Terminal Relaxation Time and Steady-State Compliance

Terminal Relaxation Time and Steady-State Compliance 

For polymers with sharp molecular weight distribution, a terminal relaxation time T] can usually be determined experimentally from the flnal stages of stress relaxation either after sudden strain or after cessation of steady-state flow the latter kind of experiment weights the desired parameter more strongly as can be shown by equations 19 and 64 of Chapter 3, when expressed in terms of a discontinuous set of relaxation times rather than a continuous spectrum. Alternatively, it can be obtained from the constant Ag (the ratio of G /(tP at very low frequencies). Since the very narrow distribution of relaxation times in the terminal zone is close to a single terminal time t, which may be approximately identified with t , of the Graessley theory or of the Doi-Edwards theory (Section C3 of Chapter 10), equation 3 of Chapter 3 applies approximately and 

Measurements of stress relaxation of polystyrenes and poly(a-metliylsty-rene)s as well as dynamic moduli of polystyrenes have shown that ti is proportional to as predicted for Th by equation 53 or for tj by 57 of Chapter 10 together with the empirically established dependence of tjo on M. 

According to the modified Rouse theory of Section A of Chapter 10 for polymers of low molecular weight, 7 should be given by equation 11 of Chapter 10  

For M M c, if there were really a single terminal relaxation time as implied by equation 14, combination of that equation with equation 34 of Chapter 3 would make the steady-state compliance the same as the plateau compliance 7 = 7/v = /G%. with J% given by equation 2. Actually, as shown by Graessley, the ratio Je/J% is the ratio of what may be termed the weight- and number-average relaxation times in the terminal zone  

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The expansion determines the terminal quantities the viscosity coefficient 7] and the elasticity coefficient u which, in their turn, determine the terminal relaxation time and steady-state compliance, correspondingly,... 

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