Absorption/expulsion of oligomers and linear macromolecules in a polymer brush

Abstract

The absorption of free linear chains in a polymer brush was studied with respect to chain size L and compatibility ψ with the brush by means of Monte Carlo (MC) simulations and density functional theory (DFT)/self-consistent field theory (SCFT) at both moderate, σg=0.25, and high, σg=1.00, grafting densities using a bead-spring model. Different concentrations of the free chains 0.0625≤ϕo≤0.375 are examined. Contrary to the case of ψ=0 when all species are almost completely ejected by the polymer brush irrespective of their length L, for ψ<0 we find that the degree of absorption (absorbed amount) Γ(L) undergoes a sharp crossover from weak to strong (≈100%) absorption, discriminating between oligomers, 1≤L≤8, and longer chains. For a moderately dense brush, σg=0.25, the longer species, L>8, populate predominantly the deep inner part of the brush, whereas in a dense brush σg=1.00 they penetrate into the “fluffy” tail of the dense brush only. Gyration radius Rg and end-to-end distance Re of absorbed chains thereby scale with length L as free polymers in the bulk. Using both MC and DFT/SCFT methods for brushes of different chain length 32≤N≤256, we demonstrate the existence of unique critical value of compatibility ψ=ψc<0. For ψc(ϕo) the energy of free chains attains the same value, irrespective of length L whereas the entropy of free chain displays a pronounced minimum. At ψc all density profiles of absorbing chains with different L intersect at the same distance from the grafting plane. The penetration/expulsion kinetics of free chains into the polymer brush after an instantaneous change in their compatibility ψ displays a rather rich behavior. We find three distinct regimes of penetration kinetics of free chains regarding the length L: I (1≤L≤8), II (8≤L≤N), and III (L>N), in which the time of absorption τ grows with L at a different rate. During the initial stages of penetration into the brush one observes a power-law increase of Γ∝tα with power α∝−ln ϕo, whereby penetration of the free chains into the brush gets slower as their concentration rises.