Persistence Length

The length at which a polymer stays essentially straight

$⟨\vec{t}(s)\cdot \vec{t}(u)⟩=e^{-|s-u|/{\xi }_p}$

• $\vec{t}(s)$ is the tangent vector at a distance $s$ along the polymer
• ${\xi }_p$ is the persistence length and is generally $\frac{a}{2}$ where $a$ is the length of one segment

$⟨R^2⟩\approx 2{\int }_0^L{\int }_0^{\infty }{e}^{-x/{\xi }_p}\mathrm{d}x\mathrm{d}s=2L{\xi }_p$

• $L$ is the contour length
• Applies for when $L\gg {\xi }_p$

${\xi }_p=\frac{a}{2}$

• $a$ is the length of one segment
• Can be found as $⟨R⟩=N{a}^2=aL=2L{\xi }_p\Rightarrow$ above equation