F2 Double Fiber Symmetry - Simplified Integral Transform

4 F2 Double Fiber Symmetry - Simplified Integral Transform 

Ruland [253] shows that in this case the integral transform Eq. (9.11) can be simplified and solved. The corresponding geometrical relationships are sketched in 

More simple solutions are found for special cases. Already in 1933 Kratky [248] has presented a method for the ease in which the observed orientation distribution has its maximum on the equator. In 1979 the problem treated by Kratky has been revisited by Leadbetter and Norris [254]. They present a different solution which is frequently applied in studies of liquid-crystalline polymers. Burger and Ruland [255] pinpoint the error in the deduction of Leadbetter and 

Norris. They show that the result of Kratky is, indeed, a special case (cp = n/2) of Ruland s general treatment [253,256], which is sketched in the sequel. 

In the deduction Ruland determines, which contribution to the observed intensity, I, is added by each reflection ring of the likewise fiber symmetrical function, Igpt. Then he adds up all the rings weighted by the orientation function g P). In this way Eq. (9.11) is simplified. A general solution is obtainable by multipole expansion. 

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