THE STRUCTURAL FEATURES OF CELLULOSE 79 



the two ends of the tube, then the volume of liquid passing down the 

 tube per second is related to the viscosity by the well-known Poiseuille's 

 equation, 



V=nPa^mi, ..(6) 



so that T] can readily be determined. For most pure liquids and for 

 many solutions, Newton's Law (eqn. 5) has been completely confirmed. 

 For most colloidal solutions, however, the proportionality between 

 shearing force and velocity gradient is absent at low velocity gradients, 

 the "apparent" viscosity decreasing as the velocity gradient is increased. 

 This is true for solutions of cellulose. The anomalous behaviour tends 

 to disappear for solutions of low concentration, since it is due in 

 large part to an interaction between the dissolved particles of a type not 

 accounted for in the simple Newtonian Law. Thus again the practice 

 is to make determinations over a range of small concentrations and to 

 extrapolate to zero. 



As regards the connection between molecular weight and this 

 limiting viscosity, mathematical relationships for spherical particles and 

 for ellipsoidal particles have been worked out, but as yet there is no 

 sound theoretical basis for treatment of linear polymers such as 

 cellulose. For the moment, therefore, recourse has to be made to 

 empirical relationships. The one most frequently used was proposed 

 many years ago by Staudinger who based his considerations on the 

 viscosity of medium and low molecular weight polymers, whose 

 molecular weights were known from osmotic and other determinations. 

 He proposed a relation of the type 



where Ty^p is defined as {yjIyiq—V), 7] being the viscosity of the solution 

 and 7/0 that of the pure solvent, and is called the specific viscosity. 

 Later, in view of the variation of rj^p. with c (the concentration), this 

 was modified to 



Lt r),Jc=K^ . M. 



For these lower molecular weight polymers, he showed that K^ can be 

 regarded as a constant for any one polymer-solvent system. Thus, for 

 cellulose, a constant Kf„ can be derived by noting the viscosity for 

 glucose, cellobiose, cellotretrahose, cellohexose, etc., when, on the 

 assumption that K^ retains its value constant however many glucose 

 units are bound into a chain, the molecular weight of cellulose can be 

 determined by a measure of its viscosity in solution in cuprammonium. 

 Criticism was soon levelled at this method, largely in terms of the vaUdity 



