Theory of gel electrophoresis in high fields: Transient regimes at the field onset

We develop a model for the reorientation mechanism of long-chain electrolytes that are initially at rest in a gel and suddenly submitted to an electric field. Two different behaviors occur. For molecules smaller than a critical size N-c, the reorientation takes place through the extremities. The tube hypothesis of the biased reptation model remains valid. For larger molecules the tube hypothesis breaks down; the motion of the molecules involves lateral loops. N-c is a function of the electric field: N-c(E) proportional to exp(E(O)/E). It is a measurable quantity. When the field is switched on, the orientation of a molecule on the scale of the Kuhn segment increases. If the molecular size is smaller than N-c, the growth of the orientation is regular and characterized by a single overshoot time tau(ov), proportional to molecular size. The growth rate is roughly inversely proportional to the size. At time tau(ov) the orientation is maximum. For molecules larger than N-c, the growth of the orientation occurs in two stages. The duration tau(c) of the first stage is size independent. It depends only on the electric field: tau(c)(E) proportional to E(-1) exp(E(O)/E). During the first stage, the growth is size independent. The second stage lasts until a time tau(ov) that is proportional to the size, as for small molecules. During the second stage, the growth rate is roughly inversely proportional to the size. Some of these predictions have been observed experimentally. More systematic investigations will be welcome.