Tensile blob (${\xi }_t\sim k_{B}T/f$)

A tensile blob is the scale below which thermal conformations of a stretched polymer are weakly disturbed by tension $f$. Balancing stretching work $f{\xi }_t$ with $k_{B}T$ gives ${\xi }_t\sim k_{B}T/f$. For free-chain size law $R\sim b{g}^{\nu }$, each blob contains $g_t\sim ({\xi }_t/b{)}^{1/\nu }$ monomers. A stretched string of blobs has extension $z\sim (n/g_t){\xi }_t$ and stretching free energy of order $k_{B}Tn/g_t$. This description requires blobs larger than individual statistical segments and smaller than the unperturbed coil.

For a long flexible polymer in a good solvent, a tensile blob of size ${\xi }_t\sim k_{B}T/f$ contains $g\sim ({\xi }_t/a{)}^{1/\nu }$ statistical segments. Aligning $N/g$ blobs gives $R\sim (N/g){\xi }_t=Na(fa/k_{B}T{)}^{1/\nu -1}$. The three-dimensional Flory approximation $\nu =3/5$ gives the displayed power. The regime requires $a\ll {\xi }_t\ll a{N}^{\nu }$: below its force range the coil has ordinary linear response, and above it finite link extension matters. Numerical amplitudes depend on solvent quality and segment conventions.^[ref]