In the physical chemistry study of

polymer A polymer (; Greek '' poly-'', "many" + ''-mer'', "part") is a substance or material consisting of very large molecules called macromolecules, composed of many repeating subunits. Due to their broad spectrum of properties, both synthetic a ...

s, the end-to-end vector is the

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

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 and its applications, the root mean square of a set of numbers x_i (abbreviated as RMS, or rms and denoted in formulas as either x_\mathrm or \mathrm_x) is defined as the square root of the mean square (the arithmetic mean of the ...

of the end-to-end distance

\left\langle r^2 \right\rangle

can be related to the quadratic mean of the

radius of gyration ''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 concentr ...

\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