FIG. 3.

The tangent propagator and the tangent free energy as functions of the deflection angle for the illustrative values L=0.2ξ and ζξ=10⁻². The solid curves are KWLC and the dashed curves are WLC with the same value of ξ. In the absence of kinking, the WLC distribution (H) is essentially zero away from small deflection. For the small value of ζ chosen above, WLC and KWLC are indistinguishable in the top panel. The presence of kinks adds a background level to the propagator which is independent of θ, but is thermally inaccessible—too small to distinguish from zero in the top panel, but visible in the free energy in the lower panel. The tangent free energy gives an intuitive picture of the system interpreted as as single-state system with an effective bending modulus which saturates due to kinking. Most thermally driven experiments measure the polymer distribution as it is pictured in the top panel and are therefore insensitive to the high-curvature constitutive relation. But experiments which do probe this regime, short-contour-length cyclization for example, will be extremely sensitive to the difference between the theories due to the large free energy difference at large deflection.