  A number of recent experiments have provided detailed observations of the
configurations of long DNA strands under nano-to-micrometer sized confinement.
We therefore revisit the problem of an excluded volume polymer chain confined
between two parallel plates with varying plate separation. We show that the
non-monotonic behavior of the overall size of the chain as a function of
plate-separation, seen in computer simulations and reproduced by earlier
theories, can already be predicted on the basis of scaling arguments. However,
the behavior of the size in a plane parallel to the plates, a quantity observed
in recent experiments, is predicted to be monotonic, in contrast to the
experimental findings. We analyze this problem in depth with a mean-field
approach that maps the confined polymer onto an anisotropic Gaussian chain,
which allows the size of the polymer to be determined separately in the
confined and unconfined directions. The theory allows the analytical
construction of a smooth cross-over between the small plate-separation de
Gennes regime and the large plate-separation Flory regime. The results show
good agreement with Langevin dynamics simulations, and confirm the scaling
predictions.
