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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 N{\displaystyle N} Kuhn segments each with a Kuhn length b{\displaystyle b}. Each Kuhn segment can be thought of as if they are freely jointed with each other. 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. Instead of considering a real chain consisting of n{\displaystyle n} bonds and with fixed bond angles, torsion angles, and bond lengths, Kuhn considered an equivalent ideal chain with N{\displaystyle N} connected segments, now called Kuhn segments, that can orient in any random direction. The length of a fully stretched chain is L=Nb{\displaystyle L=Nb} for the Kuhn segment chain. 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 ⟨R2⟩=Nb2{\displaystyle \langle R^{2}\rangle =Nb^{2}}. 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 l{\displaystyle l} and bond angle θ with a dihedral angle energy potential, the average end-to-end distance can be obtained as ⟨R2⟩=nl21+cos⁡(θ)1−cos⁡(θ)⋅1+⟨cos⁡(ϕ)⟩1−⟨cos⁡(ϕ)⟩{\displaystyle \langle R^{2}\rangle =nl^{2}{\frac {1+\cos(\theta )}{1-\cos(\theta )}}\cdot {\frac {1+\langle \cos(\textstyle \phi \,\!)\rangle }{1-\langle \cos(\textstyle \phi \,\!)\rangle }}},where ⟨cos⁡(ϕ)⟩{\displaystyle \langle \cos(\textstyle \phi \,\!)\rangle } is the average cosine of the dihedral angle.The fully stretched length L=nlcos⁡(θ/2){\displaystyle L=nl\,\cos(\theta /2)}. By equating the two expressions for ⟨R2⟩{\displaystyle \langle R^{2}\rangle } and the two expressions for L{\displaystyle L} from the actual chain and the equivalent chain with Kuhn segments, the number of Kuhn segments N{\displaystyle N} and the Kuhn segment length b{\displaystyle b} can be obtained. For worm-like chain, Kuhn length equals two times the persistence length. References. Discover the N Kuhn popular books. Find the top 100 most popular N Kuhn books.