Polymer depletion interaction between parallel walls —A Monte Carlo study

An off-lattice bead-spring model of self-assembling equilibrium (“living”) polymers is used to study the polymer-induced interaction between parallel walls immersed in polydisperse solutions of different concentration by means of Monte Carlo simulation. The two walls form an open slit in contact with an external reservoir so that the confined system may exchange monomers with the surrounding phase and adapt its polydispersity in order to relax the confinement constraint. We find that the properties of the polymers in the constrained system as well as the net force $\delta F$ acting on the walls depend essentially on the polymer concentration in the reservoir which leads to qualitative differences in their behavior with changing inter-planar distance $H$: In a dilute polymer solution at concentration $\phi$ below the semi-dilute threshold $\phi^*$ the force between the walls is attractive and decreases steadily with growing wall separation $H$, so that $\delta F\approx 0$ at $H/R_{\rm g}\ge 3$ if $H$ is measured in gyration radii $R_{\rm g}$ of the unperturbed polymers. The total monomer concentration within the slit is smaller than the concentration in the reservoir and decreases monotonically with $H/R_{\rm g}\rightarrow 0$. The ratio $N_{\rm {in}}/N_{\rm {out}}$ of mean chain length $N_{\rm {in}}$ in the slit to that in the reservoir, $N_{\rm {out}}$, decreases from unity at $H\rightarrow \infty$, goes through a minimum at $H/R_{\rm g} \approx 1$, and then rises again to $N_{\rm {in}}/N_{\rm {out}}>1$ for wall separations $H/R_{\rm g} < 1$. In contrast, in a dense solution of equilibrium polymers at $\phi >\phi^*$ one detects no indirect wall-wall interaction, $\delta F \approx 0$, for $H$ larger than the monomer size. Thus, earlier speculations about the existence of possible depletion interaction between parallel walls even in a dense polymer system cannot be confirmed. Inside the slit the monomer density is found to be always larger than in the reservoir while $N_{\rm {in}}/N_{\rm {out}}