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, $1\le L\le 8$, 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 ($1\le L\le 8$), 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.