Kuhn length

The Kuhn length is a theoretical treatment, developed by Werner Kuhn, in which a real polymer chain is considered as a collection of

Each Kuhn segment can be thought of as if they are freely jointed with each other.

[1][2][3][4] Each segment in a freely jointed chain can randomly orient in any direction without the influence of any forces, independent of the directions taken by other segments.

The length of a fully stretched chain is

[5] In the simplest treatment, such a chain follows the random walk model, where each step taken in a random direction is independent of the directions taken in the previous steps, forming a random coil.

The average end-to-end distance for a chain satisfying the random walk model is

Since the space occupied by a segment in the polymer chain cannot be taken by another segment, a self-avoiding random walk model can also be used.

The Kuhn segment construction is useful in that it allows complicated polymers to be treated with simplified models as either a random walk or a self-avoiding walk, which can simplify the treatment considerably.

For an actual homopolymer chain (consists of the same repeat units) with bond length

and bond angle θ with a dihedral angle energy potential,[clarification needed] the average end-to-end distance can be obtained as The fully stretched length

from the actual chain and the equivalent chain with Kuhn segments, the number of Kuhn segments