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Instead of considering a real chain consisting of bonds and with fixed bond angles, torsion angles, and bond lengths, Kuhn considered an equivalent ideal chain with connected segments, now called Kuhn segments, that can orient in any random direction. The length of a fully stretched chain is = for the Kuhn segment chain. [5]
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]
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 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}}}}} .
A persistence length of 51.35 nm and a contour length of 1560.9 nm were used for the model, which is depicted by the solid line. [4] Other biologically important polymers that can be effectively modeled as worm-like chains include: double-stranded DNA (persistence length 40-50 nm) and RNA (persistence length 64 nm) [3] [5]
Contour length is a term used in molecular physics. The contour length of a polymer chain (a big molecule consisting of many similar smaller molecules) is its length at maximum physically possible extension. [1] Contour length is equal to the product of the number of segments of polymer molecule(n) and its length(l).
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In the model, is the length of a rigid segment, is the number of segments of length , is the distance between the fixed and free ends, and is the "contour length" or . Above the glass transition temperature, the polymer chain oscillates and r {\displaystyle r} changes over time.