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Table 1

Designation of, and formulæ for, the major eRCN bulk material structural groups.

Carbon atom Bonding Atomic Atomic fraction
hybridisation structure fraction expression Notes

Atoms
H XH = XH
sp2 C Xs p2 = Xsp2
sp3 C Xs p3 = Xsp3
Aromatic C-H bonds
s p2 CH aromatic = η   mar  fXsp2 η = XH/(1 − XH), the [H]/[C] atom ratio
mar = (aromatic cluster coord. no.)/(no. of C atoms)
Olefinic and aliphatic C-H bonds – for XH ≤ 0.5
s p2 CH olefinic = u   η   (1 − f)Xsp2 u =  { 1 + ((1 − mar)/ [(1 − XH)/(fXsp2) − 1] ) } a
s p2 CH2 olefinic = 0
s p3 CH aliphatic = u   η   Xsp3
s p3 CH2 aliphatic = 0
s p3 CH3 aliphatic = 0
Olefinic and aliphatic C-H bonds – for XH > 0.5
s p2 CH olefinic =    u   (2 − η)   (1 − f)   Xsp2
s p2 CH2 olefinic = 2   u   (η − 1)   (1 − f)   Xsp2
s p3 CH aliphatic =    u   (2 − η)   Xsp3/(1 + φ) φ = 30(XH − 0.5)2
s p3 CH2 aliphatic = 2   u   (η − 1)   Xsp3/(1 + φ)
s p3 CH3 aliphatic = 3   u   φ   Xsp3                   /(1 + φ) (1 + φ) re-normalises for CH3
C-C bondsb
s p2 C ≃ C aromatic XC ≃ C = f = 0.5ex/(1 + ex)
s p2 C=C olefinic XC = C = x = (XH − X0)/δ , X0 = 0.35, δ = 0.085
s p3 C−C aliphatic XC−C =   Xsp3/Xbond

Notes. 

(a)

The parameter u corrects for the fact that only the peripheral aromatic cluster carbon atoms can bond with hydrogen atoms, thus “releasing” more hydrogen atoms to bond with other non-aromatic carbon atoms.

(b)

The factor Xbond in the C-C bond fractions is a required renormalisation because the total number of bonds in the eRCN  ≠  the number of atoms, as indicated by the pre-X fractions in the sp2 C-C bonds expressions.

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