Nonlinear electrophoretic velocity of DNA in slitlike confinement

We have applied zero-time-averaged alternating electric fields to DNA molecules in a cross-shaped nanofluidic slit. We observed a net drift of DNA molecules, the magnitude of which depends on the square of the electric field amplitude. From the rate of accumulation of DNA at the center of the device, we derive an estimate for the second-order electrophoretic mobility, ${\mu }_2$. We observe that focusing is absent at a dipole rotation frequency >20 Hz, which suggests that ${\mu }_2$ depends on the frequency of the alternating fields. The observation of a nonzero ${\mu }_2$ raises the possibility of frequency-dependent electrophoretic DNA separation by length achievable in the absence of a sieving matrix.

Figure 1

(a) Schematic of the rotating quadrupole (blue) and the rotating dipole (red) electric fields that are summed to create the focusing field orientation within the central region of the cross-nanoslit device. The four legs extend 0.75 cm and terminate in fluid reservoirs where electrodes are inserted in order to apply the fields (not shown). (b) An optical micrograph of the central region at 40× magnification taken in brightfield with the walls of the device traced (blue-dashed line). A cartoon of DNA molecules is overlaid (red), showing the direction of the drift velocity of each molecule (radially inward) during the application of the focusing field.

Figure 2

The potential pattern applied to one electrode in the focusing configuration. The mathematical quadrupole (red, solid) and dipole (blue, dashed) potentials are summed and discretized to four possible outputs (+15, 0, −15, or −30 V) as represented by the square wave (yellow, dot-dashed). Despite being asymmetric in time, the discretized dipole plus quadrupole potential integrates to zero over one dipole period.

Figure 3

(a) Fluorescent image of the central region of the cross-slit showing $\lambda$ DNA at the start of the application of the focusing field orientation rotating at a dipole frequency of 1.5 Hz. Walls are traced (blue-dashed line). Magnification is 40 × . Fluorescent image of the central region after applying the focusing field for 1 h (b), 2.6 h (c), 3 h (d), 5 h (e), and 22 h (f). Although fragments of $\lambda$ DNA are evident, a clear increase in the fluorescent intensity, or DNA concentration, is observed over time.

Figure 4

Plot of the fraction of connected pixels passing a brightness threshold in images of the central region over time for the focusing (quadrupole and dipole) field (black squares), quadrupole-only (red circle), and dipole-only (blue star) fields. The data are fit to a linear function by a least-squares estimate (blue-dashed line).

Figure 5

Plot of the fraction of connected pixels passing a brightness threshold in images of the central region over time for the defocusing (dipole and inverted quadrupole) field. The data are fit to a linear function by a least-squares estimate (blue-dashed line).