Detailed scaling analysis of low-force polyelectrolyte elasticity
Single-molecule force-extension data are typically compared to ideal models of polymer behavior that ignore the effects of self-avoidance. Here, we demonstrate a link between single-molecule data and the scaling pictures of a real polymer. We measure a low-force elasticity regime where the extension L of chemically denatured single-stranded DNA grows as a power law with force f: L∼fγ, with γ≈0.60–0.69. This compares favorably with the “tensile-blob” model of a self-avoiding polymer, which predicts γ=2/3. We show that the transition out of the low-force regime is highly salt dependent, and use the tensile-blob model to relate this effect to the salt dependence of the polymer’s Kuhn length and excluded-volume parameter. We find that, contrary to the well-known Odijk-Skolnick-Fixman theory, the Kuhn length of single-stranded DNA is linearly proportional to the Debye length of the solution. Finally, we show that the low-force elasticity becomes linear (γ=1) at ≈3 M salt, and interpret this as a Θ point of the polymer. At this point, the force-extension data is best described by the wormlike chain model, from which we estimate the bare (nonelectrostatic) persistence length of the polymer to be ≈0.6 nm.