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)
(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?