Polymers grown in cavities: Vesicles and droplets

Grand-canonical polymers under confinement: Dense solutions

We theoretically study dense polymer solutions under open (capillary and slit) and closed (box) confinement. The theory is formulated for grand-canonical polymers and corrections to the self-consistent mean-field results are discussed. In contrast to the mean-field prediction, we found that the partition function of a labeled chain is affected by confinement even under neutral von Neumann boundary conditions and the chain length distribution is biased to short chains. As the container size increases, the contribution of the transverse excited states to the free energy of a labeled chain is found to approach its bulk value nonmonotonically (through an extremum) for the box and the capillary confinement but not for the slit. So does the confinement free energy of a labeled chain. The confinement energy of the solution is well behaved for open confinement but formally diverges for a closed box in the limit that the average chain length goes to infinity. Counted per chain, the confinement energy of the dense solution is qualitatively weaker than for a single ideal chain under similarly strong confinement (by one power in transverse container size). The container boundary contributes a surface tension to the free energy, which makes the effective monomer-wall affinity more repulsive. This correction increases with the average chain length. If present, edge or vertex singularities also contribute to the grand potential of the solution.