the center of the pore; at medium packing fractions, monomers can be found equally in all positions of the pore; and at high packing fractions, the monomers concentrate into a double-torus formation with one ring near the pore wall and one ring nearer the center; this trend is seen independent of the length of the oligomer. We also observed that confinement has a minimal effect on the radius of gyration of 4mers confined by the pore compared to those in the bulk; however, the radius of gyration of 8mers in the pore is always less than bulk oligomers and this effect is more pronounced at lower bulk densities. The movement of oligomers through the pore as a function of the length of the chain has also been investigated (i.e. reptation vs. tumbling) and we show that the exchange of oligomers between bulk and pore is non-metastable. Throughout we discuss dissimilarities between our DMD and DFT results.