Equilibrium partitioning of long-chain polymers between bulk solution and pores in the presence of short-range attractions

The partitioning of linear polymers between small pores and bulk solution is examined theoretically for the case of long‐chain molecules which are attracted by the walls of cylindrical or slitlike pores. The polymer is considered to be a freely jointed chain of N mass points connected by rectilinear segments of length l. The interaction potential is represented as a square well with width comparable to l. It is assumed that N is very large and that l is much smaller than the pore radius, allowing the calculations to be performed by solving a “diffusion equation” with a suitable source term. The results presented cover a wide range of interaction potentials and relative polymer and pore sizes. A critical interaction potential is identified for which entropic and enthalpic effects exactly cancel, resulting in equal concentrations in the pore and bulk solution. As the critical potential is approached, the solution to the diffusion equation rapidly changes character. The critical potential may be interpreted as defining a transition from “free” to weakly adsorbed polymer.