Absorption/Expulsion of Oligomers and Linear Macromolecules in a Polymer Brush

The absorption of free linear chains in a polymer brush was studied with respect to chain size $L$ and compatibility $chi$ with the brush by means of Monte Carlo (MC) simulations and Density Functional Theory (DFT) / Self-Consistent Field Theory (SCFT) at both moderate, $sigma_g = 0.25$, and high, $sigma_g = 1.00$, grafting densities using a bead-spring model. Different concentrations of the free chains $0.0625 le phi_o le 0.375$ are examined. Contrary to the case of $chi = 0$ when all species are almost completely ejected by the polymer brush irrespective of their length $L$, for $chi < 0$ we find that the degree of absorption (absorbed amount) $Gamma(L)$ undergoes a sharp crossover from weak to strong ($approx 100%$) absorption, discriminating between oligomers, $1le Lle 8$, and longer chains. For a moderately dense brush, $sigma_g = 0.25$, the longer species, $L > 8$, populate predominantly the deep inner part of the brush whereas in a dense brush $sigma_g = 1.00$ they penetrate into the fluffy tail of the dense brush only. Gyration radius $R_g$ and end-to-end distance $R_e$ 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 $32 le N le 256$, we demonstrate the existence of unique {em critical} value of compatibility $chi = chi^{c}<0$. For $chi^{c}(phi_o)$ the energy of free chains attains the {em same} value, irrespective of length $L$ whereas the entropy of free chain displays a pronounced minimum. At $chi^{c}$ 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 $chi$ displays a rather rich behavior. We find three distinct regimes of penetration kinetics of free chains regarding the length $L$: I ($1le Lle 8$), II ($8 le L le N$), and III ($L > N$), in which the time of absorption $tau$ grows with $L$ at a different rate. During the initial stages of penetration into the brush one observes a power-law increase of $Gamma propto t^alpha$ with power $alpha propto -ln phi_o$ whereby penetration of the free chains into the brush gets {em slower} as their concentration rises.