80 THE MOLECULAR ARCHITECTURE OF PLANT CELL WALLS 



of the extrapolation to high molecular weights, and undoubtedly such 

 criticisms were, in the main, vahd. The quantitative application of the 

 Staudinger Law is therefore open to doubt, though it certainly provides 

 a ready method of estimating molecular weights roughly, and is used 

 for that purpose. More recently Flory and Alfrey, Bartovics and Mark 

 have used a different equation for higher molecular weights (> 10,000) 

 (see 30). This takes the form, 



Ltr],plc=K.M''. 



Neither Staudinger's relation nor this new one can, however, be 

 regarded as adequate to cover the whole range of molecular weights, 

 and it seems unlikely that any simple relationship will meet all require- 

 ments. 



According to Staudinger's treatment, a long chain will make a bigger 

 contribution to the viscosity than will a short chain, and the molecular 

 weight calculated is usually thought of as a weight average, 



where Wg is the weight fraction of component /. It is obvious that for 

 any system which contains more than one chain length M„<M^ and 

 the ratio MJM„ can be used as an indicator of the degree of poly- 

 dispersity. 



{d) Analytical methods. — Of these methods the most successful has 

 been the "End Group Method" which has been applied to many linear 

 polymers. For cellulose, it was first applied by Haworth and Machemer 

 (31). Referring back to the structural formula for cellulose (p. 46) it 

 will be clear that one terminal group per chain will have hydroxyls 

 available for substitution in the 2, 3, 4 and 6 positions, whereas any glu- 

 cose residues which are not terminal can be substituted only in the 2, 3 

 and 6 positions. The method was therefore to methylate the specimen 

 under the mildest possible conditions, followed by hydrolysis into the 

 substituted glucose residues and the determination of the proportion of 

 2, 3, 4, 6, derivatives among the more abundant 2, 3, 6 derivatives. 

 Other methods are also available, e.g. the use of reducing power, but 

 the principle is the same. It is, of course, now clear that this method 

 gives a minimum figure since even under the mildest treatment some 

 degradation of the cellulose chains must occur. Several years later, in 

 fact, using an improved technique, Haworth and his collaborators 

 obtained much higher figures which are also included in Table III. The 



