Tulin 



changes in the strain energy must occur in equilibrium with viscous forces 

 which may be described in terms of the dissipation: 



_3C _ _BF 

 Bxj Bxj 



We may think of the molecular response in terms of the sum of the re- 

 sponses of independent groups of equal number of links, i.e., in modal terms. 

 Accordingly, we may write dynamic equations, all based on the previous rela- 

 tion, for the molecular strains a. appropriate to each mode p: 



(«.-^) -. (ii-i^^l 



These equations are nonlinear and of first order in the strain; notice the 

 presence of a term due to the viscous stresses imposed by the flow velocities 

 (u) —which, itself, depends in part upon the stresses due to molecular strain. 

 For a small strain disturbance (Aa)^ imposed at time zero upon an equilibrium 

 state, the strain (Aa) decays exponentially in time: 



- 2 t / T 



Aa. = (Aa. ) e p . 



We call the characteristic time of decay the relaxation time r^. Note its 

 relation, in theory, to molecular size ( r^), solvent viscosity (17), temperature 

 (t), molecular dissipation function (c^p), and the mode number (p): 



^Ci, 



1 



3kT n2 



We note how the higher modes have shorter relaxation times — in analogy to 

 most mechanical systems. 



The actual state of strain experienced by molecules in flows depends very 

 much upon the relation between this molecular relaxation time and the charac- 

 teristic times of the flow ((3u/By)" ' in a shear flow); it is thus a quantity of 

 great importance. 



Twelve years ago, Prince Rouse (8) and others applied theory based on the 

 same assumptions as we have indicated here to the prediction of viscosity and 

 stiffness in unsteady Couette shearing. Provided that the fluid's relaxation time 

 Tj is determined from the experiments themselves, the experimental data of 

 Rouse and Sittel (13) are in wonderful agreement with the Rouse theory, as 

 shown in Fig. 3. This gives us courage to pursue the theory utilizing the simple 

 noninterference model of the molecule. Let us take this opportunity to notice in 

 Fig. 3 how the energy storage (Gp is enhanced at high frequencies, while the 

 dissipation is depressed — in accord with the k- t diagram presented as Fig. 1. 



