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What is the structure of carbon fiber? Wikipedia doesn't give much insight.

The atomic structure of carbon fiber is similar to that of graphite, consisting of sheets of carbon atoms (graphene sheets) arranged in a regular hexagonal pattern, the difference being in the way these sheets interlock. Graphite is a crystalline material in which the sheets are stacked parallel to one another in regular fashion. The intermolecular forces between the sheets are relatively weak Van der Waals forces, giving graphite its soft and brittle characteristics.

The Wikipedia description begs the question of how exactly are the sheets of graphene interlocked. Are there pi-stacking interactions?

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    $\begingroup$ Carbon fiber is also often a composite. That is, there is some binder or polymer keeping things together. It's also a very broad category of materials, sometimes protected by industrial trade secrets. $\endgroup$ – Geoff Hutchison Nov 14 '14 at 3:52
  • $\begingroup$ Products of carbonization may vary very strongly from source to source. Moreover, purging all heteroatoms from carbonaceous material is virtually impossible. Given that, it is safe to assume that despite short order existing for most carbon atoms, fragments of graphite-like structure are bent, interlocked and linked in various unpredictable patterns. $\endgroup$ – permeakra Nov 14 '14 at 16:15
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The key difference between graphite and carbon fibers is the degree (or range) of ordering. In graphite there are large, extensive planes of carbon stacked one atop another resulting in long-range order. In the fibers, there are small ribbons of graphite-like (it is not all carbon, due to the way the fibers are prepared there is still some nitrogen present in the molecular array) material oriented along the fiber axis and there is only short range order. As a consequence graphite with its extensive 3 dimensional planar array of ordered carbon atoms is crystalline. Whereas the fibers, being ordered over a much smaller range, are amorphous. The amorphous nature of the fiber allows the smaller ribbons to bend and fold, and mechanically interlock with one another. This mechanical interlocking is what serves to increase the fiber's strength. See here for a very nice and concise description of how the fibers are prepared. The pictures in the link make clear how the short range ordering in the fibers results in a highly folded and interlocked structure. Further heating of the fiber will convert it to graphite.

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