Physics:End-to-end vector

Short description: Vector that points from one end of a polymer to the other

[math]\displaystyle{ \vec R }[/math] 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 [math]\displaystyle{ \vec{r}_i }[/math] connect between these points. The end-to-end vector [math]\displaystyle{ \vec{R} }[/math] is the sum of these translation vectors:

[math]\displaystyle{ \vec{R} = \sum_i \vec{r}_i }[/math]

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 [math]\displaystyle{ \left\langle r^2 \right\rangle }[/math] can be related to the quadratic mean of the radius of gyration [math]\displaystyle{ \left\langle s^2 \right\rangle }[/math] of a polymer by the relation:

[math]\displaystyle{ \left\langle r^2 \right\rangle = 6 \left\langle s^2 \right\rangle }[/math]

See also

• Freely Jointed Chain
• Worm-like chain