  Force versus extension curves measure entropic elasticity of single polymer
chain in force spectroscopy experiments. A Worm-like Chain model is used to
describe force extension experiments with an intrinsic chain parameter called
persistence length, which is a measure of local bending flexibility. For
flexible polymers, there is a discrepancy in estimates of persistence length in
various force regimes. For instance, Atomic Force Microscopy (AFM) based
pulling experiments report anomaly low values which are also inconsistent with
magnetic tweezers experiments. To understand this, we investigate the role of
coupling between microscopic force probe and intrinsic elasticity of
polyethylene glycol chain in AFM-based experiments. We perform experiments
using oscillatory rheology by providing an external excitation of fixed
frequency to the probe. We show that a proper quantification of elastic
response measured directly by oscillatory technique deviates significantly from
conventional force-extension curves. The persistence length obtained by fitting
WLC to stiffness extension data matches well with equilibrium tweezers
experiments. In addition, for polystyrene chain in poor solvent no deviation in
elastic response is observed between oscillatory and constant velocity pulling
experiments. However, such deviation is seen for polystyrene in good solvent.
We attribute this to hydrophobic interaction between monomers of polystyrene in
water. Our results suggest that oscillatory rheology on single polymer chains
provide quantitative estimate of its elastic response. The consistency in
values of persistence length using magnetic tweezers experiments in low force
regime and the AFM experiments in high force regime suggests that WLC is
successful in describing the polymer elasticity in the force range typically
probed in AFM experiments.
