Force-Extension Curve of a Polymer in a High-Frequency Electric Field

We study theoretically the conformation and force-extension curve of a semiflexible polymer in a spatially uniform ac electric field. The polymer backbone minimizes its energy by aligning along one of two orientations parallel to the field. In a strong ac field, hairpin kinks develop between regions of opposite alignment. These kinks are mathematically described as sine-Gordon solitons. We calculate the equation of state of the one-dimensional kink gas, which yields the force-extension curve of the polymer. A sufficiently strong ac field causes the polymer to extend spontaneously to almost its full contour length. The theory is applied to recent experiments on dielectrophoretic stretching of DNA.

Figure 1

(a) Shape of a hairpin kink in a polymer strand subject to a strong ac field. (b) Conformation of a polymer containing ten kinks of random position and orientation. All kinks are the same size: those that appear thinner are viewed edge on.

Figure 2

Force-extension curve of a polymer in a strong ac field (bold). The Marko-Siggia interpolation formula for extension of a wormlike chain (without an ac field) is plotted for comparison. Under sufficiently strong tension, both curves reach $x/L=1$. The dimensionless nematic field strength is $V{l}_p/k_{\mathrm{B}}T=6$.