end-to-end vector

{{Short description|Vector that points from one end of a polymer to the other}}

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:{{cite book|last1= Gedde |first1= Ulf W. |title= Polymer Physics |url= https://books.google.com/books?id=Iem3fC7XdnkC |year= 1995 |publisher= Springer |isbn= 0-412-62640-3 |page= 21}}

: $\left\langle r^2 \right\rangle = 6 \left\langle s^2 \right\rangle$

end-to-end vector

Relation to other quantities

Notes

See also