“Kuhn length”的意思、由来-开放百科全书

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.^[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. 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 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,{{clarify|date=February 2012|reason=What is dihedral angle energy?}} the average end-to-end distance can be obtained as

The fully stretched length

. By equating the two expressions for

and the two expressions for

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

and the Kuhn segment length

can be obtained.

References

1. ^Flory, P.J. (1953) Principles of Polymer Chemistry, Cornell Univ. Press, {{ISBN|0-8014-0134-8}}
2. ^Flory, P.J. (1969) Statistical Mechanics of Chain Molecules, Wiley, {{ISBN|0-470-26495-0}}; reissued 1989, {{ISBN|1-56990-019-1}}
3. ^Rubinstein, M., Colby, R. H. (2003)Polymer Physics, Oxford University Press, {{ISBN|0-19-852059-X}}
4. ^{{cite book|last1=Doi|first1=M.|last2=Edwards|first2=S. F.|title=The Theory of Polymer Dynamics|date=1988|publisher=Volume 73 of International series of monographs on physics. Oxford science publications|isbn=0198520336|pages=391}}
5. ^{{citation | title=Physics 127a: Class Notes; Lecture 8: Polymers |publisher=California Institute of Technology |author=Michael Cross |date= October 2006|url=http://www.pmaweb.caltech.edu/~mcc/Ph127/a/Lecture_8.pdf|accessdate=2013-02-20}}
6. ^Gert R. Strobl (2007) The physics of polymers: concepts for understanding their structures and behavior, Springer, {{ISBN|3-540-25278-9}}