Random Walk

Topics

• Persistence Length
• Radius of Gyration
• Polymer Extension

$⟨R⟩=0$

• $R$ is the end to end length

$⟨R^2⟩=N{a}^2$

• $N$ is the number of segments
• $a$ is the length of a segment

$P(R;N)=\frac{1}{\sqrt{2\pi N{a}^2}}{e}^{-R^2/2N{a}^2}$

• 1D version

$P(\vec{R};N)={\left(\frac{3}{2\pi N{a}^2}\right)}^{3/2}{e}^{-3R^2/2N{a}^2}$

• 3D version