Shape of Confined Polymer Chains

We consider the problem of polymer chains confined between two parallel plates (a slit). The interactions between the polymer and the plates are assumed to be repulsive. A variational theory is used to derive the size of the chain as a function of the distance between plates, D, for both hard impenetrable walls as well as for soft walls. In both cases it is shown that for large and small values of D, the results coincide with the predictions of the scaling theory. For intermediate values of D the size of the polymer depends on the strength of interaction, C 0 , between the monomers and the walls. The cross-over from the fully squeezed regime (D → 0) to the case when the plate separation is infinite is non-monotonic for good solvents. In particular the mean square end-to-end distance has a minimum (the depth of which depends on C 0 ) at moderate values of D. The theoretical predictions are in accord with Monte-Carlo simulations. When the solvent quality is poor the cross-over from two-dimensional behavior to three-dimensional case is monotonic. The effect of interaction strength between the polymer and the plates is also examined. It is argued that for moderate values of D a slit of given size with a specified interaction has the same effect as one of larger slit size but with stronger interactions.