Second-Order Shape Attribute

The second-order shape attribute is defined by the count of two-bond paths, P and is related to the shape extremes represented by and For we adopt the star graph, in which all atoms but one are adjacent to a central atom. This graph or A = 7 is shown in Table 2, No. 3. The numerical value of P, , for any count of A is P, ., = (A - 1) (A - 2)/2. For the other second-order shape attribute extreme, P ,i , we use the linear graph, shown in Table 2, No. 4, where A = 7. In general, for any value of A, P = A - 2. 

An algorithm expressing this second-order attribute can now be written down using the same formalism as for k, a product of ratios. A second-order shape index, k, is defined  

The scaling factor of 2 in the numerator makes the value 2k = A - 1 for all linear graphs, where A - 1 is the number of graph edges of skeletal bonds for acyclic molecules. Equation [51] can be expressed in terms of the count of atoms, A  

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The second-order shape attribute is defined by the count of 2-bond paths, and is related to the shape extremes P a, For P, ax adopted for the extreme... 

Firstly, the two peaks attributed to the third and fourth orders of basal spacing of the layered-silicate seen in the XRD spectra for the injection-moulded specimens and feedstock compounds were absent in the fibre spectra. Because the disappearance of the third and fourth order peaks could be an effect of exfoliation or because of low X-ray beam intensity, it is not possible to distinguish which of the two effects is more prevalent. However, the first and second order peaks of the hsv fibres manifested a more depressed peak shape and exhibited a lower peak intensity compared with the Isv fibres, but, in theory, the Isv fibre should exhibit a greater peak intensity because of the larger circumference and hence area exposed for beam diffraction. It is quite apparent, therefore, that the disappearance of the third and fourth order peaks, and the suppressed peak shape and intensity for the first and second order peaks, are mainly attributed to further exfoliation of the precedently intercalated layered-sihcate through an extensional deformation effect during the melt-spinning process. 

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