Scaling theory of polymer translocation into confined regions.

We examine the voltage-driven polymer translocation from a spacious region into a confined region imposed by two parallel planes, so that the entry is impeded by the entropic confinement but aided by the electric field inside the confined region. Two modes of entry are examined: linear translocation where a chain enters the confined region with chain ends, and hairpin translocation where a chain enters the confined region by forming a hairpin. Our calculation shows that translocation time increases with polymer length for linear entries but decreases with polymer length for hairpin entries. Applying to electrophoresis of DNA molecules through periodic spacious and confined regions, our theory shows that the dominance of hairpin translocations leads to the experimentally observed faster migration of longer DNA molecules. Our theory predicts experimental conditions for the validity of this law in terms of polymer length, size of the confined region, and solution conditions.