236 BELL SYSTEM TECHNICAL JOURNAL 



3. Moisture Adsorption on Fibril Surfaces 



It appears reasonable to assume that moisture will first adsorb on 

 dry cotton on the outer surface of the hair, and by diffusion in the 

 vapor state will penetrate into the pits and adsorb on the pit walls. 

 Since cotton swells appreciably in a transverse direction, but hardly 

 at all lengthwise, it is further assumed that moisture in the pits will 

 next penetrate between the fibrils which are contiguous to one another 

 in the radial direction. At equilibrium with any humidity below that 

 required to form a monomolecular layer, it is assumed that the water 

 molecules will be distributed at random on active points over all of the 

 internal surface. For humidities above this value, polymolecular chains 

 of uniform thickness are assumed to adsorb at active points on the fibril 

 surfaces only, since moisture on the growth ring surfaces of these fibrils 

 appears to be responsible for the transverse swelling of the cotton. 



The equilibrium moisture content of cotton is reduced if the hydroxyl 

 groups on the cellulose molecules are acetylated or otherwise esterified. 

 Consequently it seems reasonable to assume that each water molecule 

 adsorbed on the cellulose surface is held by a force originating in the 

 oxygen atom of a surface hydroxyl group. As may be seen from 

 Fig. 5-^, there are six hydroxyl groups per cellobiose unit, and the 

 percentage moisture equivalent to a monomolecular layer covering 

 the surface of the fibril structure with each water molecule satisfying 

 forces of a surface hydroxyl oxygen will now be estimated. 



The fibril cross-section is estimated to be 1240 X 1300 AU, based 

 on average dimensions of the cotton hair.* Assuming the cellobiose 

 units arranged with the a-axis parallel to the fibril width (Fig. 6), 

 there will be 1240/8.3 = 150 unit cells across the fibril, and 1300/7.9 

 = 165 unit cells down through the fibril. Therefore the total number 

 of oxygen atoms per unit cell length in the four fibril surfaces is: 



6 X 150 X 2 + 6 X 165 X 2 = 3780. 



From this the moisture content equivalent to a monomolecular layer is: 



2 X '/o°x 165 X ^ X '°° = °-^^%-t 



* The considerations upon which these and subsequent calculations are based are 

 given in detail in separate publications which will appear in the April and May issues 

 of Textile Research. 



t The Angstrom unit AU is 10~* cm. From Fig. 6 it appears that only the 

 equivalent of one cellobiose unit may be available for surface adsorption per unit 

 cell in the fibril surface. Furthermore, since molecules in solid or liquid surfaces 

 are subject to unbalanced forces (surface tension) it is assumed that all surface 

 cellobiose units are so oriented that all 6 hydroxyl groups have surface forces capable 

 of adsorbing water molecules. 



