End-to-end vector

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:


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

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