On the Mass Fractal Character of Si-Based Structural Networks in Amorphous Polymer Derived Ceramics

The intermediate-range packing of SiN(x)C(4−x) (0 ≤ x ≤ 4) tetrahedra in polysilycarbodiimide and polysilazane-derived amorphous SiCN ceramics is investigated using (29)Si spin-lattice relaxation nuclear magnetic resonance (SLR NMR) spectroscopy. The SiCN network in the polysilylcarbodiimide-derived ceramic consists predominantly of SiN(4) tetrahedra that are characterized by a 3-dimensional spatial distribution signifying compact packing of such units to form amorphous Si(3)N(4) clusters. On the other hand, the SiCN network of the polysilazane-derived ceramic is characterized by mixed bonded SiN(x)C(4−x) tetrahedra that are inefficiently packed with a mass fractal dimension of D(f) ~2.5 that is significantly lower than the embedding Euclidean dimension (D = 3). This result unequivocally confirms the hypothesis that the presence of dissimilar atoms, namely, 4-coordinated C and 3-coordinated N, in the nearest neighbor environment of Si along with some exclusion in connectivity between SiC(x)N(4−x) tetrahedra with widely different N:C ratios and the absence of bonding between C and N result in steric hindrance to an efficient packing of these structural units. It is noted that similar inefficiencies in packing are observed in polymer-derived amorphous SiOC ceramics as well as in proteins and binary hard sphere systems.