Dear ChE 530 students,

Last week we ran into a discrepancy during class concerning the Kuhn segment length and statistical segment length.

The basic idea is that a real chain has an end-to-end distance of

_0 = C_\infty n l^2

with

n = # segments along the backbone l = length along each segment (could be the bond length or could be the projection along a chain, taking bond angles into account) C_\infty = characteristic ratio

A Kuhn segment or a statistical segment divides a chain into longer segments that lack the correlation found in real segments.

The text by Hiemenz and Lodge writes the effective length as some combination of \sqrt(C_\infty) and the number of bonds per repeat unit; see page 224. They call this length a statistical segment length. The number of effective lengths is then equal to the number of monomers. I have not found other books that use this definition.

The more common definition is called a Kuhn length. A new length and number of segments (l_K and n_K) are written such that

n_K l_K = n l (same length along the chain)

and

n_K l_K^2 = C_\infty n l^2 (same end to end distance)

This new Kuhn length l_K and # of Kuhn segments n_K can be calculated by solving these two equations, which leads to

l_K = l * C_\infty

n_K = n / C_\infty

I found this definition, which uses the characteristic ratio itself ratio than its square root, in the book by Hans-Georg Eliot (which is on reserve) and in Flory's _Statistical Mechanics of Chain Molecules_.

The important idea is to remember the concept and to use a consistent definition in your own calculations.

Prof. Greenfield

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