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The Kuhn length is a theoretical treatment, developed by Werner Kuhn, in which a real polymer chain is considered as a collection of Kuhn segments each with a Kuhn length . Each Kuhn segment can be thought of as if they are freely jointed with each other.
In other cases, a monomer is simply a segment of the polymer that can be modeled as behaving as a discrete, freely jointed unit. If so, l is the Kuhn length. For example, chromatin is modeled as a polymer in which each monomer is a segment approximately 14–46 kbp in length. [1]
The persistence length is considered to be one half of the Kuhn length, the length of hypothetical segments that the chain can be considered as freely joined. The persistence length equals the average projection of the end-to-end vector on the tangent to the chain contour at a chain end in the limit of infinite chain length. [4]
This can be used to show that a Kuhn segment is equal to twice the persistence length of a worm-like chain. In the limit of L 0 ≪ P {\displaystyle L_{0}\ll P} , then R 2 = L 0 2 {\displaystyle \langle R^{2}\rangle =L_{0}^{2}} , and the polymer displays rigid rod behavior. [ 2 ]
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The chain is assumed to form blobs between each entanglement, containing Kuhn length segments in each. The mathematics of random walks can show that the average end-to-end distance of a section of a polymer chain, made up of n e {\displaystyle n_{\text{e}}} Kuhn lengths is d = l n e {\displaystyle d=l{\sqrt {n_{\text{e}}}}} .