End-to-end vector explained

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

\vec{r} _{i} connect between these points. The end-to-end vector \vec{R} is the sum of these translation vectors:\vec{R} = \sum _{i} \vec{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

\left\langle r ^{2} \right\rangle can be related to the quadratic mean of the radius of gyration \left\langle s ^{2} \right\rangle of a polymer by the relation:^[1] \left\langle r ^{2} \right\rangle = 6 \left\langle s ^{2} \right\rangle

Notes

1. Book: Gedde . Ulf W. . Polymer Physics . 1995 . Springer . 0-412-62640-3 . 21.

See also

• Freely Jointed Chain
• Worm-like chain