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According to Wikipedia, a single cellulose molecule is:

a linear chain of several hundred to many thousands of β(1→4) linked D-glucose units.

which means a cellulose molecule is made of ~1μm of glucose units.

According to Trotman, 1984,

Each cotton fibre is a unicellular hair [...] Each fibre, however long or short it may be, consists of one single complete vegetable cell [...] Average fibre length 13-51 mm.

(6th ed., pages 27-33) Cotton fibre morphology

(source: Trotman, page 31)

So if cellulose molecules are only ~1μm in length, what forces keep the cellulose molecules together inside the S1,S2,S3 structures throughout the fiber? How ~1μm units end up giving cotton its mechanical properties?

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A glucose molecule is roughly 1 nanometer long (ref). There are roughly 9,000-15,000 glucose molecules in a cellulose fiber (ref, see Table 5). If we use 10,000 as the number of glucose units, then the length of a cellulose fiber will be $$10^{-9}~ \mathrm{m/molecule} \cdot 10^4 ~\mathrm{molecules/fiber}=10^{-5}~\mathrm{m/fiber} $$ or ~10 microns/fiber.

The mechanical strength of the fiber comes from two sources.

  • Structural: As your diagram illustrates there are many walls in the cellulose fiber. All of these walls reinforce one another and build up the mechanical stability of the fiber. Each wall is composed of highly-organized cellulose chains. "Highly-organized" is another way of saying "crystalline". Cotton has an average crystallinity around 75%. This allows the cellulose fibers to pack closely together further increasing mechanical stability. The cellulose fibers in the different walls are orientated in different directions, again serving to increase the fiber strength.
  • Chemical: Here is a drawing of 2 glucose molecules from a cellulose chain.

enter image description here

Note that each glucose molecule has 3 equatorial hydroxyl groups oriented out and away from the polymer chain. Because of the high crystallinity mentioned above, the cellulose chains are positioned very close to one another. This means that thousands of hydrogen bonds can form between hydroxyl groups on different chains. As a rule of thumb, a hydrogen bond might have a strength around 5 kcal/m; if we have thousands of these bonds holding the cellulose chains together, then we have the equivalent of hundreds of normal chemical bonds holding the chains together! These hydrogen bonds account for much of the stability of the cotton fiber.

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  • $\begingroup$ so the only thing preventing fibers to "slide off" (shear) of each other is the hydrogen bonding? (I imagine this as plenty of small needles layered on top of each other) $\endgroup$ – Sparkler Apr 4 '15 at 16:50
  • $\begingroup$ Hmmm, I though you were asking about what gives a single fiber its mechanical properties ("what forces keep the cellulose molecules together inside the S1,S2,S3 structures throughout the fiber?"). $\endgroup$ – ron Apr 4 '15 at 17:01
  • $\begingroup$ yeah, and you gave a good answer. this is just another part of the question... $\endgroup$ – Sparkler Apr 4 '15 at 17:06
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    $\begingroup$ I know that the fiber surface is smooth so cotton fibers can't hook onto one another. While hydrogen bonding between fibers may help hold them together, I think the actual manufacturing process of making cotton is what is most important. In the manufacturing process cotton fibers are aligned (combing) and then twisted with each other (spinning). I think this is the main reason cotton fibers hold together so well. $\endgroup$ – ron Apr 4 '15 at 17:29

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