In the physical chemistry study of

polymer A polymer () is a chemical substance, substance or material that consists of very large molecules, or macromolecules, that are constituted by many repeat unit, repeating subunits derived from one or more species of monomers. Due to their br ...

s, the end-to-end vector is the

vector Vector most often refers to: * Euclidean vector, a quantity with a magnitude and a direction * Disease vector, an agent that carries and transmits an infectious pathogen into another living organism Vector may also refer to: Mathematics a ...

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_i

connect between these points. The end-to-end vector

\vec

is the sum of these translation vectors: :

\vec = \sum_i \vec_i

The norm of the end-to-end vector is called the end-to-end distance.

Relation to other quantities

The

quadratic mean In mathematics, the root mean square (abbrev. RMS, or rms) of a set of values is the square root of the set's mean square. Given a set x_i, its RMS is denoted as either x_\mathrm or \mathrm_x. The RMS is also known as the quadratic mean (denoted M ...

of the end-to-end distance

\left\langle r^2 \right\rangle

can be related to the quadratic mean of the

radius of gyration The radius of gyration or gyradius of a body about the axis of rotation is defined as the radial distance to a point which would have a moment of inertia the same as the body's actual distribution of mass, if the total mass of the body were concent ...

\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

Relation to other quantities

Notes

See also