End-to-end vector

Error creating thumbnail:

$\overrightarrow{R}$ is the end-to-end vector of the polymer.

In the physical chemistry study of polymers, the end-to-end vector is the vector that points from one end of a polymer to the other end.

If each monomer unit in a polymer is represented by a point in space, the translation vectors ${\overrightarrow{r}}_i$ connect between these points. The end-to-end vector $\overrightarrow{R}$ is the sum of these translation vectors:

$\overrightarrow{R}=\sum _i{\overrightarrow{r}}_i$

The norm of the end-to-end vector is called the end-to-end distance.

Relation to other quantities

The quadratic mean of the end-to-end distance $⟨r^2⟩$ can be related to the quadratic mean of the radius of gyration $⟨s^2⟩$ of a polymer by the relation:

$⟨r^2⟩=6⟨s^2⟩$

See also

• Freely Jointed Chain
• Worm-like chain