Electrophoretic stretching of tethered polymer chains by travelling-wave electric fields: Tunable stretching, expedited coil-stretch transition, and a new paradigm of dynamic molecular probing

The use of low-frequency travelling wave fields in electrophoretic stretching of charged polymer chains is investigated theoretically. We find, using a simple elastic dumbbell model, that the stretching behavior with and without fluctuations can show a number of distinctive features that cannot be seen in usual steady or alternating current electric fields. In the deterministic study without fluctuations, we show that an end-tethered charged polymer chain can be pulled by asymmetric strokes generated by a travelling wave field and kept extended along the wave. It is found that while the averaged chain extension can be increased by raising the field strength, it can be decreased by increasing the wave speed. This is a new example that stretching a polymer chain can be realized in a time periodic field with zero mean. As the free energy landscape here acts like a vibrating harmonic oscillator having double or multiple wells, a stretched chain trapped in an energy groove created by a travelling wave field can hop back to the lower energy coil state due to fluctuations. In this stochastic study, we develop a theory and carry out Brownian dynamics simulations to show that as long as the wave speed does not exceed the damping threshold and fluctuations do not prevail to diminish stretching, increasing the wave speed can help the chain maintain its stretch by preventing it from hopping to the coil state. In addition, two distinct hopping kinetics, Arrhenius and Kramers modes, can exist to govern the respective coil-stretch transitions in the double-well and multiple-well scenarios, depending on the extent of stretching. These features are the results of cooperative effects of travelling wave fields and fluctuations, and further manifested by tongue-like coil-stretch phase diagrams. Applications of the present stretching to dynamic molecular probing are also illustrated by monitoring and regulating the molecular transport over a cyclically stretching polymer chain at the nanoscale or single-molecule level.