Size and shape of excluded volume polymers confined between parallel plates
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 nonmonotonic 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 crossover between the small-plate-separation de Gennes regime and the large-plate-separation Flory regime. The results show good agreement with molecular dynamics simulations in the presence of a Langevin heat bath and confirm the scaling predictions.