Английская Википедия:End-to-end vector

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Файл:Ideal chain random walk.svg

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

<math>\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>\left\langle r^2 \right\rangle</math> can be related to the quadratic mean of the radius of gyration <math>\left\langle s^2 \right\rangle</math> of a polymer by the relation:

<math>\left\langle r^2 \right\rangle = 6 \left\langle s^2 \right\rangle

</math>

See also

• Freely Jointed Chain
• Worm-like chain