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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]
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]
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}}}}} .
The area bounded by one spiral rotation and a line is 1/3 that of the circle having a radius equal to the line segment length; Use of the method of exhaustion also led to the successful evaluation of an infinite geometric series (for the first time);
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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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