title: On the Mass Fractal Character of Si-Based Structural Networks in Amorphous Polymer Derived Ceramics.
abstract: The intermediate-range packing of SiNxC4-x(0 ≤x≤ 4) tetrahedra in polysilycarbodiimide and polysilazane-derived amorphous SiCN ceramics is investigated using29Si spin-lattice relaxation nuclear magnetic resonance (SLR NMR) spectroscopy. The SiCN network in the polysilylcarbodiimide-derived ceramic consists predominantly of SiN₄ tetrahedra that are characterized by a 3-dimensional spatial distribution signifying compact packing of such units to form amorphous Si₃N₄ clusters. On the other hand, the SiCN network of the polysilazane-derived ceramic is characterized by mixed bonded SiNxC4-xtetrahedra that are inefficiently packed with a mass fractal dimension ofDf~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 SiCxN4-xtetrahedra 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.
authors.affiliation: Department of Materials Science, University of California at Davis, Davis, CA 95616, USA. sbsen@ucdavis.edu.
authors.forename: Sabyasachi
authors.initials: S
authors.lastname: Sen
authors.affiliation: Department of Materials Science, University of California at Davis, Davis, CA 95616, USA. swidgeon@engineering.ucsb.edu.
authors.forename: Scarlett
authors.initials: S
authors.lastname: Widgeon
keywords: mass fractal; nuclear magnetic resonance (NMR); polymer derived ceramics; structural packing