Distorted Structure by Infinite ID Arrangement

History. Starting from the ID point statistics of Zernike and Prins [116] J. J. Hermans [128] designs various ID statistics of black and white rods. He applies these models to the SAXS curves of cellulose. Polydispersity of rod lengths is introduced by distribution functions, Hermans describes the loss of corre- 

One of two bags contains white rods of differing lengths - the lattice constants described by a length distribution, hiix). The average rod length is L. We randomly 

This is the definition of a convolution (p. 16, Eq. (2.17)) of the distribution Iil x) with itself. Repeated induction yields the relation 

Thus the distance to the end of the n-th rod is obtained by n-fold convolution of the rod length distribution. A typical series of such lattice constant distributions is demonstrated in Fig. 8.43. Its sum is named convolution polynomial. 

Inconsistency of all Lattice Models. The decoration principle of all lattice models coupled to polydispersity leads to a fundamental inconsistency of all lattice 

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