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End to end vector

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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 unit in a polymer is represented by a point in space, translation vectors r → i connect between these joints. The end-to-end vector R → is the sum of these translation vectors:

R → = ∑ i 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 ⟨ r 2 ⟩ can be related to the quadratic mean of the radius of gyration ⟨ s 2 ⟩ of a polymer by the relation:

⟨ r 2 ⟩ = 6 ⟨ s 2 ⟩

References

End-to-end vector Wikipedia
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