Chain Tension Dependence of the Kuhn Length

Flexible polymers are characterized by their Kuhn length, the statistical segment of the chain. The Kuhn length is typically determined from the chain size measured in a theta solvent by scattering experiments, b_scat. Another method is single-molecule force spectroscopy, with force-extension curves fitted by a model in which the Kuhn length, b_pull, is a fitting parameter. We explain the long-standing discrepancy that the Kuhn lengths obtained by these two methods typically differ by factor of two: b_scat/b_pull~2. The reason is that flexible polymers in theta solvents are quasi-ideal with long-range correlations resulting in n-dependence of the Kuhn length of n-mers, approaching its infinite-chain value as ~n^-1/2. These correlations are cutoff at the size of the tension blob in chains under tension, resulting in the effective Kuhn length, b_eff, decreasing with increasing tension. We present a theory for the dependence of the Kuhn length on the applied force, use it to correct the modified Freely Jointed Chain (mFJC) model, and verify this dependence by molecular dynamics simulations.